The library adds support for decimal numbers of arbitrary length.
Downloaded from ICU, under ICU 1.8.1 license
http://download.icu-project.org/files/decNumber/decNumber-icu-368.zip
REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+
+
+jq uses parts of the open source C library "decNumber", which is distribured
+under the following license:
+
+
+ICU License - ICU 1.8.1 and later
+
+COPYRIGHT AND PERMISSION NOTICE
+
+Copyright (c) 1995-2005 International Business Machines Corporation and others
+All rights reserved.
+
+Permission is hereby granted, free of charge, to any person obtaining a
+copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, and/or sell copies of the Software, and to permit persons
+to whom the Software is furnished to do so, provided that the above
+copyright notice(s) and this permission notice appear in all copies of
+the Software and that both the above copyright notice(s) and this
+permission notice appear in supporting documentation.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
+OF THIRD PARTY RIGHTS. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR
+HOLDERS INCLUDED IN THIS NOTICE BE LIABLE FOR ANY CLAIM, OR ANY SPECIAL
+INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING
+FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,
+NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION
+WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+
+Except as contained in this notice, the name of a copyright holder
+shall not be used in advertising or otherwise to promote the sale, use
+or other dealings in this Software without prior written authorization
+of the copyright holder.
+
jq is licensed under the MIT license. For all of the gory
details, read the file `COPYING` in the source distribution.
+ jq uses a C library for decimal number support. This is an ICU 1.8.1
+ licensed code obtained from the ICU downloads archive
+ http://download.icu-project.org/files/decNumber/decNumber-icu-368.zip.
+
### Linux
--- /dev/null
+<html>\r
+\r
+<head>\r
+<meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></meta>\r
+<title>ICU License - ICU 1.8.1 and later</title>\r
+</head>\r
+\r
+<body>\r
+<h1>ICU License - ICU 1.8.1 and later</h1>\r
+<pre>\r
+COPYRIGHT AND PERMISSION NOTICE\r
+\r
+Copyright (c) 1995-2005 International Business Machines Corporation and others\r
+All rights reserved.\r
+\r
+Permission is hereby granted, free of charge, to any person obtaining a\r
+copy of this software and associated documentation files (the\r
+"Software"), to deal in the Software without restriction, including\r
+without limitation the rights to use, copy, modify, merge, publish,\r
+distribute, and/or sell copies of the Software, and to permit persons\r
+to whom the Software is furnished to do so, provided that the above\r
+copyright notice(s) and this permission notice appear in all copies of\r
+the Software and that both the above copyright notice(s) and this\r
+permission notice appear in supporting documentation.\r
+\r
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS\r
+OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF\r
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT\r
+OF THIRD PARTY RIGHTS. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR\r
+HOLDERS INCLUDED IN THIS NOTICE BE LIABLE FOR ANY CLAIM, OR ANY SPECIAL\r
+INDIRECT OR CONSEQUENTIAL DAMAGES, OR ANY DAMAGES WHATSOEVER RESULTING\r
+FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT,\r
+NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION\r
+WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.\r
+\r
+Except as contained in this notice, the name of a copyright holder\r
+shall not be used in advertising or otherwise to promote the sale, use\r
+or other dealings in this Software without prior written authorization\r
+of the copyright holder.\r
+\r
+--------------------------------------------------------------------------------\r
+All trademarks and registered trademarks mentioned herein are the property of their respective owners.\r
+</pre>\r
+</body>\r
+</html>\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decBasic.c -- common base code for Basic decimal types */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises code that is shared between decDouble and */\r
+/* decQuad (but not decSingle). The main arithmetic operations are */\r
+/* here (Add, Subtract, Multiply, FMA, and Division operators). */\r
+/* */\r
+/* Unlike decNumber, parameterization takes place at compile time */\r
+/* rather than at runtime. The parameters are set in the decDouble.c */\r
+/* (etc.) files, which then include this one to produce the compiled */\r
+/* code. The functions here, therefore, are code shared between */\r
+/* multiple formats. */\r
+/* */\r
+/* This must be included after decCommon.c. */\r
+/* ------------------------------------------------------------------ */\r
+// Names here refer to decFloat rather than to decDouble, etc., and\r
+// the functions are in strict alphabetical order.\r
+\r
+// The compile-time flags SINGLE, DOUBLE, and QUAD are set up in\r
+// decCommon.c\r
+#if !defined(QUAD)\r
+ #error decBasic.c must be included after decCommon.c\r
+#endif\r
+#if SINGLE\r
+ #error Routines in decBasic.c are for decDouble and decQuad only\r
+#endif\r
+\r
+/* Private constants */\r
+#define DIVIDE 0x80000000 // Divide operations [as flags]\r
+#define REMAINDER 0x40000000 // ..\r
+#define DIVIDEINT 0x20000000 // ..\r
+#define REMNEAR 0x10000000 // ..\r
+\r
+/* Private functions (local, used only by routines in this module) */\r
+static decFloat *decDivide(decFloat *, const decFloat *,\r
+ const decFloat *, decContext *, uInt);\r
+static decFloat *decCanonical(decFloat *, const decFloat *);\r
+static void decFiniteMultiply(bcdnum *, uByte *, const decFloat *,\r
+ const decFloat *);\r
+static decFloat *decInfinity(decFloat *, const decFloat *);\r
+static decFloat *decInvalid(decFloat *, decContext *);\r
+static decFloat *decNaNs(decFloat *, const decFloat *, const decFloat *,\r
+ decContext *);\r
+static Int decNumCompare(const decFloat *, const decFloat *, Flag);\r
+static decFloat *decToIntegral(decFloat *, const decFloat *, decContext *,\r
+ enum rounding, Flag);\r
+static uInt decToInt32(const decFloat *, decContext *, enum rounding,\r
+ Flag, Flag);\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCanonical -- copy a decFloat, making canonical */\r
+/* */\r
+/* result gets the canonicalized df */\r
+/* df is the decFloat to copy and make canonical */\r
+/* returns result */\r
+/* */\r
+/* This is exposed via decFloatCanonical for Double and Quad only. */\r
+/* This works on specials, too; no error or exception is possible. */\r
+/* ------------------------------------------------------------------ */\r
+static decFloat * decCanonical(decFloat *result, const decFloat *df) {\r
+ uInt encode, precode, dpd; // work\r
+ uInt inword, uoff, canon; // ..\r
+ Int n; // counter (down)\r
+ if (df!=result) *result=*df; // effect copy if needed\r
+ if (DFISSPECIAL(result)) {\r
+ if (DFISINF(result)) return decInfinity(result, df); // clean Infinity\r
+ // is a NaN\r
+ DFWORD(result, 0)&=~ECONNANMASK; // clear ECON except selector\r
+ if (DFISCCZERO(df)) return result; // coefficient continuation is 0\r
+ // drop through to check payload\r
+ }\r
+ // return quickly if the coefficient continuation is canonical\r
+ { // declare block\r
+ #if DOUBLE\r
+ uInt sourhi=DFWORD(df, 0);\r
+ uInt sourlo=DFWORD(df, 1);\r
+ if (CANONDPDOFF(sourhi, 8)\r
+ && CANONDPDTWO(sourhi, sourlo, 30)\r
+ && CANONDPDOFF(sourlo, 20)\r
+ && CANONDPDOFF(sourlo, 10)\r
+ && CANONDPDOFF(sourlo, 0)) return result;\r
+ #elif QUAD\r
+ uInt sourhi=DFWORD(df, 0);\r
+ uInt sourmh=DFWORD(df, 1);\r
+ uInt sourml=DFWORD(df, 2);\r
+ uInt sourlo=DFWORD(df, 3);\r
+ if (CANONDPDOFF(sourhi, 4)\r
+ && CANONDPDTWO(sourhi, sourmh, 26)\r
+ && CANONDPDOFF(sourmh, 16)\r
+ && CANONDPDOFF(sourmh, 6)\r
+ && CANONDPDTWO(sourmh, sourml, 28)\r
+ && CANONDPDOFF(sourml, 18)\r
+ && CANONDPDOFF(sourml, 8)\r
+ && CANONDPDTWO(sourml, sourlo, 30)\r
+ && CANONDPDOFF(sourlo, 20)\r
+ && CANONDPDOFF(sourlo, 10)\r
+ && CANONDPDOFF(sourlo, 0)) return result;\r
+ #endif\r
+ } // block\r
+\r
+ // Loop to repair a non-canonical coefficent, as needed\r
+ inword=DECWORDS-1; // current input word\r
+ uoff=0; // bit offset of declet\r
+ encode=DFWORD(result, inword);\r
+ for (n=DECLETS-1; n>=0; n--) { // count down declets of 10 bits\r
+ dpd=encode>>uoff;\r
+ uoff+=10;\r
+ if (uoff>32) { // crossed uInt boundary\r
+ inword--;\r
+ encode=DFWORD(result, inword);\r
+ uoff-=32;\r
+ dpd|=encode<<(10-uoff); // get pending bits\r
+ }\r
+ dpd&=0x3ff; // clear uninteresting bits\r
+ if (dpd<0x16e) continue; // must be canonical\r
+ canon=BIN2DPD[DPD2BIN[dpd]]; // determine canonical declet\r
+ if (canon==dpd) continue; // have canonical declet\r
+ // need to replace declet\r
+ if (uoff>=10) { // all within current word\r
+ encode&=~(0x3ff<<(uoff-10)); // clear the 10 bits ready for replace\r
+ encode|=canon<<(uoff-10); // insert the canonical form\r
+ DFWORD(result, inword)=encode; // .. and save\r
+ continue;\r
+ }\r
+ // straddled words\r
+ precode=DFWORD(result, inword+1); // get previous\r
+ precode&=0xffffffff>>(10-uoff); // clear top bits\r
+ DFWORD(result, inword+1)=precode|(canon<<(32-(10-uoff)));\r
+ encode&=0xffffffff<<uoff; // clear bottom bits\r
+ encode|=canon>>(10-uoff); // insert canonical\r
+ DFWORD(result, inword)=encode; // .. and save\r
+ } // n\r
+ return result;\r
+ } // decCanonical\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decDivide -- divide operations */\r
+/* */\r
+/* result gets the result of dividing dfl by dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* op is the operation selector */\r
+/* returns result */\r
+/* */\r
+/* op is one of DIVIDE, REMAINDER, DIVIDEINT, or REMNEAR. */\r
+/* ------------------------------------------------------------------ */\r
+#define DIVCOUNT 0 // 1 to instrument subtractions counter\r
+#define DIVBASE ((uInt)BILLION) // the base used for divide\r
+#define DIVOPLEN DECPMAX9 // operand length ('digits' base 10**9)\r
+#define DIVACCLEN (DIVOPLEN*3) // accumulator length (ditto)\r
+static decFloat * decDivide(decFloat *result, const decFloat *dfl,\r
+ const decFloat *dfr, decContext *set, uInt op) {\r
+ decFloat quotient; // for remainders\r
+ bcdnum num; // for final conversion\r
+ uInt acc[DIVACCLEN]; // coefficent in base-billion ..\r
+ uInt div[DIVOPLEN]; // divisor in base-billion ..\r
+ uInt quo[DIVOPLEN+1]; // quotient in base-billion ..\r
+ uByte bcdacc[(DIVOPLEN+1)*9+2]; // for quotient in BCD, +1, +1\r
+ uInt *msua, *msud, *msuq; // -> msu of acc, div, and quo\r
+ Int divunits, accunits; // lengths\r
+ Int quodigits; // digits in quotient\r
+ uInt *lsua, *lsuq; // -> current acc and quo lsus\r
+ Int length, multiplier; // work\r
+ uInt carry, sign; // ..\r
+ uInt *ua, *ud, *uq; // ..\r
+ uByte *ub; // ..\r
+ uInt uiwork; // for macros\r
+ uInt divtop; // top unit of div adjusted for estimating\r
+ #if DIVCOUNT\r
+ static uInt maxcount=0; // worst-seen subtractions count\r
+ uInt divcount=0; // subtractions count [this divide]\r
+ #endif\r
+\r
+ // calculate sign\r
+ num.sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;\r
+\r
+ if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { // either is special?\r
+ // NaNs are handled as usual\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ // one or two infinities\r
+ if (DFISINF(dfl)) {\r
+ if (DFISINF(dfr)) return decInvalid(result, set); // Two infinities bad\r
+ if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); // as is rem\r
+ // Infinity/x is infinite and quiet, even if x=0\r
+ DFWORD(result, 0)=num.sign;\r
+ return decInfinity(result, result);\r
+ }\r
+ // must be x/Infinity -- remainders are lhs\r
+ if (op&(REMAINDER|REMNEAR)) return decCanonical(result, dfl);\r
+ // divides: return zero with correct sign and exponent depending\r
+ // on op (Etiny for divide, 0 for divideInt)\r
+ decFloatZero(result);\r
+ if (op==DIVIDEINT) DFWORD(result, 0)|=num.sign; // add sign\r
+ else DFWORD(result, 0)=num.sign; // zeros the exponent, too\r
+ return result;\r
+ }\r
+ // next, handle zero operands (x/0 and 0/x)\r
+ if (DFISZERO(dfr)) { // x/0\r
+ if (DFISZERO(dfl)) { // 0/0 is undefined\r
+ decFloatZero(result);\r
+ DFWORD(result, 0)=DECFLOAT_qNaN;\r
+ set->status|=DEC_Division_undefined;\r
+ return result;\r
+ }\r
+ if (op&(REMAINDER|REMNEAR)) return decInvalid(result, set); // bad rem\r
+ set->status|=DEC_Division_by_zero;\r
+ DFWORD(result, 0)=num.sign;\r
+ return decInfinity(result, result); // x/0 -> signed Infinity\r
+ }\r
+ num.exponent=GETEXPUN(dfl)-GETEXPUN(dfr); // ideal exponent\r
+ if (DFISZERO(dfl)) { // 0/x (x!=0)\r
+ // if divide, result is 0 with ideal exponent; divideInt has\r
+ // exponent=0, remainders give zero with lower exponent\r
+ if (op&DIVIDEINT) {\r
+ decFloatZero(result);\r
+ DFWORD(result, 0)|=num.sign; // add sign\r
+ return result;\r
+ }\r
+ if (!(op&DIVIDE)) { // a remainder\r
+ // exponent is the minimum of the operands\r
+ num.exponent=MINI(GETEXPUN(dfl), GETEXPUN(dfr));\r
+ // if the result is zero the sign shall be sign of dfl\r
+ num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;\r
+ }\r
+ bcdacc[0]=0;\r
+ num.msd=bcdacc; // -> 0\r
+ num.lsd=bcdacc; // ..\r
+ return decFinalize(result, &num, set); // [divide may clamp exponent]\r
+ } // 0/x\r
+ // [here, both operands are known to be finite and non-zero]\r
+\r
+ // extract the operand coefficents into 'units' which are\r
+ // base-billion; the lhs is high-aligned in acc and the msu of both\r
+ // acc and div is at the right-hand end of array (offset length-1);\r
+ // the quotient can need one more unit than the operands as digits\r
+ // in it are not necessarily aligned neatly; further, the quotient\r
+ // may not start accumulating until after the end of the initial\r
+ // operand in acc if that is small (e.g., 1) so the accumulator\r
+ // must have at least that number of units extra (at the ls end)\r
+ GETCOEFFBILL(dfl, acc+DIVACCLEN-DIVOPLEN);\r
+ GETCOEFFBILL(dfr, div);\r
+ // zero the low uInts of acc\r
+ acc[0]=0;\r
+ acc[1]=0;\r
+ acc[2]=0;\r
+ acc[3]=0;\r
+ #if DOUBLE\r
+ #if DIVOPLEN!=2\r
+ #error Unexpected Double DIVOPLEN\r
+ #endif\r
+ #elif QUAD\r
+ acc[4]=0;\r
+ acc[5]=0;\r
+ acc[6]=0;\r
+ acc[7]=0;\r
+ #if DIVOPLEN!=4\r
+ #error Unexpected Quad DIVOPLEN\r
+ #endif\r
+ #endif\r
+\r
+ // set msu and lsu pointers\r
+ msua=acc+DIVACCLEN-1; // [leading zeros removed below]\r
+ msuq=quo+DIVOPLEN;\r
+ //[loop for div will terminate because operands are non-zero]\r
+ for (msud=div+DIVOPLEN-1; *msud==0;) msud--;\r
+ // the initial least-significant unit of acc is set so acc appears\r
+ // to have the same length as div.\r
+ // This moves one position towards the least possible for each\r
+ // iteration\r
+ divunits=(Int)(msud-div+1); // precalculate\r
+ lsua=msua-divunits+1; // initial working lsu of acc\r
+ lsuq=msuq; // and of quo\r
+\r
+ // set up the estimator for the multiplier; this is the msu of div,\r
+ // plus two bits from the unit below (if any) rounded up by one if\r
+ // there are any non-zero bits or units below that [the extra two\r
+ // bits makes for a much better estimate when the top unit is small]\r
+ divtop=*msud<<2;\r
+ if (divunits>1) {\r
+ uInt *um=msud-1;\r
+ uInt d=*um;\r
+ if (d>=750000000) {divtop+=3; d-=750000000;}\r
+ else if (d>=500000000) {divtop+=2; d-=500000000;}\r
+ else if (d>=250000000) {divtop++; d-=250000000;}\r
+ if (d) divtop++;\r
+ else for (um--; um>=div; um--) if (*um) {\r
+ divtop++;\r
+ break;\r
+ }\r
+ } // >1 unit\r
+\r
+ #if DECTRACE\r
+ {Int i;\r
+ printf("----- div=");\r
+ for (i=divunits-1; i>=0; i--) printf("%09ld ", (LI)div[i]);\r
+ printf("\n");}\r
+ #endif\r
+\r
+ // now collect up to DECPMAX+1 digits in the quotient (this may\r
+ // need OPLEN+1 uInts if unaligned)\r
+ quodigits=0; // no digits yet\r
+ for (;; lsua--) { // outer loop -- each input position\r
+ #if DECCHECK\r
+ if (lsua<acc) {\r
+ printf("Acc underrun...\n");\r
+ break;\r
+ }\r
+ #endif\r
+ #if DECTRACE\r
+ printf("Outer: quodigits=%ld acc=", (LI)quodigits);\r
+ for (ua=msua; ua>=lsua; ua--) printf("%09ld ", (LI)*ua);\r
+ printf("\n");\r
+ #endif\r
+ *lsuq=0; // default unit result is 0\r
+ for (;;) { // inner loop -- calculate quotient unit\r
+ // strip leading zero units from acc (either there initially or\r
+ // from subtraction below); this may strip all if exactly 0\r
+ for (; *msua==0 && msua>=lsua;) msua--;\r
+ accunits=(Int)(msua-lsua+1); // [maybe 0]\r
+ // subtraction is only necessary and possible if there are as\r
+ // least as many units remaining in acc for this iteration as\r
+ // there are in div\r
+ if (accunits<divunits) {\r
+ if (accunits==0) msua++; // restore\r
+ break;\r
+ }\r
+\r
+ // If acc is longer than div then subtraction is definitely\r
+ // possible (as msu of both is non-zero), but if they are the\r
+ // same length a comparison is needed.\r
+ // If a subtraction is needed then a good estimate of the\r
+ // multiplier for the subtraction is also needed in order to\r
+ // minimise the iterations of this inner loop because the\r
+ // subtractions needed dominate division performance.\r
+ if (accunits==divunits) {\r
+ // compare the high divunits of acc and div:\r
+ // acc<div: this quotient unit is unchanged; subtraction\r
+ // will be possible on the next iteration\r
+ // acc==div: quotient gains 1, set acc=0\r
+ // acc>div: subtraction necessary at this position\r
+ for (ud=msud, ua=msua; ud>div; ud--, ua--) if (*ud!=*ua) break;\r
+ // [now at first mismatch or lsu]\r
+ if (*ud>*ua) break; // next time...\r
+ if (*ud==*ua) { // all compared equal\r
+ *lsuq+=1; // increment result\r
+ msua=lsua; // collapse acc units\r
+ *msua=0; // .. to a zero\r
+ break;\r
+ }\r
+\r
+ // subtraction necessary; estimate multiplier [see above]\r
+ // if both *msud and *msua are small it is cost-effective to\r
+ // bring in part of the following units (if any) to get a\r
+ // better estimate (assume some other non-zero in div)\r
+ #define DIVLO 1000000U\r
+ #define DIVHI (DIVBASE/DIVLO)\r
+ #if DECUSE64\r
+ if (divunits>1) {\r
+ // there cannot be a *(msud-2) for DECDOUBLE so next is\r
+ // an exact calculation unless DECQUAD (which needs to\r
+ // assume bits out there if divunits>2)\r
+ uLong mul=(uLong)*msua * DIVBASE + *(msua-1);\r
+ uLong div=(uLong)*msud * DIVBASE + *(msud-1);\r
+ #if QUAD\r
+ if (divunits>2) div++;\r
+ #endif\r
+ mul/=div;\r
+ multiplier=(Int)mul;\r
+ }\r
+ else multiplier=*msua/(*msud);\r
+ #else\r
+ if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {\r
+ multiplier=(*msua*DIVHI + *(msua-1)/DIVLO)\r
+ /(*msud*DIVHI + *(msud-1)/DIVLO +1);\r
+ }\r
+ else multiplier=(*msua<<2)/divtop;\r
+ #endif\r
+ }\r
+ else { // accunits>divunits\r
+ // msud is one unit 'lower' than msua, so estimate differently\r
+ #if DECUSE64\r
+ uLong mul;\r
+ // as before, bring in extra digits if possible\r
+ if (divunits>1 && *msua<DIVLO && *msud<DIVLO) {\r
+ mul=((uLong)*msua * DIVHI * DIVBASE) + *(msua-1) * DIVHI\r
+ + *(msua-2)/DIVLO;\r
+ mul/=(*msud*DIVHI + *(msud-1)/DIVLO +1);\r
+ }\r
+ else if (divunits==1) {\r
+ mul=(uLong)*msua * DIVBASE + *(msua-1);\r
+ mul/=*msud; // no more to the right\r
+ }\r
+ else {\r
+ mul=(uLong)(*msua) * (uInt)(DIVBASE<<2)\r
+ + (*(msua-1)<<2);\r
+ mul/=divtop; // [divtop already allows for sticky bits]\r
+ }\r
+ multiplier=(Int)mul;\r
+ #else\r
+ multiplier=*msua * ((DIVBASE<<2)/divtop);\r
+ #endif\r
+ }\r
+ if (multiplier==0) multiplier=1; // marginal case\r
+ *lsuq+=multiplier;\r
+\r
+ #if DIVCOUNT\r
+ // printf("Multiplier: %ld\n", (LI)multiplier);\r
+ divcount++;\r
+ #endif\r
+\r
+ // Carry out the subtraction acc-(div*multiplier); for each\r
+ // unit in div, do the multiply, split to units (see\r
+ // decFloatMultiply for the algorithm), and subtract from acc\r
+ #define DIVMAGIC 2305843009U // 2**61/10**9\r
+ #define DIVSHIFTA 29\r
+ #define DIVSHIFTB 32\r
+ carry=0;\r
+ for (ud=div, ua=lsua; ud<=msud; ud++, ua++) {\r
+ uInt lo, hop;\r
+ #if DECUSE64\r
+ uLong sub=(uLong)multiplier*(*ud)+carry;\r
+ if (sub<DIVBASE) {\r
+ carry=0;\r
+ lo=(uInt)sub;\r
+ }\r
+ else {\r
+ hop=(uInt)(sub>>DIVSHIFTA);\r
+ carry=(uInt)(((uLong)hop*DIVMAGIC)>>DIVSHIFTB);\r
+ // the estimate is now in hi; now calculate sub-hi*10**9\r
+ // to get the remainder (which will be <DIVBASE))\r
+ lo=(uInt)sub;\r
+ lo-=carry*DIVBASE; // low word of result\r
+ if (lo>=DIVBASE) {\r
+ lo-=DIVBASE; // correct by +1\r
+ carry++;\r
+ }\r
+ }\r
+ #else // 32-bit\r
+ uInt hi;\r
+ // calculate multiplier*(*ud) into hi and lo\r
+ LONGMUL32HI(hi, *ud, multiplier); // get the high word\r
+ lo=multiplier*(*ud); // .. and the low\r
+ lo+=carry; // add the old hi\r
+ carry=hi+(lo<carry); // .. with any carry\r
+ if (carry || lo>=DIVBASE) { // split is needed\r
+ hop=(carry<<3)+(lo>>DIVSHIFTA); // hi:lo/2**29\r
+ LONGMUL32HI(carry, hop, DIVMAGIC); // only need the high word\r
+ // [DIVSHIFTB is 32, so carry can be used directly]\r
+ // the estimate is now in carry; now calculate hi:lo-est*10**9;\r
+ // happily the top word of the result is irrelevant because it\r
+ // will always be zero so this needs only one multiplication\r
+ lo-=(carry*DIVBASE);\r
+ // the correction here will be at most +1; do it\r
+ if (lo>=DIVBASE) {\r
+ lo-=DIVBASE;\r
+ carry++;\r
+ }\r
+ }\r
+ #endif\r
+ if (lo>*ua) { // borrow needed\r
+ *ua+=DIVBASE;\r
+ carry++;\r
+ }\r
+ *ua-=lo;\r
+ } // ud loop\r
+ if (carry) *ua-=carry; // accdigits>divdigits [cannot borrow]\r
+ } // inner loop\r
+\r
+ // the outer loop terminates when there is either an exact result\r
+ // or enough digits; first update the quotient digit count and\r
+ // pointer (if any significant digits)\r
+ #if DECTRACE\r
+ if (*lsuq || quodigits) printf("*lsuq=%09ld\n", (LI)*lsuq);\r
+ #endif\r
+ if (quodigits) {\r
+ quodigits+=9; // had leading unit earlier\r
+ lsuq--;\r
+ if (quodigits>DECPMAX+1) break; // have enough\r
+ }\r
+ else if (*lsuq) { // first quotient digits\r
+ const uInt *pow;\r
+ for (pow=DECPOWERS; *lsuq>=*pow; pow++) quodigits++;\r
+ lsuq--;\r
+ // [cannot have >DECPMAX+1 on first unit]\r
+ }\r
+\r
+ if (*msua!=0) continue; // not an exact result\r
+ // acc is zero iff used all of original units and zero down to lsua\r
+ // (must also continue to original lsu for correct quotient length)\r
+ if (lsua>acc+DIVACCLEN-DIVOPLEN) continue;\r
+ for (; msua>lsua && *msua==0;) msua--;\r
+ if (*msua==0 && msua==lsua) break;\r
+ } // outer loop\r
+\r
+ // all of the original operand in acc has been covered at this point\r
+ // quotient now has at least DECPMAX+2 digits\r
+ // *msua is now non-0 if inexact and sticky bits\r
+ // lsuq is one below the last uint of the quotient\r
+ lsuq++; // set -> true lsu of quo\r
+ if (*msua) *lsuq|=1; // apply sticky bit\r
+\r
+ // quo now holds the (unrounded) quotient in base-billion; one\r
+ // base-billion 'digit' per uInt.\r
+ #if DECTRACE\r
+ printf("DivQuo:");\r
+ for (uq=msuq; uq>=lsuq; uq--) printf(" %09ld", (LI)*uq);\r
+ printf("\n");\r
+ #endif\r
+\r
+ // Now convert to BCD for rounding and cleanup, starting from the\r
+ // most significant end [offset by one into bcdacc to leave room\r
+ // for a possible carry digit if rounding for REMNEAR is needed]\r
+ for (uq=msuq, ub=bcdacc+1; uq>=lsuq; uq--, ub+=9) {\r
+ uInt top, mid, rem; // work\r
+ if (*uq==0) { // no split needed\r
+ UBFROMUI(ub, 0); // clear 9 BCD8s\r
+ UBFROMUI(ub+4, 0); // ..\r
+ *(ub+8)=0; // ..\r
+ continue;\r
+ }\r
+ // *uq is non-zero -- split the base-billion digit into\r
+ // hi, mid, and low three-digits\r
+ #define divsplit9 1000000 // divisor\r
+ #define divsplit6 1000 // divisor\r
+ // The splitting is done by simple divides and remainders,\r
+ // assuming the compiler will optimize these [GCC does]\r
+ top=*uq/divsplit9;\r
+ rem=*uq%divsplit9;\r
+ mid=rem/divsplit6;\r
+ rem=rem%divsplit6;\r
+ // lay out the nine BCD digits (plus one unwanted byte)\r
+ UBFROMUI(ub, UBTOUI(&BIN2BCD8[top*4]));\r
+ UBFROMUI(ub+3, UBTOUI(&BIN2BCD8[mid*4]));\r
+ UBFROMUI(ub+6, UBTOUI(&BIN2BCD8[rem*4]));\r
+ } // BCD conversion loop\r
+ ub--; // -> lsu\r
+\r
+ // complete the bcdnum; quodigits is correct, so the position of\r
+ // the first non-zero is known\r
+ num.msd=bcdacc+1+(msuq-lsuq+1)*9-quodigits;\r
+ num.lsd=ub;\r
+\r
+ // make exponent adjustments, etc\r
+ if (lsua<acc+DIVACCLEN-DIVOPLEN) { // used extra digits\r
+ num.exponent-=(Int)((acc+DIVACCLEN-DIVOPLEN-lsua)*9);\r
+ // if the result was exact then there may be up to 8 extra\r
+ // trailing zeros in the overflowed quotient final unit\r
+ if (*msua==0) {\r
+ for (; *ub==0;) ub--; // drop zeros\r
+ num.exponent+=(Int)(num.lsd-ub); // and adjust exponent\r
+ num.lsd=ub;\r
+ }\r
+ } // adjustment needed\r
+\r
+ #if DIVCOUNT\r
+ if (divcount>maxcount) { // new high-water nark\r
+ maxcount=divcount;\r
+ printf("DivNewMaxCount: %ld\n", (LI)maxcount);\r
+ }\r
+ #endif\r
+\r
+ if (op&DIVIDE) return decFinalize(result, &num, set); // all done\r
+\r
+ // Is DIVIDEINT or a remainder; there is more to do -- first form\r
+ // the integer (this is done 'after the fact', unlike as in\r
+ // decNumber, so as not to tax DIVIDE)\r
+\r
+ // The first non-zero digit will be in the first 9 digits, known\r
+ // from quodigits and num.msd, so there is always space for DECPMAX\r
+ // digits\r
+\r
+ length=(Int)(num.lsd-num.msd+1);\r
+ //printf("Length exp: %ld %ld\n", (LI)length, (LI)num.exponent);\r
+\r
+ if (length+num.exponent>DECPMAX) { // cannot fit\r
+ decFloatZero(result);\r
+ DFWORD(result, 0)=DECFLOAT_qNaN;\r
+ set->status|=DEC_Division_impossible;\r
+ return result;\r
+ }\r
+\r
+ if (num.exponent>=0) { // already an int, or need pad zeros\r
+ for (ub=num.lsd+1; ub<=num.lsd+num.exponent; ub++) *ub=0;\r
+ num.lsd+=num.exponent;\r
+ }\r
+ else { // too long: round or truncate needed\r
+ Int drop=-num.exponent;\r
+ if (!(op&REMNEAR)) { // simple truncate\r
+ num.lsd-=drop;\r
+ if (num.lsd<num.msd) { // truncated all\r
+ num.lsd=num.msd; // make 0\r
+ *num.lsd=0; // .. [sign still relevant]\r
+ }\r
+ }\r
+ else { // round to nearest even [sigh]\r
+ // round-to-nearest, in-place; msd is at or to right of bcdacc+1\r
+ // (this is a special case of Quantize -- q.v. for commentary)\r
+ uByte *roundat; // -> re-round digit\r
+ uByte reround; // reround value\r
+ *(num.msd-1)=0; // in case of left carry, or make 0\r
+ if (drop<length) roundat=num.lsd-drop+1;\r
+ else if (drop==length) roundat=num.msd;\r
+ else roundat=num.msd-1; // [-> 0]\r
+ reround=*roundat;\r
+ for (ub=roundat+1; ub<=num.lsd; ub++) {\r
+ if (*ub!=0) {\r
+ reround=DECSTICKYTAB[reround];\r
+ break;\r
+ }\r
+ } // check stickies\r
+ if (roundat>num.msd) num.lsd=roundat-1;\r
+ else {\r
+ num.msd--; // use the 0 ..\r
+ num.lsd=num.msd; // .. at the new MSD place\r
+ }\r
+ if (reround!=0) { // discarding non-zero\r
+ uInt bump=0;\r
+ // rounding is DEC_ROUND_HALF_EVEN always\r
+ if (reround>5) bump=1; // >0.5 goes up\r
+ else if (reround==5) // exactly 0.5000 ..\r
+ bump=*(num.lsd) & 0x01; // .. up iff [new] lsd is odd\r
+ if (bump!=0) { // need increment\r
+ // increment the coefficient; this might end up with 1000...\r
+ ub=num.lsd;\r
+ for (; UBTOUI(ub-3)==0x09090909; ub-=4) UBFROMUI(ub-3, 0);\r
+ for (; *ub==9; ub--) *ub=0; // at most 3 more\r
+ *ub+=1;\r
+ if (ub<num.msd) num.msd--; // carried\r
+ } // bump needed\r
+ } // reround!=0\r
+ } // remnear\r
+ } // round or truncate needed\r
+ num.exponent=0; // all paths\r
+ //decShowNum(&num, "int");\r
+\r
+ if (op&DIVIDEINT) return decFinalize(result, &num, set); // all done\r
+\r
+ // Have a remainder to calculate\r
+ decFinalize("ient, &num, set); // lay out the integer so far\r
+ DFWORD("ient, 0)^=DECFLOAT_Sign; // negate it\r
+ sign=DFWORD(dfl, 0); // save sign of dfl\r
+ decFloatFMA(result, "ient, dfr, dfl, set);\r
+ if (!DFISZERO(result)) return result;\r
+ // if the result is zero the sign shall be sign of dfl\r
+ DFWORD("ient, 0)=sign; // construct decFloat of sign\r
+ return decFloatCopySign(result, result, "ient);\r
+ } // decDivide\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFiniteMultiply -- multiply two finite decFloats */\r
+/* */\r
+/* num gets the result of multiplying dfl and dfr */\r
+/* bcdacc .. with the coefficient in this array */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* */\r
+/* This effects the multiplication of two decFloats, both known to be */\r
+/* finite, leaving the result in a bcdnum ready for decFinalize (for */\r
+/* use in Multiply) or in a following addition (FMA). */\r
+/* */\r
+/* bcdacc must have space for at least DECPMAX9*18+1 bytes. */\r
+/* No error is possible and no status is set. */\r
+/* ------------------------------------------------------------------ */\r
+// This routine has two separate implementations of the core\r
+// multiplication; both using base-billion. One uses only 32-bit\r
+// variables (Ints and uInts) or smaller; the other uses uLongs (for\r
+// multiplication and addition only). Both implementations cover\r
+// both arithmetic sizes (DOUBLE and QUAD) in order to allow timing\r
+// comparisons. In any one compilation only one implementation for\r
+// each size can be used, and if DECUSE64 is 0 then use of the 32-bit\r
+// version is forced.\r
+//\r
+// Historical note: an earlier version of this code also supported the\r
+// 256-bit format and has been preserved. That is somewhat trickier\r
+// during lazy carry splitting because the initial quotient estimate\r
+// (est) can exceed 32 bits.\r
+\r
+#define MULTBASE ((uInt)BILLION) // the base used for multiply\r
+#define MULOPLEN DECPMAX9 // operand length ('digits' base 10**9)\r
+#define MULACCLEN (MULOPLEN*2) // accumulator length (ditto)\r
+#define LEADZEROS (MULACCLEN*9 - DECPMAX*2) // leading zeros always\r
+\r
+// Assertions: exponent not too large and MULACCLEN is a multiple of 4\r
+#if DECEMAXD>9\r
+ #error Exponent may overflow when doubled for Multiply\r
+#endif\r
+#if MULACCLEN!=(MULACCLEN/4)*4\r
+ // This assumption is used below only for initialization\r
+ #error MULACCLEN is not a multiple of 4\r
+#endif\r
+\r
+static void decFiniteMultiply(bcdnum *num, uByte *bcdacc,\r
+ const decFloat *dfl, const decFloat *dfr) {\r
+ uInt bufl[MULOPLEN]; // left coefficient (base-billion)\r
+ uInt bufr[MULOPLEN]; // right coefficient (base-billion)\r
+ uInt *ui, *uj; // work\r
+ uByte *ub; // ..\r
+ uInt uiwork; // for macros\r
+\r
+ #if DECUSE64\r
+ uLong accl[MULACCLEN]; // lazy accumulator (base-billion+)\r
+ uLong *pl; // work -> lazy accumulator\r
+ uInt acc[MULACCLEN]; // coefficent in base-billion ..\r
+ #else\r
+ uInt acc[MULACCLEN*2]; // accumulator in base-billion ..\r
+ #endif\r
+ uInt *pa; // work -> accumulator\r
+ //printf("Base10**9: OpLen=%d MulAcclen=%d\n", OPLEN, MULACCLEN);\r
+\r
+ /* Calculate sign and exponent */\r
+ num->sign=(DFWORD(dfl, 0)^DFWORD(dfr, 0)) & DECFLOAT_Sign;\r
+ num->exponent=GETEXPUN(dfl)+GETEXPUN(dfr); // [see assertion above]\r
+\r
+ /* Extract the coefficients and prepare the accumulator */\r
+ // the coefficients of the operands are decoded into base-billion\r
+ // numbers in uInt arrays (bufl and bufr, LSD at offset 0) of the\r
+ // appropriate size.\r
+ GETCOEFFBILL(dfl, bufl);\r
+ GETCOEFFBILL(dfr, bufr);\r
+ #if DECTRACE && 0\r
+ printf("CoeffbL:");\r
+ for (ui=bufl+MULOPLEN-1; ui>=bufl; ui--) printf(" %08lx", (LI)*ui);\r
+ printf("\n");\r
+ printf("CoeffbR:");\r
+ for (uj=bufr+MULOPLEN-1; uj>=bufr; uj--) printf(" %08lx", (LI)*uj);\r
+ printf("\n");\r
+ #endif\r
+\r
+ // start the 64-bit/32-bit differing paths...\r
+#if DECUSE64\r
+\r
+ // zero the accumulator\r
+ #if MULACCLEN==4\r
+ accl[0]=0; accl[1]=0; accl[2]=0; accl[3]=0;\r
+ #else // use a loop\r
+ // MULACCLEN is a multiple of four, asserted above\r
+ for (pl=accl; pl<accl+MULACCLEN; pl+=4) {\r
+ *pl=0; *(pl+1)=0; *(pl+2)=0; *(pl+3)=0;// [reduce overhead]\r
+ } // pl\r
+ #endif\r
+\r
+ /* Effect the multiplication */\r
+ // The multiplcation proceeds using MFC's lazy-carry resolution\r
+ // algorithm from decNumber. First, the multiplication is\r
+ // effected, allowing accumulation of the partial products (which\r
+ // are in base-billion at each column position) into 64 bits\r
+ // without resolving back to base=billion after each addition.\r
+ // These 64-bit numbers (which may contain up to 19 decimal digits)\r
+ // are then split using the Clark & Cowlishaw algorithm (see below).\r
+ // [Testing for 0 in the inner loop is not really a 'win']\r
+ for (ui=bufr; ui<bufr+MULOPLEN; ui++) { // over each item in rhs\r
+ if (*ui==0) continue; // product cannot affect result\r
+ pl=accl+(ui-bufr); // where to add the lhs\r
+ for (uj=bufl; uj<bufl+MULOPLEN; uj++, pl++) { // over each item in lhs\r
+ // if (*uj==0) continue; // product cannot affect result\r
+ *pl+=((uLong)*ui)*(*uj);\r
+ } // uj\r
+ } // ui\r
+\r
+ // The 64-bit carries must now be resolved; this means that a\r
+ // quotient/remainder has to be calculated for base-billion (1E+9).\r
+ // For this, Clark & Cowlishaw's quotient estimation approach (also\r
+ // used in decNumber) is needed, because 64-bit divide is generally\r
+ // extremely slow on 32-bit machines, and may be slower than this\r
+ // approach even on 64-bit machines. This algorithm splits X\r
+ // using:\r
+ //\r
+ // magic=2**(A+B)/1E+9; // 'magic number'\r
+ // hop=X/2**A; // high order part of X (by shift)\r
+ // est=magic*hop/2**B // quotient estimate (may be low by 1)\r
+ //\r
+ // A and B are quite constrained; hop and magic must fit in 32 bits,\r
+ // and 2**(A+B) must be as large as possible (which is 2**61 if\r
+ // magic is to fit). Further, maxX increases with the length of\r
+ // the operands (and hence the number of partial products\r
+ // accumulated); maxX is OPLEN*(10**18), which is up to 19 digits.\r
+ //\r
+ // It can be shown that when OPLEN is 2 then the maximum error in\r
+ // the estimated quotient is <1, but for larger maximum x the\r
+ // maximum error is above 1 so a correction that is >1 may be\r
+ // needed. Values of A and B are chosen to satisfy the constraints\r
+ // just mentioned while minimizing the maximum error (and hence the\r
+ // maximum correction), as shown in the following table:\r
+ //\r
+ // Type OPLEN A B maxX maxError maxCorrection\r
+ // ---------------------------------------------------------\r
+ // DOUBLE 2 29 32 <2*10**18 0.63 1\r
+ // QUAD 4 30 31 <4*10**18 1.17 2\r
+ //\r
+ // In the OPLEN==2 case there is most choice, but the value for B\r
+ // of 32 has a big advantage as then the calculation of the\r
+ // estimate requires no shifting; the compiler can extract the high\r
+ // word directly after multiplying magic*hop.\r
+ #define MULMAGIC 2305843009U // 2**61/10**9 [both cases]\r
+ #if DOUBLE\r
+ #define MULSHIFTA 29\r
+ #define MULSHIFTB 32\r
+ #elif QUAD\r
+ #define MULSHIFTA 30\r
+ #define MULSHIFTB 31\r
+ #else\r
+ #error Unexpected type\r
+ #endif\r
+\r
+ #if DECTRACE\r
+ printf("MulAccl:");\r
+ for (pl=accl+MULACCLEN-1; pl>=accl; pl--)\r
+ printf(" %08lx:%08lx", (LI)(*pl>>32), (LI)(*pl&0xffffffff));\r
+ printf("\n");\r
+ #endif\r
+\r
+ for (pl=accl, pa=acc; pl<accl+MULACCLEN; pl++, pa++) { // each column position\r
+ uInt lo, hop; // work\r
+ uInt est; // cannot exceed 4E+9\r
+ if (*pl>=MULTBASE) {\r
+ // *pl holds a binary number which needs to be split\r
+ hop=(uInt)(*pl>>MULSHIFTA);\r
+ est=(uInt)(((uLong)hop*MULMAGIC)>>MULSHIFTB);\r
+ // the estimate is now in est; now calculate hi:lo-est*10**9;\r
+ // happily the top word of the result is irrelevant because it\r
+ // will always be zero so this needs only one multiplication\r
+ lo=(uInt)(*pl-((uLong)est*MULTBASE)); // low word of result\r
+ // If QUAD, the correction here could be +2\r
+ if (lo>=MULTBASE) {\r
+ lo-=MULTBASE; // correct by +1\r
+ est++;\r
+ #if QUAD\r
+ // may need to correct by +2\r
+ if (lo>=MULTBASE) {\r
+ lo-=MULTBASE;\r
+ est++;\r
+ }\r
+ #endif\r
+ }\r
+ // finally place lo as the new coefficient 'digit' and add est to\r
+ // the next place up [this is safe because this path is never\r
+ // taken on the final iteration as *pl will fit]\r
+ *pa=lo;\r
+ *(pl+1)+=est;\r
+ } // *pl needed split\r
+ else { // *pl<MULTBASE\r
+ *pa=(uInt)*pl; // just copy across\r
+ }\r
+ } // pl loop\r
+\r
+#else // 32-bit\r
+ for (pa=acc;; pa+=4) { // zero the accumulator\r
+ *pa=0; *(pa+1)=0; *(pa+2)=0; *(pa+3)=0; // [reduce overhead]\r
+ if (pa==acc+MULACCLEN*2-4) break; // multiple of 4 asserted\r
+ } // pa\r
+\r
+ /* Effect the multiplication */\r
+ // uLongs are not available (and in particular, there is no uLong\r
+ // divide) but it is still possible to use MFC's lazy-carry\r
+ // resolution algorithm from decNumber. First, the multiplication\r
+ // is effected, allowing accumulation of the partial products\r
+ // (which are in base-billion at each column position) into 64 bits\r
+ // [with the high-order 32 bits in each position being held at\r
+ // offset +ACCLEN from the low-order 32 bits in the accumulator].\r
+ // These 64-bit numbers (which may contain up to 19 decimal digits)\r
+ // are then split using the Clark & Cowlishaw algorithm (see\r
+ // below).\r
+ for (ui=bufr;; ui++) { // over each item in rhs\r
+ uInt hi, lo; // words of exact multiply result\r
+ pa=acc+(ui-bufr); // where to add the lhs\r
+ for (uj=bufl;; uj++, pa++) { // over each item in lhs\r
+ LONGMUL32HI(hi, *ui, *uj); // calculate product of digits\r
+ lo=(*ui)*(*uj); // ..\r
+ *pa+=lo; // accumulate low bits and ..\r
+ *(pa+MULACCLEN)+=hi+(*pa<lo); // .. high bits with any carry\r
+ if (uj==bufl+MULOPLEN-1) break;\r
+ }\r
+ if (ui==bufr+MULOPLEN-1) break;\r
+ }\r
+\r
+ // The 64-bit carries must now be resolved; this means that a\r
+ // quotient/remainder has to be calculated for base-billion (1E+9).\r
+ // For this, Clark & Cowlishaw's quotient estimation approach (also\r
+ // used in decNumber) is needed, because 64-bit divide is generally\r
+ // extremely slow on 32-bit machines. This algorithm splits X\r
+ // using:\r
+ //\r
+ // magic=2**(A+B)/1E+9; // 'magic number'\r
+ // hop=X/2**A; // high order part of X (by shift)\r
+ // est=magic*hop/2**B // quotient estimate (may be low by 1)\r
+ //\r
+ // A and B are quite constrained; hop and magic must fit in 32 bits,\r
+ // and 2**(A+B) must be as large as possible (which is 2**61 if\r
+ // magic is to fit). Further, maxX increases with the length of\r
+ // the operands (and hence the number of partial products\r
+ // accumulated); maxX is OPLEN*(10**18), which is up to 19 digits.\r
+ //\r
+ // It can be shown that when OPLEN is 2 then the maximum error in\r
+ // the estimated quotient is <1, but for larger maximum x the\r
+ // maximum error is above 1 so a correction that is >1 may be\r
+ // needed. Values of A and B are chosen to satisfy the constraints\r
+ // just mentioned while minimizing the maximum error (and hence the\r
+ // maximum correction), as shown in the following table:\r
+ //\r
+ // Type OPLEN A B maxX maxError maxCorrection\r
+ // ---------------------------------------------------------\r
+ // DOUBLE 2 29 32 <2*10**18 0.63 1\r
+ // QUAD 4 30 31 <4*10**18 1.17 2\r
+ //\r
+ // In the OPLEN==2 case there is most choice, but the value for B\r
+ // of 32 has a big advantage as then the calculation of the\r
+ // estimate requires no shifting; the high word is simply\r
+ // calculated from multiplying magic*hop.\r
+ #define MULMAGIC 2305843009U // 2**61/10**9 [both cases]\r
+ #if DOUBLE\r
+ #define MULSHIFTA 29\r
+ #define MULSHIFTB 32\r
+ #elif QUAD\r
+ #define MULSHIFTA 30\r
+ #define MULSHIFTB 31\r
+ #else\r
+ #error Unexpected type\r
+ #endif\r
+\r
+ #if DECTRACE\r
+ printf("MulHiLo:");\r
+ for (pa=acc+MULACCLEN-1; pa>=acc; pa--)\r
+ printf(" %08lx:%08lx", (LI)*(pa+MULACCLEN), (LI)*pa);\r
+ printf("\n");\r
+ #endif\r
+\r
+ for (pa=acc;; pa++) { // each low uInt\r
+ uInt hi, lo; // words of exact multiply result\r
+ uInt hop, estlo; // work\r
+ #if QUAD\r
+ uInt esthi; // ..\r
+ #endif\r
+\r
+ lo=*pa;\r
+ hi=*(pa+MULACCLEN); // top 32 bits\r
+ // hi and lo now hold a binary number which needs to be split\r
+\r
+ #if DOUBLE\r
+ hop=(hi<<3)+(lo>>MULSHIFTA); // hi:lo/2**29\r
+ LONGMUL32HI(estlo, hop, MULMAGIC);// only need the high word\r
+ // [MULSHIFTB is 32, so estlo can be used directly]\r
+ // the estimate is now in estlo; now calculate hi:lo-est*10**9;\r
+ // happily the top word of the result is irrelevant because it\r
+ // will always be zero so this needs only one multiplication\r
+ lo-=(estlo*MULTBASE);\r
+ // esthi=0; // high word is ignored below\r
+ // the correction here will be at most +1; do it\r
+ if (lo>=MULTBASE) {\r
+ lo-=MULTBASE;\r
+ estlo++;\r
+ }\r
+ #elif QUAD\r
+ hop=(hi<<2)+(lo>>MULSHIFTA); // hi:lo/2**30\r
+ LONGMUL32HI(esthi, hop, MULMAGIC);// shift will be 31 ..\r
+ estlo=hop*MULMAGIC; // .. so low word needed\r
+ estlo=(esthi<<1)+(estlo>>MULSHIFTB); // [just the top bit]\r
+ // esthi=0; // high word is ignored below\r
+ lo-=(estlo*MULTBASE); // as above\r
+ // the correction here could be +1 or +2\r
+ if (lo>=MULTBASE) {\r
+ lo-=MULTBASE;\r
+ estlo++;\r
+ }\r
+ if (lo>=MULTBASE) {\r
+ lo-=MULTBASE;\r
+ estlo++;\r
+ }\r
+ #else\r
+ #error Unexpected type\r
+ #endif\r
+\r
+ // finally place lo as the new accumulator digit and add est to\r
+ // the next place up; this latter add could cause a carry of 1\r
+ // to the high word of the next place\r
+ *pa=lo;\r
+ *(pa+1)+=estlo;\r
+ // esthi is always 0 for DOUBLE and QUAD so this is skipped\r
+ // *(pa+1+MULACCLEN)+=esthi;\r
+ if (*(pa+1)<estlo) *(pa+1+MULACCLEN)+=1; // carry\r
+ if (pa==acc+MULACCLEN-2) break; // [MULACCLEN-1 will never need split]\r
+ } // pa loop\r
+#endif\r
+\r
+ // At this point, whether using the 64-bit or the 32-bit paths, the\r
+ // accumulator now holds the (unrounded) result in base-billion;\r
+ // one base-billion 'digit' per uInt.\r
+ #if DECTRACE\r
+ printf("MultAcc:");\r
+ for (pa=acc+MULACCLEN-1; pa>=acc; pa--) printf(" %09ld", (LI)*pa);\r
+ printf("\n");\r
+ #endif\r
+\r
+ // Now convert to BCD for rounding and cleanup, starting from the\r
+ // most significant end\r
+ pa=acc+MULACCLEN-1;\r
+ if (*pa!=0) num->msd=bcdacc+LEADZEROS;// drop known lead zeros\r
+ else { // >=1 word of leading zeros\r
+ num->msd=bcdacc; // known leading zeros are gone\r
+ pa--; // skip first word ..\r
+ for (; *pa==0; pa--) if (pa==acc) break; // .. and any more leading 0s\r
+ }\r
+ for (ub=bcdacc;; pa--, ub+=9) {\r
+ if (*pa!=0) { // split(s) needed\r
+ uInt top, mid, rem; // work\r
+ // *pa is non-zero -- split the base-billion acc digit into\r
+ // hi, mid, and low three-digits\r
+ #define mulsplit9 1000000 // divisor\r
+ #define mulsplit6 1000 // divisor\r
+ // The splitting is done by simple divides and remainders,\r
+ // assuming the compiler will optimize these where useful\r
+ // [GCC does]\r
+ top=*pa/mulsplit9;\r
+ rem=*pa%mulsplit9;\r
+ mid=rem/mulsplit6;\r
+ rem=rem%mulsplit6;\r
+ // lay out the nine BCD digits (plus one unwanted byte)\r
+ UBFROMUI(ub, UBTOUI(&BIN2BCD8[top*4]));\r
+ UBFROMUI(ub+3, UBTOUI(&BIN2BCD8[mid*4]));\r
+ UBFROMUI(ub+6, UBTOUI(&BIN2BCD8[rem*4]));\r
+ }\r
+ else { // *pa==0\r
+ UBFROMUI(ub, 0); // clear 9 BCD8s\r
+ UBFROMUI(ub+4, 0); // ..\r
+ *(ub+8)=0; // ..\r
+ }\r
+ if (pa==acc) break;\r
+ } // BCD conversion loop\r
+\r
+ num->lsd=ub+8; // complete the bcdnum ..\r
+\r
+ #if DECTRACE\r
+ decShowNum(num, "postmult");\r
+ decFloatShow(dfl, "dfl");\r
+ decFloatShow(dfr, "dfr");\r
+ #endif\r
+ return;\r
+ } // decFiniteMultiply\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatAbs -- absolute value, heeding NaNs, etc. */\r
+/* */\r
+/* result gets the canonicalized df with sign 0 */\r
+/* df is the decFloat to abs */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This has the same effect as decFloatPlus unless df is negative, */\r
+/* in which case it has the same effect as decFloatMinus. The */\r
+/* effect is also the same as decFloatCopyAbs except that NaNs are */\r
+/* handled normally (the sign of a NaN is not affected, and an sNaN */\r
+/* will signal) and the result will be canonical. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatAbs(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ if (DFISNAN(df)) return decNaNs(result, df, NULL, set);\r
+ decCanonical(result, df); // copy and check\r
+ DFBYTE(result, 0)&=~0x80; // zero sign bit\r
+ return result;\r
+ } // decFloatAbs\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatAdd -- add two decFloats */\r
+/* */\r
+/* result gets the result of adding dfl and dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+#if QUAD\r
+// Table for testing MSDs for fastpath elimination; returns the MSD of\r
+// a decDouble or decQuad (top 6 bits tested) ignoring the sign.\r
+// Infinities return -32 and NaNs return -128 so that summing the two\r
+// MSDs also allows rapid tests for the Specials (see code below).\r
+const Int DECTESTMSD[64]={\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, -32, -128,\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, -32, -128};\r
+#else\r
+// The table for testing MSDs is shared between the modules\r
+extern const Int DECTESTMSD[64];\r
+#endif\r
+\r
+decFloat * decFloatAdd(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ bcdnum num; // for final conversion\r
+ Int bexpl, bexpr; // left and right biased exponents\r
+ uByte *ub, *us, *ut; // work\r
+ uInt uiwork; // for macros\r
+ #if QUAD\r
+ uShort uswork; // ..\r
+ #endif\r
+\r
+ uInt sourhil, sourhir; // top words from source decFloats\r
+ // [valid only through end of\r
+ // fastpath code -- before swap]\r
+ uInt diffsign; // non-zero if signs differ\r
+ uInt carry; // carry: 0 or 1 before add loop\r
+ Int overlap; // coefficient overlap (if full)\r
+ Int summ; // sum of the MSDs\r
+ // the following buffers hold coefficients with various alignments\r
+ // (see commentary and diagrams below)\r
+ uByte acc[4+2+DECPMAX*3+8];\r
+ uByte buf[4+2+DECPMAX*2];\r
+ uByte *umsd, *ulsd; // local MSD and LSD pointers\r
+\r
+ #if DECLITEND\r
+ #define CARRYPAT 0x01000000 // carry=1 pattern\r
+ #else\r
+ #define CARRYPAT 0x00000001 // carry=1 pattern\r
+ #endif\r
+\r
+ /* Start decoding the arguments */\r
+ // The initial exponents are placed into the opposite Ints to\r
+ // that which might be expected; there are two sets of data to\r
+ // keep track of (each decFloat and the corresponding exponent),\r
+ // and this scheme means that at the swap point (after comparing\r
+ // exponents) only one pair of words needs to be swapped\r
+ // whichever path is taken (thereby minimising worst-case path).\r
+ // The calculated exponents will be nonsense when the arguments are\r
+ // Special, but are not used in that path\r
+ sourhil=DFWORD(dfl, 0); // LHS top word\r
+ summ=DECTESTMSD[sourhil>>26]; // get first MSD for testing\r
+ bexpr=DECCOMBEXP[sourhil>>26]; // get exponent high bits (in place)\r
+ bexpr+=GETECON(dfl); // .. + continuation\r
+\r
+ sourhir=DFWORD(dfr, 0); // RHS top word\r
+ summ+=DECTESTMSD[sourhir>>26]; // sum MSDs for testing\r
+ bexpl=DECCOMBEXP[sourhir>>26];\r
+ bexpl+=GETECON(dfr);\r
+\r
+ // here bexpr has biased exponent from lhs, and vice versa\r
+\r
+ diffsign=(sourhil^sourhir)&DECFLOAT_Sign;\r
+\r
+ // now determine whether to take a fast path or the full-function\r
+ // slow path. The slow path must be taken when:\r
+ // -- both numbers are finite, and:\r
+ // the exponents are different, or\r
+ // the signs are different, or\r
+ // the sum of the MSDs is >8 (hence might overflow)\r
+ // specialness and the sum of the MSDs can be tested at once using\r
+ // the summ value just calculated, so the test for specials is no\r
+ // longer on the worst-case path (as of 3.60)\r
+\r
+ if (summ<=8) { // MSD+MSD is good, or there is a special\r
+ if (summ<0) { // there is a special\r
+ // Inf+Inf would give -64; Inf+finite is -32 or higher\r
+ if (summ<-64) return decNaNs(result, dfl, dfr, set); // one or two NaNs\r
+ // two infinities with different signs is invalid\r
+ if (summ==-64 && diffsign) return decInvalid(result, set);\r
+ if (DFISINF(dfl)) return decInfinity(result, dfl); // LHS is infinite\r
+ return decInfinity(result, dfr); // RHS must be Inf\r
+ }\r
+ // Here when both arguments are finite; fast path is possible\r
+ // (currently only for aligned and same-sign)\r
+ if (bexpr==bexpl && !diffsign) {\r
+ uInt tac[DECLETS+1]; // base-1000 coefficient\r
+ uInt encode; // work\r
+\r
+ // Get one coefficient as base-1000 and add the other\r
+ GETCOEFFTHOU(dfl, tac); // least-significant goes to [0]\r
+ ADDCOEFFTHOU(dfr, tac);\r
+ // here the sum of the MSDs (plus any carry) will be <10 due to\r
+ // the fastpath test earlier\r
+\r
+ // construct the result; low word is the same for both formats\r
+ encode =BIN2DPD[tac[0]];\r
+ encode|=BIN2DPD[tac[1]]<<10;\r
+ encode|=BIN2DPD[tac[2]]<<20;\r
+ encode|=BIN2DPD[tac[3]]<<30;\r
+ DFWORD(result, (DECBYTES/4)-1)=encode;\r
+\r
+ // collect next two declets (all that remains, for Double)\r
+ encode =BIN2DPD[tac[3]]>>2;\r
+ encode|=BIN2DPD[tac[4]]<<8;\r
+\r
+ #if QUAD\r
+ // complete and lay out middling words\r
+ encode|=BIN2DPD[tac[5]]<<18;\r
+ encode|=BIN2DPD[tac[6]]<<28;\r
+ DFWORD(result, 2)=encode;\r
+\r
+ encode =BIN2DPD[tac[6]]>>4;\r
+ encode|=BIN2DPD[tac[7]]<<6;\r
+ encode|=BIN2DPD[tac[8]]<<16;\r
+ encode|=BIN2DPD[tac[9]]<<26;\r
+ DFWORD(result, 1)=encode;\r
+\r
+ // and final two declets\r
+ encode =BIN2DPD[tac[9]]>>6;\r
+ encode|=BIN2DPD[tac[10]]<<4;\r
+ #endif\r
+\r
+ // add exponent continuation and sign (from either argument)\r
+ encode|=sourhil & (ECONMASK | DECFLOAT_Sign);\r
+\r
+ // create lookup index = MSD + top two bits of biased exponent <<4\r
+ tac[DECLETS]|=(bexpl>>DECECONL)<<4;\r
+ encode|=DECCOMBFROM[tac[DECLETS]]; // add constructed combination field\r
+ DFWORD(result, 0)=encode; // complete\r
+\r
+ // decFloatShow(result, ">");\r
+ return result;\r
+ } // fast path OK\r
+ // drop through to slow path\r
+ } // low sum or Special(s)\r
+\r
+ /* Slow path required -- arguments are finite and might overflow, */\r
+ /* or require alignment, or might have different signs */\r
+\r
+ // now swap either exponents or argument pointers\r
+ if (bexpl<=bexpr) {\r
+ // original left is bigger\r
+ Int bexpswap=bexpl;\r
+ bexpl=bexpr;\r
+ bexpr=bexpswap;\r
+ // printf("left bigger\n");\r
+ }\r
+ else {\r
+ const decFloat *dfswap=dfl;\r
+ dfl=dfr;\r
+ dfr=dfswap;\r
+ // printf("right bigger\n");\r
+ }\r
+ // [here dfl and bexpl refer to the datum with the larger exponent,\r
+ // of if the exponents are equal then the original LHS argument]\r
+\r
+ // if lhs is zero then result will be the rhs (now known to have\r
+ // the smaller exponent), which also may need to be tested for zero\r
+ // for the weird IEEE 754 sign rules\r
+ if (DFISZERO(dfl)) {\r
+ decCanonical(result, dfr); // clean copy\r
+ // "When the sum of two operands with opposite signs is\r
+ // exactly zero, the sign of that sum shall be '+' in all\r
+ // rounding modes except round toward -Infinity, in which\r
+ // mode that sign shall be '-'."\r
+ if (diffsign && DFISZERO(result)) {\r
+ DFWORD(result, 0)&=~DECFLOAT_Sign; // assume sign 0\r
+ if (set->round==DEC_ROUND_FLOOR) DFWORD(result, 0)|=DECFLOAT_Sign;\r
+ }\r
+ return result;\r
+ } // numfl is zero\r
+ // [here, LHS is non-zero; code below assumes that]\r
+\r
+ // Coefficients layout during the calculations to follow:\r
+ //\r
+ // Overlap case:\r
+ // +------------------------------------------------+\r
+ // acc: |0000| coeffa | tail B | |\r
+ // +------------------------------------------------+\r
+ // buf: |0000| pad0s | coeffb | |\r
+ // +------------------------------------------------+\r
+ //\r
+ // Touching coefficients or gap:\r
+ // +------------------------------------------------+\r
+ // acc: |0000| coeffa | gap | coeffb |\r
+ // +------------------------------------------------+\r
+ // [buf not used or needed; gap clamped to Pmax]\r
+\r
+ // lay out lhs coefficient into accumulator; this starts at acc+4\r
+ // for decDouble or acc+6 for decQuad so the LSD is word-\r
+ // aligned; the top word gap is there only in case a carry digit\r
+ // is prefixed after the add -- it does not need to be zeroed\r
+ #if DOUBLE\r
+ #define COFF 4 // offset into acc\r
+ #elif QUAD\r
+ UBFROMUS(acc+4, 0); // prefix 00\r
+ #define COFF 6 // offset into acc\r
+ #endif\r
+\r
+ GETCOEFF(dfl, acc+COFF); // decode from decFloat\r
+ ulsd=acc+COFF+DECPMAX-1;\r
+ umsd=acc+4; // [having this here avoids\r
+\r
+ #if DECTRACE\r
+ {bcdnum tum;\r
+ tum.msd=umsd;\r
+ tum.lsd=ulsd;\r
+ tum.exponent=bexpl-DECBIAS;\r
+ tum.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;\r
+ decShowNum(&tum, "dflx");}\r
+ #endif\r
+\r
+ // if signs differ, take ten's complement of lhs (here the\r
+ // coefficient is subtracted from all-nines; the 1 is added during\r
+ // the later add cycle -- zeros to the right do not matter because\r
+ // the complement of zero is zero); these are fixed-length inverts\r
+ // where the lsd is known to be at a 4-byte boundary (so no borrow\r
+ // possible)\r
+ carry=0; // assume no carry\r
+ if (diffsign) {\r
+ carry=CARRYPAT; // for +1 during add\r
+ UBFROMUI(acc+ 4, 0x09090909-UBTOUI(acc+ 4));\r
+ UBFROMUI(acc+ 8, 0x09090909-UBTOUI(acc+ 8));\r
+ UBFROMUI(acc+12, 0x09090909-UBTOUI(acc+12));\r
+ UBFROMUI(acc+16, 0x09090909-UBTOUI(acc+16));\r
+ #if QUAD\r
+ UBFROMUI(acc+20, 0x09090909-UBTOUI(acc+20));\r
+ UBFROMUI(acc+24, 0x09090909-UBTOUI(acc+24));\r
+ UBFROMUI(acc+28, 0x09090909-UBTOUI(acc+28));\r
+ UBFROMUI(acc+32, 0x09090909-UBTOUI(acc+32));\r
+ UBFROMUI(acc+36, 0x09090909-UBTOUI(acc+36));\r
+ #endif\r
+ } // diffsign\r
+\r
+ // now process the rhs coefficient; if it cannot overlap lhs then\r
+ // it can be put straight into acc (with an appropriate gap, if\r
+ // needed) because no actual addition will be needed (except\r
+ // possibly to complete ten's complement)\r
+ overlap=DECPMAX-(bexpl-bexpr);\r
+ #if DECTRACE\r
+ printf("exps: %ld %ld\n", (LI)(bexpl-DECBIAS), (LI)(bexpr-DECBIAS));\r
+ printf("Overlap=%ld carry=%08lx\n", (LI)overlap, (LI)carry);\r
+ #endif\r
+\r
+ if (overlap<=0) { // no overlap possible\r
+ uInt gap; // local work\r
+ // since a full addition is not needed, a ten's complement\r
+ // calculation started above may need to be completed\r
+ if (carry) {\r
+ for (ub=ulsd; *ub==9; ub--) *ub=0;\r
+ *ub+=1;\r
+ carry=0; // taken care of\r
+ }\r
+ // up to DECPMAX-1 digits of the final result can extend down\r
+ // below the LSD of the lhs, so if the gap is >DECPMAX then the\r
+ // rhs will be simply sticky bits. In this case the gap is\r
+ // clamped to DECPMAX and the exponent adjusted to suit [this is\r
+ // safe because the lhs is non-zero].\r
+ gap=-overlap;\r
+ if (gap>DECPMAX) {\r
+ bexpr+=gap-1;\r
+ gap=DECPMAX;\r
+ }\r
+ ub=ulsd+gap+1; // where MSD will go\r
+ // Fill the gap with 0s; note that there is no addition to do\r
+ ut=acc+COFF+DECPMAX; // start of gap\r
+ for (; ut<ub; ut+=4) UBFROMUI(ut, 0); // mind the gap\r
+ if (overlap<-DECPMAX) { // gap was > DECPMAX\r
+ *ub=(uByte)(!DFISZERO(dfr)); // make sticky digit\r
+ }\r
+ else { // need full coefficient\r
+ GETCOEFF(dfr, ub); // decode from decFloat\r
+ ub+=DECPMAX-1; // new LSD...\r
+ }\r
+ ulsd=ub; // save new LSD\r
+ } // no overlap possible\r
+\r
+ else { // overlap>0\r
+ // coefficients overlap (perhaps completely, although also\r
+ // perhaps only where zeros)\r
+ if (overlap==DECPMAX) { // aligned\r
+ ub=buf+COFF; // where msd will go\r
+ #if QUAD\r
+ UBFROMUS(buf+4, 0); // clear quad's 00\r
+ #endif\r
+ GETCOEFF(dfr, ub); // decode from decFloat\r
+ }\r
+ else { // unaligned\r
+ ub=buf+COFF+DECPMAX-overlap; // where MSD will go\r
+ // Fill the prefix gap with 0s; 8 will cover most common\r
+ // unalignments, so start with direct assignments (a loop is\r
+ // then used for any remaining -- the loop (and the one in a\r
+ // moment) is not then on the critical path because the number\r
+ // of additions is reduced by (at least) two in this case)\r
+ UBFROMUI(buf+4, 0); // [clears decQuad 00 too]\r
+ UBFROMUI(buf+8, 0);\r
+ if (ub>buf+12) {\r
+ ut=buf+12; // start any remaining\r
+ for (; ut<ub; ut+=4) UBFROMUI(ut, 0); // fill them\r
+ }\r
+ GETCOEFF(dfr, ub); // decode from decFloat\r
+\r
+ // now move tail of rhs across to main acc; again use direct\r
+ // copies for 8 digits-worth\r
+ UBFROMUI(acc+COFF+DECPMAX, UBTOUI(buf+COFF+DECPMAX));\r
+ UBFROMUI(acc+COFF+DECPMAX+4, UBTOUI(buf+COFF+DECPMAX+4));\r
+ if (buf+COFF+DECPMAX+8<ub+DECPMAX) {\r
+ us=buf+COFF+DECPMAX+8; // source\r
+ ut=acc+COFF+DECPMAX+8; // target\r
+ for (; us<ub+DECPMAX; us+=4, ut+=4) UBFROMUI(ut, UBTOUI(us));\r
+ }\r
+ } // unaligned\r
+\r
+ ulsd=acc+(ub-buf+DECPMAX-1); // update LSD pointer\r
+\r
+ // Now do the add of the non-tail; this is all nicely aligned,\r
+ // and is over a multiple of four digits (because for Quad two\r
+ // zero digits were added on the left); words in both acc and\r
+ // buf (buf especially) will often be zero\r
+ // [byte-by-byte add, here, is about 15% slower total effect than\r
+ // the by-fours]\r
+\r
+ // Now effect the add; this is harder on a little-endian\r
+ // machine as the inter-digit carry cannot use the usual BCD\r
+ // addition trick because the bytes are loaded in the wrong order\r
+ // [this loop could be unrolled, but probably scarcely worth it]\r
+\r
+ ut=acc+COFF+DECPMAX-4; // target LSW (acc)\r
+ us=buf+COFF+DECPMAX-4; // source LSW (buf, to add to acc)\r
+\r
+ #if !DECLITEND\r
+ for (; ut>=acc+4; ut-=4, us-=4) { // big-endian add loop\r
+ // bcd8 add\r
+ carry+=UBTOUI(us); // rhs + carry\r
+ if (carry==0) continue; // no-op\r
+ carry+=UBTOUI(ut); // lhs\r
+ // Big-endian BCD adjust (uses internal carry)\r
+ carry+=0x76f6f6f6; // note top nibble not all bits\r
+ // apply BCD adjust and save\r
+ UBFROMUI(ut, (carry & 0x0f0f0f0f) - ((carry & 0x60606060)>>4));\r
+ carry>>=31; // true carry was at far left\r
+ } // add loop\r
+ #else\r
+ for (; ut>=acc+4; ut-=4, us-=4) { // little-endian add loop\r
+ // bcd8 add\r
+ carry+=UBTOUI(us); // rhs + carry\r
+ if (carry==0) continue; // no-op [common if unaligned]\r
+ carry+=UBTOUI(ut); // lhs\r
+ // Little-endian BCD adjust; inter-digit carry must be manual\r
+ // because the lsb from the array will be in the most-significant\r
+ // byte of carry\r
+ carry+=0x76767676; // note no inter-byte carries\r
+ carry+=(carry & 0x80000000)>>15;\r
+ carry+=(carry & 0x00800000)>>15;\r
+ carry+=(carry & 0x00008000)>>15;\r
+ carry-=(carry & 0x60606060)>>4; // BCD adjust back\r
+ UBFROMUI(ut, carry & 0x0f0f0f0f); // clear debris and save\r
+ // here, final carry-out bit is at 0x00000080; move it ready\r
+ // for next word-add (i.e., to 0x01000000)\r
+ carry=(carry & 0x00000080)<<17;\r
+ } // add loop\r
+ #endif\r
+\r
+ #if DECTRACE\r
+ {bcdnum tum;\r
+ printf("Add done, carry=%08lx, diffsign=%ld\n", (LI)carry, (LI)diffsign);\r
+ tum.msd=umsd; // acc+4;\r
+ tum.lsd=ulsd;\r
+ tum.exponent=0;\r
+ tum.sign=0;\r
+ decShowNum(&tum, "dfadd");}\r
+ #endif\r
+ } // overlap possible\r
+\r
+ // ordering here is a little strange in order to have slowest path\r
+ // first in GCC asm listing\r
+ if (diffsign) { // subtraction\r
+ if (!carry) { // no carry out means RHS<LHS\r
+ // borrowed -- take ten's complement\r
+ // sign is lhs sign\r
+ num.sign=DFWORD(dfl, 0) & DECFLOAT_Sign;\r
+\r
+ // invert the coefficient first by fours, then add one; space\r
+ // at the end of the buffer ensures the by-fours is always\r
+ // safe, but lsd+1 must be cleared to prevent a borrow\r
+ // if big-endian\r
+ #if !DECLITEND\r
+ *(ulsd+1)=0;\r
+ #endif\r
+ // there are always at least four coefficient words\r
+ UBFROMUI(umsd, 0x09090909-UBTOUI(umsd));\r
+ UBFROMUI(umsd+4, 0x09090909-UBTOUI(umsd+4));\r
+ UBFROMUI(umsd+8, 0x09090909-UBTOUI(umsd+8));\r
+ UBFROMUI(umsd+12, 0x09090909-UBTOUI(umsd+12));\r
+ #if DOUBLE\r
+ #define BNEXT 16\r
+ #elif QUAD\r
+ UBFROMUI(umsd+16, 0x09090909-UBTOUI(umsd+16));\r
+ UBFROMUI(umsd+20, 0x09090909-UBTOUI(umsd+20));\r
+ UBFROMUI(umsd+24, 0x09090909-UBTOUI(umsd+24));\r
+ UBFROMUI(umsd+28, 0x09090909-UBTOUI(umsd+28));\r
+ UBFROMUI(umsd+32, 0x09090909-UBTOUI(umsd+32));\r
+ #define BNEXT 36\r
+ #endif\r
+ if (ulsd>=umsd+BNEXT) { // unaligned\r
+ // eight will handle most unaligments for Double; 16 for Quad\r
+ UBFROMUI(umsd+BNEXT, 0x09090909-UBTOUI(umsd+BNEXT));\r
+ UBFROMUI(umsd+BNEXT+4, 0x09090909-UBTOUI(umsd+BNEXT+4));\r
+ #if DOUBLE\r
+ #define BNEXTY (BNEXT+8)\r
+ #elif QUAD\r
+ UBFROMUI(umsd+BNEXT+8, 0x09090909-UBTOUI(umsd+BNEXT+8));\r
+ UBFROMUI(umsd+BNEXT+12, 0x09090909-UBTOUI(umsd+BNEXT+12));\r
+ #define BNEXTY (BNEXT+16)\r
+ #endif\r
+ if (ulsd>=umsd+BNEXTY) { // very unaligned\r
+ ut=umsd+BNEXTY; // -> continue\r
+ for (;;ut+=4) {\r
+ UBFROMUI(ut, 0x09090909-UBTOUI(ut)); // invert four digits\r
+ if (ut>=ulsd-3) break; // all done\r
+ }\r
+ }\r
+ }\r
+ // complete the ten's complement by adding 1\r
+ for (ub=ulsd; *ub==9; ub--) *ub=0;\r
+ *ub+=1;\r
+ } // borrowed\r
+\r
+ else { // carry out means RHS>=LHS\r
+ num.sign=DFWORD(dfr, 0) & DECFLOAT_Sign;\r
+ // all done except for the special IEEE 754 exact-zero-result\r
+ // rule (see above); while testing for zero, strip leading\r
+ // zeros (which will save decFinalize doing it) (this is in\r
+ // diffsign path, so carry impossible and true umsd is\r
+ // acc+COFF)\r
+\r
+ // Check the initial coefficient area using the fast macro;\r
+ // this will often be all that needs to be done (as on the\r
+ // worst-case path when the subtraction was aligned and\r
+ // full-length)\r
+ if (ISCOEFFZERO(acc+COFF)) {\r
+ umsd=acc+COFF+DECPMAX-1; // so far, so zero\r
+ if (ulsd>umsd) { // more to check\r
+ umsd++; // to align after checked area\r
+ for (; UBTOUI(umsd)==0 && umsd+3<ulsd;) umsd+=4;\r
+ for (; *umsd==0 && umsd<ulsd;) umsd++;\r
+ }\r
+ if (*umsd==0) { // must be true zero (and diffsign)\r
+ num.sign=0; // assume +\r
+ if (set->round==DEC_ROUND_FLOOR) num.sign=DECFLOAT_Sign;\r
+ }\r
+ }\r
+ // [else was not zero, might still have leading zeros]\r
+ } // subtraction gave positive result\r
+ } // diffsign\r
+\r
+ else { // same-sign addition\r
+ num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;\r
+ #if DOUBLE\r
+ if (carry) { // only possible with decDouble\r
+ *(acc+3)=1; // [Quad has leading 00]\r
+ umsd=acc+3;\r
+ }\r
+ #endif\r
+ } // same sign\r
+\r
+ num.msd=umsd; // set MSD ..\r
+ num.lsd=ulsd; // .. and LSD\r
+ num.exponent=bexpr-DECBIAS; // set exponent to smaller, unbiassed\r
+\r
+ #if DECTRACE\r
+ decFloatShow(dfl, "dfl");\r
+ decFloatShow(dfr, "dfr");\r
+ decShowNum(&num, "postadd");\r
+ #endif\r
+ return decFinalize(result, &num, set); // round, check, and lay out\r
+ } // decFloatAdd\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatAnd -- logical digitwise AND of two decFloats */\r
+/* */\r
+/* result gets the result of ANDing dfl and dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result, which will be canonical with sign=0 */\r
+/* */\r
+/* The operands must be positive, finite with exponent q=0, and */\r
+/* comprise just zeros and ones; if not, Invalid operation results. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatAnd(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ if (!DFISUINT01(dfl) || !DFISUINT01(dfr)\r
+ || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);\r
+ // the operands are positive finite integers (q=0) with just 0s and 1s\r
+ #if DOUBLE\r
+ DFWORD(result, 0)=ZEROWORD\r
+ |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04009124);\r
+ DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x49124491;\r
+ #elif QUAD\r
+ DFWORD(result, 0)=ZEROWORD\r
+ |((DFWORD(dfl, 0) & DFWORD(dfr, 0))&0x04000912);\r
+ DFWORD(result, 1)=(DFWORD(dfl, 1) & DFWORD(dfr, 1))&0x44912449;\r
+ DFWORD(result, 2)=(DFWORD(dfl, 2) & DFWORD(dfr, 2))&0x12449124;\r
+ DFWORD(result, 3)=(DFWORD(dfl, 3) & DFWORD(dfr, 3))&0x49124491;\r
+ #endif\r
+ return result;\r
+ } // decFloatAnd\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCanonical -- copy a decFloat, making canonical */\r
+/* */\r
+/* result gets the canonicalized df */\r
+/* df is the decFloat to copy and make canonical */\r
+/* returns result */\r
+/* */\r
+/* This works on specials, too; no error or exception is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCanonical(decFloat *result, const decFloat *df) {\r
+ return decCanonical(result, df);\r
+ } // decFloatCanonical\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatClass -- return the class of a decFloat */\r
+/* */\r
+/* df is the decFloat to test */\r
+/* returns the decClass that df falls into */\r
+/* ------------------------------------------------------------------ */\r
+enum decClass decFloatClass(const decFloat *df) {\r
+ Int exp; // exponent\r
+ if (DFISSPECIAL(df)) {\r
+ if (DFISQNAN(df)) return DEC_CLASS_QNAN;\r
+ if (DFISSNAN(df)) return DEC_CLASS_SNAN;\r
+ // must be an infinity\r
+ if (DFISSIGNED(df)) return DEC_CLASS_NEG_INF;\r
+ return DEC_CLASS_POS_INF;\r
+ }\r
+ if (DFISZERO(df)) { // quite common\r
+ if (DFISSIGNED(df)) return DEC_CLASS_NEG_ZERO;\r
+ return DEC_CLASS_POS_ZERO;\r
+ }\r
+ // is finite and non-zero; similar code to decFloatIsNormal, here\r
+ // [this could be speeded up slightly by in-lining decFloatDigits]\r
+ exp=GETEXPUN(df) // get unbiased exponent ..\r
+ +decFloatDigits(df)-1; // .. and make adjusted exponent\r
+ if (exp>=DECEMIN) { // is normal\r
+ if (DFISSIGNED(df)) return DEC_CLASS_NEG_NORMAL;\r
+ return DEC_CLASS_POS_NORMAL;\r
+ }\r
+ // is subnormal\r
+ if (DFISSIGNED(df)) return DEC_CLASS_NEG_SUBNORMAL;\r
+ return DEC_CLASS_POS_SUBNORMAL;\r
+ } // decFloatClass\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatClassString -- return the class of a decFloat as a string */\r
+/* */\r
+/* df is the decFloat to test */\r
+/* returns a constant string describing the class df falls into */\r
+/* ------------------------------------------------------------------ */\r
+const char *decFloatClassString(const decFloat *df) {\r
+ enum decClass eclass=decFloatClass(df);\r
+ if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;\r
+ if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;\r
+ if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;\r
+ if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;\r
+ if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;\r
+ if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;\r
+ if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;\r
+ if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;\r
+ if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;\r
+ if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;\r
+ return DEC_ClassString_UN; // Unknown\r
+ } // decFloatClassString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCompare -- compare two decFloats; quiet NaNs allowed */\r
+/* */\r
+/* result gets the result of comparing dfl and dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result, which may be -1, 0, 1, or NaN (Unordered) */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCompare(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int comp; // work\r
+ // NaNs are handled as usual\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ // numeric comparison needed\r
+ comp=decNumCompare(dfl, dfr, 0);\r
+ decFloatZero(result);\r
+ if (comp==0) return result;\r
+ DFBYTE(result, DECBYTES-1)=0x01; // LSD=1\r
+ if (comp<0) DFBYTE(result, 0)|=0x80; // set sign bit\r
+ return result;\r
+ } // decFloatCompare\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCompareSignal -- compare two decFloats; all NaNs signal */\r
+/* */\r
+/* result gets the result of comparing dfl and dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result, which may be -1, 0, 1, or NaN (Unordered) */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCompareSignal(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int comp; // work\r
+ // NaNs are handled as usual, except that all NaNs signal\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) {\r
+ set->status|=DEC_Invalid_operation;\r
+ return decNaNs(result, dfl, dfr, set);\r
+ }\r
+ // numeric comparison needed\r
+ comp=decNumCompare(dfl, dfr, 0);\r
+ decFloatZero(result);\r
+ if (comp==0) return result;\r
+ DFBYTE(result, DECBYTES-1)=0x01; // LSD=1\r
+ if (comp<0) DFBYTE(result, 0)|=0x80; // set sign bit\r
+ return result;\r
+ } // decFloatCompareSignal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCompareTotal -- compare two decFloats with total ordering */\r
+/* */\r
+/* result gets the result of comparing dfl and dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* returns result, which may be -1, 0, or 1 */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCompareTotal(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr) {\r
+ Int comp; // work\r
+ uInt uiwork; // for macros\r
+ #if QUAD\r
+ uShort uswork; // ..\r
+ #endif\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) {\r
+ Int nanl, nanr; // work\r
+ // morph NaNs to +/- 1 or 2, leave numbers as 0\r
+ nanl=DFISSNAN(dfl)+DFISQNAN(dfl)*2; // quiet > signalling\r
+ if (DFISSIGNED(dfl)) nanl=-nanl;\r
+ nanr=DFISSNAN(dfr)+DFISQNAN(dfr)*2;\r
+ if (DFISSIGNED(dfr)) nanr=-nanr;\r
+ if (nanl>nanr) comp=+1;\r
+ else if (nanl<nanr) comp=-1;\r
+ else { // NaNs are the same type and sign .. must compare payload\r
+ // buffers need +2 for QUAD\r
+ uByte bufl[DECPMAX+4]; // for LHS coefficient + foot\r
+ uByte bufr[DECPMAX+4]; // for RHS coefficient + foot\r
+ uByte *ub, *uc; // work\r
+ Int sigl; // signum of LHS\r
+ sigl=(DFISSIGNED(dfl) ? -1 : +1);\r
+\r
+ // decode the coefficients\r
+ // (shift both right two if Quad to make a multiple of four)\r
+ #if QUAD\r
+ UBFROMUS(bufl, 0);\r
+ UBFROMUS(bufr, 0);\r
+ #endif\r
+ GETCOEFF(dfl, bufl+QUAD*2); // decode from decFloat\r
+ GETCOEFF(dfr, bufr+QUAD*2); // ..\r
+ // all multiples of four, here\r
+ comp=0; // assume equal\r
+ for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {\r
+ uInt ui=UBTOUI(ub);\r
+ if (ui==UBTOUI(uc)) continue; // so far so same\r
+ // about to find a winner; go by bytes in case little-endian\r
+ for (;; ub++, uc++) {\r
+ if (*ub==*uc) continue;\r
+ if (*ub>*uc) comp=sigl; // difference found\r
+ else comp=-sigl; // ..\r
+ break;\r
+ }\r
+ }\r
+ } // same NaN type and sign\r
+ }\r
+ else {\r
+ // numeric comparison needed\r
+ comp=decNumCompare(dfl, dfr, 1); // total ordering\r
+ }\r
+ decFloatZero(result);\r
+ if (comp==0) return result;\r
+ DFBYTE(result, DECBYTES-1)=0x01; // LSD=1\r
+ if (comp<0) DFBYTE(result, 0)|=0x80; // set sign bit\r
+ return result;\r
+ } // decFloatCompareTotal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCompareTotalMag -- compare magnitudes with total ordering */\r
+/* */\r
+/* result gets the result of comparing abs(dfl) and abs(dfr) */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* returns result, which may be -1, 0, or 1 */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCompareTotalMag(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr) {\r
+ decFloat a, b; // for copy if needed\r
+ // copy and redirect signed operand(s)\r
+ if (DFISSIGNED(dfl)) {\r
+ decFloatCopyAbs(&a, dfl);\r
+ dfl=&a;\r
+ }\r
+ if (DFISSIGNED(dfr)) {\r
+ decFloatCopyAbs(&b, dfr);\r
+ dfr=&b;\r
+ }\r
+ return decFloatCompareTotal(result, dfl, dfr);\r
+ } // decFloatCompareTotalMag\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCopy -- copy a decFloat as-is */\r
+/* */\r
+/* result gets the copy of dfl */\r
+/* dfl is the decFloat to copy */\r
+/* returns result */\r
+/* */\r
+/* This is a bitwise operation; no errors or exceptions are possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCopy(decFloat *result, const decFloat *dfl) {\r
+ if (dfl!=result) *result=*dfl; // copy needed\r
+ return result;\r
+ } // decFloatCopy\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCopyAbs -- copy a decFloat as-is and set sign bit to 0 */\r
+/* */\r
+/* result gets the copy of dfl with sign bit 0 */\r
+/* dfl is the decFloat to copy */\r
+/* returns result */\r
+/* */\r
+/* This is a bitwise operation; no errors or exceptions are possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCopyAbs(decFloat *result, const decFloat *dfl) {\r
+ if (dfl!=result) *result=*dfl; // copy needed\r
+ DFBYTE(result, 0)&=~0x80; // zero sign bit\r
+ return result;\r
+ } // decFloatCopyAbs\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCopyNegate -- copy a decFloat as-is with inverted sign bit */\r
+/* */\r
+/* result gets the copy of dfl with sign bit inverted */\r
+/* dfl is the decFloat to copy */\r
+/* returns result */\r
+/* */\r
+/* This is a bitwise operation; no errors or exceptions are possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCopyNegate(decFloat *result, const decFloat *dfl) {\r
+ if (dfl!=result) *result=*dfl; // copy needed\r
+ DFBYTE(result, 0)^=0x80; // invert sign bit\r
+ return result;\r
+ } // decFloatCopyNegate\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatCopySign -- copy a decFloat with the sign of another */\r
+/* */\r
+/* result gets the result of copying dfl with the sign of dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* returns result */\r
+/* */\r
+/* This is a bitwise operation; no errors or exceptions are possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatCopySign(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr) {\r
+ uByte sign=(uByte)(DFBYTE(dfr, 0)&0x80); // save sign bit\r
+ if (dfl!=result) *result=*dfl; // copy needed\r
+ DFBYTE(result, 0)&=~0x80; // clear sign ..\r
+ DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); // .. and set saved\r
+ return result;\r
+ } // decFloatCopySign\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatDigits -- return the number of digits in a decFloat */\r
+/* */\r
+/* df is the decFloat to investigate */\r
+/* returns the number of significant digits in the decFloat; a */\r
+/* zero coefficient returns 1 as does an infinity (a NaN returns */\r
+/* the number of digits in the payload) */\r
+/* ------------------------------------------------------------------ */\r
+// private macro to extract a declet according to provided formula\r
+// (form), and if it is non-zero then return the calculated digits\r
+// depending on the declet number (n), where n=0 for the most\r
+// significant declet; uses uInt dpd for work\r
+#define dpdlenchk(n, form) dpd=(form)&0x3ff; \\r
+ if (dpd) return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3])\r
+// next one is used when it is known that the declet must be\r
+// non-zero, or is the final zero declet\r
+#define dpdlendun(n, form) dpd=(form)&0x3ff; \\r
+ if (dpd==0) return 1; \\r
+ return (DECPMAX-1-3*(n))-(3-DPD2BCD8[dpd*4+3])\r
+\r
+uInt decFloatDigits(const decFloat *df) {\r
+ uInt dpd; // work\r
+ uInt sourhi=DFWORD(df, 0); // top word from source decFloat\r
+ #if QUAD\r
+ uInt sourmh, sourml;\r
+ #endif\r
+ uInt sourlo;\r
+\r
+ if (DFISINF(df)) return 1;\r
+ // A NaN effectively has an MSD of 0; otherwise if non-zero MSD\r
+ // then the coefficient is full-length\r
+ if (!DFISNAN(df) && DECCOMBMSD[sourhi>>26]) return DECPMAX;\r
+\r
+ #if DOUBLE\r
+ if (sourhi&0x0003ffff) { // ends in first\r
+ dpdlenchk(0, sourhi>>8);\r
+ sourlo=DFWORD(df, 1);\r
+ dpdlendun(1, (sourhi<<2) | (sourlo>>30));\r
+ } // [cannot drop through]\r
+ sourlo=DFWORD(df, 1); // sourhi not involved now\r
+ if (sourlo&0xfff00000) { // in one of first two\r
+ dpdlenchk(1, sourlo>>30); // very rare\r
+ dpdlendun(2, sourlo>>20);\r
+ } // [cannot drop through]\r
+ dpdlenchk(3, sourlo>>10);\r
+ dpdlendun(4, sourlo);\r
+ // [cannot drop through]\r
+\r
+ #elif QUAD\r
+ if (sourhi&0x00003fff) { // ends in first\r
+ dpdlenchk(0, sourhi>>4);\r
+ sourmh=DFWORD(df, 1);\r
+ dpdlendun(1, ((sourhi)<<6) | (sourmh>>26));\r
+ } // [cannot drop through]\r
+ sourmh=DFWORD(df, 1);\r
+ if (sourmh) {\r
+ dpdlenchk(1, sourmh>>26);\r
+ dpdlenchk(2, sourmh>>16);\r
+ dpdlenchk(3, sourmh>>6);\r
+ sourml=DFWORD(df, 2);\r
+ dpdlendun(4, ((sourmh)<<4) | (sourml>>28));\r
+ } // [cannot drop through]\r
+ sourml=DFWORD(df, 2);\r
+ if (sourml) {\r
+ dpdlenchk(4, sourml>>28);\r
+ dpdlenchk(5, sourml>>18);\r
+ dpdlenchk(6, sourml>>8);\r
+ sourlo=DFWORD(df, 3);\r
+ dpdlendun(7, ((sourml)<<2) | (sourlo>>30));\r
+ } // [cannot drop through]\r
+ sourlo=DFWORD(df, 3);\r
+ if (sourlo&0xfff00000) { // in one of first two\r
+ dpdlenchk(7, sourlo>>30); // very rare\r
+ dpdlendun(8, sourlo>>20);\r
+ } // [cannot drop through]\r
+ dpdlenchk(9, sourlo>>10);\r
+ dpdlendun(10, sourlo);\r
+ // [cannot drop through]\r
+ #endif\r
+ } // decFloatDigits\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatDivide -- divide a decFloat by another */\r
+/* */\r
+/* result gets the result of dividing dfl by dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+// This is just a wrapper.\r
+decFloat * decFloatDivide(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ return decDivide(result, dfl, dfr, set, DIVIDE);\r
+ } // decFloatDivide\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatDivideInteger -- integer divide a decFloat by another */\r
+/* */\r
+/* result gets the result of dividing dfl by dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatDivideInteger(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ return decDivide(result, dfl, dfr, set, DIVIDEINT);\r
+ } // decFloatDivideInteger\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFMA -- multiply and add three decFloats, fused */\r
+/* */\r
+/* result gets the result of (dfl*dfr)+dff with a single rounding */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* dff is the final decFloat (fhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFMA(decFloat *result, const decFloat *dfl,\r
+ const decFloat *dfr, const decFloat *dff,\r
+ decContext *set) {\r
+\r
+ // The accumulator has the bytes needed for FiniteMultiply, plus\r
+ // one byte to the left in case of carry, plus DECPMAX+2 to the\r
+ // right for the final addition (up to full fhs + round & sticky)\r
+ #define FMALEN (ROUNDUP4(1+ (DECPMAX9*18+1) +DECPMAX+2))\r
+ uByte acc[FMALEN]; // for multiplied coefficient in BCD\r
+ // .. and for final result\r
+ bcdnum mul; // for multiplication result\r
+ bcdnum fin; // for final operand, expanded\r
+ uByte coe[ROUNDUP4(DECPMAX)]; // dff coefficient in BCD\r
+ bcdnum *hi, *lo; // bcdnum with higher/lower exponent\r
+ uInt diffsign; // non-zero if signs differ\r
+ uInt hipad; // pad digit for hi if needed\r
+ Int padding; // excess exponent\r
+ uInt carry; // +1 for ten's complement and during add\r
+ uByte *ub, *uh, *ul; // work\r
+ uInt uiwork; // for macros\r
+\r
+ // handle all the special values [any special operand leads to a\r
+ // special result]\r
+ if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr) || DFISSPECIAL(dff)) {\r
+ decFloat proxy; // multiplication result proxy\r
+ // NaNs are handled as usual, giving priority to sNaNs\r
+ if (DFISSNAN(dfl) || DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ if (DFISSNAN(dff)) return decNaNs(result, dff, NULL, set);\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ if (DFISNAN(dff)) return decNaNs(result, dff, NULL, set);\r
+ // One or more of the three is infinite\r
+ // infinity times zero is bad\r
+ decFloatZero(&proxy);\r
+ if (DFISINF(dfl)) {\r
+ if (DFISZERO(dfr)) return decInvalid(result, set);\r
+ decInfinity(&proxy, &proxy);\r
+ }\r
+ else if (DFISINF(dfr)) {\r
+ if (DFISZERO(dfl)) return decInvalid(result, set);\r
+ decInfinity(&proxy, &proxy);\r
+ }\r
+ // compute sign of multiplication and place in proxy\r
+ DFWORD(&proxy, 0)|=(DFWORD(dfl, 0)^DFWORD(dfr, 0))&DECFLOAT_Sign;\r
+ if (!DFISINF(dff)) return decFloatCopy(result, &proxy);\r
+ // dff is Infinite\r
+ if (!DFISINF(&proxy)) return decInfinity(result, dff);\r
+ // both sides of addition are infinite; different sign is bad\r
+ if ((DFWORD(dff, 0)&DECFLOAT_Sign)!=(DFWORD(&proxy, 0)&DECFLOAT_Sign))\r
+ return decInvalid(result, set);\r
+ return decFloatCopy(result, &proxy);\r
+ }\r
+\r
+ /* Here when all operands are finite */\r
+\r
+ // First multiply dfl*dfr\r
+ decFiniteMultiply(&mul, acc+1, dfl, dfr);\r
+ // The multiply is complete, exact and unbounded, and described in\r
+ // mul with the coefficient held in acc[1...]\r
+\r
+ // now add in dff; the algorithm is essentially the same as\r
+ // decFloatAdd, but the code is different because the code there\r
+ // is highly optimized for adding two numbers of the same size\r
+ fin.exponent=GETEXPUN(dff); // get dff exponent and sign\r
+ fin.sign=DFWORD(dff, 0)&DECFLOAT_Sign;\r
+ diffsign=mul.sign^fin.sign; // note if signs differ\r
+ fin.msd=coe;\r
+ fin.lsd=coe+DECPMAX-1;\r
+ GETCOEFF(dff, coe); // extract the coefficient\r
+\r
+ // now set hi and lo so that hi points to whichever of mul and fin\r
+ // has the higher exponent and lo points to the other [don't care,\r
+ // if the same]. One coefficient will be in acc, the other in coe.\r
+ if (mul.exponent>=fin.exponent) {\r
+ hi=&mul;\r
+ lo=&fin;\r
+ }\r
+ else {\r
+ hi=&fin;\r
+ lo=&mul;\r
+ }\r
+\r
+ // remove leading zeros on both operands; this will save time later\r
+ // and make testing for zero trivial (tests are safe because acc\r
+ // and coe are rounded up to uInts)\r
+ for (; UBTOUI(hi->msd)==0 && hi->msd+3<hi->lsd;) hi->msd+=4;\r
+ for (; *hi->msd==0 && hi->msd<hi->lsd;) hi->msd++;\r
+ for (; UBTOUI(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;\r
+ for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;\r
+\r
+ // if hi is zero then result will be lo (which has the smaller\r
+ // exponent), which also may need to be tested for zero for the\r
+ // weird IEEE 754 sign rules\r
+ if (*hi->msd==0) { // hi is zero\r
+ // "When the sum of two operands with opposite signs is\r
+ // exactly zero, the sign of that sum shall be '+' in all\r
+ // rounding modes except round toward -Infinity, in which\r
+ // mode that sign shall be '-'."\r
+ if (diffsign) {\r
+ if (*lo->msd==0) { // lo is zero\r
+ lo->sign=0;\r
+ if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;\r
+ } // diffsign && lo=0\r
+ } // diffsign\r
+ return decFinalize(result, lo, set); // may need clamping\r
+ } // numfl is zero\r
+ // [here, both are minimal length and hi is non-zero]\r
+ // (if lo is zero then padding with zeros may be needed, below)\r
+\r
+ // if signs differ, take the ten's complement of hi (zeros to the\r
+ // right do not matter because the complement of zero is zero); the\r
+ // +1 is done later, as part of the addition, inserted at the\r
+ // correct digit\r
+ hipad=0;\r
+ carry=0;\r
+ if (diffsign) {\r
+ hipad=9;\r
+ carry=1;\r
+ // exactly the correct number of digits must be inverted\r
+ for (uh=hi->msd; uh<hi->lsd-3; uh+=4) UBFROMUI(uh, 0x09090909-UBTOUI(uh));\r
+ for (; uh<=hi->lsd; uh++) *uh=(uByte)(0x09-*uh);\r
+ }\r
+\r
+ // ready to add; note that hi has no leading zeros so gap\r
+ // calculation does not have to be as pessimistic as in decFloatAdd\r
+ // (this is much more like the arbitrary-precision algorithm in\r
+ // Rexx and decNumber)\r
+\r
+ // padding is the number of zeros that would need to be added to hi\r
+ // for its lsd to be aligned with the lsd of lo\r
+ padding=hi->exponent-lo->exponent;\r
+ // printf("FMA pad %ld\n", (LI)padding);\r
+\r
+ // the result of the addition will be built into the accumulator,\r
+ // starting from the far right; this could be either hi or lo, and\r
+ // will be aligned\r
+ ub=acc+FMALEN-1; // where lsd of result will go\r
+ ul=lo->lsd; // lsd of rhs\r
+\r
+ if (padding!=0) { // unaligned\r
+ // if the msd of lo is more than DECPMAX+2 digits to the right of\r
+ // the original msd of hi then it can be reduced to a single\r
+ // digit at the right place, as it stays clear of hi digits\r
+ // [it must be DECPMAX+2 because during a subtraction the msd\r
+ // could become 0 after a borrow from 1.000 to 0.9999...]\r
+\r
+ Int hilen=(Int)(hi->lsd-hi->msd+1); // length of hi\r
+ Int lolen=(Int)(lo->lsd-lo->msd+1); // and of lo\r
+\r
+ if (hilen+padding-lolen > DECPMAX+2) { // can reduce lo to single\r
+ // make sure it is virtually at least DECPMAX from hi->msd, at\r
+ // least to right of hi->lsd (in case of destructive subtract),\r
+ // and separated by at least two digits from either of those\r
+ // (the tricky DOUBLE case is when hi is a 1 that will become a\r
+ // 0.9999... by subtraction:\r
+ // hi: 1 E+16\r
+ // lo: .................1000000000000000 E-16\r
+ // which for the addition pads to:\r
+ // hi: 1000000000000000000 E-16\r
+ // lo: .................1000000000000000 E-16\r
+ Int newexp=MINI(hi->exponent, hi->exponent+hilen-DECPMAX)-3;\r
+\r
+ // printf("FMA reduce: %ld\n", (LI)reduce);\r
+ lo->lsd=lo->msd; // to single digit [maybe 0]\r
+ lo->exponent=newexp; // new lowest exponent\r
+ padding=hi->exponent-lo->exponent; // recalculate\r
+ ul=lo->lsd; // .. and repoint\r
+ }\r
+\r
+ // padding is still > 0, but will fit in acc (less leading carry slot)\r
+ #if DECCHECK\r
+ if (padding<=0) printf("FMA low padding: %ld\n", (LI)padding);\r
+ if (hilen+padding+1>FMALEN)\r
+ printf("FMA excess hilen+padding: %ld+%ld \n", (LI)hilen, (LI)padding);\r
+ // printf("FMA padding: %ld\n", (LI)padding);\r
+ #endif\r
+\r
+ // padding digits can now be set in the result; one or more of\r
+ // these will come from lo; others will be zeros in the gap\r
+ for (; ul-3>=lo->msd && padding>3; padding-=4, ul-=4, ub-=4) {\r
+ UBFROMUI(ub-3, UBTOUI(ul-3)); // [cannot overlap]\r
+ }\r
+ for (; ul>=lo->msd && padding>0; padding--, ul--, ub--) *ub=*ul;\r
+ for (;padding>0; padding--, ub--) *ub=0; // mind the gap\r
+ }\r
+\r
+ // addition now complete to the right of the rightmost digit of hi\r
+ uh=hi->lsd;\r
+\r
+ // dow do the add from hi->lsd to the left\r
+ // [bytewise, because either operand can run out at any time]\r
+ // carry was set up depending on ten's complement above\r
+ // first assume both operands have some digits\r
+ for (;; ub--) {\r
+ if (uh<hi->msd || ul<lo->msd) break;\r
+ *ub=(uByte)(carry+(*uh--)+(*ul--));\r
+ carry=0;\r
+ if (*ub<10) continue;\r
+ *ub-=10;\r
+ carry=1;\r
+ } // both loop\r
+\r
+ if (ul<lo->msd) { // to left of lo\r
+ for (;; ub--) {\r
+ if (uh<hi->msd) break;\r
+ *ub=(uByte)(carry+(*uh--)); // [+0]\r
+ carry=0;\r
+ if (*ub<10) continue;\r
+ *ub-=10;\r
+ carry=1;\r
+ } // hi loop\r
+ }\r
+ else { // to left of hi\r
+ for (;; ub--) {\r
+ if (ul<lo->msd) break;\r
+ *ub=(uByte)(carry+hipad+(*ul--));\r
+ carry=0;\r
+ if (*ub<10) continue;\r
+ *ub-=10;\r
+ carry=1;\r
+ } // lo loop\r
+ }\r
+\r
+ // addition complete -- now handle carry, borrow, etc.\r
+ // use lo to set up the num (its exponent is already correct, and\r
+ // sign usually is)\r
+ lo->msd=ub+1;\r
+ lo->lsd=acc+FMALEN-1;\r
+ // decShowNum(lo, "lo");\r
+ if (!diffsign) { // same-sign addition\r
+ if (carry) { // carry out\r
+ *ub=1; // place the 1 ..\r
+ lo->msd--; // .. and update\r
+ }\r
+ } // same sign\r
+ else { // signs differed (subtraction)\r
+ if (!carry) { // no carry out means hi<lo\r
+ // borrowed -- take ten's complement of the right digits\r
+ lo->sign=hi->sign; // sign is lhs sign\r
+ for (ul=lo->msd; ul<lo->lsd-3; ul+=4) UBFROMUI(ul, 0x09090909-UBTOUI(ul));\r
+ for (; ul<=lo->lsd; ul++) *ul=(uByte)(0x09-*ul); // [leaves ul at lsd+1]\r
+ // complete the ten's complement by adding 1 [cannot overrun]\r
+ for (ul--; *ul==9; ul--) *ul=0;\r
+ *ul+=1;\r
+ } // borrowed\r
+ else { // carry out means hi>=lo\r
+ // sign to use is lo->sign\r
+ // all done except for the special IEEE 754 exact-zero-result\r
+ // rule (see above); while testing for zero, strip leading\r
+ // zeros (which will save decFinalize doing it)\r
+ for (; UBTOUI(lo->msd)==0 && lo->msd+3<lo->lsd;) lo->msd+=4;\r
+ for (; *lo->msd==0 && lo->msd<lo->lsd;) lo->msd++;\r
+ if (*lo->msd==0) { // must be true zero (and diffsign)\r
+ lo->sign=0; // assume +\r
+ if (set->round==DEC_ROUND_FLOOR) lo->sign=DECFLOAT_Sign;\r
+ }\r
+ // [else was not zero, might still have leading zeros]\r
+ } // subtraction gave positive result\r
+ } // diffsign\r
+\r
+ #if DECCHECK\r
+ // assert no left underrun\r
+ if (lo->msd<acc) {\r
+ printf("FMA underrun by %ld \n", (LI)(acc-lo->msd));\r
+ }\r
+ #endif\r
+\r
+ return decFinalize(result, lo, set); // round, check, and lay out\r
+ } // decFloatFMA\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromInt -- initialise a decFloat from an Int */\r
+/* */\r
+/* result gets the converted Int */\r
+/* n is the Int to convert */\r
+/* returns result */\r
+/* */\r
+/* The result is Exact; no errors or exceptions are possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFromInt32(decFloat *result, Int n) {\r
+ uInt u=(uInt)n; // copy as bits\r
+ uInt encode; // work\r
+ DFWORD(result, 0)=ZEROWORD; // always\r
+ #if QUAD\r
+ DFWORD(result, 1)=0;\r
+ DFWORD(result, 2)=0;\r
+ #endif\r
+ if (n<0) { // handle -n with care\r
+ // [This can be done without the test, but is then slightly slower]\r
+ u=(~u)+1;\r
+ DFWORD(result, 0)|=DECFLOAT_Sign;\r
+ }\r
+ // Since the maximum value of u now is 2**31, only the low word of\r
+ // result is affected\r
+ encode=BIN2DPD[u%1000];\r
+ u/=1000;\r
+ encode|=BIN2DPD[u%1000]<<10;\r
+ u/=1000;\r
+ encode|=BIN2DPD[u%1000]<<20;\r
+ u/=1000; // now 0, 1, or 2\r
+ encode|=u<<30;\r
+ DFWORD(result, DECWORDS-1)=encode;\r
+ return result;\r
+ } // decFloatFromInt32\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromUInt -- initialise a decFloat from a uInt */\r
+/* */\r
+/* result gets the converted uInt */\r
+/* n is the uInt to convert */\r
+/* returns result */\r
+/* */\r
+/* The result is Exact; no errors or exceptions are possible. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFromUInt32(decFloat *result, uInt u) {\r
+ uInt encode; // work\r
+ DFWORD(result, 0)=ZEROWORD; // always\r
+ #if QUAD\r
+ DFWORD(result, 1)=0;\r
+ DFWORD(result, 2)=0;\r
+ #endif\r
+ encode=BIN2DPD[u%1000];\r
+ u/=1000;\r
+ encode|=BIN2DPD[u%1000]<<10;\r
+ u/=1000;\r
+ encode|=BIN2DPD[u%1000]<<20;\r
+ u/=1000; // now 0 -> 4\r
+ encode|=u<<30;\r
+ DFWORD(result, DECWORDS-1)=encode;\r
+ DFWORD(result, DECWORDS-2)|=u>>2; // rarely non-zero\r
+ return result;\r
+ } // decFloatFromUInt32\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatInvert -- logical digitwise INVERT of a decFloat */\r
+/* */\r
+/* result gets the result of INVERTing df */\r
+/* df is the decFloat to invert */\r
+/* set is the context */\r
+/* returns result, which will be canonical with sign=0 */\r
+/* */\r
+/* The operand must be positive, finite with exponent q=0, and */\r
+/* comprise just zeros and ones; if not, Invalid operation results. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatInvert(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ uInt sourhi=DFWORD(df, 0); // top word of dfs\r
+\r
+ if (!DFISUINT01(df) || !DFISCC01(df)) return decInvalid(result, set);\r
+ // the operand is a finite integer (q=0)\r
+ #if DOUBLE\r
+ DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04009124);\r
+ DFWORD(result, 1)=(~DFWORD(df, 1)) &0x49124491;\r
+ #elif QUAD\r
+ DFWORD(result, 0)=ZEROWORD|((~sourhi)&0x04000912);\r
+ DFWORD(result, 1)=(~DFWORD(df, 1)) &0x44912449;\r
+ DFWORD(result, 2)=(~DFWORD(df, 2)) &0x12449124;\r
+ DFWORD(result, 3)=(~DFWORD(df, 3)) &0x49124491;\r
+ #endif\r
+ return result;\r
+ } // decFloatInvert\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatIs -- decFloat tests (IsSigned, etc.) */\r
+/* */\r
+/* df is the decFloat to test */\r
+/* returns 0 or 1 in a uInt */\r
+/* */\r
+/* Many of these could be macros, but having them as real functions */\r
+/* is a little cleaner (and they can be referred to here by the */\r
+/* generic names) */\r
+/* ------------------------------------------------------------------ */\r
+uInt decFloatIsCanonical(const decFloat *df) {\r
+ if (DFISSPECIAL(df)) {\r
+ if (DFISINF(df)) {\r
+ if (DFWORD(df, 0)&ECONMASK) return 0; // exponent continuation\r
+ if (!DFISCCZERO(df)) return 0; // coefficient continuation\r
+ return 1;\r
+ }\r
+ // is a NaN\r
+ if (DFWORD(df, 0)&ECONNANMASK) return 0; // exponent continuation\r
+ if (DFISCCZERO(df)) return 1; // coefficient continuation\r
+ // drop through to check payload\r
+ }\r
+ { // declare block\r
+ #if DOUBLE\r
+ uInt sourhi=DFWORD(df, 0);\r
+ uInt sourlo=DFWORD(df, 1);\r
+ if (CANONDPDOFF(sourhi, 8)\r
+ && CANONDPDTWO(sourhi, sourlo, 30)\r
+ && CANONDPDOFF(sourlo, 20)\r
+ && CANONDPDOFF(sourlo, 10)\r
+ && CANONDPDOFF(sourlo, 0)) return 1;\r
+ #elif QUAD\r
+ uInt sourhi=DFWORD(df, 0);\r
+ uInt sourmh=DFWORD(df, 1);\r
+ uInt sourml=DFWORD(df, 2);\r
+ uInt sourlo=DFWORD(df, 3);\r
+ if (CANONDPDOFF(sourhi, 4)\r
+ && CANONDPDTWO(sourhi, sourmh, 26)\r
+ && CANONDPDOFF(sourmh, 16)\r
+ && CANONDPDOFF(sourmh, 6)\r
+ && CANONDPDTWO(sourmh, sourml, 28)\r
+ && CANONDPDOFF(sourml, 18)\r
+ && CANONDPDOFF(sourml, 8)\r
+ && CANONDPDTWO(sourml, sourlo, 30)\r
+ && CANONDPDOFF(sourlo, 20)\r
+ && CANONDPDOFF(sourlo, 10)\r
+ && CANONDPDOFF(sourlo, 0)) return 1;\r
+ #endif\r
+ } // block\r
+ return 0; // a declet is non-canonical\r
+ }\r
+\r
+uInt decFloatIsFinite(const decFloat *df) {\r
+ return !DFISSPECIAL(df);\r
+ }\r
+uInt decFloatIsInfinite(const decFloat *df) {\r
+ return DFISINF(df);\r
+ }\r
+uInt decFloatIsInteger(const decFloat *df) {\r
+ return DFISINT(df);\r
+ }\r
+uInt decFloatIsLogical(const decFloat *df) {\r
+ return DFISUINT01(df) & DFISCC01(df);\r
+ }\r
+uInt decFloatIsNaN(const decFloat *df) {\r
+ return DFISNAN(df);\r
+ }\r
+uInt decFloatIsNegative(const decFloat *df) {\r
+ return DFISSIGNED(df) && !DFISZERO(df) && !DFISNAN(df);\r
+ }\r
+uInt decFloatIsNormal(const decFloat *df) {\r
+ Int exp; // exponent\r
+ if (DFISSPECIAL(df)) return 0;\r
+ if (DFISZERO(df)) return 0;\r
+ // is finite and non-zero\r
+ exp=GETEXPUN(df) // get unbiased exponent ..\r
+ +decFloatDigits(df)-1; // .. and make adjusted exponent\r
+ return (exp>=DECEMIN); // < DECEMIN is subnormal\r
+ }\r
+uInt decFloatIsPositive(const decFloat *df) {\r
+ return !DFISSIGNED(df) && !DFISZERO(df) && !DFISNAN(df);\r
+ }\r
+uInt decFloatIsSignaling(const decFloat *df) {\r
+ return DFISSNAN(df);\r
+ }\r
+uInt decFloatIsSignalling(const decFloat *df) {\r
+ return DFISSNAN(df);\r
+ }\r
+uInt decFloatIsSigned(const decFloat *df) {\r
+ return DFISSIGNED(df);\r
+ }\r
+uInt decFloatIsSubnormal(const decFloat *df) {\r
+ if (DFISSPECIAL(df)) return 0;\r
+ // is finite\r
+ if (decFloatIsNormal(df)) return 0;\r
+ // it is <Nmin, but could be zero\r
+ if (DFISZERO(df)) return 0;\r
+ return 1; // is subnormal\r
+ }\r
+uInt decFloatIsZero(const decFloat *df) {\r
+ return DFISZERO(df);\r
+ } // decFloatIs...\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatLogB -- return adjusted exponent, by 754 rules */\r
+/* */\r
+/* result gets the adjusted exponent as an integer, or a NaN etc. */\r
+/* df is the decFloat to be examined */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* Notable cases: */\r
+/* A<0 -> Use |A| */\r
+/* A=0 -> -Infinity (Division by zero) */\r
+/* A=Infinite -> +Infinity (Exact) */\r
+/* A=1 exactly -> 0 (Exact) */\r
+/* NaNs are propagated as usual */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatLogB(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ Int ae; // adjusted exponent\r
+ if (DFISNAN(df)) return decNaNs(result, df, NULL, set);\r
+ if (DFISINF(df)) {\r
+ DFWORD(result, 0)=0; // need +ve\r
+ return decInfinity(result, result); // canonical +Infinity\r
+ }\r
+ if (DFISZERO(df)) {\r
+ set->status|=DEC_Division_by_zero; // as per 754\r
+ DFWORD(result, 0)=DECFLOAT_Sign; // make negative\r
+ return decInfinity(result, result); // canonical -Infinity\r
+ }\r
+ ae=GETEXPUN(df) // get unbiased exponent ..\r
+ +decFloatDigits(df)-1; // .. and make adjusted exponent\r
+ // ae has limited range (3 digits for DOUBLE and 4 for QUAD), so\r
+ // it is worth using a special case of decFloatFromInt32\r
+ DFWORD(result, 0)=ZEROWORD; // always\r
+ if (ae<0) {\r
+ DFWORD(result, 0)|=DECFLOAT_Sign; // -0 so far\r
+ ae=-ae;\r
+ }\r
+ #if DOUBLE\r
+ DFWORD(result, 1)=BIN2DPD[ae]; // a single declet\r
+ #elif QUAD\r
+ DFWORD(result, 1)=0;\r
+ DFWORD(result, 2)=0;\r
+ DFWORD(result, 3)=(ae/1000)<<10; // is <10, so need no DPD encode\r
+ DFWORD(result, 3)|=BIN2DPD[ae%1000];\r
+ #endif\r
+ return result;\r
+ } // decFloatLogB\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatMax -- return maxnum of two operands */\r
+/* */\r
+/* result gets the chosen decFloat */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* If just one operand is a quiet NaN it is ignored. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatMax(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int comp;\r
+ if (DFISNAN(dfl)) {\r
+ // sNaN or both NaNs leads to normal NaN processing\r
+ if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);\r
+ return decCanonical(result, dfr); // RHS is numeric\r
+ }\r
+ if (DFISNAN(dfr)) {\r
+ // sNaN leads to normal NaN processing (both NaN handled above)\r
+ if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ return decCanonical(result, dfl); // LHS is numeric\r
+ }\r
+ // Both operands are numeric; numeric comparison needed -- use\r
+ // total order for a well-defined choice (and +0 > -0)\r
+ comp=decNumCompare(dfl, dfr, 1);\r
+ if (comp>=0) return decCanonical(result, dfl);\r
+ return decCanonical(result, dfr);\r
+ } // decFloatMax\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatMaxMag -- return maxnummag of two operands */\r
+/* */\r
+/* result gets the chosen decFloat */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* Returns according to the magnitude comparisons if both numeric and */\r
+/* unequal, otherwise returns maxnum */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatMaxMag(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int comp;\r
+ decFloat absl, absr;\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMax(result, dfl, dfr, set);\r
+\r
+ decFloatCopyAbs(&absl, dfl);\r
+ decFloatCopyAbs(&absr, dfr);\r
+ comp=decNumCompare(&absl, &absr, 0);\r
+ if (comp>0) return decCanonical(result, dfl);\r
+ if (comp<0) return decCanonical(result, dfr);\r
+ return decFloatMax(result, dfl, dfr, set);\r
+ } // decFloatMaxMag\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatMin -- return minnum of two operands */\r
+/* */\r
+/* result gets the chosen decFloat */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* If just one operand is a quiet NaN it is ignored. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatMin(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int comp;\r
+ if (DFISNAN(dfl)) {\r
+ // sNaN or both NaNs leads to normal NaN processing\r
+ if (DFISNAN(dfr) || DFISSNAN(dfl)) return decNaNs(result, dfl, dfr, set);\r
+ return decCanonical(result, dfr); // RHS is numeric\r
+ }\r
+ if (DFISNAN(dfr)) {\r
+ // sNaN leads to normal NaN processing (both NaN handled above)\r
+ if (DFISSNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ return decCanonical(result, dfl); // LHS is numeric\r
+ }\r
+ // Both operands are numeric; numeric comparison needed -- use\r
+ // total order for a well-defined choice (and +0 > -0)\r
+ comp=decNumCompare(dfl, dfr, 1);\r
+ if (comp<=0) return decCanonical(result, dfl);\r
+ return decCanonical(result, dfr);\r
+ } // decFloatMin\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatMinMag -- return minnummag of two operands */\r
+/* */\r
+/* result gets the chosen decFloat */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* Returns according to the magnitude comparisons if both numeric and */\r
+/* unequal, otherwise returns minnum */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatMinMag(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int comp;\r
+ decFloat absl, absr;\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decFloatMin(result, dfl, dfr, set);\r
+\r
+ decFloatCopyAbs(&absl, dfl);\r
+ decFloatCopyAbs(&absr, dfr);\r
+ comp=decNumCompare(&absl, &absr, 0);\r
+ if (comp<0) return decCanonical(result, dfl);\r
+ if (comp>0) return decCanonical(result, dfr);\r
+ return decFloatMin(result, dfl, dfr, set);\r
+ } // decFloatMinMag\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatMinus -- negate value, heeding NaNs, etc. */\r
+/* */\r
+/* result gets the canonicalized 0-df */\r
+/* df is the decFloat to minus */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This has the same effect as 0-df where the exponent of the zero is */\r
+/* the same as that of df (if df is finite). */\r
+/* The effect is also the same as decFloatCopyNegate except that NaNs */\r
+/* are handled normally (the sign of a NaN is not affected, and an */\r
+/* sNaN will signal), the result is canonical, and zero gets sign 0. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatMinus(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ if (DFISNAN(df)) return decNaNs(result, df, NULL, set);\r
+ decCanonical(result, df); // copy and check\r
+ if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; // turn off sign bit\r
+ else DFBYTE(result, 0)^=0x80; // flip sign bit\r
+ return result;\r
+ } // decFloatMinus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatMultiply -- multiply two decFloats */\r
+/* */\r
+/* result gets the result of multiplying dfl and dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatMultiply(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ bcdnum num; // for final conversion\r
+ uByte bcdacc[DECPMAX9*18+1]; // for coefficent in BCD\r
+\r
+ if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) { // either is special?\r
+ // NaNs are handled as usual\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ // infinity times zero is bad\r
+ if (DFISINF(dfl) && DFISZERO(dfr)) return decInvalid(result, set);\r
+ if (DFISINF(dfr) && DFISZERO(dfl)) return decInvalid(result, set);\r
+ // both infinite; return canonical infinity with computed sign\r
+ DFWORD(result, 0)=DFWORD(dfl, 0)^DFWORD(dfr, 0); // compute sign\r
+ return decInfinity(result, result);\r
+ }\r
+\r
+ /* Here when both operands are finite */\r
+ decFiniteMultiply(&num, bcdacc, dfl, dfr);\r
+ return decFinalize(result, &num, set); // round, check, and lay out\r
+ } // decFloatMultiply\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatNextMinus -- next towards -Infinity */\r
+/* */\r
+/* result gets the next lesser decFloat */\r
+/* dfl is the decFloat to start with */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This is 754 nextdown; Invalid is the only status possible (from */\r
+/* an sNaN). */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatNextMinus(decFloat *result, const decFloat *dfl,\r
+ decContext *set) {\r
+ decFloat delta; // tiny increment\r
+ uInt savestat; // saves status\r
+ enum rounding saveround; // .. and mode\r
+\r
+ // +Infinity is the special case\r
+ if (DFISINF(dfl) && !DFISSIGNED(dfl)) {\r
+ DFSETNMAX(result);\r
+ return result; // [no status to set]\r
+ }\r
+ // other cases are effected by sutracting a tiny delta -- this\r
+ // should be done in a wider format as the delta is unrepresentable\r
+ // here (but can be done with normal add if the sign of zero is\r
+ // treated carefully, because no Inexactitude is interesting);\r
+ // rounding to -Infinity then pushes the result to next below\r
+ decFloatZero(&delta); // set up tiny delta\r
+ DFWORD(&delta, DECWORDS-1)=1; // coefficient=1\r
+ DFWORD(&delta, 0)=DECFLOAT_Sign; // Sign=1 + biased exponent=0\r
+ // set up for the directional round\r
+ saveround=set->round; // save mode\r
+ set->round=DEC_ROUND_FLOOR; // .. round towards -Infinity\r
+ savestat=set->status; // save status\r
+ decFloatAdd(result, dfl, &delta, set);\r
+ // Add rules mess up the sign when going from +Ntiny to 0\r
+ if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; // correct\r
+ set->status&=DEC_Invalid_operation; // preserve only sNaN status\r
+ set->status|=savestat; // restore pending flags\r
+ set->round=saveround; // .. and mode\r
+ return result;\r
+ } // decFloatNextMinus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatNextPlus -- next towards +Infinity */\r
+/* */\r
+/* result gets the next larger decFloat */\r
+/* dfl is the decFloat to start with */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This is 754 nextup; Invalid is the only status possible (from */\r
+/* an sNaN). */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatNextPlus(decFloat *result, const decFloat *dfl,\r
+ decContext *set) {\r
+ uInt savestat; // saves status\r
+ enum rounding saveround; // .. and mode\r
+ decFloat delta; // tiny increment\r
+\r
+ // -Infinity is the special case\r
+ if (DFISINF(dfl) && DFISSIGNED(dfl)) {\r
+ DFSETNMAX(result);\r
+ DFWORD(result, 0)|=DECFLOAT_Sign; // make negative\r
+ return result; // [no status to set]\r
+ }\r
+ // other cases are effected by sutracting a tiny delta -- this\r
+ // should be done in a wider format as the delta is unrepresentable\r
+ // here (but can be done with normal add if the sign of zero is\r
+ // treated carefully, because no Inexactitude is interesting);\r
+ // rounding to +Infinity then pushes the result to next above\r
+ decFloatZero(&delta); // set up tiny delta\r
+ DFWORD(&delta, DECWORDS-1)=1; // coefficient=1\r
+ DFWORD(&delta, 0)=0; // Sign=0 + biased exponent=0\r
+ // set up for the directional round\r
+ saveround=set->round; // save mode\r
+ set->round=DEC_ROUND_CEILING; // .. round towards +Infinity\r
+ savestat=set->status; // save status\r
+ decFloatAdd(result, dfl, &delta, set);\r
+ // Add rules mess up the sign when going from -Ntiny to -0\r
+ if (DFISZERO(result)) DFWORD(result, 0)^=DECFLOAT_Sign; // correct\r
+ set->status&=DEC_Invalid_operation; // preserve only sNaN status\r
+ set->status|=savestat; // restore pending flags\r
+ set->round=saveround; // .. and mode\r
+ return result;\r
+ } // decFloatNextPlus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatNextToward -- next towards a decFloat */\r
+/* */\r
+/* result gets the next decFloat */\r
+/* dfl is the decFloat to start with */\r
+/* dfr is the decFloat to move toward */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This is 754-1985 nextafter, as modified during revision (dropped */\r
+/* from 754-2008); status may be set unless the result is a normal */\r
+/* number. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatNextToward(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ decFloat delta; // tiny increment or decrement\r
+ decFloat pointone; // 1e-1\r
+ uInt savestat; // saves status\r
+ enum rounding saveround; // .. and mode\r
+ uInt deltatop; // top word for delta\r
+ Int comp; // work\r
+\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ // Both are numeric, so Invalid no longer a possibility\r
+ comp=decNumCompare(dfl, dfr, 0);\r
+ if (comp==0) return decFloatCopySign(result, dfl, dfr); // equal\r
+ // unequal; do NextPlus or NextMinus but with different status rules\r
+\r
+ if (comp<0) { // lhs<rhs, do NextPlus, see above for commentary\r
+ if (DFISINF(dfl) && DFISSIGNED(dfl)) { // -Infinity special case\r
+ DFSETNMAX(result);\r
+ DFWORD(result, 0)|=DECFLOAT_Sign;\r
+ return result;\r
+ }\r
+ saveround=set->round; // save mode\r
+ set->round=DEC_ROUND_CEILING; // .. round towards +Infinity\r
+ deltatop=0; // positive delta\r
+ }\r
+ else { // lhs>rhs, do NextMinus, see above for commentary\r
+ if (DFISINF(dfl) && !DFISSIGNED(dfl)) { // +Infinity special case\r
+ DFSETNMAX(result);\r
+ return result;\r
+ }\r
+ saveround=set->round; // save mode\r
+ set->round=DEC_ROUND_FLOOR; // .. round towards -Infinity\r
+ deltatop=DECFLOAT_Sign; // negative delta\r
+ }\r
+ savestat=set->status; // save status\r
+ // Here, Inexact is needed where appropriate (and hence Underflow,\r
+ // etc.). Therefore the tiny delta which is otherwise\r
+ // unrepresentable (see NextPlus and NextMinus) is constructed\r
+ // using the multiplication of FMA.\r
+ decFloatZero(&delta); // set up tiny delta\r
+ DFWORD(&delta, DECWORDS-1)=1; // coefficient=1\r
+ DFWORD(&delta, 0)=deltatop; // Sign + biased exponent=0\r
+ decFloatFromString(&pointone, "1E-1", set); // set up multiplier\r
+ decFloatFMA(result, &delta, &pointone, dfl, set);\r
+ // [Delta is truly tiny, so no need to correct sign of zero]\r
+ // use new status unless the result is normal\r
+ if (decFloatIsNormal(result)) set->status=savestat; // else goes forward\r
+ set->round=saveround; // restore mode\r
+ return result;\r
+ } // decFloatNextToward\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatOr -- logical digitwise OR of two decFloats */\r
+/* */\r
+/* result gets the result of ORing dfl and dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result, which will be canonical with sign=0 */\r
+/* */\r
+/* The operands must be positive, finite with exponent q=0, and */\r
+/* comprise just zeros and ones; if not, Invalid operation results. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatOr(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ if (!DFISUINT01(dfl) || !DFISUINT01(dfr)\r
+ || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);\r
+ // the operands are positive finite integers (q=0) with just 0s and 1s\r
+ #if DOUBLE\r
+ DFWORD(result, 0)=ZEROWORD\r
+ |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04009124);\r
+ DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x49124491;\r
+ #elif QUAD\r
+ DFWORD(result, 0)=ZEROWORD\r
+ |((DFWORD(dfl, 0) | DFWORD(dfr, 0))&0x04000912);\r
+ DFWORD(result, 1)=(DFWORD(dfl, 1) | DFWORD(dfr, 1))&0x44912449;\r
+ DFWORD(result, 2)=(DFWORD(dfl, 2) | DFWORD(dfr, 2))&0x12449124;\r
+ DFWORD(result, 3)=(DFWORD(dfl, 3) | DFWORD(dfr, 3))&0x49124491;\r
+ #endif\r
+ return result;\r
+ } // decFloatOr\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatPlus -- add value to 0, heeding NaNs, etc. */\r
+/* */\r
+/* result gets the canonicalized 0+df */\r
+/* df is the decFloat to plus */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This has the same effect as 0+df where the exponent of the zero is */\r
+/* the same as that of df (if df is finite). */\r
+/* The effect is also the same as decFloatCopy except that NaNs */\r
+/* are handled normally (the sign of a NaN is not affected, and an */\r
+/* sNaN will signal), the result is canonical, and zero gets sign 0. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatPlus(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ if (DFISNAN(df)) return decNaNs(result, df, NULL, set);\r
+ decCanonical(result, df); // copy and check\r
+ if (DFISZERO(df)) DFBYTE(result, 0)&=~0x80; // turn off sign bit\r
+ return result;\r
+ } // decFloatPlus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatQuantize -- quantize a decFloat */\r
+/* */\r
+/* result gets the result of quantizing dfl to match dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs), which sets the exponent */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* Unless there is an error or the result is infinite, the exponent */\r
+/* of result is guaranteed to be the same as that of dfr. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatQuantize(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int explb, exprb; // left and right biased exponents\r
+ uByte *ulsd; // local LSD pointer\r
+ uByte *ub, *uc; // work\r
+ Int drop; // ..\r
+ uInt dpd; // ..\r
+ uInt encode; // encoding accumulator\r
+ uInt sourhil, sourhir; // top words from source decFloats\r
+ uInt uiwork; // for macros\r
+ #if QUAD\r
+ uShort uswork; // ..\r
+ #endif\r
+ // the following buffer holds the coefficient for manipulation\r
+ uByte buf[4+DECPMAX*3+2*QUAD]; // + space for zeros to left or right\r
+ #if DECTRACE\r
+ bcdnum num; // for trace displays\r
+ #endif\r
+\r
+ /* Start decoding the arguments */\r
+ sourhil=DFWORD(dfl, 0); // LHS top word\r
+ explb=DECCOMBEXP[sourhil>>26]; // get exponent high bits (in place)\r
+ sourhir=DFWORD(dfr, 0); // RHS top word\r
+ exprb=DECCOMBEXP[sourhir>>26];\r
+\r
+ if (EXPISSPECIAL(explb | exprb)) { // either is special?\r
+ // NaNs are handled as usual\r
+ if (DFISNAN(dfl) || DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ // one infinity but not both is bad\r
+ if (DFISINF(dfl)!=DFISINF(dfr)) return decInvalid(result, set);\r
+ // both infinite; return canonical infinity with sign of LHS\r
+ return decInfinity(result, dfl);\r
+ }\r
+\r
+ /* Here when both arguments are finite */\r
+ // complete extraction of the exponents [no need to unbias]\r
+ explb+=GETECON(dfl); // + continuation\r
+ exprb+=GETECON(dfr); // ..\r
+\r
+ // calculate the number of digits to drop from the coefficient\r
+ drop=exprb-explb; // 0 if nothing to do\r
+ if (drop==0) return decCanonical(result, dfl); // return canonical\r
+\r
+ // the coefficient is needed; lay it out into buf, offset so zeros\r
+ // can be added before or after as needed -- an extra heading is\r
+ // added so can safely pad Quad DECPMAX-1 zeros to the left by\r
+ // fours\r
+ #define BUFOFF (buf+4+DECPMAX)\r
+ GETCOEFF(dfl, BUFOFF); // decode from decFloat\r
+ // [now the msd is at BUFOFF and the lsd is at BUFOFF+DECPMAX-1]\r
+\r
+ #if DECTRACE\r
+ num.msd=BUFOFF;\r
+ num.lsd=BUFOFF+DECPMAX-1;\r
+ num.exponent=explb-DECBIAS;\r
+ num.sign=sourhil & DECFLOAT_Sign;\r
+ decShowNum(&num, "dfl");\r
+ #endif\r
+\r
+ if (drop>0) { // [most common case]\r
+ // (this code is very similar to that in decFloatFinalize, but\r
+ // has many differences so is duplicated here -- so any changes\r
+ // may need to be made there, too)\r
+ uByte *roundat; // -> re-round digit\r
+ uByte reround; // reround value\r
+ // printf("Rounding; drop=%ld\n", (LI)drop);\r
+\r
+ // there is at least one zero needed to the left, in all but one\r
+ // exceptional (all-nines) case, so place four zeros now; this is\r
+ // needed almost always and makes rounding all-nines by fours safe\r
+ UBFROMUI(BUFOFF-4, 0);\r
+\r
+ // Three cases here:\r
+ // 1. new LSD is in coefficient (almost always)\r
+ // 2. new LSD is digit to left of coefficient (so MSD is\r
+ // round-for-reround digit)\r
+ // 3. new LSD is to left of case 2 (whole coefficient is sticky)\r
+ // Note that leading zeros can safely be treated as useful digits\r
+\r
+ // [duplicate check-stickies code to save a test]\r
+ // [by-digit check for stickies as runs of zeros are rare]\r
+ if (drop<DECPMAX) { // NB lengths not addresses\r
+ roundat=BUFOFF+DECPMAX-drop;\r
+ reround=*roundat;\r
+ for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {\r
+ if (*ub!=0) { // non-zero to be discarded\r
+ reround=DECSTICKYTAB[reround]; // apply sticky bit\r
+ break; // [remainder don't-care]\r
+ }\r
+ } // check stickies\r
+ ulsd=roundat-1; // set LSD\r
+ }\r
+ else { // edge case\r
+ if (drop==DECPMAX) {\r
+ roundat=BUFOFF;\r
+ reround=*roundat;\r
+ }\r
+ else {\r
+ roundat=BUFOFF-1;\r
+ reround=0;\r
+ }\r
+ for (ub=roundat+1; ub<BUFOFF+DECPMAX; ub++) {\r
+ if (*ub!=0) { // non-zero to be discarded\r
+ reround=DECSTICKYTAB[reround]; // apply sticky bit\r
+ break; // [remainder don't-care]\r
+ }\r
+ } // check stickies\r
+ *BUFOFF=0; // make a coefficient of 0\r
+ ulsd=BUFOFF; // .. at the MSD place\r
+ }\r
+\r
+ if (reround!=0) { // discarding non-zero\r
+ uInt bump=0;\r
+ set->status|=DEC_Inexact;\r
+\r
+ // next decide whether to increment the coefficient\r
+ if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case\r
+ if (reround>5) bump=1; // >0.5 goes up\r
+ else if (reround==5) // exactly 0.5000 ..\r
+ bump=*ulsd & 0x01; // .. up iff [new] lsd is odd\r
+ } // r-h-e\r
+ else switch (set->round) {\r
+ case DEC_ROUND_DOWN: {\r
+ // no change\r
+ break;} // r-d\r
+ case DEC_ROUND_HALF_DOWN: {\r
+ if (reround>5) bump=1;\r
+ break;} // r-h-d\r
+ case DEC_ROUND_HALF_UP: {\r
+ if (reround>=5) bump=1;\r
+ break;} // r-h-u\r
+ case DEC_ROUND_UP: {\r
+ if (reround>0) bump=1;\r
+ break;} // r-u\r
+ case DEC_ROUND_CEILING: {\r
+ // same as _UP for positive numbers, and as _DOWN for negatives\r
+ if (!(sourhil&DECFLOAT_Sign) && reround>0) bump=1;\r
+ break;} // r-c\r
+ case DEC_ROUND_FLOOR: {\r
+ // same as _UP for negative numbers, and as _DOWN for positive\r
+ // [negative reround cannot occur on 0]\r
+ if (sourhil&DECFLOAT_Sign && reround>0) bump=1;\r
+ break;} // r-f\r
+ case DEC_ROUND_05UP: {\r
+ if (reround>0) { // anything out there is 'sticky'\r
+ // bump iff lsd=0 or 5; this cannot carry so it could be\r
+ // effected immediately with no bump -- but the code\r
+ // is clearer if this is done the same way as the others\r
+ if (*ulsd==0 || *ulsd==5) bump=1;\r
+ }\r
+ break;} // r-r\r
+ default: { // e.g., DEC_ROUND_MAX\r
+ set->status|=DEC_Invalid_context;\r
+ #if DECCHECK\r
+ printf("Unknown rounding mode: %ld\n", (LI)set->round);\r
+ #endif\r
+ break;}\r
+ } // switch (not r-h-e)\r
+ // printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump);\r
+\r
+ if (bump!=0) { // need increment\r
+ // increment the coefficient; this could give 1000... (after\r
+ // the all nines case)\r
+ ub=ulsd;\r
+ for (; UBTOUI(ub-3)==0x09090909; ub-=4) UBFROMUI(ub-3, 0);\r
+ // now at most 3 digits left to non-9 (usually just the one)\r
+ for (; *ub==9; ub--) *ub=0;\r
+ *ub+=1;\r
+ // [the all-nines case will have carried one digit to the\r
+ // left of the original MSD -- just where it is needed]\r
+ } // bump needed\r
+ } // inexact rounding\r
+\r
+ // now clear zeros to the left so exactly DECPMAX digits will be\r
+ // available in the coefficent -- the first word to the left was\r
+ // cleared earlier for safe carry; now add any more needed\r
+ if (drop>4) {\r
+ UBFROMUI(BUFOFF-8, 0); // must be at least 5\r
+ for (uc=BUFOFF-12; uc>ulsd-DECPMAX-3; uc-=4) UBFROMUI(uc, 0);\r
+ }\r
+ } // need round (drop>0)\r
+\r
+ else { // drop<0; padding with -drop digits is needed\r
+ // This is the case where an error can occur if the padded\r
+ // coefficient will not fit; checking for this can be done in the\r
+ // same loop as padding for zeros if the no-hope and zero cases\r
+ // are checked first\r
+ if (-drop>DECPMAX-1) { // cannot fit unless 0\r
+ if (!ISCOEFFZERO(BUFOFF)) return decInvalid(result, set);\r
+ // a zero can have any exponent; just drop through and use it\r
+ ulsd=BUFOFF+DECPMAX-1;\r
+ }\r
+ else { // padding will fit (but may still be too long)\r
+ // final-word mask depends on endianess\r
+ #if DECLITEND\r
+ static const uInt dmask[]={0, 0x000000ff, 0x0000ffff, 0x00ffffff};\r
+ #else\r
+ static const uInt dmask[]={0, 0xff000000, 0xffff0000, 0xffffff00};\r
+ #endif\r
+ // note that here zeros to the right are added by fours, so in\r
+ // the Quad case this could write 36 zeros if the coefficient has\r
+ // fewer than three significant digits (hence the +2*QUAD for buf)\r
+ for (uc=BUFOFF+DECPMAX;; uc+=4) {\r
+ UBFROMUI(uc, 0);\r
+ if (UBTOUI(uc-DECPMAX)!=0) { // could be bad\r
+ // if all four digits should be zero, definitely bad\r
+ if (uc<=BUFOFF+DECPMAX+(-drop)-4)\r
+ return decInvalid(result, set);\r
+ // must be a 1- to 3-digit sequence; check more carefully\r
+ if ((UBTOUI(uc-DECPMAX)&dmask[(-drop)%4])!=0)\r
+ return decInvalid(result, set);\r
+ break; // no need for loop end test\r
+ }\r
+ if (uc>=BUFOFF+DECPMAX+(-drop)-4) break; // done\r
+ }\r
+ ulsd=BUFOFF+DECPMAX+(-drop)-1;\r
+ } // pad and check leading zeros\r
+ } // drop<0\r
+\r
+ #if DECTRACE\r
+ num.msd=ulsd-DECPMAX+1;\r
+ num.lsd=ulsd;\r
+ num.exponent=explb-DECBIAS;\r
+ num.sign=sourhil & DECFLOAT_Sign;\r
+ decShowNum(&num, "res");\r
+ #endif\r
+\r
+ /*------------------------------------------------------------------*/\r
+ /* At this point the result is DECPMAX digits, ending at ulsd, so */\r
+ /* fits the encoding exactly; there is no possibility of error */\r
+ /*------------------------------------------------------------------*/\r
+ encode=((exprb>>DECECONL)<<4) + *(ulsd-DECPMAX+1); // make index\r
+ encode=DECCOMBFROM[encode]; // indexed by (0-2)*16+msd\r
+ // the exponent continuation can be extracted from the original RHS\r
+ encode|=sourhir & ECONMASK;\r
+ encode|=sourhil&DECFLOAT_Sign; // add the sign from LHS\r
+\r
+ // finally encode the coefficient\r
+ // private macro to encode a declet; this version can be used\r
+ // because all coefficient digits exist\r
+ #define getDPD3q(dpd, n) ub=ulsd-(3*(n))-2; \\r
+ dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];\r
+\r
+ #if DOUBLE\r
+ getDPD3q(dpd, 4); encode|=dpd<<8;\r
+ getDPD3q(dpd, 3); encode|=dpd>>2;\r
+ DFWORD(result, 0)=encode;\r
+ encode=dpd<<30;\r
+ getDPD3q(dpd, 2); encode|=dpd<<20;\r
+ getDPD3q(dpd, 1); encode|=dpd<<10;\r
+ getDPD3q(dpd, 0); encode|=dpd;\r
+ DFWORD(result, 1)=encode;\r
+\r
+ #elif QUAD\r
+ getDPD3q(dpd,10); encode|=dpd<<4;\r
+ getDPD3q(dpd, 9); encode|=dpd>>6;\r
+ DFWORD(result, 0)=encode;\r
+ encode=dpd<<26;\r
+ getDPD3q(dpd, 8); encode|=dpd<<16;\r
+ getDPD3q(dpd, 7); encode|=dpd<<6;\r
+ getDPD3q(dpd, 6); encode|=dpd>>4;\r
+ DFWORD(result, 1)=encode;\r
+ encode=dpd<<28;\r
+ getDPD3q(dpd, 5); encode|=dpd<<18;\r
+ getDPD3q(dpd, 4); encode|=dpd<<8;\r
+ getDPD3q(dpd, 3); encode|=dpd>>2;\r
+ DFWORD(result, 2)=encode;\r
+ encode=dpd<<30;\r
+ getDPD3q(dpd, 2); encode|=dpd<<20;\r
+ getDPD3q(dpd, 1); encode|=dpd<<10;\r
+ getDPD3q(dpd, 0); encode|=dpd;\r
+ DFWORD(result, 3)=encode;\r
+ #endif\r
+ return result;\r
+ } // decFloatQuantize\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatReduce -- reduce finite coefficient to minimum length */\r
+/* */\r
+/* result gets the reduced decFloat */\r
+/* df is the source decFloat */\r
+/* set is the context */\r
+/* returns result, which will be canonical */\r
+/* */\r
+/* This removes all possible trailing zeros from the coefficient; */\r
+/* some may remain when the number is very close to Nmax. */\r
+/* Special values are unchanged and no status is set unless df=sNaN. */\r
+/* Reduced zero has an exponent q=0. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatReduce(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ bcdnum num; // work\r
+ uByte buf[DECPMAX], *ub; // coefficient and pointer\r
+ if (df!=result) *result=*df; // copy, if needed\r
+ if (DFISNAN(df)) return decNaNs(result, df, NULL, set); // sNaN\r
+ // zeros and infinites propagate too\r
+ if (DFISINF(df)) return decInfinity(result, df); // canonical\r
+ if (DFISZERO(df)) {\r
+ uInt sign=DFWORD(df, 0)&DECFLOAT_Sign;\r
+ decFloatZero(result);\r
+ DFWORD(result, 0)|=sign;\r
+ return result; // exponent dropped, sign OK\r
+ }\r
+ // non-zero finite\r
+ GETCOEFF(df, buf);\r
+ ub=buf+DECPMAX-1; // -> lsd\r
+ if (*ub) return result; // no trailing zeros\r
+ for (ub--; *ub==0;) ub--; // terminates because non-zero\r
+ // *ub is the first non-zero from the right\r
+ num.sign=DFWORD(df, 0)&DECFLOAT_Sign; // set up number...\r
+ num.exponent=GETEXPUN(df)+(Int)(buf+DECPMAX-1-ub); // adjusted exponent\r
+ num.msd=buf;\r
+ num.lsd=ub;\r
+ return decFinalize(result, &num, set);\r
+ } // decFloatReduce\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatRemainder -- integer divide and return remainder */\r
+/* */\r
+/* result gets the remainder of dividing dfl by dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatRemainder(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ return decDivide(result, dfl, dfr, set, REMAINDER);\r
+ } // decFloatRemainder\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatRemainderNear -- integer divide to nearest and remainder */\r
+/* */\r
+/* result gets the remainder of dividing dfl by dfr: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This is the IEEE remainder, where the nearest integer is used. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatRemainderNear(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ return decDivide(result, dfl, dfr, set, REMNEAR);\r
+ } // decFloatRemainderNear\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatRotate -- rotate the coefficient of a decFloat left/right */\r
+/* */\r
+/* result gets the result of rotating dfl */\r
+/* dfl is the source decFloat to rotate */\r
+/* dfr is the count of digits to rotate, an integer (with q=0) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* The digits of the coefficient of dfl are rotated to the left (if */\r
+/* dfr is positive) or to the right (if dfr is negative) without */\r
+/* adjusting the exponent or the sign of dfl. */\r
+/* */\r
+/* dfr must be in the range -DECPMAX through +DECPMAX. */\r
+/* NaNs are propagated as usual. An infinite dfl is unaffected (but */\r
+/* dfr must be valid). No status is set unless dfr is invalid or an */\r
+/* operand is an sNaN. The result is canonical. */\r
+/* ------------------------------------------------------------------ */\r
+#define PHALF (ROUNDUP(DECPMAX/2, 4)) // half length, rounded up\r
+decFloat * decFloatRotate(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int rotate; // dfr as an Int\r
+ uByte buf[DECPMAX+PHALF]; // coefficient + half\r
+ uInt digits, savestat; // work\r
+ bcdnum num; // ..\r
+ uByte *ub; // ..\r
+\r
+ if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ if (!DFISINT(dfr)) return decInvalid(result, set);\r
+ digits=decFloatDigits(dfr); // calculate digits\r
+ if (digits>2) return decInvalid(result, set); // definitely out of range\r
+ rotate=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; // is in bottom declet\r
+ if (rotate>DECPMAX) return decInvalid(result, set); // too big\r
+ // [from here on no error or status change is possible]\r
+ if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical\r
+ // handle no-rotate cases\r
+ if (rotate==0 || rotate==DECPMAX) return decCanonical(result, dfl);\r
+ // a real rotate is needed: 0 < rotate < DECPMAX\r
+ // reduce the rotation to no more than half to reduce copying later\r
+ // (for QUAD in fact half + 2 digits)\r
+ if (DFISSIGNED(dfr)) rotate=-rotate;\r
+ if (abs(rotate)>PHALF) {\r
+ if (rotate<0) rotate=DECPMAX+rotate;\r
+ else rotate=rotate-DECPMAX;\r
+ }\r
+ // now lay out the coefficient, leaving room to the right or the\r
+ // left depending on the direction of rotation\r
+ ub=buf;\r
+ if (rotate<0) ub+=PHALF; // rotate right, so space to left\r
+ GETCOEFF(dfl, ub);\r
+ // copy half the digits to left or right, and set num.msd\r
+ if (rotate<0) {\r
+ memcpy(buf, buf+DECPMAX, PHALF);\r
+ num.msd=buf+PHALF+rotate;\r
+ }\r
+ else {\r
+ memcpy(buf+DECPMAX, buf, PHALF);\r
+ num.msd=buf+rotate;\r
+ }\r
+ // fill in rest of num\r
+ num.lsd=num.msd+DECPMAX-1;\r
+ num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;\r
+ num.exponent=GETEXPUN(dfl);\r
+ savestat=set->status; // record\r
+ decFinalize(result, &num, set);\r
+ set->status=savestat; // restore\r
+ return result;\r
+ } // decFloatRotate\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatSameQuantum -- test decFloats for same quantum */\r
+/* */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* returns 1 if the operands have the same quantum, 0 otherwise */\r
+/* */\r
+/* No error is possible and no status results. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decFloatSameQuantum(const decFloat *dfl, const decFloat *dfr) {\r
+ if (DFISSPECIAL(dfl) || DFISSPECIAL(dfr)) {\r
+ if (DFISNAN(dfl) && DFISNAN(dfr)) return 1;\r
+ if (DFISINF(dfl) && DFISINF(dfr)) return 1;\r
+ return 0; // any other special mixture gives false\r
+ }\r
+ if (GETEXP(dfl)==GETEXP(dfr)) return 1; // biased exponents match\r
+ return 0;\r
+ } // decFloatSameQuantum\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatScaleB -- multiply by a power of 10, as per 754 */\r
+/* */\r
+/* result gets the result of the operation */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs), am integer (with q=0) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* This computes result=dfl x 10**dfr where dfr is an integer in the */\r
+/* range +/-2*(emax+pmax), typically resulting from LogB. */\r
+/* Underflow and Overflow (with Inexact) may occur. NaNs propagate */\r
+/* as usual. */\r
+/* ------------------------------------------------------------------ */\r
+#define SCALEBMAX 2*(DECEMAX+DECPMAX) // D=800, Q=12356\r
+decFloat * decFloatScaleB(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ uInt digits; // work\r
+ Int expr; // dfr as an Int\r
+\r
+ if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ if (!DFISINT(dfr)) return decInvalid(result, set);\r
+ digits=decFloatDigits(dfr); // calculate digits\r
+\r
+ #if DOUBLE\r
+ if (digits>3) return decInvalid(result, set); // definitely out of range\r
+ expr=DPD2BIN[DFWORD(dfr, 1)&0x3ff]; // must be in bottom declet\r
+ #elif QUAD\r
+ if (digits>5) return decInvalid(result, set); // definitely out of range\r
+ expr=DPD2BIN[DFWORD(dfr, 3)&0x3ff] // in bottom 2 declets ..\r
+ +DPD2BIN[(DFWORD(dfr, 3)>>10)&0x3ff]*1000; // ..\r
+ #endif\r
+ if (expr>SCALEBMAX) return decInvalid(result, set); // oops\r
+ // [from now on no error possible]\r
+ if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical\r
+ if (DFISSIGNED(dfr)) expr=-expr;\r
+ // dfl is finite and expr is valid\r
+ *result=*dfl; // copy to target\r
+ return decFloatSetExponent(result, set, GETEXPUN(result)+expr);\r
+ } // decFloatScaleB\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatShift -- shift the coefficient of a decFloat left or right */\r
+/* */\r
+/* result gets the result of shifting dfl */\r
+/* dfl is the source decFloat to shift */\r
+/* dfr is the count of digits to shift, an integer (with q=0) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* The digits of the coefficient of dfl are shifted to the left (if */\r
+/* dfr is positive) or to the right (if dfr is negative) without */\r
+/* adjusting the exponent or the sign of dfl. */\r
+/* */\r
+/* dfr must be in the range -DECPMAX through +DECPMAX. */\r
+/* NaNs are propagated as usual. An infinite dfl is unaffected (but */\r
+/* dfr must be valid). No status is set unless dfr is invalid or an */\r
+/* operand is an sNaN. The result is canonical. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatShift(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ Int shift; // dfr as an Int\r
+ uByte buf[DECPMAX*2]; // coefficient + padding\r
+ uInt digits, savestat; // work\r
+ bcdnum num; // ..\r
+ uInt uiwork; // for macros\r
+\r
+ if (DFISNAN(dfl)||DFISNAN(dfr)) return decNaNs(result, dfl, dfr, set);\r
+ if (!DFISINT(dfr)) return decInvalid(result, set);\r
+ digits=decFloatDigits(dfr); // calculate digits\r
+ if (digits>2) return decInvalid(result, set); // definitely out of range\r
+ shift=DPD2BIN[DFWORD(dfr, DECWORDS-1)&0x3ff]; // is in bottom declet\r
+ if (shift>DECPMAX) return decInvalid(result, set); // too big\r
+ // [from here on no error or status change is possible]\r
+\r
+ if (DFISINF(dfl)) return decInfinity(result, dfl); // canonical\r
+ // handle no-shift and all-shift (clear to zero) cases\r
+ if (shift==0) return decCanonical(result, dfl);\r
+ if (shift==DECPMAX) { // zero with sign\r
+ uByte sign=(uByte)(DFBYTE(dfl, 0)&0x80); // save sign bit\r
+ decFloatZero(result); // make +0\r
+ DFBYTE(result, 0)=(uByte)(DFBYTE(result, 0)|sign); // and set sign\r
+ // [cannot safely use CopySign]\r
+ return result;\r
+ }\r
+ // a real shift is needed: 0 < shift < DECPMAX\r
+ num.sign=DFWORD(dfl, 0)&DECFLOAT_Sign;\r
+ num.exponent=GETEXPUN(dfl);\r
+ num.msd=buf;\r
+ GETCOEFF(dfl, buf);\r
+ if (DFISSIGNED(dfr)) { // shift right\r
+ // edge cases are taken care of, so this is easy\r
+ num.lsd=buf+DECPMAX-shift-1;\r
+ }\r
+ else { // shift left -- zero padding needed to right\r
+ UBFROMUI(buf+DECPMAX, 0); // 8 will handle most cases\r
+ UBFROMUI(buf+DECPMAX+4, 0); // ..\r
+ if (shift>8) memset(buf+DECPMAX+8, 0, 8+QUAD*18); // all other cases\r
+ num.msd+=shift;\r
+ num.lsd=num.msd+DECPMAX-1;\r
+ }\r
+ savestat=set->status; // record\r
+ decFinalize(result, &num, set);\r
+ set->status=savestat; // restore\r
+ return result;\r
+ } // decFloatShift\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatSubtract -- subtract a decFloat from another */\r
+/* */\r
+/* result gets the result of subtracting dfr from dfl: */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatSubtract(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ decFloat temp;\r
+ // NaNs must propagate without sign change\r
+ if (DFISNAN(dfr)) return decFloatAdd(result, dfl, dfr, set);\r
+ temp=*dfr; // make a copy\r
+ DFBYTE(&temp, 0)^=0x80; // flip sign\r
+ return decFloatAdd(result, dfl, &temp, set); // and add to the lhs\r
+ } // decFloatSubtract\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToInt -- round to 32-bit binary integer (4 flavours) */\r
+/* */\r
+/* df is the decFloat to round */\r
+/* set is the context */\r
+/* round is the rounding mode to use */\r
+/* returns a uInt or an Int, rounded according to the name */\r
+/* */\r
+/* Invalid will always be signaled if df is a NaN, is Infinite, or is */\r
+/* outside the range of the target; Inexact will not be signaled for */\r
+/* simple rounding unless 'Exact' appears in the name. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decFloatToUInt32(const decFloat *df, decContext *set,\r
+ enum rounding round) {\r
+ return decToInt32(df, set, round, 0, 1);}\r
+\r
+uInt decFloatToUInt32Exact(const decFloat *df, decContext *set,\r
+ enum rounding round) {\r
+ return decToInt32(df, set, round, 1, 1);}\r
+\r
+Int decFloatToInt32(const decFloat *df, decContext *set,\r
+ enum rounding round) {\r
+ return (Int)decToInt32(df, set, round, 0, 0);}\r
+\r
+Int decFloatToInt32Exact(const decFloat *df, decContext *set,\r
+ enum rounding round) {\r
+ return (Int)decToInt32(df, set, round, 1, 0);}\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToIntegral -- round to integral value (two flavours) */\r
+/* */\r
+/* result gets the result */\r
+/* df is the decFloat to round */\r
+/* set is the context */\r
+/* round is the rounding mode to use */\r
+/* returns result */\r
+/* */\r
+/* No exceptions, even Inexact, are raised except for sNaN input, or */\r
+/* if 'Exact' appears in the name. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatToIntegralValue(decFloat *result, const decFloat *df,\r
+ decContext *set, enum rounding round) {\r
+ return decToIntegral(result, df, set, round, 0);}\r
+\r
+decFloat * decFloatToIntegralExact(decFloat *result, const decFloat *df,\r
+ decContext *set) {\r
+ return decToIntegral(result, df, set, set->round, 1);}\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatXor -- logical digitwise XOR of two decFloats */\r
+/* */\r
+/* result gets the result of XORing dfl and dfr */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) */\r
+/* set is the context */\r
+/* returns result, which will be canonical with sign=0 */\r
+/* */\r
+/* The operands must be positive, finite with exponent q=0, and */\r
+/* comprise just zeros and ones; if not, Invalid operation results. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatXor(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ if (!DFISUINT01(dfl) || !DFISUINT01(dfr)\r
+ || !DFISCC01(dfl) || !DFISCC01(dfr)) return decInvalid(result, set);\r
+ // the operands are positive finite integers (q=0) with just 0s and 1s\r
+ #if DOUBLE\r
+ DFWORD(result, 0)=ZEROWORD\r
+ |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04009124);\r
+ DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x49124491;\r
+ #elif QUAD\r
+ DFWORD(result, 0)=ZEROWORD\r
+ |((DFWORD(dfl, 0) ^ DFWORD(dfr, 0))&0x04000912);\r
+ DFWORD(result, 1)=(DFWORD(dfl, 1) ^ DFWORD(dfr, 1))&0x44912449;\r
+ DFWORD(result, 2)=(DFWORD(dfl, 2) ^ DFWORD(dfr, 2))&0x12449124;\r
+ DFWORD(result, 3)=(DFWORD(dfl, 3) ^ DFWORD(dfr, 3))&0x49124491;\r
+ #endif\r
+ return result;\r
+ } // decFloatXor\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decInvalid -- set Invalid_operation result */\r
+/* */\r
+/* result gets a canonical NaN */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* status has Invalid_operation added */\r
+/* ------------------------------------------------------------------ */\r
+static decFloat *decInvalid(decFloat *result, decContext *set) {\r
+ decFloatZero(result);\r
+ DFWORD(result, 0)=DECFLOAT_qNaN;\r
+ set->status|=DEC_Invalid_operation;\r
+ return result;\r
+ } // decInvalid\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decInfinity -- set canonical Infinity with sign from a decFloat */\r
+/* */\r
+/* result gets a canonical Infinity */\r
+/* df is source decFloat (only the sign is used) */\r
+/* returns result */\r
+/* */\r
+/* df may be the same as result */\r
+/* ------------------------------------------------------------------ */\r
+static decFloat *decInfinity(decFloat *result, const decFloat *df) {\r
+ uInt sign=DFWORD(df, 0); // save source signword\r
+ decFloatZero(result); // clear everything\r
+ DFWORD(result, 0)=DECFLOAT_Inf | (sign & DECFLOAT_Sign);\r
+ return result;\r
+ } // decInfinity\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNaNs -- handle NaN argument(s) */\r
+/* */\r
+/* result gets the result of handling dfl and dfr, one or both of */\r
+/* which is a NaN */\r
+/* dfl is the first decFloat (lhs) */\r
+/* dfr is the second decFloat (rhs) -- may be NULL for a single- */\r
+/* operand operation */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* Called when one or both operands is a NaN, and propagates the */\r
+/* appropriate result to res. When an sNaN is found, it is changed */\r
+/* to a qNaN and Invalid operation is set. */\r
+/* ------------------------------------------------------------------ */\r
+static decFloat *decNaNs(decFloat *result,\r
+ const decFloat *dfl, const decFloat *dfr,\r
+ decContext *set) {\r
+ // handle sNaNs first\r
+ if (dfr!=NULL && DFISSNAN(dfr) && !DFISSNAN(dfl)) dfl=dfr; // use RHS\r
+ if (DFISSNAN(dfl)) {\r
+ decCanonical(result, dfl); // propagate canonical sNaN\r
+ DFWORD(result, 0)&=~(DECFLOAT_qNaN ^ DECFLOAT_sNaN); // quiet\r
+ set->status|=DEC_Invalid_operation;\r
+ return result;\r
+ }\r
+ // one or both is a quiet NaN\r
+ if (!DFISNAN(dfl)) dfl=dfr; // RHS must be NaN, use it\r
+ return decCanonical(result, dfl); // propagate canonical qNaN\r
+ } // decNaNs\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumCompare -- numeric comparison of two decFloats */\r
+/* */\r
+/* dfl is the left-hand decFloat, which is not a NaN */\r
+/* dfr is the right-hand decFloat, which is not a NaN */\r
+/* tot is 1 for total order compare, 0 for simple numeric */\r
+/* returns -1, 0, or +1 for dfl<dfr, dfl=dfr, dfl>dfr */\r
+/* */\r
+/* No error is possible; status and mode are unchanged. */\r
+/* ------------------------------------------------------------------ */\r
+static Int decNumCompare(const decFloat *dfl, const decFloat *dfr, Flag tot) {\r
+ Int sigl, sigr; // LHS and RHS non-0 signums\r
+ Int shift; // shift needed to align operands\r
+ uByte *ub, *uc; // work\r
+ uInt uiwork; // for macros\r
+ // buffers +2 if Quad (36 digits), need double plus 4 for safe padding\r
+ uByte bufl[DECPMAX*2+QUAD*2+4]; // for LHS coefficient + padding\r
+ uByte bufr[DECPMAX*2+QUAD*2+4]; // for RHS coefficient + padding\r
+\r
+ sigl=1;\r
+ if (DFISSIGNED(dfl)) {\r
+ if (!DFISSIGNED(dfr)) { // -LHS +RHS\r
+ if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;\r
+ return -1; // RHS wins\r
+ }\r
+ sigl=-1;\r
+ }\r
+ if (DFISSIGNED(dfr)) {\r
+ if (!DFISSIGNED(dfl)) { // +LHS -RHS\r
+ if (DFISZERO(dfl) && DFISZERO(dfr) && !tot) return 0;\r
+ return +1; // LHS wins\r
+ }\r
+ }\r
+\r
+ // signs are the same; operand(s) could be zero\r
+ sigr=-sigl; // sign to return if abs(RHS) wins\r
+\r
+ if (DFISINF(dfl)) {\r
+ if (DFISINF(dfr)) return 0; // both infinite & same sign\r
+ return sigl; // inf > n\r
+ }\r
+ if (DFISINF(dfr)) return sigr; // n < inf [dfl is finite]\r
+\r
+ // here, both are same sign and finite; calculate their offset\r
+ shift=GETEXP(dfl)-GETEXP(dfr); // [0 means aligned]\r
+ // [bias can be ignored -- the absolute exponent is not relevant]\r
+\r
+ if (DFISZERO(dfl)) {\r
+ if (!DFISZERO(dfr)) return sigr; // LHS=0, RHS!=0\r
+ // both are zero, return 0 if both same exponent or numeric compare\r
+ if (shift==0 || !tot) return 0;\r
+ if (shift>0) return sigl;\r
+ return sigr; // [shift<0]\r
+ }\r
+ else { // LHS!=0\r
+ if (DFISZERO(dfr)) return sigl; // LHS!=0, RHS=0\r
+ }\r
+ // both are known to be non-zero at this point\r
+\r
+ // if the exponents are so different that the coefficients do not\r
+ // overlap (by even one digit) then a full comparison is not needed\r
+ if (abs(shift)>=DECPMAX) { // no overlap\r
+ // coefficients are known to be non-zero\r
+ if (shift>0) return sigl;\r
+ return sigr; // [shift<0]\r
+ }\r
+\r
+ // decode the coefficients\r
+ // (shift both right two if Quad to make a multiple of four)\r
+ #if QUAD\r
+ UBFROMUI(bufl, 0);\r
+ UBFROMUI(bufr, 0);\r
+ #endif\r
+ GETCOEFF(dfl, bufl+QUAD*2); // decode from decFloat\r
+ GETCOEFF(dfr, bufr+QUAD*2); // ..\r
+ if (shift==0) { // aligned; common and easy\r
+ // all multiples of four, here\r
+ for (ub=bufl, uc=bufr; ub<bufl+DECPMAX+QUAD*2; ub+=4, uc+=4) {\r
+ uInt ui=UBTOUI(ub);\r
+ if (ui==UBTOUI(uc)) continue; // so far so same\r
+ // about to find a winner; go by bytes in case little-endian\r
+ for (;; ub++, uc++) {\r
+ if (*ub>*uc) return sigl; // difference found\r
+ if (*ub<*uc) return sigr; // ..\r
+ }\r
+ }\r
+ } // aligned\r
+ else if (shift>0) { // lhs to left\r
+ ub=bufl; // RHS pointer\r
+ // pad bufl so right-aligned; most shifts will fit in 8\r
+ UBFROMUI(bufl+DECPMAX+QUAD*2, 0); // add eight zeros\r
+ UBFROMUI(bufl+DECPMAX+QUAD*2+4, 0); // ..\r
+ if (shift>8) {\r
+ // more than eight; fill the rest, and also worth doing the\r
+ // lead-in by fours\r
+ uByte *up; // work\r
+ uByte *upend=bufl+DECPMAX+QUAD*2+shift;\r
+ for (up=bufl+DECPMAX+QUAD*2+8; up<upend; up+=4) UBFROMUI(up, 0);\r
+ // [pads up to 36 in all for Quad]\r
+ for (;; ub+=4) {\r
+ if (UBTOUI(ub)!=0) return sigl;\r
+ if (ub+4>bufl+shift-4) break;\r
+ }\r
+ }\r
+ // check remaining leading digits\r
+ for (; ub<bufl+shift; ub++) if (*ub!=0) return sigl;\r
+ // now start the overlapped part; bufl has been padded, so the\r
+ // comparison can go for the full length of bufr, which is a\r
+ // multiple of 4 bytes\r
+ for (uc=bufr; ; uc+=4, ub+=4) {\r
+ uInt ui=UBTOUI(ub);\r
+ if (ui!=UBTOUI(uc)) { // mismatch found\r
+ for (;; uc++, ub++) { // check from left [little-endian?]\r
+ if (*ub>*uc) return sigl; // difference found\r
+ if (*ub<*uc) return sigr; // ..\r
+ }\r
+ } // mismatch\r
+ if (uc==bufr+QUAD*2+DECPMAX-4) break; // all checked\r
+ }\r
+ } // shift>0\r
+\r
+ else { // shift<0) .. RHS is to left of LHS; mirror shift>0\r
+ uc=bufr; // RHS pointer\r
+ // pad bufr so right-aligned; most shifts will fit in 8\r
+ UBFROMUI(bufr+DECPMAX+QUAD*2, 0); // add eight zeros\r
+ UBFROMUI(bufr+DECPMAX+QUAD*2+4, 0); // ..\r
+ if (shift<-8) {\r
+ // more than eight; fill the rest, and also worth doing the\r
+ // lead-in by fours\r
+ uByte *up; // work\r
+ uByte *upend=bufr+DECPMAX+QUAD*2-shift;\r
+ for (up=bufr+DECPMAX+QUAD*2+8; up<upend; up+=4) UBFROMUI(up, 0);\r
+ // [pads up to 36 in all for Quad]\r
+ for (;; uc+=4) {\r
+ if (UBTOUI(uc)!=0) return sigr;\r
+ if (uc+4>bufr-shift-4) break;\r
+ }\r
+ }\r
+ // check remaining leading digits\r
+ for (; uc<bufr-shift; uc++) if (*uc!=0) return sigr;\r
+ // now start the overlapped part; bufr has been padded, so the\r
+ // comparison can go for the full length of bufl, which is a\r
+ // multiple of 4 bytes\r
+ for (ub=bufl; ; ub+=4, uc+=4) {\r
+ uInt ui=UBTOUI(ub);\r
+ if (ui!=UBTOUI(uc)) { // mismatch found\r
+ for (;; ub++, uc++) { // check from left [little-endian?]\r
+ if (*ub>*uc) return sigl; // difference found\r
+ if (*ub<*uc) return sigr; // ..\r
+ }\r
+ } // mismatch\r
+ if (ub==bufl+QUAD*2+DECPMAX-4) break; // all checked\r
+ }\r
+ } // shift<0\r
+\r
+ // Here when compare equal\r
+ if (!tot) return 0; // numerically equal\r
+ // total ordering .. exponent matters\r
+ if (shift>0) return sigl; // total order by exponent\r
+ if (shift<0) return sigr; // ..\r
+ return 0;\r
+ } // decNumCompare\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decToInt32 -- local routine to effect ToInteger conversions */\r
+/* */\r
+/* df is the decFloat to convert */\r
+/* set is the context */\r
+/* rmode is the rounding mode to use */\r
+/* exact is 1 if Inexact should be signalled */\r
+/* unsign is 1 if the result a uInt, 0 if an Int (cast to uInt) */\r
+/* returns 32-bit result as a uInt */\r
+/* */\r
+/* Invalid is set is df is a NaN, is infinite, or is out-of-range; in */\r
+/* these cases 0 is returned. */\r
+/* ------------------------------------------------------------------ */\r
+static uInt decToInt32(const decFloat *df, decContext *set,\r
+ enum rounding rmode, Flag exact, Flag unsign) {\r
+ Int exp; // exponent\r
+ uInt sourhi, sourpen, sourlo; // top word from source decFloat ..\r
+ uInt hi, lo; // .. penultimate, least, etc.\r
+ decFloat zero, result; // work\r
+ Int i; // ..\r
+\r
+ /* Start decoding the argument */\r
+ sourhi=DFWORD(df, 0); // top word\r
+ exp=DECCOMBEXP[sourhi>>26]; // get exponent high bits (in place)\r
+ if (EXPISSPECIAL(exp)) { // is special?\r
+ set->status|=DEC_Invalid_operation; // signal\r
+ return 0;\r
+ }\r
+\r
+ /* Here when the argument is finite */\r
+ if (GETEXPUN(df)==0) result=*df; // already a true integer\r
+ else { // need to round to integer\r
+ enum rounding saveround; // saver\r
+ uInt savestatus; // ..\r
+ saveround=set->round; // save rounding mode ..\r
+ savestatus=set->status; // .. and status\r
+ set->round=rmode; // set mode\r
+ decFloatZero(&zero); // make 0E+0\r
+ set->status=0; // clear\r
+ decFloatQuantize(&result, df, &zero, set); // [this may fail]\r
+ set->round=saveround; // restore rounding mode ..\r
+ if (exact) set->status|=savestatus; // include Inexact\r
+ else set->status=savestatus; // .. or just original status\r
+ }\r
+\r
+ // only the last four declets of the coefficient can contain\r
+ // non-zero; check for others (and also NaN or Infinity from the\r
+ // Quantize) first (see DFISZERO for explanation):\r
+ // decFloatShow(&result, "sofar");\r
+ #if DOUBLE\r
+ if ((DFWORD(&result, 0)&0x1c03ff00)!=0\r
+ || (DFWORD(&result, 0)&0x60000000)==0x60000000) {\r
+ #elif QUAD\r
+ if ((DFWORD(&result, 2)&0xffffff00)!=0\r
+ || DFWORD(&result, 1)!=0\r
+ || (DFWORD(&result, 0)&0x1c003fff)!=0\r
+ || (DFWORD(&result, 0)&0x60000000)==0x60000000) {\r
+ #endif\r
+ set->status|=DEC_Invalid_operation; // Invalid or out of range\r
+ return 0;\r
+ }\r
+ // get last twelve digits of the coefficent into hi & ho, base\r
+ // 10**9 (see GETCOEFFBILL):\r
+ sourlo=DFWORD(&result, DECWORDS-1);\r
+ lo=DPD2BIN0[sourlo&0x3ff]\r
+ +DPD2BINK[(sourlo>>10)&0x3ff]\r
+ +DPD2BINM[(sourlo>>20)&0x3ff];\r
+ sourpen=DFWORD(&result, DECWORDS-2);\r
+ hi=DPD2BIN0[((sourpen<<2) | (sourlo>>30))&0x3ff];\r
+\r
+ // according to request, check range carefully\r
+ if (unsign) {\r
+ if (hi>4 || (hi==4 && lo>294967295) || (hi+lo!=0 && DFISSIGNED(&result))) {\r
+ set->status|=DEC_Invalid_operation; // out of range\r
+ return 0;\r
+ }\r
+ return hi*BILLION+lo;\r
+ }\r
+ // signed\r
+ if (hi>2 || (hi==2 && lo>147483647)) {\r
+ // handle the usual edge case\r
+ if (lo==147483648 && hi==2 && DFISSIGNED(&result)) return 0x80000000;\r
+ set->status|=DEC_Invalid_operation; // truly out of range\r
+ return 0;\r
+ }\r
+ i=hi*BILLION+lo;\r
+ if (DFISSIGNED(&result)) i=-i;\r
+ return (uInt)i;\r
+ } // decToInt32\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decToIntegral -- local routine to effect ToIntegral value */\r
+/* */\r
+/* result gets the result */\r
+/* df is the decFloat to round */\r
+/* set is the context */\r
+/* rmode is the rounding mode to use */\r
+/* exact is 1 if Inexact should be signalled */\r
+/* returns result */\r
+/* ------------------------------------------------------------------ */\r
+static decFloat * decToIntegral(decFloat *result, const decFloat *df,\r
+ decContext *set, enum rounding rmode,\r
+ Flag exact) {\r
+ Int exp; // exponent\r
+ uInt sourhi; // top word from source decFloat\r
+ enum rounding saveround; // saver\r
+ uInt savestatus; // ..\r
+ decFloat zero; // work\r
+\r
+ /* Start decoding the argument */\r
+ sourhi=DFWORD(df, 0); // top word\r
+ exp=DECCOMBEXP[sourhi>>26]; // get exponent high bits (in place)\r
+\r
+ if (EXPISSPECIAL(exp)) { // is special?\r
+ // NaNs are handled as usual\r
+ if (DFISNAN(df)) return decNaNs(result, df, NULL, set);\r
+ // must be infinite; return canonical infinity with sign of df\r
+ return decInfinity(result, df);\r
+ }\r
+\r
+ /* Here when the argument is finite */\r
+ // complete extraction of the exponent\r
+ exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias\r
+\r
+ if (exp>=0) return decCanonical(result, df); // already integral\r
+\r
+ saveround=set->round; // save rounding mode ..\r
+ savestatus=set->status; // .. and status\r
+ set->round=rmode; // set mode\r
+ decFloatZero(&zero); // make 0E+0\r
+ decFloatQuantize(result, df, &zero, set); // 'integrate'; cannot fail\r
+ set->round=saveround; // restore rounding mode ..\r
+ if (!exact) set->status=savestatus; // .. and status, unless exact\r
+ return result;\r
+ } // decToIntegral\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decCommon.c -- common code for all three fixed-size types */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises code that is shared between all the formats */\r
+/* (decSingle, decDouble, and decQuad); it includes set and extract */\r
+/* of format components, widening, narrowing, and string conversions. */\r
+/* */\r
+/* Unlike decNumber, parameterization takes place at compile time */\r
+/* rather than at runtime. The parameters are set in the decDouble.c */\r
+/* (etc.) files, which then include this one to produce the compiled */\r
+/* code. The functions here, therefore, are code shared between */\r
+/* multiple formats. */\r
+/* ------------------------------------------------------------------ */\r
+// Names here refer to decFloat rather than to decDouble, etc., and\r
+// the functions are in strict alphabetical order.\r
+// Constants, tables, and debug function(s) are included only for QUAD\r
+// (which will always be compiled if DOUBLE or SINGLE are used).\r
+//\r
+// Whenever a decContext is used, only the status may be set (using\r
+// OR) or the rounding mode read; all other fields are ignored and\r
+// untouched.\r
+\r
+// names for simpler testing and default context\r
+#if DECPMAX==7\r
+ #define SINGLE 1\r
+ #define DOUBLE 0\r
+ #define QUAD 0\r
+ #define DEFCONTEXT DEC_INIT_DECIMAL32\r
+#elif DECPMAX==16\r
+ #define SINGLE 0\r
+ #define DOUBLE 1\r
+ #define QUAD 0\r
+ #define DEFCONTEXT DEC_INIT_DECIMAL64\r
+#elif DECPMAX==34\r
+ #define SINGLE 0\r
+ #define DOUBLE 0\r
+ #define QUAD 1\r
+ #define DEFCONTEXT DEC_INIT_DECIMAL128\r
+#else\r
+ #error Unexpected DECPMAX value\r
+#endif\r
+\r
+/* Assertions */\r
+\r
+#if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34\r
+ #error Unexpected Pmax (DECPMAX) value for this module\r
+#endif\r
+\r
+// Assert facts about digit characters, etc.\r
+#if ('9'&0x0f)!=9\r
+ #error This module assumes characters are of the form 0b....nnnn\r
+ // where .... are don't care 4 bits and nnnn is 0000 through 1001\r
+#endif\r
+#if ('9'&0xf0)==('.'&0xf0)\r
+ #error This module assumes '.' has a different mask than a digit\r
+#endif\r
+\r
+// Assert ToString lay-out conditions\r
+#if DECSTRING<DECPMAX+9\r
+ #error ToString needs at least 8 characters for lead-in and dot\r
+#endif\r
+#if DECPMAX+DECEMAXD+5 > DECSTRING\r
+ #error Exponent form can be too long for ToString to lay out safely\r
+#endif\r
+#if DECEMAXD > 4\r
+ #error Exponent form is too long for ToString to lay out\r
+ // Note: code for up to 9 digits exists in archives [decOct]\r
+#endif\r
+\r
+/* Private functions used here and possibly in decBasic.c, etc. */\r
+static decFloat * decFinalize(decFloat *, bcdnum *, decContext *);\r
+static Flag decBiStr(const char *, const char *, const char *);\r
+\r
+/* Macros and private tables; those which are not format-dependent */\r
+/* are only included if decQuad is being built. */\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* Combination field lookup tables (uInts to save measurable work) */\r
+/* */\r
+/* DECCOMBEXP - 2 most-significant-bits of exponent (00, 01, or */\r
+/* 10), shifted left for format, or DECFLOAT_Inf/NaN */\r
+/* DECCOMBWEXP - The same, for the next-wider format (unless QUAD) */\r
+/* DECCOMBMSD - 4-bit most-significant-digit */\r
+/* [0 if the index is a special (Infinity or NaN)] */\r
+/* DECCOMBFROM - 5-bit combination field from EXP top bits and MSD */\r
+/* (placed in uInt so no shift is needed) */\r
+/* */\r
+/* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign */\r
+/* and 5-bit combination field (0-63, the second half of the table */\r
+/* identical to the first half) */\r
+/* DECCOMBFROM is indexed by expTopTwoBits*16 + msd */\r
+/* */\r
+/* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are */\r
+/* only included once, when QUAD is being built */\r
+/* ------------------------------------------------------------------ */\r
+static const uInt DECCOMBEXP[64]={\r
+ 0, 0, 0, 0, 0, 0, 0, 0,\r
+ 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,\r
+ 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,\r
+ 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,\r
+ 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,\r
+ 0, 0, 1<<DECECONL, 1<<DECECONL,\r
+ 2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN,\r
+ 0, 0, 0, 0, 0, 0, 0, 0,\r
+ 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,\r
+ 1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,\r
+ 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,\r
+ 2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,\r
+ 0, 0, 1<<DECECONL, 1<<DECECONL,\r
+ 2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN};\r
+#if !QUAD\r
+static const uInt DECCOMBWEXP[64]={\r
+ 0, 0, 0, 0, 0, 0, 0, 0,\r
+ 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,\r
+ 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,\r
+ 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,\r
+ 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,\r
+ 0, 0, 1<<DECWECONL, 1<<DECWECONL,\r
+ 2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN,\r
+ 0, 0, 0, 0, 0, 0, 0, 0,\r
+ 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,\r
+ 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,\r
+ 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,\r
+ 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,\r
+ 0, 0, 1<<DECWECONL, 1<<DECWECONL,\r
+ 2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN};\r
+#endif\r
+\r
+#if QUAD\r
+const uInt DECCOMBMSD[64]={\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0,\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,\r
+ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0};\r
+\r
+const uInt DECCOMBFROM[48]={\r
+ 0x00000000, 0x04000000, 0x08000000, 0x0C000000, 0x10000000, 0x14000000,\r
+ 0x18000000, 0x1C000000, 0x60000000, 0x64000000, 0x00000000, 0x00000000,\r
+ 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000, 0x24000000,\r
+ 0x28000000, 0x2C000000, 0x30000000, 0x34000000, 0x38000000, 0x3C000000,\r
+ 0x68000000, 0x6C000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,\r
+ 0x00000000, 0x00000000, 0x40000000, 0x44000000, 0x48000000, 0x4C000000,\r
+ 0x50000000, 0x54000000, 0x58000000, 0x5C000000, 0x70000000, 0x74000000,\r
+ 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* Request and include the tables to use for conversions */\r
+/* ------------------------------------------------------------------ */\r
+#define DEC_BCD2DPD 1 // 0-0x999 -> DPD\r
+#define DEC_BIN2DPD 1 // 0-999 -> DPD\r
+#define DEC_BIN2BCD8 1 // 0-999 -> ddd, len\r
+#define DEC_DPD2BCD8 1 // DPD -> ddd, len\r
+#define DEC_DPD2BIN 1 // DPD -> 0-999\r
+#define DEC_DPD2BINK 1 // DPD -> 0-999000\r
+#define DEC_DPD2BINM 1 // DPD -> 0-999000000\r
+#include "decDPD.h" // source of the lookup tables\r
+\r
+#endif\r
+\r
+/* ----------------------------------------------------------------- */\r
+/* decBiStr -- compare string with pairwise options */\r
+/* */\r
+/* targ is the string to compare */\r
+/* str1 is one of the strings to compare against (length may be 0) */\r
+/* str2 is the other; it must be the same length as str1 */\r
+/* */\r
+/* returns 1 if strings compare equal, (that is, targ is the same */\r
+/* length as str1 and str2, and each character of targ is in one */\r
+/* of str1 or str2 in the corresponding position), or 0 otherwise */\r
+/* */\r
+/* This is used for generic caseless compare, including the awkward */\r
+/* case of the Turkish dotted and dotless Is. Use as (for example): */\r
+/* if (decBiStr(test, "mike", "MIKE")) ... */\r
+/* ----------------------------------------------------------------- */\r
+static Flag decBiStr(const char *targ, const char *str1, const char *str2) {\r
+ for (;;targ++, str1++, str2++) {\r
+ if (*targ!=*str1 && *targ!=*str2) return 0;\r
+ // *targ has a match in one (or both, if terminator)\r
+ if (*targ=='\0') break;\r
+ } // forever\r
+ return 1;\r
+ } // decBiStr\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFinalize -- adjust and store a final result */\r
+/* */\r
+/* df is the decFloat format number which gets the final result */\r
+/* num is the descriptor of the number to be checked and encoded */\r
+/* [its values, including the coefficient, may be modified] */\r
+/* set is the context to use */\r
+/* returns df */\r
+/* */\r
+/* The num descriptor may point to a bcd8 string of any length; this */\r
+/* string may have leading insignificant zeros. If it has more than */\r
+/* DECPMAX digits then the final digit can be a round-for-reround */\r
+/* digit (i.e., it may include a sticky bit residue). */\r
+/* */\r
+/* The exponent (q) may be one of the codes for a special value and */\r
+/* can be up to 999999999 for conversion from string. */\r
+/* */\r
+/* No error is possible, but Inexact, Underflow, and/or Overflow may */\r
+/* be set. */\r
+/* ------------------------------------------------------------------ */\r
+// Constant whose size varies with format; also the check for surprises\r
+static uByte allnines[DECPMAX]=\r
+#if SINGLE\r
+ {9, 9, 9, 9, 9, 9, 9};\r
+#elif DOUBLE\r
+ {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};\r
+#elif QUAD\r
+ {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,\r
+ 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};\r
+#endif\r
+\r
+static decFloat * decFinalize(decFloat *df, bcdnum *num,\r
+ decContext *set) {\r
+ uByte *ub; // work\r
+ uInt dpd; // ..\r
+ uInt uiwork; // for macros\r
+ uByte *umsd=num->msd; // local copy\r
+ uByte *ulsd=num->lsd; // ..\r
+ uInt encode; // encoding accumulator\r
+ Int length; // coefficient length\r
+\r
+ #if DECCHECK\r
+ Int clen=ulsd-umsd+1;\r
+ #if QUAD\r
+ #define COEXTRA 2 // extra-long coefficent\r
+ #else\r
+ #define COEXTRA 0\r
+ #endif\r
+ if (clen<1 || clen>DECPMAX*3+2+COEXTRA)\r
+ printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen);\r
+ if (num->sign!=0 && num->sign!=DECFLOAT_Sign)\r
+ printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign);\r
+ if (!EXPISSPECIAL(num->exponent)\r
+ && (num->exponent>1999999999 || num->exponent<-1999999999))\r
+ printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent);\r
+ // decShowNum(num, "final");\r
+ #endif\r
+\r
+ // A special will have an 'exponent' which is very positive and a\r
+ // coefficient < DECPMAX\r
+ length=(uInt)(ulsd-umsd+1); // coefficient length\r
+\r
+ if (!NUMISSPECIAL(num)) {\r
+ Int drop; // digits to be dropped\r
+ // skip leading insignificant zeros to calculate an exact length\r
+ // [this is quite expensive]\r
+ if (*umsd==0) {\r
+ for (; umsd+3<ulsd && UBTOUI(umsd)==0;) umsd+=4;\r
+ for (; *umsd==0 && umsd<ulsd;) umsd++;\r
+ length=ulsd-umsd+1; // recalculate\r
+ }\r
+ drop=MAXI(length-DECPMAX, DECQTINY-num->exponent);\r
+ // drop can now be > digits for bottom-clamp (subnormal) cases\r
+ if (drop>0) { // rounding needed\r
+ // (decFloatQuantize has very similar code to this, so any\r
+ // changes may need to be made there, too)\r
+ uByte *roundat; // -> re-round digit\r
+ uByte reround; // reround value\r
+ // printf("Rounding; drop=%ld\n", (LI)drop);\r
+\r
+ num->exponent+=drop; // always update exponent\r
+\r
+ // Three cases here:\r
+ // 1. new LSD is in coefficient (almost always)\r
+ // 2. new LSD is digit to left of coefficient (so MSD is\r
+ // round-for-reround digit)\r
+ // 3. new LSD is to left of case 2 (whole coefficient is sticky)\r
+ // [duplicate check-stickies code to save a test]\r
+ // [by-digit check for stickies as runs of zeros are rare]\r
+ if (drop<length) { // NB lengths not addresses\r
+ roundat=umsd+length-drop;\r
+ reround=*roundat;\r
+ for (ub=roundat+1; ub<=ulsd; ub++) {\r
+ if (*ub!=0) { // non-zero to be discarded\r
+ reround=DECSTICKYTAB[reround]; // apply sticky bit\r
+ break; // [remainder don't-care]\r
+ }\r
+ } // check stickies\r
+ ulsd=roundat-1; // new LSD\r
+ }\r
+ else { // edge case\r
+ if (drop==length) {\r
+ roundat=umsd;\r
+ reround=*roundat;\r
+ }\r
+ else {\r
+ roundat=umsd-1;\r
+ reround=0;\r
+ }\r
+ for (ub=roundat+1; ub<=ulsd; ub++) {\r
+ if (*ub!=0) { // non-zero to be discarded\r
+ reround=DECSTICKYTAB[reround]; // apply sticky bit\r
+ break; // [remainder don't-care]\r
+ }\r
+ } // check stickies\r
+ *umsd=0; // coefficient is a 0\r
+ ulsd=umsd; // ..\r
+ }\r
+\r
+ if (reround!=0) { // discarding non-zero\r
+ uInt bump=0;\r
+ set->status|=DEC_Inexact;\r
+ // if adjusted exponent [exp+digits-1] is < EMIN then num is\r
+ // subnormal -- so raise Underflow\r
+ if (num->exponent<DECEMIN && (num->exponent+(ulsd-umsd+1)-1)<DECEMIN)\r
+ set->status|=DEC_Underflow;\r
+\r
+ // next decide whether increment of the coefficient is needed\r
+ if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case\r
+ if (reround>5) bump=1; // >0.5 goes up\r
+ else if (reround==5) // exactly 0.5000 ..\r
+ bump=*ulsd & 0x01; // .. up iff [new] lsd is odd\r
+ } // r-h-e\r
+ else switch (set->round) {\r
+ case DEC_ROUND_DOWN: {\r
+ // no change\r
+ break;} // r-d\r
+ case DEC_ROUND_HALF_DOWN: {\r
+ if (reround>5) bump=1;\r
+ break;} // r-h-d\r
+ case DEC_ROUND_HALF_UP: {\r
+ if (reround>=5) bump=1;\r
+ break;} // r-h-u\r
+ case DEC_ROUND_UP: {\r
+ if (reround>0) bump=1;\r
+ break;} // r-u\r
+ case DEC_ROUND_CEILING: {\r
+ // same as _UP for positive numbers, and as _DOWN for negatives\r
+ if (!num->sign && reround>0) bump=1;\r
+ break;} // r-c\r
+ case DEC_ROUND_FLOOR: {\r
+ // same as _UP for negative numbers, and as _DOWN for positive\r
+ // [negative reround cannot occur on 0]\r
+ if (num->sign && reround>0) bump=1;\r
+ break;} // r-f\r
+ case DEC_ROUND_05UP: {\r
+ if (reround>0) { // anything out there is 'sticky'\r
+ // bump iff lsd=0 or 5; this cannot carry so it could be\r
+ // effected immediately with no bump -- but the code\r
+ // is clearer if this is done the same way as the others\r
+ if (*ulsd==0 || *ulsd==5) bump=1;\r
+ }\r
+ break;} // r-r\r
+ default: { // e.g., DEC_ROUND_MAX\r
+ set->status|=DEC_Invalid_context;\r
+ #if DECCHECK\r
+ printf("Unknown rounding mode: %ld\n", (LI)set->round);\r
+ #endif\r
+ break;}\r
+ } // switch (not r-h-e)\r
+ // printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump);\r
+\r
+ if (bump!=0) { // need increment\r
+ // increment the coefficient; this might end up with 1000...\r
+ // (after the all nines case)\r
+ ub=ulsd;\r
+ for(; ub-3>=umsd && UBTOUI(ub-3)==0x09090909; ub-=4) {\r
+ UBFROMUI(ub-3, 0); // to 00000000\r
+ }\r
+ // [note ub could now be to left of msd, and it is not safe\r
+ // to write to the the left of the msd]\r
+ // now at most 3 digits left to non-9 (usually just the one)\r
+ for (; ub>=umsd; *ub=0, ub--) {\r
+ if (*ub==9) continue; // carry\r
+ *ub+=1;\r
+ break;\r
+ }\r
+ if (ub<umsd) { // had all-nines\r
+ *umsd=1; // coefficient to 1000...\r
+ // usually the 1000... coefficient can be used as-is\r
+ if ((ulsd-umsd+1)==DECPMAX) {\r
+ num->exponent++;\r
+ }\r
+ else {\r
+ // if coefficient is shorter than Pmax then num is\r
+ // subnormal, so extend it; this is safe as drop>0\r
+ // (or, if the coefficient was supplied above, it could\r
+ // not be 9); this may make the result normal.\r
+ ulsd++;\r
+ *ulsd=0;\r
+ // [exponent unchanged]\r
+ #if DECCHECK\r
+ if (num->exponent!=DECQTINY) // sanity check\r
+ printf("decFinalize: bad all-nines extend [^%ld, %ld]\n",\r
+ (LI)num->exponent, (LI)(ulsd-umsd+1));\r
+ #endif\r
+ } // subnormal extend\r
+ } // had all-nines\r
+ } // bump needed\r
+ } // inexact rounding\r
+\r
+ length=ulsd-umsd+1; // recalculate (may be <DECPMAX)\r
+ } // need round (drop>0)\r
+\r
+ // The coefficient will now fit and has final length unless overflow\r
+ // decShowNum(num, "rounded");\r
+\r
+ // if exponent is >=emax may have to clamp, overflow, or fold-down\r
+ if (num->exponent>DECEMAX-(DECPMAX-1)) { // is edge case\r
+ // printf("overflow checks...\n");\r
+ if (*ulsd==0 && ulsd==umsd) { // have zero\r
+ num->exponent=DECEMAX-(DECPMAX-1); // clamp to max\r
+ }\r
+ else if ((num->exponent+length-1)>DECEMAX) { // > Nmax\r
+ // Overflow -- these could go straight to encoding, here, but\r
+ // instead num is adjusted to keep the code cleaner\r
+ Flag needmax=0; // 1 for finite result\r
+ set->status|=(DEC_Overflow | DEC_Inexact);\r
+ switch (set->round) {\r
+ case DEC_ROUND_DOWN: {\r
+ needmax=1; // never Infinity\r
+ break;} // r-d\r
+ case DEC_ROUND_05UP: {\r
+ needmax=1; // never Infinity\r
+ break;} // r-05\r
+ case DEC_ROUND_CEILING: {\r
+ if (num->sign) needmax=1; // Infinity iff non-negative\r
+ break;} // r-c\r
+ case DEC_ROUND_FLOOR: {\r
+ if (!num->sign) needmax=1; // Infinity iff negative\r
+ break;} // r-f\r
+ default: break; // Infinity in all other cases\r
+ }\r
+ if (!needmax) { // easy .. set Infinity\r
+ num->exponent=DECFLOAT_Inf;\r
+ *umsd=0; // be clean: coefficient to 0\r
+ ulsd=umsd; // ..\r
+ }\r
+ else { // return Nmax\r
+ umsd=allnines; // use constant array\r
+ ulsd=allnines+DECPMAX-1;\r
+ num->exponent=DECEMAX-(DECPMAX-1);\r
+ }\r
+ }\r
+ else { // no overflow but non-zero and may have to fold-down\r
+ Int shift=num->exponent-(DECEMAX-(DECPMAX-1));\r
+ if (shift>0) { // fold-down needed\r
+ // fold down needed; must copy to buffer in order to pad\r
+ // with zeros safely; fortunately this is not the worst case\r
+ // path because cannot have had a round\r
+ uByte buffer[ROUNDUP(DECPMAX+3, 4)]; // [+3 allows uInt padding]\r
+ uByte *s=umsd; // source\r
+ uByte *t=buffer; // safe target\r
+ uByte *tlsd=buffer+(ulsd-umsd)+shift; // target LSD\r
+ // printf("folddown shift=%ld\n", (LI)shift);\r
+ for (; s<=ulsd; s+=4, t+=4) UBFROMUI(t, UBTOUI(s));\r
+ for (t=tlsd-shift+1; t<=tlsd; t+=4) UBFROMUI(t, 0); // pad 0s\r
+ num->exponent-=shift;\r
+ umsd=buffer;\r
+ ulsd=tlsd;\r
+ }\r
+ } // fold-down?\r
+ length=ulsd-umsd+1; // recalculate length\r
+ } // high-end edge case\r
+ } // finite number\r
+\r
+ /*------------------------------------------------------------------*/\r
+ /* At this point the result will properly fit the decFloat */\r
+ /* encoding, and it can be encoded with no possibility of error */\r
+ /*------------------------------------------------------------------*/\r
+ // Following code does not alter coefficient (could be allnines array)\r
+\r
+ // fast path possible when DECPMAX digits\r
+ if (length==DECPMAX) {\r
+ return decFloatFromBCD(df, num->exponent, umsd, num->sign);\r
+ } // full-length\r
+\r
+ // slower path when not a full-length number; must care about length\r
+ // [coefficient length here will be < DECPMAX]\r
+ if (!NUMISSPECIAL(num)) { // is still finite\r
+ // encode the combination field and exponent continuation\r
+ uInt uexp=(uInt)(num->exponent+DECBIAS); // biased exponent\r
+ uInt code=(uexp>>DECECONL)<<4; // top two bits of exp\r
+ // [msd==0]\r
+ // look up the combination field and make high word\r
+ encode=DECCOMBFROM[code]; // indexed by (0-2)*16+msd\r
+ encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation\r
+ }\r
+ else encode=num->exponent; // special [already in word]\r
+ encode|=num->sign; // add sign\r
+\r
+ // private macro to extract a declet, n (where 0<=n<DECLETS and 0\r
+ // refers to the declet from the least significant three digits)\r
+ // and put the corresponding DPD code into dpd. Access to umsd and\r
+ // ulsd (pointers to the most and least significant digit of the\r
+ // variable-length coefficient) is assumed, along with use of a\r
+ // working pointer, uInt *ub.\r
+ // As not full-length then chances are there are many leading zeros\r
+ // [and there may be a partial triad]\r
+ #define getDPDt(dpd, n) ub=ulsd-(3*(n))-2; \\r
+ if (ub<umsd-2) dpd=0; \\r
+ else if (ub>=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; \\r
+ else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];}\r
+\r
+ // place the declets in the encoding words and copy to result (df),\r
+ // according to endianness; in all cases complete the sign word\r
+ // first\r
+ #if DECPMAX==7\r
+ getDPDt(dpd, 1);\r
+ encode|=dpd<<10;\r
+ getDPDt(dpd, 0);\r
+ encode|=dpd;\r
+ DFWORD(df, 0)=encode; // just the one word\r
+\r
+ #elif DECPMAX==16\r
+ getDPDt(dpd, 4); encode|=dpd<<8;\r
+ getDPDt(dpd, 3); encode|=dpd>>2;\r
+ DFWORD(df, 0)=encode;\r
+ encode=dpd<<30;\r
+ getDPDt(dpd, 2); encode|=dpd<<20;\r
+ getDPDt(dpd, 1); encode|=dpd<<10;\r
+ getDPDt(dpd, 0); encode|=dpd;\r
+ DFWORD(df, 1)=encode;\r
+\r
+ #elif DECPMAX==34\r
+ getDPDt(dpd,10); encode|=dpd<<4;\r
+ getDPDt(dpd, 9); encode|=dpd>>6;\r
+ DFWORD(df, 0)=encode;\r
+\r
+ encode=dpd<<26;\r
+ getDPDt(dpd, 8); encode|=dpd<<16;\r
+ getDPDt(dpd, 7); encode|=dpd<<6;\r
+ getDPDt(dpd, 6); encode|=dpd>>4;\r
+ DFWORD(df, 1)=encode;\r
+\r
+ encode=dpd<<28;\r
+ getDPDt(dpd, 5); encode|=dpd<<18;\r
+ getDPDt(dpd, 4); encode|=dpd<<8;\r
+ getDPDt(dpd, 3); encode|=dpd>>2;\r
+ DFWORD(df, 2)=encode;\r
+\r
+ encode=dpd<<30;\r
+ getDPDt(dpd, 2); encode|=dpd<<20;\r
+ getDPDt(dpd, 1); encode|=dpd<<10;\r
+ getDPDt(dpd, 0); encode|=dpd;\r
+ DFWORD(df, 3)=encode;\r
+ #endif\r
+\r
+ // printf("Status: %08lx\n", (LI)set->status);\r
+ // decFloatShow(df, "final2");\r
+ return df;\r
+ } // decFinalize\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign */\r
+/* */\r
+/* df is the target decFloat */\r
+/* exp is the in-range unbiased exponent, q, or a special value in */\r
+/* the form returned by decFloatGetExponent */\r
+/* bcdar holds DECPMAX digits to set the coefficient from, one */\r
+/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */\r
+/* if df is a NaN; all are ignored if df is infinite. */\r
+/* All bytes must be in 0-9; results are undefined otherwise. */\r
+/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */\r
+/* returns df, which will be canonical */\r
+/* */\r
+/* No error is possible, and no status will be set. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar,\r
+ Int sig) {\r
+ uInt encode, dpd; // work\r
+ const uByte *ub; // ..\r
+\r
+ if (EXPISSPECIAL(exp)) encode=exp|sig;// specials already encoded\r
+ else { // is finite\r
+ // encode the combination field and exponent continuation\r
+ uInt uexp=(uInt)(exp+DECBIAS); // biased exponent\r
+ uInt code=(uexp>>DECECONL)<<4; // top two bits of exp\r
+ code+=bcdar[0]; // add msd\r
+ // look up the combination field and make high word\r
+ encode=DECCOMBFROM[code]|sig; // indexed by (0-2)*16+msd\r
+ encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation\r
+ }\r
+\r
+ // private macro to extract a declet, n (where 0<=n<DECLETS and 0\r
+ // refers to the declet from the least significant three digits)\r
+ // and put the corresponding DPD code into dpd.\r
+ // Use of a working pointer, uInt *ub, is assumed.\r
+\r
+ #define getDPDb(dpd, n) ub=bcdar+DECPMAX-1-(3*(n))-2; \\r
+ dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];\r
+\r
+ // place the declets in the encoding words and copy to result (df),\r
+ // according to endianness; in all cases complete the sign word\r
+ // first\r
+ #if DECPMAX==7\r
+ getDPDb(dpd, 1);\r
+ encode|=dpd<<10;\r
+ getDPDb(dpd, 0);\r
+ encode|=dpd;\r
+ DFWORD(df, 0)=encode; // just the one word\r
+\r
+ #elif DECPMAX==16\r
+ getDPDb(dpd, 4); encode|=dpd<<8;\r
+ getDPDb(dpd, 3); encode|=dpd>>2;\r
+ DFWORD(df, 0)=encode;\r
+ encode=dpd<<30;\r
+ getDPDb(dpd, 2); encode|=dpd<<20;\r
+ getDPDb(dpd, 1); encode|=dpd<<10;\r
+ getDPDb(dpd, 0); encode|=dpd;\r
+ DFWORD(df, 1)=encode;\r
+\r
+ #elif DECPMAX==34\r
+ getDPDb(dpd,10); encode|=dpd<<4;\r
+ getDPDb(dpd, 9); encode|=dpd>>6;\r
+ DFWORD(df, 0)=encode;\r
+\r
+ encode=dpd<<26;\r
+ getDPDb(dpd, 8); encode|=dpd<<16;\r
+ getDPDb(dpd, 7); encode|=dpd<<6;\r
+ getDPDb(dpd, 6); encode|=dpd>>4;\r
+ DFWORD(df, 1)=encode;\r
+\r
+ encode=dpd<<28;\r
+ getDPDb(dpd, 5); encode|=dpd<<18;\r
+ getDPDb(dpd, 4); encode|=dpd<<8;\r
+ getDPDb(dpd, 3); encode|=dpd>>2;\r
+ DFWORD(df, 2)=encode;\r
+\r
+ encode=dpd<<30;\r
+ getDPDb(dpd, 2); encode|=dpd<<20;\r
+ getDPDb(dpd, 1); encode|=dpd<<10;\r
+ getDPDb(dpd, 0); encode|=dpd;\r
+ DFWORD(df, 3)=encode;\r
+ #endif\r
+ // decFloatShow(df, "fromB");\r
+ return df;\r
+ } // decFloatFromBCD\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromPacked -- set decFloat from exponent and packed BCD */\r
+/* */\r
+/* df is the target decFloat */\r
+/* exp is the in-range unbiased exponent, q, or a special value in */\r
+/* the form returned by decFloatGetExponent */\r
+/* packed holds DECPMAX packed decimal digits plus a sign nibble */\r
+/* (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */\r
+/* and all except sign are ignored if df is infinite. For DOUBLE */\r
+/* and QUAD the first (pad) nibble is also ignored in all cases. */\r
+/* All coefficient nibbles must be in 0-9 and sign in A-F; results */\r
+/* are undefined otherwise. */\r
+/* returns df, which will be canonical */\r
+/* */\r
+/* No error is possible, and no status will be set. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) {\r
+ uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign]\r
+ const uByte *ip; // ..\r
+ uByte *op; // ..\r
+ Int sig=0; // sign\r
+\r
+ // expand coefficient and sign to BCDAR\r
+ #if SINGLE\r
+ op=bcdar+1; // no pad digit\r
+ #else\r
+ op=bcdar; // first (pad) digit ignored\r
+ #endif\r
+ for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {\r
+ *op++=*ip>>4;\r
+ *op++=(uByte)(*ip&0x0f); // [final nibble is sign]\r
+ }\r
+ op--; // -> sign byte\r
+ if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;\r
+\r
+ if (EXPISSPECIAL(exp)) { // Infinity or NaN\r
+ if (!EXPISINF(exp)) bcdar[1]=0; // a NaN: ignore MSD\r
+ else memset(bcdar+1, 0, DECPMAX); // Infinite: coefficient to 0\r
+ }\r
+ return decFloatFromBCD(df, exp, bcdar+1, sig);\r
+ } // decFloatFromPacked\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromPackedChecked -- set from exponent and packed; checked */\r
+/* */\r
+/* df is the target decFloat */\r
+/* exp is the in-range unbiased exponent, q, or a special value in */\r
+/* the form returned by decFloatGetExponent */\r
+/* packed holds DECPMAX packed decimal digits plus a sign nibble */\r
+/* (all 6 codes are OK); the first (MSD) must be 0 if df is a NaN */\r
+/* and all digits must be 0 if df is infinite. For DOUBLE and */\r
+/* QUAD the first (pad) nibble must be 0. */\r
+/* All coefficient nibbles must be in 0-9 and sign in A-F. */\r
+/* returns df, which will be canonical or NULL if any of the */\r
+/* requirements are not met (if this case df is unchanged); that */\r
+/* is, the input data must be as returned by decFloatToPacked, */\r
+/* except that all six sign codes are acccepted. */\r
+/* */\r
+/* No status will be set. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFromPackedChecked(decFloat *df, Int exp,\r
+ const uByte *packed) {\r
+ uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign]\r
+ const uByte *ip; // ..\r
+ uByte *op; // ..\r
+ Int sig=0; // sign\r
+\r
+ // expand coefficient and sign to BCDAR\r
+ #if SINGLE\r
+ op=bcdar+1; // no pad digit\r
+ #else\r
+ op=bcdar; // first (pad) digit here\r
+ #endif\r
+ for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {\r
+ *op=*ip>>4;\r
+ if (*op>9) return NULL;\r
+ op++;\r
+ *op=(uByte)(*ip&0x0f); // [final nibble is sign]\r
+ if (*op>9 && ip<packed+((DECPMAX+2)/2)-1) return NULL;\r
+ op++;\r
+ }\r
+ op--; // -> sign byte\r
+ if (*op<=9) return NULL; // bad sign\r
+ if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;\r
+\r
+ #if !SINGLE\r
+ if (bcdar[0]!=0) return NULL; // bad pad nibble\r
+ #endif\r
+\r
+ if (EXPISNAN(exp)) { // a NaN\r
+ if (bcdar[1]!=0) return NULL; // bad msd\r
+ } // NaN\r
+ else if (EXPISINF(exp)) { // is infinite\r
+ Int i;\r
+ for (i=0; i<DECPMAX; i++) {\r
+ if (bcdar[i+1]!=0) return NULL; // should be all zeros\r
+ }\r
+ } // infinity\r
+ else { // finite\r
+ // check the exponent is in range\r
+ if (exp>DECEMAX-DECPMAX+1) return NULL;\r
+ if (exp<DECEMIN-DECPMAX+1) return NULL;\r
+ }\r
+ return decFloatFromBCD(df, exp, bcdar+1, sig);\r
+ } // decFloatFromPacked\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromString -- conversion from numeric string */\r
+/* */\r
+/* result is the decFloat format number which gets the result of */\r
+/* the conversion */\r
+/* *string is the character string which should contain a valid */\r
+/* number (which may be a special value), \0-terminated */\r
+/* If there are too many significant digits in the */\r
+/* coefficient it will be rounded. */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* The length of the coefficient and the size of the exponent are */\r
+/* checked by this routine, so the correct error (Underflow or */\r
+/* Overflow) can be reported or rounding applied, as necessary. */\r
+/* */\r
+/* There is no limit to the coefficient length for finite inputs; */\r
+/* NaN payloads must be integers with no more than DECPMAX-1 digits. */\r
+/* Exponents may have up to nine significant digits. */\r
+/* */\r
+/* If bad syntax is detected, the result will be a quiet NaN. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatFromString(decFloat *result, const char *string,\r
+ decContext *set) {\r
+ Int digits; // count of digits in coefficient\r
+ const char *dotchar=NULL; // where dot was found [NULL if none]\r
+ const char *cfirst=string; // -> first character of decimal part\r
+ const char *c; // work\r
+ uByte *ub; // ..\r
+ uInt uiwork; // for macros\r
+ bcdnum num; // collects data for finishing\r
+ uInt error=DEC_Conversion_syntax; // assume the worst\r
+ uByte buffer[ROUNDUP(DECSTRING+11, 8)]; // room for most coefficents,\r
+ // some common rounding, +3, & pad\r
+ #if DECTRACE\r
+ // printf("FromString %s ...\n", string);\r
+ #endif\r
+\r
+ for(;;) { // once-only 'loop'\r
+ num.sign=0; // assume non-negative\r
+ num.msd=buffer; // MSD is here always\r
+\r
+ // detect and validate the coefficient, including any leading,\r
+ // trailing, or embedded '.'\r
+ // [could test four-at-a-time here (saving 10% for decQuads),\r
+ // but that risks storage violation because the position of the\r
+ // terminator is unknown]\r
+ for (c=string;; c++) { // -> input character\r
+ if (((unsigned)(*c-'0'))<=9) continue; // '0' through '9' is good\r
+ if (*c=='\0') break; // most common non-digit\r
+ if (*c=='.') {\r
+ if (dotchar!=NULL) break; // not first '.'\r
+ dotchar=c; // record offset into decimal part\r
+ continue;}\r
+ if (c==string) { // first in string...\r
+ if (*c=='-') { // valid - sign\r
+ cfirst++;\r
+ num.sign=DECFLOAT_Sign;\r
+ continue;}\r
+ if (*c=='+') { // valid + sign\r
+ cfirst++;\r
+ continue;}\r
+ }\r
+ // *c is not a digit, terminator, or a valid +, -, or '.'\r
+ break;\r
+ } // c loop\r
+\r
+ digits=(uInt)(c-cfirst); // digits (+1 if a dot)\r
+\r
+ if (digits>0) { // had digits and/or dot\r
+ const char *clast=c-1; // note last coefficient char position\r
+ Int exp=0; // exponent accumulator\r
+ if (*c!='\0') { // something follows the coefficient\r
+ uInt edig; // unsigned work\r
+ // had some digits and more to come; expect E[+|-]nnn now\r
+ const char *firstexp; // exponent first non-zero\r
+ if (*c!='E' && *c!='e') break;\r
+ c++; // to (optional) sign\r
+ if (*c=='-' || *c=='+') c++; // step over sign (c=clast+2)\r
+ if (*c=='\0') break; // no digits! (e.g., '1.2E')\r
+ for (; *c=='0';) c++; // skip leading zeros [even last]\r
+ firstexp=c; // remember start [maybe '\0']\r
+ // gather exponent digits\r
+ edig=(uInt)*c-(uInt)'0';\r
+ if (edig<=9) { // [check not bad or terminator]\r
+ exp+=edig; // avoid initial X10\r
+ c++;\r
+ for (;; c++) {\r
+ edig=(uInt)*c-(uInt)'0';\r
+ if (edig>9) break;\r
+ exp=exp*10+edig;\r
+ }\r
+ }\r
+ // if not now on the '\0', *c must not be a digit\r
+ if (*c!='\0') break;\r
+\r
+ // (this next test must be after the syntax checks)\r
+ // if definitely more than the possible digits for format then\r
+ // the exponent may have wrapped, so simply set it to a certain\r
+ // over/underflow value\r
+ if (c>firstexp+DECEMAXD) exp=DECEMAX*2;\r
+ if (*(clast+2)=='-') exp=-exp; // was negative\r
+ } // exponent part\r
+\r
+ if (dotchar!=NULL) { // had a '.'\r
+ digits--; // remove from digits count\r
+ if (digits==0) break; // was dot alone: bad syntax\r
+ exp-=(Int)(clast-dotchar); // adjust exponent\r
+ // [the '.' can now be ignored]\r
+ }\r
+ num.exponent=exp; // exponent is good; store it\r
+\r
+ // Here when whole string has been inspected and syntax is good\r
+ // cfirst->first digit or dot, clast->last digit or dot\r
+ error=0; // no error possible now\r
+\r
+ // if the number of digits in the coefficient will fit in buffer\r
+ // then it can simply be converted to bcd8 and copied -- decFinalize\r
+ // will take care of leading zeros and rounding; the buffer is big\r
+ // enough for all canonical coefficients, including 0.00000nn...\r
+ ub=buffer;\r
+ if (digits<=(Int)(sizeof(buffer)-3)) { // [-3 allows by-4s copy]\r
+ c=cfirst;\r
+ if (dotchar!=NULL) { // a dot to worry about\r
+ if (*(c+1)=='.') { // common canonical case\r
+ *ub++=(uByte)(*c-'0'); // copy leading digit\r
+ c+=2; // prepare to handle rest\r
+ }\r
+ else for (; c<=clast;) { // '.' could be anywhere\r
+ // as usual, go by fours when safe; NB it has been asserted\r
+ // that a '.' does not have the same mask as a digit\r
+ if (c<=clast-3 // safe for four\r
+ && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // test four\r
+ UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8\r
+ ub+=4;\r
+ c+=4;\r
+ continue;\r
+ }\r
+ if (*c=='.') { // found the dot\r
+ c++; // step over it ..\r
+ break; // .. and handle the rest\r
+ }\r
+ *ub++=(uByte)(*c++-'0');\r
+ }\r
+ } // had dot\r
+ // Now no dot; do this by fours (where safe)\r
+ for (; c<=clast-3; c+=4, ub+=4) UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f);\r
+ for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0');\r
+ num.lsd=buffer+digits-1; // record new LSD\r
+ } // fits\r
+\r
+ else { // too long for buffer\r
+ // [This is a rare and unusual case; arbitrary-length input]\r
+ // strip leading zeros [but leave final 0 if all 0's]\r
+ if (*cfirst=='.') cfirst++; // step past dot at start\r
+ if (*cfirst=='0') { // [cfirst always -> digit]\r
+ for (; cfirst<clast; cfirst++) {\r
+ if (*cfirst!='0') { // non-zero found\r
+ if (*cfirst=='.') continue; // [ignore]\r
+ break; // done\r
+ }\r
+ digits--; // 0 stripped\r
+ } // cfirst\r
+ } // at least one leading 0\r
+\r
+ // the coefficient is now as short as possible, but may still\r
+ // be too long; copy up to Pmax+1 digits to the buffer, then\r
+ // just record any non-zeros (set round-for-reround digit)\r
+ for (c=cfirst; c<=clast && ub<=buffer+DECPMAX; c++) {\r
+ // (see commentary just above)\r
+ if (c<=clast-3 // safe for four\r
+ && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // four digits\r
+ UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8\r
+ ub+=4;\r
+ c+=3; // [will become 4]\r
+ continue;\r
+ }\r
+ if (*c=='.') continue; // [ignore]\r
+ *ub++=(uByte)(*c-'0');\r
+ }\r
+ ub--; // -> LSD\r
+ for (; c<=clast; c++) { // inspect remaining chars\r
+ if (*c!='0') { // sticky bit needed\r
+ if (*c=='.') continue; // [ignore]\r
+ *ub=DECSTICKYTAB[*ub]; // update round-for-reround\r
+ break; // no need to look at more\r
+ }\r
+ }\r
+ num.lsd=ub; // record LSD\r
+ // adjust exponent for dropped digits\r
+ num.exponent+=digits-(Int)(ub-buffer+1);\r
+ } // too long for buffer\r
+ } // digits and/or dot\r
+\r
+ else { // no digits or dot were found\r
+ // only Infinities and NaNs are allowed, here\r
+ if (*c=='\0') break; // nothing there is bad\r
+ buffer[0]=0; // default a coefficient of 0\r
+ num.lsd=buffer; // ..\r
+ if (decBiStr(c, "infinity", "INFINITY")\r
+ || decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf;\r
+ else { // should be a NaN\r
+ num.exponent=DECFLOAT_qNaN; // assume quiet NaN\r
+ if (*c=='s' || *c=='S') { // probably an sNaN\r
+ num.exponent=DECFLOAT_sNaN; // effect the 's'\r
+ c++; // and step over it\r
+ }\r
+ if (*c!='N' && *c!='n') break; // check caseless "NaN"\r
+ c++;\r
+ if (*c!='a' && *c!='A') break; // ..\r
+ c++;\r
+ if (*c!='N' && *c!='n') break; // ..\r
+ c++;\r
+ // now either nothing, or nnnn payload (no dots), expected\r
+ // -> start of integer, and skip leading 0s [including plain 0]\r
+ for (cfirst=c; *cfirst=='0';) cfirst++;\r
+ if (*cfirst!='\0') { // not empty or all-0, payload\r
+ // payload found; check all valid digits and copy to buffer as bcd8\r
+ ub=buffer;\r
+ for (c=cfirst;; c++, ub++) {\r
+ if ((unsigned)(*c-'0')>9) break; // quit if not 0-9\r
+ if (c-cfirst==DECPMAX-1) break; // too many digits\r
+ *ub=(uByte)(*c-'0'); // good bcd8\r
+ }\r
+ if (*c!='\0') break; // not all digits, or too many\r
+ num.lsd=ub-1; // record new LSD\r
+ }\r
+ } // NaN or sNaN\r
+ error=0; // syntax is OK\r
+ } // digits=0 (special expected)\r
+ break; // drop out\r
+ } // [for(;;) once-loop]\r
+\r
+ // decShowNum(&num, "fromStr");\r
+\r
+ if (error!=0) {\r
+ set->status|=error;\r
+ num.exponent=DECFLOAT_qNaN; // set up quiet NaN\r
+ num.sign=0; // .. with 0 sign\r
+ buffer[0]=0; // .. and coefficient\r
+ num.lsd=buffer; // ..\r
+ // decShowNum(&num, "oops");\r
+ }\r
+\r
+ // decShowNum(&num, "dffs");\r
+ decFinalize(result, &num, set); // round, check, and lay out\r
+ // decFloatShow(result, "fromString");\r
+ return result;\r
+ } // decFloatFromString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatFromWider -- conversion from next-wider format */\r
+/* */\r
+/* result is the decFloat format number which gets the result of */\r
+/* the conversion */\r
+/* wider is the decFloatWider format number which will be narrowed */\r
+/* set is the context */\r
+/* returns result */\r
+/* */\r
+/* Narrowing can cause rounding, overflow, etc., but not Invalid */\r
+/* operation (sNaNs are copied and do not signal). */\r
+/* ------------------------------------------------------------------ */\r
+// narrow-to is not possible for decQuad format numbers; simply omit\r
+#if !QUAD\r
+decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider,\r
+ decContext *set) {\r
+ bcdnum num; // collects data for finishing\r
+ uByte bcdar[DECWPMAX]; // room for wider coefficient\r
+ uInt widerhi=DFWWORD(wider, 0); // top word\r
+ Int exp;\r
+\r
+ GETWCOEFF(wider, bcdar);\r
+\r
+ num.msd=bcdar; // MSD is here always\r
+ num.lsd=bcdar+DECWPMAX-1; // LSD is here always\r
+ num.sign=widerhi&0x80000000; // extract sign [DECFLOAT_Sign=Neg]\r
+\r
+ // decode the wider combination field to exponent\r
+ exp=DECCOMBWEXP[widerhi>>26]; // decode from wider combination field\r
+ // if it is a special there's nothing to do unless sNaN; if it's\r
+ // finite then add the (wider) exponent continuation and unbias\r
+ if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; // include sNaN selector\r
+ else exp+=GETWECON(wider)-DECWBIAS;\r
+ num.exponent=exp;\r
+\r
+ // decShowNum(&num, "dffw");\r
+ return decFinalize(result, &num, set);// round, check, and lay out\r
+ } // decFloatFromWider\r
+#endif\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatGetCoefficient -- get coefficient as BCD8 */\r
+/* */\r
+/* df is the decFloat from which to extract the coefficient */\r
+/* bcdar is where DECPMAX bytes will be written, one BCD digit in */\r
+/* each byte (BCD8 encoding); if df is a NaN the first byte will */\r
+/* be zero, and if it is infinite they will all be zero */\r
+/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */\r
+/* 0 otherwise) */\r
+/* */\r
+/* No error is possible, and no status will be set. If df is a */\r
+/* special value the array is set to zeros (for Infinity) or to the */\r
+/* payload of a qNaN or sNaN. */\r
+/* ------------------------------------------------------------------ */\r
+Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) {\r
+ if (DFISINF(df)) memset(bcdar, 0, DECPMAX);\r
+ else {\r
+ GETCOEFF(df, bcdar); // use macro\r
+ if (DFISNAN(df)) bcdar[0]=0; // MSD needs correcting\r
+ }\r
+ return GETSIGN(df);\r
+ } // decFloatGetCoefficient\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatGetExponent -- get unbiased exponent */\r
+/* */\r
+/* df is the decFloat from which to extract the exponent */\r
+/* returns the exponent, q. */\r
+/* */\r
+/* No error is possible, and no status will be set. If df is a */\r
+/* special value the first seven bits of the decFloat are returned, */\r
+/* left adjusted and with the first (sign) bit set to 0 (followed by */\r
+/* 25 0 bits). e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN). */\r
+/* ------------------------------------------------------------------ */\r
+Int decFloatGetExponent(const decFloat *df) {\r
+ if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000;\r
+ return GETEXPUN(df);\r
+ } // decFloatGetExponent\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatSetCoefficient -- set coefficient from BCD8 */\r
+/* */\r
+/* df is the target decFloat (and source of exponent/special value) */\r
+/* bcdar holds DECPMAX digits to set the coefficient from, one */\r
+/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */\r
+/* if df is a NaN; all are ignored if df is infinite. */\r
+/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */\r
+/* returns df, which will be canonical */\r
+/* */\r
+/* No error is possible, and no status will be set. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar,\r
+ Int sig) {\r
+ uInt exp; // for exponent\r
+ uByte bcdzero[DECPMAX]; // for infinities\r
+\r
+ // Exponent/special code is extracted from df\r
+ if (DFISSPECIAL(df)) {\r
+ exp=DFWORD(df, 0)&0x7e000000;\r
+ if (DFISINF(df)) {\r
+ memset(bcdzero, 0, DECPMAX);\r
+ return decFloatFromBCD(df, exp, bcdzero, sig);\r
+ }\r
+ }\r
+ else exp=GETEXPUN(df);\r
+ return decFloatFromBCD(df, exp, bcdar, sig);\r
+ } // decFloatSetCoefficient\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatSetExponent -- set exponent or special value */\r
+/* */\r
+/* df is the target decFloat (and source of coefficient/payload) */\r
+/* set is the context for reporting status */\r
+/* exp is the unbiased exponent, q, or a special value in the form */\r
+/* returned by decFloatGetExponent */\r
+/* returns df, which will be canonical */\r
+/* */\r
+/* No error is possible, but Overflow or Underflow might occur. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) {\r
+ uByte bcdcopy[DECPMAX]; // for coefficient\r
+ bcdnum num; // work\r
+ num.exponent=exp;\r
+ num.sign=decFloatGetCoefficient(df, bcdcopy); // extract coefficient\r
+ if (DFISSPECIAL(df)) { // MSD or more needs correcting\r
+ if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX);\r
+ bcdcopy[0]=0;\r
+ }\r
+ num.msd=bcdcopy;\r
+ num.lsd=bcdcopy+DECPMAX-1;\r
+ return decFinalize(df, &num, set);\r
+ } // decFloatSetExponent\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatRadix -- returns the base (10) */\r
+/* */\r
+/* df is any decFloat of this format */\r
+/* ------------------------------------------------------------------ */\r
+uInt decFloatRadix(const decFloat *df) {\r
+ if (df) return 10; // to placate compiler\r
+ return 10;\r
+ } // decFloatRadix\r
+\r
+/* The following function is not available if DECPRINT=0 */\r
+#if DECPRINT\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatShow -- printf a decFloat in hexadecimal and decimal */\r
+/* df is the decFloat to show */\r
+/* tag is a tag string displayed with the number */\r
+/* */\r
+/* This is a debug aid; the precise format of the string may change. */\r
+/* ------------------------------------------------------------------ */\r
+void decFloatShow(const decFloat *df, const char *tag) {\r
+ char hexbuf[DECBYTES*2+DECBYTES/4+1]; // NB blank after every fourth\r
+ char buff[DECSTRING]; // for value in decimal\r
+ Int i, j=0;\r
+\r
+ for (i=0; i<DECBYTES; i++) {\r
+ #if DECLITEND\r
+ sprintf(&hexbuf[j], "%02x", df->bytes[DECBYTES-1-i]);\r
+ #else\r
+ sprintf(&hexbuf[j], "%02x", df->bytes[i]);\r
+ #endif\r
+ j+=2;\r
+ // the next line adds blank (and terminator) after final pair, too\r
+ if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;}\r
+ }\r
+ decFloatToString(df, buff);\r
+ printf(">%s> %s [big-endian] %s\n", tag, hexbuf, buff);\r
+ return;\r
+ } // decFloatShow\r
+#endif\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat */\r
+/* */\r
+/* df is the source decFloat */\r
+/* exp will be set to the unbiased exponent, q, or to a special */\r
+/* value in the form returned by decFloatGetExponent */\r
+/* bcdar is where DECPMAX bytes will be written, one BCD digit in */\r
+/* each byte (BCD8 encoding); if df is a NaN the first byte will */\r
+/* be zero, and if it is infinite they will all be zero */\r
+/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */\r
+/* 0 otherwise) */\r
+/* */\r
+/* No error is possible, and no status will be set. */\r
+/* ------------------------------------------------------------------ */\r
+Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) {\r
+ if (DFISINF(df)) {\r
+ memset(bcdar, 0, DECPMAX);\r
+ *exp=DFWORD(df, 0)&0x7e000000;\r
+ }\r
+ else {\r
+ GETCOEFF(df, bcdar); // use macro\r
+ if (DFISNAN(df)) {\r
+ bcdar[0]=0; // MSD needs correcting\r
+ *exp=DFWORD(df, 0)&0x7e000000;\r
+ }\r
+ else { // finite\r
+ *exp=GETEXPUN(df);\r
+ }\r
+ }\r
+ return GETSIGN(df);\r
+ } // decFloatToBCD\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToEngString -- conversion to numeric string, engineering */\r
+/* */\r
+/* df is the decFloat format number to convert */\r
+/* string is the string where the result will be laid out */\r
+/* */\r
+/* string must be at least DECPMAX+9 characters (the worst case is */\r
+/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */\r
+/* DECEMAXD<=4); this condition is asserted above */\r
+/* */\r
+/* No error is possible, and no status will be set */\r
+/* ------------------------------------------------------------------ */\r
+char * decFloatToEngString(const decFloat *df, char *string){\r
+ uInt msd; // coefficient MSD\r
+ Int exp; // exponent top two bits or full\r
+ uInt comb; // combination field\r
+ char *cstart; // coefficient start\r
+ char *c; // output pointer in string\r
+ char *s, *t; // .. (source, target)\r
+ Int pre, e; // work\r
+ const uByte *u; // ..\r
+ uInt uiwork; // for macros [one compiler needs\r
+ // volatile here to avoid bug, but\r
+ // that doubles execution time]\r
+\r
+ // Source words; macro handles endianness\r
+ uInt sourhi=DFWORD(df, 0); // word with sign\r
+ #if DECPMAX==16\r
+ uInt sourlo=DFWORD(df, 1);\r
+ #elif DECPMAX==34\r
+ uInt sourmh=DFWORD(df, 1);\r
+ uInt sourml=DFWORD(df, 2);\r
+ uInt sourlo=DFWORD(df, 3);\r
+ #endif\r
+\r
+ c=string; // where result will go\r
+ if (((Int)sourhi)<0) *c++='-'; // handle sign\r
+ comb=sourhi>>26; // sign+combination field\r
+ msd=DECCOMBMSD[comb]; // decode the combination field\r
+ exp=DECCOMBEXP[comb]; // ..\r
+\r
+ if (EXPISSPECIAL(exp)) { // special\r
+ if (exp==DECFLOAT_Inf) { // infinity\r
+ strcpy(c, "Inf");\r
+ strcpy(c+3, "inity");\r
+ return string; // easy\r
+ }\r
+ if (sourhi&0x02000000) *c++='s'; // sNaN\r
+ strcpy(c, "NaN"); // complete word\r
+ c+=3; // step past\r
+ // quick exit if the payload is zero\r
+ #if DECPMAX==7\r
+ if ((sourhi&0x000fffff)==0) return string;\r
+ #elif DECPMAX==16\r
+ if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;\r
+ #elif DECPMAX==34\r
+ if (sourlo==0 && sourml==0 && sourmh==0\r
+ && (sourhi&0x00003fff)==0) return string;\r
+ #endif\r
+ // otherwise drop through to add integer; set correct exp etc.\r
+ exp=0; msd=0; // setup for following code\r
+ }\r
+ else { // complete exponent; top two bits are in place\r
+ exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias\r
+ }\r
+\r
+ /* convert the digits of the significand to characters */\r
+ cstart=c; // save start of coefficient\r
+ if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit\r
+\r
+ // Decode the declets. After extracting each declet, it is\r
+ // decoded to a 4-uByte sequence by table lookup; the four uBytes\r
+ // are the three encoded BCD8 digits followed by a 1-byte length\r
+ // (significant digits, except that 000 has length 0). This allows\r
+ // us to left-align the first declet with non-zero content, then\r
+ // the remaining ones are full 3-char length. Fixed-length copies\r
+ // are used because variable-length memcpy causes a subroutine call\r
+ // in at least two compilers. (The copies are length 4 for speed\r
+ // and are safe because the last item in the array is of length\r
+ // three and has the length byte following.)\r
+ #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \\r
+ if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \\r
+ else if (*(u+3)) { \\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}\r
+\r
+ #if DECPMAX==7\r
+ dpd2char(sourhi>>10); // declet 1\r
+ dpd2char(sourhi); // declet 2\r
+\r
+ #elif DECPMAX==16\r
+ dpd2char(sourhi>>8); // declet 1\r
+ dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2\r
+ dpd2char(sourlo>>20); // declet 3\r
+ dpd2char(sourlo>>10); // declet 4\r
+ dpd2char(sourlo); // declet 5\r
+\r
+ #elif DECPMAX==34\r
+ dpd2char(sourhi>>4); // declet 1\r
+ dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2\r
+ dpd2char(sourmh>>16); // declet 3\r
+ dpd2char(sourmh>>6); // declet 4\r
+ dpd2char((sourmh<<4) | (sourml>>28)); // declet 5\r
+ dpd2char(sourml>>18); // declet 6\r
+ dpd2char(sourml>>8); // declet 7\r
+ dpd2char((sourml<<2) | (sourlo>>30)); // declet 8\r
+ dpd2char(sourlo>>20); // declet 9\r
+ dpd2char(sourlo>>10); // declet 10\r
+ dpd2char(sourlo); // declet 11\r
+ #endif\r
+\r
+ if (c==cstart) *c++='0'; // all zeros, empty -- make "0"\r
+\r
+ if (exp==0) { // integer or NaN case -- easy\r
+ *c='\0'; // terminate\r
+ return string;\r
+ }\r
+ /* non-0 exponent */\r
+\r
+ e=0; // assume no E\r
+ pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1]\r
+ // [here, pre-exp is the digits count (==1 for zero)]\r
+\r
+ if (exp>0 || pre<-5) { // need exponential form\r
+ e=pre-1; // calculate E value\r
+ pre=1; // assume one digit before '.'\r
+ if (e!=0) { // engineering: may need to adjust\r
+ Int adj; // adjustment\r
+ // The C remainder operator is undefined for negative numbers, so\r
+ // a positive remainder calculation must be used here\r
+ if (e<0) {\r
+ adj=(-e)%3;\r
+ if (adj!=0) adj=3-adj;\r
+ }\r
+ else { // e>0\r
+ adj=e%3;\r
+ }\r
+ e=e-adj;\r
+ // if dealing with zero still produce an exponent which is a\r
+ // multiple of three, as expected, but there will only be the\r
+ // one zero before the E, still. Otherwise note the padding.\r
+ if (!DFISZERO(df)) pre+=adj;\r
+ else { // is zero\r
+ if (adj!=0) { // 0.00Esnn needed\r
+ e=e+3;\r
+ pre=-(2-adj);\r
+ }\r
+ } // zero\r
+ } // engineering adjustment\r
+ } // exponential form\r
+ // printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp);\r
+\r
+ /* modify the coefficient, adding 0s, '.', and E+nn as needed */\r
+ if (pre>0) { // ddd.ddd (plain), perhaps with E\r
+ // or dd00 padding for engineering\r
+ char *dotat=cstart+pre;\r
+ if (dotat<c) { // if embedded dot needed...\r
+ // move by fours; there must be space for junk at the end\r
+ // because there is still space for exponent\r
+ s=dotat+ROUNDDOWN4(c-dotat); // source\r
+ t=s+1; // target\r
+ // open the gap [cannot use memcpy]\r
+ for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));\r
+ *dotat='.';\r
+ c++; // length increased by one\r
+ } // need dot?\r
+ else for (; c<dotat; c++) *c='0'; // pad for engineering\r
+ } // pre>0\r
+ else {\r
+ /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have\r
+ E, but only for 0.00E+3 kind of case -- with plenty of spare\r
+ space in this case */\r
+ pre=-pre+2; // gap width, including "0."\r
+ t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point\r
+ // backoff if too far to the right\r
+ if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit\r
+ // now shift the entire coefficient to the right, being careful not\r
+ // to access to the left of string [cannot use memcpy]\r
+ for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));\r
+ // for Quads and Singles there may be a character or two left...\r
+ s+=3; // where next would come from\r
+ for(; s>=cstart; s--, t--) *(t+3)=*(s);\r
+ // now have fill 0. through 0.00000; use overlaps to avoid tests\r
+ if (pre>=4) {\r
+ memcpy(cstart+pre-4, "0000", 4);\r
+ memcpy(cstart, "0.00", 4);\r
+ }\r
+ else { // 2 or 3\r
+ *(cstart+pre-1)='0';\r
+ memcpy(cstart, "0.", 2);\r
+ }\r
+ c+=pre; // to end\r
+ }\r
+\r
+ // finally add the E-part, if needed; it will never be 0, and has\r
+ // a maximum length of 3 or 4 digits (asserted above)\r
+ if (e!=0) {\r
+ memcpy(c, "E+", 2); // starts with E, assume +\r
+ c++;\r
+ if (e<0) {\r
+ *c='-'; // oops, need '-'\r
+ e=-e; // uInt, please\r
+ }\r
+ c++;\r
+ // Three-character exponents are easy; 4-character a little trickier\r
+ #if DECEMAXD<=3\r
+ u=&BIN2BCD8[e*4]; // -> 3 digits + length byte\r
+ // copy fixed 4 characters [is safe], starting at non-zero\r
+ // and with character mask to convert BCD to char\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);\r
+ c+=*(u+3); // bump pointer appropriately\r
+ #elif DECEMAXD==4\r
+ if (e<1000) { // 3 (or fewer) digits case\r
+ u=&BIN2BCD8[e*4]; // -> 3 digits + length byte\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]\r
+ c+=*(u+3); // bump pointer appropriately\r
+ }\r
+ else { // 4-digits\r
+ Int thou=((e>>3)*1049)>>17; // e/1000\r
+ Int rem=e-(1000*thou); // e%1000\r
+ *c++=(char)('0'+(char)thou); // the thousands digit\r
+ u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte\r
+ UBFROMUI(c, UBTOUI(u)|CHARMASK);// copy fixed 3+1 characters [is safe]\r
+ c+=3; // bump pointer, always 3 digits\r
+ }\r
+ #endif\r
+ }\r
+ *c='\0'; // terminate\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // decFloatToEngString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToPacked -- convert decFloat to Packed decimal + exponent */\r
+/* */\r
+/* df is the source decFloat */\r
+/* exp will be set to the unbiased exponent, q, or to a special */\r
+/* value in the form returned by decFloatGetExponent */\r
+/* packed is where DECPMAX nibbles will be written with the sign as */\r
+/* final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */\r
+/* of zero, and an infinity is all zeros. decDouble and decQuad */\r
+/* have a additional leading zero nibble, leading to result */\r
+/* lengths of 4, 9, and 18 bytes. */\r
+/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */\r
+/* 0 otherwise) */\r
+/* */\r
+/* No error is possible, and no status will be set. */\r
+/* ------------------------------------------------------------------ */\r
+Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) {\r
+ uByte bcdar[DECPMAX+2]; // work buffer\r
+ uByte *ip=bcdar, *op=packed; // work pointers\r
+ if (DFISINF(df)) {\r
+ memset(bcdar, 0, DECPMAX+2);\r
+ *exp=DECFLOAT_Inf;\r
+ }\r
+ else {\r
+ GETCOEFF(df, bcdar+1); // use macro\r
+ if (DFISNAN(df)) {\r
+ bcdar[1]=0; // MSD needs clearing\r
+ *exp=DFWORD(df, 0)&0x7e000000;\r
+ }\r
+ else { // finite\r
+ *exp=GETEXPUN(df);\r
+ }\r
+ }\r
+ // now pack; coefficient currently at bcdar+1\r
+ #if SINGLE\r
+ ip++; // ignore first byte\r
+ #else\r
+ *ip=0; // need leading zero\r
+ #endif\r
+ // set final byte to Packed BCD sign value\r
+ bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS);\r
+ // pack an even number of bytes...\r
+ for (; op<packed+((DECPMAX+2)/2); op++, ip+=2) {\r
+ *op=(uByte)((*ip<<4)+*(ip+1));\r
+ }\r
+ return (bcdar[DECPMAX+1]==DECPMINUS ? DECFLOAT_Sign : 0);\r
+ } // decFloatToPacked\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToString -- conversion to numeric string */\r
+/* */\r
+/* df is the decFloat format number to convert */\r
+/* string is the string where the result will be laid out */\r
+/* */\r
+/* string must be at least DECPMAX+9 characters (the worst case is */\r
+/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */\r
+/* DECEMAXD<=4); this condition is asserted above */\r
+/* */\r
+/* No error is possible, and no status will be set */\r
+/* ------------------------------------------------------------------ */\r
+char * decFloatToString(const decFloat *df, char *string){\r
+ uInt msd; // coefficient MSD\r
+ Int exp; // exponent top two bits or full\r
+ uInt comb; // combination field\r
+ char *cstart; // coefficient start\r
+ char *c; // output pointer in string\r
+ char *s, *t; // .. (source, target)\r
+ Int pre, e; // work\r
+ const uByte *u; // ..\r
+ uInt uiwork; // for macros [one compiler needs\r
+ // volatile here to avoid bug, but\r
+ // that doubles execution time]\r
+\r
+ // Source words; macro handles endianness\r
+ uInt sourhi=DFWORD(df, 0); // word with sign\r
+ #if DECPMAX==16\r
+ uInt sourlo=DFWORD(df, 1);\r
+ #elif DECPMAX==34\r
+ uInt sourmh=DFWORD(df, 1);\r
+ uInt sourml=DFWORD(df, 2);\r
+ uInt sourlo=DFWORD(df, 3);\r
+ #endif\r
+\r
+ c=string; // where result will go\r
+ if (((Int)sourhi)<0) *c++='-'; // handle sign\r
+ comb=sourhi>>26; // sign+combination field\r
+ msd=DECCOMBMSD[comb]; // decode the combination field\r
+ exp=DECCOMBEXP[comb]; // ..\r
+\r
+ if (!EXPISSPECIAL(exp)) { // finite\r
+ // complete exponent; top two bits are in place\r
+ exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias\r
+ }\r
+ else { // IS special\r
+ if (exp==DECFLOAT_Inf) { // infinity\r
+ strcpy(c, "Infinity");\r
+ return string; // easy\r
+ }\r
+ if (sourhi&0x02000000) *c++='s'; // sNaN\r
+ strcpy(c, "NaN"); // complete word\r
+ c+=3; // step past\r
+ // quick exit if the payload is zero\r
+ #if DECPMAX==7\r
+ if ((sourhi&0x000fffff)==0) return string;\r
+ #elif DECPMAX==16\r
+ if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;\r
+ #elif DECPMAX==34\r
+ if (sourlo==0 && sourml==0 && sourmh==0\r
+ && (sourhi&0x00003fff)==0) return string;\r
+ #endif\r
+ // otherwise drop through to add integer; set correct exp etc.\r
+ exp=0; msd=0; // setup for following code\r
+ }\r
+\r
+ /* convert the digits of the significand to characters */\r
+ cstart=c; // save start of coefficient\r
+ if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit\r
+\r
+ // Decode the declets. After extracting each declet, it is\r
+ // decoded to a 4-uByte sequence by table lookup; the four uBytes\r
+ // are the three encoded BCD8 digits followed by a 1-byte length\r
+ // (significant digits, except that 000 has length 0). This allows\r
+ // us to left-align the first declet with non-zero content, then\r
+ // the remaining ones are full 3-char length. Fixed-length copies\r
+ // are used because variable-length memcpy causes a subroutine call\r
+ // in at least two compilers. (The copies are length 4 for speed\r
+ // and are safe because the last item in the array is of length\r
+ // three and has the length byte following.)\r
+ #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \\r
+ if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \\r
+ else if (*(u+3)) { \\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}\r
+\r
+ #if DECPMAX==7\r
+ dpd2char(sourhi>>10); // declet 1\r
+ dpd2char(sourhi); // declet 2\r
+\r
+ #elif DECPMAX==16\r
+ dpd2char(sourhi>>8); // declet 1\r
+ dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2\r
+ dpd2char(sourlo>>20); // declet 3\r
+ dpd2char(sourlo>>10); // declet 4\r
+ dpd2char(sourlo); // declet 5\r
+\r
+ #elif DECPMAX==34\r
+ dpd2char(sourhi>>4); // declet 1\r
+ dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2\r
+ dpd2char(sourmh>>16); // declet 3\r
+ dpd2char(sourmh>>6); // declet 4\r
+ dpd2char((sourmh<<4) | (sourml>>28)); // declet 5\r
+ dpd2char(sourml>>18); // declet 6\r
+ dpd2char(sourml>>8); // declet 7\r
+ dpd2char((sourml<<2) | (sourlo>>30)); // declet 8\r
+ dpd2char(sourlo>>20); // declet 9\r
+ dpd2char(sourlo>>10); // declet 10\r
+ dpd2char(sourlo); // declet 11\r
+ #endif\r
+\r
+ if (c==cstart) *c++='0'; // all zeros, empty -- make "0"\r
+\r
+ //[This fast path is valid but adds 3-5 cycles to worst case length]\r
+ //if (exp==0) { // integer or NaN case -- easy\r
+ // *c='\0'; // terminate\r
+ // return string;\r
+ // }\r
+\r
+ e=0; // assume no E\r
+ pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1]\r
+ // [here, pre-exp is the digits count (==1 for zero)]\r
+\r
+ if (exp>0 || pre<-5) { // need exponential form\r
+ e=pre-1; // calculate E value\r
+ pre=1; // assume one digit before '.'\r
+ } // exponential form\r
+\r
+ /* modify the coefficient, adding 0s, '.', and E+nn as needed */\r
+ if (pre>0) { // ddd.ddd (plain), perhaps with E\r
+ char *dotat=cstart+pre;\r
+ if (dotat<c) { // if embedded dot needed...\r
+ // [memmove is a disaster, here]\r
+ // move by fours; there must be space for junk at the end\r
+ // because exponent is still possible\r
+ s=dotat+ROUNDDOWN4(c-dotat); // source\r
+ t=s+1; // target\r
+ // open the gap [cannot use memcpy]\r
+ for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));\r
+ *dotat='.';\r
+ c++; // length increased by one\r
+ } // need dot?\r
+\r
+ // finally add the E-part, if needed; it will never be 0, and has\r
+ // a maximum length of 3 or 4 digits (asserted above)\r
+ if (e!=0) {\r
+ memcpy(c, "E+", 2); // starts with E, assume +\r
+ c++;\r
+ if (e<0) {\r
+ *c='-'; // oops, need '-'\r
+ e=-e; // uInt, please\r
+ }\r
+ c++;\r
+ // Three-character exponents are easy; 4-character a little trickier\r
+ #if DECEMAXD<=3\r
+ u=&BIN2BCD8[e*4]; // -> 3 digits + length byte\r
+ // copy fixed 4 characters [is safe], starting at non-zero\r
+ // and with character mask to convert BCD to char\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);\r
+ c+=*(u+3); // bump pointer appropriately\r
+ #elif DECEMAXD==4\r
+ if (e<1000) { // 3 (or fewer) digits case\r
+ u=&BIN2BCD8[e*4]; // -> 3 digits + length byte\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]\r
+ c+=*(u+3); // bump pointer appropriately\r
+ }\r
+ else { // 4-digits\r
+ Int thou=((e>>3)*1049)>>17; // e/1000\r
+ Int rem=e-(1000*thou); // e%1000\r
+ *c++=(char)('0'+(char)thou); // the thousands digit\r
+ u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte\r
+ UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe]\r
+ c+=3; // bump pointer, always 3 digits\r
+ }\r
+ #endif\r
+ }\r
+ *c='\0'; // add terminator\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // pre>0\r
+\r
+ /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */\r
+ // Surprisingly, this is close to being the worst-case path, so the\r
+ // shift is done by fours; this is a little tricky because the\r
+ // rightmost character to be written must not be beyond where the\r
+ // rightmost terminator could be -- so backoff to not touch\r
+ // terminator position if need be (this can make exact alignments\r
+ // for full Doubles, but in some cases needs care not to access too\r
+ // far to the left)\r
+\r
+ pre=-pre+2; // gap width, including "0."\r
+ t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point\r
+ // backoff if too far to the right\r
+ if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit\r
+ // now shift the entire coefficient to the right, being careful not\r
+ // to access to the left of string [cannot use memcpy]\r
+ for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));\r
+ // for Quads and Singles there may be a character or two left...\r
+ s+=3; // where next would come from\r
+ for(; s>=cstart; s--, t--) *(t+3)=*(s);\r
+ // now have fill 0. through 0.00000; use overlaps to avoid tests\r
+ if (pre>=4) {\r
+ memcpy(cstart+pre-4, "0000", 4);\r
+ memcpy(cstart, "0.00", 4);\r
+ }\r
+ else { // 2 or 3\r
+ *(cstart+pre-1)='0';\r
+ memcpy(cstart, "0.", 2);\r
+ }\r
+ *(c+pre)='\0'; // terminate\r
+ return string;\r
+ } // decFloatToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatToWider -- conversion to next-wider format */\r
+/* */\r
+/* source is the decFloat format number which gets the result of */\r
+/* the conversion */\r
+/* wider is the decFloatWider format number which will be narrowed */\r
+/* returns wider */\r
+/* */\r
+/* Widening is always exact; no status is set (sNaNs are copied and */\r
+/* do not signal). The result will be canonical if the source is, */\r
+/* and may or may not be if the source is not. */\r
+/* ------------------------------------------------------------------ */\r
+// widening is not possible for decQuad format numbers; simply omit\r
+#if !QUAD\r
+decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) {\r
+ uInt msd;\r
+\r
+ /* Construct and copy the sign word */\r
+ if (DFISSPECIAL(source)) {\r
+ // copy sign, combination, and first bit of exponent (sNaN selector)\r
+ DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000;\r
+ msd=0;\r
+ }\r
+ else { // is finite number\r
+ uInt exp=GETEXPUN(source)+DECWBIAS; // get unbiased exponent and rebias\r
+ uInt code=(exp>>DECWECONL)<<29; // set two bits of exp [msd=0]\r
+ code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; // add exponent continuation\r
+ code|=DFWORD(source, 0)&0x80000000; // add sign\r
+ DFWWORD(wider, 0)=code; // .. and place top word in wider\r
+ msd=GETMSD(source); // get source coefficient MSD [0-9]\r
+ }\r
+ /* Copy the coefficient and clear any 'unused' words to left */\r
+ #if SINGLE\r
+ DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20);\r
+ #elif DOUBLE\r
+ DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18);\r
+ DFWWORD(wider, 3)=DFWORD(source, 1);\r
+ DFWWORD(wider, 1)=0;\r
+ #endif\r
+ return wider;\r
+ } // decFloatToWider\r
+#endif\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatVersion -- return package version string */\r
+/* */\r
+/* returns a constant string describing this package */\r
+/* ------------------------------------------------------------------ */\r
+const char *decFloatVersion(void) {\r
+ return DECVERSION;\r
+ } // decFloatVersion\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFloatZero -- set to canonical (integer) zero */\r
+/* */\r
+/* df is the decFloat format number to integer +0 (q=0, c=+0) */\r
+/* returns df */\r
+/* */\r
+/* No error is possible, and no status can be set. */\r
+/* ------------------------------------------------------------------ */\r
+decFloat * decFloatZero(decFloat *df){\r
+ DFWORD(df, 0)=ZEROWORD; // set appropriate top word\r
+ #if DOUBLE || QUAD\r
+ DFWORD(df, 1)=0;\r
+ #if QUAD\r
+ DFWORD(df, 2)=0;\r
+ DFWORD(df, 3)=0;\r
+ #endif\r
+ #endif\r
+ // decFloatShow(df, "zero");\r
+ return df;\r
+ } // decFloatZero\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* Private generic function (not format-specific) for development use */\r
+/* ------------------------------------------------------------------ */\r
+// This is included once only, for all to use\r
+#if QUAD && (DECCHECK || DECTRACE)\r
+ /* ---------------------------------------------------------------- */\r
+ /* decShowNum -- display bcd8 number in debug form */\r
+ /* */\r
+ /* num is the bcdnum to display */\r
+ /* tag is a string to label the display */\r
+ /* ---------------------------------------------------------------- */\r
+ void decShowNum(const bcdnum *num, const char *tag) {\r
+ const char *csign="+"; // sign character\r
+ uByte *ub; // work\r
+ uInt uiwork; // for macros\r
+ if (num->sign==DECFLOAT_Sign) csign="-";\r
+\r
+ printf(">%s> ", tag);\r
+ if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign);\r
+ else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign);\r
+ else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign);\r
+ else { // finite\r
+ char qbuf[10]; // for right-aligned q\r
+ char *c; // work\r
+ const uByte *u; // ..\r
+ Int e=num->exponent; // .. exponent\r
+ strcpy(qbuf, "q=");\r
+ c=&qbuf[2]; // where exponent will go\r
+ // lay out the exponent\r
+ if (e<0) {\r
+ *c++='-'; // add '-'\r
+ e=-e; // uInt, please\r
+ }\r
+ #if DECEMAXD>4\r
+ #error Exponent form is too long for ShowNum to lay out\r
+ #endif\r
+ if (e==0) *c++='0'; // 0-length case\r
+ else if (e<1000) { // 3 (or fewer) digits case\r
+ u=&BIN2BCD8[e*4]; // -> 3 digits + length byte\r
+ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]\r
+ c+=*(u+3); // bump pointer appropriately\r
+ }\r
+ else { // 4-digits\r
+ Int thou=((e>>3)*1049)>>17; // e/1000\r
+ Int rem=e-(1000*thou); // e%1000\r
+ *c++=(char)('0'+(char)thou); // the thousands digit\r
+ u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte\r
+ UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe]\r
+ c+=3; // bump pointer, always 3 digits\r
+ }\r
+ *c='\0'; // add terminator\r
+ printf("%7s c=%s", qbuf, csign);\r
+ }\r
+\r
+ if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) {\r
+ for (ub=num->msd; ub<=num->lsd; ub++) { // coefficient...\r
+ printf("%1x", *ub);\r
+ if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); // 4-space\r
+ }\r
+ }\r
+ printf("\n");\r
+ } // decShowNum\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Context module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises the routines for handling arithmetic */\r
+/* context structures. */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#include <string.h> // for strcmp\r
+#include <stdio.h> // for printf if DECCHECK\r
+#include "decContext.h" // context and base types\r
+#include "decNumberLocal.h" // decNumber local types, etc.\r
+\r
+/* compile-time endian tester [assumes sizeof(Int)>1] */\r
+static const Int mfcone=1; // constant 1\r
+static const Flag *mfctop=(const Flag *)&mfcone; // -> top byte\r
+#define LITEND *mfctop // named flag; 1=little-endian\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* round-for-reround digits */\r
+/* ------------------------------------------------------------------ */\r
+const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* Powers of ten (powers[n]==10**n, 0<=n<=9) */\r
+/* ------------------------------------------------------------------ */\r
+const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000,\r
+ 10000000, 100000000, 1000000000};\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextClearStatus -- clear bits in current status */\r
+/* */\r
+/* context is the context structure to be queried */\r
+/* mask indicates the bits to be cleared (the status bit that */\r
+/* corresponds to each 1 bit in the mask is cleared) */\r
+/* returns context */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decContext *decContextClearStatus(decContext *context, uInt mask) {\r
+ context->status&=~mask;\r
+ return context;\r
+ } // decContextClearStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextDefault -- initialize a context structure */\r
+/* */\r
+/* context is the structure to be initialized */\r
+/* kind selects the required set of default values, one of: */\r
+/* DEC_INIT_BASE -- select ANSI X3-274 defaults */\r
+/* DEC_INIT_DECIMAL32 -- select IEEE 754 defaults, 32-bit */\r
+/* DEC_INIT_DECIMAL64 -- select IEEE 754 defaults, 64-bit */\r
+/* DEC_INIT_DECIMAL128 -- select IEEE 754 defaults, 128-bit */\r
+/* For any other value a valid context is returned, but with */\r
+/* Invalid_operation set in the status field. */\r
+/* returns a context structure with the appropriate initial values. */\r
+/* ------------------------------------------------------------------ */\r
+decContext * decContextDefault(decContext *context, Int kind) {\r
+ // set defaults...\r
+ context->digits=9; // 9 digits\r
+ context->emax=DEC_MAX_EMAX; // 9-digit exponents\r
+ context->emin=DEC_MIN_EMIN; // .. balanced\r
+ context->round=DEC_ROUND_HALF_UP; // 0.5 rises\r
+ context->traps=DEC_Errors; // all but informational\r
+ context->status=0; // cleared\r
+ context->clamp=0; // no clamping\r
+ #if DECSUBSET\r
+ context->extended=0; // cleared\r
+ #endif\r
+ switch (kind) {\r
+ case DEC_INIT_BASE:\r
+ // [use defaults]\r
+ break;\r
+ case DEC_INIT_DECIMAL32:\r
+ context->digits=7; // digits\r
+ context->emax=96; // Emax\r
+ context->emin=-95; // Emin\r
+ context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even\r
+ context->traps=0; // no traps set\r
+ context->clamp=1; // clamp exponents\r
+ #if DECSUBSET\r
+ context->extended=1; // set\r
+ #endif\r
+ break;\r
+ case DEC_INIT_DECIMAL64:\r
+ context->digits=16; // digits\r
+ context->emax=384; // Emax\r
+ context->emin=-383; // Emin\r
+ context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even\r
+ context->traps=0; // no traps set\r
+ context->clamp=1; // clamp exponents\r
+ #if DECSUBSET\r
+ context->extended=1; // set\r
+ #endif\r
+ break;\r
+ case DEC_INIT_DECIMAL128:\r
+ context->digits=34; // digits\r
+ context->emax=6144; // Emax\r
+ context->emin=-6143; // Emin\r
+ context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even\r
+ context->traps=0; // no traps set\r
+ context->clamp=1; // clamp exponents\r
+ #if DECSUBSET\r
+ context->extended=1; // set\r
+ #endif\r
+ break;\r
+\r
+ default: // invalid Kind\r
+ // use defaults, and ..\r
+ decContextSetStatus(context, DEC_Invalid_operation); // trap\r
+ }\r
+\r
+ return context;} // decContextDefault\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextGetRounding -- return current rounding mode */\r
+/* */\r
+/* context is the context structure to be queried */\r
+/* returns the rounding mode */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+enum rounding decContextGetRounding(decContext *context) {\r
+ return context->round;\r
+ } // decContextGetRounding\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextGetStatus -- return current status */\r
+/* */\r
+/* context is the context structure to be queried */\r
+/* returns status */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decContextGetStatus(decContext *context) {\r
+ return context->status;\r
+ } // decContextGetStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextRestoreStatus -- restore bits in current status */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* newstatus is the source for the bits to be restored */\r
+/* mask indicates the bits to be restored (the status bit that */\r
+/* corresponds to each 1 bit in the mask is set to the value of */\r
+/* the correspnding bit in newstatus) */\r
+/* returns context */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decContext *decContextRestoreStatus(decContext *context,\r
+ uInt newstatus, uInt mask) {\r
+ context->status&=~mask; // clear the selected bits\r
+ context->status|=(mask&newstatus); // or in the new bits\r
+ return context;\r
+ } // decContextRestoreStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextSaveStatus -- save bits in current status */\r
+/* */\r
+/* context is the context structure to be queried */\r
+/* mask indicates the bits to be saved (the status bits that */\r
+/* correspond to each 1 bit in the mask are saved) */\r
+/* returns the AND of the mask and the current status */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decContextSaveStatus(decContext *context, uInt mask) {\r
+ return context->status&mask;\r
+ } // decContextSaveStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextSetRounding -- set current rounding mode */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* newround is the value which will replace the current mode */\r
+/* returns context */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decContext *decContextSetRounding(decContext *context,\r
+ enum rounding newround) {\r
+ context->round=newround;\r
+ return context;\r
+ } // decContextSetRounding\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextSetStatus -- set status and raise trap if appropriate */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* status is the DEC_ exception code */\r
+/* returns the context structure */\r
+/* */\r
+/* Control may never return from this routine, if there is a signal */\r
+/* handler and it takes a long jump. */\r
+/* ------------------------------------------------------------------ */\r
+decContext * decContextSetStatus(decContext *context, uInt status) {\r
+ context->status|=status;\r
+ if (status & context->traps) raise(SIGFPE);\r
+ return context;} // decContextSetStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextSetStatusFromString -- set status from a string + trap */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* string is a string exactly equal to one that might be returned */\r
+/* by decContextStatusToString */\r
+/* */\r
+/* The status bit corresponding to the string is set, and a trap */\r
+/* is raised if appropriate. */\r
+/* */\r
+/* returns the context structure, unless the string is equal to */\r
+/* DEC_Condition_MU or is not recognized. In these cases NULL is */\r
+/* returned. */\r
+/* ------------------------------------------------------------------ */\r
+decContext * decContextSetStatusFromString(decContext *context,\r
+ const char *string) {\r
+ if (strcmp(string, DEC_Condition_CS)==0)\r
+ return decContextSetStatus(context, DEC_Conversion_syntax);\r
+ if (strcmp(string, DEC_Condition_DZ)==0)\r
+ return decContextSetStatus(context, DEC_Division_by_zero);\r
+ if (strcmp(string, DEC_Condition_DI)==0)\r
+ return decContextSetStatus(context, DEC_Division_impossible);\r
+ if (strcmp(string, DEC_Condition_DU)==0)\r
+ return decContextSetStatus(context, DEC_Division_undefined);\r
+ if (strcmp(string, DEC_Condition_IE)==0)\r
+ return decContextSetStatus(context, DEC_Inexact);\r
+ if (strcmp(string, DEC_Condition_IS)==0)\r
+ return decContextSetStatus(context, DEC_Insufficient_storage);\r
+ if (strcmp(string, DEC_Condition_IC)==0)\r
+ return decContextSetStatus(context, DEC_Invalid_context);\r
+ if (strcmp(string, DEC_Condition_IO)==0)\r
+ return decContextSetStatus(context, DEC_Invalid_operation);\r
+ #if DECSUBSET\r
+ if (strcmp(string, DEC_Condition_LD)==0)\r
+ return decContextSetStatus(context, DEC_Lost_digits);\r
+ #endif\r
+ if (strcmp(string, DEC_Condition_OV)==0)\r
+ return decContextSetStatus(context, DEC_Overflow);\r
+ if (strcmp(string, DEC_Condition_PA)==0)\r
+ return decContextSetStatus(context, DEC_Clamped);\r
+ if (strcmp(string, DEC_Condition_RO)==0)\r
+ return decContextSetStatus(context, DEC_Rounded);\r
+ if (strcmp(string, DEC_Condition_SU)==0)\r
+ return decContextSetStatus(context, DEC_Subnormal);\r
+ if (strcmp(string, DEC_Condition_UN)==0)\r
+ return decContextSetStatus(context, DEC_Underflow);\r
+ if (strcmp(string, DEC_Condition_ZE)==0)\r
+ return context;\r
+ return NULL; // Multiple status, or unknown\r
+ } // decContextSetStatusFromString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextSetStatusFromStringQuiet -- set status from a string */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* string is a string exactly equal to one that might be returned */\r
+/* by decContextStatusToString */\r
+/* */\r
+/* The status bit corresponding to the string is set; no trap is */\r
+/* raised. */\r
+/* */\r
+/* returns the context structure, unless the string is equal to */\r
+/* DEC_Condition_MU or is not recognized. In these cases NULL is */\r
+/* returned. */\r
+/* ------------------------------------------------------------------ */\r
+decContext * decContextSetStatusFromStringQuiet(decContext *context,\r
+ const char *string) {\r
+ if (strcmp(string, DEC_Condition_CS)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Conversion_syntax);\r
+ if (strcmp(string, DEC_Condition_DZ)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Division_by_zero);\r
+ if (strcmp(string, DEC_Condition_DI)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Division_impossible);\r
+ if (strcmp(string, DEC_Condition_DU)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Division_undefined);\r
+ if (strcmp(string, DEC_Condition_IE)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Inexact);\r
+ if (strcmp(string, DEC_Condition_IS)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Insufficient_storage);\r
+ if (strcmp(string, DEC_Condition_IC)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Invalid_context);\r
+ if (strcmp(string, DEC_Condition_IO)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Invalid_operation);\r
+ #if DECSUBSET\r
+ if (strcmp(string, DEC_Condition_LD)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Lost_digits);\r
+ #endif\r
+ if (strcmp(string, DEC_Condition_OV)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Overflow);\r
+ if (strcmp(string, DEC_Condition_PA)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Clamped);\r
+ if (strcmp(string, DEC_Condition_RO)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Rounded);\r
+ if (strcmp(string, DEC_Condition_SU)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Subnormal);\r
+ if (strcmp(string, DEC_Condition_UN)==0)\r
+ return decContextSetStatusQuiet(context, DEC_Underflow);\r
+ if (strcmp(string, DEC_Condition_ZE)==0)\r
+ return context;\r
+ return NULL; // Multiple status, or unknown\r
+ } // decContextSetStatusFromStringQuiet\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextSetStatusQuiet -- set status without trap */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* status is the DEC_ exception code */\r
+/* returns the context structure */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decContext * decContextSetStatusQuiet(decContext *context, uInt status) {\r
+ context->status|=status;\r
+ return context;} // decContextSetStatusQuiet\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextStatusToString -- convert status flags to a string */\r
+/* */\r
+/* context is a context with valid status field */\r
+/* */\r
+/* returns a constant string describing the condition. If multiple */\r
+/* (or no) flags are set, a generic constant message is returned. */\r
+/* ------------------------------------------------------------------ */\r
+const char *decContextStatusToString(const decContext *context) {\r
+ Int status=context->status;\r
+\r
+ // test the five IEEE first, as some of the others are ambiguous when\r
+ // DECEXTFLAG=0\r
+ if (status==DEC_Invalid_operation ) return DEC_Condition_IO;\r
+ if (status==DEC_Division_by_zero ) return DEC_Condition_DZ;\r
+ if (status==DEC_Overflow ) return DEC_Condition_OV;\r
+ if (status==DEC_Underflow ) return DEC_Condition_UN;\r
+ if (status==DEC_Inexact ) return DEC_Condition_IE;\r
+\r
+ if (status==DEC_Division_impossible ) return DEC_Condition_DI;\r
+ if (status==DEC_Division_undefined ) return DEC_Condition_DU;\r
+ if (status==DEC_Rounded ) return DEC_Condition_RO;\r
+ if (status==DEC_Clamped ) return DEC_Condition_PA;\r
+ if (status==DEC_Subnormal ) return DEC_Condition_SU;\r
+ if (status==DEC_Conversion_syntax ) return DEC_Condition_CS;\r
+ if (status==DEC_Insufficient_storage ) return DEC_Condition_IS;\r
+ if (status==DEC_Invalid_context ) return DEC_Condition_IC;\r
+ #if DECSUBSET\r
+ if (status==DEC_Lost_digits ) return DEC_Condition_LD;\r
+ #endif\r
+ if (status==0 ) return DEC_Condition_ZE;\r
+ return DEC_Condition_MU; // Multiple errors\r
+ } // decContextStatusToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextTestEndian -- test whether DECLITEND is set correctly */\r
+/* */\r
+/* quiet is 1 to suppress message; 0 otherwise */\r
+/* returns 0 if DECLITEND is correct */\r
+/* 1 if DECLITEND is incorrect and should be 1 */\r
+/* -1 if DECLITEND is incorrect and should be 0 */\r
+/* */\r
+/* A message is displayed if the return value is not 0 and quiet==0. */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+Int decContextTestEndian(Flag quiet) {\r
+ Int res=0; // optimist\r
+ uInt dle=(uInt)DECLITEND; // unsign\r
+ if (dle>1) dle=1; // ensure 0 or 1\r
+\r
+ if (LITEND!=DECLITEND) {\r
+ if (!quiet) { // always refer to this\r
+ #if DECPRINT\r
+ const char *adj;\r
+ if (LITEND) adj="little";\r
+ else adj="big";\r
+ printf("Warning: DECLITEND is set to %d, but this computer appears to be %s-endian\n",\r
+ DECLITEND, adj);\r
+ #endif\r
+ }\r
+ res=(Int)LITEND-dle;\r
+ }\r
+ return res;\r
+ } // decContextTestEndian\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextTestSavedStatus -- test bits in saved status */\r
+/* */\r
+/* oldstatus is the status word to be tested */\r
+/* mask indicates the bits to be tested (the oldstatus bits that */\r
+/* correspond to each 1 bit in the mask are tested) */\r
+/* returns 1 if any of the tested bits are 1, or 0 otherwise */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decContextTestSavedStatus(uInt oldstatus, uInt mask) {\r
+ return (oldstatus&mask)!=0;\r
+ } // decContextTestSavedStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextTestStatus -- test bits in current status */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* mask indicates the bits to be tested (the status bits that */\r
+/* correspond to each 1 bit in the mask are tested) */\r
+/* returns 1 if any of the tested bits are 1, or 0 otherwise */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decContextTestStatus(decContext *context, uInt mask) {\r
+ return (context->status&mask)!=0;\r
+ } // decContextTestStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decContextZeroStatus -- clear all status bits */\r
+/* */\r
+/* context is the context structure to be updated */\r
+/* returns context */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decContext *decContextZeroStatus(decContext *context) {\r
+ context->status=0;\r
+ return context;\r
+ } // decContextZeroStatus\r
+\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Context module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* */\r
+/* Context variables must always have valid values: */\r
+/* */\r
+/* status -- [any bits may be cleared, but not set, by user] */\r
+/* round -- must be one of the enumerated rounding modes */\r
+/* */\r
+/* The following variables are implied for fixed size formats (i.e., */\r
+/* they are ignored) but should still be set correctly in case used */\r
+/* with decNumber functions: */\r
+/* */\r
+/* clamp -- must be either 0 or 1 */\r
+/* digits -- must be in the range 1 through 999999999 */\r
+/* emax -- must be in the range 0 through 999999999 */\r
+/* emin -- must be in the range 0 through -999999999 */\r
+/* extended -- must be either 0 or 1 [present only if DECSUBSET] */\r
+/* traps -- only defined bits may be set */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECCONTEXT)\r
+ #define DECCONTEXT\r
+ #define DECCNAME "decContext" /* Short name */\r
+ #define DECCFULLNAME "Decimal Context Descriptor" /* Verbose name */\r
+ #define DECCAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ #if !defined(int32_t)\r
+ #include <stdint.h> /* C99 standard integers */\r
+ #endif\r
+ #include <stdio.h> /* for printf, etc. */\r
+ #include <signal.h> /* for traps */\r
+\r
+ /* Extended flags setting -- set this to 0 to use only IEEE flags */\r
+ #if !defined(DECEXTFLAG)\r
+ #define DECEXTFLAG 1 /* 1=enable extended flags */\r
+ #endif\r
+\r
+ /* Conditional code flag -- set this to 0 for best performance */\r
+ #if !defined(DECSUBSET)\r
+ #define DECSUBSET 0 /* 1=enable subset arithmetic */\r
+ #endif\r
+\r
+ /* Context for operations, with associated constants */\r
+ enum rounding {\r
+ DEC_ROUND_CEILING, /* round towards +infinity */\r
+ DEC_ROUND_UP, /* round away from 0 */\r
+ DEC_ROUND_HALF_UP, /* 0.5 rounds up */\r
+ DEC_ROUND_HALF_EVEN, /* 0.5 rounds to nearest even */\r
+ DEC_ROUND_HALF_DOWN, /* 0.5 rounds down */\r
+ DEC_ROUND_DOWN, /* round towards 0 (truncate) */\r
+ DEC_ROUND_FLOOR, /* round towards -infinity */\r
+ DEC_ROUND_05UP, /* round for reround */\r
+ DEC_ROUND_MAX /* enum must be less than this */\r
+ };\r
+ #define DEC_ROUND_DEFAULT DEC_ROUND_HALF_EVEN;\r
+\r
+ typedef struct {\r
+ int32_t digits; /* working precision */\r
+ int32_t emax; /* maximum positive exponent */\r
+ int32_t emin; /* minimum negative exponent */\r
+ enum rounding round; /* rounding mode */\r
+ uint32_t traps; /* trap-enabler flags */\r
+ uint32_t status; /* status flags */\r
+ uint8_t clamp; /* flag: apply IEEE exponent clamp */\r
+ #if DECSUBSET\r
+ uint8_t extended; /* flag: special-values allowed */\r
+ #endif\r
+ } decContext;\r
+\r
+ /* Maxima and Minima for context settings */\r
+ #define DEC_MAX_DIGITS 999999999\r
+ #define DEC_MIN_DIGITS 1\r
+ #define DEC_MAX_EMAX 999999999\r
+ #define DEC_MIN_EMAX 0\r
+ #define DEC_MAX_EMIN 0\r
+ #define DEC_MIN_EMIN -999999999\r
+ #define DEC_MAX_MATH 999999 /* max emax, etc., for math funcs. */\r
+\r
+ /* Classifications for decimal numbers, aligned with 754 (note that */\r
+ /* 'normal' and 'subnormal' are meaningful only with a decContext */\r
+ /* or a fixed size format). */\r
+ enum decClass {\r
+ DEC_CLASS_SNAN,\r
+ DEC_CLASS_QNAN,\r
+ DEC_CLASS_NEG_INF,\r
+ DEC_CLASS_NEG_NORMAL,\r
+ DEC_CLASS_NEG_SUBNORMAL,\r
+ DEC_CLASS_NEG_ZERO,\r
+ DEC_CLASS_POS_ZERO,\r
+ DEC_CLASS_POS_SUBNORMAL,\r
+ DEC_CLASS_POS_NORMAL,\r
+ DEC_CLASS_POS_INF\r
+ };\r
+ /* Strings for the decClasses */\r
+ #define DEC_ClassString_SN "sNaN"\r
+ #define DEC_ClassString_QN "NaN"\r
+ #define DEC_ClassString_NI "-Infinity"\r
+ #define DEC_ClassString_NN "-Normal"\r
+ #define DEC_ClassString_NS "-Subnormal"\r
+ #define DEC_ClassString_NZ "-Zero"\r
+ #define DEC_ClassString_PZ "+Zero"\r
+ #define DEC_ClassString_PS "+Subnormal"\r
+ #define DEC_ClassString_PN "+Normal"\r
+ #define DEC_ClassString_PI "+Infinity"\r
+ #define DEC_ClassString_UN "Invalid"\r
+\r
+ /* Trap-enabler and Status flags (exceptional conditions), and */\r
+ /* their names. The top byte is reserved for internal use */\r
+ #if DECEXTFLAG\r
+ /* Extended flags */\r
+ #define DEC_Conversion_syntax 0x00000001\r
+ #define DEC_Division_by_zero 0x00000002\r
+ #define DEC_Division_impossible 0x00000004\r
+ #define DEC_Division_undefined 0x00000008\r
+ #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */\r
+ #define DEC_Inexact 0x00000020\r
+ #define DEC_Invalid_context 0x00000040\r
+ #define DEC_Invalid_operation 0x00000080\r
+ #if DECSUBSET\r
+ #define DEC_Lost_digits 0x00000100\r
+ #endif\r
+ #define DEC_Overflow 0x00000200\r
+ #define DEC_Clamped 0x00000400\r
+ #define DEC_Rounded 0x00000800\r
+ #define DEC_Subnormal 0x00001000\r
+ #define DEC_Underflow 0x00002000\r
+ #else\r
+ /* IEEE flags only */\r
+ #define DEC_Conversion_syntax 0x00000010\r
+ #define DEC_Division_by_zero 0x00000002\r
+ #define DEC_Division_impossible 0x00000010\r
+ #define DEC_Division_undefined 0x00000010\r
+ #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */\r
+ #define DEC_Inexact 0x00000001\r
+ #define DEC_Invalid_context 0x00000010\r
+ #define DEC_Invalid_operation 0x00000010\r
+ #if DECSUBSET\r
+ #define DEC_Lost_digits 0x00000000\r
+ #endif\r
+ #define DEC_Overflow 0x00000008\r
+ #define DEC_Clamped 0x00000000\r
+ #define DEC_Rounded 0x00000000\r
+ #define DEC_Subnormal 0x00000000\r
+ #define DEC_Underflow 0x00000004\r
+ #endif\r
+\r
+ /* IEEE 754 groupings for the flags */\r
+ /* [DEC_Clamped, DEC_Lost_digits, DEC_Rounded, and DEC_Subnormal */\r
+ /* are not in IEEE 754] */\r
+ #define DEC_IEEE_754_Division_by_zero (DEC_Division_by_zero)\r
+ #if DECSUBSET\r
+ #define DEC_IEEE_754_Inexact (DEC_Inexact | DEC_Lost_digits)\r
+ #else\r
+ #define DEC_IEEE_754_Inexact (DEC_Inexact)\r
+ #endif\r
+ #define DEC_IEEE_754_Invalid_operation (DEC_Conversion_syntax | \\r
+ DEC_Division_impossible | \\r
+ DEC_Division_undefined | \\r
+ DEC_Insufficient_storage | \\r
+ DEC_Invalid_context | \\r
+ DEC_Invalid_operation)\r
+ #define DEC_IEEE_754_Overflow (DEC_Overflow)\r
+ #define DEC_IEEE_754_Underflow (DEC_Underflow)\r
+\r
+ /* flags which are normally errors (result is qNaN, infinite, or 0) */\r
+ #define DEC_Errors (DEC_IEEE_754_Division_by_zero | \\r
+ DEC_IEEE_754_Invalid_operation | \\r
+ DEC_IEEE_754_Overflow | DEC_IEEE_754_Underflow)\r
+ /* flags which cause a result to become qNaN */\r
+ #define DEC_NaNs DEC_IEEE_754_Invalid_operation\r
+\r
+ /* flags which are normally for information only (finite results) */\r
+ #if DECSUBSET\r
+ #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact \\r
+ | DEC_Lost_digits)\r
+ #else\r
+ #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact)\r
+ #endif\r
+\r
+ /* IEEE 854 names (for compatibility with older decNumber versions) */\r
+ #define DEC_IEEE_854_Division_by_zero DEC_IEEE_754_Division_by_zero\r
+ #define DEC_IEEE_854_Inexact DEC_IEEE_754_Inexact\r
+ #define DEC_IEEE_854_Invalid_operation DEC_IEEE_754_Invalid_operation\r
+ #define DEC_IEEE_854_Overflow DEC_IEEE_754_Overflow\r
+ #define DEC_IEEE_854_Underflow DEC_IEEE_754_Underflow\r
+\r
+ /* Name strings for the exceptional conditions */\r
+ #define DEC_Condition_CS "Conversion syntax"\r
+ #define DEC_Condition_DZ "Division by zero"\r
+ #define DEC_Condition_DI "Division impossible"\r
+ #define DEC_Condition_DU "Division undefined"\r
+ #define DEC_Condition_IE "Inexact"\r
+ #define DEC_Condition_IS "Insufficient storage"\r
+ #define DEC_Condition_IC "Invalid context"\r
+ #define DEC_Condition_IO "Invalid operation"\r
+ #if DECSUBSET\r
+ #define DEC_Condition_LD "Lost digits"\r
+ #endif\r
+ #define DEC_Condition_OV "Overflow"\r
+ #define DEC_Condition_PA "Clamped"\r
+ #define DEC_Condition_RO "Rounded"\r
+ #define DEC_Condition_SU "Subnormal"\r
+ #define DEC_Condition_UN "Underflow"\r
+ #define DEC_Condition_ZE "No status"\r
+ #define DEC_Condition_MU "Multiple status"\r
+ #define DEC_Condition_Length 21 /* length of the longest string, */\r
+ /* including terminator */\r
+\r
+ /* Initialization descriptors, used by decContextDefault */\r
+ #define DEC_INIT_BASE 0\r
+ #define DEC_INIT_DECIMAL32 32\r
+ #define DEC_INIT_DECIMAL64 64\r
+ #define DEC_INIT_DECIMAL128 128\r
+ /* Synonyms */\r
+ #define DEC_INIT_DECSINGLE DEC_INIT_DECIMAL32\r
+ #define DEC_INIT_DECDOUBLE DEC_INIT_DECIMAL64\r
+ #define DEC_INIT_DECQUAD DEC_INIT_DECIMAL128\r
+\r
+ /* decContext routines */\r
+ extern decContext * decContextClearStatus(decContext *, uint32_t);\r
+ extern decContext * decContextDefault(decContext *, int32_t);\r
+ extern enum rounding decContextGetRounding(decContext *);\r
+ extern uint32_t decContextGetStatus(decContext *);\r
+ extern decContext * decContextRestoreStatus(decContext *, uint32_t, uint32_t);\r
+ extern uint32_t decContextSaveStatus(decContext *, uint32_t);\r
+ extern decContext * decContextSetRounding(decContext *, enum rounding);\r
+ extern decContext * decContextSetStatus(decContext *, uint32_t);\r
+ extern decContext * decContextSetStatusFromString(decContext *, const char *);\r
+ extern decContext * decContextSetStatusFromStringQuiet(decContext *, const char *);\r
+ extern decContext * decContextSetStatusQuiet(decContext *, uint32_t);\r
+ extern const char * decContextStatusToString(const decContext *);\r
+ extern int32_t decContextTestEndian(uint8_t);\r
+ extern uint32_t decContextTestSavedStatus(uint32_t, uint32_t);\r
+ extern uint32_t decContextTestStatus(decContext *, uint32_t);\r
+ extern decContext * decContextZeroStatus(decContext *);\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------------ */\r
+/* Binary Coded Decimal and Densely Packed Decimal conversion lookup tables */\r
+/* [Automatically generated -- do not edit. 2008.06.21] */\r
+/* ------------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */\r
+/* ------------------------------------------------------------------------ */\r
+/* For details, see DPDecimal.html on the General Decimal Arithmetic page. */\r
+/* */\r
+/* This include file defines several DPD and BCD conversion tables: */\r
+/* */\r
+/* uint16_t BCD2DPD[2458]; -- BCD -> DPD (0x999 => 2457) */\r
+/* uint16_t BIN2DPD[1000]; -- Bin -> DPD (999 => 2457) */\r
+/* uint8_t BIN2CHAR[4001]; -- Bin -> CHAR (999 => '\3' '9' '9' '9') */\r
+/* uint8_t BIN2BCD8[4000]; -- Bin -> bytes (999 => 9 9 9 3) */\r
+/* uint16_t DPD2BCD[1024]; -- DPD -> BCD (0x3FF => 0x999) */\r
+/* uint16_t DPD2BIN[1024]; -- DPD -> BIN (0x3FF => 999) */\r
+/* uint32_t DPD2BINK[1024]; -- DPD -> BIN * 1000 (0x3FF => 999000) */\r
+/* uint32_t DPD2BINM[1024]; -- DPD -> BIN * 1E+6 (0x3FF => 999000000) */\r
+/* uint8_t DPD2BCD8[4096]; -- DPD -> bytes (x3FF => 9 9 9 3) */\r
+/* */\r
+/* In all cases the result (10 bits or 12 bits, or binary) is right-aligned */\r
+/* in the table entry. BIN2CHAR entries are a single byte length (0 for */\r
+/* value 0) followed by three digit characters; a trailing terminator is */\r
+/* included to allow 4-char moves always. BIN2BCD8 and DPD2BCD8 entries */\r
+/* are similar with the three BCD8 digits followed by a one-byte length */\r
+/* (again, length=0 for value 0). */\r
+/* */\r
+/* To use a table, its name, prefixed with DEC_, must be defined with a */\r
+/* value of 1 before this header file is included. For example: */\r
+/* #define DEC_BCD2DPD 1 */\r
+/* This mechanism allows software to only include tables that are needed. */\r
+/* ------------------------------------------------------------------------ */\r
+ \r
+#if defined(DEC_BCD2DPD) && DEC_BCD2DPD==1 && !defined(DECBCD2DPD)\r
+#define DECBCD2DPD\r
+ \r
+const uint16_t BCD2DPD[2458]={ 0, 1, 2, 3, 4, 5, 6, 7, \r
+ 8, 9, 0, 0, 0, 0, 0, 0, 16, 17, 18, 19, 20, \r
+ 21, 22, 23, 24, 25, 0, 0, 0, 0, 0, 0, 32, 33, \r
+ 34, 35, 36, 37, 38, 39, 40, 41, 0, 0, 0, 0, 0, \r
+ 0, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 0, 0, \r
+ 0, 0, 0, 0, 64, 65, 66, 67, 68, 69, 70, 71, 72, \r
+ 73, 0, 0, 0, 0, 0, 0, 80, 81, 82, 83, 84, 85, \r
+ 86, 87, 88, 89, 0, 0, 0, 0, 0, 0, 96, 97, 98, \r
+ 99, 100, 101, 102, 103, 104, 105, 0, 0, 0, 0, 0, 0, \r
+ 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 0, 0, 0, \r
+ 0, 0, 0, 10, 11, 42, 43, 74, 75, 106, 107, 78, 79, \r
+ 0, 0, 0, 0, 0, 0, 26, 27, 58, 59, 90, 91, 122, \r
+ 123, 94, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 0, 0, \r
+ 0, 0, 0, 0, 144, 145, 146, 147, 148, 149, 150, 151, 152, \r
+ 153, 0, 0, 0, 0, 0, 0, 160, 161, 162, 163, 164, 165, \r
+ 166, 167, 168, 169, 0, 0, 0, 0, 0, 0, 176, 177, 178, \r
+ 179, 180, 181, 182, 183, 184, 185, 0, 0, 0, 0, 0, 0, \r
+ 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 0, 0, 0, \r
+ 0, 0, 0, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, \r
+ 0, 0, 0, 0, 0, 0, 224, 225, 226, 227, 228, 229, 230, \r
+ 231, 232, 233, 0, 0, 0, 0, 0, 0, 240, 241, 242, 243, \r
+ 244, 245, 246, 247, 248, 249, 0, 0, 0, 0, 0, 0, 138, \r
+ 139, 170, 171, 202, 203, 234, 235, 206, 207, 0, 0, 0, 0, \r
+ 0, 0, 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 257, 258, \r
+ 259, 260, 261, 262, 263, 264, 265, 0, 0, 0, 0, 0, 0, \r
+ 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 0, 0, 0, \r
+ 0, 0, 0, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, \r
+ 0, 0, 0, 0, 0, 0, 304, 305, 306, 307, 308, 309, 310, \r
+ 311, 312, 313, 0, 0, 0, 0, 0, 0, 320, 321, 322, 323, \r
+ 324, 325, 326, 327, 328, 329, 0, 0, 0, 0, 0, 0, 336, \r
+ 337, 338, 339, 340, 341, 342, 343, 344, 345, 0, 0, 0, 0, \r
+ 0, 0, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 0, \r
+ 0, 0, 0, 0, 0, 368, 369, 370, 371, 372, 373, 374, 375, \r
+ 376, 377, 0, 0, 0, 0, 0, 0, 266, 267, 298, 299, 330, \r
+ 331, 362, 363, 334, 335, 0, 0, 0, 0, 0, 0, 282, 283, \r
+ 314, 315, 346, 347, 378, 379, 350, 351, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 384, 385, 386, 387, 388, 389, 390, \r
+ 391, 392, 393, 0, 0, 0, 0, 0, 0, 400, 401, 402, 403, \r
+ 404, 405, 406, 407, 408, 409, 0, 0, 0, 0, 0, 0, 416, \r
+ 417, 418, 419, 420, 421, 422, 423, 424, 425, 0, 0, 0, 0, \r
+ 0, 0, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 0, \r
+ 0, 0, 0, 0, 0, 448, 449, 450, 451, 452, 453, 454, 455, \r
+ 456, 457, 0, 0, 0, 0, 0, 0, 464, 465, 466, 467, 468, \r
+ 469, 470, 471, 472, 473, 0, 0, 0, 0, 0, 0, 480, 481, \r
+ 482, 483, 484, 485, 486, 487, 488, 489, 0, 0, 0, 0, 0, \r
+ 0, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 0, 0, \r
+ 0, 0, 0, 0, 394, 395, 426, 427, 458, 459, 490, 491, 462, \r
+ 463, 0, 0, 0, 0, 0, 0, 410, 411, 442, 443, 474, 475, \r
+ 506, 507, 478, 479, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 0, \r
+ 0, 0, 0, 0, 0, 528, 529, 530, 531, 532, 533, 534, 535, \r
+ 536, 537, 0, 0, 0, 0, 0, 0, 544, 545, 546, 547, 548, \r
+ 549, 550, 551, 552, 553, 0, 0, 0, 0, 0, 0, 560, 561, \r
+ 562, 563, 564, 565, 566, 567, 568, 569, 0, 0, 0, 0, 0, \r
+ 0, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 0, 0, \r
+ 0, 0, 0, 0, 592, 593, 594, 595, 596, 597, 598, 599, 600, \r
+ 601, 0, 0, 0, 0, 0, 0, 608, 609, 610, 611, 612, 613, \r
+ 614, 615, 616, 617, 0, 0, 0, 0, 0, 0, 624, 625, 626, \r
+ 627, 628, 629, 630, 631, 632, 633, 0, 0, 0, 0, 0, 0, \r
+ 522, 523, 554, 555, 586, 587, 618, 619, 590, 591, 0, 0, 0, \r
+ 0, 0, 0, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 640, 641, \r
+ 642, 643, 644, 645, 646, 647, 648, 649, 0, 0, 0, 0, 0, \r
+ 0, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 0, 0, \r
+ 0, 0, 0, 0, 672, 673, 674, 675, 676, 677, 678, 679, 680, \r
+ 681, 0, 0, 0, 0, 0, 0, 688, 689, 690, 691, 692, 693, \r
+ 694, 695, 696, 697, 0, 0, 0, 0, 0, 0, 704, 705, 706, \r
+ 707, 708, 709, 710, 711, 712, 713, 0, 0, 0, 0, 0, 0, \r
+ 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 0, 0, 0, \r
+ 0, 0, 0, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, \r
+ 0, 0, 0, 0, 0, 0, 752, 753, 754, 755, 756, 757, 758, \r
+ 759, 760, 761, 0, 0, 0, 0, 0, 0, 650, 651, 682, 683, \r
+ 714, 715, 746, 747, 718, 719, 0, 0, 0, 0, 0, 0, 666, \r
+ 667, 698, 699, 730, 731, 762, 763, 734, 735, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 768, 769, 770, 771, 772, 773, \r
+ 774, 775, 776, 777, 0, 0, 0, 0, 0, 0, 784, 785, 786, \r
+ 787, 788, 789, 790, 791, 792, 793, 0, 0, 0, 0, 0, 0, \r
+ 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 0, 0, 0, \r
+ 0, 0, 0, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, \r
+ 0, 0, 0, 0, 0, 0, 832, 833, 834, 835, 836, 837, 838, \r
+ 839, 840, 841, 0, 0, 0, 0, 0, 0, 848, 849, 850, 851, \r
+ 852, 853, 854, 855, 856, 857, 0, 0, 0, 0, 0, 0, 864, \r
+ 865, 866, 867, 868, 869, 870, 871, 872, 873, 0, 0, 0, 0, \r
+ 0, 0, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 0, \r
+ 0, 0, 0, 0, 0, 778, 779, 810, 811, 842, 843, 874, 875, \r
+ 846, 847, 0, 0, 0, 0, 0, 0, 794, 795, 826, 827, 858, \r
+ 859, 890, 891, 862, 863, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, \r
+ 0, 0, 0, 0, 0, 0, 912, 913, 914, 915, 916, 917, 918, \r
+ 919, 920, 921, 0, 0, 0, 0, 0, 0, 928, 929, 930, 931, \r
+ 932, 933, 934, 935, 936, 937, 0, 0, 0, 0, 0, 0, 944, \r
+ 945, 946, 947, 948, 949, 950, 951, 952, 953, 0, 0, 0, 0, \r
+ 0, 0, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 0, \r
+ 0, 0, 0, 0, 0, 976, 977, 978, 979, 980, 981, 982, 983, \r
+ 984, 985, 0, 0, 0, 0, 0, 0, 992, 993, 994, 995, 996, \r
+ 997, 998, 999, 1000, 1001, 0, 0, 0, 0, 0, 0, 1008, 1009, \r
+ 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 0, 0, 0, 0, 0, \r
+ 0, 906, 907, 938, 939, 970, 971, 1002, 1003, 974, 975, 0, 0, \r
+ 0, 0, 0, 0, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, \r
+ 991, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, \r
+ 13, 268, 269, 524, 525, 780, 781, 46, 47, 0, 0, 0, 0, \r
+ 0, 0, 28, 29, 284, 285, 540, 541, 796, 797, 62, 63, 0, \r
+ 0, 0, 0, 0, 0, 44, 45, 300, 301, 556, 557, 812, 813, \r
+ 302, 303, 0, 0, 0, 0, 0, 0, 60, 61, 316, 317, 572, \r
+ 573, 828, 829, 318, 319, 0, 0, 0, 0, 0, 0, 76, 77, \r
+ 332, 333, 588, 589, 844, 845, 558, 559, 0, 0, 0, 0, 0, \r
+ 0, 92, 93, 348, 349, 604, 605, 860, 861, 574, 575, 0, 0, \r
+ 0, 0, 0, 0, 108, 109, 364, 365, 620, 621, 876, 877, 814, \r
+ 815, 0, 0, 0, 0, 0, 0, 124, 125, 380, 381, 636, 637, \r
+ 892, 893, 830, 831, 0, 0, 0, 0, 0, 0, 14, 15, 270, \r
+ 271, 526, 527, 782, 783, 110, 111, 0, 0, 0, 0, 0, 0, \r
+ 30, 31, 286, 287, 542, 543, 798, 799, 126, 127, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \r
+ 0, 0, 0, 0, 0, 0, 0, 0, 140, 141, 396, 397, 652, \r
+ 653, 908, 909, 174, 175, 0, 0, 0, 0, 0, 0, 156, 157, \r
+ 412, 413, 668, 669, 924, 925, 190, 191, 0, 0, 0, 0, 0, \r
+ 0, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 0, 0, \r
+ 0, 0, 0, 0, 188, 189, 444, 445, 700, 701, 956, 957, 446, \r
+ 447, 0, 0, 0, 0, 0, 0, 204, 205, 460, 461, 716, 717, \r
+ 972, 973, 686, 687, 0, 0, 0, 0, 0, 0, 220, 221, 476, \r
+ 477, 732, 733, 988, 989, 702, 703, 0, 0, 0, 0, 0, 0, \r
+ 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, 0, 0, 0, \r
+ 0, 0, 0, 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, \r
+ 0, 0, 0, 0, 0, 0, 142, 143, 398, 399, 654, 655, 910, \r
+ 911, 238, 239, 0, 0, 0, 0, 0, 0, 158, 159, 414, 415, \r
+ 670, 671, 926, 927, 254, 255};\r
+#endif\r
+ \r
+#if defined(DEC_DPD2BCD) && DEC_DPD2BCD==1 && !defined(DECDPD2BCD)\r
+#define DECDPD2BCD\r
+ \r
+const uint16_t DPD2BCD[1024]={ 0, 1, 2, 3, 4, 5, 6, 7, \r
+ 8, 9, 128, 129, 2048, 2049, 2176, 2177, 16, 17, 18, 19, 20, \r
+ 21, 22, 23, 24, 25, 144, 145, 2064, 2065, 2192, 2193, 32, 33, \r
+ 34, 35, 36, 37, 38, 39, 40, 41, 130, 131, 2080, 2081, 2056, \r
+ 2057, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 146, 147, \r
+ 2096, 2097, 2072, 2073, 64, 65, 66, 67, 68, 69, 70, 71, 72, \r
+ 73, 132, 133, 2112, 2113, 136, 137, 80, 81, 82, 83, 84, 85, \r
+ 86, 87, 88, 89, 148, 149, 2128, 2129, 152, 153, 96, 97, 98, \r
+ 99, 100, 101, 102, 103, 104, 105, 134, 135, 2144, 2145, 2184, 2185, \r
+ 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 150, 151, 2160, \r
+ 2161, 2200, 2201, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, \r
+ 384, 385, 2304, 2305, 2432, 2433, 272, 273, 274, 275, 276, 277, 278, \r
+ 279, 280, 281, 400, 401, 2320, 2321, 2448, 2449, 288, 289, 290, 291, \r
+ 292, 293, 294, 295, 296, 297, 386, 387, 2336, 2337, 2312, 2313, 304, \r
+ 305, 306, 307, 308, 309, 310, 311, 312, 313, 402, 403, 2352, 2353, \r
+ 2328, 2329, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 388, \r
+ 389, 2368, 2369, 392, 393, 336, 337, 338, 339, 340, 341, 342, 343, \r
+ 344, 345, 404, 405, 2384, 2385, 408, 409, 352, 353, 354, 355, 356, \r
+ 357, 358, 359, 360, 361, 390, 391, 2400, 2401, 2440, 2441, 368, 369, \r
+ 370, 371, 372, 373, 374, 375, 376, 377, 406, 407, 2416, 2417, 2456, \r
+ 2457, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 640, 641, \r
+ 2050, 2051, 2178, 2179, 528, 529, 530, 531, 532, 533, 534, 535, 536, \r
+ 537, 656, 657, 2066, 2067, 2194, 2195, 544, 545, 546, 547, 548, 549, \r
+ 550, 551, 552, 553, 642, 643, 2082, 2083, 2088, 2089, 560, 561, 562, \r
+ 563, 564, 565, 566, 567, 568, 569, 658, 659, 2098, 2099, 2104, 2105, \r
+ 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 644, 645, 2114, \r
+ 2115, 648, 649, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, \r
+ 660, 661, 2130, 2131, 664, 665, 608, 609, 610, 611, 612, 613, 614, \r
+ 615, 616, 617, 646, 647, 2146, 2147, 2184, 2185, 624, 625, 626, 627, \r
+ 628, 629, 630, 631, 632, 633, 662, 663, 2162, 2163, 2200, 2201, 768, \r
+ 769, 770, 771, 772, 773, 774, 775, 776, 777, 896, 897, 2306, 2307, \r
+ 2434, 2435, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 912, \r
+ 913, 2322, 2323, 2450, 2451, 800, 801, 802, 803, 804, 805, 806, 807, \r
+ 808, 809, 898, 899, 2338, 2339, 2344, 2345, 816, 817, 818, 819, 820, \r
+ 821, 822, 823, 824, 825, 914, 915, 2354, 2355, 2360, 2361, 832, 833, \r
+ 834, 835, 836, 837, 838, 839, 840, 841, 900, 901, 2370, 2371, 904, \r
+ 905, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 916, 917, \r
+ 2386, 2387, 920, 921, 864, 865, 866, 867, 868, 869, 870, 871, 872, \r
+ 873, 902, 903, 2402, 2403, 2440, 2441, 880, 881, 882, 883, 884, 885, \r
+ 886, 887, 888, 889, 918, 919, 2418, 2419, 2456, 2457, 1024, 1025, 1026, \r
+ 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1152, 1153, 2052, 2053, 2180, 2181, \r
+ 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1168, 1169, 2068, \r
+ 2069, 2196, 2197, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, \r
+ 1154, 1155, 2084, 2085, 2120, 2121, 1072, 1073, 1074, 1075, 1076, 1077, 1078, \r
+ 1079, 1080, 1081, 1170, 1171, 2100, 2101, 2136, 2137, 1088, 1089, 1090, 1091, \r
+ 1092, 1093, 1094, 1095, 1096, 1097, 1156, 1157, 2116, 2117, 1160, 1161, 1104, \r
+ 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1172, 1173, 2132, 2133, \r
+ 1176, 1177, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1158, \r
+ 1159, 2148, 2149, 2184, 2185, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, \r
+ 1144, 1145, 1174, 1175, 2164, 2165, 2200, 2201, 1280, 1281, 1282, 1283, 1284, \r
+ 1285, 1286, 1287, 1288, 1289, 1408, 1409, 2308, 2309, 2436, 2437, 1296, 1297, \r
+ 1298, 1299, 1300, 1301, 1302, 1303, 1304, 1305, 1424, 1425, 2324, 2325, 2452, \r
+ 2453, 1312, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1410, 1411, \r
+ 2340, 2341, 2376, 2377, 1328, 1329, 1330, 1331, 1332, 1333, 1334, 1335, 1336, \r
+ 1337, 1426, 1427, 2356, 2357, 2392, 2393, 1344, 1345, 1346, 1347, 1348, 1349, \r
+ 1350, 1351, 1352, 1353, 1412, 1413, 2372, 2373, 1416, 1417, 1360, 1361, 1362, \r
+ 1363, 1364, 1365, 1366, 1367, 1368, 1369, 1428, 1429, 2388, 2389, 1432, 1433, \r
+ 1376, 1377, 1378, 1379, 1380, 1381, 1382, 1383, 1384, 1385, 1414, 1415, 2404, \r
+ 2405, 2440, 2441, 1392, 1393, 1394, 1395, 1396, 1397, 1398, 1399, 1400, 1401, \r
+ 1430, 1431, 2420, 2421, 2456, 2457, 1536, 1537, 1538, 1539, 1540, 1541, 1542, \r
+ 1543, 1544, 1545, 1664, 1665, 2054, 2055, 2182, 2183, 1552, 1553, 1554, 1555, \r
+ 1556, 1557, 1558, 1559, 1560, 1561, 1680, 1681, 2070, 2071, 2198, 2199, 1568, \r
+ 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1666, 1667, 2086, 2087, \r
+ 2152, 2153, 1584, 1585, 1586, 1587, 1588, 1589, 1590, 1591, 1592, 1593, 1682, \r
+ 1683, 2102, 2103, 2168, 2169, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, \r
+ 1608, 1609, 1668, 1669, 2118, 2119, 1672, 1673, 1616, 1617, 1618, 1619, 1620, \r
+ 1621, 1622, 1623, 1624, 1625, 1684, 1685, 2134, 2135, 1688, 1689, 1632, 1633, \r
+ 1634, 1635, 1636, 1637, 1638, 1639, 1640, 1641, 1670, 1671, 2150, 2151, 2184, \r
+ 2185, 1648, 1649, 1650, 1651, 1652, 1653, 1654, 1655, 1656, 1657, 1686, 1687, \r
+ 2166, 2167, 2200, 2201, 1792, 1793, 1794, 1795, 1796, 1797, 1798, 1799, 1800, \r
+ 1801, 1920, 1921, 2310, 2311, 2438, 2439, 1808, 1809, 1810, 1811, 1812, 1813, \r
+ 1814, 1815, 1816, 1817, 1936, 1937, 2326, 2327, 2454, 2455, 1824, 1825, 1826, \r
+ 1827, 1828, 1829, 1830, 1831, 1832, 1833, 1922, 1923, 2342, 2343, 2408, 2409, \r
+ 1840, 1841, 1842, 1843, 1844, 1845, 1846, 1847, 1848, 1849, 1938, 1939, 2358, \r
+ 2359, 2424, 2425, 1856, 1857, 1858, 1859, 1860, 1861, 1862, 1863, 1864, 1865, \r
+ 1924, 1925, 2374, 2375, 1928, 1929, 1872, 1873, 1874, 1875, 1876, 1877, 1878, \r
+ 1879, 1880, 1881, 1940, 1941, 2390, 2391, 1944, 1945, 1888, 1889, 1890, 1891, \r
+ 1892, 1893, 1894, 1895, 1896, 1897, 1926, 1927, 2406, 2407, 2440, 2441, 1904, \r
+ 1905, 1906, 1907, 1908, 1909, 1910, 1911, 1912, 1913, 1942, 1943, 2422, 2423, \r
+ 2456, 2457};\r
+#endif\r
+ \r
+#if defined(DEC_BIN2DPD) && DEC_BIN2DPD==1 && !defined(DECBIN2DPD)\r
+#define DECBIN2DPD\r
+ \r
+const uint16_t BIN2DPD[1000]={ 0, 1, 2, 3, 4, 5, 6, 7, \r
+ 8, 9, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32, \r
+ 33, 34, 35, 36, 37, 38, 39, 40, 41, 48, 49, 50, 51, \r
+ 52, 53, 54, 55, 56, 57, 64, 65, 66, 67, 68, 69, 70, \r
+ 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, \r
+ 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 112, 113, 114, \r
+ 115, 116, 117, 118, 119, 120, 121, 10, 11, 42, 43, 74, 75, \r
+ 106, 107, 78, 79, 26, 27, 58, 59, 90, 91, 122, 123, 94, \r
+ 95, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 144, 145, \r
+ 146, 147, 148, 149, 150, 151, 152, 153, 160, 161, 162, 163, 164, \r
+ 165, 166, 167, 168, 169, 176, 177, 178, 179, 180, 181, 182, 183, \r
+ 184, 185, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, \r
+ 209, 210, 211, 212, 213, 214, 215, 216, 217, 224, 225, 226, 227, \r
+ 228, 229, 230, 231, 232, 233, 240, 241, 242, 243, 244, 245, 246, \r
+ 247, 248, 249, 138, 139, 170, 171, 202, 203, 234, 235, 206, 207, \r
+ 154, 155, 186, 187, 218, 219, 250, 251, 222, 223, 256, 257, 258, \r
+ 259, 260, 261, 262, 263, 264, 265, 272, 273, 274, 275, 276, 277, \r
+ 278, 279, 280, 281, 288, 289, 290, 291, 292, 293, 294, 295, 296, \r
+ 297, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 320, 321, \r
+ 322, 323, 324, 325, 326, 327, 328, 329, 336, 337, 338, 339, 340, \r
+ 341, 342, 343, 344, 345, 352, 353, 354, 355, 356, 357, 358, 359, \r
+ 360, 361, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 266, \r
+ 267, 298, 299, 330, 331, 362, 363, 334, 335, 282, 283, 314, 315, \r
+ 346, 347, 378, 379, 350, 351, 384, 385, 386, 387, 388, 389, 390, \r
+ 391, 392, 393, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, \r
+ 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 432, 433, 434, \r
+ 435, 436, 437, 438, 439, 440, 441, 448, 449, 450, 451, 452, 453, \r
+ 454, 455, 456, 457, 464, 465, 466, 467, 468, 469, 470, 471, 472, \r
+ 473, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 496, 497, \r
+ 498, 499, 500, 501, 502, 503, 504, 505, 394, 395, 426, 427, 458, \r
+ 459, 490, 491, 462, 463, 410, 411, 442, 443, 474, 475, 506, 507, \r
+ 478, 479, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 528, \r
+ 529, 530, 531, 532, 533, 534, 535, 536, 537, 544, 545, 546, 547, \r
+ 548, 549, 550, 551, 552, 553, 560, 561, 562, 563, 564, 565, 566, \r
+ 567, 568, 569, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, \r
+ 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 608, 609, 610, \r
+ 611, 612, 613, 614, 615, 616, 617, 624, 625, 626, 627, 628, 629, \r
+ 630, 631, 632, 633, 522, 523, 554, 555, 586, 587, 618, 619, 590, \r
+ 591, 538, 539, 570, 571, 602, 603, 634, 635, 606, 607, 640, 641, \r
+ 642, 643, 644, 645, 646, 647, 648, 649, 656, 657, 658, 659, 660, \r
+ 661, 662, 663, 664, 665, 672, 673, 674, 675, 676, 677, 678, 679, \r
+ 680, 681, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 704, \r
+ 705, 706, 707, 708, 709, 710, 711, 712, 713, 720, 721, 722, 723, \r
+ 724, 725, 726, 727, 728, 729, 736, 737, 738, 739, 740, 741, 742, \r
+ 743, 744, 745, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, \r
+ 650, 651, 682, 683, 714, 715, 746, 747, 718, 719, 666, 667, 698, \r
+ 699, 730, 731, 762, 763, 734, 735, 768, 769, 770, 771, 772, 773, \r
+ 774, 775, 776, 777, 784, 785, 786, 787, 788, 789, 790, 791, 792, \r
+ 793, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 816, 817, \r
+ 818, 819, 820, 821, 822, 823, 824, 825, 832, 833, 834, 835, 836, \r
+ 837, 838, 839, 840, 841, 848, 849, 850, 851, 852, 853, 854, 855, \r
+ 856, 857, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 880, \r
+ 881, 882, 883, 884, 885, 886, 887, 888, 889, 778, 779, 810, 811, \r
+ 842, 843, 874, 875, 846, 847, 794, 795, 826, 827, 858, 859, 890, \r
+ 891, 862, 863, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, \r
+ 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 928, 929, 930, \r
+ 931, 932, 933, 934, 935, 936, 937, 944, 945, 946, 947, 948, 949, \r
+ 950, 951, 952, 953, 960, 961, 962, 963, 964, 965, 966, 967, 968, \r
+ 969, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 992, 993, \r
+ 994, 995, 996, 997, 998, 999, 1000, 1001, 1008, 1009, 1010, 1011, 1012, \r
+ 1013, 1014, 1015, 1016, 1017, 906, 907, 938, 939, 970, 971, 1002, 1003, \r
+ 974, 975, 922, 923, 954, 955, 986, 987, 1018, 1019, 990, 991, 12, \r
+ 13, 268, 269, 524, 525, 780, 781, 46, 47, 28, 29, 284, 285, \r
+ 540, 541, 796, 797, 62, 63, 44, 45, 300, 301, 556, 557, 812, \r
+ 813, 302, 303, 60, 61, 316, 317, 572, 573, 828, 829, 318, 319, \r
+ 76, 77, 332, 333, 588, 589, 844, 845, 558, 559, 92, 93, 348, \r
+ 349, 604, 605, 860, 861, 574, 575, 108, 109, 364, 365, 620, 621, \r
+ 876, 877, 814, 815, 124, 125, 380, 381, 636, 637, 892, 893, 830, \r
+ 831, 14, 15, 270, 271, 526, 527, 782, 783, 110, 111, 30, 31, \r
+ 286, 287, 542, 543, 798, 799, 126, 127, 140, 141, 396, 397, 652, \r
+ 653, 908, 909, 174, 175, 156, 157, 412, 413, 668, 669, 924, 925, \r
+ 190, 191, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 188, \r
+ 189, 444, 445, 700, 701, 956, 957, 446, 447, 204, 205, 460, 461, \r
+ 716, 717, 972, 973, 686, 687, 220, 221, 476, 477, 732, 733, 988, \r
+ 989, 702, 703, 236, 237, 492, 493, 748, 749, 1004, 1005, 942, 943, \r
+ 252, 253, 508, 509, 764, 765, 1020, 1021, 958, 959, 142, 143, 398, \r
+ 399, 654, 655, 910, 911, 238, 239, 158, 159, 414, 415, 670, 671, \r
+ 926, 927, 254, 255};\r
+#endif \r
+ \r
+#if defined(DEC_DPD2BIN) && DEC_DPD2BIN==1 && !defined(DECDPD2BIN)\r
+#define DECDPD2BIN\r
+ \r
+const uint16_t DPD2BIN[1024]={ 0, 1, 2, 3, 4, 5, 6, 7, \r
+ 8, 9, 80, 81, 800, 801, 880, 881, 10, 11, 12, 13, 14, \r
+ 15, 16, 17, 18, 19, 90, 91, 810, 811, 890, 891, 20, 21, \r
+ 22, 23, 24, 25, 26, 27, 28, 29, 82, 83, 820, 821, 808, \r
+ 809, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 92, 93, \r
+ 830, 831, 818, 819, 40, 41, 42, 43, 44, 45, 46, 47, 48, \r
+ 49, 84, 85, 840, 841, 88, 89, 50, 51, 52, 53, 54, 55, \r
+ 56, 57, 58, 59, 94, 95, 850, 851, 98, 99, 60, 61, 62, \r
+ 63, 64, 65, 66, 67, 68, 69, 86, 87, 860, 861, 888, 889, \r
+ 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 96, 97, 870, \r
+ 871, 898, 899, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, \r
+ 180, 181, 900, 901, 980, 981, 110, 111, 112, 113, 114, 115, 116, \r
+ 117, 118, 119, 190, 191, 910, 911, 990, 991, 120, 121, 122, 123, \r
+ 124, 125, 126, 127, 128, 129, 182, 183, 920, 921, 908, 909, 130, \r
+ 131, 132, 133, 134, 135, 136, 137, 138, 139, 192, 193, 930, 931, \r
+ 918, 919, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 184, \r
+ 185, 940, 941, 188, 189, 150, 151, 152, 153, 154, 155, 156, 157, \r
+ 158, 159, 194, 195, 950, 951, 198, 199, 160, 161, 162, 163, 164, \r
+ 165, 166, 167, 168, 169, 186, 187, 960, 961, 988, 989, 170, 171, \r
+ 172, 173, 174, 175, 176, 177, 178, 179, 196, 197, 970, 971, 998, \r
+ 999, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 280, 281, \r
+ 802, 803, 882, 883, 210, 211, 212, 213, 214, 215, 216, 217, 218, \r
+ 219, 290, 291, 812, 813, 892, 893, 220, 221, 222, 223, 224, 225, \r
+ 226, 227, 228, 229, 282, 283, 822, 823, 828, 829, 230, 231, 232, \r
+ 233, 234, 235, 236, 237, 238, 239, 292, 293, 832, 833, 838, 839, \r
+ 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 284, 285, 842, \r
+ 843, 288, 289, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, \r
+ 294, 295, 852, 853, 298, 299, 260, 261, 262, 263, 264, 265, 266, \r
+ 267, 268, 269, 286, 287, 862, 863, 888, 889, 270, 271, 272, 273, \r
+ 274, 275, 276, 277, 278, 279, 296, 297, 872, 873, 898, 899, 300, \r
+ 301, 302, 303, 304, 305, 306, 307, 308, 309, 380, 381, 902, 903, \r
+ 982, 983, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 390, \r
+ 391, 912, 913, 992, 993, 320, 321, 322, 323, 324, 325, 326, 327, \r
+ 328, 329, 382, 383, 922, 923, 928, 929, 330, 331, 332, 333, 334, \r
+ 335, 336, 337, 338, 339, 392, 393, 932, 933, 938, 939, 340, 341, \r
+ 342, 343, 344, 345, 346, 347, 348, 349, 384, 385, 942, 943, 388, \r
+ 389, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 394, 395, \r
+ 952, 953, 398, 399, 360, 361, 362, 363, 364, 365, 366, 367, 368, \r
+ 369, 386, 387, 962, 963, 988, 989, 370, 371, 372, 373, 374, 375, \r
+ 376, 377, 378, 379, 396, 397, 972, 973, 998, 999, 400, 401, 402, \r
+ 403, 404, 405, 406, 407, 408, 409, 480, 481, 804, 805, 884, 885, \r
+ 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 490, 491, 814, \r
+ 815, 894, 895, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, \r
+ 482, 483, 824, 825, 848, 849, 430, 431, 432, 433, 434, 435, 436, \r
+ 437, 438, 439, 492, 493, 834, 835, 858, 859, 440, 441, 442, 443, \r
+ 444, 445, 446, 447, 448, 449, 484, 485, 844, 845, 488, 489, 450, \r
+ 451, 452, 453, 454, 455, 456, 457, 458, 459, 494, 495, 854, 855, \r
+ 498, 499, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 486, \r
+ 487, 864, 865, 888, 889, 470, 471, 472, 473, 474, 475, 476, 477, \r
+ 478, 479, 496, 497, 874, 875, 898, 899, 500, 501, 502, 503, 504, \r
+ 505, 506, 507, 508, 509, 580, 581, 904, 905, 984, 985, 510, 511, \r
+ 512, 513, 514, 515, 516, 517, 518, 519, 590, 591, 914, 915, 994, \r
+ 995, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 582, 583, \r
+ 924, 925, 948, 949, 530, 531, 532, 533, 534, 535, 536, 537, 538, \r
+ 539, 592, 593, 934, 935, 958, 959, 540, 541, 542, 543, 544, 545, \r
+ 546, 547, 548, 549, 584, 585, 944, 945, 588, 589, 550, 551, 552, \r
+ 553, 554, 555, 556, 557, 558, 559, 594, 595, 954, 955, 598, 599, \r
+ 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 586, 587, 964, \r
+ 965, 988, 989, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, \r
+ 596, 597, 974, 975, 998, 999, 600, 601, 602, 603, 604, 605, 606, \r
+ 607, 608, 609, 680, 681, 806, 807, 886, 887, 610, 611, 612, 613, \r
+ 614, 615, 616, 617, 618, 619, 690, 691, 816, 817, 896, 897, 620, \r
+ 621, 622, 623, 624, 625, 626, 627, 628, 629, 682, 683, 826, 827, \r
+ 868, 869, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 692, \r
+ 693, 836, 837, 878, 879, 640, 641, 642, 643, 644, 645, 646, 647, \r
+ 648, 649, 684, 685, 846, 847, 688, 689, 650, 651, 652, 653, 654, \r
+ 655, 656, 657, 658, 659, 694, 695, 856, 857, 698, 699, 660, 661, \r
+ 662, 663, 664, 665, 666, 667, 668, 669, 686, 687, 866, 867, 888, \r
+ 889, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 696, 697, \r
+ 876, 877, 898, 899, 700, 701, 702, 703, 704, 705, 706, 707, 708, \r
+ 709, 780, 781, 906, 907, 986, 987, 710, 711, 712, 713, 714, 715, \r
+ 716, 717, 718, 719, 790, 791, 916, 917, 996, 997, 720, 721, 722, \r
+ 723, 724, 725, 726, 727, 728, 729, 782, 783, 926, 927, 968, 969, \r
+ 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 792, 793, 936, \r
+ 937, 978, 979, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, \r
+ 784, 785, 946, 947, 788, 789, 750, 751, 752, 753, 754, 755, 756, \r
+ 757, 758, 759, 794, 795, 956, 957, 798, 799, 760, 761, 762, 763, \r
+ 764, 765, 766, 767, 768, 769, 786, 787, 966, 967, 988, 989, 770, \r
+ 771, 772, 773, 774, 775, 776, 777, 778, 779, 796, 797, 976, 977, \r
+ 998, 999};\r
+#endif\r
+ \r
+#if defined(DEC_DPD2BINK) && DEC_DPD2BINK==1 && !defined(DECDPD2BINK)\r
+#define DECDPD2BINK\r
+ \r
+const uint32_t DPD2BINK[1024]={ 0, 1000, 2000, 3000, 4000, 5000, \r
+ 6000, 7000, 8000, 9000, 80000, 81000, 800000, 801000, 880000, 881000, \r
+ 10000, 11000, 12000, 13000, 14000, 15000, 16000, 17000, 18000, 19000, \r
+ 90000, 91000, 810000, 811000, 890000, 891000, 20000, 21000, 22000, 23000, \r
+ 24000, 25000, 26000, 27000, 28000, 29000, 82000, 83000, 820000, 821000, \r
+ 808000, 809000, 30000, 31000, 32000, 33000, 34000, 35000, 36000, 37000, \r
+ 38000, 39000, 92000, 93000, 830000, 831000, 818000, 819000, 40000, 41000, \r
+ 42000, 43000, 44000, 45000, 46000, 47000, 48000, 49000, 84000, 85000, \r
+ 840000, 841000, 88000, 89000, 50000, 51000, 52000, 53000, 54000, 55000, \r
+ 56000, 57000, 58000, 59000, 94000, 95000, 850000, 851000, 98000, 99000, \r
+ 60000, 61000, 62000, 63000, 64000, 65000, 66000, 67000, 68000, 69000, \r
+ 86000, 87000, 860000, 861000, 888000, 889000, 70000, 71000, 72000, 73000, \r
+ 74000, 75000, 76000, 77000, 78000, 79000, 96000, 97000, 870000, 871000, \r
+ 898000, 899000, 100000, 101000, 102000, 103000, 104000, 105000, 106000, 107000, \r
+ 108000, 109000, 180000, 181000, 900000, 901000, 980000, 981000, 110000, 111000, \r
+ 112000, 113000, 114000, 115000, 116000, 117000, 118000, 119000, 190000, 191000, \r
+ 910000, 911000, 990000, 991000, 120000, 121000, 122000, 123000, 124000, 125000, \r
+ 126000, 127000, 128000, 129000, 182000, 183000, 920000, 921000, 908000, 909000, \r
+ 130000, 131000, 132000, 133000, 134000, 135000, 136000, 137000, 138000, 139000, \r
+ 192000, 193000, 930000, 931000, 918000, 919000, 140000, 141000, 142000, 143000, \r
+ 144000, 145000, 146000, 147000, 148000, 149000, 184000, 185000, 940000, 941000, \r
+ 188000, 189000, 150000, 151000, 152000, 153000, 154000, 155000, 156000, 157000, \r
+ 158000, 159000, 194000, 195000, 950000, 951000, 198000, 199000, 160000, 161000, \r
+ 162000, 163000, 164000, 165000, 166000, 167000, 168000, 169000, 186000, 187000, \r
+ 960000, 961000, 988000, 989000, 170000, 171000, 172000, 173000, 174000, 175000, \r
+ 176000, 177000, 178000, 179000, 196000, 197000, 970000, 971000, 998000, 999000, \r
+ 200000, 201000, 202000, 203000, 204000, 205000, 206000, 207000, 208000, 209000, \r
+ 280000, 281000, 802000, 803000, 882000, 883000, 210000, 211000, 212000, 213000, \r
+ 214000, 215000, 216000, 217000, 218000, 219000, 290000, 291000, 812000, 813000, \r
+ 892000, 893000, 220000, 221000, 222000, 223000, 224000, 225000, 226000, 227000, \r
+ 228000, 229000, 282000, 283000, 822000, 823000, 828000, 829000, 230000, 231000, \r
+ 232000, 233000, 234000, 235000, 236000, 237000, 238000, 239000, 292000, 293000, \r
+ 832000, 833000, 838000, 839000, 240000, 241000, 242000, 243000, 244000, 245000, \r
+ 246000, 247000, 248000, 249000, 284000, 285000, 842000, 843000, 288000, 289000, \r
+ 250000, 251000, 252000, 253000, 254000, 255000, 256000, 257000, 258000, 259000, \r
+ 294000, 295000, 852000, 853000, 298000, 299000, 260000, 261000, 262000, 263000, \r
+ 264000, 265000, 266000, 267000, 268000, 269000, 286000, 287000, 862000, 863000, \r
+ 888000, 889000, 270000, 271000, 272000, 273000, 274000, 275000, 276000, 277000, \r
+ 278000, 279000, 296000, 297000, 872000, 873000, 898000, 899000, 300000, 301000, \r
+ 302000, 303000, 304000, 305000, 306000, 307000, 308000, 309000, 380000, 381000, \r
+ 902000, 903000, 982000, 983000, 310000, 311000, 312000, 313000, 314000, 315000, \r
+ 316000, 317000, 318000, 319000, 390000, 391000, 912000, 913000, 992000, 993000, \r
+ 320000, 321000, 322000, 323000, 324000, 325000, 326000, 327000, 328000, 329000, \r
+ 382000, 383000, 922000, 923000, 928000, 929000, 330000, 331000, 332000, 333000, \r
+ 334000, 335000, 336000, 337000, 338000, 339000, 392000, 393000, 932000, 933000, \r
+ 938000, 939000, 340000, 341000, 342000, 343000, 344000, 345000, 346000, 347000, \r
+ 348000, 349000, 384000, 385000, 942000, 943000, 388000, 389000, 350000, 351000, \r
+ 352000, 353000, 354000, 355000, 356000, 357000, 358000, 359000, 394000, 395000, \r
+ 952000, 953000, 398000, 399000, 360000, 361000, 362000, 363000, 364000, 365000, \r
+ 366000, 367000, 368000, 369000, 386000, 387000, 962000, 963000, 988000, 989000, \r
+ 370000, 371000, 372000, 373000, 374000, 375000, 376000, 377000, 378000, 379000, \r
+ 396000, 397000, 972000, 973000, 998000, 999000, 400000, 401000, 402000, 403000, \r
+ 404000, 405000, 406000, 407000, 408000, 409000, 480000, 481000, 804000, 805000, \r
+ 884000, 885000, 410000, 411000, 412000, 413000, 414000, 415000, 416000, 417000, \r
+ 418000, 419000, 490000, 491000, 814000, 815000, 894000, 895000, 420000, 421000, \r
+ 422000, 423000, 424000, 425000, 426000, 427000, 428000, 429000, 482000, 483000, \r
+ 824000, 825000, 848000, 849000, 430000, 431000, 432000, 433000, 434000, 435000, \r
+ 436000, 437000, 438000, 439000, 492000, 493000, 834000, 835000, 858000, 859000, \r
+ 440000, 441000, 442000, 443000, 444000, 445000, 446000, 447000, 448000, 449000, \r
+ 484000, 485000, 844000, 845000, 488000, 489000, 450000, 451000, 452000, 453000, \r
+ 454000, 455000, 456000, 457000, 458000, 459000, 494000, 495000, 854000, 855000, \r
+ 498000, 499000, 460000, 461000, 462000, 463000, 464000, 465000, 466000, 467000, \r
+ 468000, 469000, 486000, 487000, 864000, 865000, 888000, 889000, 470000, 471000, \r
+ 472000, 473000, 474000, 475000, 476000, 477000, 478000, 479000, 496000, 497000, \r
+ 874000, 875000, 898000, 899000, 500000, 501000, 502000, 503000, 504000, 505000, \r
+ 506000, 507000, 508000, 509000, 580000, 581000, 904000, 905000, 984000, 985000, \r
+ 510000, 511000, 512000, 513000, 514000, 515000, 516000, 517000, 518000, 519000, \r
+ 590000, 591000, 914000, 915000, 994000, 995000, 520000, 521000, 522000, 523000, \r
+ 524000, 525000, 526000, 527000, 528000, 529000, 582000, 583000, 924000, 925000, \r
+ 948000, 949000, 530000, 531000, 532000, 533000, 534000, 535000, 536000, 537000, \r
+ 538000, 539000, 592000, 593000, 934000, 935000, 958000, 959000, 540000, 541000, \r
+ 542000, 543000, 544000, 545000, 546000, 547000, 548000, 549000, 584000, 585000, \r
+ 944000, 945000, 588000, 589000, 550000, 551000, 552000, 553000, 554000, 555000, \r
+ 556000, 557000, 558000, 559000, 594000, 595000, 954000, 955000, 598000, 599000, \r
+ 560000, 561000, 562000, 563000, 564000, 565000, 566000, 567000, 568000, 569000, \r
+ 586000, 587000, 964000, 965000, 988000, 989000, 570000, 571000, 572000, 573000, \r
+ 574000, 575000, 576000, 577000, 578000, 579000, 596000, 597000, 974000, 975000, \r
+ 998000, 999000, 600000, 601000, 602000, 603000, 604000, 605000, 606000, 607000, \r
+ 608000, 609000, 680000, 681000, 806000, 807000, 886000, 887000, 610000, 611000, \r
+ 612000, 613000, 614000, 615000, 616000, 617000, 618000, 619000, 690000, 691000, \r
+ 816000, 817000, 896000, 897000, 620000, 621000, 622000, 623000, 624000, 625000, \r
+ 626000, 627000, 628000, 629000, 682000, 683000, 826000, 827000, 868000, 869000, \r
+ 630000, 631000, 632000, 633000, 634000, 635000, 636000, 637000, 638000, 639000, \r
+ 692000, 693000, 836000, 837000, 878000, 879000, 640000, 641000, 642000, 643000, \r
+ 644000, 645000, 646000, 647000, 648000, 649000, 684000, 685000, 846000, 847000, \r
+ 688000, 689000, 650000, 651000, 652000, 653000, 654000, 655000, 656000, 657000, \r
+ 658000, 659000, 694000, 695000, 856000, 857000, 698000, 699000, 660000, 661000, \r
+ 662000, 663000, 664000, 665000, 666000, 667000, 668000, 669000, 686000, 687000, \r
+ 866000, 867000, 888000, 889000, 670000, 671000, 672000, 673000, 674000, 675000, \r
+ 676000, 677000, 678000, 679000, 696000, 697000, 876000, 877000, 898000, 899000, \r
+ 700000, 701000, 702000, 703000, 704000, 705000, 706000, 707000, 708000, 709000, \r
+ 780000, 781000, 906000, 907000, 986000, 987000, 710000, 711000, 712000, 713000, \r
+ 714000, 715000, 716000, 717000, 718000, 719000, 790000, 791000, 916000, 917000, \r
+ 996000, 997000, 720000, 721000, 722000, 723000, 724000, 725000, 726000, 727000, \r
+ 728000, 729000, 782000, 783000, 926000, 927000, 968000, 969000, 730000, 731000, \r
+ 732000, 733000, 734000, 735000, 736000, 737000, 738000, 739000, 792000, 793000, \r
+ 936000, 937000, 978000, 979000, 740000, 741000, 742000, 743000, 744000, 745000, \r
+ 746000, 747000, 748000, 749000, 784000, 785000, 946000, 947000, 788000, 789000, \r
+ 750000, 751000, 752000, 753000, 754000, 755000, 756000, 757000, 758000, 759000, \r
+ 794000, 795000, 956000, 957000, 798000, 799000, 760000, 761000, 762000, 763000, \r
+ 764000, 765000, 766000, 767000, 768000, 769000, 786000, 787000, 966000, 967000, \r
+ 988000, 989000, 770000, 771000, 772000, 773000, 774000, 775000, 776000, 777000, \r
+ 778000, 779000, 796000, 797000, 976000, 977000, 998000, 999000};\r
+#endif\r
+ \r
+#if defined(DEC_DPD2BINM) && DEC_DPD2BINM==1 && !defined(DECDPD2BINM)\r
+#define DECDPD2BINM\r
+ \r
+const uint32_t DPD2BINM[1024]={0, 1000000, 2000000, 3000000, 4000000, \r
+ 5000000, 6000000, 7000000, 8000000, 9000000, 80000000, 81000000, \r
+ 800000000, 801000000, 880000000, 881000000, 10000000, 11000000, 12000000, \r
+ 13000000, 14000000, 15000000, 16000000, 17000000, 18000000, 19000000, \r
+ 90000000, 91000000, 810000000, 811000000, 890000000, 891000000, 20000000, \r
+ 21000000, 22000000, 23000000, 24000000, 25000000, 26000000, 27000000, \r
+ 28000000, 29000000, 82000000, 83000000, 820000000, 821000000, 808000000, \r
+ 809000000, 30000000, 31000000, 32000000, 33000000, 34000000, 35000000, \r
+ 36000000, 37000000, 38000000, 39000000, 92000000, 93000000, 830000000, \r
+ 831000000, 818000000, 819000000, 40000000, 41000000, 42000000, 43000000, \r
+ 44000000, 45000000, 46000000, 47000000, 48000000, 49000000, 84000000, \r
+ 85000000, 840000000, 841000000, 88000000, 89000000, 50000000, 51000000, \r
+ 52000000, 53000000, 54000000, 55000000, 56000000, 57000000, 58000000, \r
+ 59000000, 94000000, 95000000, 850000000, 851000000, 98000000, 99000000, \r
+ 60000000, 61000000, 62000000, 63000000, 64000000, 65000000, 66000000, \r
+ 67000000, 68000000, 69000000, 86000000, 87000000, 860000000, 861000000, \r
+ 888000000, 889000000, 70000000, 71000000, 72000000, 73000000, 74000000, \r
+ 75000000, 76000000, 77000000, 78000000, 79000000, 96000000, 97000000, \r
+ 870000000, 871000000, 898000000, 899000000, 100000000, 101000000, 102000000, \r
+ 103000000, 104000000, 105000000, 106000000, 107000000, 108000000, 109000000, \r
+ 180000000, 181000000, 900000000, 901000000, 980000000, 981000000, 110000000, \r
+ 111000000, 112000000, 113000000, 114000000, 115000000, 116000000, 117000000, \r
+ 118000000, 119000000, 190000000, 191000000, 910000000, 911000000, 990000000, \r
+ 991000000, 120000000, 121000000, 122000000, 123000000, 124000000, 125000000, \r
+ 126000000, 127000000, 128000000, 129000000, 182000000, 183000000, 920000000, \r
+ 921000000, 908000000, 909000000, 130000000, 131000000, 132000000, 133000000, \r
+ 134000000, 135000000, 136000000, 137000000, 138000000, 139000000, 192000000, \r
+ 193000000, 930000000, 931000000, 918000000, 919000000, 140000000, 141000000, \r
+ 142000000, 143000000, 144000000, 145000000, 146000000, 147000000, 148000000, \r
+ 149000000, 184000000, 185000000, 940000000, 941000000, 188000000, 189000000, \r
+ 150000000, 151000000, 152000000, 153000000, 154000000, 155000000, 156000000, \r
+ 157000000, 158000000, 159000000, 194000000, 195000000, 950000000, 951000000, \r
+ 198000000, 199000000, 160000000, 161000000, 162000000, 163000000, 164000000, \r
+ 165000000, 166000000, 167000000, 168000000, 169000000, 186000000, 187000000, \r
+ 960000000, 961000000, 988000000, 989000000, 170000000, 171000000, 172000000, \r
+ 173000000, 174000000, 175000000, 176000000, 177000000, 178000000, 179000000, \r
+ 196000000, 197000000, 970000000, 971000000, 998000000, 999000000, 200000000, \r
+ 201000000, 202000000, 203000000, 204000000, 205000000, 206000000, 207000000, \r
+ 208000000, 209000000, 280000000, 281000000, 802000000, 803000000, 882000000, \r
+ 883000000, 210000000, 211000000, 212000000, 213000000, 214000000, 215000000, \r
+ 216000000, 217000000, 218000000, 219000000, 290000000, 291000000, 812000000, \r
+ 813000000, 892000000, 893000000, 220000000, 221000000, 222000000, 223000000, \r
+ 224000000, 225000000, 226000000, 227000000, 228000000, 229000000, 282000000, \r
+ 283000000, 822000000, 823000000, 828000000, 829000000, 230000000, 231000000, \r
+ 232000000, 233000000, 234000000, 235000000, 236000000, 237000000, 238000000, \r
+ 239000000, 292000000, 293000000, 832000000, 833000000, 838000000, 839000000, \r
+ 240000000, 241000000, 242000000, 243000000, 244000000, 245000000, 246000000, \r
+ 247000000, 248000000, 249000000, 284000000, 285000000, 842000000, 843000000, \r
+ 288000000, 289000000, 250000000, 251000000, 252000000, 253000000, 254000000, \r
+ 255000000, 256000000, 257000000, 258000000, 259000000, 294000000, 295000000, \r
+ 852000000, 853000000, 298000000, 299000000, 260000000, 261000000, 262000000, \r
+ 263000000, 264000000, 265000000, 266000000, 267000000, 268000000, 269000000, \r
+ 286000000, 287000000, 862000000, 863000000, 888000000, 889000000, 270000000, \r
+ 271000000, 272000000, 273000000, 274000000, 275000000, 276000000, 277000000, \r
+ 278000000, 279000000, 296000000, 297000000, 872000000, 873000000, 898000000, \r
+ 899000000, 300000000, 301000000, 302000000, 303000000, 304000000, 305000000, \r
+ 306000000, 307000000, 308000000, 309000000, 380000000, 381000000, 902000000, \r
+ 903000000, 982000000, 983000000, 310000000, 311000000, 312000000, 313000000, \r
+ 314000000, 315000000, 316000000, 317000000, 318000000, 319000000, 390000000, \r
+ 391000000, 912000000, 913000000, 992000000, 993000000, 320000000, 321000000, \r
+ 322000000, 323000000, 324000000, 325000000, 326000000, 327000000, 328000000, \r
+ 329000000, 382000000, 383000000, 922000000, 923000000, 928000000, 929000000, \r
+ 330000000, 331000000, 332000000, 333000000, 334000000, 335000000, 336000000, \r
+ 337000000, 338000000, 339000000, 392000000, 393000000, 932000000, 933000000, \r
+ 938000000, 939000000, 340000000, 341000000, 342000000, 343000000, 344000000, \r
+ 345000000, 346000000, 347000000, 348000000, 349000000, 384000000, 385000000, \r
+ 942000000, 943000000, 388000000, 389000000, 350000000, 351000000, 352000000, \r
+ 353000000, 354000000, 355000000, 356000000, 357000000, 358000000, 359000000, \r
+ 394000000, 395000000, 952000000, 953000000, 398000000, 399000000, 360000000, \r
+ 361000000, 362000000, 363000000, 364000000, 365000000, 366000000, 367000000, \r
+ 368000000, 369000000, 386000000, 387000000, 962000000, 963000000, 988000000, \r
+ 989000000, 370000000, 371000000, 372000000, 373000000, 374000000, 375000000, \r
+ 376000000, 377000000, 378000000, 379000000, 396000000, 397000000, 972000000, \r
+ 973000000, 998000000, 999000000, 400000000, 401000000, 402000000, 403000000, \r
+ 404000000, 405000000, 406000000, 407000000, 408000000, 409000000, 480000000, \r
+ 481000000, 804000000, 805000000, 884000000, 885000000, 410000000, 411000000, \r
+ 412000000, 413000000, 414000000, 415000000, 416000000, 417000000, 418000000, \r
+ 419000000, 490000000, 491000000, 814000000, 815000000, 894000000, 895000000, \r
+ 420000000, 421000000, 422000000, 423000000, 424000000, 425000000, 426000000, \r
+ 427000000, 428000000, 429000000, 482000000, 483000000, 824000000, 825000000, \r
+ 848000000, 849000000, 430000000, 431000000, 432000000, 433000000, 434000000, \r
+ 435000000, 436000000, 437000000, 438000000, 439000000, 492000000, 493000000, \r
+ 834000000, 835000000, 858000000, 859000000, 440000000, 441000000, 442000000, \r
+ 443000000, 444000000, 445000000, 446000000, 447000000, 448000000, 449000000, \r
+ 484000000, 485000000, 844000000, 845000000, 488000000, 489000000, 450000000, \r
+ 451000000, 452000000, 453000000, 454000000, 455000000, 456000000, 457000000, \r
+ 458000000, 459000000, 494000000, 495000000, 854000000, 855000000, 498000000, \r
+ 499000000, 460000000, 461000000, 462000000, 463000000, 464000000, 465000000, \r
+ 466000000, 467000000, 468000000, 469000000, 486000000, 487000000, 864000000, \r
+ 865000000, 888000000, 889000000, 470000000, 471000000, 472000000, 473000000, \r
+ 474000000, 475000000, 476000000, 477000000, 478000000, 479000000, 496000000, \r
+ 497000000, 874000000, 875000000, 898000000, 899000000, 500000000, 501000000, \r
+ 502000000, 503000000, 504000000, 505000000, 506000000, 507000000, 508000000, \r
+ 509000000, 580000000, 581000000, 904000000, 905000000, 984000000, 985000000, \r
+ 510000000, 511000000, 512000000, 513000000, 514000000, 515000000, 516000000, \r
+ 517000000, 518000000, 519000000, 590000000, 591000000, 914000000, 915000000, \r
+ 994000000, 995000000, 520000000, 521000000, 522000000, 523000000, 524000000, \r
+ 525000000, 526000000, 527000000, 528000000, 529000000, 582000000, 583000000, \r
+ 924000000, 925000000, 948000000, 949000000, 530000000, 531000000, 532000000, \r
+ 533000000, 534000000, 535000000, 536000000, 537000000, 538000000, 539000000, \r
+ 592000000, 593000000, 934000000, 935000000, 958000000, 959000000, 540000000, \r
+ 541000000, 542000000, 543000000, 544000000, 545000000, 546000000, 547000000, \r
+ 548000000, 549000000, 584000000, 585000000, 944000000, 945000000, 588000000, \r
+ 589000000, 550000000, 551000000, 552000000, 553000000, 554000000, 555000000, \r
+ 556000000, 557000000, 558000000, 559000000, 594000000, 595000000, 954000000, \r
+ 955000000, 598000000, 599000000, 560000000, 561000000, 562000000, 563000000, \r
+ 564000000, 565000000, 566000000, 567000000, 568000000, 569000000, 586000000, \r
+ 587000000, 964000000, 965000000, 988000000, 989000000, 570000000, 571000000, \r
+ 572000000, 573000000, 574000000, 575000000, 576000000, 577000000, 578000000, \r
+ 579000000, 596000000, 597000000, 974000000, 975000000, 998000000, 999000000, \r
+ 600000000, 601000000, 602000000, 603000000, 604000000, 605000000, 606000000, \r
+ 607000000, 608000000, 609000000, 680000000, 681000000, 806000000, 807000000, \r
+ 886000000, 887000000, 610000000, 611000000, 612000000, 613000000, 614000000, \r
+ 615000000, 616000000, 617000000, 618000000, 619000000, 690000000, 691000000, \r
+ 816000000, 817000000, 896000000, 897000000, 620000000, 621000000, 622000000, \r
+ 623000000, 624000000, 625000000, 626000000, 627000000, 628000000, 629000000, \r
+ 682000000, 683000000, 826000000, 827000000, 868000000, 869000000, 630000000, \r
+ 631000000, 632000000, 633000000, 634000000, 635000000, 636000000, 637000000, \r
+ 638000000, 639000000, 692000000, 693000000, 836000000, 837000000, 878000000, \r
+ 879000000, 640000000, 641000000, 642000000, 643000000, 644000000, 645000000, \r
+ 646000000, 647000000, 648000000, 649000000, 684000000, 685000000, 846000000, \r
+ 847000000, 688000000, 689000000, 650000000, 651000000, 652000000, 653000000, \r
+ 654000000, 655000000, 656000000, 657000000, 658000000, 659000000, 694000000, \r
+ 695000000, 856000000, 857000000, 698000000, 699000000, 660000000, 661000000, \r
+ 662000000, 663000000, 664000000, 665000000, 666000000, 667000000, 668000000, \r
+ 669000000, 686000000, 687000000, 866000000, 867000000, 888000000, 889000000, \r
+ 670000000, 671000000, 672000000, 673000000, 674000000, 675000000, 676000000, \r
+ 677000000, 678000000, 679000000, 696000000, 697000000, 876000000, 877000000, \r
+ 898000000, 899000000, 700000000, 701000000, 702000000, 703000000, 704000000, \r
+ 705000000, 706000000, 707000000, 708000000, 709000000, 780000000, 781000000, \r
+ 906000000, 907000000, 986000000, 987000000, 710000000, 711000000, 712000000, \r
+ 713000000, 714000000, 715000000, 716000000, 717000000, 718000000, 719000000, \r
+ 790000000, 791000000, 916000000, 917000000, 996000000, 997000000, 720000000, \r
+ 721000000, 722000000, 723000000, 724000000, 725000000, 726000000, 727000000, \r
+ 728000000, 729000000, 782000000, 783000000, 926000000, 927000000, 968000000, \r
+ 969000000, 730000000, 731000000, 732000000, 733000000, 734000000, 735000000, \r
+ 736000000, 737000000, 738000000, 739000000, 792000000, 793000000, 936000000, \r
+ 937000000, 978000000, 979000000, 740000000, 741000000, 742000000, 743000000, \r
+ 744000000, 745000000, 746000000, 747000000, 748000000, 749000000, 784000000, \r
+ 785000000, 946000000, 947000000, 788000000, 789000000, 750000000, 751000000, \r
+ 752000000, 753000000, 754000000, 755000000, 756000000, 757000000, 758000000, \r
+ 759000000, 794000000, 795000000, 956000000, 957000000, 798000000, 799000000, \r
+ 760000000, 761000000, 762000000, 763000000, 764000000, 765000000, 766000000, \r
+ 767000000, 768000000, 769000000, 786000000, 787000000, 966000000, 967000000, \r
+ 988000000, 989000000, 770000000, 771000000, 772000000, 773000000, 774000000, \r
+ 775000000, 776000000, 777000000, 778000000, 779000000, 796000000, 797000000, \r
+ 976000000, 977000000, 998000000, 999000000};\r
+#endif\r
+ \r
+#if defined(DEC_BIN2CHAR) && DEC_BIN2CHAR==1 && !defined(DECBIN2CHAR)\r
+#define DECBIN2CHAR\r
+ \r
+const uint8_t BIN2CHAR[4001]={\r
+ '\0','0','0','0', '\1','0','0','1', '\1','0','0','2', '\1','0','0','3', '\1','0','0','4', \r
+ '\1','0','0','5', '\1','0','0','6', '\1','0','0','7', '\1','0','0','8', '\1','0','0','9', \r
+ '\2','0','1','0', '\2','0','1','1', '\2','0','1','2', '\2','0','1','3', '\2','0','1','4', \r
+ '\2','0','1','5', '\2','0','1','6', '\2','0','1','7', '\2','0','1','8', '\2','0','1','9', \r
+ '\2','0','2','0', '\2','0','2','1', '\2','0','2','2', '\2','0','2','3', '\2','0','2','4', \r
+ '\2','0','2','5', '\2','0','2','6', '\2','0','2','7', '\2','0','2','8', '\2','0','2','9', \r
+ '\2','0','3','0', '\2','0','3','1', '\2','0','3','2', '\2','0','3','3', '\2','0','3','4', \r
+ '\2','0','3','5', '\2','0','3','6', '\2','0','3','7', '\2','0','3','8', '\2','0','3','9', \r
+ '\2','0','4','0', '\2','0','4','1', '\2','0','4','2', '\2','0','4','3', '\2','0','4','4', \r
+ '\2','0','4','5', '\2','0','4','6', '\2','0','4','7', '\2','0','4','8', '\2','0','4','9', \r
+ '\2','0','5','0', '\2','0','5','1', '\2','0','5','2', '\2','0','5','3', '\2','0','5','4', \r
+ '\2','0','5','5', '\2','0','5','6', '\2','0','5','7', '\2','0','5','8', '\2','0','5','9', \r
+ '\2','0','6','0', '\2','0','6','1', '\2','0','6','2', '\2','0','6','3', '\2','0','6','4', \r
+ '\2','0','6','5', '\2','0','6','6', '\2','0','6','7', '\2','0','6','8', '\2','0','6','9', \r
+ '\2','0','7','0', '\2','0','7','1', '\2','0','7','2', '\2','0','7','3', '\2','0','7','4', \r
+ '\2','0','7','5', '\2','0','7','6', '\2','0','7','7', '\2','0','7','8', '\2','0','7','9', \r
+ '\2','0','8','0', '\2','0','8','1', '\2','0','8','2', '\2','0','8','3', '\2','0','8','4', \r
+ '\2','0','8','5', '\2','0','8','6', '\2','0','8','7', '\2','0','8','8', '\2','0','8','9', \r
+ '\2','0','9','0', '\2','0','9','1', '\2','0','9','2', '\2','0','9','3', '\2','0','9','4', \r
+ '\2','0','9','5', '\2','0','9','6', '\2','0','9','7', '\2','0','9','8', '\2','0','9','9', \r
+ '\3','1','0','0', '\3','1','0','1', '\3','1','0','2', '\3','1','0','3', '\3','1','0','4', \r
+ '\3','1','0','5', '\3','1','0','6', '\3','1','0','7', '\3','1','0','8', '\3','1','0','9', \r
+ '\3','1','1','0', '\3','1','1','1', '\3','1','1','2', '\3','1','1','3', '\3','1','1','4', \r
+ '\3','1','1','5', '\3','1','1','6', '\3','1','1','7', '\3','1','1','8', '\3','1','1','9', \r
+ '\3','1','2','0', '\3','1','2','1', '\3','1','2','2', '\3','1','2','3', '\3','1','2','4', \r
+ '\3','1','2','5', '\3','1','2','6', '\3','1','2','7', '\3','1','2','8', '\3','1','2','9', \r
+ '\3','1','3','0', '\3','1','3','1', '\3','1','3','2', '\3','1','3','3', '\3','1','3','4', \r
+ '\3','1','3','5', '\3','1','3','6', '\3','1','3','7', '\3','1','3','8', '\3','1','3','9', \r
+ '\3','1','4','0', '\3','1','4','1', '\3','1','4','2', '\3','1','4','3', '\3','1','4','4', \r
+ '\3','1','4','5', '\3','1','4','6', '\3','1','4','7', '\3','1','4','8', '\3','1','4','9', \r
+ '\3','1','5','0', '\3','1','5','1', '\3','1','5','2', '\3','1','5','3', '\3','1','5','4', \r
+ '\3','1','5','5', '\3','1','5','6', '\3','1','5','7', '\3','1','5','8', '\3','1','5','9', \r
+ '\3','1','6','0', '\3','1','6','1', '\3','1','6','2', '\3','1','6','3', '\3','1','6','4', \r
+ '\3','1','6','5', '\3','1','6','6', '\3','1','6','7', '\3','1','6','8', '\3','1','6','9', \r
+ '\3','1','7','0', '\3','1','7','1', '\3','1','7','2', '\3','1','7','3', '\3','1','7','4', \r
+ '\3','1','7','5', '\3','1','7','6', '\3','1','7','7', '\3','1','7','8', '\3','1','7','9', \r
+ '\3','1','8','0', '\3','1','8','1', '\3','1','8','2', '\3','1','8','3', '\3','1','8','4', \r
+ '\3','1','8','5', '\3','1','8','6', '\3','1','8','7', '\3','1','8','8', '\3','1','8','9', \r
+ '\3','1','9','0', '\3','1','9','1', '\3','1','9','2', '\3','1','9','3', '\3','1','9','4', \r
+ '\3','1','9','5', '\3','1','9','6', '\3','1','9','7', '\3','1','9','8', '\3','1','9','9', \r
+ '\3','2','0','0', '\3','2','0','1', '\3','2','0','2', '\3','2','0','3', '\3','2','0','4', \r
+ '\3','2','0','5', '\3','2','0','6', '\3','2','0','7', '\3','2','0','8', '\3','2','0','9', \r
+ '\3','2','1','0', '\3','2','1','1', '\3','2','1','2', '\3','2','1','3', '\3','2','1','4', \r
+ '\3','2','1','5', '\3','2','1','6', '\3','2','1','7', '\3','2','1','8', '\3','2','1','9', \r
+ '\3','2','2','0', '\3','2','2','1', '\3','2','2','2', '\3','2','2','3', '\3','2','2','4', \r
+ '\3','2','2','5', '\3','2','2','6', '\3','2','2','7', '\3','2','2','8', '\3','2','2','9', \r
+ '\3','2','3','0', '\3','2','3','1', '\3','2','3','2', '\3','2','3','3', '\3','2','3','4', \r
+ '\3','2','3','5', '\3','2','3','6', '\3','2','3','7', '\3','2','3','8', '\3','2','3','9', \r
+ '\3','2','4','0', '\3','2','4','1', '\3','2','4','2', '\3','2','4','3', '\3','2','4','4', \r
+ '\3','2','4','5', '\3','2','4','6', '\3','2','4','7', '\3','2','4','8', '\3','2','4','9', \r
+ '\3','2','5','0', '\3','2','5','1', '\3','2','5','2', '\3','2','5','3', '\3','2','5','4', \r
+ '\3','2','5','5', '\3','2','5','6', '\3','2','5','7', '\3','2','5','8', '\3','2','5','9', \r
+ '\3','2','6','0', '\3','2','6','1', '\3','2','6','2', '\3','2','6','3', '\3','2','6','4', \r
+ '\3','2','6','5', '\3','2','6','6', '\3','2','6','7', '\3','2','6','8', '\3','2','6','9', \r
+ '\3','2','7','0', '\3','2','7','1', '\3','2','7','2', '\3','2','7','3', '\3','2','7','4', \r
+ '\3','2','7','5', '\3','2','7','6', '\3','2','7','7', '\3','2','7','8', '\3','2','7','9', \r
+ '\3','2','8','0', '\3','2','8','1', '\3','2','8','2', '\3','2','8','3', '\3','2','8','4', \r
+ '\3','2','8','5', '\3','2','8','6', '\3','2','8','7', '\3','2','8','8', '\3','2','8','9', \r
+ '\3','2','9','0', '\3','2','9','1', '\3','2','9','2', '\3','2','9','3', '\3','2','9','4', \r
+ '\3','2','9','5', '\3','2','9','6', '\3','2','9','7', '\3','2','9','8', '\3','2','9','9', \r
+ '\3','3','0','0', '\3','3','0','1', '\3','3','0','2', '\3','3','0','3', '\3','3','0','4', \r
+ '\3','3','0','5', '\3','3','0','6', '\3','3','0','7', '\3','3','0','8', '\3','3','0','9', \r
+ '\3','3','1','0', '\3','3','1','1', '\3','3','1','2', '\3','3','1','3', '\3','3','1','4', \r
+ '\3','3','1','5', '\3','3','1','6', '\3','3','1','7', '\3','3','1','8', '\3','3','1','9', \r
+ '\3','3','2','0', '\3','3','2','1', '\3','3','2','2', '\3','3','2','3', '\3','3','2','4', \r
+ '\3','3','2','5', '\3','3','2','6', '\3','3','2','7', '\3','3','2','8', '\3','3','2','9', \r
+ '\3','3','3','0', '\3','3','3','1', '\3','3','3','2', '\3','3','3','3', '\3','3','3','4', \r
+ '\3','3','3','5', '\3','3','3','6', '\3','3','3','7', '\3','3','3','8', '\3','3','3','9', \r
+ '\3','3','4','0', '\3','3','4','1', '\3','3','4','2', '\3','3','4','3', '\3','3','4','4', \r
+ '\3','3','4','5', '\3','3','4','6', '\3','3','4','7', '\3','3','4','8', '\3','3','4','9', \r
+ '\3','3','5','0', '\3','3','5','1', '\3','3','5','2', '\3','3','5','3', '\3','3','5','4', \r
+ '\3','3','5','5', '\3','3','5','6', '\3','3','5','7', '\3','3','5','8', '\3','3','5','9', \r
+ '\3','3','6','0', '\3','3','6','1', '\3','3','6','2', '\3','3','6','3', '\3','3','6','4', \r
+ '\3','3','6','5', '\3','3','6','6', '\3','3','6','7', '\3','3','6','8', '\3','3','6','9', \r
+ '\3','3','7','0', '\3','3','7','1', '\3','3','7','2', '\3','3','7','3', '\3','3','7','4', \r
+ '\3','3','7','5', '\3','3','7','6', '\3','3','7','7', '\3','3','7','8', '\3','3','7','9', \r
+ '\3','3','8','0', '\3','3','8','1', '\3','3','8','2', '\3','3','8','3', '\3','3','8','4', \r
+ '\3','3','8','5', '\3','3','8','6', '\3','3','8','7', '\3','3','8','8', '\3','3','8','9', \r
+ '\3','3','9','0', '\3','3','9','1', '\3','3','9','2', '\3','3','9','3', '\3','3','9','4', \r
+ '\3','3','9','5', '\3','3','9','6', '\3','3','9','7', '\3','3','9','8', '\3','3','9','9', \r
+ '\3','4','0','0', '\3','4','0','1', '\3','4','0','2', '\3','4','0','3', '\3','4','0','4', \r
+ '\3','4','0','5', '\3','4','0','6', '\3','4','0','7', '\3','4','0','8', '\3','4','0','9', \r
+ '\3','4','1','0', '\3','4','1','1', '\3','4','1','2', '\3','4','1','3', '\3','4','1','4', \r
+ '\3','4','1','5', '\3','4','1','6', '\3','4','1','7', '\3','4','1','8', '\3','4','1','9', \r
+ '\3','4','2','0', '\3','4','2','1', '\3','4','2','2', '\3','4','2','3', '\3','4','2','4', \r
+ '\3','4','2','5', '\3','4','2','6', '\3','4','2','7', '\3','4','2','8', '\3','4','2','9', \r
+ '\3','4','3','0', '\3','4','3','1', '\3','4','3','2', '\3','4','3','3', '\3','4','3','4', \r
+ '\3','4','3','5', '\3','4','3','6', '\3','4','3','7', '\3','4','3','8', '\3','4','3','9', \r
+ '\3','4','4','0', '\3','4','4','1', '\3','4','4','2', '\3','4','4','3', '\3','4','4','4', \r
+ '\3','4','4','5', '\3','4','4','6', '\3','4','4','7', '\3','4','4','8', '\3','4','4','9', \r
+ '\3','4','5','0', '\3','4','5','1', '\3','4','5','2', '\3','4','5','3', '\3','4','5','4', \r
+ '\3','4','5','5', '\3','4','5','6', '\3','4','5','7', '\3','4','5','8', '\3','4','5','9', \r
+ '\3','4','6','0', '\3','4','6','1', '\3','4','6','2', '\3','4','6','3', '\3','4','6','4', \r
+ '\3','4','6','5', '\3','4','6','6', '\3','4','6','7', '\3','4','6','8', '\3','4','6','9', \r
+ '\3','4','7','0', '\3','4','7','1', '\3','4','7','2', '\3','4','7','3', '\3','4','7','4', \r
+ '\3','4','7','5', '\3','4','7','6', '\3','4','7','7', '\3','4','7','8', '\3','4','7','9', \r
+ '\3','4','8','0', '\3','4','8','1', '\3','4','8','2', '\3','4','8','3', '\3','4','8','4', \r
+ '\3','4','8','5', '\3','4','8','6', '\3','4','8','7', '\3','4','8','8', '\3','4','8','9', \r
+ '\3','4','9','0', '\3','4','9','1', '\3','4','9','2', '\3','4','9','3', '\3','4','9','4', \r
+ '\3','4','9','5', '\3','4','9','6', '\3','4','9','7', '\3','4','9','8', '\3','4','9','9', \r
+ '\3','5','0','0', '\3','5','0','1', '\3','5','0','2', '\3','5','0','3', '\3','5','0','4', \r
+ '\3','5','0','5', '\3','5','0','6', '\3','5','0','7', '\3','5','0','8', '\3','5','0','9', \r
+ '\3','5','1','0', '\3','5','1','1', '\3','5','1','2', '\3','5','1','3', '\3','5','1','4', \r
+ '\3','5','1','5', '\3','5','1','6', '\3','5','1','7', '\3','5','1','8', '\3','5','1','9', \r
+ '\3','5','2','0', '\3','5','2','1', '\3','5','2','2', '\3','5','2','3', '\3','5','2','4', \r
+ '\3','5','2','5', '\3','5','2','6', '\3','5','2','7', '\3','5','2','8', '\3','5','2','9', \r
+ '\3','5','3','0', '\3','5','3','1', '\3','5','3','2', '\3','5','3','3', '\3','5','3','4', \r
+ '\3','5','3','5', '\3','5','3','6', '\3','5','3','7', '\3','5','3','8', '\3','5','3','9', \r
+ '\3','5','4','0', '\3','5','4','1', '\3','5','4','2', '\3','5','4','3', '\3','5','4','4', \r
+ '\3','5','4','5', '\3','5','4','6', '\3','5','4','7', '\3','5','4','8', '\3','5','4','9', \r
+ '\3','5','5','0', '\3','5','5','1', '\3','5','5','2', '\3','5','5','3', '\3','5','5','4', \r
+ '\3','5','5','5', '\3','5','5','6', '\3','5','5','7', '\3','5','5','8', '\3','5','5','9', \r
+ '\3','5','6','0', '\3','5','6','1', '\3','5','6','2', '\3','5','6','3', '\3','5','6','4', \r
+ '\3','5','6','5', '\3','5','6','6', '\3','5','6','7', '\3','5','6','8', '\3','5','6','9', \r
+ '\3','5','7','0', '\3','5','7','1', '\3','5','7','2', '\3','5','7','3', '\3','5','7','4', \r
+ '\3','5','7','5', '\3','5','7','6', '\3','5','7','7', '\3','5','7','8', '\3','5','7','9', \r
+ '\3','5','8','0', '\3','5','8','1', '\3','5','8','2', '\3','5','8','3', '\3','5','8','4', \r
+ '\3','5','8','5', '\3','5','8','6', '\3','5','8','7', '\3','5','8','8', '\3','5','8','9', \r
+ '\3','5','9','0', '\3','5','9','1', '\3','5','9','2', '\3','5','9','3', '\3','5','9','4', \r
+ '\3','5','9','5', '\3','5','9','6', '\3','5','9','7', '\3','5','9','8', '\3','5','9','9', \r
+ '\3','6','0','0', '\3','6','0','1', '\3','6','0','2', '\3','6','0','3', '\3','6','0','4', \r
+ '\3','6','0','5', '\3','6','0','6', '\3','6','0','7', '\3','6','0','8', '\3','6','0','9', \r
+ '\3','6','1','0', '\3','6','1','1', '\3','6','1','2', '\3','6','1','3', '\3','6','1','4', \r
+ '\3','6','1','5', '\3','6','1','6', '\3','6','1','7', '\3','6','1','8', '\3','6','1','9', \r
+ '\3','6','2','0', '\3','6','2','1', '\3','6','2','2', '\3','6','2','3', '\3','6','2','4', \r
+ '\3','6','2','5', '\3','6','2','6', '\3','6','2','7', '\3','6','2','8', '\3','6','2','9', \r
+ '\3','6','3','0', '\3','6','3','1', '\3','6','3','2', '\3','6','3','3', '\3','6','3','4', \r
+ '\3','6','3','5', '\3','6','3','6', '\3','6','3','7', '\3','6','3','8', '\3','6','3','9', \r
+ '\3','6','4','0', '\3','6','4','1', '\3','6','4','2', '\3','6','4','3', '\3','6','4','4', \r
+ '\3','6','4','5', '\3','6','4','6', '\3','6','4','7', '\3','6','4','8', '\3','6','4','9', \r
+ '\3','6','5','0', '\3','6','5','1', '\3','6','5','2', '\3','6','5','3', '\3','6','5','4', \r
+ '\3','6','5','5', '\3','6','5','6', '\3','6','5','7', '\3','6','5','8', '\3','6','5','9', \r
+ '\3','6','6','0', '\3','6','6','1', '\3','6','6','2', '\3','6','6','3', '\3','6','6','4', \r
+ '\3','6','6','5', '\3','6','6','6', '\3','6','6','7', '\3','6','6','8', '\3','6','6','9', \r
+ '\3','6','7','0', '\3','6','7','1', '\3','6','7','2', '\3','6','7','3', '\3','6','7','4', \r
+ '\3','6','7','5', '\3','6','7','6', '\3','6','7','7', '\3','6','7','8', '\3','6','7','9', \r
+ '\3','6','8','0', '\3','6','8','1', '\3','6','8','2', '\3','6','8','3', '\3','6','8','4', \r
+ '\3','6','8','5', '\3','6','8','6', '\3','6','8','7', '\3','6','8','8', '\3','6','8','9', \r
+ '\3','6','9','0', '\3','6','9','1', '\3','6','9','2', '\3','6','9','3', '\3','6','9','4', \r
+ '\3','6','9','5', '\3','6','9','6', '\3','6','9','7', '\3','6','9','8', '\3','6','9','9', \r
+ '\3','7','0','0', '\3','7','0','1', '\3','7','0','2', '\3','7','0','3', '\3','7','0','4', \r
+ '\3','7','0','5', '\3','7','0','6', '\3','7','0','7', '\3','7','0','8', '\3','7','0','9', \r
+ '\3','7','1','0', '\3','7','1','1', '\3','7','1','2', '\3','7','1','3', '\3','7','1','4', \r
+ '\3','7','1','5', '\3','7','1','6', '\3','7','1','7', '\3','7','1','8', '\3','7','1','9', \r
+ '\3','7','2','0', '\3','7','2','1', '\3','7','2','2', '\3','7','2','3', '\3','7','2','4', \r
+ '\3','7','2','5', '\3','7','2','6', '\3','7','2','7', '\3','7','2','8', '\3','7','2','9', \r
+ '\3','7','3','0', '\3','7','3','1', '\3','7','3','2', '\3','7','3','3', '\3','7','3','4', \r
+ '\3','7','3','5', '\3','7','3','6', '\3','7','3','7', '\3','7','3','8', '\3','7','3','9', \r
+ '\3','7','4','0', '\3','7','4','1', '\3','7','4','2', '\3','7','4','3', '\3','7','4','4', \r
+ '\3','7','4','5', '\3','7','4','6', '\3','7','4','7', '\3','7','4','8', '\3','7','4','9', \r
+ '\3','7','5','0', '\3','7','5','1', '\3','7','5','2', '\3','7','5','3', '\3','7','5','4', \r
+ '\3','7','5','5', '\3','7','5','6', '\3','7','5','7', '\3','7','5','8', '\3','7','5','9', \r
+ '\3','7','6','0', '\3','7','6','1', '\3','7','6','2', '\3','7','6','3', '\3','7','6','4', \r
+ '\3','7','6','5', '\3','7','6','6', '\3','7','6','7', '\3','7','6','8', '\3','7','6','9', \r
+ '\3','7','7','0', '\3','7','7','1', '\3','7','7','2', '\3','7','7','3', '\3','7','7','4', \r
+ '\3','7','7','5', '\3','7','7','6', '\3','7','7','7', '\3','7','7','8', '\3','7','7','9', \r
+ '\3','7','8','0', '\3','7','8','1', '\3','7','8','2', '\3','7','8','3', '\3','7','8','4', \r
+ '\3','7','8','5', '\3','7','8','6', '\3','7','8','7', '\3','7','8','8', '\3','7','8','9', \r
+ '\3','7','9','0', '\3','7','9','1', '\3','7','9','2', '\3','7','9','3', '\3','7','9','4', \r
+ '\3','7','9','5', '\3','7','9','6', '\3','7','9','7', '\3','7','9','8', '\3','7','9','9', \r
+ '\3','8','0','0', '\3','8','0','1', '\3','8','0','2', '\3','8','0','3', '\3','8','0','4', \r
+ '\3','8','0','5', '\3','8','0','6', '\3','8','0','7', '\3','8','0','8', '\3','8','0','9', \r
+ '\3','8','1','0', '\3','8','1','1', '\3','8','1','2', '\3','8','1','3', '\3','8','1','4', \r
+ '\3','8','1','5', '\3','8','1','6', '\3','8','1','7', '\3','8','1','8', '\3','8','1','9', \r
+ '\3','8','2','0', '\3','8','2','1', '\3','8','2','2', '\3','8','2','3', '\3','8','2','4', \r
+ '\3','8','2','5', '\3','8','2','6', '\3','8','2','7', '\3','8','2','8', '\3','8','2','9', \r
+ '\3','8','3','0', '\3','8','3','1', '\3','8','3','2', '\3','8','3','3', '\3','8','3','4', \r
+ '\3','8','3','5', '\3','8','3','6', '\3','8','3','7', '\3','8','3','8', '\3','8','3','9', \r
+ '\3','8','4','0', '\3','8','4','1', '\3','8','4','2', '\3','8','4','3', '\3','8','4','4', \r
+ '\3','8','4','5', '\3','8','4','6', '\3','8','4','7', '\3','8','4','8', '\3','8','4','9', \r
+ '\3','8','5','0', '\3','8','5','1', '\3','8','5','2', '\3','8','5','3', '\3','8','5','4', \r
+ '\3','8','5','5', '\3','8','5','6', '\3','8','5','7', '\3','8','5','8', '\3','8','5','9', \r
+ '\3','8','6','0', '\3','8','6','1', '\3','8','6','2', '\3','8','6','3', '\3','8','6','4', \r
+ '\3','8','6','5', '\3','8','6','6', '\3','8','6','7', '\3','8','6','8', '\3','8','6','9', \r
+ '\3','8','7','0', '\3','8','7','1', '\3','8','7','2', '\3','8','7','3', '\3','8','7','4', \r
+ '\3','8','7','5', '\3','8','7','6', '\3','8','7','7', '\3','8','7','8', '\3','8','7','9', \r
+ '\3','8','8','0', '\3','8','8','1', '\3','8','8','2', '\3','8','8','3', '\3','8','8','4', \r
+ '\3','8','8','5', '\3','8','8','6', '\3','8','8','7', '\3','8','8','8', '\3','8','8','9', \r
+ '\3','8','9','0', '\3','8','9','1', '\3','8','9','2', '\3','8','9','3', '\3','8','9','4', \r
+ '\3','8','9','5', '\3','8','9','6', '\3','8','9','7', '\3','8','9','8', '\3','8','9','9', \r
+ '\3','9','0','0', '\3','9','0','1', '\3','9','0','2', '\3','9','0','3', '\3','9','0','4', \r
+ '\3','9','0','5', '\3','9','0','6', '\3','9','0','7', '\3','9','0','8', '\3','9','0','9', \r
+ '\3','9','1','0', '\3','9','1','1', '\3','9','1','2', '\3','9','1','3', '\3','9','1','4', \r
+ '\3','9','1','5', '\3','9','1','6', '\3','9','1','7', '\3','9','1','8', '\3','9','1','9', \r
+ '\3','9','2','0', '\3','9','2','1', '\3','9','2','2', '\3','9','2','3', '\3','9','2','4', \r
+ '\3','9','2','5', '\3','9','2','6', '\3','9','2','7', '\3','9','2','8', '\3','9','2','9', \r
+ '\3','9','3','0', '\3','9','3','1', '\3','9','3','2', '\3','9','3','3', '\3','9','3','4', \r
+ '\3','9','3','5', '\3','9','3','6', '\3','9','3','7', '\3','9','3','8', '\3','9','3','9', \r
+ '\3','9','4','0', '\3','9','4','1', '\3','9','4','2', '\3','9','4','3', '\3','9','4','4', \r
+ '\3','9','4','5', '\3','9','4','6', '\3','9','4','7', '\3','9','4','8', '\3','9','4','9', \r
+ '\3','9','5','0', '\3','9','5','1', '\3','9','5','2', '\3','9','5','3', '\3','9','5','4', \r
+ '\3','9','5','5', '\3','9','5','6', '\3','9','5','7', '\3','9','5','8', '\3','9','5','9', \r
+ '\3','9','6','0', '\3','9','6','1', '\3','9','6','2', '\3','9','6','3', '\3','9','6','4', \r
+ '\3','9','6','5', '\3','9','6','6', '\3','9','6','7', '\3','9','6','8', '\3','9','6','9', \r
+ '\3','9','7','0', '\3','9','7','1', '\3','9','7','2', '\3','9','7','3', '\3','9','7','4', \r
+ '\3','9','7','5', '\3','9','7','6', '\3','9','7','7', '\3','9','7','8', '\3','9','7','9', \r
+ '\3','9','8','0', '\3','9','8','1', '\3','9','8','2', '\3','9','8','3', '\3','9','8','4', \r
+ '\3','9','8','5', '\3','9','8','6', '\3','9','8','7', '\3','9','8','8', '\3','9','8','9', \r
+ '\3','9','9','0', '\3','9','9','1', '\3','9','9','2', '\3','9','9','3', '\3','9','9','4', \r
+ '\3','9','9','5', '\3','9','9','6', '\3','9','9','7', '\3','9','9','8', '\3','9','9','9', '\0'};\r
+#endif\r
+ \r
+#if defined(DEC_DPD2BCD8) && DEC_DPD2BCD8==1 && !defined(DECDPD2BCD8)\r
+#define DECDPD2BCD8\r
+ \r
+const uint8_t DPD2BCD8[4096]={\r
+ 0,0,0,0, 0,0,1,1, 0,0,2,1, 0,0,3,1, 0,0,4,1, 0,0,5,1, 0,0,6,1, 0,0,7,1, 0,0,8,1, \r
+ 0,0,9,1, 0,8,0,2, 0,8,1,2, 8,0,0,3, 8,0,1,3, 8,8,0,3, 8,8,1,3, 0,1,0,2, 0,1,1,2, \r
+ 0,1,2,2, 0,1,3,2, 0,1,4,2, 0,1,5,2, 0,1,6,2, 0,1,7,2, 0,1,8,2, 0,1,9,2, 0,9,0,2, \r
+ 0,9,1,2, 8,1,0,3, 8,1,1,3, 8,9,0,3, 8,9,1,3, 0,2,0,2, 0,2,1,2, 0,2,2,2, 0,2,3,2, \r
+ 0,2,4,2, 0,2,5,2, 0,2,6,2, 0,2,7,2, 0,2,8,2, 0,2,9,2, 0,8,2,2, 0,8,3,2, 8,2,0,3, \r
+ 8,2,1,3, 8,0,8,3, 8,0,9,3, 0,3,0,2, 0,3,1,2, 0,3,2,2, 0,3,3,2, 0,3,4,2, 0,3,5,2, \r
+ 0,3,6,2, 0,3,7,2, 0,3,8,2, 0,3,9,2, 0,9,2,2, 0,9,3,2, 8,3,0,3, 8,3,1,3, 8,1,8,3, \r
+ 8,1,9,3, 0,4,0,2, 0,4,1,2, 0,4,2,2, 0,4,3,2, 0,4,4,2, 0,4,5,2, 0,4,6,2, 0,4,7,2, \r
+ 0,4,8,2, 0,4,9,2, 0,8,4,2, 0,8,5,2, 8,4,0,3, 8,4,1,3, 0,8,8,2, 0,8,9,2, 0,5,0,2, \r
+ 0,5,1,2, 0,5,2,2, 0,5,3,2, 0,5,4,2, 0,5,5,2, 0,5,6,2, 0,5,7,2, 0,5,8,2, 0,5,9,2, \r
+ 0,9,4,2, 0,9,5,2, 8,5,0,3, 8,5,1,3, 0,9,8,2, 0,9,9,2, 0,6,0,2, 0,6,1,2, 0,6,2,2, \r
+ 0,6,3,2, 0,6,4,2, 0,6,5,2, 0,6,6,2, 0,6,7,2, 0,6,8,2, 0,6,9,2, 0,8,6,2, 0,8,7,2, \r
+ 8,6,0,3, 8,6,1,3, 8,8,8,3, 8,8,9,3, 0,7,0,2, 0,7,1,2, 0,7,2,2, 0,7,3,2, 0,7,4,2, \r
+ 0,7,5,2, 0,7,6,2, 0,7,7,2, 0,7,8,2, 0,7,9,2, 0,9,6,2, 0,9,7,2, 8,7,0,3, 8,7,1,3, \r
+ 8,9,8,3, 8,9,9,3, 1,0,0,3, 1,0,1,3, 1,0,2,3, 1,0,3,3, 1,0,4,3, 1,0,5,3, 1,0,6,3, \r
+ 1,0,7,3, 1,0,8,3, 1,0,9,3, 1,8,0,3, 1,8,1,3, 9,0,0,3, 9,0,1,3, 9,8,0,3, 9,8,1,3, \r
+ 1,1,0,3, 1,1,1,3, 1,1,2,3, 1,1,3,3, 1,1,4,3, 1,1,5,3, 1,1,6,3, 1,1,7,3, 1,1,8,3, \r
+ 1,1,9,3, 1,9,0,3, 1,9,1,3, 9,1,0,3, 9,1,1,3, 9,9,0,3, 9,9,1,3, 1,2,0,3, 1,2,1,3, \r
+ 1,2,2,3, 1,2,3,3, 1,2,4,3, 1,2,5,3, 1,2,6,3, 1,2,7,3, 1,2,8,3, 1,2,9,3, 1,8,2,3, \r
+ 1,8,3,3, 9,2,0,3, 9,2,1,3, 9,0,8,3, 9,0,9,3, 1,3,0,3, 1,3,1,3, 1,3,2,3, 1,3,3,3, \r
+ 1,3,4,3, 1,3,5,3, 1,3,6,3, 1,3,7,3, 1,3,8,3, 1,3,9,3, 1,9,2,3, 1,9,3,3, 9,3,0,3, \r
+ 9,3,1,3, 9,1,8,3, 9,1,9,3, 1,4,0,3, 1,4,1,3, 1,4,2,3, 1,4,3,3, 1,4,4,3, 1,4,5,3, \r
+ 1,4,6,3, 1,4,7,3, 1,4,8,3, 1,4,9,3, 1,8,4,3, 1,8,5,3, 9,4,0,3, 9,4,1,3, 1,8,8,3, \r
+ 1,8,9,3, 1,5,0,3, 1,5,1,3, 1,5,2,3, 1,5,3,3, 1,5,4,3, 1,5,5,3, 1,5,6,3, 1,5,7,3, \r
+ 1,5,8,3, 1,5,9,3, 1,9,4,3, 1,9,5,3, 9,5,0,3, 9,5,1,3, 1,9,8,3, 1,9,9,3, 1,6,0,3, \r
+ 1,6,1,3, 1,6,2,3, 1,6,3,3, 1,6,4,3, 1,6,5,3, 1,6,6,3, 1,6,7,3, 1,6,8,3, 1,6,9,3, \r
+ 1,8,6,3, 1,8,7,3, 9,6,0,3, 9,6,1,3, 9,8,8,3, 9,8,9,3, 1,7,0,3, 1,7,1,3, 1,7,2,3, \r
+ 1,7,3,3, 1,7,4,3, 1,7,5,3, 1,7,6,3, 1,7,7,3, 1,7,8,3, 1,7,9,3, 1,9,6,3, 1,9,7,3, \r
+ 9,7,0,3, 9,7,1,3, 9,9,8,3, 9,9,9,3, 2,0,0,3, 2,0,1,3, 2,0,2,3, 2,0,3,3, 2,0,4,3, \r
+ 2,0,5,3, 2,0,6,3, 2,0,7,3, 2,0,8,3, 2,0,9,3, 2,8,0,3, 2,8,1,3, 8,0,2,3, 8,0,3,3, \r
+ 8,8,2,3, 8,8,3,3, 2,1,0,3, 2,1,1,3, 2,1,2,3, 2,1,3,3, 2,1,4,3, 2,1,5,3, 2,1,6,3, \r
+ 2,1,7,3, 2,1,8,3, 2,1,9,3, 2,9,0,3, 2,9,1,3, 8,1,2,3, 8,1,3,3, 8,9,2,3, 8,9,3,3, \r
+ 2,2,0,3, 2,2,1,3, 2,2,2,3, 2,2,3,3, 2,2,4,3, 2,2,5,3, 2,2,6,3, 2,2,7,3, 2,2,8,3, \r
+ 2,2,9,3, 2,8,2,3, 2,8,3,3, 8,2,2,3, 8,2,3,3, 8,2,8,3, 8,2,9,3, 2,3,0,3, 2,3,1,3, \r
+ 2,3,2,3, 2,3,3,3, 2,3,4,3, 2,3,5,3, 2,3,6,3, 2,3,7,3, 2,3,8,3, 2,3,9,3, 2,9,2,3, \r
+ 2,9,3,3, 8,3,2,3, 8,3,3,3, 8,3,8,3, 8,3,9,3, 2,4,0,3, 2,4,1,3, 2,4,2,3, 2,4,3,3, \r
+ 2,4,4,3, 2,4,5,3, 2,4,6,3, 2,4,7,3, 2,4,8,3, 2,4,9,3, 2,8,4,3, 2,8,5,3, 8,4,2,3, \r
+ 8,4,3,3, 2,8,8,3, 2,8,9,3, 2,5,0,3, 2,5,1,3, 2,5,2,3, 2,5,3,3, 2,5,4,3, 2,5,5,3, \r
+ 2,5,6,3, 2,5,7,3, 2,5,8,3, 2,5,9,3, 2,9,4,3, 2,9,5,3, 8,5,2,3, 8,5,3,3, 2,9,8,3, \r
+ 2,9,9,3, 2,6,0,3, 2,6,1,3, 2,6,2,3, 2,6,3,3, 2,6,4,3, 2,6,5,3, 2,6,6,3, 2,6,7,3, \r
+ 2,6,8,3, 2,6,9,3, 2,8,6,3, 2,8,7,3, 8,6,2,3, 8,6,3,3, 8,8,8,3, 8,8,9,3, 2,7,0,3, \r
+ 2,7,1,3, 2,7,2,3, 2,7,3,3, 2,7,4,3, 2,7,5,3, 2,7,6,3, 2,7,7,3, 2,7,8,3, 2,7,9,3, \r
+ 2,9,6,3, 2,9,7,3, 8,7,2,3, 8,7,3,3, 8,9,8,3, 8,9,9,3, 3,0,0,3, 3,0,1,3, 3,0,2,3, \r
+ 3,0,3,3, 3,0,4,3, 3,0,5,3, 3,0,6,3, 3,0,7,3, 3,0,8,3, 3,0,9,3, 3,8,0,3, 3,8,1,3, \r
+ 9,0,2,3, 9,0,3,3, 9,8,2,3, 9,8,3,3, 3,1,0,3, 3,1,1,3, 3,1,2,3, 3,1,3,3, 3,1,4,3, \r
+ 3,1,5,3, 3,1,6,3, 3,1,7,3, 3,1,8,3, 3,1,9,3, 3,9,0,3, 3,9,1,3, 9,1,2,3, 9,1,3,3, \r
+ 9,9,2,3, 9,9,3,3, 3,2,0,3, 3,2,1,3, 3,2,2,3, 3,2,3,3, 3,2,4,3, 3,2,5,3, 3,2,6,3, \r
+ 3,2,7,3, 3,2,8,3, 3,2,9,3, 3,8,2,3, 3,8,3,3, 9,2,2,3, 9,2,3,3, 9,2,8,3, 9,2,9,3, \r
+ 3,3,0,3, 3,3,1,3, 3,3,2,3, 3,3,3,3, 3,3,4,3, 3,3,5,3, 3,3,6,3, 3,3,7,3, 3,3,8,3, \r
+ 3,3,9,3, 3,9,2,3, 3,9,3,3, 9,3,2,3, 9,3,3,3, 9,3,8,3, 9,3,9,3, 3,4,0,3, 3,4,1,3, \r
+ 3,4,2,3, 3,4,3,3, 3,4,4,3, 3,4,5,3, 3,4,6,3, 3,4,7,3, 3,4,8,3, 3,4,9,3, 3,8,4,3, \r
+ 3,8,5,3, 9,4,2,3, 9,4,3,3, 3,8,8,3, 3,8,9,3, 3,5,0,3, 3,5,1,3, 3,5,2,3, 3,5,3,3, \r
+ 3,5,4,3, 3,5,5,3, 3,5,6,3, 3,5,7,3, 3,5,8,3, 3,5,9,3, 3,9,4,3, 3,9,5,3, 9,5,2,3, \r
+ 9,5,3,3, 3,9,8,3, 3,9,9,3, 3,6,0,3, 3,6,1,3, 3,6,2,3, 3,6,3,3, 3,6,4,3, 3,6,5,3, \r
+ 3,6,6,3, 3,6,7,3, 3,6,8,3, 3,6,9,3, 3,8,6,3, 3,8,7,3, 9,6,2,3, 9,6,3,3, 9,8,8,3, \r
+ 9,8,9,3, 3,7,0,3, 3,7,1,3, 3,7,2,3, 3,7,3,3, 3,7,4,3, 3,7,5,3, 3,7,6,3, 3,7,7,3, \r
+ 3,7,8,3, 3,7,9,3, 3,9,6,3, 3,9,7,3, 9,7,2,3, 9,7,3,3, 9,9,8,3, 9,9,9,3, 4,0,0,3, \r
+ 4,0,1,3, 4,0,2,3, 4,0,3,3, 4,0,4,3, 4,0,5,3, 4,0,6,3, 4,0,7,3, 4,0,8,3, 4,0,9,3, \r
+ 4,8,0,3, 4,8,1,3, 8,0,4,3, 8,0,5,3, 8,8,4,3, 8,8,5,3, 4,1,0,3, 4,1,1,3, 4,1,2,3, \r
+ 4,1,3,3, 4,1,4,3, 4,1,5,3, 4,1,6,3, 4,1,7,3, 4,1,8,3, 4,1,9,3, 4,9,0,3, 4,9,1,3, \r
+ 8,1,4,3, 8,1,5,3, 8,9,4,3, 8,9,5,3, 4,2,0,3, 4,2,1,3, 4,2,2,3, 4,2,3,3, 4,2,4,3, \r
+ 4,2,5,3, 4,2,6,3, 4,2,7,3, 4,2,8,3, 4,2,9,3, 4,8,2,3, 4,8,3,3, 8,2,4,3, 8,2,5,3, \r
+ 8,4,8,3, 8,4,9,3, 4,3,0,3, 4,3,1,3, 4,3,2,3, 4,3,3,3, 4,3,4,3, 4,3,5,3, 4,3,6,3, \r
+ 4,3,7,3, 4,3,8,3, 4,3,9,3, 4,9,2,3, 4,9,3,3, 8,3,4,3, 8,3,5,3, 8,5,8,3, 8,5,9,3, \r
+ 4,4,0,3, 4,4,1,3, 4,4,2,3, 4,4,3,3, 4,4,4,3, 4,4,5,3, 4,4,6,3, 4,4,7,3, 4,4,8,3, \r
+ 4,4,9,3, 4,8,4,3, 4,8,5,3, 8,4,4,3, 8,4,5,3, 4,8,8,3, 4,8,9,3, 4,5,0,3, 4,5,1,3, \r
+ 4,5,2,3, 4,5,3,3, 4,5,4,3, 4,5,5,3, 4,5,6,3, 4,5,7,3, 4,5,8,3, 4,5,9,3, 4,9,4,3, \r
+ 4,9,5,3, 8,5,4,3, 8,5,5,3, 4,9,8,3, 4,9,9,3, 4,6,0,3, 4,6,1,3, 4,6,2,3, 4,6,3,3, \r
+ 4,6,4,3, 4,6,5,3, 4,6,6,3, 4,6,7,3, 4,6,8,3, 4,6,9,3, 4,8,6,3, 4,8,7,3, 8,6,4,3, \r
+ 8,6,5,3, 8,8,8,3, 8,8,9,3, 4,7,0,3, 4,7,1,3, 4,7,2,3, 4,7,3,3, 4,7,4,3, 4,7,5,3, \r
+ 4,7,6,3, 4,7,7,3, 4,7,8,3, 4,7,9,3, 4,9,6,3, 4,9,7,3, 8,7,4,3, 8,7,5,3, 8,9,8,3, \r
+ 8,9,9,3, 5,0,0,3, 5,0,1,3, 5,0,2,3, 5,0,3,3, 5,0,4,3, 5,0,5,3, 5,0,6,3, 5,0,7,3, \r
+ 5,0,8,3, 5,0,9,3, 5,8,0,3, 5,8,1,3, 9,0,4,3, 9,0,5,3, 9,8,4,3, 9,8,5,3, 5,1,0,3, \r
+ 5,1,1,3, 5,1,2,3, 5,1,3,3, 5,1,4,3, 5,1,5,3, 5,1,6,3, 5,1,7,3, 5,1,8,3, 5,1,9,3, \r
+ 5,9,0,3, 5,9,1,3, 9,1,4,3, 9,1,5,3, 9,9,4,3, 9,9,5,3, 5,2,0,3, 5,2,1,3, 5,2,2,3, \r
+ 5,2,3,3, 5,2,4,3, 5,2,5,3, 5,2,6,3, 5,2,7,3, 5,2,8,3, 5,2,9,3, 5,8,2,3, 5,8,3,3, \r
+ 9,2,4,3, 9,2,5,3, 9,4,8,3, 9,4,9,3, 5,3,0,3, 5,3,1,3, 5,3,2,3, 5,3,3,3, 5,3,4,3, \r
+ 5,3,5,3, 5,3,6,3, 5,3,7,3, 5,3,8,3, 5,3,9,3, 5,9,2,3, 5,9,3,3, 9,3,4,3, 9,3,5,3, \r
+ 9,5,8,3, 9,5,9,3, 5,4,0,3, 5,4,1,3, 5,4,2,3, 5,4,3,3, 5,4,4,3, 5,4,5,3, 5,4,6,3, \r
+ 5,4,7,3, 5,4,8,3, 5,4,9,3, 5,8,4,3, 5,8,5,3, 9,4,4,3, 9,4,5,3, 5,8,8,3, 5,8,9,3, \r
+ 5,5,0,3, 5,5,1,3, 5,5,2,3, 5,5,3,3, 5,5,4,3, 5,5,5,3, 5,5,6,3, 5,5,7,3, 5,5,8,3, \r
+ 5,5,9,3, 5,9,4,3, 5,9,5,3, 9,5,4,3, 9,5,5,3, 5,9,8,3, 5,9,9,3, 5,6,0,3, 5,6,1,3, \r
+ 5,6,2,3, 5,6,3,3, 5,6,4,3, 5,6,5,3, 5,6,6,3, 5,6,7,3, 5,6,8,3, 5,6,9,3, 5,8,6,3, \r
+ 5,8,7,3, 9,6,4,3, 9,6,5,3, 9,8,8,3, 9,8,9,3, 5,7,0,3, 5,7,1,3, 5,7,2,3, 5,7,3,3, \r
+ 5,7,4,3, 5,7,5,3, 5,7,6,3, 5,7,7,3, 5,7,8,3, 5,7,9,3, 5,9,6,3, 5,9,7,3, 9,7,4,3, \r
+ 9,7,5,3, 9,9,8,3, 9,9,9,3, 6,0,0,3, 6,0,1,3, 6,0,2,3, 6,0,3,3, 6,0,4,3, 6,0,5,3, \r
+ 6,0,6,3, 6,0,7,3, 6,0,8,3, 6,0,9,3, 6,8,0,3, 6,8,1,3, 8,0,6,3, 8,0,7,3, 8,8,6,3, \r
+ 8,8,7,3, 6,1,0,3, 6,1,1,3, 6,1,2,3, 6,1,3,3, 6,1,4,3, 6,1,5,3, 6,1,6,3, 6,1,7,3, \r
+ 6,1,8,3, 6,1,9,3, 6,9,0,3, 6,9,1,3, 8,1,6,3, 8,1,7,3, 8,9,6,3, 8,9,7,3, 6,2,0,3, \r
+ 6,2,1,3, 6,2,2,3, 6,2,3,3, 6,2,4,3, 6,2,5,3, 6,2,6,3, 6,2,7,3, 6,2,8,3, 6,2,9,3, \r
+ 6,8,2,3, 6,8,3,3, 8,2,6,3, 8,2,7,3, 8,6,8,3, 8,6,9,3, 6,3,0,3, 6,3,1,3, 6,3,2,3, \r
+ 6,3,3,3, 6,3,4,3, 6,3,5,3, 6,3,6,3, 6,3,7,3, 6,3,8,3, 6,3,9,3, 6,9,2,3, 6,9,3,3, \r
+ 8,3,6,3, 8,3,7,3, 8,7,8,3, 8,7,9,3, 6,4,0,3, 6,4,1,3, 6,4,2,3, 6,4,3,3, 6,4,4,3, \r
+ 6,4,5,3, 6,4,6,3, 6,4,7,3, 6,4,8,3, 6,4,9,3, 6,8,4,3, 6,8,5,3, 8,4,6,3, 8,4,7,3, \r
+ 6,8,8,3, 6,8,9,3, 6,5,0,3, 6,5,1,3, 6,5,2,3, 6,5,3,3, 6,5,4,3, 6,5,5,3, 6,5,6,3, \r
+ 6,5,7,3, 6,5,8,3, 6,5,9,3, 6,9,4,3, 6,9,5,3, 8,5,6,3, 8,5,7,3, 6,9,8,3, 6,9,9,3, \r
+ 6,6,0,3, 6,6,1,3, 6,6,2,3, 6,6,3,3, 6,6,4,3, 6,6,5,3, 6,6,6,3, 6,6,7,3, 6,6,8,3, \r
+ 6,6,9,3, 6,8,6,3, 6,8,7,3, 8,6,6,3, 8,6,7,3, 8,8,8,3, 8,8,9,3, 6,7,0,3, 6,7,1,3, \r
+ 6,7,2,3, 6,7,3,3, 6,7,4,3, 6,7,5,3, 6,7,6,3, 6,7,7,3, 6,7,8,3, 6,7,9,3, 6,9,6,3, \r
+ 6,9,7,3, 8,7,6,3, 8,7,7,3, 8,9,8,3, 8,9,9,3, 7,0,0,3, 7,0,1,3, 7,0,2,3, 7,0,3,3, \r
+ 7,0,4,3, 7,0,5,3, 7,0,6,3, 7,0,7,3, 7,0,8,3, 7,0,9,3, 7,8,0,3, 7,8,1,3, 9,0,6,3, \r
+ 9,0,7,3, 9,8,6,3, 9,8,7,3, 7,1,0,3, 7,1,1,3, 7,1,2,3, 7,1,3,3, 7,1,4,3, 7,1,5,3, \r
+ 7,1,6,3, 7,1,7,3, 7,1,8,3, 7,1,9,3, 7,9,0,3, 7,9,1,3, 9,1,6,3, 9,1,7,3, 9,9,6,3, \r
+ 9,9,7,3, 7,2,0,3, 7,2,1,3, 7,2,2,3, 7,2,3,3, 7,2,4,3, 7,2,5,3, 7,2,6,3, 7,2,7,3, \r
+ 7,2,8,3, 7,2,9,3, 7,8,2,3, 7,8,3,3, 9,2,6,3, 9,2,7,3, 9,6,8,3, 9,6,9,3, 7,3,0,3, \r
+ 7,3,1,3, 7,3,2,3, 7,3,3,3, 7,3,4,3, 7,3,5,3, 7,3,6,3, 7,3,7,3, 7,3,8,3, 7,3,9,3, \r
+ 7,9,2,3, 7,9,3,3, 9,3,6,3, 9,3,7,3, 9,7,8,3, 9,7,9,3, 7,4,0,3, 7,4,1,3, 7,4,2,3, \r
+ 7,4,3,3, 7,4,4,3, 7,4,5,3, 7,4,6,3, 7,4,7,3, 7,4,8,3, 7,4,9,3, 7,8,4,3, 7,8,5,3, \r
+ 9,4,6,3, 9,4,7,3, 7,8,8,3, 7,8,9,3, 7,5,0,3, 7,5,1,3, 7,5,2,3, 7,5,3,3, 7,5,4,3, \r
+ 7,5,5,3, 7,5,6,3, 7,5,7,3, 7,5,8,3, 7,5,9,3, 7,9,4,3, 7,9,5,3, 9,5,6,3, 9,5,7,3, \r
+ 7,9,8,3, 7,9,9,3, 7,6,0,3, 7,6,1,3, 7,6,2,3, 7,6,3,3, 7,6,4,3, 7,6,5,3, 7,6,6,3, \r
+ 7,6,7,3, 7,6,8,3, 7,6,9,3, 7,8,6,3, 7,8,7,3, 9,6,6,3, 9,6,7,3, 9,8,8,3, 9,8,9,3, \r
+ 7,7,0,3, 7,7,1,3, 7,7,2,3, 7,7,3,3, 7,7,4,3, 7,7,5,3, 7,7,6,3, 7,7,7,3, 7,7,8,3, \r
+ 7,7,9,3, 7,9,6,3, 7,9,7,3, 9,7,6,3, 9,7,7,3, 9,9,8,3, 9,9,9,3};\r
+#endif\r
+ \r
+#if defined(DEC_BIN2BCD8) && DEC_BIN2BCD8==1 && !defined(DECBIN2BCD8)\r
+#define DECBIN2BCD8\r
+ \r
+const uint8_t BIN2BCD8[4000]={\r
+ 0,0,0,0, 0,0,1,1, 0,0,2,1, 0,0,3,1, 0,0,4,1, 0,0,5,1, 0,0,6,1, 0,0,7,1, 0,0,8,1, \r
+ 0,0,9,1, 0,1,0,2, 0,1,1,2, 0,1,2,2, 0,1,3,2, 0,1,4,2, 0,1,5,2, 0,1,6,2, 0,1,7,2, \r
+ 0,1,8,2, 0,1,9,2, 0,2,0,2, 0,2,1,2, 0,2,2,2, 0,2,3,2, 0,2,4,2, 0,2,5,2, 0,2,6,2, \r
+ 0,2,7,2, 0,2,8,2, 0,2,9,2, 0,3,0,2, 0,3,1,2, 0,3,2,2, 0,3,3,2, 0,3,4,2, 0,3,5,2, \r
+ 0,3,6,2, 0,3,7,2, 0,3,8,2, 0,3,9,2, 0,4,0,2, 0,4,1,2, 0,4,2,2, 0,4,3,2, 0,4,4,2, \r
+ 0,4,5,2, 0,4,6,2, 0,4,7,2, 0,4,8,2, 0,4,9,2, 0,5,0,2, 0,5,1,2, 0,5,2,2, 0,5,3,2, \r
+ 0,5,4,2, 0,5,5,2, 0,5,6,2, 0,5,7,2, 0,5,8,2, 0,5,9,2, 0,6,0,2, 0,6,1,2, 0,6,2,2, \r
+ 0,6,3,2, 0,6,4,2, 0,6,5,2, 0,6,6,2, 0,6,7,2, 0,6,8,2, 0,6,9,2, 0,7,0,2, 0,7,1,2, \r
+ 0,7,2,2, 0,7,3,2, 0,7,4,2, 0,7,5,2, 0,7,6,2, 0,7,7,2, 0,7,8,2, 0,7,9,2, 0,8,0,2, \r
+ 0,8,1,2, 0,8,2,2, 0,8,3,2, 0,8,4,2, 0,8,5,2, 0,8,6,2, 0,8,7,2, 0,8,8,2, 0,8,9,2, \r
+ 0,9,0,2, 0,9,1,2, 0,9,2,2, 0,9,3,2, 0,9,4,2, 0,9,5,2, 0,9,6,2, 0,9,7,2, 0,9,8,2, \r
+ 0,9,9,2, 1,0,0,3, 1,0,1,3, 1,0,2,3, 1,0,3,3, 1,0,4,3, 1,0,5,3, 1,0,6,3, 1,0,7,3, \r
+ 1,0,8,3, 1,0,9,3, 1,1,0,3, 1,1,1,3, 1,1,2,3, 1,1,3,3, 1,1,4,3, 1,1,5,3, 1,1,6,3, \r
+ 1,1,7,3, 1,1,8,3, 1,1,9,3, 1,2,0,3, 1,2,1,3, 1,2,2,3, 1,2,3,3, 1,2,4,3, 1,2,5,3, \r
+ 1,2,6,3, 1,2,7,3, 1,2,8,3, 1,2,9,3, 1,3,0,3, 1,3,1,3, 1,3,2,3, 1,3,3,3, 1,3,4,3, \r
+ 1,3,5,3, 1,3,6,3, 1,3,7,3, 1,3,8,3, 1,3,9,3, 1,4,0,3, 1,4,1,3, 1,4,2,3, 1,4,3,3, \r
+ 1,4,4,3, 1,4,5,3, 1,4,6,3, 1,4,7,3, 1,4,8,3, 1,4,9,3, 1,5,0,3, 1,5,1,3, 1,5,2,3, \r
+ 1,5,3,3, 1,5,4,3, 1,5,5,3, 1,5,6,3, 1,5,7,3, 1,5,8,3, 1,5,9,3, 1,6,0,3, 1,6,1,3, \r
+ 1,6,2,3, 1,6,3,3, 1,6,4,3, 1,6,5,3, 1,6,6,3, 1,6,7,3, 1,6,8,3, 1,6,9,3, 1,7,0,3, \r
+ 1,7,1,3, 1,7,2,3, 1,7,3,3, 1,7,4,3, 1,7,5,3, 1,7,6,3, 1,7,7,3, 1,7,8,3, 1,7,9,3, \r
+ 1,8,0,3, 1,8,1,3, 1,8,2,3, 1,8,3,3, 1,8,4,3, 1,8,5,3, 1,8,6,3, 1,8,7,3, 1,8,8,3, \r
+ 1,8,9,3, 1,9,0,3, 1,9,1,3, 1,9,2,3, 1,9,3,3, 1,9,4,3, 1,9,5,3, 1,9,6,3, 1,9,7,3, \r
+ 1,9,8,3, 1,9,9,3, 2,0,0,3, 2,0,1,3, 2,0,2,3, 2,0,3,3, 2,0,4,3, 2,0,5,3, 2,0,6,3, \r
+ 2,0,7,3, 2,0,8,3, 2,0,9,3, 2,1,0,3, 2,1,1,3, 2,1,2,3, 2,1,3,3, 2,1,4,3, 2,1,5,3, \r
+ 2,1,6,3, 2,1,7,3, 2,1,8,3, 2,1,9,3, 2,2,0,3, 2,2,1,3, 2,2,2,3, 2,2,3,3, 2,2,4,3, \r
+ 2,2,5,3, 2,2,6,3, 2,2,7,3, 2,2,8,3, 2,2,9,3, 2,3,0,3, 2,3,1,3, 2,3,2,3, 2,3,3,3, \r
+ 2,3,4,3, 2,3,5,3, 2,3,6,3, 2,3,7,3, 2,3,8,3, 2,3,9,3, 2,4,0,3, 2,4,1,3, 2,4,2,3, \r
+ 2,4,3,3, 2,4,4,3, 2,4,5,3, 2,4,6,3, 2,4,7,3, 2,4,8,3, 2,4,9,3, 2,5,0,3, 2,5,1,3, \r
+ 2,5,2,3, 2,5,3,3, 2,5,4,3, 2,5,5,3, 2,5,6,3, 2,5,7,3, 2,5,8,3, 2,5,9,3, 2,6,0,3, \r
+ 2,6,1,3, 2,6,2,3, 2,6,3,3, 2,6,4,3, 2,6,5,3, 2,6,6,3, 2,6,7,3, 2,6,8,3, 2,6,9,3, \r
+ 2,7,0,3, 2,7,1,3, 2,7,2,3, 2,7,3,3, 2,7,4,3, 2,7,5,3, 2,7,6,3, 2,7,7,3, 2,7,8,3, \r
+ 2,7,9,3, 2,8,0,3, 2,8,1,3, 2,8,2,3, 2,8,3,3, 2,8,4,3, 2,8,5,3, 2,8,6,3, 2,8,7,3, \r
+ 2,8,8,3, 2,8,9,3, 2,9,0,3, 2,9,1,3, 2,9,2,3, 2,9,3,3, 2,9,4,3, 2,9,5,3, 2,9,6,3, \r
+ 2,9,7,3, 2,9,8,3, 2,9,9,3, 3,0,0,3, 3,0,1,3, 3,0,2,3, 3,0,3,3, 3,0,4,3, 3,0,5,3, \r
+ 3,0,6,3, 3,0,7,3, 3,0,8,3, 3,0,9,3, 3,1,0,3, 3,1,1,3, 3,1,2,3, 3,1,3,3, 3,1,4,3, \r
+ 3,1,5,3, 3,1,6,3, 3,1,7,3, 3,1,8,3, 3,1,9,3, 3,2,0,3, 3,2,1,3, 3,2,2,3, 3,2,3,3, \r
+ 3,2,4,3, 3,2,5,3, 3,2,6,3, 3,2,7,3, 3,2,8,3, 3,2,9,3, 3,3,0,3, 3,3,1,3, 3,3,2,3, \r
+ 3,3,3,3, 3,3,4,3, 3,3,5,3, 3,3,6,3, 3,3,7,3, 3,3,8,3, 3,3,9,3, 3,4,0,3, 3,4,1,3, \r
+ 3,4,2,3, 3,4,3,3, 3,4,4,3, 3,4,5,3, 3,4,6,3, 3,4,7,3, 3,4,8,3, 3,4,9,3, 3,5,0,3, \r
+ 3,5,1,3, 3,5,2,3, 3,5,3,3, 3,5,4,3, 3,5,5,3, 3,5,6,3, 3,5,7,3, 3,5,8,3, 3,5,9,3, \r
+ 3,6,0,3, 3,6,1,3, 3,6,2,3, 3,6,3,3, 3,6,4,3, 3,6,5,3, 3,6,6,3, 3,6,7,3, 3,6,8,3, \r
+ 3,6,9,3, 3,7,0,3, 3,7,1,3, 3,7,2,3, 3,7,3,3, 3,7,4,3, 3,7,5,3, 3,7,6,3, 3,7,7,3, \r
+ 3,7,8,3, 3,7,9,3, 3,8,0,3, 3,8,1,3, 3,8,2,3, 3,8,3,3, 3,8,4,3, 3,8,5,3, 3,8,6,3, \r
+ 3,8,7,3, 3,8,8,3, 3,8,9,3, 3,9,0,3, 3,9,1,3, 3,9,2,3, 3,9,3,3, 3,9,4,3, 3,9,5,3, \r
+ 3,9,6,3, 3,9,7,3, 3,9,8,3, 3,9,9,3, 4,0,0,3, 4,0,1,3, 4,0,2,3, 4,0,3,3, 4,0,4,3, \r
+ 4,0,5,3, 4,0,6,3, 4,0,7,3, 4,0,8,3, 4,0,9,3, 4,1,0,3, 4,1,1,3, 4,1,2,3, 4,1,3,3, \r
+ 4,1,4,3, 4,1,5,3, 4,1,6,3, 4,1,7,3, 4,1,8,3, 4,1,9,3, 4,2,0,3, 4,2,1,3, 4,2,2,3, \r
+ 4,2,3,3, 4,2,4,3, 4,2,5,3, 4,2,6,3, 4,2,7,3, 4,2,8,3, 4,2,9,3, 4,3,0,3, 4,3,1,3, \r
+ 4,3,2,3, 4,3,3,3, 4,3,4,3, 4,3,5,3, 4,3,6,3, 4,3,7,3, 4,3,8,3, 4,3,9,3, 4,4,0,3, \r
+ 4,4,1,3, 4,4,2,3, 4,4,3,3, 4,4,4,3, 4,4,5,3, 4,4,6,3, 4,4,7,3, 4,4,8,3, 4,4,9,3, \r
+ 4,5,0,3, 4,5,1,3, 4,5,2,3, 4,5,3,3, 4,5,4,3, 4,5,5,3, 4,5,6,3, 4,5,7,3, 4,5,8,3, \r
+ 4,5,9,3, 4,6,0,3, 4,6,1,3, 4,6,2,3, 4,6,3,3, 4,6,4,3, 4,6,5,3, 4,6,6,3, 4,6,7,3, \r
+ 4,6,8,3, 4,6,9,3, 4,7,0,3, 4,7,1,3, 4,7,2,3, 4,7,3,3, 4,7,4,3, 4,7,5,3, 4,7,6,3, \r
+ 4,7,7,3, 4,7,8,3, 4,7,9,3, 4,8,0,3, 4,8,1,3, 4,8,2,3, 4,8,3,3, 4,8,4,3, 4,8,5,3, \r
+ 4,8,6,3, 4,8,7,3, 4,8,8,3, 4,8,9,3, 4,9,0,3, 4,9,1,3, 4,9,2,3, 4,9,3,3, 4,9,4,3, \r
+ 4,9,5,3, 4,9,6,3, 4,9,7,3, 4,9,8,3, 4,9,9,3, 5,0,0,3, 5,0,1,3, 5,0,2,3, 5,0,3,3, \r
+ 5,0,4,3, 5,0,5,3, 5,0,6,3, 5,0,7,3, 5,0,8,3, 5,0,9,3, 5,1,0,3, 5,1,1,3, 5,1,2,3, \r
+ 5,1,3,3, 5,1,4,3, 5,1,5,3, 5,1,6,3, 5,1,7,3, 5,1,8,3, 5,1,9,3, 5,2,0,3, 5,2,1,3, \r
+ 5,2,2,3, 5,2,3,3, 5,2,4,3, 5,2,5,3, 5,2,6,3, 5,2,7,3, 5,2,8,3, 5,2,9,3, 5,3,0,3, \r
+ 5,3,1,3, 5,3,2,3, 5,3,3,3, 5,3,4,3, 5,3,5,3, 5,3,6,3, 5,3,7,3, 5,3,8,3, 5,3,9,3, \r
+ 5,4,0,3, 5,4,1,3, 5,4,2,3, 5,4,3,3, 5,4,4,3, 5,4,5,3, 5,4,6,3, 5,4,7,3, 5,4,8,3, \r
+ 5,4,9,3, 5,5,0,3, 5,5,1,3, 5,5,2,3, 5,5,3,3, 5,5,4,3, 5,5,5,3, 5,5,6,3, 5,5,7,3, \r
+ 5,5,8,3, 5,5,9,3, 5,6,0,3, 5,6,1,3, 5,6,2,3, 5,6,3,3, 5,6,4,3, 5,6,5,3, 5,6,6,3, \r
+ 5,6,7,3, 5,6,8,3, 5,6,9,3, 5,7,0,3, 5,7,1,3, 5,7,2,3, 5,7,3,3, 5,7,4,3, 5,7,5,3, \r
+ 5,7,6,3, 5,7,7,3, 5,7,8,3, 5,7,9,3, 5,8,0,3, 5,8,1,3, 5,8,2,3, 5,8,3,3, 5,8,4,3, \r
+ 5,8,5,3, 5,8,6,3, 5,8,7,3, 5,8,8,3, 5,8,9,3, 5,9,0,3, 5,9,1,3, 5,9,2,3, 5,9,3,3, \r
+ 5,9,4,3, 5,9,5,3, 5,9,6,3, 5,9,7,3, 5,9,8,3, 5,9,9,3, 6,0,0,3, 6,0,1,3, 6,0,2,3, \r
+ 6,0,3,3, 6,0,4,3, 6,0,5,3, 6,0,6,3, 6,0,7,3, 6,0,8,3, 6,0,9,3, 6,1,0,3, 6,1,1,3, \r
+ 6,1,2,3, 6,1,3,3, 6,1,4,3, 6,1,5,3, 6,1,6,3, 6,1,7,3, 6,1,8,3, 6,1,9,3, 6,2,0,3, \r
+ 6,2,1,3, 6,2,2,3, 6,2,3,3, 6,2,4,3, 6,2,5,3, 6,2,6,3, 6,2,7,3, 6,2,8,3, 6,2,9,3, \r
+ 6,3,0,3, 6,3,1,3, 6,3,2,3, 6,3,3,3, 6,3,4,3, 6,3,5,3, 6,3,6,3, 6,3,7,3, 6,3,8,3, \r
+ 6,3,9,3, 6,4,0,3, 6,4,1,3, 6,4,2,3, 6,4,3,3, 6,4,4,3, 6,4,5,3, 6,4,6,3, 6,4,7,3, \r
+ 6,4,8,3, 6,4,9,3, 6,5,0,3, 6,5,1,3, 6,5,2,3, 6,5,3,3, 6,5,4,3, 6,5,5,3, 6,5,6,3, \r
+ 6,5,7,3, 6,5,8,3, 6,5,9,3, 6,6,0,3, 6,6,1,3, 6,6,2,3, 6,6,3,3, 6,6,4,3, 6,6,5,3, \r
+ 6,6,6,3, 6,6,7,3, 6,6,8,3, 6,6,9,3, 6,7,0,3, 6,7,1,3, 6,7,2,3, 6,7,3,3, 6,7,4,3, \r
+ 6,7,5,3, 6,7,6,3, 6,7,7,3, 6,7,8,3, 6,7,9,3, 6,8,0,3, 6,8,1,3, 6,8,2,3, 6,8,3,3, \r
+ 6,8,4,3, 6,8,5,3, 6,8,6,3, 6,8,7,3, 6,8,8,3, 6,8,9,3, 6,9,0,3, 6,9,1,3, 6,9,2,3, \r
+ 6,9,3,3, 6,9,4,3, 6,9,5,3, 6,9,6,3, 6,9,7,3, 6,9,8,3, 6,9,9,3, 7,0,0,3, 7,0,1,3, \r
+ 7,0,2,3, 7,0,3,3, 7,0,4,3, 7,0,5,3, 7,0,6,3, 7,0,7,3, 7,0,8,3, 7,0,9,3, 7,1,0,3, \r
+ 7,1,1,3, 7,1,2,3, 7,1,3,3, 7,1,4,3, 7,1,5,3, 7,1,6,3, 7,1,7,3, 7,1,8,3, 7,1,9,3, \r
+ 7,2,0,3, 7,2,1,3, 7,2,2,3, 7,2,3,3, 7,2,4,3, 7,2,5,3, 7,2,6,3, 7,2,7,3, 7,2,8,3, \r
+ 7,2,9,3, 7,3,0,3, 7,3,1,3, 7,3,2,3, 7,3,3,3, 7,3,4,3, 7,3,5,3, 7,3,6,3, 7,3,7,3, \r
+ 7,3,8,3, 7,3,9,3, 7,4,0,3, 7,4,1,3, 7,4,2,3, 7,4,3,3, 7,4,4,3, 7,4,5,3, 7,4,6,3, \r
+ 7,4,7,3, 7,4,8,3, 7,4,9,3, 7,5,0,3, 7,5,1,3, 7,5,2,3, 7,5,3,3, 7,5,4,3, 7,5,5,3, \r
+ 7,5,6,3, 7,5,7,3, 7,5,8,3, 7,5,9,3, 7,6,0,3, 7,6,1,3, 7,6,2,3, 7,6,3,3, 7,6,4,3, \r
+ 7,6,5,3, 7,6,6,3, 7,6,7,3, 7,6,8,3, 7,6,9,3, 7,7,0,3, 7,7,1,3, 7,7,2,3, 7,7,3,3, \r
+ 7,7,4,3, 7,7,5,3, 7,7,6,3, 7,7,7,3, 7,7,8,3, 7,7,9,3, 7,8,0,3, 7,8,1,3, 7,8,2,3, \r
+ 7,8,3,3, 7,8,4,3, 7,8,5,3, 7,8,6,3, 7,8,7,3, 7,8,8,3, 7,8,9,3, 7,9,0,3, 7,9,1,3, \r
+ 7,9,2,3, 7,9,3,3, 7,9,4,3, 7,9,5,3, 7,9,6,3, 7,9,7,3, 7,9,8,3, 7,9,9,3, 8,0,0,3, \r
+ 8,0,1,3, 8,0,2,3, 8,0,3,3, 8,0,4,3, 8,0,5,3, 8,0,6,3, 8,0,7,3, 8,0,8,3, 8,0,9,3, \r
+ 8,1,0,3, 8,1,1,3, 8,1,2,3, 8,1,3,3, 8,1,4,3, 8,1,5,3, 8,1,6,3, 8,1,7,3, 8,1,8,3, \r
+ 8,1,9,3, 8,2,0,3, 8,2,1,3, 8,2,2,3, 8,2,3,3, 8,2,4,3, 8,2,5,3, 8,2,6,3, 8,2,7,3, \r
+ 8,2,8,3, 8,2,9,3, 8,3,0,3, 8,3,1,3, 8,3,2,3, 8,3,3,3, 8,3,4,3, 8,3,5,3, 8,3,6,3, \r
+ 8,3,7,3, 8,3,8,3, 8,3,9,3, 8,4,0,3, 8,4,1,3, 8,4,2,3, 8,4,3,3, 8,4,4,3, 8,4,5,3, \r
+ 8,4,6,3, 8,4,7,3, 8,4,8,3, 8,4,9,3, 8,5,0,3, 8,5,1,3, 8,5,2,3, 8,5,3,3, 8,5,4,3, \r
+ 8,5,5,3, 8,5,6,3, 8,5,7,3, 8,5,8,3, 8,5,9,3, 8,6,0,3, 8,6,1,3, 8,6,2,3, 8,6,3,3, \r
+ 8,6,4,3, 8,6,5,3, 8,6,6,3, 8,6,7,3, 8,6,8,3, 8,6,9,3, 8,7,0,3, 8,7,1,3, 8,7,2,3, \r
+ 8,7,3,3, 8,7,4,3, 8,7,5,3, 8,7,6,3, 8,7,7,3, 8,7,8,3, 8,7,9,3, 8,8,0,3, 8,8,1,3, \r
+ 8,8,2,3, 8,8,3,3, 8,8,4,3, 8,8,5,3, 8,8,6,3, 8,8,7,3, 8,8,8,3, 8,8,9,3, 8,9,0,3, \r
+ 8,9,1,3, 8,9,2,3, 8,9,3,3, 8,9,4,3, 8,9,5,3, 8,9,6,3, 8,9,7,3, 8,9,8,3, 8,9,9,3, \r
+ 9,0,0,3, 9,0,1,3, 9,0,2,3, 9,0,3,3, 9,0,4,3, 9,0,5,3, 9,0,6,3, 9,0,7,3, 9,0,8,3, \r
+ 9,0,9,3, 9,1,0,3, 9,1,1,3, 9,1,2,3, 9,1,3,3, 9,1,4,3, 9,1,5,3, 9,1,6,3, 9,1,7,3, \r
+ 9,1,8,3, 9,1,9,3, 9,2,0,3, 9,2,1,3, 9,2,2,3, 9,2,3,3, 9,2,4,3, 9,2,5,3, 9,2,6,3, \r
+ 9,2,7,3, 9,2,8,3, 9,2,9,3, 9,3,0,3, 9,3,1,3, 9,3,2,3, 9,3,3,3, 9,3,4,3, 9,3,5,3, \r
+ 9,3,6,3, 9,3,7,3, 9,3,8,3, 9,3,9,3, 9,4,0,3, 9,4,1,3, 9,4,2,3, 9,4,3,3, 9,4,4,3, \r
+ 9,4,5,3, 9,4,6,3, 9,4,7,3, 9,4,8,3, 9,4,9,3, 9,5,0,3, 9,5,1,3, 9,5,2,3, 9,5,3,3, \r
+ 9,5,4,3, 9,5,5,3, 9,5,6,3, 9,5,7,3, 9,5,8,3, 9,5,9,3, 9,6,0,3, 9,6,1,3, 9,6,2,3, \r
+ 9,6,3,3, 9,6,4,3, 9,6,5,3, 9,6,6,3, 9,6,7,3, 9,6,8,3, 9,6,9,3, 9,7,0,3, 9,7,1,3, \r
+ 9,7,2,3, 9,7,3,3, 9,7,4,3, 9,7,5,3, 9,7,6,3, 9,7,7,3, 9,7,8,3, 9,7,9,3, 9,8,0,3, \r
+ 9,8,1,3, 9,8,2,3, 9,8,3,3, 9,8,4,3, 9,8,5,3, 9,8,6,3, 9,8,7,3, 9,8,8,3, 9,8,9,3, \r
+ 9,9,0,3, 9,9,1,3, 9,9,2,3, 9,9,3,3, 9,9,4,3, 9,9,5,3, 9,9,6,3, 9,9,7,3, 9,9,8,3, \r
+ 9,9,9,3};\r
+#endif\r
+ \r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decDouble.c -- decDouble operations module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises decDouble operations (including conversions) */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#include "decContext.h" // public includes\r
+#include "decDouble.h" // ..\r
+\r
+/* Constant mappings for shared code */\r
+#define DECPMAX DECDOUBLE_Pmax\r
+#define DECEMIN DECDOUBLE_Emin\r
+#define DECEMAX DECDOUBLE_Emax\r
+#define DECEMAXD DECDOUBLE_EmaxD\r
+#define DECBYTES DECDOUBLE_Bytes\r
+#define DECSTRING DECDOUBLE_String\r
+#define DECECONL DECDOUBLE_EconL\r
+#define DECBIAS DECDOUBLE_Bias\r
+#define DECLETS DECDOUBLE_Declets\r
+#define DECQTINY (-DECDOUBLE_Bias)\r
+// parameters of next-wider format\r
+#define DECWBYTES DECQUAD_Bytes\r
+#define DECWPMAX DECQUAD_Pmax\r
+#define DECWECONL DECQUAD_EconL\r
+#define DECWBIAS DECQUAD_Bias\r
+\r
+/* Type and function mappings for shared code */\r
+#define decFloat decDouble // Type name\r
+#define decFloatWider decQuad // Type name\r
+\r
+// Utilities and conversions (binary results, extractors, etc.)\r
+#define decFloatFromBCD decDoubleFromBCD\r
+#define decFloatFromInt32 decDoubleFromInt32\r
+#define decFloatFromPacked decDoubleFromPacked\r
+#define decFloatFromPackedChecked decDoubleFromPackedChecked\r
+#define decFloatFromString decDoubleFromString\r
+#define decFloatFromUInt32 decDoubleFromUInt32\r
+#define decFloatFromWider decDoubleFromWider\r
+#define decFloatGetCoefficient decDoubleGetCoefficient\r
+#define decFloatGetExponent decDoubleGetExponent\r
+#define decFloatSetCoefficient decDoubleSetCoefficient\r
+#define decFloatSetExponent decDoubleSetExponent\r
+#define decFloatShow decDoubleShow\r
+#define decFloatToBCD decDoubleToBCD\r
+#define decFloatToEngString decDoubleToEngString\r
+#define decFloatToInt32 decDoubleToInt32\r
+#define decFloatToInt32Exact decDoubleToInt32Exact\r
+#define decFloatToPacked decDoubleToPacked\r
+#define decFloatToString decDoubleToString\r
+#define decFloatToUInt32 decDoubleToUInt32\r
+#define decFloatToUInt32Exact decDoubleToUInt32Exact\r
+#define decFloatToWider decDoubleToWider\r
+#define decFloatZero decDoubleZero\r
+\r
+// Computational (result is a decFloat)\r
+#define decFloatAbs decDoubleAbs\r
+#define decFloatAdd decDoubleAdd\r
+#define decFloatAnd decDoubleAnd\r
+#define decFloatDivide decDoubleDivide\r
+#define decFloatDivideInteger decDoubleDivideInteger\r
+#define decFloatFMA decDoubleFMA\r
+#define decFloatInvert decDoubleInvert\r
+#define decFloatLogB decDoubleLogB\r
+#define decFloatMax decDoubleMax\r
+#define decFloatMaxMag decDoubleMaxMag\r
+#define decFloatMin decDoubleMin\r
+#define decFloatMinMag decDoubleMinMag\r
+#define decFloatMinus decDoubleMinus\r
+#define decFloatMultiply decDoubleMultiply\r
+#define decFloatNextMinus decDoubleNextMinus\r
+#define decFloatNextPlus decDoubleNextPlus\r
+#define decFloatNextToward decDoubleNextToward\r
+#define decFloatOr decDoubleOr\r
+#define decFloatPlus decDoublePlus\r
+#define decFloatQuantize decDoubleQuantize\r
+#define decFloatReduce decDoubleReduce\r
+#define decFloatRemainder decDoubleRemainder\r
+#define decFloatRemainderNear decDoubleRemainderNear\r
+#define decFloatRotate decDoubleRotate\r
+#define decFloatScaleB decDoubleScaleB\r
+#define decFloatShift decDoubleShift\r
+#define decFloatSubtract decDoubleSubtract\r
+#define decFloatToIntegralValue decDoubleToIntegralValue\r
+#define decFloatToIntegralExact decDoubleToIntegralExact\r
+#define decFloatXor decDoubleXor\r
+\r
+// Comparisons\r
+#define decFloatCompare decDoubleCompare\r
+#define decFloatCompareSignal decDoubleCompareSignal\r
+#define decFloatCompareTotal decDoubleCompareTotal\r
+#define decFloatCompareTotalMag decDoubleCompareTotalMag\r
+\r
+// Copies\r
+#define decFloatCanonical decDoubleCanonical\r
+#define decFloatCopy decDoubleCopy\r
+#define decFloatCopyAbs decDoubleCopyAbs\r
+#define decFloatCopyNegate decDoubleCopyNegate\r
+#define decFloatCopySign decDoubleCopySign\r
+\r
+// Non-computational\r
+#define decFloatClass decDoubleClass\r
+#define decFloatClassString decDoubleClassString\r
+#define decFloatDigits decDoubleDigits\r
+#define decFloatIsCanonical decDoubleIsCanonical\r
+#define decFloatIsFinite decDoubleIsFinite\r
+#define decFloatIsInfinite decDoubleIsInfinite\r
+#define decFloatIsInteger decDoubleIsInteger\r
+#define decFloatIsLogical decDoubleIsLogical\r
+#define decFloatIsNaN decDoubleIsNaN\r
+#define decFloatIsNegative decDoubleIsNegative\r
+#define decFloatIsNormal decDoubleIsNormal\r
+#define decFloatIsPositive decDoubleIsPositive\r
+#define decFloatIsSignaling decDoubleIsSignaling\r
+#define decFloatIsSignalling decDoubleIsSignalling\r
+#define decFloatIsSigned decDoubleIsSigned\r
+#define decFloatIsSubnormal decDoubleIsSubnormal\r
+#define decFloatIsZero decDoubleIsZero\r
+#define decFloatRadix decDoubleRadix\r
+#define decFloatSameQuantum decDoubleSameQuantum\r
+#define decFloatVersion decDoubleVersion\r
+\r
+#include "decNumberLocal.h" // local includes (need DECPMAX)\r
+#include "decCommon.c" // non-arithmetic decFloat routines\r
+#include "decBasic.c" // basic formats routines\r
+\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decDouble.h -- Decimal 64-bit format module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECDOUBLE)\r
+ #define DECDOUBLE\r
+\r
+ #define DECDOUBLENAME "decimalDouble" /* Short name */\r
+ #define DECDOUBLETITLE "Decimal 64-bit datum" /* Verbose name */\r
+ #define DECDOUBLEAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ /* parameters for decDoubles */\r
+ #define DECDOUBLE_Bytes 8 /* length */\r
+ #define DECDOUBLE_Pmax 16 /* maximum precision (digits) */\r
+ #define DECDOUBLE_Emin -383 /* minimum adjusted exponent */\r
+ #define DECDOUBLE_Emax 384 /* maximum adjusted exponent */\r
+ #define DECDOUBLE_EmaxD 3 /* maximum exponent digits */\r
+ #define DECDOUBLE_Bias 398 /* bias for the exponent */\r
+ #define DECDOUBLE_String 25 /* maximum string length, +1 */\r
+ #define DECDOUBLE_EconL 8 /* exponent continuation length */\r
+ #define DECDOUBLE_Declets 5 /* count of declets */\r
+ /* highest biased exponent (Elimit-1) */\r
+ #define DECDOUBLE_Ehigh (DECDOUBLE_Emax + DECDOUBLE_Bias - (DECDOUBLE_Pmax-1))\r
+\r
+ /* Required includes */\r
+ #include "decContext.h"\r
+ #include "decQuad.h"\r
+\r
+ /* The decDouble decimal 64-bit type, accessible by all sizes */\r
+ typedef union {\r
+ uint8_t bytes[DECDOUBLE_Bytes]; /* fields: 1, 5, 8, 50 bits */\r
+ uint16_t shorts[DECDOUBLE_Bytes/2];\r
+ uint32_t words[DECDOUBLE_Bytes/4];\r
+ #if DECUSE64\r
+ uint64_t longs[DECDOUBLE_Bytes/8];\r
+ #endif\r
+ } decDouble;\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Routines -- implemented as decFloat routines in common files */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* Utilities and conversions, extractors, etc.) */\r
+ extern decDouble * decDoubleFromBCD(decDouble *, int32_t, const uint8_t *, int32_t);\r
+ extern decDouble * decDoubleFromInt32(decDouble *, int32_t);\r
+ extern decDouble * decDoubleFromPacked(decDouble *, int32_t, const uint8_t *);\r
+ extern decDouble * decDoubleFromPackedChecked(decDouble *, int32_t, const uint8_t *);\r
+ extern decDouble * decDoubleFromString(decDouble *, const char *, decContext *);\r
+ extern decDouble * decDoubleFromUInt32(decDouble *, uint32_t);\r
+ extern decDouble * decDoubleFromWider(decDouble *, const decQuad *, decContext *);\r
+ extern int32_t decDoubleGetCoefficient(const decDouble *, uint8_t *);\r
+ extern int32_t decDoubleGetExponent(const decDouble *);\r
+ extern decDouble * decDoubleSetCoefficient(decDouble *, const uint8_t *, int32_t);\r
+ extern decDouble * decDoubleSetExponent(decDouble *, decContext *, int32_t);\r
+ extern void decDoubleShow(const decDouble *, const char *);\r
+ extern int32_t decDoubleToBCD(const decDouble *, int32_t *, uint8_t *);\r
+ extern char * decDoubleToEngString(const decDouble *, char *);\r
+ extern int32_t decDoubleToInt32(const decDouble *, decContext *, enum rounding);\r
+ extern int32_t decDoubleToInt32Exact(const decDouble *, decContext *, enum rounding);\r
+ extern int32_t decDoubleToPacked(const decDouble *, int32_t *, uint8_t *);\r
+ extern char * decDoubleToString(const decDouble *, char *);\r
+ extern uint32_t decDoubleToUInt32(const decDouble *, decContext *, enum rounding);\r
+ extern uint32_t decDoubleToUInt32Exact(const decDouble *, decContext *, enum rounding);\r
+ extern decQuad * decDoubleToWider(const decDouble *, decQuad *);\r
+ extern decDouble * decDoubleZero(decDouble *);\r
+\r
+ /* Computational (result is a decDouble) */\r
+ extern decDouble * decDoubleAbs(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleAdd(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleAnd(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleDivide(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleDivideInteger(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleFMA(decDouble *, const decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleInvert(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleLogB(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleMax(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleMaxMag(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleMin(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleMinMag(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleMinus(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleMultiply(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleNextMinus(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleNextPlus(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleNextToward(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleOr(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoublePlus(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleQuantize(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleReduce(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleRemainder(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleRemainderNear(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleRotate(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleScaleB(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleShift(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleSubtract(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleToIntegralValue(decDouble *, const decDouble *, decContext *, enum rounding);\r
+ extern decDouble * decDoubleToIntegralExact(decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleXor(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+\r
+ /* Comparisons */\r
+ extern decDouble * decDoubleCompare(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleCompareSignal(decDouble *, const decDouble *, const decDouble *, decContext *);\r
+ extern decDouble * decDoubleCompareTotal(decDouble *, const decDouble *, const decDouble *);\r
+ extern decDouble * decDoubleCompareTotalMag(decDouble *, const decDouble *, const decDouble *);\r
+\r
+ /* Copies */\r
+ extern decDouble * decDoubleCanonical(decDouble *, const decDouble *);\r
+ extern decDouble * decDoubleCopy(decDouble *, const decDouble *);\r
+ extern decDouble * decDoubleCopyAbs(decDouble *, const decDouble *);\r
+ extern decDouble * decDoubleCopyNegate(decDouble *, const decDouble *);\r
+ extern decDouble * decDoubleCopySign(decDouble *, const decDouble *, const decDouble *);\r
+\r
+ /* Non-computational */\r
+ extern enum decClass decDoubleClass(const decDouble *);\r
+ extern const char * decDoubleClassString(const decDouble *);\r
+ extern uint32_t decDoubleDigits(const decDouble *);\r
+ extern uint32_t decDoubleIsCanonical(const decDouble *);\r
+ extern uint32_t decDoubleIsFinite(const decDouble *);\r
+ extern uint32_t decDoubleIsInfinite(const decDouble *);\r
+ extern uint32_t decDoubleIsInteger(const decDouble *);\r
+ extern uint32_t decDoubleIsLogical(const decDouble *);\r
+ extern uint32_t decDoubleIsNaN(const decDouble *);\r
+ extern uint32_t decDoubleIsNegative(const decDouble *);\r
+ extern uint32_t decDoubleIsNormal(const decDouble *);\r
+ extern uint32_t decDoubleIsPositive(const decDouble *);\r
+ extern uint32_t decDoubleIsSignaling(const decDouble *);\r
+ extern uint32_t decDoubleIsSignalling(const decDouble *);\r
+ extern uint32_t decDoubleIsSigned(const decDouble *);\r
+ extern uint32_t decDoubleIsSubnormal(const decDouble *);\r
+ extern uint32_t decDoubleIsZero(const decDouble *);\r
+ extern uint32_t decDoubleRadix(const decDouble *);\r
+ extern uint32_t decDoubleSameQuantum(const decDouble *, const decDouble *);\r
+ extern const char * decDoubleVersion(void);\r
+\r
+ /* decNumber conversions; these are implemented as macros so as not */\r
+ /* to force a dependency on decimal64 and decNumber in decDouble. */\r
+ /* decDoubleFromNumber returns a decimal64 * to avoid warnings. */\r
+ #define decDoubleToNumber(dq, dn) decimal64ToNumber((decimal64 *)(dq), dn)\r
+ #define decDoubleFromNumber(dq, dn, set) decimal64FromNumber((decimal64 *)(dq), dn, set)\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number arithmetic module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises the routines for arbitrary-precision General */\r
+/* Decimal Arithmetic as defined in the specification which may be */\r
+/* found on the General Decimal Arithmetic pages. It implements both */\r
+/* the full ('extended') arithmetic and the simpler ('subset') */\r
+/* arithmetic. */\r
+/* */\r
+/* Usage notes: */\r
+/* */\r
+/* 1. This code is ANSI C89 except: */\r
+/* */\r
+/* a) C99 line comments (double forward slash) are used. (Most C */\r
+/* compilers accept these. If yours does not, a simple script */\r
+/* can be used to convert them to ANSI C comments.) */\r
+/* */\r
+/* b) Types from C99 stdint.h are used. If you do not have this */\r
+/* header file, see the User's Guide section of the decNumber */\r
+/* documentation; this lists the necessary definitions. */\r
+/* */\r
+/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */\r
+/* uint64_t types may be used. To avoid these, set DECUSE64=0 */\r
+/* and DECDPUN<=4 (see documentation). */\r
+/* */\r
+/* The code also conforms to C99 restrictions; in particular, */\r
+/* strict aliasing rules are observed. */\r
+/* */\r
+/* 2. The decNumber format which this library uses is optimized for */\r
+/* efficient processing of relatively short numbers; in particular */\r
+/* it allows the use of fixed sized structures and minimizes copy */\r
+/* and move operations. It does, however, support arbitrary */\r
+/* precision (up to 999,999,999 digits) and arbitrary exponent */\r
+/* range (Emax in the range 0 through 999,999,999 and Emin in the */\r
+/* range -999,999,999 through 0). Mathematical functions (for */\r
+/* example decNumberExp) as identified below are restricted more */\r
+/* tightly: digits, emax, and -emin in the context must be <= */\r
+/* DEC_MAX_MATH (999999), and their operand(s) must be within */\r
+/* these bounds. */\r
+/* */\r
+/* 3. Logical functions are further restricted; their operands must */\r
+/* be finite, positive, have an exponent of zero, and all digits */\r
+/* must be either 0 or 1. The result will only contain digits */\r
+/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */\r
+/* */\r
+/* 4. Operands to operator functions are never modified unless they */\r
+/* are also specified to be the result number (which is always */\r
+/* permitted). Other than that case, operands must not overlap. */\r
+/* */\r
+/* 5. Error handling: the type of the error is ORed into the status */\r
+/* flags in the current context (decContext structure). The */\r
+/* SIGFPE signal is then raised if the corresponding trap-enabler */\r
+/* flag in the decContext is set (is 1). */\r
+/* */\r
+/* It is the responsibility of the caller to clear the status */\r
+/* flags as required. */\r
+/* */\r
+/* The result of any routine which returns a number will always */\r
+/* be a valid number (which may be a special value, such as an */\r
+/* Infinity or NaN). */\r
+/* */\r
+/* 6. The decNumber format is not an exchangeable concrete */\r
+/* representation as it comprises fields which may be machine- */\r
+/* dependent (packed or unpacked, or special length, for example). */\r
+/* Canonical conversions to and from strings are provided; other */\r
+/* conversions are available in separate modules. */\r
+/* */\r
+/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */\r
+/* to 1 for extended operand checking (including NULL operands). */\r
+/* Results are undefined if a badly-formed structure (or a NULL */\r
+/* pointer to a structure) is provided, though with DECCHECK */\r
+/* enabled the operator routines are protected against exceptions. */\r
+/* (Except if the result pointer is NULL, which is unrecoverable.) */\r
+/* */\r
+/* However, the routines will never cause exceptions if they are */\r
+/* given well-formed operands, even if the value of the operands */\r
+/* is inappropriate for the operation and DECCHECK is not set. */\r
+/* (Except for SIGFPE, as and where documented.) */\r
+/* */\r
+/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */\r
+/* ------------------------------------------------------------------ */\r
+/* Implementation notes for maintenance of this module: */\r
+/* */\r
+/* 1. Storage leak protection: Routines which use malloc are not */\r
+/* permitted to use return for fastpath or error exits (i.e., */\r
+/* they follow strict structured programming conventions). */\r
+/* Instead they have a do{}while(0); construct surrounding the */\r
+/* code which is protected -- break may be used to exit this. */\r
+/* Other routines can safely use the return statement inline. */\r
+/* */\r
+/* Storage leak accounting can be enabled using DECALLOC. */\r
+/* */\r
+/* 2. All loops use the for(;;) construct. Any do construct does */\r
+/* not loop; it is for allocation protection as just described. */\r
+/* */\r
+/* 3. Setting status in the context must always be the very last */\r
+/* action in a routine, as non-0 status may raise a trap and hence */\r
+/* the call to set status may not return (if the handler uses long */\r
+/* jump). Therefore all cleanup must be done first. In general, */\r
+/* to achieve this status is accumulated and is only applied just */\r
+/* before return by calling decContextSetStatus (via decStatus). */\r
+/* */\r
+/* Routines which allocate storage cannot, in general, use the */\r
+/* 'top level' routines which could cause a non-returning */\r
+/* transfer of control. The decXxxxOp routines are safe (do not */\r
+/* call decStatus even if traps are set in the context) and should */\r
+/* be used instead (they are also a little faster). */\r
+/* */\r
+/* 4. Exponent checking is minimized by allowing the exponent to */\r
+/* grow outside its limits during calculations, provided that */\r
+/* the decFinalize function is called later. Multiplication and */\r
+/* division, and intermediate calculations in exponentiation, */\r
+/* require more careful checks because of the risk of 31-bit */\r
+/* overflow (the most negative valid exponent is -1999999997, for */\r
+/* a 999999999-digit number with adjusted exponent of -999999999). */\r
+/* */\r
+/* 5. Rounding is deferred until finalization of results, with any */\r
+/* 'off to the right' data being represented as a single digit */\r
+/* residue (in the range -1 through 9). This avoids any double- */\r
+/* rounding when more than one shortening takes place (for */\r
+/* example, when a result is subnormal). */\r
+/* */\r
+/* 6. The digits count is allowed to rise to a multiple of DECDPUN */\r
+/* during many operations, so whole Units are handled and exact */\r
+/* accounting of digits is not needed. The correct digits value */\r
+/* is found by decGetDigits, which accounts for leading zeros. */\r
+/* This must be called before any rounding if the number of digits */\r
+/* is not known exactly. */\r
+/* */\r
+/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */\r
+/* numbers up to four digits, using appropriate constants. This */\r
+/* is not useful for longer numbers because overflow of 32 bits */\r
+/* would lead to 4 multiplies, which is almost as expensive as */\r
+/* a divide (unless a floating-point or 64-bit multiply is */\r
+/* assumed to be available). */\r
+/* */\r
+/* 8. Unusual abbreviations that may be used in the commentary: */\r
+/* lhs -- left hand side (operand, of an operation) */\r
+/* lsd -- least significant digit (of coefficient) */\r
+/* lsu -- least significant Unit (of coefficient) */\r
+/* msd -- most significant digit (of coefficient) */\r
+/* msi -- most significant item (in an array) */\r
+/* msu -- most significant Unit (of coefficient) */\r
+/* rhs -- right hand side (operand, of an operation) */\r
+/* +ve -- positive */\r
+/* -ve -- negative */\r
+/* ** -- raise to the power */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#include <stdlib.h> // for malloc, free, etc.\r
+#include <stdio.h> // for printf [if needed]\r
+#include <string.h> // for strcpy\r
+#include <ctype.h> // for lower\r
+#include "decNumber.h" // base number library\r
+#include "decNumberLocal.h" // decNumber local types, etc.\r
+\r
+/* Constants */\r
+// Public lookup table used by the D2U macro\r
+const uByte d2utable[DECMAXD2U+1]=D2UTABLE;\r
+\r
+#define DECVERB 1 // set to 1 for verbose DECCHECK\r
+#define powers DECPOWERS // old internal name\r
+\r
+// Local constants\r
+#define DIVIDE 0x80 // Divide operators\r
+#define REMAINDER 0x40 // ..\r
+#define DIVIDEINT 0x20 // ..\r
+#define REMNEAR 0x10 // ..\r
+#define COMPARE 0x01 // Compare operators\r
+#define COMPMAX 0x02 // ..\r
+#define COMPMIN 0x03 // ..\r
+#define COMPTOTAL 0x04 // ..\r
+#define COMPNAN 0x05 // .. [NaN processing]\r
+#define COMPSIG 0x06 // .. [signaling COMPARE]\r
+#define COMPMAXMAG 0x07 // ..\r
+#define COMPMINMAG 0x08 // ..\r
+\r
+#define DEC_sNaN 0x40000000 // local status: sNaN signal\r
+#define BADINT (Int)0x80000000 // most-negative Int; error indicator\r
+// Next two indicate an integer >= 10**6, and its parity (bottom bit)\r
+#define BIGEVEN (Int)0x80000002\r
+#define BIGODD (Int)0x80000003\r
+\r
+static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing\r
+\r
+/* Granularity-dependent code */\r
+#if DECDPUN<=4\r
+ #define eInt Int // extended integer\r
+ #define ueInt uInt // unsigned extended integer\r
+ // Constant multipliers for divide-by-power-of five using reciprocal\r
+ // multiply, after removing powers of 2 by shifting, and final shift\r
+ // of 17 [we only need up to **4]\r
+ static const uInt multies[]={131073, 26215, 5243, 1049, 210};\r
+ // QUOT10 -- macro to return the quotient of unit u divided by 10**n\r
+ #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)\r
+#else\r
+ // For DECDPUN>4 non-ANSI-89 64-bit types are needed.\r
+ #if !DECUSE64\r
+ #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4\r
+ #endif\r
+ #define eInt Long // extended integer\r
+ #define ueInt uLong // unsigned extended integer\r
+#endif\r
+\r
+/* Local routines */\r
+static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,\r
+ decContext *, uByte, uInt *);\r
+static Flag decBiStr(const char *, const char *, const char *);\r
+static uInt decCheckMath(const decNumber *, decContext *, uInt *);\r
+static void decApplyRound(decNumber *, decContext *, Int, uInt *);\r
+static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);\r
+static decNumber * decCompareOp(decNumber *, const decNumber *,\r
+ const decNumber *, decContext *,\r
+ Flag, uInt *);\r
+static void decCopyFit(decNumber *, const decNumber *, decContext *,\r
+ Int *, uInt *);\r
+static decNumber * decDecap(decNumber *, Int);\r
+static decNumber * decDivideOp(decNumber *, const decNumber *,\r
+ const decNumber *, decContext *, Flag, uInt *);\r
+static decNumber * decExpOp(decNumber *, const decNumber *,\r
+ decContext *, uInt *);\r
+static void decFinalize(decNumber *, decContext *, Int *, uInt *);\r
+static Int decGetDigits(Unit *, Int);\r
+static Int decGetInt(const decNumber *);\r
+static decNumber * decLnOp(decNumber *, const decNumber *,\r
+ decContext *, uInt *);\r
+static decNumber * decMultiplyOp(decNumber *, const decNumber *,\r
+ const decNumber *, decContext *,\r
+ uInt *);\r
+static decNumber * decNaNs(decNumber *, const decNumber *,\r
+ const decNumber *, decContext *, uInt *);\r
+static decNumber * decQuantizeOp(decNumber *, const decNumber *,\r
+ const decNumber *, decContext *, Flag,\r
+ uInt *);\r
+static void decReverse(Unit *, Unit *);\r
+static void decSetCoeff(decNumber *, decContext *, const Unit *,\r
+ Int, Int *, uInt *);\r
+static void decSetMaxValue(decNumber *, decContext *);\r
+static void decSetOverflow(decNumber *, decContext *, uInt *);\r
+static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);\r
+static Int decShiftToLeast(Unit *, Int, Int);\r
+static Int decShiftToMost(Unit *, Int, Int);\r
+static void decStatus(decNumber *, uInt, decContext *);\r
+static void decToString(const decNumber *, char[], Flag);\r
+static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);\r
+static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,\r
+ Unit *, Int);\r
+static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);\r
+\r
+#if !DECSUBSET\r
+/* decFinish == decFinalize when no subset arithmetic needed */\r
+#define decFinish(a,b,c,d) decFinalize(a,b,c,d)\r
+#else\r
+static void decFinish(decNumber *, decContext *, Int *, uInt *);\r
+static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);\r
+#endif\r
+\r
+/* Local macros */\r
+// masked special-values bits\r
+#define SPECIALARG (rhs->bits & DECSPECIAL)\r
+#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)\r
+\r
+/* Diagnostic macros, etc. */\r
+#if DECALLOC\r
+// Handle malloc/free accounting. If enabled, our accountable routines\r
+// are used; otherwise the code just goes straight to the system malloc\r
+// and free routines.\r
+#define malloc(a) decMalloc(a)\r
+#define free(a) decFree(a)\r
+#define DECFENCE 0x5a // corruption detector\r
+// 'Our' malloc and free:\r
+static void *decMalloc(size_t);\r
+static void decFree(void *);\r
+uInt decAllocBytes=0; // count of bytes allocated\r
+// Note that DECALLOC code only checks for storage buffer overflow.\r
+// To check for memory leaks, the decAllocBytes variable must be\r
+// checked to be 0 at appropriate times (e.g., after the test\r
+// harness completes a set of tests). This checking may be unreliable\r
+// if the testing is done in a multi-thread environment.\r
+#endif\r
+\r
+#if DECCHECK\r
+// Optional checking routines. Enabling these means that decNumber\r
+// and decContext operands to operator routines are checked for\r
+// correctness. This roughly doubles the execution time of the\r
+// fastest routines (and adds 600+ bytes), so should not normally be\r
+// used in 'production'.\r
+// decCheckInexact is used to check that inexact results have a full\r
+// complement of digits (where appropriate -- this is not the case\r
+// for Quantize, for example)\r
+#define DECUNRESU ((decNumber *)(void *)0xffffffff)\r
+#define DECUNUSED ((const decNumber *)(void *)0xffffffff)\r
+#define DECUNCONT ((decContext *)(void *)(0xffffffff))\r
+static Flag decCheckOperands(decNumber *, const decNumber *,\r
+ const decNumber *, decContext *);\r
+static Flag decCheckNumber(const decNumber *);\r
+static void decCheckInexact(const decNumber *, decContext *);\r
+#endif\r
+\r
+#if DECTRACE || DECCHECK\r
+// Optional trace/debugging routines (may or may not be used)\r
+void decNumberShow(const decNumber *); // displays the components of a number\r
+static void decDumpAr(char, const Unit *, Int);\r
+#endif\r
+\r
+/* ================================================================== */\r
+/* Conversions */\r
+/* ================================================================== */\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* from-int32 -- conversion from Int or uInt */\r
+/* */\r
+/* dn is the decNumber to receive the integer */\r
+/* in or uin is the integer to be converted */\r
+/* returns dn */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberFromInt32(decNumber *dn, Int in) {\r
+ uInt unsig;\r
+ if (in>=0) unsig=in;\r
+ else { // negative (possibly BADINT)\r
+ if (in==BADINT) unsig=(uInt)1073741824*2; // special case\r
+ else unsig=-in; // invert\r
+ }\r
+ // in is now positive\r
+ decNumberFromUInt32(dn, unsig);\r
+ if (in<0) dn->bits=DECNEG; // sign needed\r
+ return dn;\r
+ } // decNumberFromInt32\r
+\r
+decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {\r
+ Unit *up; // work pointer\r
+ decNumberZero(dn); // clean\r
+ if (uin==0) return dn; // [or decGetDigits bad call]\r
+ for (up=dn->lsu; uin>0; up++) {\r
+ *up=(Unit)(uin%(DECDPUNMAX+1));\r
+ uin=uin/(DECDPUNMAX+1);\r
+ }\r
+ dn->digits=decGetDigits(dn->lsu, up-dn->lsu);\r
+ return dn;\r
+ } // decNumberFromUInt32\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-int32 -- conversion to Int or uInt */\r
+/* */\r
+/* dn is the decNumber to convert */\r
+/* set is the context for reporting errors */\r
+/* returns the converted decNumber, or 0 if Invalid is set */\r
+/* */\r
+/* Invalid is set if the decNumber does not have exponent==0 or if */\r
+/* it is a NaN, Infinite, or out-of-range. */\r
+/* ------------------------------------------------------------------ */\r
+Int decNumberToInt32(const decNumber *dn, decContext *set) {\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;\r
+ #endif\r
+\r
+ // special or too many digits, or bad exponent\r
+ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad\r
+ else { // is a finite integer with 10 or fewer digits\r
+ Int d; // work\r
+ const Unit *up; // ..\r
+ uInt hi=0, lo; // ..\r
+ up=dn->lsu; // -> lsu\r
+ lo=*up; // get 1 to 9 digits\r
+ #if DECDPUN>1 // split to higher\r
+ hi=lo/10;\r
+ lo=lo%10;\r
+ #endif\r
+ up++;\r
+ // collect remaining Units, if any, into hi\r
+ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];\r
+ // now low has the lsd, hi the remainder\r
+ if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range?\r
+ // most-negative is a reprieve\r
+ if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;\r
+ // bad -- drop through\r
+ }\r
+ else { // in-range always\r
+ Int i=X10(hi)+lo;\r
+ if (dn->bits&DECNEG) return -i;\r
+ return i;\r
+ }\r
+ } // integer\r
+ decContextSetStatus(set, DEC_Invalid_operation); // [may not return]\r
+ return 0;\r
+ } // decNumberToInt32\r
+\r
+uInt decNumberToUInt32(const decNumber *dn, decContext *set) {\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;\r
+ #endif\r
+ // special or too many digits, or bad exponent, or negative (<0)\r
+ if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0\r
+ || (dn->bits&DECNEG && !ISZERO(dn))); // bad\r
+ else { // is a finite integer with 10 or fewer digits\r
+ Int d; // work\r
+ const Unit *up; // ..\r
+ uInt hi=0, lo; // ..\r
+ up=dn->lsu; // -> lsu\r
+ lo=*up; // get 1 to 9 digits\r
+ #if DECDPUN>1 // split to higher\r
+ hi=lo/10;\r
+ lo=lo%10;\r
+ #endif\r
+ up++;\r
+ // collect remaining Units, if any, into hi\r
+ for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];\r
+\r
+ // now low has the lsd, hi the remainder\r
+ if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible\r
+ else return X10(hi)+lo;\r
+ } // integer\r
+ decContextSetStatus(set, DEC_Invalid_operation); // [may not return]\r
+ return 0;\r
+ } // decNumberToUInt32\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-scientific-string -- conversion to numeric string */\r
+/* to-engineering-string -- conversion to numeric string */\r
+/* */\r
+/* decNumberToString(dn, string); */\r
+/* decNumberToEngString(dn, string); */\r
+/* */\r
+/* dn is the decNumber to convert */\r
+/* string is the string where the result will be laid out */\r
+/* */\r
+/* string must be at least dn->digits+14 characters long */\r
+/* */\r
+/* No error is possible, and no status can be set. */\r
+/* ------------------------------------------------------------------ */\r
+char * decNumberToString(const decNumber *dn, char *string){\r
+ decToString(dn, string, 0);\r
+ return string;\r
+ } // DecNumberToString\r
+\r
+char * decNumberToEngString(const decNumber *dn, char *string){\r
+ decToString(dn, string, 1);\r
+ return string;\r
+ } // DecNumberToEngString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-number -- conversion from numeric string */\r
+/* */\r
+/* decNumberFromString -- convert string to decNumber */\r
+/* dn -- the number structure to fill */\r
+/* chars[] -- the string to convert ('\0' terminated) */\r
+/* set -- the context used for processing any error, */\r
+/* determining the maximum precision available */\r
+/* (set.digits), determining the maximum and minimum */\r
+/* exponent (set.emax and set.emin), determining if */\r
+/* extended values are allowed, and checking the */\r
+/* rounding mode if overflow occurs or rounding is */\r
+/* needed. */\r
+/* */\r
+/* The length of the coefficient and the size of the exponent are */\r
+/* checked by this routine, so the correct error (Underflow or */\r
+/* Overflow) can be reported or rounding applied, as necessary. */\r
+/* */\r
+/* If bad syntax is detected, the result will be a quiet NaN. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberFromString(decNumber *dn, const char chars[],\r
+ decContext *set) {\r
+ Int exponent=0; // working exponent [assume 0]\r
+ uByte bits=0; // working flags [assume +ve]\r
+ Unit *res; // where result will be built\r
+ Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary\r
+ // [+9 allows for ln() constants]\r
+ Unit *allocres=NULL; // -> allocated result, iff allocated\r
+ Int d=0; // count of digits found in decimal part\r
+ const char *dotchar=NULL; // where dot was found\r
+ const char *cfirst=chars; // -> first character of decimal part\r
+ const char *last=NULL; // -> last digit of decimal part\r
+ const char *c; // work\r
+ Unit *up; // ..\r
+ #if DECDPUN>1\r
+ Int cut, out; // ..\r
+ #endif\r
+ Int residue; // rounding residue\r
+ uInt status=0; // error code\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))\r
+ return decNumberZero(dn);\r
+ #endif\r
+\r
+ do { // status & malloc protection\r
+ for (c=chars;; c++) { // -> input character\r
+ if (*c>='0' && *c<='9') { // test for Arabic digit\r
+ last=c;\r
+ d++; // count of real digits\r
+ continue; // still in decimal part\r
+ }\r
+ if (*c=='.' && dotchar==NULL) { // first '.'\r
+ dotchar=c; // record offset into decimal part\r
+ if (c==cfirst) cfirst++; // first digit must follow\r
+ continue;}\r
+ if (c==chars) { // first in string...\r
+ if (*c=='-') { // valid - sign\r
+ cfirst++;\r
+ bits=DECNEG;\r
+ continue;}\r
+ if (*c=='+') { // valid + sign\r
+ cfirst++;\r
+ continue;}\r
+ }\r
+ // *c is not a digit, or a valid +, -, or '.'\r
+ break;\r
+ } // c\r
+\r
+ if (last==NULL) { // no digits yet\r
+ status=DEC_Conversion_syntax;// assume the worst\r
+ if (*c=='\0') break; // and no more to come...\r
+ #if DECSUBSET\r
+ // if subset then infinities and NaNs are not allowed\r
+ if (!set->extended) break; // hopeless\r
+ #endif\r
+ // Infinities and NaNs are possible, here\r
+ if (dotchar!=NULL) break; // .. unless had a dot\r
+ decNumberZero(dn); // be optimistic\r
+ if (decBiStr(c, "infinity", "INFINITY")\r
+ || decBiStr(c, "inf", "INF")) {\r
+ dn->bits=bits | DECINF;\r
+ status=0; // is OK\r
+ break; // all done\r
+ }\r
+ // a NaN expected\r
+ // 2003.09.10 NaNs are now permitted to have a sign\r
+ dn->bits=bits | DECNAN; // assume simple NaN\r
+ if (*c=='s' || *c=='S') { // looks like an sNaN\r
+ c++;\r
+ dn->bits=bits | DECSNAN;\r
+ }\r
+ if (*c!='n' && *c!='N') break; // check caseless "NaN"\r
+ c++;\r
+ if (*c!='a' && *c!='A') break; // ..\r
+ c++;\r
+ if (*c!='n' && *c!='N') break; // ..\r
+ c++;\r
+ // now either nothing, or nnnn payload, expected\r
+ // -> start of integer and skip leading 0s [including plain 0]\r
+ for (cfirst=c; *cfirst=='0';) cfirst++;\r
+ if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s\r
+ status=0; // it's good\r
+ break; // ..\r
+ }\r
+ // something other than 0s; setup last and d as usual [no dots]\r
+ for (c=cfirst;; c++, d++) {\r
+ if (*c<'0' || *c>'9') break; // test for Arabic digit\r
+ last=c;\r
+ }\r
+ if (*c!='\0') break; // not all digits\r
+ if (d>set->digits-1) {\r
+ // [NB: payload in a decNumber can be full length unless\r
+ // clamped, in which case can only be digits-1]\r
+ if (set->clamp) break;\r
+ if (d>set->digits) break;\r
+ } // too many digits?\r
+ // good; drop through to convert the integer to coefficient\r
+ status=0; // syntax is OK\r
+ bits=dn->bits; // for copy-back\r
+ } // last==NULL\r
+\r
+ else if (*c!='\0') { // more to process...\r
+ // had some digits; exponent is only valid sequence now\r
+ Flag nege; // 1=negative exponent\r
+ const char *firstexp; // -> first significant exponent digit\r
+ status=DEC_Conversion_syntax;// assume the worst\r
+ if (*c!='e' && *c!='E') break;\r
+ /* Found 'e' or 'E' -- now process explicit exponent */\r
+ // 1998.07.11: sign no longer required\r
+ nege=0;\r
+ c++; // to (possible) sign\r
+ if (*c=='-') {nege=1; c++;}\r
+ else if (*c=='+') c++;\r
+ if (*c=='\0') break;\r
+\r
+ for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros\r
+ firstexp=c; // save exponent digit place\r
+ for (; ;c++) {\r
+ if (*c<'0' || *c>'9') break; // not a digit\r
+ exponent=X10(exponent)+(Int)*c-(Int)'0';\r
+ } // c\r
+ // if not now on a '\0', *c must not be a digit\r
+ if (*c!='\0') break;\r
+\r
+ // (this next test must be after the syntax checks)\r
+ // if it was too long the exponent may have wrapped, so check\r
+ // carefully and set it to a certain overflow if wrap possible\r
+ if (c>=firstexp+9+1) {\r
+ if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;\r
+ // [up to 1999999999 is OK, for example 1E-1000000998]\r
+ }\r
+ if (nege) exponent=-exponent; // was negative\r
+ status=0; // is OK\r
+ } // stuff after digits\r
+\r
+ // Here when whole string has been inspected; syntax is good\r
+ // cfirst->first digit (never dot), last->last digit (ditto)\r
+\r
+ // strip leading zeros/dot [leave final 0 if all 0's]\r
+ if (*cfirst=='0') { // [cfirst has stepped over .]\r
+ for (c=cfirst; c<last; c++, cfirst++) {\r
+ if (*c=='.') continue; // ignore dots\r
+ if (*c!='0') break; // non-zero found\r
+ d--; // 0 stripped\r
+ } // c\r
+ #if DECSUBSET\r
+ // make a rapid exit for easy zeros if !extended\r
+ if (*cfirst=='0' && !set->extended) {\r
+ decNumberZero(dn); // clean result\r
+ break; // [could be return]\r
+ }\r
+ #endif\r
+ } // at least one leading 0\r
+\r
+ // Handle decimal point...\r
+ if (dotchar!=NULL && dotchar<last) // non-trailing '.' found?\r
+ exponent-=(last-dotchar); // adjust exponent\r
+ // [we can now ignore the .]\r
+\r
+ // OK, the digits string is good. Assemble in the decNumber, or in\r
+ // a temporary units array if rounding is needed\r
+ if (d<=set->digits) res=dn->lsu; // fits into supplied decNumber\r
+ else { // rounding needed\r
+ Int needbytes=D2U(d)*sizeof(Unit);// bytes needed\r
+ res=resbuff; // assume use local buffer\r
+ if (needbytes>(Int)sizeof(resbuff)) { // too big for local\r
+ allocres=(Unit *)malloc(needbytes);\r
+ if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}\r
+ res=allocres;\r
+ }\r
+ }\r
+ // res now -> number lsu, buffer, or allocated storage for Unit array\r
+\r
+ // Place the coefficient into the selected Unit array\r
+ // [this is often 70% of the cost of this function when DECDPUN>1]\r
+ #if DECDPUN>1\r
+ out=0; // accumulator\r
+ up=res+D2U(d)-1; // -> msu\r
+ cut=d-(up-res)*DECDPUN; // digits in top unit\r
+ for (c=cfirst;; c++) { // along the digits\r
+ if (*c=='.') continue; // ignore '.' [don't decrement cut]\r
+ out=X10(out)+(Int)*c-(Int)'0';\r
+ if (c==last) break; // done [never get to trailing '.']\r
+ cut--;\r
+ if (cut>0) continue; // more for this unit\r
+ *up=(Unit)out; // write unit\r
+ up--; // prepare for unit below..\r
+ cut=DECDPUN; // ..\r
+ out=0; // ..\r
+ } // c\r
+ *up=(Unit)out; // write lsu\r
+\r
+ #else\r
+ // DECDPUN==1\r
+ up=res; // -> lsu\r
+ for (c=last; c>=cfirst; c--) { // over each character, from least\r
+ if (*c=='.') continue; // ignore . [don't step up]\r
+ *up=(Unit)((Int)*c-(Int)'0');\r
+ up++;\r
+ } // c\r
+ #endif\r
+\r
+ dn->bits=bits;\r
+ dn->exponent=exponent;\r
+ dn->digits=d;\r
+\r
+ // if not in number (too long) shorten into the number\r
+ if (d>set->digits) {\r
+ residue=0;\r
+ decSetCoeff(dn, set, res, d, &residue, &status);\r
+ // always check for overflow or subnormal and round as needed\r
+ decFinalize(dn, set, &residue, &status);\r
+ }\r
+ else { // no rounding, but may still have overflow or subnormal\r
+ // [these tests are just for performance; finalize repeats them]\r
+ if ((dn->exponent-1<set->emin-dn->digits)\r
+ || (dn->exponent-1>set->emax-set->digits)) {\r
+ residue=0;\r
+ decFinalize(dn, set, &residue, &status);\r
+ }\r
+ }\r
+ // decNumberShow(dn);\r
+ } while(0); // [for break]\r
+\r
+ if (allocres!=NULL) free(allocres); // drop any storage used\r
+ if (status!=0) decStatus(dn, status, set);\r
+ return dn;\r
+ } /* decNumberFromString */\r
+\r
+/* ================================================================== */\r
+/* Operators */\r
+/* ================================================================== */\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberAbs -- absolute value operator */\r
+/* */\r
+/* This computes C = abs(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context */\r
+/* */\r
+/* See also decNumberCopyAbs for a quiet bitwise version of this. */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+/* This has the same effect as decNumberPlus unless A is negative, */\r
+/* in which case it has the same effect as decNumberMinus. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decNumber dzero; // for 0\r
+ uInt status=0; // accumulator\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ decNumberZero(&dzero); // set 0\r
+ dzero.exponent=rhs->exponent; // [no coefficient expansion]\r
+ decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberAbs\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberAdd -- add two Numbers */\r
+/* */\r
+/* This computes C = A + B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+/* This just calls the routine shared with Subtract */\r
+decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decAddOp(res, lhs, rhs, set, 0, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberAdd\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberAnd -- AND two Numbers, digitwise */\r
+/* */\r
+/* This computes C = A & B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X&X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context (used for result length and error report) */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Logical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ const Unit *ua, *ub; // -> operands\r
+ const Unit *msua, *msub; // -> operand msus\r
+ Unit *uc, *msuc; // -> result and its msu\r
+ Int msudigs; // digits in res msu\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)\r
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+\r
+ // operands are valid\r
+ ua=lhs->lsu; // bottom-up\r
+ ub=rhs->lsu; // ..\r
+ uc=res->lsu; // ..\r
+ msua=ua+D2U(lhs->digits)-1; // -> msu of lhs\r
+ msub=ub+D2U(rhs->digits)-1; // -> msu of rhs\r
+ msuc=uc+D2U(set->digits)-1; // -> msu of result\r
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]\r
+ for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop\r
+ Unit a, b; // extract units\r
+ if (ua>msua) a=0;\r
+ else a=*ua;\r
+ if (ub>msub) b=0;\r
+ else b=*ub;\r
+ *uc=0; // can now write back\r
+ if (a|b) { // maybe 1 bits to examine\r
+ Int i, j;\r
+ *uc=0; // can now write back\r
+ // This loop could be unrolled and/or use BIN2BCD tables\r
+ for (i=0; i<DECDPUN; i++) {\r
+ if (a&b&1) *uc=*uc+(Unit)powers[i]; // effect AND\r
+ j=a%10;\r
+ a=a/10;\r
+ j|=b%10;\r
+ b=b/10;\r
+ if (j>1) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ if (uc==msuc && i==msudigs-1) break; // just did final digit\r
+ } // each digit\r
+ } // both OK\r
+ } // each unit\r
+ // [here uc-1 is the msu of the result]\r
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);\r
+ res->exponent=0; // integer\r
+ res->bits=0; // sign=0\r
+ return res; // [no status to set]\r
+ } // decNumberAnd\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCompare -- compare two Numbers */\r
+/* */\r
+/* This computes C = A ? B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for one digit (or NaN). */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPARE, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberCompare\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCompareSignal -- compare, signalling on all NaNs */\r
+/* */\r
+/* This computes C = A ? B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for one digit (or NaN). */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPSIG, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberCompareSignal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCompareTotal -- compare two Numbers, using total ordering */\r
+/* */\r
+/* This computes C = A ? B, under total ordering */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for one digit; the result will always be one of */\r
+/* -1, 0, or 1. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberCompareTotal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */\r
+/* */\r
+/* This computes C = |A| ? |B|, under total ordering */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for one digit; the result will always be one of */\r
+/* -1, 0, or 1. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ uInt needbytes; // for space calculations\r
+ decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0\r
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated\r
+ decNumber bufb[D2N(DECBUFFER+1)];\r
+ decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated\r
+ decNumber *a, *b; // temporary pointers\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ // if either is negative, take a copy and absolute\r
+ if (decNumberIsNegative(lhs)) { // lhs<0\r
+ a=bufa;\r
+ needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufa)) { // need malloc space\r
+ allocbufa=(decNumber *)malloc(needbytes);\r
+ if (allocbufa==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ a=allocbufa; // use the allocated space\r
+ }\r
+ decNumberCopy(a, lhs); // copy content\r
+ a->bits&=~DECNEG; // .. and clear the sign\r
+ lhs=a; // use copy from here on\r
+ }\r
+ if (decNumberIsNegative(rhs)) { // rhs<0\r
+ b=bufb;\r
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufb)) { // need malloc space\r
+ allocbufb=(decNumber *)malloc(needbytes);\r
+ if (allocbufb==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ b=allocbufb; // use the allocated space\r
+ }\r
+ decNumberCopy(b, rhs); // copy content\r
+ b->bits&=~DECNEG; // .. and clear the sign\r
+ rhs=b; // use copy from here on\r
+ }\r
+ decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);\r
+ } while(0); // end protected\r
+\r
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used\r
+ if (allocbufb!=NULL) free(allocbufb); // ..\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberCompareTotalMag\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberDivide -- divide one number by another */\r
+/* */\r
+/* This computes C = A / B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X/X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decDivideOp(res, lhs, rhs, set, DIVIDE, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberDivide\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberDivideInteger -- divide and return integer quotient */\r
+/* */\r
+/* This computes C = A # B, where # is the integer divide operator */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X#X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberDivideInteger\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberExp -- exponentiation */\r
+/* */\r
+/* This computes C = exp(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context; note that rounding mode has no effect */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Mathematical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* */\r
+/* Finite results will always be full precision and Inexact, except */\r
+/* when A is a zero or -Infinity (giving 1 or 0 respectively). */\r
+/* */\r
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */\r
+/* almost always be correctly rounded, but may be up to 1 ulp in */\r
+/* error in rare cases. */\r
+/* ------------------------------------------------------------------ */\r
+/* This is a wrapper for decExpOp which can handle the slightly wider */\r
+/* (double) range needed by Ln (which has to be able to calculate */\r
+/* exp(-a) where a can be the tiniest number (Ntiny). */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberExp(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ uInt status=0; // accumulator\r
+ #if DECSUBSET\r
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated\r
+ #endif\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // Check restrictions; these restrictions ensure that if h=8 (see\r
+ // decExpOp) then the result will either overflow or underflow to 0.\r
+ // Other math functions restrict the input range, too, for inverses.\r
+ // If not violated then carry out the operation.\r
+ if (!decCheckMath(rhs, set, &status)) do { // protect allocation\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operand and set lostDigits status, as needed\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, &status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ decExpOp(res, rhs, set, &status);\r
+ } while(0); // end protected\r
+\r
+ #if DECSUBSET\r
+ if (allocrhs !=NULL) free(allocrhs); // drop any storage used\r
+ #endif\r
+ // apply significant status\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberExp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberFMA -- fused multiply add */\r
+/* */\r
+/* This computes D = (A * B) + C with only one rounding */\r
+/* */\r
+/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* fhs is C [far hand side] */\r
+/* set is the context */\r
+/* */\r
+/* Mathematical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, const decNumber *fhs,\r
+ decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decContext dcmul; // context for the multiplication\r
+ uInt needbytes; // for space calculations\r
+ decNumber bufa[D2N(DECBUFFER*2+1)];\r
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated\r
+ decNumber *acc; // accumulator pointer\r
+ decNumber dzero; // work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) { // [undefined if subset]\r
+ status|=DEC_Invalid_operation;\r
+ break;}\r
+ #endif\r
+ // Check math restrictions [these ensure no overflow or underflow]\r
+ if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))\r
+ || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))\r
+ || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;\r
+ // set up context for multiply\r
+ dcmul=*set;\r
+ dcmul.digits=lhs->digits+rhs->digits; // just enough\r
+ // [The above may be an over-estimate for subset arithmetic, but that's OK]\r
+ dcmul.emax=DEC_MAX_EMAX; // effectively unbounded ..\r
+ dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions]\r
+ // set up decNumber space to receive the result of the multiply\r
+ acc=bufa; // may fit\r
+ needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufa)) { // need malloc space\r
+ allocbufa=(decNumber *)malloc(needbytes);\r
+ if (allocbufa==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ acc=allocbufa; // use the allocated space\r
+ }\r
+ // multiply with extended range and necessary precision\r
+ //printf("emin=%ld\n", dcmul.emin);\r
+ decMultiplyOp(acc, lhs, rhs, &dcmul, &status);\r
+ // Only Invalid operation (from sNaN or Inf * 0) is possible in\r
+ // status; if either is seen than ignore fhs (in case it is\r
+ // another sNaN) and set acc to NaN unless we had an sNaN\r
+ // [decMultiplyOp leaves that to caller]\r
+ // Note sNaN has to go through addOp to shorten payload if\r
+ // necessary\r
+ if ((status&DEC_Invalid_operation)!=0) {\r
+ if (!(status&DEC_sNaN)) { // but be true invalid\r
+ decNumberZero(res); // acc not yet set\r
+ res->bits=DECNAN;\r
+ break;\r
+ }\r
+ decNumberZero(&dzero); // make 0 (any non-NaN would do)\r
+ fhs=&dzero; // use that\r
+ }\r
+ #if DECCHECK\r
+ else { // multiply was OK\r
+ if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);\r
+ }\r
+ #endif\r
+ // add the third operand and result -> res, and all is done\r
+ decAddOp(res, acc, fhs, set, 0, &status);\r
+ } while(0); // end protected\r
+\r
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberFMA\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberInvert -- invert a Number, digitwise */\r
+/* */\r
+/* This computes C = ~A */\r
+/* */\r
+/* res is C, the result. C may be A (e.g., X=~X) */\r
+/* rhs is A */\r
+/* set is the context (used for result length and error report) */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Logical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ const Unit *ua, *msua; // -> operand and its msu\r
+ Unit *uc, *msuc; // -> result and its msu\r
+ Int msudigs; // digits in res msu\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ // operand is valid\r
+ ua=rhs->lsu; // bottom-up\r
+ uc=res->lsu; // ..\r
+ msua=ua+D2U(rhs->digits)-1; // -> msu of rhs\r
+ msuc=uc+D2U(set->digits)-1; // -> msu of result\r
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]\r
+ for (; uc<=msuc; ua++, uc++) { // Unit loop\r
+ Unit a; // extract unit\r
+ Int i, j; // work\r
+ if (ua>msua) a=0;\r
+ else a=*ua;\r
+ *uc=0; // can now write back\r
+ // always need to examine all bits in rhs\r
+ // This loop could be unrolled and/or use BIN2BCD tables\r
+ for (i=0; i<DECDPUN; i++) {\r
+ if ((~a)&1) *uc=*uc+(Unit)powers[i]; // effect INVERT\r
+ j=a%10;\r
+ a=a/10;\r
+ if (j>1) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ if (uc==msuc && i==msudigs-1) break; // just did final digit\r
+ } // each digit\r
+ } // each unit\r
+ // [here uc-1 is the msu of the result]\r
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);\r
+ res->exponent=0; // integer\r
+ res->bits=0; // sign=0\r
+ return res; // [no status to set]\r
+ } // decNumberInvert\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberLn -- natural logarithm */\r
+/* */\r
+/* This computes C = ln(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context; note that rounding mode has no effect */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Notable cases: */\r
+/* A<0 -> Invalid */\r
+/* A=0 -> -Infinity (Exact) */\r
+/* A=+Infinity -> +Infinity (Exact) */\r
+/* A=1 exactly -> 0 (Exact) */\r
+/* */\r
+/* Mathematical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* */\r
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */\r
+/* almost always be correctly rounded, but may be up to 1 ulp in */\r
+/* error in rare cases. */\r
+/* ------------------------------------------------------------------ */\r
+/* This is a wrapper for decLnOp which can handle the slightly wider */\r
+/* (+11) range needed by Ln, Log10, etc. (which may have to be able */\r
+/* to calculate at p+e+2). */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberLn(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ uInt status=0; // accumulator\r
+ #if DECSUBSET\r
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated\r
+ #endif\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // Check restrictions; this is a math function; if not violated\r
+ // then carry out the operation.\r
+ if (!decCheckMath(rhs, set, &status)) do { // protect allocation\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operand and set lostDigits status, as needed\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, &status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ // special check in subset for rhs=0\r
+ if (ISZERO(rhs)) { // +/- zeros -> error\r
+ status|=DEC_Invalid_operation;\r
+ break;}\r
+ } // extended=0\r
+ #endif\r
+ decLnOp(res, rhs, set, &status);\r
+ } while(0); // end protected\r
+\r
+ #if DECSUBSET\r
+ if (allocrhs !=NULL) free(allocrhs); // drop any storage used\r
+ #endif\r
+ // apply significant status\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberLn\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberLogB - get adjusted exponent, by 754 rules */\r
+/* */\r
+/* This computes C = adjustedexponent(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context, used only for digits and status */\r
+/* */\r
+/* For an unrounded result, digits may need to be 10 (A might have */\r
+/* 10**9 digits and an exponent of +999999999, or one digit and an */\r
+/* exponent of -1999999999). */\r
+/* */\r
+/* This returns the adjusted exponent of A after (in theory) padding */\r
+/* with zeros on the right to set->digits digits while keeping the */\r
+/* same value. The exponent is not limited by emin/emax. */\r
+/* */\r
+/* Notable cases: */\r
+/* A<0 -> Use |A| */\r
+/* A=0 -> -Infinity (Division by zero) */\r
+/* A=Infinite -> +Infinity (Exact) */\r
+/* A=1 exactly -> 0 (Exact) */\r
+/* NaNs are propagated as usual */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ uInt status=0; // accumulator\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // NaNs as usual; Infinities return +Infinity; 0->oops\r
+ if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);\r
+ else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);\r
+ else if (decNumberIsZero(rhs)) {\r
+ decNumberZero(res); // prepare for Infinity\r
+ res->bits=DECNEG|DECINF; // -Infinity\r
+ status|=DEC_Division_by_zero; // as per 754\r
+ }\r
+ else { // finite non-zero\r
+ Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent\r
+ if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out\r
+ else {\r
+ decNumber buft[D2N(10)]; // temporary number\r
+ decNumber *t=buft; // ..\r
+ decNumberFromInt32(t, ae); // lay it out\r
+ decNumberPlus(res, t, set); // round as necessary\r
+ }\r
+ }\r
+\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberLogB\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberLog10 -- logarithm in base 10 */\r
+/* */\r
+/* This computes C = log10(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context; note that rounding mode has no effect */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Notable cases: */\r
+/* A<0 -> Invalid */\r
+/* A=0 -> -Infinity (Exact) */\r
+/* A=+Infinity -> +Infinity (Exact) */\r
+/* A=10**n (if n is an integer) -> n (Exact) */\r
+/* */\r
+/* Mathematical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* */\r
+/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */\r
+/* almost always be correctly rounded, but may be up to 1 ulp in */\r
+/* error in rare cases. */\r
+/* ------------------------------------------------------------------ */\r
+/* This calculates ln(A)/ln(10) using appropriate precision. For */\r
+/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */\r
+/* requested digits and t is the number of digits in the exponent */\r
+/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */\r
+/* fastpath in decLnOp. The final division is done to the requested */\r
+/* precision. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ uInt status=0, ignore=0; // status accumulators\r
+ uInt needbytes; // for space calculations\r
+ Int p; // working precision\r
+ Int t; // digits in exponent of A\r
+\r
+ // buffers for a and b working decimals\r
+ // (adjustment calculator, same size)\r
+ decNumber bufa[D2N(DECBUFFER+2)];\r
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated\r
+ decNumber *a=bufa; // temporary a\r
+ decNumber bufb[D2N(DECBUFFER+2)];\r
+ decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated\r
+ decNumber *b=bufb; // temporary b\r
+ decNumber bufw[D2N(10)]; // working 2-10 digit number\r
+ decNumber *w=bufw; // ..\r
+ #if DECSUBSET\r
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated\r
+ #endif\r
+\r
+ decContext aset; // working context\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // Check restrictions; this is a math function; if not violated\r
+ // then carry out the operation.\r
+ if (!decCheckMath(rhs, set, &status)) do { // protect malloc\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operand and set lostDigits status, as needed\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, &status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ // special check in subset for rhs=0\r
+ if (ISZERO(rhs)) { // +/- zeros -> error\r
+ status|=DEC_Invalid_operation;\r
+ break;}\r
+ } // extended=0\r
+ #endif\r
+\r
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context\r
+\r
+ // handle exact powers of 10; only check if +ve finite\r
+ if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {\r
+ Int residue=0; // (no residue)\r
+ uInt copystat=0; // clean status\r
+\r
+ // round to a single digit...\r
+ aset.digits=1;\r
+ decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten\r
+ // if exact and the digit is 1, rhs is a power of 10\r
+ if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {\r
+ // the exponent, conveniently, is the power of 10; making\r
+ // this the result needs a little care as it might not fit,\r
+ // so first convert it into the working number, and then move\r
+ // to res\r
+ decNumberFromInt32(w, w->exponent);\r
+ residue=0;\r
+ decCopyFit(res, w, set, &residue, &status); // copy & round\r
+ decFinish(res, set, &residue, &status); // cleanup/set flags\r
+ break;\r
+ } // not a power of 10\r
+ } // not a candidate for exact\r
+\r
+ // simplify the information-content calculation to use 'total\r
+ // number of digits in a, including exponent' as compared to the\r
+ // requested digits, as increasing this will only rarely cost an\r
+ // iteration in ln(a) anyway\r
+ t=6; // it can never be >6\r
+\r
+ // allocate space when needed...\r
+ p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;\r
+ needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufa)) { // need malloc space\r
+ allocbufa=(decNumber *)malloc(needbytes);\r
+ if (allocbufa==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ a=allocbufa; // use the allocated space\r
+ }\r
+ aset.digits=p; // as calculated\r
+ aset.emax=DEC_MAX_MATH; // usual bounds\r
+ aset.emin=-DEC_MAX_MATH; // ..\r
+ aset.clamp=0; // and no concrete format\r
+ decLnOp(a, rhs, &aset, &status); // a=ln(rhs)\r
+\r
+ // skip the division if the result so far is infinite, NaN, or\r
+ // zero, or there was an error; note NaN from sNaN needs copy\r
+ if (status&DEC_NaNs && !(status&DEC_sNaN)) break;\r
+ if (a->bits&DECSPECIAL || ISZERO(a)) {\r
+ decNumberCopy(res, a); // [will fit]\r
+ break;}\r
+\r
+ // for ln(10) an extra 3 digits of precision are needed\r
+ p=set->digits+3;\r
+ needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufb)) { // need malloc space\r
+ allocbufb=(decNumber *)malloc(needbytes);\r
+ if (allocbufb==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ b=allocbufb; // use the allocated space\r
+ }\r
+ decNumberZero(w); // set up 10...\r
+ #if DECDPUN==1\r
+ w->lsu[1]=1; w->lsu[0]=0; // ..\r
+ #else\r
+ w->lsu[0]=10; // ..\r
+ #endif\r
+ w->digits=2; // ..\r
+\r
+ aset.digits=p;\r
+ decLnOp(b, w, &aset, &ignore); // b=ln(10)\r
+\r
+ aset.digits=set->digits; // for final divide\r
+ decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result\r
+ } while(0); // [for break]\r
+\r
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used\r
+ if (allocbufb!=NULL) free(allocbufb); // ..\r
+ #if DECSUBSET\r
+ if (allocrhs !=NULL) free(allocrhs); // ..\r
+ #endif\r
+ // apply significant status\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberLog10\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberMax -- compare two Numbers and return the maximum */\r
+/* */\r
+/* This computes C = A ? B, returning the maximum by 754 rules */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberMax(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPMAX, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberMax\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberMaxMag -- compare and return the maximum by magnitude */\r
+/* */\r
+/* This computes C = A ? B, returning the maximum by 754 rules */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberMaxMag\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberMin -- compare two Numbers and return the minimum */\r
+/* */\r
+/* This computes C = A ? B, returning the minimum by 754 rules */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberMin(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPMIN, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberMin\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberMinMag -- compare and return the minimum by magnitude */\r
+/* */\r
+/* This computes C = A ? B, returning the minimum by 754 rules */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberMinMag\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberMinus -- prefix minus operator */\r
+/* */\r
+/* This computes C = 0 - A */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context */\r
+/* */\r
+/* See also decNumberCopyNegate for a quiet bitwise version of this. */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+/* Simply use AddOp for the subtract, which will do the necessary. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decNumber dzero;\r
+ uInt status=0; // accumulator\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ decNumberZero(&dzero); // make 0\r
+ dzero.exponent=rhs->exponent; // [no coefficient expansion]\r
+ decAddOp(res, &dzero, rhs, set, DECNEG, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberMinus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberNextMinus -- next towards -Infinity */\r
+/* */\r
+/* This computes C = A - infinitesimal, rounded towards -Infinity */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context */\r
+/* */\r
+/* This is a generalization of 754 NextDown. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decNumber dtiny; // constant\r
+ decContext workset=*set; // work\r
+ uInt status=0; // accumulator\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // +Infinity is the special case\r
+ if ((rhs->bits&(DECINF|DECNEG))==DECINF) {\r
+ decSetMaxValue(res, set); // is +ve\r
+ // there is no status to set\r
+ return res;\r
+ }\r
+ decNumberZero(&dtiny); // start with 0\r
+ dtiny.lsu[0]=1; // make number that is ..\r
+ dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest\r
+ workset.round=DEC_ROUND_FLOOR;\r
+ decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);\r
+ status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberNextMinus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberNextPlus -- next towards +Infinity */\r
+/* */\r
+/* This computes C = A + infinitesimal, rounded towards +Infinity */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context */\r
+/* */\r
+/* This is a generalization of 754 NextUp. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decNumber dtiny; // constant\r
+ decContext workset=*set; // work\r
+ uInt status=0; // accumulator\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // -Infinity is the special case\r
+ if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {\r
+ decSetMaxValue(res, set);\r
+ res->bits=DECNEG; // negative\r
+ // there is no status to set\r
+ return res;\r
+ }\r
+ decNumberZero(&dtiny); // start with 0\r
+ dtiny.lsu[0]=1; // make number that is ..\r
+ dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest\r
+ workset.round=DEC_ROUND_CEILING;\r
+ decAddOp(res, rhs, &dtiny, &workset, 0, &status);\r
+ status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberNextPlus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberNextToward -- next towards rhs */\r
+/* */\r
+/* This computes C = A +/- infinitesimal, rounded towards */\r
+/* +/-Infinity in the direction of B, as per 754-1985 nextafter */\r
+/* modified during revision but dropped from 754-2008. */\r
+/* */\r
+/* res is C, the result. C may be A or B. */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* This is a generalization of 754-1985 NextAfter. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ decNumber dtiny; // constant\r
+ decContext workset=*set; // work\r
+ Int result; // ..\r
+ uInt status=0; // accumulator\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {\r
+ decNaNs(res, lhs, rhs, set, &status);\r
+ }\r
+ else { // Is numeric, so no chance of sNaN Invalid, etc.\r
+ result=decCompare(lhs, rhs, 0); // sign matters\r
+ if (result==BADINT) status|=DEC_Insufficient_storage; // rare\r
+ else { // valid compare\r
+ if (result==0) decNumberCopySign(res, lhs, rhs); // easy\r
+ else { // differ: need NextPlus or NextMinus\r
+ uByte sub; // add or subtract\r
+ if (result<0) { // lhs<rhs, do nextplus\r
+ // -Infinity is the special case\r
+ if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {\r
+ decSetMaxValue(res, set);\r
+ res->bits=DECNEG; // negative\r
+ return res; // there is no status to set\r
+ }\r
+ workset.round=DEC_ROUND_CEILING;\r
+ sub=0; // add, please\r
+ } // plus\r
+ else { // lhs>rhs, do nextminus\r
+ // +Infinity is the special case\r
+ if ((lhs->bits&(DECINF|DECNEG))==DECINF) {\r
+ decSetMaxValue(res, set);\r
+ return res; // there is no status to set\r
+ }\r
+ workset.round=DEC_ROUND_FLOOR;\r
+ sub=DECNEG; // subtract, please\r
+ } // minus\r
+ decNumberZero(&dtiny); // start with 0\r
+ dtiny.lsu[0]=1; // make number that is ..\r
+ dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest\r
+ decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or -\r
+ // turn off exceptions if the result is a normal number\r
+ // (including Nmin), otherwise let all status through\r
+ if (decNumberIsNormal(res, set)) status=0;\r
+ } // unequal\r
+ } // compare OK\r
+ } // numeric\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberNextToward\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberOr -- OR two Numbers, digitwise */\r
+/* */\r
+/* This computes C = A | B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X|X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context (used for result length and error report) */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Logical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberOr(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ const Unit *ua, *ub; // -> operands\r
+ const Unit *msua, *msub; // -> operand msus\r
+ Unit *uc, *msuc; // -> result and its msu\r
+ Int msudigs; // digits in res msu\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)\r
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ // operands are valid\r
+ ua=lhs->lsu; // bottom-up\r
+ ub=rhs->lsu; // ..\r
+ uc=res->lsu; // ..\r
+ msua=ua+D2U(lhs->digits)-1; // -> msu of lhs\r
+ msub=ub+D2U(rhs->digits)-1; // -> msu of rhs\r
+ msuc=uc+D2U(set->digits)-1; // -> msu of result\r
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]\r
+ for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop\r
+ Unit a, b; // extract units\r
+ if (ua>msua) a=0;\r
+ else a=*ua;\r
+ if (ub>msub) b=0;\r
+ else b=*ub;\r
+ *uc=0; // can now write back\r
+ if (a|b) { // maybe 1 bits to examine\r
+ Int i, j;\r
+ // This loop could be unrolled and/or use BIN2BCD tables\r
+ for (i=0; i<DECDPUN; i++) {\r
+ if ((a|b)&1) *uc=*uc+(Unit)powers[i]; // effect OR\r
+ j=a%10;\r
+ a=a/10;\r
+ j|=b%10;\r
+ b=b/10;\r
+ if (j>1) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ if (uc==msuc && i==msudigs-1) break; // just did final digit\r
+ } // each digit\r
+ } // non-zero\r
+ } // each unit\r
+ // [here uc-1 is the msu of the result]\r
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);\r
+ res->exponent=0; // integer\r
+ res->bits=0; // sign=0\r
+ return res; // [no status to set]\r
+ } // decNumberOr\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberPlus -- prefix plus operator */\r
+/* */\r
+/* This computes C = 0 + A */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context */\r
+/* */\r
+/* See also decNumberCopy for a quiet bitwise version of this. */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+/* This simply uses AddOp; Add will take fast path after preparing A. */\r
+/* Performance is a concern here, as this routine is often used to */\r
+/* check operands and apply rounding and overflow/underflow testing. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decNumber dzero;\r
+ uInt status=0; // accumulator\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ decNumberZero(&dzero); // make 0\r
+ dzero.exponent=rhs->exponent; // [no coefficient expansion]\r
+ decAddOp(res, &dzero, rhs, set, 0, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberPlus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberMultiply -- multiply two Numbers */\r
+/* */\r
+/* This computes C = A x B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decMultiplyOp(res, lhs, rhs, set, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberMultiply\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberPower -- raise a number to a power */\r
+/* */\r
+/* This computes C = A ** B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X**X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Mathematical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* */\r
+/* However, if 1999999997<=B<=999999999 and B is an integer then the */\r
+/* restrictions on A and the context are relaxed to the usual bounds, */\r
+/* for compatibility with the earlier (integer power only) version */\r
+/* of this function. */\r
+/* */\r
+/* When B is an integer, the result may be exact, even if rounded. */\r
+/* */\r
+/* The final result is rounded according to the context; it will */\r
+/* almost always be correctly rounded, but may be up to 1 ulp in */\r
+/* error in rare cases. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberPower(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ #if DECSUBSET\r
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated\r
+ decNumber *allocrhs=NULL; // .., rhs\r
+ #endif\r
+ decNumber *allocdac=NULL; // -> allocated acc buffer, iff used\r
+ decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used\r
+ Int reqdigits=set->digits; // requested DIGITS\r
+ Int n; // rhs in binary\r
+ Flag rhsint=0; // 1 if rhs is an integer\r
+ Flag useint=0; // 1 if can use integer calculation\r
+ Flag isoddint=0; // 1 if rhs is an integer and odd\r
+ Int i; // work\r
+ #if DECSUBSET\r
+ Int dropped; // ..\r
+ #endif\r
+ uInt needbytes; // buffer size needed\r
+ Flag seenbit; // seen a bit while powering\r
+ Int residue=0; // rounding residue\r
+ uInt status=0; // accumulators\r
+ uByte bits=0; // result sign if errors\r
+ decContext aset; // working context\r
+ decNumber dnOne; // work value 1...\r
+ // local accumulator buffer [a decNumber, with digits+elength+1 digits]\r
+ decNumber dacbuff[D2N(DECBUFFER+9)];\r
+ decNumber *dac=dacbuff; // -> result accumulator\r
+ // same again for possible 1/lhs calculation\r
+ decNumber invbuff[D2N(DECBUFFER+9)];\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) { // reduce operands and set status, as needed\r
+ if (lhs->digits>reqdigits) {\r
+ alloclhs=decRoundOperand(lhs, set, &status);\r
+ if (alloclhs==NULL) break;\r
+ lhs=alloclhs;\r
+ }\r
+ if (rhs->digits>reqdigits) {\r
+ allocrhs=decRoundOperand(rhs, set, &status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ // handle NaNs and rhs Infinity (lhs infinity is harder)\r
+ if (SPECIALARGS) {\r
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs\r
+ decNaNs(res, lhs, rhs, set, &status);\r
+ break;}\r
+ if (decNumberIsInfinite(rhs)) { // rhs Infinity\r
+ Flag rhsneg=rhs->bits&DECNEG; // save rhs sign\r
+ if (decNumberIsNegative(lhs) // lhs<0\r
+ && !decNumberIsZero(lhs)) // ..\r
+ status|=DEC_Invalid_operation;\r
+ else { // lhs >=0\r
+ decNumberZero(&dnOne); // set up 1\r
+ dnOne.lsu[0]=1;\r
+ decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1\r
+ decNumberZero(res); // prepare for 0/1/Infinity\r
+ if (decNumberIsNegative(dac)) { // lhs<1\r
+ if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0]\r
+ }\r
+ else if (dac->lsu[0]==0) { // lhs=1\r
+ // 1**Infinity is inexact, so return fully-padded 1.0000\r
+ Int shift=set->digits-1;\r
+ *res->lsu=1; // was 0, make int 1\r
+ res->digits=decShiftToMost(res->lsu, 1, shift);\r
+ res->exponent=-shift; // make 1.0000...\r
+ status|=DEC_Inexact|DEC_Rounded; // deemed inexact\r
+ }\r
+ else { // lhs>1\r
+ if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0]\r
+ }\r
+ } // lhs>=0\r
+ break;}\r
+ // [lhs infinity drops through]\r
+ } // specials\r
+\r
+ // Original rhs may be an integer that fits and is in range\r
+ n=decGetInt(rhs);\r
+ if (n!=BADINT) { // it is an integer\r
+ rhsint=1; // record the fact for 1**n\r
+ isoddint=(Flag)n&1; // [works even if big]\r
+ if (n!=BIGEVEN && n!=BIGODD) // can use integer path?\r
+ useint=1; // looks good\r
+ }\r
+\r
+ if (decNumberIsNegative(lhs) // -x ..\r
+ && isoddint) bits=DECNEG; // .. to an odd power\r
+\r
+ // handle LHS infinity\r
+ if (decNumberIsInfinite(lhs)) { // [NaNs already handled]\r
+ uByte rbits=rhs->bits; // save\r
+ decNumberZero(res); // prepare\r
+ if (n==0) *res->lsu=1; // [-]Inf**0 => 1\r
+ else {\r
+ // -Inf**nonint -> error\r
+ if (!rhsint && decNumberIsNegative(lhs)) {\r
+ status|=DEC_Invalid_operation; // -Inf**nonint is error\r
+ break;}\r
+ if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n\r
+ // [otherwise will be 0 or -0]\r
+ res->bits=bits;\r
+ }\r
+ break;}\r
+\r
+ // similarly handle LHS zero\r
+ if (decNumberIsZero(lhs)) {\r
+ if (n==0) { // 0**0 => Error\r
+ #if DECSUBSET\r
+ if (!set->extended) { // [unless subset]\r
+ decNumberZero(res);\r
+ *res->lsu=1; // return 1\r
+ break;}\r
+ #endif\r
+ status|=DEC_Invalid_operation;\r
+ }\r
+ else { // 0**x\r
+ uByte rbits=rhs->bits; // save\r
+ if (rbits & DECNEG) { // was a 0**(-n)\r
+ #if DECSUBSET\r
+ if (!set->extended) { // [bad if subset]\r
+ status|=DEC_Invalid_operation;\r
+ break;}\r
+ #endif\r
+ bits|=DECINF;\r
+ }\r
+ decNumberZero(res); // prepare\r
+ // [otherwise will be 0 or -0]\r
+ res->bits=bits;\r
+ }\r
+ break;}\r
+\r
+ // here both lhs and rhs are finite; rhs==0 is handled in the\r
+ // integer path. Next handle the non-integer cases\r
+ if (!useint) { // non-integral rhs\r
+ // any -ve lhs is bad, as is either operand or context out of\r
+ // bounds\r
+ if (decNumberIsNegative(lhs)) {\r
+ status|=DEC_Invalid_operation;\r
+ break;}\r
+ if (decCheckMath(lhs, set, &status)\r
+ || decCheckMath(rhs, set, &status)) break; // variable status\r
+\r
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context\r
+ aset.emax=DEC_MAX_MATH; // usual bounds\r
+ aset.emin=-DEC_MAX_MATH; // ..\r
+ aset.clamp=0; // and no concrete format\r
+\r
+ // calculate the result using exp(ln(lhs)*rhs), which can\r
+ // all be done into the accumulator, dac. The precision needed\r
+ // is enough to contain the full information in the lhs (which\r
+ // is the total digits, including exponent), or the requested\r
+ // precision, if larger, + 4; 6 is used for the exponent\r
+ // maximum length, and this is also used when it is shorter\r
+ // than the requested digits as it greatly reduces the >0.5 ulp\r
+ // cases at little cost (because Ln doubles digits each\r
+ // iteration so a few extra digits rarely causes an extra\r
+ // iteration)\r
+ aset.digits=MAXI(lhs->digits, set->digits)+6+4;\r
+ } // non-integer rhs\r
+\r
+ else { // rhs is in-range integer\r
+ if (n==0) { // x**0 = 1\r
+ // (0**0 was handled above)\r
+ decNumberZero(res); // result=1\r
+ *res->lsu=1; // ..\r
+ break;}\r
+ // rhs is a non-zero integer\r
+ if (n<0) n=-n; // use abs(n)\r
+\r
+ aset=*set; // clone the context\r
+ aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced\r
+ // calculate the working DIGITS\r
+ aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;\r
+ #if DECSUBSET\r
+ if (!set->extended) aset.digits--; // use classic precision\r
+ #endif\r
+ // it's an error if this is more than can be handled\r
+ if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}\r
+ } // integer path\r
+\r
+ // aset.digits is the count of digits for the accumulator needed\r
+ // if accumulator is too long for local storage, then allocate\r
+ needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);\r
+ // [needbytes also used below if 1/lhs needed]\r
+ if (needbytes>sizeof(dacbuff)) {\r
+ allocdac=(decNumber *)malloc(needbytes);\r
+ if (allocdac==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ dac=allocdac; // use the allocated space\r
+ }\r
+ // here, aset is set up and accumulator is ready for use\r
+\r
+ if (!useint) { // non-integral rhs\r
+ // x ** y; special-case x=1 here as it will otherwise always\r
+ // reduce to integer 1; decLnOp has a fastpath which detects\r
+ // the case of x=1\r
+ decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs)\r
+ // [no error possible, as lhs 0 already handled]\r
+ if (ISZERO(dac)) { // x==1, 1.0, etc.\r
+ // need to return fully-padded 1.0000 etc., but rhsint->1\r
+ *dac->lsu=1; // was 0, make int 1\r
+ if (!rhsint) { // add padding\r
+ Int shift=set->digits-1;\r
+ dac->digits=decShiftToMost(dac->lsu, 1, shift);\r
+ dac->exponent=-shift; // make 1.0000...\r
+ status|=DEC_Inexact|DEC_Rounded; // deemed inexact\r
+ }\r
+ }\r
+ else {\r
+ decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs\r
+ decExpOp(dac, dac, &aset, &status); // dac=exp(dac)\r
+ }\r
+ // and drop through for final rounding\r
+ } // non-integer rhs\r
+\r
+ else { // carry on with integer\r
+ decNumberZero(dac); // acc=1\r
+ *dac->lsu=1; // ..\r
+\r
+ // if a negative power the constant 1 is needed, and if not subset\r
+ // invert the lhs now rather than inverting the result later\r
+ if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]\r
+ decNumber *inv=invbuff; // asssume use fixed buffer\r
+ decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later]\r
+ #if DECSUBSET\r
+ if (set->extended) { // need to calculate 1/lhs\r
+ #endif\r
+ // divide lhs into 1, putting result in dac [dac=1/dac]\r
+ decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);\r
+ // now locate or allocate space for the inverted lhs\r
+ if (needbytes>sizeof(invbuff)) {\r
+ allocinv=(decNumber *)malloc(needbytes);\r
+ if (allocinv==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ inv=allocinv; // use the allocated space\r
+ }\r
+ // [inv now points to big-enough buffer or allocated storage]\r
+ decNumberCopy(inv, dac); // copy the 1/lhs\r
+ decNumberCopy(dac, &dnOne); // restore acc=1\r
+ lhs=inv; // .. and go forward with new lhs\r
+ #if DECSUBSET\r
+ }\r
+ #endif\r
+ }\r
+\r
+ // Raise-to-the-power loop...\r
+ seenbit=0; // set once a 1-bit is encountered\r
+ for (i=1;;i++){ // for each bit [top bit ignored]\r
+ // abandon if had overflow or terminal underflow\r
+ if (status & (DEC_Overflow|DEC_Underflow)) { // interesting?\r
+ if (status&DEC_Overflow || ISZERO(dac)) break;\r
+ }\r
+ // [the following two lines revealed an optimizer bug in a C++\r
+ // compiler, with symptom: 5**3 -> 25, when n=n+n was used]\r
+ n=n<<1; // move next bit to testable position\r
+ if (n<0) { // top bit is set\r
+ seenbit=1; // OK, significant bit seen\r
+ decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x\r
+ }\r
+ if (i==31) break; // that was the last bit\r
+ if (!seenbit) continue; // no need to square 1\r
+ decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square]\r
+ } /*i*/ // 32 bits\r
+\r
+ // complete internal overflow or underflow processing\r
+ if (status & (DEC_Overflow|DEC_Underflow)) {\r
+ #if DECSUBSET\r
+ // If subset, and power was negative, reverse the kind of -erflow\r
+ // [1/x not yet done]\r
+ if (!set->extended && decNumberIsNegative(rhs)) {\r
+ if (status & DEC_Overflow)\r
+ status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;\r
+ else { // trickier -- Underflow may or may not be set\r
+ status&=~(DEC_Underflow | DEC_Subnormal); // [one or both]\r
+ status|=DEC_Overflow;\r
+ }\r
+ }\r
+ #endif\r
+ dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign\r
+ // round subnormals [to set.digits rather than aset.digits]\r
+ // or set overflow result similarly as required\r
+ decFinalize(dac, set, &residue, &status);\r
+ decNumberCopy(res, dac); // copy to result (is now OK length)\r
+ break;\r
+ }\r
+\r
+ #if DECSUBSET\r
+ if (!set->extended && // subset math\r
+ decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]\r
+ // so divide result into 1 [dac=1/dac]\r
+ decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);\r
+ }\r
+ #endif\r
+ } // rhs integer path\r
+\r
+ // reduce result to the requested length and copy to result\r
+ decCopyFit(res, dac, set, &residue, &status);\r
+ decFinish(res, set, &residue, &status); // final cleanup\r
+ #if DECSUBSET\r
+ if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros\r
+ #endif\r
+ } while(0); // end protected\r
+\r
+ if (allocdac!=NULL) free(allocdac); // drop any storage used\r
+ if (allocinv!=NULL) free(allocinv); // ..\r
+ #if DECSUBSET\r
+ if (alloclhs!=NULL) free(alloclhs); // ..\r
+ if (allocrhs!=NULL) free(allocrhs); // ..\r
+ #endif\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberPower\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberQuantize -- force exponent to requested value */\r
+/* */\r
+/* This computes C = op(A, B), where op adjusts the coefficient */\r
+/* of C (by rounding or shifting) such that the exponent (-scale) */\r
+/* of C has exponent of B. The numerical value of C will equal A, */\r
+/* except for the effects of any rounding that occurred. */\r
+/* */\r
+/* res is C, the result. C may be A or B */\r
+/* lhs is A, the number to adjust */\r
+/* rhs is B, the number with exponent to match */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Unless there is an error or the result is infinite, the exponent */\r
+/* after the operation is guaranteed to be equal to that of B. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decQuantizeOp(res, lhs, rhs, set, 1, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberQuantize\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberReduce -- remove trailing zeros */\r
+/* */\r
+/* This computes C = 0 + A, and normalizes the result */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+// Previously known as Normalize\r
+decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ return decNumberReduce(res, rhs, set);\r
+ } // decNumberNormalize\r
+\r
+decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ #if DECSUBSET\r
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated\r
+ #endif\r
+ uInt status=0; // as usual\r
+ Int residue=0; // as usual\r
+ Int dropped; // work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operand and set lostDigits status, as needed\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, &status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ // Infinities copy through; NaNs need usual treatment\r
+ if (decNumberIsNaN(rhs)) {\r
+ decNaNs(res, rhs, NULL, set, &status);\r
+ break;\r
+ }\r
+\r
+ // reduce result to the requested length and copy to result\r
+ decCopyFit(res, rhs, set, &residue, &status); // copy & round\r
+ decFinish(res, set, &residue, &status); // cleanup/set flags\r
+ decTrim(res, set, 1, 0, &dropped); // normalize in place\r
+ // [may clamp]\r
+ } while(0); // end protected\r
+\r
+ #if DECSUBSET\r
+ if (allocrhs !=NULL) free(allocrhs); // ..\r
+ #endif\r
+ if (status!=0) decStatus(res, status, set);// then report status\r
+ return res;\r
+ } // decNumberReduce\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberRescale -- force exponent to requested value */\r
+/* */\r
+/* This computes C = op(A, B), where op adjusts the coefficient */\r
+/* of C (by rounding or shifting) such that the exponent (-scale) */\r
+/* of C has the value B. The numerical value of C will equal A, */\r
+/* except for the effects of any rounding that occurred. */\r
+/* */\r
+/* res is C, the result. C may be A or B */\r
+/* lhs is A, the number to adjust */\r
+/* rhs is B, the requested exponent */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Unless there is an error or the result is infinite, the exponent */\r
+/* after the operation is guaranteed to be equal to B. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decQuantizeOp(res, lhs, rhs, set, 0, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberRescale\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberRemainder -- divide and return remainder */\r
+/* */\r
+/* This computes C = A % B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X%X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decDivideOp(res, lhs, rhs, set, REMAINDER, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberRemainder\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberRemainderNear -- divide and return remainder from nearest */\r
+/* */\r
+/* This computes C = A % B, where % is the IEEE remainder operator */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X%X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ decDivideOp(res, lhs, rhs, set, REMNEAR, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberRemainderNear\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberRotate -- rotate the coefficient of a Number left/right */\r
+/* */\r
+/* This computes C = A rot B (in base ten and rotating set->digits */\r
+/* digits). */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */\r
+/* lhs is A */\r
+/* rhs is B, the number of digits to rotate (-ve to right) */\r
+/* set is the context */\r
+/* */\r
+/* The digits of the coefficient of A are rotated to the left (if B */\r
+/* is positive) or to the right (if B is negative) without adjusting */\r
+/* the exponent or the sign of A. If lhs->digits is less than */\r
+/* set->digits the coefficient is padded with zeros on the left */\r
+/* before the rotate. Any leading zeros in the result are removed */\r
+/* as usual. */\r
+/* */\r
+/* B must be an integer (q=0) and in the range -set->digits through */\r
+/* +set->digits. */\r
+/* C must have space for set->digits digits. */\r
+/* NaNs are propagated as usual. Infinities are unaffected (but */\r
+/* B must be valid). No status is set unless B is invalid or an */\r
+/* operand is an sNaN. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ Int rotate; // rhs as an Int\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ // NaNs propagate as normal\r
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))\r
+ decNaNs(res, lhs, rhs, set, &status);\r
+ // rhs must be an integer\r
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)\r
+ status=DEC_Invalid_operation;\r
+ else { // both numeric, rhs is an integer\r
+ rotate=decGetInt(rhs); // [cannot fail]\r
+ if (rotate==BADINT // something bad ..\r
+ || rotate==BIGODD || rotate==BIGEVEN // .. very big ..\r
+ || abs(rotate)>set->digits) // .. or out of range\r
+ status=DEC_Invalid_operation;\r
+ else { // rhs is OK\r
+ decNumberCopy(res, lhs);\r
+ // convert -ve rotate to equivalent positive rotation\r
+ if (rotate<0) rotate=set->digits+rotate;\r
+ if (rotate!=0 && rotate!=set->digits // zero or full rotation\r
+ && !decNumberIsInfinite(res)) { // lhs was infinite\r
+ // left-rotate to do; 0 < rotate < set->digits\r
+ uInt units, shift; // work\r
+ uInt msudigits; // digits in result msu\r
+ Unit *msu=res->lsu+D2U(res->digits)-1; // current msu\r
+ Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu\r
+ for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0\r
+ res->digits=set->digits; // now full-length\r
+ msudigits=MSUDIGITS(res->digits); // actual digits in msu\r
+\r
+ // rotation here is done in-place, in three steps\r
+ // 1. shift all to least up to one unit to unit-align final\r
+ // lsd [any digits shifted out are rotated to the left,\r
+ // abutted to the original msd (which may require split)]\r
+ //\r
+ // [if there are no whole units left to rotate, the\r
+ // rotation is now complete]\r
+ //\r
+ // 2. shift to least, from below the split point only, so that\r
+ // the final msd is in the right place in its Unit [any\r
+ // digits shifted out will fit exactly in the current msu,\r
+ // left aligned, no split required]\r
+ //\r
+ // 3. rotate all the units by reversing left part, right\r
+ // part, and then whole\r
+ //\r
+ // example: rotate right 8 digits (2 units + 2), DECDPUN=3.\r
+ //\r
+ // start: 00a bcd efg hij klm npq\r
+ //\r
+ // 1a 000 0ab cde fgh|ijk lmn [pq saved]\r
+ // 1b 00p qab cde fgh|ijk lmn\r
+ //\r
+ // 2a 00p qab cde fgh|00i jkl [mn saved]\r
+ // 2b mnp qab cde fgh|00i jkl\r
+ //\r
+ // 3a fgh cde qab mnp|00i jkl\r
+ // 3b fgh cde qab mnp|jkl 00i\r
+ // 3c 00i jkl mnp qab cde fgh\r
+\r
+ // Step 1: amount to shift is the partial right-rotate count\r
+ rotate=set->digits-rotate; // make it right-rotate\r
+ units=rotate/DECDPUN; // whole units to rotate\r
+ shift=rotate%DECDPUN; // left-over digits count\r
+ if (shift>0) { // not an exact number of units\r
+ uInt save=res->lsu[0]%powers[shift]; // save low digit(s)\r
+ decShiftToLeast(res->lsu, D2U(res->digits), shift);\r
+ if (shift>msudigits) { // msumax-1 needs >0 digits\r
+ uInt rem=save%powers[shift-msudigits];// split save\r
+ *msumax=(Unit)(save/powers[shift-msudigits]); // and insert\r
+ *(msumax-1)=*(msumax-1)\r
+ +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // ..\r
+ }\r
+ else { // all fits in msumax\r
+ *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1]\r
+ }\r
+ } // digits shift needed\r
+\r
+ // If whole units to rotate...\r
+ if (units>0) { // some to do\r
+ // Step 2: the units to touch are the whole ones in rotate,\r
+ // if any, and the shift is DECDPUN-msudigits (which may be\r
+ // 0, again)\r
+ shift=DECDPUN-msudigits;\r
+ if (shift>0) { // not an exact number of units\r
+ uInt save=res->lsu[0]%powers[shift]; // save low digit(s)\r
+ decShiftToLeast(res->lsu, units, shift);\r
+ *msumax=*msumax+(Unit)(save*powers[msudigits]);\r
+ } // partial shift needed\r
+\r
+ // Step 3: rotate the units array using triple reverse\r
+ // (reversing is easy and fast)\r
+ decReverse(res->lsu+units, msumax); // left part\r
+ decReverse(res->lsu, res->lsu+units-1); // right part\r
+ decReverse(res->lsu, msumax); // whole\r
+ } // whole units to rotate\r
+ // the rotation may have left an undetermined number of zeros\r
+ // on the left, so true length needs to be calculated\r
+ res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);\r
+ } // rotate needed\r
+ } // rhs OK\r
+ } // numerics\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberRotate\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberSameQuantum -- test for equal exponents */\r
+/* */\r
+/* res is the result number, which will contain either 0 or 1 */\r
+/* lhs is a number to test */\r
+/* rhs is the second (usually a pattern) */\r
+/* */\r
+/* No errors are possible and no context is needed. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs) {\r
+ Unit ret=0; // return value\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;\r
+ #endif\r
+\r
+ if (SPECIALARGS) {\r
+ if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;\r
+ else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;\r
+ // [anything else with a special gives 0]\r
+ }\r
+ else if (lhs->exponent==rhs->exponent) ret=1;\r
+\r
+ decNumberZero(res); // OK to overwrite an operand now\r
+ *res->lsu=ret;\r
+ return res;\r
+ } // decNumberSameQuantum\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberScaleB -- multiply by a power of 10 */\r
+/* */\r
+/* This computes C = A x 10**B where B is an integer (q=0) with */\r
+/* maximum magnitude 2*(emax+digits) */\r
+/* */\r
+/* res is C, the result. C may be A or B */\r
+/* lhs is A, the number to adjust */\r
+/* rhs is B, the requested power of ten to use */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* The result may underflow or overflow. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ Int reqexp; // requested exponent change [B]\r
+ uInt status=0; // accumulator\r
+ Int residue; // work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ // Handle special values except lhs infinite\r
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))\r
+ decNaNs(res, lhs, rhs, set, &status);\r
+ // rhs must be an integer\r
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)\r
+ status=DEC_Invalid_operation;\r
+ else {\r
+ // lhs is a number; rhs is a finite with q==0\r
+ reqexp=decGetInt(rhs); // [cannot fail]\r
+ // maximum range is larger than getInt can handle, so this is\r
+ // more restrictive than the specification\r
+ if (reqexp==BADINT // something bad ..\r
+ || reqexp==BIGODD || reqexp==BIGEVEN // it was huge\r
+ || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range\r
+ status=DEC_Invalid_operation;\r
+ else { // rhs is OK\r
+ decNumberCopy(res, lhs); // all done if infinite lhs\r
+ if (!decNumberIsInfinite(res)) { // prepare to scale\r
+ Int exp=res->exponent; // save for overflow test\r
+ res->exponent+=reqexp; // adjust the exponent\r
+ if (((exp^reqexp)>=0) // same sign ...\r
+ && ((exp^res->exponent)<0)) { // .. but result had different\r
+ // the calculation overflowed, so force right treatment\r
+ if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS;\r
+ else res->exponent=DEC_MAX_EMAX+1;\r
+ }\r
+ residue=0;\r
+ decFinalize(res, set, &residue, &status); // final check\r
+ } // finite LHS\r
+ } // rhs OK\r
+ } // rhs finite\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberScaleB\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberShift -- shift the coefficient of a Number left or right */\r
+/* */\r
+/* This computes C = A << B or C = A >> -B (in base ten). */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */\r
+/* lhs is A */\r
+/* rhs is B, the number of digits to shift (-ve to right) */\r
+/* set is the context */\r
+/* */\r
+/* The digits of the coefficient of A are shifted to the left (if B */\r
+/* is positive) or to the right (if B is negative) without adjusting */\r
+/* the exponent or the sign of A. */\r
+/* */\r
+/* B must be an integer (q=0) and in the range -set->digits through */\r
+/* +set->digits. */\r
+/* C must have space for set->digits digits. */\r
+/* NaNs are propagated as usual. Infinities are unaffected (but */\r
+/* B must be valid). No status is set unless B is invalid or an */\r
+/* operand is an sNaN. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberShift(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+ Int shift; // rhs as an Int\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ // NaNs propagate as normal\r
+ if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))\r
+ decNaNs(res, lhs, rhs, set, &status);\r
+ // rhs must be an integer\r
+ else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)\r
+ status=DEC_Invalid_operation;\r
+ else { // both numeric, rhs is an integer\r
+ shift=decGetInt(rhs); // [cannot fail]\r
+ if (shift==BADINT // something bad ..\r
+ || shift==BIGODD || shift==BIGEVEN // .. very big ..\r
+ || abs(shift)>set->digits) // .. or out of range\r
+ status=DEC_Invalid_operation;\r
+ else { // rhs is OK\r
+ decNumberCopy(res, lhs);\r
+ if (shift!=0 && !decNumberIsInfinite(res)) { // something to do\r
+ if (shift>0) { // to left\r
+ if (shift==set->digits) { // removing all\r
+ *res->lsu=0; // so place 0\r
+ res->digits=1; // ..\r
+ }\r
+ else { //\r
+ // first remove leading digits if necessary\r
+ if (res->digits+shift>set->digits) {\r
+ decDecap(res, res->digits+shift-set->digits);\r
+ // that updated res->digits; may have gone to 1 (for a\r
+ // single digit or for zero\r
+ }\r
+ if (res->digits>1 || *res->lsu) // if non-zero..\r
+ res->digits=decShiftToMost(res->lsu, res->digits, shift);\r
+ } // partial left\r
+ } // left\r
+ else { // to right\r
+ if (-shift>=res->digits) { // discarding all\r
+ *res->lsu=0; // so place 0\r
+ res->digits=1; // ..\r
+ }\r
+ else {\r
+ decShiftToLeast(res->lsu, D2U(res->digits), -shift);\r
+ res->digits-=(-shift);\r
+ }\r
+ } // to right\r
+ } // non-0 non-Inf shift\r
+ } // rhs OK\r
+ } // numerics\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberShift\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberSquareRoot -- square root operator */\r
+/* */\r
+/* This computes C = squareroot(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context; note that rounding mode has no effect */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+/* This uses the following varying-precision algorithm in: */\r
+/* */\r
+/* Properly Rounded Variable Precision Square Root, T. E. Hull and */\r
+/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */\r
+/* pp229-237, ACM, September 1985. */\r
+/* */\r
+/* The square-root is calculated using Newton's method, after which */\r
+/* a check is made to ensure the result is correctly rounded. */\r
+/* */\r
+/* % [Reformatted original Numerical Turing source code follows.] */\r
+/* function sqrt(x : real) : real */\r
+/* % sqrt(x) returns the properly rounded approximation to the square */\r
+/* % root of x, in the precision of the calling environment, or it */\r
+/* % fails if x < 0. */\r
+/* % t e hull and a abrham, august, 1984 */\r
+/* if x <= 0 then */\r
+/* if x < 0 then */\r
+/* assert false */\r
+/* else */\r
+/* result 0 */\r
+/* end if */\r
+/* end if */\r
+/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */\r
+/* var e := getexp(x) % exponent part of x */\r
+/* var approx : real */\r
+/* if e mod 2 = 0 then */\r
+/* approx := .259 + .819 * f % approx to root of f */\r
+/* else */\r
+/* f := f/l0 % adjustments */\r
+/* e := e + 1 % for odd */\r
+/* approx := .0819 + 2.59 * f % exponent */\r
+/* end if */\r
+/* */\r
+/* var p:= 3 */\r
+/* const maxp := currentprecision + 2 */\r
+/* loop */\r
+/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */\r
+/* precision p */\r
+/* approx := .5 * (approx + f/approx) */\r
+/* exit when p = maxp */\r
+/* end loop */\r
+/* */\r
+/* % approx is now within 1 ulp of the properly rounded square root */\r
+/* % of f; to ensure proper rounding, compare squares of (approx - */\r
+/* % l/2 ulp) and (approx + l/2 ulp) with f. */\r
+/* p := currentprecision */\r
+/* begin */\r
+/* precision p + 2 */\r
+/* const approxsubhalf := approx - setexp(.5, -p) */\r
+/* if mulru(approxsubhalf, approxsubhalf) > f then */\r
+/* approx := approx - setexp(.l, -p + 1) */\r
+/* else */\r
+/* const approxaddhalf := approx + setexp(.5, -p) */\r
+/* if mulrd(approxaddhalf, approxaddhalf) < f then */\r
+/* approx := approx + setexp(.l, -p + 1) */\r
+/* end if */\r
+/* end if */\r
+/* end */\r
+/* result setexp(approx, e div 2) % fix exponent */\r
+/* end sqrt */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decContext workset, approxset; // work contexts\r
+ decNumber dzero; // used for constant zero\r
+ Int maxp; // largest working precision\r
+ Int workp; // working precision\r
+ Int residue=0; // rounding residue\r
+ uInt status=0, ignore=0; // status accumulators\r
+ uInt rstatus; // ..\r
+ Int exp; // working exponent\r
+ Int ideal; // ideal (preferred) exponent\r
+ Int needbytes; // work\r
+ Int dropped; // ..\r
+\r
+ #if DECSUBSET\r
+ decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated\r
+ #endif\r
+ // buffer for f [needs +1 in case DECBUFFER 0]\r
+ decNumber buff[D2N(DECBUFFER+1)];\r
+ // buffer for a [needs +2 to match likely maxp]\r
+ decNumber bufa[D2N(DECBUFFER+2)];\r
+ // buffer for temporary, b [must be same size as a]\r
+ decNumber bufb[D2N(DECBUFFER+2)];\r
+ decNumber *allocbuff=NULL; // -> allocated buff, iff allocated\r
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated\r
+ decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated\r
+ decNumber *f=buff; // reduced fraction\r
+ decNumber *a=bufa; // approximation to result\r
+ decNumber *b=bufb; // intermediate result\r
+ // buffer for temporary variable, up to 3 digits\r
+ decNumber buft[D2N(3)];\r
+ decNumber *t=buft; // up-to-3-digit constant or work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operand and set lostDigits status, as needed\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, &status);\r
+ if (allocrhs==NULL) break;\r
+ // [Note: 'f' allocation below could reuse this buffer if\r
+ // used, but as this is rare they are kept separate for clarity.]\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ // handle infinities and NaNs\r
+ if (SPECIALARG) {\r
+ if (decNumberIsInfinite(rhs)) { // an infinity\r
+ if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;\r
+ else decNumberCopy(res, rhs); // +Infinity\r
+ }\r
+ else decNaNs(res, rhs, NULL, set, &status); // a NaN\r
+ break;\r
+ }\r
+\r
+ // calculate the ideal (preferred) exponent [floor(exp/2)]\r
+ // [It would be nicer to write: ideal=rhs->exponent>>1, but this\r
+ // generates a compiler warning. Generated code is the same.]\r
+ ideal=(rhs->exponent&~1)/2; // target\r
+\r
+ // handle zeros\r
+ if (ISZERO(rhs)) {\r
+ decNumberCopy(res, rhs); // could be 0 or -0\r
+ res->exponent=ideal; // use the ideal [safe]\r
+ // use decFinish to clamp any out-of-range exponent, etc.\r
+ decFinish(res, set, &residue, &status);\r
+ break;\r
+ }\r
+\r
+ // any other -x is an oops\r
+ if (decNumberIsNegative(rhs)) {\r
+ status|=DEC_Invalid_operation;\r
+ break;\r
+ }\r
+\r
+ // space is needed for three working variables\r
+ // f -- the same precision as the RHS, reduced to 0.01->0.99...\r
+ // a -- Hull's approximation -- precision, when assigned, is\r
+ // currentprecision+1 or the input argument precision,\r
+ // whichever is larger (+2 for use as temporary)\r
+ // b -- intermediate temporary result (same size as a)\r
+ // if any is too long for local storage, then allocate\r
+ workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision\r
+ workp=MAXI(workp, 7); // at least 7 for low cases\r
+ maxp=workp+2; // largest working precision\r
+\r
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);\r
+ if (needbytes>(Int)sizeof(buff)) {\r
+ allocbuff=(decNumber *)malloc(needbytes);\r
+ if (allocbuff==NULL) { // hopeless -- abandon\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ f=allocbuff; // use the allocated space\r
+ }\r
+ // a and b both need to be able to hold a maxp-length number\r
+ needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);\r
+ if (needbytes>(Int)sizeof(bufa)) { // [same applies to b]\r
+ allocbufa=(decNumber *)malloc(needbytes);\r
+ allocbufb=(decNumber *)malloc(needbytes);\r
+ if (allocbufa==NULL || allocbufb==NULL) { // hopeless\r
+ status|=DEC_Insufficient_storage;\r
+ break;}\r
+ a=allocbufa; // use the allocated spaces\r
+ b=allocbufb; // ..\r
+ }\r
+\r
+ // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1\r
+ decNumberCopy(f, rhs);\r
+ exp=f->exponent+f->digits; // adjusted to Hull rules\r
+ f->exponent=-(f->digits); // to range\r
+\r
+ // set up working context\r
+ decContextDefault(&workset, DEC_INIT_DECIMAL64);\r
+ workset.emax=DEC_MAX_EMAX;\r
+ workset.emin=DEC_MIN_EMIN;\r
+\r
+ // [Until further notice, no error is possible and status bits\r
+ // (Rounded, etc.) should be ignored, not accumulated.]\r
+\r
+ // Calculate initial approximation, and allow for odd exponent\r
+ workset.digits=workp; // p for initial calculation\r
+ t->bits=0; t->digits=3;\r
+ a->bits=0; a->digits=3;\r
+ if ((exp & 1)==0) { // even exponent\r
+ // Set t=0.259, a=0.819\r
+ t->exponent=-3;\r
+ a->exponent=-3;\r
+ #if DECDPUN>=3\r
+ t->lsu[0]=259;\r
+ a->lsu[0]=819;\r
+ #elif DECDPUN==2\r
+ t->lsu[0]=59; t->lsu[1]=2;\r
+ a->lsu[0]=19; a->lsu[1]=8;\r
+ #else\r
+ t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;\r
+ a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;\r
+ #endif\r
+ }\r
+ else { // odd exponent\r
+ // Set t=0.0819, a=2.59\r
+ f->exponent--; // f=f/10\r
+ exp++; // e=e+1\r
+ t->exponent=-4;\r
+ a->exponent=-2;\r
+ #if DECDPUN>=3\r
+ t->lsu[0]=819;\r
+ a->lsu[0]=259;\r
+ #elif DECDPUN==2\r
+ t->lsu[0]=19; t->lsu[1]=8;\r
+ a->lsu[0]=59; a->lsu[1]=2;\r
+ #else\r
+ t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;\r
+ a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;\r
+ #endif\r
+ }\r
+\r
+ decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f\r
+ decAddOp(a, a, t, &workset, 0, &ignore); // ..+t\r
+ // [a is now the initial approximation for sqrt(f), calculated with\r
+ // currentprecision, which is also a's precision.]\r
+\r
+ // the main calculation loop\r
+ decNumberZero(&dzero); // make 0\r
+ decNumberZero(t); // set t = 0.5\r
+ t->lsu[0]=5; // ..\r
+ t->exponent=-1; // ..\r
+ workset.digits=3; // initial p\r
+ for (; workset.digits<maxp;) {\r
+ // set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp]\r
+ workset.digits=MINI(workset.digits*2-2, maxp);\r
+ // a = 0.5 * (a + f/a)\r
+ // [calculated at p then rounded to currentprecision]\r
+ decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a\r
+ decAddOp(b, b, a, &workset, 0, &ignore); // b=b+a\r
+ decMultiplyOp(a, b, t, &workset, &ignore); // a=b*0.5\r
+ } // loop\r
+\r
+ // Here, 0.1 <= a < 1 [Hull], and a has maxp digits\r
+ // now reduce to length, etc.; this needs to be done with a\r
+ // having the correct exponent so as to handle subnormals\r
+ // correctly\r
+ approxset=*set; // get emin, emax, etc.\r
+ approxset.round=DEC_ROUND_HALF_EVEN;\r
+ a->exponent+=exp/2; // set correct exponent\r
+ rstatus=0; // clear status\r
+ residue=0; // .. and accumulator\r
+ decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed)\r
+ decFinish(a, &approxset, &residue, &rstatus); // clean and finalize\r
+\r
+ // Overflow was possible if the input exponent was out-of-range,\r
+ // in which case quit\r
+ if (rstatus&DEC_Overflow) {\r
+ status=rstatus; // use the status as-is\r
+ decNumberCopy(res, a); // copy to result\r
+ break;\r
+ }\r
+\r
+ // Preserve status except Inexact/Rounded\r
+ status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));\r
+\r
+ // Carry out the Hull correction\r
+ a->exponent-=exp/2; // back to 0.1->1\r
+\r
+ // a is now at final precision and within 1 ulp of the properly\r
+ // rounded square root of f; to ensure proper rounding, compare\r
+ // squares of (a - l/2 ulp) and (a + l/2 ulp) with f.\r
+ // Here workset.digits=maxp and t=0.5, and a->digits determines\r
+ // the ulp\r
+ workset.digits--; // maxp-1 is OK now\r
+ t->exponent=-a->digits-1; // make 0.5 ulp\r
+ decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp\r
+ workset.round=DEC_ROUND_UP;\r
+ decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b)\r
+ decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed\r
+ if (decNumberIsNegative(b)) { // f < b [i.e., b > f]\r
+ // this is the more common adjustment, though both are rare\r
+ t->exponent++; // make 1.0 ulp\r
+ t->lsu[0]=1; // ..\r
+ decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp\r
+ // assign to approx [round to length]\r
+ approxset.emin-=exp/2; // adjust to match a\r
+ approxset.emax-=exp/2;\r
+ decAddOp(a, &dzero, a, &approxset, 0, &ignore);\r
+ }\r
+ else {\r
+ decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp\r
+ workset.round=DEC_ROUND_DOWN;\r
+ decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b)\r
+ decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f\r
+ if (decNumberIsNegative(b)) { // b < f\r
+ t->exponent++; // make 1.0 ulp\r
+ t->lsu[0]=1; // ..\r
+ decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp\r
+ // assign to approx [round to length]\r
+ approxset.emin-=exp/2; // adjust to match a\r
+ approxset.emax-=exp/2;\r
+ decAddOp(a, &dzero, a, &approxset, 0, &ignore);\r
+ }\r
+ }\r
+ // [no errors are possible in the above, and rounding/inexact during\r
+ // estimation are irrelevant, so status was not accumulated]\r
+\r
+ // Here, 0.1 <= a < 1 (still), so adjust back\r
+ a->exponent+=exp/2; // set correct exponent\r
+\r
+ // count droppable zeros [after any subnormal rounding] by\r
+ // trimming a copy\r
+ decNumberCopy(b, a);\r
+ decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros]\r
+\r
+ // Set Inexact and Rounded. The answer can only be exact if\r
+ // it is short enough so that squaring it could fit in workp\r
+ // digits, so this is the only (relatively rare) condition that\r
+ // a careful check is needed\r
+ if (b->digits*2-1 > workp) { // cannot fit\r
+ status|=DEC_Inexact|DEC_Rounded;\r
+ }\r
+ else { // could be exact/unrounded\r
+ uInt mstatus=0; // local status\r
+ decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply\r
+ if (mstatus&DEC_Overflow) { // result just won't fit\r
+ status|=DEC_Inexact|DEC_Rounded;\r
+ }\r
+ else { // plausible\r
+ decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs\r
+ if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal\r
+ else { // is Exact\r
+ // here, dropped is the count of trailing zeros in 'a'\r
+ // use closest exponent to ideal...\r
+ Int todrop=ideal-a->exponent; // most that can be dropped\r
+ if (todrop<0) status|=DEC_Rounded; // ideally would add 0s\r
+ else { // unrounded\r
+ // there are some to drop, but emax may not allow all\r
+ Int maxexp=set->emax-set->digits+1;\r
+ Int maxdrop=maxexp-a->exponent;\r
+ if (todrop>maxdrop && set->clamp) { // apply clamping\r
+ todrop=maxdrop;\r
+ status|=DEC_Clamped;\r
+ }\r
+ if (dropped<todrop) { // clamp to those available\r
+ todrop=dropped;\r
+ status|=DEC_Clamped;\r
+ }\r
+ if (todrop>0) { // have some to drop\r
+ decShiftToLeast(a->lsu, D2U(a->digits), todrop);\r
+ a->exponent+=todrop; // maintain numerical value\r
+ a->digits-=todrop; // new length\r
+ }\r
+ }\r
+ }\r
+ }\r
+ }\r
+\r
+ // double-check Underflow, as perhaps the result could not have\r
+ // been subnormal (initial argument too big), or it is now Exact\r
+ if (status&DEC_Underflow) {\r
+ Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent\r
+ // check if truly subnormal\r
+ #if DECEXTFLAG // DEC_Subnormal too\r
+ if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);\r
+ #else\r
+ if (ae>=set->emin*2) status&=~DEC_Underflow;\r
+ #endif\r
+ // check if truly inexact\r
+ if (!(status&DEC_Inexact)) status&=~DEC_Underflow;\r
+ }\r
+\r
+ decNumberCopy(res, a); // a is now the result\r
+ } while(0); // end protected\r
+\r
+ if (allocbuff!=NULL) free(allocbuff); // drop any storage used\r
+ if (allocbufa!=NULL) free(allocbufa); // ..\r
+ if (allocbufb!=NULL) free(allocbufb); // ..\r
+ #if DECSUBSET\r
+ if (allocrhs !=NULL) free(allocrhs); // ..\r
+ #endif\r
+ if (status!=0) decStatus(res, status, set);// then report status\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberSquareRoot\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberSubtract -- subtract two Numbers */\r
+/* */\r
+/* This computes C = A - B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X-X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ uInt status=0; // accumulator\r
+\r
+ decAddOp(res, lhs, rhs, set, DECNEG, &status);\r
+ if (status!=0) decStatus(res, status, set);\r
+ #if DECCHECK\r
+ decCheckInexact(res, set);\r
+ #endif\r
+ return res;\r
+ } // decNumberSubtract\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberToIntegralExact -- round-to-integral-value with InExact */\r
+/* decNumberToIntegralValue -- round-to-integral-value */\r
+/* */\r
+/* res is the result */\r
+/* rhs is input number */\r
+/* set is the context */\r
+/* */\r
+/* res must have space for any value of rhs. */\r
+/* */\r
+/* This implements the IEEE special operators and therefore treats */\r
+/* special values as valid. For finite numbers it returns */\r
+/* rescale(rhs, 0) if rhs->exponent is <0. */\r
+/* Otherwise the result is rhs (so no error is possible, except for */\r
+/* sNaN). */\r
+/* */\r
+/* The context is used for rounding mode and status after sNaN, but */\r
+/* the digits setting is ignored. The Exact version will signal */\r
+/* Inexact if the result differs numerically from rhs; the other */\r
+/* never signals Inexact. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decNumber dn;\r
+ decContext workset; // working context\r
+ uInt status=0; // accumulator\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ // handle infinities and NaNs\r
+ if (SPECIALARG) {\r
+ if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity\r
+ else decNaNs(res, rhs, NULL, set, &status); // a NaN\r
+ }\r
+ else { // finite\r
+ // have a finite number; no error possible (res must be big enough)\r
+ if (rhs->exponent>=0) return decNumberCopy(res, rhs);\r
+ // that was easy, but if negative exponent there is work to do...\r
+ workset=*set; // clone rounding, etc.\r
+ workset.digits=rhs->digits; // no length rounding\r
+ workset.traps=0; // no traps\r
+ decNumberZero(&dn); // make a number with exponent 0\r
+ decNumberQuantize(res, rhs, &dn, &workset);\r
+ status|=workset.status;\r
+ }\r
+ if (status!=0) decStatus(res, status, set);\r
+ return res;\r
+ } // decNumberToIntegralExact\r
+\r
+decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,\r
+ decContext *set) {\r
+ decContext workset=*set; // working context\r
+ workset.traps=0; // no traps\r
+ decNumberToIntegralExact(res, rhs, &workset);\r
+ // this never affects set, except for sNaNs; NaN will have been set\r
+ // or propagated already, so no need to call decStatus\r
+ set->status|=workset.status&DEC_Invalid_operation;\r
+ return res;\r
+ } // decNumberToIntegralValue\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberXor -- XOR two Numbers, digitwise */\r
+/* */\r
+/* This computes C = A ^ B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X^X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context (used for result length and error report) */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Logical function restrictions apply (see above); a NaN is */\r
+/* returned with Invalid_operation if a restriction is violated. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberXor(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ const Unit *ua, *ub; // -> operands\r
+ const Unit *msua, *msub; // -> operand msus\r
+ Unit *uc, *msuc; // -> result and its msu\r
+ Int msudigs; // digits in res msu\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)\r
+ || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ // operands are valid\r
+ ua=lhs->lsu; // bottom-up\r
+ ub=rhs->lsu; // ..\r
+ uc=res->lsu; // ..\r
+ msua=ua+D2U(lhs->digits)-1; // -> msu of lhs\r
+ msub=ub+D2U(rhs->digits)-1; // -> msu of rhs\r
+ msuc=uc+D2U(set->digits)-1; // -> msu of result\r
+ msudigs=MSUDIGITS(set->digits); // [faster than remainder]\r
+ for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop\r
+ Unit a, b; // extract units\r
+ if (ua>msua) a=0;\r
+ else a=*ua;\r
+ if (ub>msub) b=0;\r
+ else b=*ub;\r
+ *uc=0; // can now write back\r
+ if (a|b) { // maybe 1 bits to examine\r
+ Int i, j;\r
+ // This loop could be unrolled and/or use BIN2BCD tables\r
+ for (i=0; i<DECDPUN; i++) {\r
+ if ((a^b)&1) *uc=*uc+(Unit)powers[i]; // effect XOR\r
+ j=a%10;\r
+ a=a/10;\r
+ j|=b%10;\r
+ b=b/10;\r
+ if (j>1) {\r
+ decStatus(res, DEC_Invalid_operation, set);\r
+ return res;\r
+ }\r
+ if (uc==msuc && i==msudigs-1) break; // just did final digit\r
+ } // each digit\r
+ } // non-zero\r
+ } // each unit\r
+ // [here uc-1 is the msu of the result]\r
+ res->digits=decGetDigits(res->lsu, uc-res->lsu);\r
+ res->exponent=0; // integer\r
+ res->bits=0; // sign=0\r
+ return res; // [no status to set]\r
+ } // decNumberXor\r
+\r
+\r
+/* ================================================================== */\r
+/* Utility routines */\r
+/* ================================================================== */\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberClass -- return the decClass of a decNumber */\r
+/* dn -- the decNumber to test */\r
+/* set -- the context to use for Emin */\r
+/* returns the decClass enum */\r
+/* ------------------------------------------------------------------ */\r
+enum decClass decNumberClass(const decNumber *dn, decContext *set) {\r
+ if (decNumberIsSpecial(dn)) {\r
+ if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;\r
+ if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;\r
+ // must be an infinity\r
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;\r
+ return DEC_CLASS_POS_INF;\r
+ }\r
+ // is finite\r
+ if (decNumberIsNormal(dn, set)) { // most common\r
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;\r
+ return DEC_CLASS_POS_NORMAL;\r
+ }\r
+ // is subnormal or zero\r
+ if (decNumberIsZero(dn)) { // most common\r
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;\r
+ return DEC_CLASS_POS_ZERO;\r
+ }\r
+ if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;\r
+ return DEC_CLASS_POS_SUBNORMAL;\r
+ } // decNumberClass\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberClassToString -- convert decClass to a string */\r
+/* */\r
+/* eclass is a valid decClass */\r
+/* returns a constant string describing the class (max 13+1 chars) */\r
+/* ------------------------------------------------------------------ */\r
+const char *decNumberClassToString(enum decClass eclass) {\r
+ if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;\r
+ if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;\r
+ if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;\r
+ if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;\r
+ if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;\r
+ if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;\r
+ if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;\r
+ if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;\r
+ if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;\r
+ if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;\r
+ return DEC_ClassString_UN; // Unknown\r
+ } // decNumberClassToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCopy -- copy a number */\r
+/* */\r
+/* dest is the target decNumber */\r
+/* src is the source decNumber */\r
+/* returns dest */\r
+/* */\r
+/* (dest==src is allowed and is a no-op) */\r
+/* All fields are updated as required. This is a utility operation, */\r
+/* so special values are unchanged and no error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {\r
+\r
+ #if DECCHECK\r
+ if (src==NULL) return decNumberZero(dest);\r
+ #endif\r
+\r
+ if (dest==src) return dest; // no copy required\r
+\r
+ // Use explicit assignments here as structure assignment could copy\r
+ // more than just the lsu (for small DECDPUN). This would not affect\r
+ // the value of the results, but could disturb test harness spill\r
+ // checking.\r
+ dest->bits=src->bits;\r
+ dest->exponent=src->exponent;\r
+ dest->digits=src->digits;\r
+ dest->lsu[0]=src->lsu[0];\r
+ if (src->digits>DECDPUN) { // more Units to come\r
+ const Unit *smsup, *s; // work\r
+ Unit *d; // ..\r
+ // memcpy for the remaining Units would be safe as they cannot\r
+ // overlap. However, this explicit loop is faster in short cases.\r
+ d=dest->lsu+1; // -> first destination\r
+ smsup=src->lsu+D2U(src->digits); // -> source msu+1\r
+ for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;\r
+ }\r
+ return dest;\r
+ } // decNumberCopy\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCopyAbs -- quiet absolute value operator */\r
+/* */\r
+/* This sets C = abs(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* No exception or error can occur; this is a quiet bitwise operation.*/\r
+/* See also decNumberAbs for a checking version of this. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;\r
+ #endif\r
+ decNumberCopy(res, rhs);\r
+ res->bits&=~DECNEG; // turn off sign\r
+ return res;\r
+ } // decNumberCopyAbs\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCopyNegate -- quiet negate value operator */\r
+/* */\r
+/* This sets C = negate(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* No exception or error can occur; this is a quiet bitwise operation.*/\r
+/* See also decNumberMinus for a checking version of this. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;\r
+ #endif\r
+ decNumberCopy(res, rhs);\r
+ res->bits^=DECNEG; // invert the sign\r
+ return res;\r
+ } // decNumberCopyNegate\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberCopySign -- quiet copy and set sign operator */\r
+/* */\r
+/* This sets C = A with the sign of B */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* No exception or error can occur; this is a quiet bitwise operation.*/\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs) {\r
+ uByte sign; // rhs sign\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;\r
+ #endif\r
+ sign=rhs->bits & DECNEG; // save sign bit\r
+ decNumberCopy(res, lhs);\r
+ res->bits&=~DECNEG; // clear the sign\r
+ res->bits|=sign; // set from rhs\r
+ return res;\r
+ } // decNumberCopySign\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberGetBCD -- get the coefficient in BCD8 */\r
+/* dn is the source decNumber */\r
+/* bcd is the uInt array that will receive dn->digits BCD bytes, */\r
+/* most-significant at offset 0 */\r
+/* returns bcd */\r
+/* */\r
+/* bcd must have at least dn->digits bytes. No error is possible; if */\r
+/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */\r
+/* ------------------------------------------------------------------ */\r
+uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {\r
+ uByte *ub=bcd+dn->digits-1; // -> lsd\r
+ const Unit *up=dn->lsu; // Unit pointer, -> lsu\r
+\r
+ #if DECDPUN==1 // trivial simple copy\r
+ for (; ub>=bcd; ub--, up++) *ub=*up;\r
+ #else // chopping needed\r
+ uInt u=*up; // work\r
+ uInt cut=DECDPUN; // downcounter through unit\r
+ for (; ub>=bcd; ub--) {\r
+ *ub=(uByte)(u%10); // [*6554 trick inhibits, here]\r
+ u=u/10;\r
+ cut--;\r
+ if (cut>0) continue; // more in this unit\r
+ up++;\r
+ u=*up;\r
+ cut=DECDPUN;\r
+ }\r
+ #endif\r
+ return bcd;\r
+ } // decNumberGetBCD\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */\r
+/* dn is the target decNumber */\r
+/* bcd is the uInt array that will source n BCD bytes, most- */\r
+/* significant at offset 0 */\r
+/* n is the number of digits in the source BCD array (bcd) */\r
+/* returns dn */\r
+/* */\r
+/* dn must have space for at least n digits. No error is possible; */\r
+/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */\r
+/* and bcd[0] zero. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {\r
+ Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer]\r
+ const uByte *ub=bcd; // -> source msd\r
+\r
+ #if DECDPUN==1 // trivial simple copy\r
+ for (; ub<bcd+n; ub++, up--) *up=*ub;\r
+ #else // some assembly needed\r
+ // calculate how many digits in msu, and hence first cut\r
+ Int cut=MSUDIGITS(n); // [faster than remainder]\r
+ for (;up>=dn->lsu; up--) { // each Unit from msu\r
+ *up=0; // will take <=DECDPUN digits\r
+ for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;\r
+ cut=DECDPUN; // next Unit has all digits\r
+ }\r
+ #endif\r
+ dn->digits=n; // set digit count\r
+ return dn;\r
+ } // decNumberSetBCD\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberIsNormal -- test normality of a decNumber */\r
+/* dn is the decNumber to test */\r
+/* set is the context to use for Emin */\r
+/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */\r
+/* ------------------------------------------------------------------ */\r
+Int decNumberIsNormal(const decNumber *dn, decContext *set) {\r
+ Int ae; // adjusted exponent\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;\r
+ #endif\r
+\r
+ if (decNumberIsSpecial(dn)) return 0; // not finite\r
+ if (decNumberIsZero(dn)) return 0; // not non-zero\r
+\r
+ ae=dn->exponent+dn->digits-1; // adjusted exponent\r
+ if (ae<set->emin) return 0; // is subnormal\r
+ return 1;\r
+ } // decNumberIsNormal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberIsSubnormal -- test subnormality of a decNumber */\r
+/* dn is the decNumber to test */\r
+/* set is the context to use for Emin */\r
+/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */\r
+/* ------------------------------------------------------------------ */\r
+Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {\r
+ Int ae; // adjusted exponent\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;\r
+ #endif\r
+\r
+ if (decNumberIsSpecial(dn)) return 0; // not finite\r
+ if (decNumberIsZero(dn)) return 0; // not non-zero\r
+\r
+ ae=dn->exponent+dn->digits-1; // adjusted exponent\r
+ if (ae<set->emin) return 1; // is subnormal\r
+ return 0;\r
+ } // decNumberIsSubnormal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberTrim -- remove insignificant zeros */\r
+/* */\r
+/* dn is the number to trim */\r
+/* returns dn */\r
+/* */\r
+/* All fields are updated as required. This is a utility operation, */\r
+/* so special values are unchanged and no error is possible. The */\r
+/* zeros are removed unconditionally. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decNumberTrim(decNumber *dn) {\r
+ Int dropped; // work\r
+ decContext set; // ..\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;\r
+ #endif\r
+ decContextDefault(&set, DEC_INIT_BASE); // clamp=0\r
+ return decTrim(dn, &set, 0, 1, &dropped);\r
+ } // decNumberTrim\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberVersion -- return the name and version of this module */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+const char * decNumberVersion(void) {\r
+ return DECVERSION;\r
+ } // decNumberVersion\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberZero -- set a number to 0 */\r
+/* */\r
+/* dn is the number to set, with space for one digit */\r
+/* returns dn */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+// Memset is not used as it is much slower in some environments.\r
+decNumber * decNumberZero(decNumber *dn) {\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;\r
+ #endif\r
+\r
+ dn->bits=0;\r
+ dn->exponent=0;\r
+ dn->digits=1;\r
+ dn->lsu[0]=0;\r
+ return dn;\r
+ } // decNumberZero\r
+\r
+/* ================================================================== */\r
+/* Local routines */\r
+/* ================================================================== */\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decToString -- lay out a number into a string */\r
+/* */\r
+/* dn is the number to lay out */\r
+/* string is where to lay out the number */\r
+/* eng is 1 if Engineering, 0 if Scientific */\r
+/* */\r
+/* string must be at least dn->digits+14 characters long */\r
+/* No error is possible. */\r
+/* */\r
+/* Note that this routine can generate a -0 or 0.000. These are */\r
+/* never generated in subset to-number or arithmetic, but can occur */\r
+/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */\r
+/* ------------------------------------------------------------------ */\r
+// If DECCHECK is enabled the string "?" is returned if a number is\r
+// invalid.\r
+static void decToString(const decNumber *dn, char *string, Flag eng) {\r
+ Int exp=dn->exponent; // local copy\r
+ Int e; // E-part value\r
+ Int pre; // digits before the '.'\r
+ Int cut; // for counting digits in a Unit\r
+ char *c=string; // work [output pointer]\r
+ const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer]\r
+ uInt u, pow; // work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {\r
+ strcpy(string, "?");\r
+ return;}\r
+ #endif\r
+\r
+ if (decNumberIsNegative(dn)) { // Negatives get a minus\r
+ *c='-';\r
+ c++;\r
+ }\r
+ if (dn->bits&DECSPECIAL) { // Is a special value\r
+ if (decNumberIsInfinite(dn)) {\r
+ strcpy(c, "Inf");\r
+ strcpy(c+3, "inity");\r
+ return;}\r
+ // a NaN\r
+ if (dn->bits&DECSNAN) { // signalling NaN\r
+ *c='s';\r
+ c++;\r
+ }\r
+ strcpy(c, "NaN");\r
+ c+=3; // step past\r
+ // if not a clean non-zero coefficient, that's all there is in a\r
+ // NaN string\r
+ if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;\r
+ // [drop through to add integer]\r
+ }\r
+\r
+ // calculate how many digits in msu, and hence first cut\r
+ cut=MSUDIGITS(dn->digits); // [faster than remainder]\r
+ cut--; // power of ten for digit\r
+\r
+ if (exp==0) { // simple integer [common fastpath]\r
+ for (;up>=dn->lsu; up--) { // each Unit from msu\r
+ u=*up; // contains DECDPUN digits to lay out\r
+ for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);\r
+ cut=DECDPUN-1; // next Unit has all digits\r
+ }\r
+ *c='\0'; // terminate the string\r
+ return;}\r
+\r
+ /* non-0 exponent -- assume plain form */\r
+ pre=dn->digits+exp; // digits before '.'\r
+ e=0; // no E\r
+ if ((exp>0) || (pre<-5)) { // need exponential form\r
+ e=exp+dn->digits-1; // calculate E value\r
+ pre=1; // assume one digit before '.'\r
+ if (eng && (e!=0)) { // engineering: may need to adjust\r
+ Int adj; // adjustment\r
+ // The C remainder operator is undefined for negative numbers, so\r
+ // a positive remainder calculation must be used here\r
+ if (e<0) {\r
+ adj=(-e)%3;\r
+ if (adj!=0) adj=3-adj;\r
+ }\r
+ else { // e>0\r
+ adj=e%3;\r
+ }\r
+ e=e-adj;\r
+ // if dealing with zero still produce an exponent which is a\r
+ // multiple of three, as expected, but there will only be the\r
+ // one zero before the E, still. Otherwise note the padding.\r
+ if (!ISZERO(dn)) pre+=adj;\r
+ else { // is zero\r
+ if (adj!=0) { // 0.00Esnn needed\r
+ e=e+3;\r
+ pre=-(2-adj);\r
+ }\r
+ } // zero\r
+ } // eng\r
+ } // need exponent\r
+\r
+ /* lay out the digits of the coefficient, adding 0s and . as needed */\r
+ u=*up;\r
+ if (pre>0) { // xxx.xxx or xx00 (engineering) form\r
+ Int n=pre;\r
+ for (; pre>0; pre--, c++, cut--) {\r
+ if (cut<0) { // need new Unit\r
+ if (up==dn->lsu) break; // out of input digits (pre>digits)\r
+ up--;\r
+ cut=DECDPUN-1;\r
+ u=*up;\r
+ }\r
+ TODIGIT(u, cut, c, pow);\r
+ }\r
+ if (n<dn->digits) { // more to come, after '.'\r
+ *c='.'; c++;\r
+ for (;; c++, cut--) {\r
+ if (cut<0) { // need new Unit\r
+ if (up==dn->lsu) break; // out of input digits\r
+ up--;\r
+ cut=DECDPUN-1;\r
+ u=*up;\r
+ }\r
+ TODIGIT(u, cut, c, pow);\r
+ }\r
+ }\r
+ else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed\r
+ }\r
+ else { // 0.xxx or 0.000xxx form\r
+ *c='0'; c++;\r
+ *c='.'; c++;\r
+ for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.'\r
+ for (; ; c++, cut--) {\r
+ if (cut<0) { // need new Unit\r
+ if (up==dn->lsu) break; // out of input digits\r
+ up--;\r
+ cut=DECDPUN-1;\r
+ u=*up;\r
+ }\r
+ TODIGIT(u, cut, c, pow);\r
+ }\r
+ }\r
+\r
+ /* Finally add the E-part, if needed. It will never be 0, has a\r
+ base maximum and minimum of +999999999 through -999999999, but\r
+ could range down to -1999999998 for anormal numbers */\r
+ if (e!=0) {\r
+ Flag had=0; // 1=had non-zero\r
+ *c='E'; c++;\r
+ *c='+'; c++; // assume positive\r
+ u=e; // ..\r
+ if (e<0) {\r
+ *(c-1)='-'; // oops, need -\r
+ u=-e; // uInt, please\r
+ }\r
+ // lay out the exponent [_itoa or equivalent is not ANSI C]\r
+ for (cut=9; cut>=0; cut--) {\r
+ TODIGIT(u, cut, c, pow);\r
+ if (*c=='0' && !had) continue; // skip leading zeros\r
+ had=1; // had non-0\r
+ c++; // step for next\r
+ } // cut\r
+ }\r
+ *c='\0'; // terminate the string (all paths)\r
+ return;\r
+ } // decToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decAddOp -- add/subtract operation */\r
+/* */\r
+/* This computes C = A + B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X+X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* negate is DECNEG if rhs should be negated, or 0 otherwise */\r
+/* status accumulates status for the caller */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* Inexact in status must be 0 for correct Exact zero sign in result */\r
+/* ------------------------------------------------------------------ */\r
+/* If possible, the coefficient is calculated directly into C. */\r
+/* However, if: */\r
+/* -- a digits+1 calculation is needed because the numbers are */\r
+/* unaligned and span more than set->digits digits */\r
+/* -- a carry to digits+1 digits looks possible */\r
+/* -- C is the same as A or B, and the result would destructively */\r
+/* overlap the A or B coefficient */\r
+/* then the result must be calculated into a temporary buffer. In */\r
+/* this case a local (stack) buffer is used if possible, and only if */\r
+/* too long for that does malloc become the final resort. */\r
+/* */\r
+/* Misalignment is handled as follows: */\r
+/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */\r
+/* BPad: Apply the padding by a combination of shifting (whole */\r
+/* units) and multiplication (part units). */\r
+/* */\r
+/* Addition, especially x=x+1, is speed-critical. */\r
+/* The static buffer is larger than might be expected to allow for */\r
+/* calls from higher-level funtions (notable exp). */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber * decAddOp(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set,\r
+ uByte negate, uInt *status) {\r
+ #if DECSUBSET\r
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated\r
+ decNumber *allocrhs=NULL; // .., rhs\r
+ #endif\r
+ Int rhsshift; // working shift (in Units)\r
+ Int maxdigits; // longest logical length\r
+ Int mult; // multiplier\r
+ Int residue; // rounding accumulator\r
+ uByte bits; // result bits\r
+ Flag diffsign; // non-0 if arguments have different sign\r
+ Unit *acc; // accumulator for result\r
+ Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many\r
+ // allocations when called from\r
+ // other operations, notable exp]\r
+ Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated\r
+ Int reqdigits=set->digits; // local copy; requested DIGITS\r
+ Int padding; // work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operands and set lostDigits status, as needed\r
+ if (lhs->digits>reqdigits) {\r
+ alloclhs=decRoundOperand(lhs, set, status);\r
+ if (alloclhs==NULL) break;\r
+ lhs=alloclhs;\r
+ }\r
+ if (rhs->digits>reqdigits) {\r
+ allocrhs=decRoundOperand(rhs, set, status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ // note whether signs differ [used all paths]\r
+ diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);\r
+\r
+ // handle infinities and NaNs\r
+ if (SPECIALARGS) { // a special bit set\r
+ if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN\r
+ decNaNs(res, lhs, rhs, set, status);\r
+ else { // one or two infinities\r
+ if (decNumberIsInfinite(lhs)) { // LHS is infinity\r
+ // two infinities with different signs is invalid\r
+ if (decNumberIsInfinite(rhs) && diffsign) {\r
+ *status|=DEC_Invalid_operation;\r
+ break;\r
+ }\r
+ bits=lhs->bits & DECNEG; // get sign from LHS\r
+ }\r
+ else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity\r
+ bits|=DECINF;\r
+ decNumberZero(res);\r
+ res->bits=bits; // set +/- infinity\r
+ } // an infinity\r
+ break;\r
+ }\r
+\r
+ // Quick exit for add 0s; return the non-0, modified as need be\r
+ if (ISZERO(lhs)) {\r
+ Int adjust; // work\r
+ Int lexp=lhs->exponent; // save in case LHS==RES\r
+ bits=lhs->bits; // ..\r
+ residue=0; // clear accumulator\r
+ decCopyFit(res, rhs, set, &residue, status); // copy (as needed)\r
+ res->bits^=negate; // flip if rhs was negated\r
+ #if DECSUBSET\r
+ if (set->extended) { // exponents on zeros count\r
+ #endif\r
+ // exponent will be the lower of the two\r
+ adjust=lexp-res->exponent; // adjustment needed [if -ve]\r
+ if (ISZERO(res)) { // both 0: special IEEE 754 rules\r
+ if (adjust<0) res->exponent=lexp; // set exponent\r
+ // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0\r
+ if (diffsign) {\r
+ if (set->round!=DEC_ROUND_FLOOR) res->bits=0;\r
+ else res->bits=DECNEG; // preserve 0 sign\r
+ }\r
+ }\r
+ else { // non-0 res\r
+ if (adjust<0) { // 0-padding needed\r
+ if ((res->digits-adjust)>set->digits) {\r
+ adjust=res->digits-set->digits; // to fit exactly\r
+ *status|=DEC_Rounded; // [but exact]\r
+ }\r
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);\r
+ res->exponent+=adjust; // set the exponent.\r
+ }\r
+ } // non-0 res\r
+ #if DECSUBSET\r
+ } // extended\r
+ #endif\r
+ decFinish(res, set, &residue, status); // clean and finalize\r
+ break;}\r
+\r
+ if (ISZERO(rhs)) { // [lhs is non-zero]\r
+ Int adjust; // work\r
+ Int rexp=rhs->exponent; // save in case RHS==RES\r
+ bits=rhs->bits; // be clean\r
+ residue=0; // clear accumulator\r
+ decCopyFit(res, lhs, set, &residue, status); // copy (as needed)\r
+ #if DECSUBSET\r
+ if (set->extended) { // exponents on zeros count\r
+ #endif\r
+ // exponent will be the lower of the two\r
+ // [0-0 case handled above]\r
+ adjust=rexp-res->exponent; // adjustment needed [if -ve]\r
+ if (adjust<0) { // 0-padding needed\r
+ if ((res->digits-adjust)>set->digits) {\r
+ adjust=res->digits-set->digits; // to fit exactly\r
+ *status|=DEC_Rounded; // [but exact]\r
+ }\r
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);\r
+ res->exponent+=adjust; // set the exponent.\r
+ }\r
+ #if DECSUBSET\r
+ } // extended\r
+ #endif\r
+ decFinish(res, set, &residue, status); // clean and finalize\r
+ break;}\r
+\r
+ // [NB: both fastpath and mainpath code below assume these cases\r
+ // (notably 0-0) have already been handled]\r
+\r
+ // calculate the padding needed to align the operands\r
+ padding=rhs->exponent-lhs->exponent;\r
+\r
+ // Fastpath cases where the numbers are aligned and normal, the RHS\r
+ // is all in one unit, no operand rounding is needed, and no carry,\r
+ // lengthening, or borrow is needed\r
+ if (padding==0\r
+ && rhs->digits<=DECDPUN\r
+ && rhs->exponent>=set->emin // [some normals drop through]\r
+ && rhs->exponent<=set->emax-set->digits+1 // [could clamp]\r
+ && rhs->digits<=reqdigits\r
+ && lhs->digits<=reqdigits) {\r
+ Int partial=*lhs->lsu;\r
+ if (!diffsign) { // adding\r
+ partial+=*rhs->lsu;\r
+ if ((partial<=DECDPUNMAX) // result fits in unit\r
+ && (lhs->digits>=DECDPUN || // .. and no digits-count change\r
+ partial<(Int)powers[lhs->digits])) { // ..\r
+ if (res!=lhs) decNumberCopy(res, lhs); // not in place\r
+ *res->lsu=(Unit)partial; // [copy could have overwritten RHS]\r
+ break;\r
+ }\r
+ // else drop out for careful add\r
+ }\r
+ else { // signs differ\r
+ partial-=*rhs->lsu;\r
+ if (partial>0) { // no borrow needed, and non-0 result\r
+ if (res!=lhs) decNumberCopy(res, lhs); // not in place\r
+ *res->lsu=(Unit)partial;\r
+ // this could have reduced digits [but result>0]\r
+ res->digits=decGetDigits(res->lsu, D2U(res->digits));\r
+ break;\r
+ }\r
+ // else drop out for careful subtract\r
+ }\r
+ }\r
+\r
+ // Now align (pad) the lhs or rhs so they can be added or\r
+ // subtracted, as necessary. If one number is much larger than\r
+ // the other (that is, if in plain form there is a least one\r
+ // digit between the lowest digit of one and the highest of the\r
+ // other) padding with up to DIGITS-1 trailing zeros may be\r
+ // needed; then apply rounding (as exotic rounding modes may be\r
+ // affected by the residue).\r
+ rhsshift=0; // rhs shift to left (padding) in Units\r
+ bits=lhs->bits; // assume sign is that of LHS\r
+ mult=1; // likely multiplier\r
+\r
+ // [if padding==0 the operands are aligned; no padding is needed]\r
+ if (padding!=0) {\r
+ // some padding needed; always pad the RHS, as any required\r
+ // padding can then be effected by a simple combination of\r
+ // shifts and a multiply\r
+ Flag swapped=0;\r
+ if (padding<0) { // LHS needs the padding\r
+ const decNumber *t;\r
+ padding=-padding; // will be +ve\r
+ bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS\r
+ t=lhs; lhs=rhs; rhs=t;\r
+ swapped=1;\r
+ }\r
+\r
+ // If, after pad, rhs would be longer than lhs by digits+1 or\r
+ // more then lhs cannot affect the answer, except as a residue,\r
+ // so only need to pad up to a length of DIGITS+1.\r
+ if (rhs->digits+padding > lhs->digits+reqdigits+1) {\r
+ // The RHS is sufficient\r
+ // for residue use the relative sign indication...\r
+ Int shift=reqdigits-rhs->digits; // left shift needed\r
+ residue=1; // residue for rounding\r
+ if (diffsign) residue=-residue; // signs differ\r
+ // copy, shortening if necessary\r
+ decCopyFit(res, rhs, set, &residue, status);\r
+ // if it was already shorter, then need to pad with zeros\r
+ if (shift>0) {\r
+ res->digits=decShiftToMost(res->lsu, res->digits, shift);\r
+ res->exponent-=shift; // adjust the exponent.\r
+ }\r
+ // flip the result sign if unswapped and rhs was negated\r
+ if (!swapped) res->bits^=negate;\r
+ decFinish(res, set, &residue, status); // done\r
+ break;}\r
+\r
+ // LHS digits may affect result\r
+ rhsshift=D2U(padding+1)-1; // this much by Unit shift ..\r
+ mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication\r
+ } // padding needed\r
+\r
+ if (diffsign) mult=-mult; // signs differ\r
+\r
+ // determine the longer operand\r
+ maxdigits=rhs->digits+padding; // virtual length of RHS\r
+ if (lhs->digits>maxdigits) maxdigits=lhs->digits;\r
+\r
+ // Decide on the result buffer to use; if possible place directly\r
+ // into result.\r
+ acc=res->lsu; // assume add direct to result\r
+ // If destructive overlap, or the number is too long, or a carry or\r
+ // borrow to DIGITS+1 might be possible, a buffer must be used.\r
+ // [Might be worth more sophisticated tests when maxdigits==reqdigits]\r
+ if ((maxdigits>=reqdigits) // is, or could be, too large\r
+ || (res==rhs && rhsshift>0)) { // destructive overlap\r
+ // buffer needed, choose it; units for maxdigits digits will be\r
+ // needed, +1 Unit for carry or borrow\r
+ Int need=D2U(maxdigits)+1;\r
+ acc=accbuff; // assume use local buffer\r
+ if (need*sizeof(Unit)>sizeof(accbuff)) {\r
+ // printf("malloc add %ld %ld\n", need, sizeof(accbuff));\r
+ allocacc=(Unit *)malloc(need*sizeof(Unit));\r
+ if (allocacc==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ acc=allocacc;\r
+ }\r
+ }\r
+\r
+ res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite..\r
+ res->exponent=lhs->exponent; // .. operands (even if aliased)\r
+\r
+ #if DECTRACE\r
+ decDumpAr('A', lhs->lsu, D2U(lhs->digits));\r
+ decDumpAr('B', rhs->lsu, D2U(rhs->digits));\r
+ printf(" :h: %ld %ld\n", rhsshift, mult);\r
+ #endif\r
+\r
+ // add [A+B*m] or subtract [A+B*(-m)]\r
+ res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),\r
+ rhs->lsu, D2U(rhs->digits),\r
+ rhsshift, acc, mult)\r
+ *DECDPUN; // [units -> digits]\r
+ if (res->digits<0) { // borrowed...\r
+ res->digits=-res->digits;\r
+ res->bits^=DECNEG; // flip the sign\r
+ }\r
+ #if DECTRACE\r
+ decDumpAr('+', acc, D2U(res->digits));\r
+ #endif\r
+\r
+ // If a buffer was used the result must be copied back, possibly\r
+ // shortening. (If no buffer was used then the result must have\r
+ // fit, so can't need rounding and residue must be 0.)\r
+ residue=0; // clear accumulator\r
+ if (acc!=res->lsu) {\r
+ #if DECSUBSET\r
+ if (set->extended) { // round from first significant digit\r
+ #endif\r
+ // remove leading zeros that were added due to rounding up to\r
+ // integral Units -- before the test for rounding.\r
+ if (res->digits>reqdigits)\r
+ res->digits=decGetDigits(acc, D2U(res->digits));\r
+ decSetCoeff(res, set, acc, res->digits, &residue, status);\r
+ #if DECSUBSET\r
+ }\r
+ else { // subset arithmetic rounds from original significant digit\r
+ // May have an underestimate. This only occurs when both\r
+ // numbers fit in DECDPUN digits and are padding with a\r
+ // negative multiple (-10, -100...) and the top digit(s) become\r
+ // 0. (This only matters when using X3.274 rules where the\r
+ // leading zero could be included in the rounding.)\r
+ if (res->digits<maxdigits) {\r
+ *(acc+D2U(res->digits))=0; // ensure leading 0 is there\r
+ res->digits=maxdigits;\r
+ }\r
+ else {\r
+ // remove leading zeros that added due to rounding up to\r
+ // integral Units (but only those in excess of the original\r
+ // maxdigits length, unless extended) before test for rounding.\r
+ if (res->digits>reqdigits) {\r
+ res->digits=decGetDigits(acc, D2U(res->digits));\r
+ if (res->digits<maxdigits) res->digits=maxdigits;\r
+ }\r
+ }\r
+ decSetCoeff(res, set, acc, res->digits, &residue, status);\r
+ // Now apply rounding if needed before removing leading zeros.\r
+ // This is safe because subnormals are not a possibility\r
+ if (residue!=0) {\r
+ decApplyRound(res, set, residue, status);\r
+ residue=0; // did what needed to be done\r
+ }\r
+ } // subset\r
+ #endif\r
+ } // used buffer\r
+\r
+ // strip leading zeros [these were left on in case of subset subtract]\r
+ res->digits=decGetDigits(res->lsu, D2U(res->digits));\r
+\r
+ // apply checks and rounding\r
+ decFinish(res, set, &residue, status);\r
+\r
+ // "When the sum of two operands with opposite signs is exactly\r
+ // zero, the sign of that sum shall be '+' in all rounding modes\r
+ // except round toward -Infinity, in which mode that sign shall be\r
+ // '-'." [Subset zeros also never have '-', set by decFinish.]\r
+ if (ISZERO(res) && diffsign\r
+ #if DECSUBSET\r
+ && set->extended\r
+ #endif\r
+ && (*status&DEC_Inexact)==0) {\r
+ if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign -\r
+ else res->bits&=~DECNEG; // sign +\r
+ }\r
+ } while(0); // end protected\r
+\r
+ if (allocacc!=NULL) free(allocacc); // drop any storage used\r
+ #if DECSUBSET\r
+ if (allocrhs!=NULL) free(allocrhs); // ..\r
+ if (alloclhs!=NULL) free(alloclhs); // ..\r
+ #endif\r
+ return res;\r
+ } // decAddOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decDivideOp -- division operation */\r
+/* */\r
+/* This routine performs the calculations for all four division */\r
+/* operators (divide, divideInteger, remainder, remainderNear). */\r
+/* */\r
+/* C=A op B */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X/X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */\r
+/* status is the usual accumulator */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+/* The underlying algorithm of this routine is the same as in the */\r
+/* 1981 S/370 implementation, that is, non-restoring long division */\r
+/* with bi-unit (rather than bi-digit) estimation for each unit */\r
+/* multiplier. In this pseudocode overview, complications for the */\r
+/* Remainder operators and division residues for exact rounding are */\r
+/* omitted for clarity. */\r
+/* */\r
+/* Prepare operands and handle special values */\r
+/* Test for x/0 and then 0/x */\r
+/* Exp =Exp1 - Exp2 */\r
+/* Exp =Exp +len(var1) -len(var2) */\r
+/* Sign=Sign1 * Sign2 */\r
+/* Pad accumulator (Var1) to double-length with 0's (pad1) */\r
+/* Pad Var2 to same length as Var1 */\r
+/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */\r
+/* have=0 */\r
+/* Do until (have=digits+1 OR residue=0) */\r
+/* if exp<0 then if integer divide/residue then leave */\r
+/* this_unit=0 */\r
+/* Do forever */\r
+/* compare numbers */\r
+/* if <0 then leave inner_loop */\r
+/* if =0 then (* quick exit without subtract *) do */\r
+/* this_unit=this_unit+1; output this_unit */\r
+/* leave outer_loop; end */\r
+/* Compare lengths of numbers (mantissae): */\r
+/* If same then tops2=msu2pair -- {units 1&2 of var2} */\r
+/* else tops2=msu2plus -- {0, unit 1 of var2} */\r
+/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */\r
+/* mult=tops1/tops2 -- Good and safe guess at divisor */\r
+/* if mult=0 then mult=1 */\r
+/* this_unit=this_unit+mult */\r
+/* subtract */\r
+/* end inner_loop */\r
+/* if have\=0 | this_unit\=0 then do */\r
+/* output this_unit */\r
+/* have=have+1; end */\r
+/* var2=var2/10 */\r
+/* exp=exp-1 */\r
+/* end outer_loop */\r
+/* exp=exp+1 -- set the proper exponent */\r
+/* if have=0 then generate answer=0 */\r
+/* Return (Result is defined by Var1) */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+/* Two working buffers are needed during the division; one (digits+ */\r
+/* 1) to accumulate the result, and the other (up to 2*digits+1) for */\r
+/* long subtractions. These are acc and var1 respectively. */\r
+/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/\r
+/* The static buffers may be larger than might be expected to allow */\r
+/* for calls from higher-level funtions (notable exp). */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber * decDivideOp(decNumber *res,\r
+ const decNumber *lhs, const decNumber *rhs,\r
+ decContext *set, Flag op, uInt *status) {\r
+ #if DECSUBSET\r
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated\r
+ decNumber *allocrhs=NULL; // .., rhs\r
+ #endif\r
+ Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer\r
+ Unit *acc=accbuff; // -> accumulator array for result\r
+ Unit *allocacc=NULL; // -> allocated buffer, iff allocated\r
+ Unit *accnext; // -> where next digit will go\r
+ Int acclength; // length of acc needed [Units]\r
+ Int accunits; // count of units accumulated\r
+ Int accdigits; // count of digits accumulated\r
+\r
+ Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1\r
+ Unit *var1=varbuff; // -> var1 array for long subtraction\r
+ Unit *varalloc=NULL; // -> allocated buffer, iff used\r
+ Unit *msu1; // -> msu of var1\r
+\r
+ const Unit *var2; // -> var2 array\r
+ const Unit *msu2; // -> msu of var2\r
+ Int msu2plus; // msu2 plus one [does not vary]\r
+ eInt msu2pair; // msu2 pair plus one [does not vary]\r
+\r
+ Int var1units, var2units; // actual lengths\r
+ Int var2ulen; // logical length (units)\r
+ Int var1initpad=0; // var1 initial padding (digits)\r
+ Int maxdigits; // longest LHS or required acc length\r
+ Int mult; // multiplier for subtraction\r
+ Unit thisunit; // current unit being accumulated\r
+ Int residue; // for rounding\r
+ Int reqdigits=set->digits; // requested DIGITS\r
+ Int exponent; // working exponent\r
+ Int maxexponent=0; // DIVIDE maximum exponent if unrounded\r
+ uByte bits; // working sign\r
+ Unit *target; // work\r
+ const Unit *source; // ..\r
+ uInt const *pow; // ..\r
+ Int shift, cut; // ..\r
+ #if DECSUBSET\r
+ Int dropped; // work\r
+ #endif\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operands and set lostDigits status, as needed\r
+ if (lhs->digits>reqdigits) {\r
+ alloclhs=decRoundOperand(lhs, set, status);\r
+ if (alloclhs==NULL) break;\r
+ lhs=alloclhs;\r
+ }\r
+ if (rhs->digits>reqdigits) {\r
+ allocrhs=decRoundOperand(rhs, set, status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions\r
+\r
+ // handle infinities and NaNs\r
+ if (SPECIALARGS) { // a special bit set\r
+ if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs\r
+ decNaNs(res, lhs, rhs, set, status);\r
+ break;\r
+ }\r
+ // one or two infinities\r
+ if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite\r
+ if (decNumberIsInfinite(rhs) || // two infinities are invalid ..\r
+ op & (REMAINDER | REMNEAR)) { // as is remainder of infinity\r
+ *status|=DEC_Invalid_operation;\r
+ break;\r
+ }\r
+ // [Note that infinity/0 raises no exceptions]\r
+ decNumberZero(res);\r
+ res->bits=bits|DECINF; // set +/- infinity\r
+ break;\r
+ }\r
+ else { // RHS (divisor) is infinite\r
+ residue=0;\r
+ if (op&(REMAINDER|REMNEAR)) {\r
+ // result is [finished clone of] lhs\r
+ decCopyFit(res, lhs, set, &residue, status);\r
+ }\r
+ else { // a division\r
+ decNumberZero(res);\r
+ res->bits=bits; // set +/- zero\r
+ // for DIVIDEINT the exponent is always 0. For DIVIDE, result\r
+ // is a 0 with infinitely negative exponent, clamped to minimum\r
+ if (op&DIVIDE) {\r
+ res->exponent=set->emin-set->digits+1;\r
+ *status|=DEC_Clamped;\r
+ }\r
+ }\r
+ decFinish(res, set, &residue, status);\r
+ break;\r
+ }\r
+ }\r
+\r
+ // handle 0 rhs (x/0)\r
+ if (ISZERO(rhs)) { // x/0 is always exceptional\r
+ if (ISZERO(lhs)) {\r
+ decNumberZero(res); // [after lhs test]\r
+ *status|=DEC_Division_undefined;// 0/0 will become NaN\r
+ }\r
+ else {\r
+ decNumberZero(res);\r
+ if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;\r
+ else {\r
+ *status|=DEC_Division_by_zero; // x/0\r
+ res->bits=bits|DECINF; // .. is +/- Infinity\r
+ }\r
+ }\r
+ break;}\r
+\r
+ // handle 0 lhs (0/x)\r
+ if (ISZERO(lhs)) { // 0/x [x!=0]\r
+ #if DECSUBSET\r
+ if (!set->extended) decNumberZero(res);\r
+ else {\r
+ #endif\r
+ if (op&DIVIDE) {\r
+ residue=0;\r
+ exponent=lhs->exponent-rhs->exponent; // ideal exponent\r
+ decNumberCopy(res, lhs); // [zeros always fit]\r
+ res->bits=bits; // sign as computed\r
+ res->exponent=exponent; // exponent, too\r
+ decFinalize(res, set, &residue, status); // check exponent\r
+ }\r
+ else if (op&DIVIDEINT) {\r
+ decNumberZero(res); // integer 0\r
+ res->bits=bits; // sign as computed\r
+ }\r
+ else { // a remainder\r
+ exponent=rhs->exponent; // [save in case overwrite]\r
+ decNumberCopy(res, lhs); // [zeros always fit]\r
+ if (exponent<res->exponent) res->exponent=exponent; // use lower\r
+ }\r
+ #if DECSUBSET\r
+ }\r
+ #endif\r
+ break;}\r
+\r
+ // Precalculate exponent. This starts off adjusted (and hence fits\r
+ // in 31 bits) and becomes the usual unadjusted exponent as the\r
+ // division proceeds. The order of evaluation is important, here,\r
+ // to avoid wrap.\r
+ exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);\r
+\r
+ // If the working exponent is -ve, then some quick exits are\r
+ // possible because the quotient is known to be <1\r
+ // [for REMNEAR, it needs to be < -1, as -0.5 could need work]\r
+ if (exponent<0 && !(op==DIVIDE)) {\r
+ if (op&DIVIDEINT) {\r
+ decNumberZero(res); // integer part is 0\r
+ #if DECSUBSET\r
+ if (set->extended)\r
+ #endif\r
+ res->bits=bits; // set +/- zero\r
+ break;}\r
+ // fastpath remainders so long as the lhs has the smaller\r
+ // (or equal) exponent\r
+ if (lhs->exponent<=rhs->exponent) {\r
+ if (op&REMAINDER || exponent<-1) {\r
+ // It is REMAINDER or safe REMNEAR; result is [finished\r
+ // clone of] lhs (r = x - 0*y)\r
+ residue=0;\r
+ decCopyFit(res, lhs, set, &residue, status);\r
+ decFinish(res, set, &residue, status);\r
+ break;\r
+ }\r
+ // [unsafe REMNEAR drops through]\r
+ }\r
+ } // fastpaths\r
+\r
+ /* Long (slow) division is needed; roll up the sleeves... */\r
+\r
+ // The accumulator will hold the quotient of the division.\r
+ // If it needs to be too long for stack storage, then allocate.\r
+ acclength=D2U(reqdigits+DECDPUN); // in Units\r
+ if (acclength*sizeof(Unit)>sizeof(accbuff)) {\r
+ // printf("malloc dvacc %ld units\n", acclength);\r
+ allocacc=(Unit *)malloc(acclength*sizeof(Unit));\r
+ if (allocacc==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ acc=allocacc; // use the allocated space\r
+ }\r
+\r
+ // var1 is the padded LHS ready for subtractions.\r
+ // If it needs to be too long for stack storage, then allocate.\r
+ // The maximum units needed for var1 (long subtraction) is:\r
+ // Enough for\r
+ // (rhs->digits+reqdigits-1) -- to allow full slide to right\r
+ // or (lhs->digits) -- to allow for long lhs\r
+ // whichever is larger\r
+ // +1 -- for rounding of slide to right\r
+ // +1 -- for leading 0s\r
+ // +1 -- for pre-adjust if a remainder or DIVIDEINT\r
+ // [Note: unused units do not participate in decUnitAddSub data]\r
+ maxdigits=rhs->digits+reqdigits-1;\r
+ if (lhs->digits>maxdigits) maxdigits=lhs->digits;\r
+ var1units=D2U(maxdigits)+2;\r
+ // allocate a guard unit above msu1 for REMAINDERNEAR\r
+ if (!(op&DIVIDE)) var1units++;\r
+ if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {\r
+ // printf("malloc dvvar %ld units\n", var1units+1);\r
+ varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));\r
+ if (varalloc==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ var1=varalloc; // use the allocated space\r
+ }\r
+\r
+ // Extend the lhs and rhs to full long subtraction length. The lhs\r
+ // is truly extended into the var1 buffer, with 0 padding, so a\r
+ // subtract in place is always possible. The rhs (var2) has\r
+ // virtual padding (implemented by decUnitAddSub).\r
+ // One guard unit was allocated above msu1 for rem=rem+rem in\r
+ // REMAINDERNEAR.\r
+ msu1=var1+var1units-1; // msu of var1\r
+ source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array\r
+ for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;\r
+ for (; target>=var1; target--) *target=0;\r
+\r
+ // rhs (var2) is left-aligned with var1 at the start\r
+ var2ulen=var1units; // rhs logical length (units)\r
+ var2units=D2U(rhs->digits); // rhs actual length (units)\r
+ var2=rhs->lsu; // -> rhs array\r
+ msu2=var2+var2units-1; // -> msu of var2 [never changes]\r
+ // now set up the variables which will be used for estimating the\r
+ // multiplication factor. If these variables are not exact, add\r
+ // 1 to make sure that the multiplier is never overestimated.\r
+ msu2plus=*msu2; // it's value ..\r
+ if (var2units>1) msu2plus++; // .. +1 if any more\r
+ msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair ..\r
+ if (var2units>1) { // .. [else treat 2nd as 0]\r
+ msu2pair+=*(msu2-1); // ..\r
+ if (var2units>2) msu2pair++; // .. +1 if any more\r
+ }\r
+\r
+ // The calculation is working in units, which may have leading zeros,\r
+ // but the exponent was calculated on the assumption that they are\r
+ // both left-aligned. Adjust the exponent to compensate: add the\r
+ // number of leading zeros in var1 msu and subtract those in var2 msu.\r
+ // [This is actually done by counting the digits and negating, as\r
+ // lead1=DECDPUN-digits1, and similarly for lead2.]\r
+ for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;\r
+ for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;\r
+\r
+ // Now, if doing an integer divide or remainder, ensure that\r
+ // the result will be Unit-aligned. To do this, shift the var1\r
+ // accumulator towards least if need be. (It's much easier to\r
+ // do this now than to reassemble the residue afterwards, if\r
+ // doing a remainder.) Also ensure the exponent is not negative.\r
+ if (!(op&DIVIDE)) {\r
+ Unit *u; // work\r
+ // save the initial 'false' padding of var1, in digits\r
+ var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;\r
+ // Determine the shift to do.\r
+ if (exponent<0) cut=-exponent;\r
+ else cut=DECDPUN-exponent%DECDPUN;\r
+ decShiftToLeast(var1, var1units, cut);\r
+ exponent+=cut; // maintain numerical value\r
+ var1initpad-=cut; // .. and reduce padding\r
+ // clean any most-significant units which were just emptied\r
+ for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;\r
+ } // align\r
+ else { // is DIVIDE\r
+ maxexponent=lhs->exponent-rhs->exponent; // save\r
+ // optimization: if the first iteration will just produce 0,\r
+ // preadjust to skip it [valid for DIVIDE only]\r
+ if (*msu1<*msu2) {\r
+ var2ulen--; // shift down\r
+ exponent-=DECDPUN; // update the exponent\r
+ }\r
+ }\r
+\r
+ // ---- start the long-division loops ------------------------------\r
+ accunits=0; // no units accumulated yet\r
+ accdigits=0; // .. or digits\r
+ accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1]\r
+ for (;;) { // outer forever loop\r
+ thisunit=0; // current unit assumed 0\r
+ // find the next unit\r
+ for (;;) { // inner forever loop\r
+ // strip leading zero units [from either pre-adjust or from\r
+ // subtract last time around]. Leave at least one unit.\r
+ for (; *msu1==0 && msu1>var1; msu1--) var1units--;\r
+\r
+ if (var1units<var2ulen) break; // var1 too low for subtract\r
+ if (var1units==var2ulen) { // unit-by-unit compare needed\r
+ // compare the two numbers, from msu\r
+ const Unit *pv1, *pv2;\r
+ Unit v2; // units to compare\r
+ pv2=msu2; // -> msu\r
+ for (pv1=msu1; ; pv1--, pv2--) {\r
+ // v1=*pv1 -- always OK\r
+ v2=0; // assume in padding\r
+ if (pv2>=var2) v2=*pv2; // in range\r
+ if (*pv1!=v2) break; // no longer the same\r
+ if (pv1==var1) break; // done; leave pv1 as is\r
+ }\r
+ // here when all inspected or a difference seen\r
+ if (*pv1<v2) break; // var1 too low to subtract\r
+ if (*pv1==v2) { // var1 == var2\r
+ // reach here if var1 and var2 are identical; subtraction\r
+ // would increase digit by one, and the residue will be 0 so\r
+ // the calculation is done; leave the loop with residue=0.\r
+ thisunit++; // as though subtracted\r
+ *var1=0; // set var1 to 0\r
+ var1units=1; // ..\r
+ break; // from inner\r
+ } // var1 == var2\r
+ // *pv1>v2. Prepare for real subtraction; the lengths are equal\r
+ // Estimate the multiplier (there's always a msu1-1)...\r
+ // Bring in two units of var2 to provide a good estimate.\r
+ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);\r
+ } // lengths the same\r
+ else { // var1units > var2ulen, so subtraction is safe\r
+ // The var2 msu is one unit towards the lsu of the var1 msu,\r
+ // so only one unit for var2 can be used.\r
+ mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);\r
+ }\r
+ if (mult==0) mult=1; // must always be at least 1\r
+ // subtraction needed; var1 is > var2\r
+ thisunit=(Unit)(thisunit+mult); // accumulate\r
+ // subtract var1-var2, into var1; only the overlap needs\r
+ // processing, as this is an in-place calculation\r
+ shift=var2ulen-var2units;\r
+ #if DECTRACE\r
+ decDumpAr('1', &var1[shift], var1units-shift);\r
+ decDumpAr('2', var2, var2units);\r
+ printf("m=%ld\n", -mult);\r
+ #endif\r
+ decUnitAddSub(&var1[shift], var1units-shift,\r
+ var2, var2units, 0,\r
+ &var1[shift], -mult);\r
+ #if DECTRACE\r
+ decDumpAr('#', &var1[shift], var1units-shift);\r
+ #endif\r
+ // var1 now probably has leading zeros; these are removed at the\r
+ // top of the inner loop.\r
+ } // inner loop\r
+\r
+ // The next unit has been calculated in full; unless it's a\r
+ // leading zero, add to acc\r
+ if (accunits!=0 || thisunit!=0) { // is first or non-zero\r
+ *accnext=thisunit; // store in accumulator\r
+ // account exactly for the new digits\r
+ if (accunits==0) {\r
+ accdigits++; // at least one\r
+ for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;\r
+ }\r
+ else accdigits+=DECDPUN;\r
+ accunits++; // update count\r
+ accnext--; // ready for next\r
+ if (accdigits>reqdigits) break; // have enough digits\r
+ }\r
+\r
+ // if the residue is zero, the operation is done (unless divide\r
+ // or divideInteger and still not enough digits yet)\r
+ if (*var1==0 && var1units==1) { // residue is 0\r
+ if (op&(REMAINDER|REMNEAR)) break;\r
+ if ((op&DIVIDE) && (exponent<=maxexponent)) break;\r
+ // [drop through if divideInteger]\r
+ }\r
+ // also done enough if calculating remainder or integer\r
+ // divide and just did the last ('units') unit\r
+ if (exponent==0 && !(op&DIVIDE)) break;\r
+\r
+ // to get here, var1 is less than var2, so divide var2 by the per-\r
+ // Unit power of ten and go for the next digit\r
+ var2ulen--; // shift down\r
+ exponent-=DECDPUN; // update the exponent\r
+ } // outer loop\r
+\r
+ // ---- division is complete ---------------------------------------\r
+ // here: acc has at least reqdigits+1 of good results (or fewer\r
+ // if early stop), starting at accnext+1 (its lsu)\r
+ // var1 has any residue at the stopping point\r
+ // accunits is the number of digits collected in acc\r
+ if (accunits==0) { // acc is 0\r
+ accunits=1; // show have a unit ..\r
+ accdigits=1; // ..\r
+ *accnext=0; // .. whose value is 0\r
+ }\r
+ else accnext++; // back to last placed\r
+ // accnext now -> lowest unit of result\r
+\r
+ residue=0; // assume no residue\r
+ if (op&DIVIDE) {\r
+ // record the presence of any residue, for rounding\r
+ if (*var1!=0 || var1units>1) residue=1;\r
+ else { // no residue\r
+ // Had an exact division; clean up spurious trailing 0s.\r
+ // There will be at most DECDPUN-1, from the final multiply,\r
+ // and then only if the result is non-0 (and even) and the\r
+ // exponent is 'loose'.\r
+ #if DECDPUN>1\r
+ Unit lsu=*accnext;\r
+ if (!(lsu&0x01) && (lsu!=0)) {\r
+ // count the trailing zeros\r
+ Int drop=0;\r
+ for (;; drop++) { // [will terminate because lsu!=0]\r
+ if (exponent>=maxexponent) break; // don't chop real 0s\r
+ #if DECDPUN<=4\r
+ if ((lsu-QUOT10(lsu, drop+1)\r
+ *powers[drop+1])!=0) break; // found non-0 digit\r
+ #else\r
+ if (lsu%powers[drop+1]!=0) break; // found non-0 digit\r
+ #endif\r
+ exponent++;\r
+ }\r
+ if (drop>0) {\r
+ accunits=decShiftToLeast(accnext, accunits, drop);\r
+ accdigits=decGetDigits(accnext, accunits);\r
+ accunits=D2U(accdigits);\r
+ // [exponent was adjusted in the loop]\r
+ }\r
+ } // neither odd nor 0\r
+ #endif\r
+ } // exact divide\r
+ } // divide\r
+ else /* op!=DIVIDE */ {\r
+ // check for coefficient overflow\r
+ if (accdigits+exponent>reqdigits) {\r
+ *status|=DEC_Division_impossible;\r
+ break;\r
+ }\r
+ if (op & (REMAINDER|REMNEAR)) {\r
+ // [Here, the exponent will be 0, because var1 was adjusted\r
+ // appropriately.]\r
+ Int postshift; // work\r
+ Flag wasodd=0; // integer was odd\r
+ Unit *quotlsu; // for save\r
+ Int quotdigits; // ..\r
+\r
+ bits=lhs->bits; // remainder sign is always as lhs\r
+\r
+ // Fastpath when residue is truly 0 is worthwhile [and\r
+ // simplifies the code below]\r
+ if (*var1==0 && var1units==1) { // residue is 0\r
+ Int exp=lhs->exponent; // save min(exponents)\r
+ if (rhs->exponent<exp) exp=rhs->exponent;\r
+ decNumberZero(res); // 0 coefficient\r
+ #if DECSUBSET\r
+ if (set->extended)\r
+ #endif\r
+ res->exponent=exp; // .. with proper exponent\r
+ res->bits=(uByte)(bits&DECNEG); // [cleaned]\r
+ decFinish(res, set, &residue, status); // might clamp\r
+ break;\r
+ }\r
+ // note if the quotient was odd\r
+ if (*accnext & 0x01) wasodd=1; // acc is odd\r
+ quotlsu=accnext; // save in case need to reinspect\r
+ quotdigits=accdigits; // ..\r
+\r
+ // treat the residue, in var1, as the value to return, via acc\r
+ // calculate the unused zero digits. This is the smaller of:\r
+ // var1 initial padding (saved above)\r
+ // var2 residual padding, which happens to be given by:\r
+ postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;\r
+ // [the 'exponent' term accounts for the shifts during divide]\r
+ if (var1initpad<postshift) postshift=var1initpad;\r
+\r
+ // shift var1 the requested amount, and adjust its digits\r
+ var1units=decShiftToLeast(var1, var1units, postshift);\r
+ accnext=var1;\r
+ accdigits=decGetDigits(var1, var1units);\r
+ accunits=D2U(accdigits);\r
+\r
+ exponent=lhs->exponent; // exponent is smaller of lhs & rhs\r
+ if (rhs->exponent<exponent) exponent=rhs->exponent;\r
+\r
+ // Now correct the result if doing remainderNear; if it\r
+ // (looking just at coefficients) is > rhs/2, or == rhs/2 and\r
+ // the integer was odd then the result should be rem-rhs.\r
+ if (op&REMNEAR) {\r
+ Int compare, tarunits; // work\r
+ Unit *up; // ..\r
+ // calculate remainder*2 into the var1 buffer (which has\r
+ // 'headroom' of an extra unit and hence enough space)\r
+ // [a dedicated 'double' loop would be faster, here]\r
+ tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,\r
+ 0, accnext, 1);\r
+ // decDumpAr('r', accnext, tarunits);\r
+\r
+ // Here, accnext (var1) holds tarunits Units with twice the\r
+ // remainder's coefficient, which must now be compared to the\r
+ // RHS. The remainder's exponent may be smaller than the RHS's.\r
+ compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),\r
+ rhs->exponent-exponent);\r
+ if (compare==BADINT) { // deep trouble\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+\r
+ // now restore the remainder by dividing by two; the lsu\r
+ // is known to be even.\r
+ for (up=accnext; up<accnext+tarunits; up++) {\r
+ Int half; // half to add to lower unit\r
+ half=*up & 0x01;\r
+ *up/=2; // [shift]\r
+ if (!half) continue;\r
+ *(up-1)+=(DECDPUNMAX+1)/2;\r
+ }\r
+ // [accunits still describes the original remainder length]\r
+\r
+ if (compare>0 || (compare==0 && wasodd)) { // adjustment needed\r
+ Int exp, expunits, exprem; // work\r
+ // This is effectively causing round-up of the quotient,\r
+ // so if it was the rare case where it was full and all\r
+ // nines, it would overflow and hence division-impossible\r
+ // should be raised\r
+ Flag allnines=0; // 1 if quotient all nines\r
+ if (quotdigits==reqdigits) { // could be borderline\r
+ for (up=quotlsu; ; up++) {\r
+ if (quotdigits>DECDPUN) {\r
+ if (*up!=DECDPUNMAX) break;// non-nines\r
+ }\r
+ else { // this is the last Unit\r
+ if (*up==powers[quotdigits]-1) allnines=1;\r
+ break;\r
+ }\r
+ quotdigits-=DECDPUN; // checked those digits\r
+ } // up\r
+ } // borderline check\r
+ if (allnines) {\r
+ *status|=DEC_Division_impossible;\r
+ break;}\r
+\r
+ // rem-rhs is needed; the sign will invert. Again, var1\r
+ // can safely be used for the working Units array.\r
+ exp=rhs->exponent-exponent; // RHS padding needed\r
+ // Calculate units and remainder from exponent.\r
+ expunits=exp/DECDPUN;\r
+ exprem=exp%DECDPUN;\r
+ // subtract [A+B*(-m)]; the result will always be negative\r
+ accunits=-decUnitAddSub(accnext, accunits,\r
+ rhs->lsu, D2U(rhs->digits),\r
+ expunits, accnext, -(Int)powers[exprem]);\r
+ accdigits=decGetDigits(accnext, accunits); // count digits exactly\r
+ accunits=D2U(accdigits); // and recalculate the units for copy\r
+ // [exponent is as for original remainder]\r
+ bits^=DECNEG; // flip the sign\r
+ }\r
+ } // REMNEAR\r
+ } // REMAINDER or REMNEAR\r
+ } // not DIVIDE\r
+\r
+ // Set exponent and bits\r
+ res->exponent=exponent;\r
+ res->bits=(uByte)(bits&DECNEG); // [cleaned]\r
+\r
+ // Now the coefficient.\r
+ decSetCoeff(res, set, accnext, accdigits, &residue, status);\r
+\r
+ decFinish(res, set, &residue, status); // final cleanup\r
+\r
+ #if DECSUBSET\r
+ // If a divide then strip trailing zeros if subset [after round]\r
+ if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);\r
+ #endif\r
+ } while(0); // end protected\r
+\r
+ if (varalloc!=NULL) free(varalloc); // drop any storage used\r
+ if (allocacc!=NULL) free(allocacc); // ..\r
+ #if DECSUBSET\r
+ if (allocrhs!=NULL) free(allocrhs); // ..\r
+ if (alloclhs!=NULL) free(alloclhs); // ..\r
+ #endif\r
+ return res;\r
+ } // decDivideOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decMultiplyOp -- multiplication operation */\r
+/* */\r
+/* This routine performs the multiplication C=A x B. */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X*X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* status is the usual accumulator */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+/* 'Classic' multiplication is used rather than Karatsuba, as the */\r
+/* latter would give only a minor improvement for the short numbers */\r
+/* expected to be handled most (and uses much more memory). */\r
+/* */\r
+/* There are two major paths here: the general-purpose ('old code') */\r
+/* path which handles all DECDPUN values, and a fastpath version */\r
+/* which is used if 64-bit ints are available, DECDPUN<=4, and more */\r
+/* than two calls to decUnitAddSub would be made. */\r
+/* */\r
+/* The fastpath version lumps units together into 8-digit or 9-digit */\r
+/* chunks, and also uses a lazy carry strategy to minimise expensive */\r
+/* 64-bit divisions. The chunks are then broken apart again into */\r
+/* units for continuing processing. Despite this overhead, the */\r
+/* fastpath can speed up some 16-digit operations by 10x (and much */\r
+/* more for higher-precision calculations). */\r
+/* */\r
+/* A buffer always has to be used for the accumulator; in the */\r
+/* fastpath, buffers are also always needed for the chunked copies of */\r
+/* of the operand coefficients. */\r
+/* Static buffers are larger than needed just for multiply, to allow */\r
+/* for calls from other operations (notably exp). */\r
+/* ------------------------------------------------------------------ */\r
+#define FASTMUL (DECUSE64 && DECDPUN<5)\r
+static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set,\r
+ uInt *status) {\r
+ Int accunits; // Units of accumulator in use\r
+ Int exponent; // work\r
+ Int residue=0; // rounding residue\r
+ uByte bits; // result sign\r
+ Unit *acc; // -> accumulator Unit array\r
+ Int needbytes; // size calculator\r
+ void *allocacc=NULL; // -> allocated accumulator, iff allocated\r
+ Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0,\r
+ // *4 for calls from other operations)\r
+ const Unit *mer, *mermsup; // work\r
+ Int madlength; // Units in multiplicand\r
+ Int shift; // Units to shift multiplicand by\r
+\r
+ #if FASTMUL\r
+ // if DECDPUN is 1 or 3 work in base 10**9, otherwise\r
+ // (DECDPUN is 2 or 4) then work in base 10**8\r
+ #if DECDPUN & 1 // odd\r
+ #define FASTBASE 1000000000 // base\r
+ #define FASTDIGS 9 // digits in base\r
+ #define FASTLAZY 18 // carry resolution point [1->18]\r
+ #else\r
+ #define FASTBASE 100000000\r
+ #define FASTDIGS 8\r
+ #define FASTLAZY 1844 // carry resolution point [1->1844]\r
+ #endif\r
+ // three buffers are used, two for chunked copies of the operands\r
+ // (base 10**8 or base 10**9) and one base 2**64 accumulator with\r
+ // lazy carry evaluation\r
+ uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)\r
+ uInt *zlhi=zlhibuff; // -> lhs array\r
+ uInt *alloclhi=NULL; // -> allocated buffer, iff allocated\r
+ uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)\r
+ uInt *zrhi=zrhibuff; // -> rhs array\r
+ uInt *allocrhi=NULL; // -> allocated buffer, iff allocated\r
+ uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0)\r
+ // [allocacc is shared for both paths, as only one will run]\r
+ uLong *zacc=zaccbuff; // -> accumulator array for exact result\r
+ #if DECDPUN==1\r
+ Int zoff; // accumulator offset\r
+ #endif\r
+ uInt *lip, *rip; // item pointers\r
+ uInt *lmsi, *rmsi; // most significant items\r
+ Int ilhs, irhs, iacc; // item counts in the arrays\r
+ Int lazy; // lazy carry counter\r
+ uLong lcarry; // uLong carry\r
+ uInt carry; // carry (NB not uLong)\r
+ Int count; // work\r
+ const Unit *cup; // ..\r
+ Unit *up; // ..\r
+ uLong *lp; // ..\r
+ Int p; // ..\r
+ #endif\r
+\r
+ #if DECSUBSET\r
+ decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated\r
+ decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated\r
+ #endif\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ // precalculate result sign\r
+ bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);\r
+\r
+ // handle infinities and NaNs\r
+ if (SPECIALARGS) { // a special bit set\r
+ if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs\r
+ decNaNs(res, lhs, rhs, set, status);\r
+ return res;}\r
+ // one or two infinities; Infinity * 0 is invalid\r
+ if (((lhs->bits & DECINF)==0 && ISZERO(lhs))\r
+ ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {\r
+ *status|=DEC_Invalid_operation;\r
+ return res;}\r
+ decNumberZero(res);\r
+ res->bits=bits|DECINF; // infinity\r
+ return res;}\r
+\r
+ // For best speed, as in DMSRCN [the original Rexx numerics\r
+ // module], use the shorter number as the multiplier (rhs) and\r
+ // the longer as the multiplicand (lhs) to minimise the number of\r
+ // adds (partial products)\r
+ if (lhs->digits<rhs->digits) { // swap...\r
+ const decNumber *hold=lhs;\r
+ lhs=rhs;\r
+ rhs=hold;\r
+ }\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operands and set lostDigits status, as needed\r
+ if (lhs->digits>set->digits) {\r
+ alloclhs=decRoundOperand(lhs, set, status);\r
+ if (alloclhs==NULL) break;\r
+ lhs=alloclhs;\r
+ }\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ #if FASTMUL // fastpath can be used\r
+ // use the fast path if there are enough digits in the shorter\r
+ // operand to make the setup and takedown worthwhile\r
+ #define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls\r
+ if (rhs->digits>NEEDTWO) { // use fastpath...\r
+ // calculate the number of elements in each array\r
+ ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling]\r
+ irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // ..\r
+ iacc=ilhs+irhs;\r
+\r
+ // allocate buffers if required, as usual\r
+ needbytes=ilhs*sizeof(uInt);\r
+ if (needbytes>(Int)sizeof(zlhibuff)) {\r
+ alloclhi=(uInt *)malloc(needbytes);\r
+ zlhi=alloclhi;}\r
+ needbytes=irhs*sizeof(uInt);\r
+ if (needbytes>(Int)sizeof(zrhibuff)) {\r
+ allocrhi=(uInt *)malloc(needbytes);\r
+ zrhi=allocrhi;}\r
+\r
+ // Allocating the accumulator space needs a special case when\r
+ // DECDPUN=1 because when converting the accumulator to Units\r
+ // after the multiplication each 8-byte item becomes 9 1-byte\r
+ // units. Therefore iacc extra bytes are needed at the front\r
+ // (rounded up to a multiple of 8 bytes), and the uLong\r
+ // accumulator starts offset the appropriate number of units\r
+ // to the right to avoid overwrite during the unchunking.\r
+ needbytes=iacc*sizeof(uLong);\r
+ #if DECDPUN==1\r
+ zoff=(iacc+7)/8; // items to offset by\r
+ needbytes+=zoff*8;\r
+ #endif\r
+ if (needbytes>(Int)sizeof(zaccbuff)) {\r
+ allocacc=(uLong *)malloc(needbytes);\r
+ zacc=(uLong *)allocacc;}\r
+ if (zlhi==NULL||zrhi==NULL||zacc==NULL) {\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+\r
+ acc=(Unit *)zacc; // -> target Unit array\r
+ #if DECDPUN==1\r
+ zacc+=zoff; // start uLong accumulator to right\r
+ #endif\r
+\r
+ // assemble the chunked copies of the left and right sides\r
+ for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)\r
+ for (p=0, *lip=0; p<FASTDIGS && count>0;\r
+ p+=DECDPUN, cup++, count-=DECDPUN)\r
+ *lip+=*cup*powers[p];\r
+ lmsi=lip-1; // save -> msi\r
+ for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)\r
+ for (p=0, *rip=0; p<FASTDIGS && count>0;\r
+ p+=DECDPUN, cup++, count-=DECDPUN)\r
+ *rip+=*cup*powers[p];\r
+ rmsi=rip-1; // save -> msi\r
+\r
+ // zero the accumulator\r
+ for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;\r
+\r
+ /* Start the multiplication */\r
+ // Resolving carries can dominate the cost of accumulating the\r
+ // partial products, so this is only done when necessary.\r
+ // Each uLong item in the accumulator can hold values up to\r
+ // 2**64-1, and each partial product can be as large as\r
+ // (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to\r
+ // itself 18.4 times in a uLong without overflowing, so during\r
+ // the main calculation resolution is carried out every 18th\r
+ // add -- every 162 digits. Similarly, when FASTDIGS=8, the\r
+ // partial products can be added to themselves 1844.6 times in\r
+ // a uLong without overflowing, so intermediate carry\r
+ // resolution occurs only every 14752 digits. Hence for common\r
+ // short numbers usually only the one final carry resolution\r
+ // occurs.\r
+ // (The count is set via FASTLAZY to simplify experiments to\r
+ // measure the value of this approach: a 35% improvement on a\r
+ // [34x34] multiply.)\r
+ lazy=FASTLAZY; // carry delay count\r
+ for (rip=zrhi; rip<=rmsi; rip++) { // over each item in rhs\r
+ lp=zacc+(rip-zrhi); // where to add the lhs\r
+ for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs\r
+ *lp+=(uLong)(*lip)*(*rip); // [this should in-line]\r
+ } // lip loop\r
+ lazy--;\r
+ if (lazy>0 && rip!=rmsi) continue;\r
+ lazy=FASTLAZY; // reset delay count\r
+ // spin up the accumulator resolving overflows\r
+ for (lp=zacc; lp<zacc+iacc; lp++) {\r
+ if (*lp<FASTBASE) continue; // it fits\r
+ lcarry=*lp/FASTBASE; // top part [slow divide]\r
+ // lcarry can exceed 2**32-1, so check again; this check\r
+ // and occasional extra divide (slow) is well worth it, as\r
+ // it allows FASTLAZY to be increased to 18 rather than 4\r
+ // in the FASTDIGS=9 case\r
+ if (lcarry<FASTBASE) carry=(uInt)lcarry; // [usual]\r
+ else { // two-place carry [fairly rare]\r
+ uInt carry2=(uInt)(lcarry/FASTBASE); // top top part\r
+ *(lp+2)+=carry2; // add to item+2\r
+ *lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow]\r
+ carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline]\r
+ }\r
+ *(lp+1)+=carry; // add to item above [inline]\r
+ *lp-=((uLong)FASTBASE*carry); // [inline]\r
+ } // carry resolution\r
+ } // rip loop\r
+\r
+ // The multiplication is complete; time to convert back into\r
+ // units. This can be done in-place in the accumulator and in\r
+ // 32-bit operations, because carries were resolved after the\r
+ // final add. This needs N-1 divides and multiplies for\r
+ // each item in the accumulator (which will become up to N\r
+ // units, where 2<=N<=9).\r
+ for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {\r
+ uInt item=(uInt)*lp; // decapitate to uInt\r
+ for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {\r
+ uInt part=item/(DECDPUNMAX+1);\r
+ *up=(Unit)(item-(part*(DECDPUNMAX+1)));\r
+ item=part;\r
+ } // p\r
+ *up=(Unit)item; up++; // [final needs no division]\r
+ } // lp\r
+ accunits=up-acc; // count of units\r
+ }\r
+ else { // here to use units directly, without chunking ['old code']\r
+ #endif\r
+\r
+ // if accumulator will be too long for local storage, then allocate\r
+ acc=accbuff; // -> assume buffer for accumulator\r
+ needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);\r
+ if (needbytes>(Int)sizeof(accbuff)) {\r
+ allocacc=(Unit *)malloc(needbytes);\r
+ if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}\r
+ acc=(Unit *)allocacc; // use the allocated space\r
+ }\r
+\r
+ /* Now the main long multiplication loop */\r
+ // Unlike the equivalent in the IBM Java implementation, there\r
+ // is no advantage in calculating from msu to lsu. So, do it\r
+ // by the book, as it were.\r
+ // Each iteration calculates ACC=ACC+MULTAND*MULT\r
+ accunits=1; // accumulator starts at '0'\r
+ *acc=0; // .. (lsu=0)\r
+ shift=0; // no multiplicand shift at first\r
+ madlength=D2U(lhs->digits); // this won't change\r
+ mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier\r
+\r
+ for (mer=rhs->lsu; mer<mermsup; mer++) {\r
+ // Here, *mer is the next Unit in the multiplier to use\r
+ // If non-zero [optimization] add it...\r
+ if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,\r
+ lhs->lsu, madlength, 0,\r
+ &acc[shift], *mer)\r
+ + shift;\r
+ else { // extend acc with a 0; it will be used shortly\r
+ *(acc+accunits)=0; // [this avoids length of <=0 later]\r
+ accunits++;\r
+ }\r
+ // multiply multiplicand by 10**DECDPUN for next Unit to left\r
+ shift++; // add this for 'logical length'\r
+ } // n\r
+ #if FASTMUL\r
+ } // unchunked units\r
+ #endif\r
+ // common end-path\r
+ #if DECTRACE\r
+ decDumpAr('*', acc, accunits); // Show exact result\r
+ #endif\r
+\r
+ // acc now contains the exact result of the multiplication,\r
+ // possibly with a leading zero unit; build the decNumber from\r
+ // it, noting if any residue\r
+ res->bits=bits; // set sign\r
+ res->digits=decGetDigits(acc, accunits); // count digits exactly\r
+\r
+ // There can be a 31-bit wrap in calculating the exponent.\r
+ // This can only happen if both input exponents are negative and\r
+ // both their magnitudes are large. If there was a wrap, set a\r
+ // safe very negative exponent, from which decFinalize() will\r
+ // raise a hard underflow shortly.\r
+ exponent=lhs->exponent+rhs->exponent; // calculate exponent\r
+ if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)\r
+ exponent=-2*DECNUMMAXE; // force underflow\r
+ res->exponent=exponent; // OK to overwrite now\r
+\r
+\r
+ // Set the coefficient. If any rounding, residue records\r
+ decSetCoeff(res, set, acc, res->digits, &residue, status);\r
+ decFinish(res, set, &residue, status); // final cleanup\r
+ } while(0); // end protected\r
+\r
+ if (allocacc!=NULL) free(allocacc); // drop any storage used\r
+ #if DECSUBSET\r
+ if (allocrhs!=NULL) free(allocrhs); // ..\r
+ if (alloclhs!=NULL) free(alloclhs); // ..\r
+ #endif\r
+ #if FASTMUL\r
+ if (allocrhi!=NULL) free(allocrhi); // ..\r
+ if (alloclhi!=NULL) free(alloclhi); // ..\r
+ #endif\r
+ return res;\r
+ } // decMultiplyOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decExpOp -- effect exponentiation */\r
+/* */\r
+/* This computes C = exp(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context; note that rounding mode has no effect */\r
+/* */\r
+/* C must have space for set->digits digits. status is updated but */\r
+/* not set. */\r
+/* */\r
+/* Restrictions: */\r
+/* */\r
+/* digits, emax, and -emin in the context must be less than */\r
+/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */\r
+/* bounds or a zero. This is an internal routine, so these */\r
+/* restrictions are contractual and not enforced. */\r
+/* */\r
+/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */\r
+/* almost always be correctly rounded, but may be up to 1 ulp in */\r
+/* error in rare cases. */\r
+/* */\r
+/* Finite results will always be full precision and Inexact, except */\r
+/* when A is a zero or -Infinity (giving 1 or 0 respectively). */\r
+/* ------------------------------------------------------------------ */\r
+/* This approach used here is similar to the algorithm described in */\r
+/* */\r
+/* Variable Precision Exponential Function, T. E. Hull and */\r
+/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */\r
+/* pp79-91, ACM, June 1986. */\r
+/* */\r
+/* with the main difference being that the iterations in the series */\r
+/* evaluation are terminated dynamically (which does not require the */\r
+/* extra variable-precision variables which are expensive in this */\r
+/* context). */\r
+/* */\r
+/* The error analysis in Hull & Abrham's paper applies except for the */\r
+/* round-off error accumulation during the series evaluation. This */\r
+/* code does not precalculate the number of iterations and so cannot */\r
+/* use Horner's scheme. Instead, the accumulation is done at double- */\r
+/* precision, which ensures that the additions of the terms are exact */\r
+/* and do not accumulate round-off (and any round-off errors in the */\r
+/* terms themselves move 'to the right' faster than they can */\r
+/* accumulate). This code also extends the calculation by allowing, */\r
+/* in the spirit of other decNumber operators, the input to be more */\r
+/* precise than the result (the precision used is based on the more */\r
+/* precise of the input or requested result). */\r
+/* */\r
+/* Implementation notes: */\r
+/* */\r
+/* 1. This is separated out as decExpOp so it can be called from */\r
+/* other Mathematical functions (notably Ln) with a wider range */\r
+/* than normal. In particular, it can handle the slightly wider */\r
+/* (double) range needed by Ln (which has to be able to calculate */\r
+/* exp(-x) where x can be the tiniest number (Ntiny). */\r
+/* */\r
+/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */\r
+/* iterations by appoximately a third with additional (although */\r
+/* diminishing) returns as the range is reduced to even smaller */\r
+/* fractions. However, h (the power of 10 used to correct the */\r
+/* result at the end, see below) must be kept <=8 as otherwise */\r
+/* the final result cannot be computed. Hence the leverage is a */\r
+/* sliding value (8-h), where potentially the range is reduced */\r
+/* more for smaller values. */\r
+/* */\r
+/* The leverage that can be applied in this way is severely */\r
+/* limited by the cost of the raise-to-the power at the end, */\r
+/* which dominates when the number of iterations is small (less */\r
+/* than ten) or when rhs is short. As an example, the adjustment */\r
+/* x**10,000,000 needs 31 multiplications, all but one full-width. */\r
+/* */\r
+/* 3. The restrictions (especially precision) could be raised with */\r
+/* care, but the full decNumber range seems very hard within the */\r
+/* 32-bit limits. */\r
+/* */\r
+/* 4. The working precisions for the static buffers are twice the */\r
+/* obvious size to allow for calls from decNumberPower. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decExpOp(decNumber *res, const decNumber *rhs,\r
+ decContext *set, uInt *status) {\r
+ uInt ignore=0; // working status\r
+ Int h; // adjusted exponent for 0.xxxx\r
+ Int p; // working precision\r
+ Int residue; // rounding residue\r
+ uInt needbytes; // for space calculations\r
+ const decNumber *x=rhs; // (may point to safe copy later)\r
+ decContext aset, tset, dset; // working contexts\r
+ Int comp; // work\r
+\r
+ // the argument is often copied to normalize it, so (unusually) it\r
+ // is treated like other buffers, using DECBUFFER, +1 in case\r
+ // DECBUFFER is 0\r
+ decNumber bufr[D2N(DECBUFFER*2+1)];\r
+ decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated\r
+\r
+ // the working precision will be no more than set->digits+8+1\r
+ // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER\r
+ // is 0 (and twice that for the accumulator)\r
+\r
+ // buffer for t, term (working precision plus)\r
+ decNumber buft[D2N(DECBUFFER*2+9+1)];\r
+ decNumber *allocbuft=NULL; // -> allocated buft, iff allocated\r
+ decNumber *t=buft; // term\r
+ // buffer for a, accumulator (working precision * 2), at least 9\r
+ decNumber bufa[D2N(DECBUFFER*4+18+1)];\r
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated\r
+ decNumber *a=bufa; // accumulator\r
+ // decNumber for the divisor term; this needs at most 9 digits\r
+ // and so can be fixed size [16 so can use standard context]\r
+ decNumber bufd[D2N(16)];\r
+ decNumber *d=bufd; // divisor\r
+ decNumber numone; // constant 1\r
+\r
+ #if DECCHECK\r
+ Int iterations=0; // for later sanity check\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ if (SPECIALARG) { // handle infinities and NaNs\r
+ if (decNumberIsInfinite(rhs)) { // an infinity\r
+ if (decNumberIsNegative(rhs)) // -Infinity -> +0\r
+ decNumberZero(res);\r
+ else decNumberCopy(res, rhs); // +Infinity -> self\r
+ }\r
+ else decNaNs(res, rhs, NULL, set, status); // a NaN\r
+ break;}\r
+\r
+ if (ISZERO(rhs)) { // zeros -> exact 1\r
+ decNumberZero(res); // make clean 1\r
+ *res->lsu=1; // ..\r
+ break;} // [no status to set]\r
+\r
+ // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path\r
+ // positive and negative tiny cases which will result in inexact\r
+ // 1. This also allows the later add-accumulate to always be\r
+ // exact (because its length will never be more than twice the\r
+ // working precision).\r
+ // The comparator (tiny) needs just one digit, so use the\r
+ // decNumber d for it (reused as the divisor, etc., below); its\r
+ // exponent is such that if x is positive it will have\r
+ // set->digits-1 zeros between the decimal point and the digit,\r
+ // which is 4, and if x is negative one more zero there as the\r
+ // more precise result will be of the form 0.9999999 rather than\r
+ // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0\r
+ // or 0.00000004 if digits=7 and x<0. If RHS not larger than\r
+ // this then the result will be 1.000000\r
+ decNumberZero(d); // clean\r
+ *d->lsu=4; // set 4 ..\r
+ d->exponent=-set->digits; // * 10**(-d)\r
+ if (decNumberIsNegative(rhs)) d->exponent--; // negative case\r
+ comp=decCompare(d, rhs, 1); // signless compare\r
+ if (comp==BADINT) {\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ if (comp>=0) { // rhs < d\r
+ Int shift=set->digits-1;\r
+ decNumberZero(res); // set 1\r
+ *res->lsu=1; // ..\r
+ res->digits=decShiftToMost(res->lsu, 1, shift);\r
+ res->exponent=-shift; // make 1.0000...\r
+ *status|=DEC_Inexact | DEC_Rounded; // .. inexactly\r
+ break;} // tiny\r
+\r
+ // set up the context to be used for calculating a, as this is\r
+ // used on both paths below\r
+ decContextDefault(&aset, DEC_INIT_DECIMAL64);\r
+ // accumulator bounds are as requested (could underflow)\r
+ aset.emax=set->emax; // usual bounds\r
+ aset.emin=set->emin; // ..\r
+ aset.clamp=0; // and no concrete format\r
+\r
+ // calculate the adjusted (Hull & Abrham) exponent (where the\r
+ // decimal point is just to the left of the coefficient msd)\r
+ h=rhs->exponent+rhs->digits;\r
+ // if h>8 then 10**h cannot be calculated safely; however, when\r
+ // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at\r
+ // least 6.59E+4342944, so (due to the restriction on Emax/Emin)\r
+ // overflow (or underflow to 0) is guaranteed -- so this case can\r
+ // be handled by simply forcing the appropriate excess\r
+ if (h>8) { // overflow/underflow\r
+ // set up here so Power call below will over or underflow to\r
+ // zero; set accumulator to either 2 or 0.02\r
+ // [stack buffer for a is always big enough for this]\r
+ decNumberZero(a);\r
+ *a->lsu=2; // not 1 but < exp(1)\r
+ if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02\r
+ h=8; // clamp so 10**h computable\r
+ p=9; // set a working precision\r
+ }\r
+ else { // h<=8\r
+ Int maxlever=(rhs->digits>8?1:0);\r
+ // [could/should increase this for precisions >40 or so, too]\r
+\r
+ // if h is 8, cannot normalize to a lower upper limit because\r
+ // the final result will not be computable (see notes above),\r
+ // but leverage can be applied whenever h is less than 8.\r
+ // Apply as much as possible, up to a MAXLEVER digits, which\r
+ // sets the tradeoff against the cost of the later a**(10**h).\r
+ // As h is increased, the working precision below also\r
+ // increases to compensate for the "constant digits at the\r
+ // front" effect.\r
+ Int lever=MINI(8-h, maxlever); // leverage attainable\r
+ Int use=-rhs->digits-lever; // exponent to use for RHS\r
+ h+=lever; // apply leverage selected\r
+ if (h<0) { // clamp\r
+ use+=h; // [may end up subnormal]\r
+ h=0;\r
+ }\r
+ // Take a copy of RHS if it needs normalization (true whenever x>=1)\r
+ if (rhs->exponent!=use) {\r
+ decNumber *newrhs=bufr; // assume will fit on stack\r
+ needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufr)) { // need malloc space\r
+ allocrhs=(decNumber *)malloc(needbytes);\r
+ if (allocrhs==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ newrhs=allocrhs; // use the allocated space\r
+ }\r
+ decNumberCopy(newrhs, rhs); // copy to safe space\r
+ newrhs->exponent=use; // normalize; now <1\r
+ x=newrhs; // ready for use\r
+ // decNumberShow(x);\r
+ }\r
+\r
+ // Now use the usual power series to evaluate exp(x). The\r
+ // series starts as 1 + x + x^2/2 ... so prime ready for the\r
+ // third term by setting the term variable t=x, the accumulator\r
+ // a=1, and the divisor d=2.\r
+\r
+ // First determine the working precision. From Hull & Abrham\r
+ // this is set->digits+h+2. However, if x is 'over-precise' we\r
+ // need to allow for all its digits to potentially participate\r
+ // (consider an x where all the excess digits are 9s) so in\r
+ // this case use x->digits+h+2\r
+ p=MAXI(x->digits, set->digits)+h+2; // [h<=8]\r
+\r
+ // a and t are variable precision, and depend on p, so space\r
+ // must be allocated for them if necessary\r
+\r
+ // the accumulator needs to be able to hold 2p digits so that\r
+ // the additions on the second and subsequent iterations are\r
+ // sufficiently exact.\r
+ needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufa)) { // need malloc space\r
+ allocbufa=(decNumber *)malloc(needbytes);\r
+ if (allocbufa==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ a=allocbufa; // use the allocated space\r
+ }\r
+ // the term needs to be able to hold p digits (which is\r
+ // guaranteed to be larger than x->digits, so the initial copy\r
+ // is safe); it may also be used for the raise-to-power\r
+ // calculation below, which needs an extra two digits\r
+ needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(buft)) { // need malloc space\r
+ allocbuft=(decNumber *)malloc(needbytes);\r
+ if (allocbuft==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ t=allocbuft; // use the allocated space\r
+ }\r
+\r
+ decNumberCopy(t, x); // term=x\r
+ decNumberZero(a); *a->lsu=1; // accumulator=1\r
+ decNumberZero(d); *d->lsu=2; // divisor=2\r
+ decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment\r
+\r
+ // set up the contexts for calculating a, t, and d\r
+ decContextDefault(&tset, DEC_INIT_DECIMAL64);\r
+ dset=tset;\r
+ // accumulator bounds are set above, set precision now\r
+ aset.digits=p*2; // double\r
+ // term bounds avoid any underflow or overflow\r
+ tset.digits=p;\r
+ tset.emin=DEC_MIN_EMIN; // [emax is plenty]\r
+ // [dset.digits=16, etc., are sufficient]\r
+\r
+ // finally ready to roll\r
+ for (;;) {\r
+ #if DECCHECK\r
+ iterations++;\r
+ #endif\r
+ // only the status from the accumulation is interesting\r
+ // [but it should remain unchanged after first add]\r
+ decAddOp(a, a, t, &aset, 0, status); // a=a+t\r
+ decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x\r
+ decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d\r
+ // the iteration ends when the term cannot affect the result,\r
+ // if rounded to p digits, which is when its value is smaller\r
+ // than the accumulator by p+1 digits. There must also be\r
+ // full precision in a.\r
+ if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))\r
+ && (a->digits>=p)) break;\r
+ decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1\r
+ } // iterate\r
+\r
+ #if DECCHECK\r
+ // just a sanity check; comment out test to show always\r
+ if (iterations>p+3)\r
+ printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",\r
+ (LI)iterations, (LI)*status, (LI)p, (LI)x->digits);\r
+ #endif\r
+ } // h<=8\r
+\r
+ // apply postconditioning: a=a**(10**h) -- this is calculated\r
+ // at a slightly higher precision than Hull & Abrham suggest\r
+ if (h>0) {\r
+ Int seenbit=0; // set once a 1-bit is seen\r
+ Int i; // counter\r
+ Int n=powers[h]; // always positive\r
+ aset.digits=p+2; // sufficient precision\r
+ // avoid the overhead and many extra digits of decNumberPower\r
+ // as all that is needed is the short 'multipliers' loop; here\r
+ // accumulate the answer into t\r
+ decNumberZero(t); *t->lsu=1; // acc=1\r
+ for (i=1;;i++){ // for each bit [top bit ignored]\r
+ // abandon if have had overflow or terminal underflow\r
+ if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting?\r
+ if (*status&DEC_Overflow || ISZERO(t)) break;}\r
+ n=n<<1; // move next bit to testable position\r
+ if (n<0) { // top bit is set\r
+ seenbit=1; // OK, have a significant bit\r
+ decMultiplyOp(t, t, a, &aset, status); // acc=acc*x\r
+ }\r
+ if (i==31) break; // that was the last bit\r
+ if (!seenbit) continue; // no need to square 1\r
+ decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square]\r
+ } /*i*/ // 32 bits\r
+ // decNumberShow(t);\r
+ a=t; // and carry on using t instead of a\r
+ }\r
+\r
+ // Copy and round the result to res\r
+ residue=1; // indicate dirt to right ..\r
+ if (ISZERO(a)) residue=0; // .. unless underflowed to 0\r
+ aset.digits=set->digits; // [use default rounding]\r
+ decCopyFit(res, a, &aset, &residue, status); // copy & shorten\r
+ decFinish(res, set, &residue, status); // cleanup/set flags\r
+ } while(0); // end protected\r
+\r
+ if (allocrhs !=NULL) free(allocrhs); // drop any storage used\r
+ if (allocbufa!=NULL) free(allocbufa); // ..\r
+ if (allocbuft!=NULL) free(allocbuft); // ..\r
+ // [status is handled by caller]\r
+ return res;\r
+ } // decExpOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* Initial-estimate natural logarithm table */\r
+/* */\r
+/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */\r
+/* The result is a 4-digit encode of the coefficient (c=the */\r
+/* top 14 bits encoding 0-9999) and a 2-digit encode of the */\r
+/* exponent (e=the bottom 2 bits encoding 0-3) */\r
+/* */\r
+/* The resulting value is given by: */\r
+/* */\r
+/* v = -c * 10**(-e-3) */\r
+/* */\r
+/* where e and c are extracted from entry k = LNnn[x-10] */\r
+/* where x is truncated (NB) into the range 10 through 99, */\r
+/* and then c = k>>2 and e = k&3. */\r
+/* ------------------------------------------------------------------ */\r
+const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,\r
+ 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,\r
+ 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,\r
+ 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,\r
+ 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,\r
+ 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,\r
+ 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,\r
+ 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,\r
+ 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,\r
+ 10130, 6046, 20055};\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decLnOp -- effect natural logarithm */\r
+/* */\r
+/* This computes C = ln(A) */\r
+/* */\r
+/* res is C, the result. C may be A */\r
+/* rhs is A */\r
+/* set is the context; note that rounding mode has no effect */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Notable cases: */\r
+/* A<0 -> Invalid */\r
+/* A=0 -> -Infinity (Exact) */\r
+/* A=+Infinity -> +Infinity (Exact) */\r
+/* A=1 exactly -> 0 (Exact) */\r
+/* */\r
+/* Restrictions (as for Exp): */\r
+/* */\r
+/* digits, emax, and -emin in the context must be less than */\r
+/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */\r
+/* bounds or a zero. This is an internal routine, so these */\r
+/* restrictions are contractual and not enforced. */\r
+/* */\r
+/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */\r
+/* almost always be correctly rounded, but may be up to 1 ulp in */\r
+/* error in rare cases. */\r
+/* ------------------------------------------------------------------ */\r
+/* The result is calculated using Newton's method, with each */\r
+/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */\r
+/* Epperson 1989. */\r
+/* */\r
+/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */\r
+/* This has to be calculated at the sum of the precision of x and the */\r
+/* working precision. */\r
+/* */\r
+/* Implementation notes: */\r
+/* */\r
+/* 1. This is separated out as decLnOp so it can be called from */\r
+/* other Mathematical functions (e.g., Log 10) with a wider range */\r
+/* than normal. In particular, it can handle the slightly wider */\r
+/* (+9+2) range needed by a power function. */\r
+/* */\r
+/* 2. The speed of this function is about 10x slower than exp, as */\r
+/* it typically needs 4-6 iterations for short numbers, and the */\r
+/* extra precision needed adds a squaring effect, twice. */\r
+/* */\r
+/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */\r
+/* as these are common requests. ln(10) is used by log10(x). */\r
+/* */\r
+/* 4. An iteration might be saved by widening the LNnn table, and */\r
+/* would certainly save at least one if it were made ten times */\r
+/* bigger, too (for truncated fractions 0.100 through 0.999). */\r
+/* However, for most practical evaluations, at least four or five */\r
+/* iterations will be neede -- so this would only speed up by */\r
+/* 20-25% and that probably does not justify increasing the table */\r
+/* size. */\r
+/* */\r
+/* 5. The static buffers are larger than might be expected to allow */\r
+/* for calls from decNumberPower. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decLnOp(decNumber *res, const decNumber *rhs,\r
+ decContext *set, uInt *status) {\r
+ uInt ignore=0; // working status accumulator\r
+ uInt needbytes; // for space calculations\r
+ Int residue; // rounding residue\r
+ Int r; // rhs=f*10**r [see below]\r
+ Int p; // working precision\r
+ Int pp; // precision for iteration\r
+ Int t; // work\r
+\r
+ // buffers for a (accumulator, typically precision+2) and b\r
+ // (adjustment calculator, same size)\r
+ decNumber bufa[D2N(DECBUFFER+12)];\r
+ decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated\r
+ decNumber *a=bufa; // accumulator/work\r
+ decNumber bufb[D2N(DECBUFFER*2+2)];\r
+ decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated\r
+ decNumber *b=bufb; // adjustment/work\r
+\r
+ decNumber numone; // constant 1\r
+ decNumber cmp; // work\r
+ decContext aset, bset; // working contexts\r
+\r
+ #if DECCHECK\r
+ Int iterations=0; // for later sanity check\r
+ if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ if (SPECIALARG) { // handle infinities and NaNs\r
+ if (decNumberIsInfinite(rhs)) { // an infinity\r
+ if (decNumberIsNegative(rhs)) // -Infinity -> error\r
+ *status|=DEC_Invalid_operation;\r
+ else decNumberCopy(res, rhs); // +Infinity -> self\r
+ }\r
+ else decNaNs(res, rhs, NULL, set, status); // a NaN\r
+ break;}\r
+\r
+ if (ISZERO(rhs)) { // +/- zeros -> -Infinity\r
+ decNumberZero(res); // make clean\r
+ res->bits=DECINF|DECNEG; // set - infinity\r
+ break;} // [no status to set]\r
+\r
+ // Non-zero negatives are bad...\r
+ if (decNumberIsNegative(rhs)) { // -x -> error\r
+ *status|=DEC_Invalid_operation;\r
+ break;}\r
+\r
+ // Here, rhs is positive, finite, and in range\r
+\r
+ // lookaside fastpath code for ln(2) and ln(10) at common lengths\r
+ if (rhs->exponent==0 && set->digits<=40) {\r
+ #if DECDPUN==1\r
+ if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10)\r
+ #else\r
+ if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10)\r
+ #endif\r
+ aset=*set; aset.round=DEC_ROUND_HALF_EVEN;\r
+ #define LN10 "2.302585092994045684017991454684364207601"\r
+ decNumberFromString(res, LN10, &aset);\r
+ *status|=(DEC_Inexact | DEC_Rounded); // is inexact\r
+ break;}\r
+ if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2)\r
+ aset=*set; aset.round=DEC_ROUND_HALF_EVEN;\r
+ #define LN2 "0.6931471805599453094172321214581765680755"\r
+ decNumberFromString(res, LN2, &aset);\r
+ *status|=(DEC_Inexact | DEC_Rounded);\r
+ break;}\r
+ } // integer and short\r
+\r
+ // Determine the working precision. This is normally the\r
+ // requested precision + 2, with a minimum of 9. However, if\r
+ // the rhs is 'over-precise' then allow for all its digits to\r
+ // potentially participate (consider an rhs where all the excess\r
+ // digits are 9s) so in this case use rhs->digits+2.\r
+ p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;\r
+\r
+ // Allocate space for the accumulator and the high-precision\r
+ // adjustment calculator, if necessary. The accumulator must\r
+ // be able to hold p digits, and the adjustment up to\r
+ // rhs->digits+p digits. They are also made big enough for 16\r
+ // digits so that they can be used for calculating the initial\r
+ // estimate.\r
+ needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufa)) { // need malloc space\r
+ allocbufa=(decNumber *)malloc(needbytes);\r
+ if (allocbufa==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ a=allocbufa; // use the allocated space\r
+ }\r
+ pp=p+rhs->digits;\r
+ needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);\r
+ if (needbytes>sizeof(bufb)) { // need malloc space\r
+ allocbufb=(decNumber *)malloc(needbytes);\r
+ if (allocbufb==NULL) { // hopeless -- abandon\r
+ *status|=DEC_Insufficient_storage;\r
+ break;}\r
+ b=allocbufb; // use the allocated space\r
+ }\r
+\r
+ // Prepare an initial estimate in acc. Calculate this by\r
+ // considering the coefficient of x to be a normalized fraction,\r
+ // f, with the decimal point at far left and multiplied by\r
+ // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and\r
+ // ln(x) = ln(f) + ln(10)*r\r
+ // Get the initial estimate for ln(f) from a small lookup\r
+ // table (see above) indexed by the first two digits of f,\r
+ // truncated.\r
+\r
+ decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended\r
+ r=rhs->exponent+rhs->digits; // 'normalised' exponent\r
+ decNumberFromInt32(a, r); // a=r\r
+ decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585)\r
+ b->exponent=-6; // ..\r
+ decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b\r
+ // now get top two digits of rhs into b by simple truncate and\r
+ // force to integer\r
+ residue=0; // (no residue)\r
+ aset.digits=2; aset.round=DEC_ROUND_DOWN;\r
+ decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten\r
+ b->exponent=0; // make integer\r
+ t=decGetInt(b); // [cannot fail]\r
+ if (t<10) t=X10(t); // adjust single-digit b\r
+ t=LNnn[t-10]; // look up ln(b)\r
+ decNumberFromInt32(b, t>>2); // b=ln(b) coefficient\r
+ b->exponent=-(t&3)-3; // set exponent\r
+ b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve\r
+ aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore\r
+ decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b\r
+ // the initial estimate is now in a, with up to 4 digits correct.\r
+ // When rhs is at or near Nmax the estimate will be low, so we\r
+ // will approach it from below, avoiding overflow when calling exp.\r
+\r
+ decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment\r
+\r
+ // accumulator bounds are as requested (could underflow, but\r
+ // cannot overflow)\r
+ aset.emax=set->emax;\r
+ aset.emin=set->emin;\r
+ aset.clamp=0; // no concrete format\r
+ // set up a context to be used for the multiply and subtract\r
+ bset=aset;\r
+ bset.emax=DEC_MAX_MATH*2; // use double bounds for the\r
+ bset.emin=-DEC_MAX_MATH*2; // adjustment calculation\r
+ // [see decExpOp call below]\r
+ // for each iteration double the number of digits to calculate,\r
+ // up to a maximum of p\r
+ pp=9; // initial precision\r
+ // [initially 9 as then the sequence starts 7+2, 16+2, and\r
+ // 34+2, which is ideal for standard-sized numbers]\r
+ aset.digits=pp; // working context\r
+ bset.digits=pp+rhs->digits; // wider context\r
+ for (;;) { // iterate\r
+ #if DECCHECK\r
+ iterations++;\r
+ if (iterations>24) break; // consider 9 * 2**24\r
+ #endif\r
+ // calculate the adjustment (exp(-a)*x-1) into b. This is a\r
+ // catastrophic subtraction but it really is the difference\r
+ // from 1 that is of interest.\r
+ // Use the internal entry point to Exp as it allows the double\r
+ // range for calculating exp(-a) when a is the tiniest subnormal.\r
+ a->bits^=DECNEG; // make -a\r
+ decExpOp(b, a, &bset, &ignore); // b=exp(-a)\r
+ a->bits^=DECNEG; // restore sign of a\r
+ // now multiply by rhs and subtract 1, at the wider precision\r
+ decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs\r
+ decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1\r
+\r
+ // the iteration ends when the adjustment cannot affect the\r
+ // result by >=0.5 ulp (at the requested digits), which\r
+ // is when its value is smaller than the accumulator by\r
+ // set->digits+1 digits (or it is zero) -- this is a looser\r
+ // requirement than for Exp because all that happens to the\r
+ // accumulator after this is the final rounding (but note that\r
+ // there must also be full precision in a, or a=0).\r
+\r
+ if (decNumberIsZero(b) ||\r
+ (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {\r
+ if (a->digits==p) break;\r
+ if (decNumberIsZero(a)) {\r
+ decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ?\r
+ if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0\r
+ else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact\r
+ break;\r
+ }\r
+ // force padding if adjustment has gone to 0 before full length\r
+ if (decNumberIsZero(b)) b->exponent=a->exponent-p;\r
+ }\r
+\r
+ // not done yet ...\r
+ decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate\r
+ if (pp==p) continue; // precision is at maximum\r
+ // lengthen the next calculation\r
+ pp=pp*2; // double precision\r
+ if (pp>p) pp=p; // clamp to maximum\r
+ aset.digits=pp; // working context\r
+ bset.digits=pp+rhs->digits; // wider context\r
+ } // Newton's iteration\r
+\r
+ #if DECCHECK\r
+ // just a sanity check; remove the test to show always\r
+ if (iterations>24)\r
+ printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",\r
+ (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);\r
+ #endif\r
+\r
+ // Copy and round the result to res\r
+ residue=1; // indicate dirt to right\r
+ if (ISZERO(a)) residue=0; // .. unless underflowed to 0\r
+ aset.digits=set->digits; // [use default rounding]\r
+ decCopyFit(res, a, &aset, &residue, status); // copy & shorten\r
+ decFinish(res, set, &residue, status); // cleanup/set flags\r
+ } while(0); // end protected\r
+\r
+ if (allocbufa!=NULL) free(allocbufa); // drop any storage used\r
+ if (allocbufb!=NULL) free(allocbufb); // ..\r
+ // [status is handled by caller]\r
+ return res;\r
+ } // decLnOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decQuantizeOp -- force exponent to requested value */\r
+/* */\r
+/* This computes C = op(A, B), where op adjusts the coefficient */\r
+/* of C (by rounding or shifting) such that the exponent (-scale) */\r
+/* of C has the value B or matches the exponent of B. */\r
+/* The numerical value of C will equal A, except for the effects of */\r
+/* any rounding that occurred. */\r
+/* */\r
+/* res is C, the result. C may be A or B */\r
+/* lhs is A, the number to adjust */\r
+/* rhs is B, the requested exponent */\r
+/* set is the context */\r
+/* quant is 1 for quantize or 0 for rescale */\r
+/* status is the status accumulator (this can be called without */\r
+/* risk of control loss) */\r
+/* */\r
+/* C must have space for set->digits digits. */\r
+/* */\r
+/* Unless there is an error or the result is infinite, the exponent */\r
+/* after the operation is guaranteed to be that requested. */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set,\r
+ Flag quant, uInt *status) {\r
+ #if DECSUBSET\r
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated\r
+ decNumber *allocrhs=NULL; // .., rhs\r
+ #endif\r
+ const decNumber *inrhs=rhs; // save original rhs\r
+ Int reqdigits=set->digits; // requested DIGITS\r
+ Int reqexp; // requested exponent [-scale]\r
+ Int residue=0; // rounding residue\r
+ Int etiny=set->emin-(reqdigits-1);\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operands and set lostDigits status, as needed\r
+ if (lhs->digits>reqdigits) {\r
+ alloclhs=decRoundOperand(lhs, set, status);\r
+ if (alloclhs==NULL) break;\r
+ lhs=alloclhs;\r
+ }\r
+ if (rhs->digits>reqdigits) { // [this only checks lostDigits]\r
+ allocrhs=decRoundOperand(rhs, set, status);\r
+ if (allocrhs==NULL) break;\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ // Handle special values\r
+ if (SPECIALARGS) {\r
+ // NaNs get usual processing\r
+ if (SPECIALARGS & (DECSNAN | DECNAN))\r
+ decNaNs(res, lhs, rhs, set, status);\r
+ // one infinity but not both is bad\r
+ else if ((lhs->bits ^ rhs->bits) & DECINF)\r
+ *status|=DEC_Invalid_operation;\r
+ // both infinity: return lhs\r
+ else decNumberCopy(res, lhs); // [nop if in place]\r
+ break;\r
+ }\r
+\r
+ // set requested exponent\r
+ if (quant) reqexp=inrhs->exponent; // quantize -- match exponents\r
+ else { // rescale -- use value of rhs\r
+ // Original rhs must be an integer that fits and is in range,\r
+ // which could be from -1999999997 to +999999999, thanks to\r
+ // subnormals\r
+ reqexp=decGetInt(inrhs); // [cannot fail]\r
+ }\r
+\r
+ #if DECSUBSET\r
+ if (!set->extended) etiny=set->emin; // no subnormals\r
+ #endif\r
+\r
+ if (reqexp==BADINT // bad (rescale only) or ..\r
+ || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or ..\r
+ || (reqexp<etiny) // < lowest\r
+ || (reqexp>set->emax)) { // > emax\r
+ *status|=DEC_Invalid_operation;\r
+ break;}\r
+\r
+ // the RHS has been processed, so it can be overwritten now if necessary\r
+ if (ISZERO(lhs)) { // zero coefficient unchanged\r
+ decNumberCopy(res, lhs); // [nop if in place]\r
+ res->exponent=reqexp; // .. just set exponent\r
+ #if DECSUBSET\r
+ if (!set->extended) res->bits=0; // subset specification; no -0\r
+ #endif\r
+ }\r
+ else { // non-zero lhs\r
+ Int adjust=reqexp-lhs->exponent; // digit adjustment needed\r
+ // if adjusted coefficient will definitely not fit, give up now\r
+ if ((lhs->digits-adjust)>reqdigits) {\r
+ *status|=DEC_Invalid_operation;\r
+ break;\r
+ }\r
+\r
+ if (adjust>0) { // increasing exponent\r
+ // this will decrease the length of the coefficient by adjust\r
+ // digits, and must round as it does so\r
+ decContext workset; // work\r
+ workset=*set; // clone rounding, etc.\r
+ workset.digits=lhs->digits-adjust; // set requested length\r
+ // [note that the latter can be <1, here]\r
+ decCopyFit(res, lhs, &workset, &residue, status); // fit to result\r
+ decApplyRound(res, &workset, residue, status); // .. and round\r
+ residue=0; // [used]\r
+ // If just rounded a 999s case, exponent will be off by one;\r
+ // adjust back (after checking space), if so.\r
+ if (res->exponent>reqexp) {\r
+ // re-check needed, e.g., for quantize(0.9999, 0.001) under\r
+ // set->digits==3\r
+ if (res->digits==reqdigits) { // cannot shift by 1\r
+ *status&=~(DEC_Inexact | DEC_Rounded); // [clean these]\r
+ *status|=DEC_Invalid_operation;\r
+ break;\r
+ }\r
+ res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift\r
+ res->exponent--; // (re)adjust the exponent.\r
+ }\r
+ #if DECSUBSET\r
+ if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0\r
+ #endif\r
+ } // increase\r
+ else /* adjust<=0 */ { // decreasing or = exponent\r
+ // this will increase the length of the coefficient by -adjust\r
+ // digits, by adding zero or more trailing zeros; this is\r
+ // already checked for fit, above\r
+ decNumberCopy(res, lhs); // [it will fit]\r
+ // if padding needed (adjust<0), add it now...\r
+ if (adjust<0) {\r
+ res->digits=decShiftToMost(res->lsu, res->digits, -adjust);\r
+ res->exponent+=adjust; // adjust the exponent\r
+ }\r
+ } // decrease\r
+ } // non-zero\r
+\r
+ // Check for overflow [do not use Finalize in this case, as an\r
+ // overflow here is a "don't fit" situation]\r
+ if (res->exponent>set->emax-res->digits+1) { // too big\r
+ *status|=DEC_Invalid_operation;\r
+ break;\r
+ }\r
+ else {\r
+ decFinalize(res, set, &residue, status); // set subnormal flags\r
+ *status&=~DEC_Underflow; // suppress Underflow [as per 754]\r
+ }\r
+ } while(0); // end protected\r
+\r
+ #if DECSUBSET\r
+ if (allocrhs!=NULL) free(allocrhs); // drop any storage used\r
+ if (alloclhs!=NULL) free(alloclhs); // ..\r
+ #endif\r
+ return res;\r
+ } // decQuantizeOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCompareOp -- compare, min, or max two Numbers */\r
+/* */\r
+/* This computes C = A ? B and carries out one of four operations: */\r
+/* COMPARE -- returns the signum (as a number) giving the */\r
+/* result of a comparison unless one or both */\r
+/* operands is a NaN (in which case a NaN results) */\r
+/* COMPSIG -- as COMPARE except that a quiet NaN raises */\r
+/* Invalid operation. */\r
+/* COMPMAX -- returns the larger of the operands, using the */\r
+/* 754 maxnum operation */\r
+/* COMPMAXMAG -- ditto, comparing absolute values */\r
+/* COMPMIN -- the 754 minnum operation */\r
+/* COMPMINMAG -- ditto, comparing absolute values */\r
+/* COMTOTAL -- returns the signum (as a number) giving the */\r
+/* result of a comparison using 754 total ordering */\r
+/* */\r
+/* res is C, the result. C may be A and/or B (e.g., X=X?X) */\r
+/* lhs is A */\r
+/* rhs is B */\r
+/* set is the context */\r
+/* op is the operation flag */\r
+/* status is the usual accumulator */\r
+/* */\r
+/* C must have space for one digit for COMPARE or set->digits for */\r
+/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */\r
+/* ------------------------------------------------------------------ */\r
+/* The emphasis here is on speed for common cases, and avoiding */\r
+/* coefficient comparison if possible. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decCompareOp(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set,\r
+ Flag op, uInt *status) {\r
+ #if DECSUBSET\r
+ decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated\r
+ decNumber *allocrhs=NULL; // .., rhs\r
+ #endif\r
+ Int result=0; // default result value\r
+ uByte merged; // work\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(res, lhs, rhs, set)) return res;\r
+ #endif\r
+\r
+ do { // protect allocated storage\r
+ #if DECSUBSET\r
+ if (!set->extended) {\r
+ // reduce operands and set lostDigits status, as needed\r
+ if (lhs->digits>set->digits) {\r
+ alloclhs=decRoundOperand(lhs, set, status);\r
+ if (alloclhs==NULL) {result=BADINT; break;}\r
+ lhs=alloclhs;\r
+ }\r
+ if (rhs->digits>set->digits) {\r
+ allocrhs=decRoundOperand(rhs, set, status);\r
+ if (allocrhs==NULL) {result=BADINT; break;}\r
+ rhs=allocrhs;\r
+ }\r
+ }\r
+ #endif\r
+ // [following code does not require input rounding]\r
+\r
+ // If total ordering then handle differing signs 'up front'\r
+ if (op==COMPTOTAL) { // total ordering\r
+ if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {\r
+ result=-1;\r
+ break;\r
+ }\r
+ if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {\r
+ result=+1;\r
+ break;\r
+ }\r
+ }\r
+\r
+ // handle NaNs specially; let infinities drop through\r
+ // This assumes sNaN (even just one) leads to NaN.\r
+ merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);\r
+ if (merged) { // a NaN bit set\r
+ if (op==COMPARE); // result will be NaN\r
+ else if (op==COMPSIG) // treat qNaN as sNaN\r
+ *status|=DEC_Invalid_operation | DEC_sNaN;\r
+ else if (op==COMPTOTAL) { // total ordering, always finite\r
+ // signs are known to be the same; compute the ordering here\r
+ // as if the signs are both positive, then invert for negatives\r
+ if (!decNumberIsNaN(lhs)) result=-1;\r
+ else if (!decNumberIsNaN(rhs)) result=+1;\r
+ // here if both NaNs\r
+ else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;\r
+ else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;\r
+ else { // both NaN or both sNaN\r
+ // now it just depends on the payload\r
+ result=decUnitCompare(lhs->lsu, D2U(lhs->digits),\r
+ rhs->lsu, D2U(rhs->digits), 0);\r
+ // [Error not possible, as these are 'aligned']\r
+ } // both same NaNs\r
+ if (decNumberIsNegative(lhs)) result=-result;\r
+ break;\r
+ } // total order\r
+\r
+ else if (merged & DECSNAN); // sNaN -> qNaN\r
+ else { // here if MIN or MAX and one or two quiet NaNs\r
+ // min or max -- 754 rules ignore single NaN\r
+ if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {\r
+ // just one NaN; force choice to be the non-NaN operand\r
+ op=COMPMAX;\r
+ if (lhs->bits & DECNAN) result=-1; // pick rhs\r
+ else result=+1; // pick lhs\r
+ break;\r
+ }\r
+ } // max or min\r
+ op=COMPNAN; // use special path\r
+ decNaNs(res, lhs, rhs, set, status); // propagate NaN\r
+ break;\r
+ }\r
+ // have numbers\r
+ if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);\r
+ else result=decCompare(lhs, rhs, 0); // sign matters\r
+ } while(0); // end protected\r
+\r
+ if (result==BADINT) *status|=DEC_Insufficient_storage; // rare\r
+ else {\r
+ if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum\r
+ if (op==COMPTOTAL && result==0) {\r
+ // operands are numerically equal or same NaN (and same sign,\r
+ // tested first); if identical, leave result 0\r
+ if (lhs->exponent!=rhs->exponent) {\r
+ if (lhs->exponent<rhs->exponent) result=-1;\r
+ else result=+1;\r
+ if (decNumberIsNegative(lhs)) result=-result;\r
+ } // lexp!=rexp\r
+ } // total-order by exponent\r
+ decNumberZero(res); // [always a valid result]\r
+ if (result!=0) { // must be -1 or +1\r
+ *res->lsu=1;\r
+ if (result<0) res->bits=DECNEG;\r
+ }\r
+ }\r
+ else if (op==COMPNAN); // special, drop through\r
+ else { // MAX or MIN, non-NaN result\r
+ Int residue=0; // rounding accumulator\r
+ // choose the operand for the result\r
+ const decNumber *choice;\r
+ if (result==0) { // operands are numerically equal\r
+ // choose according to sign then exponent (see 754)\r
+ uByte slhs=(lhs->bits & DECNEG);\r
+ uByte srhs=(rhs->bits & DECNEG);\r
+ #if DECSUBSET\r
+ if (!set->extended) { // subset: force left-hand\r
+ op=COMPMAX;\r
+ result=+1;\r
+ }\r
+ else\r
+ #endif\r
+ if (slhs!=srhs) { // signs differ\r
+ if (slhs) result=-1; // rhs is max\r
+ else result=+1; // lhs is max\r
+ }\r
+ else if (slhs && srhs) { // both negative\r
+ if (lhs->exponent<rhs->exponent) result=+1;\r
+ else result=-1;\r
+ // [if equal, use lhs, technically identical]\r
+ }\r
+ else { // both positive\r
+ if (lhs->exponent>rhs->exponent) result=+1;\r
+ else result=-1;\r
+ // [ditto]\r
+ }\r
+ } // numerically equal\r
+ // here result will be non-0; reverse if looking for MIN\r
+ if (op==COMPMIN || op==COMPMINMAG) result=-result;\r
+ choice=(result>0 ? lhs : rhs); // choose\r
+ // copy chosen to result, rounding if need be\r
+ decCopyFit(res, choice, set, &residue, status);\r
+ decFinish(res, set, &residue, status);\r
+ }\r
+ }\r
+ #if DECSUBSET\r
+ if (allocrhs!=NULL) free(allocrhs); // free any storage used\r
+ if (alloclhs!=NULL) free(alloclhs); // ..\r
+ #endif\r
+ return res;\r
+ } // decCompareOp\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCompare -- compare two decNumbers by numerical value */\r
+/* */\r
+/* This routine compares A ? B without altering them. */\r
+/* */\r
+/* Arg1 is A, a decNumber which is not a NaN */\r
+/* Arg2 is B, a decNumber which is not a NaN */\r
+/* Arg3 is 1 for a sign-independent compare, 0 otherwise */\r
+/* */\r
+/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */\r
+/* (the only possible failure is an allocation error) */\r
+/* ------------------------------------------------------------------ */\r
+static Int decCompare(const decNumber *lhs, const decNumber *rhs,\r
+ Flag abs) {\r
+ Int result; // result value\r
+ Int sigr; // rhs signum\r
+ Int compare; // work\r
+\r
+ result=1; // assume signum(lhs)\r
+ if (ISZERO(lhs)) result=0;\r
+ if (abs) {\r
+ if (ISZERO(rhs)) return result; // LHS wins or both 0\r
+ // RHS is non-zero\r
+ if (result==0) return -1; // LHS is 0; RHS wins\r
+ // [here, both non-zero, result=1]\r
+ }\r
+ else { // signs matter\r
+ if (result && decNumberIsNegative(lhs)) result=-1;\r
+ sigr=1; // compute signum(rhs)\r
+ if (ISZERO(rhs)) sigr=0;\r
+ else if (decNumberIsNegative(rhs)) sigr=-1;\r
+ if (result > sigr) return +1; // L > R, return 1\r
+ if (result < sigr) return -1; // L < R, return -1\r
+ if (result==0) return 0; // both 0\r
+ }\r
+\r
+ // signums are the same; both are non-zero\r
+ if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities\r
+ if (decNumberIsInfinite(rhs)) {\r
+ if (decNumberIsInfinite(lhs)) result=0;// both infinite\r
+ else result=-result; // only rhs infinite\r
+ }\r
+ return result;\r
+ }\r
+ // must compare the coefficients, allowing for exponents\r
+ if (lhs->exponent>rhs->exponent) { // LHS exponent larger\r
+ // swap sides, and sign\r
+ const decNumber *temp=lhs;\r
+ lhs=rhs;\r
+ rhs=temp;\r
+ result=-result;\r
+ }\r
+ compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),\r
+ rhs->lsu, D2U(rhs->digits),\r
+ rhs->exponent-lhs->exponent);\r
+ if (compare!=BADINT) compare*=result; // comparison succeeded\r
+ return compare;\r
+ } // decCompare\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decUnitCompare -- compare two >=0 integers in Unit arrays */\r
+/* */\r
+/* This routine compares A ? B*10**E where A and B are unit arrays */\r
+/* A is a plain integer */\r
+/* B has an exponent of E (which must be non-negative) */\r
+/* */\r
+/* Arg1 is A first Unit (lsu) */\r
+/* Arg2 is A length in Units */\r
+/* Arg3 is B first Unit (lsu) */\r
+/* Arg4 is B length in Units */\r
+/* Arg5 is E (0 if the units are aligned) */\r
+/* */\r
+/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */\r
+/* (the only possible failure is an allocation error, which can */\r
+/* only occur if E!=0) */\r
+/* ------------------------------------------------------------------ */\r
+static Int decUnitCompare(const Unit *a, Int alength,\r
+ const Unit *b, Int blength, Int exp) {\r
+ Unit *acc; // accumulator for result\r
+ Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer\r
+ Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated\r
+ Int accunits, need; // units in use or needed for acc\r
+ const Unit *l, *r, *u; // work\r
+ Int expunits, exprem, result; // ..\r
+\r
+ if (exp==0) { // aligned; fastpath\r
+ if (alength>blength) return 1;\r
+ if (alength<blength) return -1;\r
+ // same number of units in both -- need unit-by-unit compare\r
+ l=a+alength-1;\r
+ r=b+alength-1;\r
+ for (;l>=a; l--, r--) {\r
+ if (*l>*r) return 1;\r
+ if (*l<*r) return -1;\r
+ }\r
+ return 0; // all units match\r
+ } // aligned\r
+\r
+ // Unaligned. If one is >1 unit longer than the other, padded\r
+ // approximately, then can return easily\r
+ if (alength>blength+(Int)D2U(exp)) return 1;\r
+ if (alength+1<blength+(Int)D2U(exp)) return -1;\r
+\r
+ // Need to do a real subtract. For this, a result buffer is needed\r
+ // even though only the sign is of interest. Its length needs\r
+ // to be the larger of alength and padded blength, +2\r
+ need=blength+D2U(exp); // maximum real length of B\r
+ if (need<alength) need=alength;\r
+ need+=2;\r
+ acc=accbuff; // assume use local buffer\r
+ if (need*sizeof(Unit)>sizeof(accbuff)) {\r
+ allocacc=(Unit *)malloc(need*sizeof(Unit));\r
+ if (allocacc==NULL) return BADINT; // hopeless -- abandon\r
+ acc=allocacc;\r
+ }\r
+ // Calculate units and remainder from exponent.\r
+ expunits=exp/DECDPUN;\r
+ exprem=exp%DECDPUN;\r
+ // subtract [A+B*(-m)]\r
+ accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,\r
+ -(Int)powers[exprem]);\r
+ // [UnitAddSub result may have leading zeros, even on zero]\r
+ if (accunits<0) result=-1; // negative result\r
+ else { // non-negative result\r
+ // check units of the result before freeing any storage\r
+ for (u=acc; u<acc+accunits-1 && *u==0;) u++;\r
+ result=(*u==0 ? 0 : +1);\r
+ }\r
+ // clean up and return the result\r
+ if (allocacc!=NULL) free(allocacc); // drop any storage used\r
+ return result;\r
+ } // decUnitCompare\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */\r
+/* */\r
+/* This routine performs the calculation: */\r
+/* */\r
+/* C=A+(B*M) */\r
+/* */\r
+/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */\r
+/* */\r
+/* A may be shorter or longer than B. */\r
+/* */\r
+/* Leading zeros are not removed after a calculation. The result is */\r
+/* either the same length as the longer of A and B (adding any */\r
+/* shift), or one Unit longer than that (if a Unit carry occurred). */\r
+/* */\r
+/* A and B content are not altered unless C is also A or B. */\r
+/* C may be the same array as A or B, but only if no zero padding is */\r
+/* requested (that is, C may be B only if bshift==0). */\r
+/* C is filled from the lsu; only those units necessary to complete */\r
+/* the calculation are referenced. */\r
+/* */\r
+/* Arg1 is A first Unit (lsu) */\r
+/* Arg2 is A length in Units */\r
+/* Arg3 is B first Unit (lsu) */\r
+/* Arg4 is B length in Units */\r
+/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */\r
+/* Arg6 is C first Unit (lsu) */\r
+/* Arg7 is M, the multiplier */\r
+/* */\r
+/* returns the count of Units written to C, which will be non-zero */\r
+/* and negated if the result is negative. That is, the sign of the */\r
+/* returned Int is the sign of the result (positive for zero) and */\r
+/* the absolute value of the Int is the count of Units. */\r
+/* */\r
+/* It is the caller's responsibility to make sure that C size is */\r
+/* safe, allowing space if necessary for a one-Unit carry. */\r
+/* */\r
+/* This routine is severely performance-critical; *any* change here */\r
+/* must be measured (timed) to assure no performance degradation. */\r
+/* In particular, trickery here tends to be counter-productive, as */\r
+/* increased complexity of code hurts register optimizations on */\r
+/* register-poor architectures. Avoiding divisions is nearly */\r
+/* always a Good Idea, however. */\r
+/* */\r
+/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */\r
+/* (IBM Warwick, UK) for some of the ideas used in this routine. */\r
+/* ------------------------------------------------------------------ */\r
+static Int decUnitAddSub(const Unit *a, Int alength,\r
+ const Unit *b, Int blength, Int bshift,\r
+ Unit *c, Int m) {\r
+ const Unit *alsu=a; // A lsu [need to remember it]\r
+ Unit *clsu=c; // C ditto\r
+ Unit *minC; // low water mark for C\r
+ Unit *maxC; // high water mark for C\r
+ eInt carry=0; // carry integer (could be Long)\r
+ Int add; // work\r
+ #if DECDPUN<=4 // myriadal, millenary, etc.\r
+ Int est; // estimated quotient\r
+ #endif\r
+\r
+ #if DECTRACE\r
+ if (alength<1 || blength<1)\r
+ printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);\r
+ #endif\r
+\r
+ maxC=c+alength; // A is usually the longer\r
+ minC=c+blength; // .. and B the shorter\r
+ if (bshift!=0) { // B is shifted; low As copy across\r
+ minC+=bshift;\r
+ // if in place [common], skip copy unless there's a gap [rare]\r
+ if (a==c && bshift<=alength) {\r
+ c+=bshift;\r
+ a+=bshift;\r
+ }\r
+ else for (; c<clsu+bshift; a++, c++) { // copy needed\r
+ if (a<alsu+alength) *c=*a;\r
+ else *c=0;\r
+ }\r
+ }\r
+ if (minC>maxC) { // swap\r
+ Unit *hold=minC;\r
+ minC=maxC;\r
+ maxC=hold;\r
+ }\r
+\r
+ // For speed, do the addition as two loops; the first where both A\r
+ // and B contribute, and the second (if necessary) where only one or\r
+ // other of the numbers contribute.\r
+ // Carry handling is the same (i.e., duplicated) in each case.\r
+ for (; c<minC; c++) {\r
+ carry+=*a;\r
+ a++;\r
+ carry+=((eInt)*b)*m; // [special-casing m=1/-1\r
+ b++; // here is not a win]\r
+ // here carry is new Unit of digits; it could be +ve or -ve\r
+ if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX\r
+ *c=(Unit)carry;\r
+ carry=0;\r
+ continue;\r
+ }\r
+ #if DECDPUN==4 // use divide-by-multiply\r
+ if (carry>=0) {\r
+ est=(((ueInt)carry>>11)*53687)>>18;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder\r
+ carry=est; // likely quotient [89%]\r
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ est=(((ueInt)carry>>11)*53687)>>18;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));\r
+ carry=est-(DECDPUNMAX+1); // correctly negative\r
+ if (*c<DECDPUNMAX+1) continue; // was OK\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ #elif DECDPUN==3\r
+ if (carry>=0) {\r
+ est=(((ueInt)carry>>3)*16777)>>21;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder\r
+ carry=est; // likely quotient [99%]\r
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ est=(((ueInt)carry>>3)*16777)>>21;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));\r
+ carry=est-(DECDPUNMAX+1); // correctly negative\r
+ if (*c<DECDPUNMAX+1) continue; // was OK\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ #elif DECDPUN<=2\r
+ // Can use QUOT10 as carry <= 4 digits\r
+ if (carry>=0) {\r
+ est=QUOT10(carry, DECDPUN);\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder\r
+ carry=est; // quotient\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ est=QUOT10(carry, DECDPUN);\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));\r
+ carry=est-(DECDPUNMAX+1); // correctly negative\r
+ #else\r
+ // remainder operator is undefined if negative, so must test\r
+ if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1\r
+ *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions]\r
+ carry=1;\r
+ continue;\r
+ }\r
+ if (carry>=0) {\r
+ *c=(Unit)(carry%(DECDPUNMAX+1));\r
+ carry=carry/(DECDPUNMAX+1);\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ *c=(Unit)(carry%(DECDPUNMAX+1));\r
+ carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);\r
+ #endif\r
+ } // c\r
+\r
+ // now may have one or other to complete\r
+ // [pretest to avoid loop setup/shutdown]\r
+ if (c<maxC) for (; c<maxC; c++) {\r
+ if (a<alsu+alength) { // still in A\r
+ carry+=*a;\r
+ a++;\r
+ }\r
+ else { // inside B\r
+ carry+=((eInt)*b)*m;\r
+ b++;\r
+ }\r
+ // here carry is new Unit of digits; it could be +ve or -ve and\r
+ // magnitude up to DECDPUNMAX squared\r
+ if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX\r
+ *c=(Unit)carry;\r
+ carry=0;\r
+ continue;\r
+ }\r
+ // result for this unit is negative or >DECDPUNMAX\r
+ #if DECDPUN==4 // use divide-by-multiply\r
+ if (carry>=0) {\r
+ est=(((ueInt)carry>>11)*53687)>>18;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder\r
+ carry=est; // likely quotient [79.7%]\r
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ est=(((ueInt)carry>>11)*53687)>>18;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));\r
+ carry=est-(DECDPUNMAX+1); // correctly negative\r
+ if (*c<DECDPUNMAX+1) continue; // was OK\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ #elif DECDPUN==3\r
+ if (carry>=0) {\r
+ est=(((ueInt)carry>>3)*16777)>>21;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder\r
+ carry=est; // likely quotient [99%]\r
+ if (*c<DECDPUNMAX+1) continue; // estimate was correct\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ est=(((ueInt)carry>>3)*16777)>>21;\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));\r
+ carry=est-(DECDPUNMAX+1); // correctly negative\r
+ if (*c<DECDPUNMAX+1) continue; // was OK\r
+ carry++;\r
+ *c-=DECDPUNMAX+1;\r
+ #elif DECDPUN<=2\r
+ if (carry>=0) {\r
+ est=QUOT10(carry, DECDPUN);\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder\r
+ carry=est; // quotient\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ est=QUOT10(carry, DECDPUN);\r
+ *c=(Unit)(carry-est*(DECDPUNMAX+1));\r
+ carry=est-(DECDPUNMAX+1); // correctly negative\r
+ #else\r
+ if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1\r
+ *c=(Unit)(carry-(DECDPUNMAX+1));\r
+ carry=1;\r
+ continue;\r
+ }\r
+ // remainder operator is undefined if negative, so must test\r
+ if (carry>=0) {\r
+ *c=(Unit)(carry%(DECDPUNMAX+1));\r
+ carry=carry/(DECDPUNMAX+1);\r
+ continue;\r
+ }\r
+ // negative case\r
+ carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive\r
+ *c=(Unit)(carry%(DECDPUNMAX+1));\r
+ carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);\r
+ #endif\r
+ } // c\r
+\r
+ // OK, all A and B processed; might still have carry or borrow\r
+ // return number of Units in the result, negated if a borrow\r
+ if (carry==0) return c-clsu; // no carry, so no more to do\r
+ if (carry>0) { // positive carry\r
+ *c=(Unit)carry; // place as new unit\r
+ c++; // ..\r
+ return c-clsu;\r
+ }\r
+ // -ve carry: it's a borrow; complement needed\r
+ add=1; // temporary carry...\r
+ for (c=clsu; c<maxC; c++) {\r
+ add=DECDPUNMAX+add-*c;\r
+ if (add<=DECDPUNMAX) {\r
+ *c=(Unit)add;\r
+ add=0;\r
+ }\r
+ else {\r
+ *c=0;\r
+ add=1;\r
+ }\r
+ }\r
+ // add an extra unit iff it would be non-zero\r
+ #if DECTRACE\r
+ printf("UAS borrow: add %ld, carry %ld\n", add, carry);\r
+ #endif\r
+ if ((add-carry-1)!=0) {\r
+ *c=(Unit)(add-carry-1);\r
+ c++; // interesting, include it\r
+ }\r
+ return clsu-c; // -ve result indicates borrowed\r
+ } // decUnitAddSub\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decTrim -- trim trailing zeros or normalize */\r
+/* */\r
+/* dn is the number to trim or normalize */\r
+/* set is the context to use to check for clamp */\r
+/* all is 1 to remove all trailing zeros, 0 for just fraction ones */\r
+/* noclamp is 1 to unconditional (unclamped) trim */\r
+/* dropped returns the number of discarded trailing zeros */\r
+/* returns dn */\r
+/* */\r
+/* If clamp is set in the context then the number of zeros trimmed */\r
+/* may be limited if the exponent is high. */\r
+/* All fields are updated as required. This is a utility operation, */\r
+/* so special values are unchanged and no error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,\r
+ Flag noclamp, Int *dropped) {\r
+ Int d, exp; // work\r
+ uInt cut; // ..\r
+ Unit *up; // -> current Unit\r
+\r
+ #if DECCHECK\r
+ if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;\r
+ #endif\r
+\r
+ *dropped=0; // assume no zeros dropped\r
+ if ((dn->bits & DECSPECIAL) // fast exit if special ..\r
+ || (*dn->lsu & 0x01)) return dn; // .. or odd\r
+ if (ISZERO(dn)) { // .. or 0\r
+ dn->exponent=0; // (sign is preserved)\r
+ return dn;\r
+ }\r
+\r
+ // have a finite number which is even\r
+ exp=dn->exponent;\r
+ cut=1; // digit (1-DECDPUN) in Unit\r
+ up=dn->lsu; // -> current Unit\r
+ for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit]\r
+ // slice by powers\r
+ #if DECDPUN<=4\r
+ uInt quot=QUOT10(*up, cut);\r
+ if ((*up-quot*powers[cut])!=0) break; // found non-0 digit\r
+ #else\r
+ if (*up%powers[cut]!=0) break; // found non-0 digit\r
+ #endif\r
+ // have a trailing 0\r
+ if (!all) { // trimming\r
+ // [if exp>0 then all trailing 0s are significant for trim]\r
+ if (exp<=0) { // if digit might be significant\r
+ if (exp==0) break; // then quit\r
+ exp++; // next digit might be significant\r
+ }\r
+ }\r
+ cut++; // next power\r
+ if (cut>DECDPUN) { // need new Unit\r
+ up++;\r
+ cut=1;\r
+ }\r
+ } // d\r
+ if (d==0) return dn; // none to drop\r
+\r
+ // may need to limit drop if clamping\r
+ if (set->clamp && !noclamp) {\r
+ Int maxd=set->emax-set->digits+1-dn->exponent;\r
+ if (maxd<=0) return dn; // nothing possible\r
+ if (d>maxd) d=maxd;\r
+ }\r
+\r
+ // effect the drop\r
+ decShiftToLeast(dn->lsu, D2U(dn->digits), d);\r
+ dn->exponent+=d; // maintain numerical value\r
+ dn->digits-=d; // new length\r
+ *dropped=d; // report the count\r
+ return dn;\r
+ } // decTrim\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decReverse -- reverse a Unit array in place */\r
+/* */\r
+/* ulo is the start of the array */\r
+/* uhi is the end of the array (highest Unit to include) */\r
+/* */\r
+/* The units ulo through uhi are reversed in place (if the number */\r
+/* of units is odd, the middle one is untouched). Note that the */\r
+/* digit(s) in each unit are unaffected. */\r
+/* ------------------------------------------------------------------ */\r
+static void decReverse(Unit *ulo, Unit *uhi) {\r
+ Unit temp;\r
+ for (; ulo<uhi; ulo++, uhi--) {\r
+ temp=*ulo;\r
+ *ulo=*uhi;\r
+ *uhi=temp;\r
+ }\r
+ return;\r
+ } // decReverse\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decShiftToMost -- shift digits in array towards most significant */\r
+/* */\r
+/* uar is the array */\r
+/* digits is the count of digits in use in the array */\r
+/* shift is the number of zeros to pad with (least significant); */\r
+/* it must be zero or positive */\r
+/* */\r
+/* returns the new length of the integer in the array, in digits */\r
+/* */\r
+/* No overflow is permitted (that is, the uar array must be known to */\r
+/* be large enough to hold the result, after shifting). */\r
+/* ------------------------------------------------------------------ */\r
+static Int decShiftToMost(Unit *uar, Int digits, Int shift) {\r
+ Unit *target, *source, *first; // work\r
+ Int cut; // odd 0's to add\r
+ uInt next; // work\r
+\r
+ if (shift==0) return digits; // [fastpath] nothing to do\r
+ if ((digits+shift)<=DECDPUN) { // [fastpath] single-unit case\r
+ *uar=(Unit)(*uar*powers[shift]);\r
+ return digits+shift;\r
+ }\r
+\r
+ next=0; // all paths\r
+ source=uar+D2U(digits)-1; // where msu comes from\r
+ target=source+D2U(shift); // where upper part of first cut goes\r
+ cut=DECDPUN-MSUDIGITS(shift); // where to slice\r
+ if (cut==0) { // unit-boundary case\r
+ for (; source>=uar; source--, target--) *target=*source;\r
+ }\r
+ else {\r
+ first=uar+D2U(digits+shift)-1; // where msu of source will end up\r
+ for (; source>=uar; source--, target--) {\r
+ // split the source Unit and accumulate remainder for next\r
+ #if DECDPUN<=4\r
+ uInt quot=QUOT10(*source, cut);\r
+ uInt rem=*source-quot*powers[cut];\r
+ next+=quot;\r
+ #else\r
+ uInt rem=*source%powers[cut];\r
+ next+=*source/powers[cut];\r
+ #endif\r
+ if (target<=first) *target=(Unit)next; // write to target iff valid\r
+ next=rem*powers[DECDPUN-cut]; // save remainder for next Unit\r
+ }\r
+ } // shift-move\r
+\r
+ // propagate any partial unit to one below and clear the rest\r
+ for (; target>=uar; target--) {\r
+ *target=(Unit)next;\r
+ next=0;\r
+ }\r
+ return digits+shift;\r
+ } // decShiftToMost\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decShiftToLeast -- shift digits in array towards least significant */\r
+/* */\r
+/* uar is the array */\r
+/* units is length of the array, in units */\r
+/* shift is the number of digits to remove from the lsu end; it */\r
+/* must be zero or positive and <= than units*DECDPUN. */\r
+/* */\r
+/* returns the new length of the integer in the array, in units */\r
+/* */\r
+/* Removed digits are discarded (lost). Units not required to hold */\r
+/* the final result are unchanged. */\r
+/* ------------------------------------------------------------------ */\r
+static Int decShiftToLeast(Unit *uar, Int units, Int shift) {\r
+ Unit *target, *up; // work\r
+ Int cut, count; // work\r
+ Int quot, rem; // for division\r
+\r
+ if (shift==0) return units; // [fastpath] nothing to do\r
+ if (shift==units*DECDPUN) { // [fastpath] little to do\r
+ *uar=0; // all digits cleared gives zero\r
+ return 1; // leaves just the one\r
+ }\r
+\r
+ target=uar; // both paths\r
+ cut=MSUDIGITS(shift);\r
+ if (cut==DECDPUN) { // unit-boundary case; easy\r
+ up=uar+D2U(shift);\r
+ for (; up<uar+units; target++, up++) *target=*up;\r
+ return target-uar;\r
+ }\r
+\r
+ // messier\r
+ up=uar+D2U(shift-cut); // source; correct to whole Units\r
+ count=units*DECDPUN-shift; // the maximum new length\r
+ #if DECDPUN<=4\r
+ quot=QUOT10(*up, cut);\r
+ #else\r
+ quot=*up/powers[cut];\r
+ #endif\r
+ for (; ; target++) {\r
+ *target=(Unit)quot;\r
+ count-=(DECDPUN-cut);\r
+ if (count<=0) break;\r
+ up++;\r
+ quot=*up;\r
+ #if DECDPUN<=4\r
+ quot=QUOT10(quot, cut);\r
+ rem=*up-quot*powers[cut];\r
+ #else\r
+ rem=quot%powers[cut];\r
+ quot=quot/powers[cut];\r
+ #endif\r
+ *target=(Unit)(*target+rem*powers[DECDPUN-cut]);\r
+ count-=cut;\r
+ if (count<=0) break;\r
+ }\r
+ return target-uar+1;\r
+ } // decShiftToLeast\r
+\r
+#if DECSUBSET\r
+/* ------------------------------------------------------------------ */\r
+/* decRoundOperand -- round an operand [used for subset only] */\r
+/* */\r
+/* dn is the number to round (dn->digits is > set->digits) */\r
+/* set is the relevant context */\r
+/* status is the status accumulator */\r
+/* */\r
+/* returns an allocated decNumber with the rounded result. */\r
+/* */\r
+/* lostDigits and other status may be set by this. */\r
+/* */\r
+/* Since the input is an operand, it must not be modified. */\r
+/* Instead, return an allocated decNumber, rounded as required. */\r
+/* It is the caller's responsibility to free the allocated storage. */\r
+/* */\r
+/* If no storage is available then the result cannot be used, so NULL */\r
+/* is returned. */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber *decRoundOperand(const decNumber *dn, decContext *set,\r
+ uInt *status) {\r
+ decNumber *res; // result structure\r
+ uInt newstatus=0; // status from round\r
+ Int residue=0; // rounding accumulator\r
+\r
+ // Allocate storage for the returned decNumber, big enough for the\r
+ // length specified by the context\r
+ res=(decNumber *)malloc(sizeof(decNumber)\r
+ +(D2U(set->digits)-1)*sizeof(Unit));\r
+ if (res==NULL) {\r
+ *status|=DEC_Insufficient_storage;\r
+ return NULL;\r
+ }\r
+ decCopyFit(res, dn, set, &residue, &newstatus);\r
+ decApplyRound(res, set, residue, &newstatus);\r
+\r
+ // If that set Inexact then "lost digits" is raised...\r
+ if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;\r
+ *status|=newstatus;\r
+ return res;\r
+ } // decRoundOperand\r
+#endif\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCopyFit -- copy a number, truncating the coefficient if needed */\r
+/* */\r
+/* dest is the target decNumber */\r
+/* src is the source decNumber */\r
+/* set is the context [used for length (digits) and rounding mode] */\r
+/* residue is the residue accumulator */\r
+/* status contains the current status to be updated */\r
+/* */\r
+/* (dest==src is allowed and will be a no-op if fits) */\r
+/* All fields are updated as required. */\r
+/* ------------------------------------------------------------------ */\r
+static void decCopyFit(decNumber *dest, const decNumber *src,\r
+ decContext *set, Int *residue, uInt *status) {\r
+ dest->bits=src->bits;\r
+ dest->exponent=src->exponent;\r
+ decSetCoeff(dest, set, src->lsu, src->digits, residue, status);\r
+ } // decCopyFit\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decSetCoeff -- set the coefficient of a number */\r
+/* */\r
+/* dn is the number whose coefficient array is to be set. */\r
+/* It must have space for set->digits digits */\r
+/* set is the context [for size] */\r
+/* lsu -> lsu of the source coefficient [may be dn->lsu] */\r
+/* len is digits in the source coefficient [may be dn->digits] */\r
+/* residue is the residue accumulator. This has values as in */\r
+/* decApplyRound, and will be unchanged unless the */\r
+/* target size is less than len. In this case, the */\r
+/* coefficient is truncated and the residue is updated to */\r
+/* reflect the previous residue and the dropped digits. */\r
+/* status is the status accumulator, as usual */\r
+/* */\r
+/* The coefficient may already be in the number, or it can be an */\r
+/* external intermediate array. If it is in the number, lsu must == */\r
+/* dn->lsu and len must == dn->digits. */\r
+/* */\r
+/* Note that the coefficient length (len) may be < set->digits, and */\r
+/* in this case this merely copies the coefficient (or is a no-op */\r
+/* if dn->lsu==lsu). */\r
+/* */\r
+/* Note also that (only internally, from decQuantizeOp and */\r
+/* decSetSubnormal) the value of set->digits may be less than one, */\r
+/* indicating a round to left. This routine handles that case */\r
+/* correctly; caller ensures space. */\r
+/* */\r
+/* dn->digits, dn->lsu (and as required), and dn->exponent are */\r
+/* updated as necessary. dn->bits (sign) is unchanged. */\r
+/* */\r
+/* DEC_Rounded status is set if any digits are discarded. */\r
+/* DEC_Inexact status is set if any non-zero digits are discarded, or */\r
+/* incoming residue was non-0 (implies rounded) */\r
+/* ------------------------------------------------------------------ */\r
+// mapping array: maps 0-9 to canonical residues, so that a residue\r
+// can be adjusted in the range [-1, +1] and achieve correct rounding\r
+// 0 1 2 3 4 5 6 7 8 9\r
+static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};\r
+static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,\r
+ Int len, Int *residue, uInt *status) {\r
+ Int discard; // number of digits to discard\r
+ uInt cut; // cut point in Unit\r
+ const Unit *up; // work\r
+ Unit *target; // ..\r
+ Int count; // ..\r
+ #if DECDPUN<=4\r
+ uInt temp; // ..\r
+ #endif\r
+\r
+ discard=len-set->digits; // digits to discard\r
+ if (discard<=0) { // no digits are being discarded\r
+ if (dn->lsu!=lsu) { // copy needed\r
+ // copy the coefficient array to the result number; no shift needed\r
+ count=len; // avoids D2U\r
+ up=lsu;\r
+ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)\r
+ *target=*up;\r
+ dn->digits=len; // set the new length\r
+ }\r
+ // dn->exponent and residue are unchanged, record any inexactitude\r
+ if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);\r
+ return;\r
+ }\r
+\r
+ // some digits must be discarded ...\r
+ dn->exponent+=discard; // maintain numerical value\r
+ *status|=DEC_Rounded; // accumulate Rounded status\r
+ if (*residue>1) *residue=1; // previous residue now to right, so reduce\r
+\r
+ if (discard>len) { // everything, +1, is being discarded\r
+ // guard digit is 0\r
+ // residue is all the number [NB could be all 0s]\r
+ if (*residue<=0) { // not already positive\r
+ count=len; // avoids D2U\r
+ for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0\r
+ *residue=1;\r
+ break; // no need to check any others\r
+ }\r
+ }\r
+ if (*residue!=0) *status|=DEC_Inexact; // record inexactitude\r
+ *dn->lsu=0; // coefficient will now be 0\r
+ dn->digits=1; // ..\r
+ return;\r
+ } // total discard\r
+\r
+ // partial discard [most common case]\r
+ // here, at least the first (most significant) discarded digit exists\r
+\r
+ // spin up the number, noting residue during the spin, until get to\r
+ // the Unit with the first discarded digit. When reach it, extract\r
+ // it and remember its position\r
+ count=0;\r
+ for (up=lsu;; up++) {\r
+ count+=DECDPUN;\r
+ if (count>=discard) break; // full ones all checked\r
+ if (*up!=0) *residue=1;\r
+ } // up\r
+\r
+ // here up -> Unit with first discarded digit\r
+ cut=discard-(count-DECDPUN)-1;\r
+ if (cut==DECDPUN-1) { // unit-boundary case (fast)\r
+ Unit half=(Unit)powers[DECDPUN]>>1;\r
+ // set residue directly\r
+ if (*up>=half) {\r
+ if (*up>half) *residue=7;\r
+ else *residue+=5; // add sticky bit\r
+ }\r
+ else { // <half\r
+ if (*up!=0) *residue=3; // [else is 0, leave as sticky bit]\r
+ }\r
+ if (set->digits<=0) { // special for Quantize/Subnormal :-(\r
+ *dn->lsu=0; // .. result is 0\r
+ dn->digits=1; // ..\r
+ }\r
+ else { // shift to least\r
+ count=set->digits; // now digits to end up with\r
+ dn->digits=count; // set the new length\r
+ up++; // move to next\r
+ // on unit boundary, so shift-down copy loop is simple\r
+ for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)\r
+ *target=*up;\r
+ }\r
+ } // unit-boundary case\r
+\r
+ else { // discard digit is in low digit(s), and not top digit\r
+ uInt discard1; // first discarded digit\r
+ uInt quot, rem; // for divisions\r
+ if (cut==0) quot=*up; // is at bottom of unit\r
+ else /* cut>0 */ { // it's not at bottom of unit\r
+ #if DECDPUN<=4\r
+ quot=QUOT10(*up, cut);\r
+ rem=*up-quot*powers[cut];\r
+ #else\r
+ rem=*up%powers[cut];\r
+ quot=*up/powers[cut];\r
+ #endif\r
+ if (rem!=0) *residue=1;\r
+ }\r
+ // discard digit is now at bottom of quot\r
+ #if DECDPUN<=4\r
+ temp=(quot*6554)>>16; // fast /10\r
+ // Vowels algorithm here not a win (9 instructions)\r
+ discard1=quot-X10(temp);\r
+ quot=temp;\r
+ #else\r
+ discard1=quot%10;\r
+ quot=quot/10;\r
+ #endif\r
+ // here, discard1 is the guard digit, and residue is everything\r
+ // else [use mapping array to accumulate residue safely]\r
+ *residue+=resmap[discard1];\r
+ cut++; // update cut\r
+ // here: up -> Unit of the array with bottom digit\r
+ // cut is the division point for each Unit\r
+ // quot holds the uncut high-order digits for the current unit\r
+ if (set->digits<=0) { // special for Quantize/Subnormal :-(\r
+ *dn->lsu=0; // .. result is 0\r
+ dn->digits=1; // ..\r
+ }\r
+ else { // shift to least needed\r
+ count=set->digits; // now digits to end up with\r
+ dn->digits=count; // set the new length\r
+ // shift-copy the coefficient array to the result number\r
+ for (target=dn->lsu; ; target++) {\r
+ *target=(Unit)quot;\r
+ count-=(DECDPUN-cut);\r
+ if (count<=0) break;\r
+ up++;\r
+ quot=*up;\r
+ #if DECDPUN<=4\r
+ quot=QUOT10(quot, cut);\r
+ rem=*up-quot*powers[cut];\r
+ #else\r
+ rem=quot%powers[cut];\r
+ quot=quot/powers[cut];\r
+ #endif\r
+ *target=(Unit)(*target+rem*powers[DECDPUN-cut]);\r
+ count-=cut;\r
+ if (count<=0) break;\r
+ } // shift-copy loop\r
+ } // shift to least\r
+ } // not unit boundary\r
+\r
+ if (*residue!=0) *status|=DEC_Inexact; // record inexactitude\r
+ return;\r
+ } // decSetCoeff\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decApplyRound -- apply pending rounding to a number */\r
+/* */\r
+/* dn is the number, with space for set->digits digits */\r
+/* set is the context [for size and rounding mode] */\r
+/* residue indicates pending rounding, being any accumulated */\r
+/* guard and sticky information. It may be: */\r
+/* 6-9: rounding digit is >5 */\r
+/* 5: rounding digit is exactly half-way */\r
+/* 1-4: rounding digit is <5 and >0 */\r
+/* 0: the coefficient is exact */\r
+/* -1: as 1, but the hidden digits are subtractive, that */\r
+/* is, of the opposite sign to dn. In this case the */\r
+/* coefficient must be non-0. This case occurs when */\r
+/* subtracting a small number (which can be reduced to */\r
+/* a sticky bit); see decAddOp. */\r
+/* status is the status accumulator, as usual */\r
+/* */\r
+/* This routine applies rounding while keeping the length of the */\r
+/* coefficient constant. The exponent and status are unchanged */\r
+/* except if: */\r
+/* */\r
+/* -- the coefficient was increased and is all nines (in which */\r
+/* case Overflow could occur, and is handled directly here so */\r
+/* the caller does not need to re-test for overflow) */\r
+/* */\r
+/* -- the coefficient was decreased and becomes all nines (in which */\r
+/* case Underflow could occur, and is also handled directly). */\r
+/* */\r
+/* All fields in dn are updated as required. */\r
+/* */\r
+/* ------------------------------------------------------------------ */\r
+static void decApplyRound(decNumber *dn, decContext *set, Int residue,\r
+ uInt *status) {\r
+ Int bump; // 1 if coefficient needs to be incremented\r
+ // -1 if coefficient needs to be decremented\r
+\r
+ if (residue==0) return; // nothing to apply\r
+\r
+ bump=0; // assume a smooth ride\r
+\r
+ // now decide whether, and how, to round, depending on mode\r
+ switch (set->round) {\r
+ case DEC_ROUND_05UP: { // round zero or five up (for reround)\r
+ // This is the same as DEC_ROUND_DOWN unless there is a\r
+ // positive residue and the lsd of dn is 0 or 5, in which case\r
+ // it is bumped; when residue is <0, the number is therefore\r
+ // bumped down unless the final digit was 1 or 6 (in which\r
+ // case it is bumped down and then up -- a no-op)\r
+ Int lsd5=*dn->lsu%5; // get lsd and quintate\r
+ if (residue<0 && lsd5!=1) bump=-1;\r
+ else if (residue>0 && lsd5==0) bump=1;\r
+ // [bump==1 could be applied directly; use common path for clarity]\r
+ break;} // r-05\r
+\r
+ case DEC_ROUND_DOWN: {\r
+ // no change, except if negative residue\r
+ if (residue<0) bump=-1;\r
+ break;} // r-d\r
+\r
+ case DEC_ROUND_HALF_DOWN: {\r
+ if (residue>5) bump=1;\r
+ break;} // r-h-d\r
+\r
+ case DEC_ROUND_HALF_EVEN: {\r
+ if (residue>5) bump=1; // >0.5 goes up\r
+ else if (residue==5) { // exactly 0.5000...\r
+ // 0.5 goes up iff [new] lsd is odd\r
+ if (*dn->lsu & 0x01) bump=1;\r
+ }\r
+ break;} // r-h-e\r
+\r
+ case DEC_ROUND_HALF_UP: {\r
+ if (residue>=5) bump=1;\r
+ break;} // r-h-u\r
+\r
+ case DEC_ROUND_UP: {\r
+ if (residue>0) bump=1;\r
+ break;} // r-u\r
+\r
+ case DEC_ROUND_CEILING: {\r
+ // same as _UP for positive numbers, and as _DOWN for negatives\r
+ // [negative residue cannot occur on 0]\r
+ if (decNumberIsNegative(dn)) {\r
+ if (residue<0) bump=-1;\r
+ }\r
+ else {\r
+ if (residue>0) bump=1;\r
+ }\r
+ break;} // r-c\r
+\r
+ case DEC_ROUND_FLOOR: {\r
+ // same as _UP for negative numbers, and as _DOWN for positive\r
+ // [negative residue cannot occur on 0]\r
+ if (!decNumberIsNegative(dn)) {\r
+ if (residue<0) bump=-1;\r
+ }\r
+ else {\r
+ if (residue>0) bump=1;\r
+ }\r
+ break;} // r-f\r
+\r
+ default: { // e.g., DEC_ROUND_MAX\r
+ *status|=DEC_Invalid_context;\r
+ #if DECTRACE || (DECCHECK && DECVERB)\r
+ printf("Unknown rounding mode: %d\n", set->round);\r
+ #endif\r
+ break;}\r
+ } // switch\r
+\r
+ // now bump the number, up or down, if need be\r
+ if (bump==0) return; // no action required\r
+\r
+ // Simply use decUnitAddSub unless bumping up and the number is\r
+ // all nines. In this special case set to 100... explicitly\r
+ // and adjust the exponent by one (as otherwise could overflow\r
+ // the array)\r
+ // Similarly handle all-nines result if bumping down.\r
+ if (bump>0) {\r
+ Unit *up; // work\r
+ uInt count=dn->digits; // digits to be checked\r
+ for (up=dn->lsu; ; up++) {\r
+ if (count<=DECDPUN) {\r
+ // this is the last Unit (the msu)\r
+ if (*up!=powers[count]-1) break; // not still 9s\r
+ // here if it, too, is all nines\r
+ *up=(Unit)powers[count-1]; // here 999 -> 100 etc.\r
+ for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0\r
+ dn->exponent++; // and bump exponent\r
+ // [which, very rarely, could cause Overflow...]\r
+ if ((dn->exponent+dn->digits)>set->emax+1) {\r
+ decSetOverflow(dn, set, status);\r
+ }\r
+ return; // done\r
+ }\r
+ // a full unit to check, with more to come\r
+ if (*up!=DECDPUNMAX) break; // not still 9s\r
+ count-=DECDPUN;\r
+ } // up\r
+ } // bump>0\r
+ else { // -1\r
+ // here checking for a pre-bump of 1000... (leading 1, all\r
+ // other digits zero)\r
+ Unit *up, *sup; // work\r
+ uInt count=dn->digits; // digits to be checked\r
+ for (up=dn->lsu; ; up++) {\r
+ if (count<=DECDPUN) {\r
+ // this is the last Unit (the msu)\r
+ if (*up!=powers[count-1]) break; // not 100..\r
+ // here if have the 1000... case\r
+ sup=up; // save msu pointer\r
+ *up=(Unit)powers[count]-1; // here 100 in msu -> 999\r
+ // others all to all-nines, too\r
+ for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;\r
+ dn->exponent--; // and bump exponent\r
+\r
+ // iff the number was at the subnormal boundary (exponent=etiny)\r
+ // then the exponent is now out of range, so it will in fact get\r
+ // clamped to etiny and the final 9 dropped.\r
+ // printf(">> emin=%d exp=%d sdig=%d\n", set->emin,\r
+ // dn->exponent, set->digits);\r
+ if (dn->exponent+1==set->emin-set->digits+1) {\r
+ if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9]\r
+ else {\r
+ *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99..\r
+ dn->digits--;\r
+ }\r
+ dn->exponent++;\r
+ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;\r
+ }\r
+ return; // done\r
+ }\r
+\r
+ // a full unit to check, with more to come\r
+ if (*up!=0) break; // not still 0s\r
+ count-=DECDPUN;\r
+ } // up\r
+\r
+ } // bump<0\r
+\r
+ // Actual bump needed. Do it.\r
+ decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);\r
+ } // decApplyRound\r
+\r
+#if DECSUBSET\r
+/* ------------------------------------------------------------------ */\r
+/* decFinish -- finish processing a number */\r
+/* */\r
+/* dn is the number */\r
+/* set is the context */\r
+/* residue is the rounding accumulator (as in decApplyRound) */\r
+/* status is the accumulator */\r
+/* */\r
+/* This finishes off the current number by: */\r
+/* 1. If not extended: */\r
+/* a. Converting a zero result to clean '0' */\r
+/* b. Reducing positive exponents to 0, if would fit in digits */\r
+/* 2. Checking for overflow and subnormals (always) */\r
+/* Note this is just Finalize when no subset arithmetic. */\r
+/* All fields are updated as required. */\r
+/* ------------------------------------------------------------------ */\r
+static void decFinish(decNumber *dn, decContext *set, Int *residue,\r
+ uInt *status) {\r
+ if (!set->extended) {\r
+ if ISZERO(dn) { // value is zero\r
+ dn->exponent=0; // clean exponent ..\r
+ dn->bits=0; // .. and sign\r
+ return; // no error possible\r
+ }\r
+ if (dn->exponent>=0) { // non-negative exponent\r
+ // >0; reduce to integer if possible\r
+ if (set->digits >= (dn->exponent+dn->digits)) {\r
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);\r
+ dn->exponent=0;\r
+ }\r
+ }\r
+ } // !extended\r
+\r
+ decFinalize(dn, set, residue, status);\r
+ } // decFinish\r
+#endif\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFinalize -- final check, clamp, and round of a number */\r
+/* */\r
+/* dn is the number */\r
+/* set is the context */\r
+/* residue is the rounding accumulator (as in decApplyRound) */\r
+/* status is the status accumulator */\r
+/* */\r
+/* This finishes off the current number by checking for subnormal */\r
+/* results, applying any pending rounding, checking for overflow, */\r
+/* and applying any clamping. */\r
+/* Underflow and overflow conditions are raised as appropriate. */\r
+/* All fields are updated as required. */\r
+/* ------------------------------------------------------------------ */\r
+static void decFinalize(decNumber *dn, decContext *set, Int *residue,\r
+ uInt *status) {\r
+ Int shift; // shift needed if clamping\r
+ Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary\r
+\r
+ // Must be careful, here, when checking the exponent as the\r
+ // adjusted exponent could overflow 31 bits [because it may already\r
+ // be up to twice the expected].\r
+\r
+ // First test for subnormal. This must be done before any final\r
+ // round as the result could be rounded to Nmin or 0.\r
+ if (dn->exponent<=tinyexp) { // prefilter\r
+ Int comp;\r
+ decNumber nmin;\r
+ // A very nasty case here is dn == Nmin and residue<0\r
+ if (dn->exponent<tinyexp) {\r
+ // Go handle subnormals; this will apply round if needed.\r
+ decSetSubnormal(dn, set, residue, status);\r
+ return;\r
+ }\r
+ // Equals case: only subnormal if dn=Nmin and negative residue\r
+ decNumberZero(&nmin);\r
+ nmin.lsu[0]=1;\r
+ nmin.exponent=set->emin;\r
+ comp=decCompare(dn, &nmin, 1); // (signless compare)\r
+ if (comp==BADINT) { // oops\r
+ *status|=DEC_Insufficient_storage; // abandon...\r
+ return;\r
+ }\r
+ if (*residue<0 && comp==0) { // neg residue and dn==Nmin\r
+ decApplyRound(dn, set, *residue, status); // might force down\r
+ decSetSubnormal(dn, set, residue, status);\r
+ return;\r
+ }\r
+ }\r
+\r
+ // now apply any pending round (this could raise overflow).\r
+ if (*residue!=0) decApplyRound(dn, set, *residue, status);\r
+\r
+ // Check for overflow [redundant in the 'rare' case] or clamp\r
+ if (dn->exponent<=set->emax-set->digits+1) return; // neither needed\r
+\r
+\r
+ // here when might have an overflow or clamp to do\r
+ if (dn->exponent>set->emax-dn->digits+1) { // too big\r
+ decSetOverflow(dn, set, status);\r
+ return;\r
+ }\r
+ // here when the result is normal but in clamp range\r
+ if (!set->clamp) return;\r
+\r
+ // here when need to apply the IEEE exponent clamp (fold-down)\r
+ shift=dn->exponent-(set->emax-set->digits+1);\r
+\r
+ // shift coefficient (if non-zero)\r
+ if (!ISZERO(dn)) {\r
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);\r
+ }\r
+ dn->exponent-=shift; // adjust the exponent to match\r
+ *status|=DEC_Clamped; // and record the dirty deed\r
+ return;\r
+ } // decFinalize\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decSetOverflow -- set number to proper overflow value */\r
+/* */\r
+/* dn is the number (used for sign [only] and result) */\r
+/* set is the context [used for the rounding mode, etc.] */\r
+/* status contains the current status to be updated */\r
+/* */\r
+/* This sets the sign of a number and sets its value to either */\r
+/* Infinity or the maximum finite value, depending on the sign of */\r
+/* dn and the rounding mode, following IEEE 754 rules. */\r
+/* ------------------------------------------------------------------ */\r
+static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {\r
+ Flag needmax=0; // result is maximum finite value\r
+ uByte sign=dn->bits&DECNEG; // clean and save sign bit\r
+\r
+ if (ISZERO(dn)) { // zero does not overflow magnitude\r
+ Int emax=set->emax; // limit value\r
+ if (set->clamp) emax-=set->digits-1; // lower if clamping\r
+ if (dn->exponent>emax) { // clamp required\r
+ dn->exponent=emax;\r
+ *status|=DEC_Clamped;\r
+ }\r
+ return;\r
+ }\r
+\r
+ decNumberZero(dn);\r
+ switch (set->round) {\r
+ case DEC_ROUND_DOWN: {\r
+ needmax=1; // never Infinity\r
+ break;} // r-d\r
+ case DEC_ROUND_05UP: {\r
+ needmax=1; // never Infinity\r
+ break;} // r-05\r
+ case DEC_ROUND_CEILING: {\r
+ if (sign) needmax=1; // Infinity if non-negative\r
+ break;} // r-c\r
+ case DEC_ROUND_FLOOR: {\r
+ if (!sign) needmax=1; // Infinity if negative\r
+ break;} // r-f\r
+ default: break; // Infinity in all other cases\r
+ }\r
+ if (needmax) {\r
+ decSetMaxValue(dn, set);\r
+ dn->bits=sign; // set sign\r
+ }\r
+ else dn->bits=sign|DECINF; // Value is +/-Infinity\r
+ *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;\r
+ } // decSetOverflow\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decSetMaxValue -- set number to +Nmax (maximum normal value) */\r
+/* */\r
+/* dn is the number to set */\r
+/* set is the context [used for digits and emax] */\r
+/* */\r
+/* This sets the number to the maximum positive value. */\r
+/* ------------------------------------------------------------------ */\r
+static void decSetMaxValue(decNumber *dn, decContext *set) {\r
+ Unit *up; // work\r
+ Int count=set->digits; // nines to add\r
+ dn->digits=count;\r
+ // fill in all nines to set maximum value\r
+ for (up=dn->lsu; ; up++) {\r
+ if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines\r
+ else { // this is the msu\r
+ *up=(Unit)(powers[count]-1);\r
+ break;\r
+ }\r
+ count-=DECDPUN; // filled those digits\r
+ } // up\r
+ dn->bits=0; // + sign\r
+ dn->exponent=set->emax-set->digits+1;\r
+ } // decSetMaxValue\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decSetSubnormal -- process value whose exponent is <Emin */\r
+/* */\r
+/* dn is the number (used as input as well as output; it may have */\r
+/* an allowed subnormal value, which may need to be rounded) */\r
+/* set is the context [used for the rounding mode] */\r
+/* residue is any pending residue */\r
+/* status contains the current status to be updated */\r
+/* */\r
+/* If subset mode, set result to zero and set Underflow flags. */\r
+/* */\r
+/* Value may be zero with a low exponent; this does not set Subnormal */\r
+/* but the exponent will be clamped to Etiny. */\r
+/* */\r
+/* Otherwise ensure exponent is not out of range, and round as */\r
+/* necessary. Underflow is set if the result is Inexact. */\r
+/* ------------------------------------------------------------------ */\r
+static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,\r
+ uInt *status) {\r
+ decContext workset; // work\r
+ Int etiny, adjust; // ..\r
+\r
+ #if DECSUBSET\r
+ // simple set to zero and 'hard underflow' for subset\r
+ if (!set->extended) {\r
+ decNumberZero(dn);\r
+ // always full overflow\r
+ *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;\r
+ return;\r
+ }\r
+ #endif\r
+\r
+ // Full arithmetic -- allow subnormals, rounded to minimum exponent\r
+ // (Etiny) if needed\r
+ etiny=set->emin-(set->digits-1); // smallest allowed exponent\r
+\r
+ if ISZERO(dn) { // value is zero\r
+ // residue can never be non-zero here\r
+ #if DECCHECK\r
+ if (*residue!=0) {\r
+ printf("++ Subnormal 0 residue %ld\n", (LI)*residue);\r
+ *status|=DEC_Invalid_operation;\r
+ }\r
+ #endif\r
+ if (dn->exponent<etiny) { // clamp required\r
+ dn->exponent=etiny;\r
+ *status|=DEC_Clamped;\r
+ }\r
+ return;\r
+ }\r
+\r
+ *status|=DEC_Subnormal; // have a non-zero subnormal\r
+ adjust=etiny-dn->exponent; // calculate digits to remove\r
+ if (adjust<=0) { // not out of range; unrounded\r
+ // residue can never be non-zero here, except in the Nmin-residue\r
+ // case (which is a subnormal result), so can take fast-path here\r
+ // it may already be inexact (from setting the coefficient)\r
+ if (*status&DEC_Inexact) *status|=DEC_Underflow;\r
+ return;\r
+ }\r
+\r
+ // adjust>0, so need to rescale the result so exponent becomes Etiny\r
+ // [this code is similar to that in rescale]\r
+ workset=*set; // clone rounding, etc.\r
+ workset.digits=dn->digits-adjust; // set requested length\r
+ workset.emin-=adjust; // and adjust emin to match\r
+ // [note that the latter can be <1, here, similar to Rescale case]\r
+ decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);\r
+ decApplyRound(dn, &workset, *residue, status);\r
+\r
+ // Use 754 default rule: Underflow is set iff Inexact\r
+ // [independent of whether trapped]\r
+ if (*status&DEC_Inexact) *status|=DEC_Underflow;\r
+\r
+ // if rounded up a 999s case, exponent will be off by one; adjust\r
+ // back if so [it will fit, because it was shortened earlier]\r
+ if (dn->exponent>etiny) {\r
+ dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);\r
+ dn->exponent--; // (re)adjust the exponent.\r
+ }\r
+\r
+ // if rounded to zero, it is by definition clamped...\r
+ if (ISZERO(dn)) *status|=DEC_Clamped;\r
+ } // decSetSubnormal\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCheckMath - check entry conditions for a math function */\r
+/* */\r
+/* This checks the context and the operand */\r
+/* */\r
+/* rhs is the operand to check */\r
+/* set is the context to check */\r
+/* status is unchanged if both are good */\r
+/* */\r
+/* returns non-zero if status is changed, 0 otherwise */\r
+/* */\r
+/* Restrictions enforced: */\r
+/* */\r
+/* digits, emax, and -emin in the context must be less than */\r
+/* DEC_MAX_MATH (999999), and A must be within these bounds if */\r
+/* non-zero. Invalid_operation is set in the status if a */\r
+/* restriction is violated. */\r
+/* ------------------------------------------------------------------ */\r
+static uInt decCheckMath(const decNumber *rhs, decContext *set,\r
+ uInt *status) {\r
+ uInt save=*status; // record\r
+ if (set->digits>DEC_MAX_MATH\r
+ || set->emax>DEC_MAX_MATH\r
+ || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;\r
+ else if ((rhs->digits>DEC_MAX_MATH\r
+ || rhs->exponent+rhs->digits>DEC_MAX_MATH+1\r
+ || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))\r
+ && !ISZERO(rhs)) *status|=DEC_Invalid_operation;\r
+ return (*status!=save);\r
+ } // decCheckMath\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decGetInt -- get integer from a number */\r
+/* */\r
+/* dn is the number [which will not be altered] */\r
+/* */\r
+/* returns one of: */\r
+/* BADINT if there is a non-zero fraction */\r
+/* the converted integer */\r
+/* BIGEVEN if the integer is even and magnitude > 2*10**9 */\r
+/* BIGODD if the integer is odd and magnitude > 2*10**9 */\r
+/* */\r
+/* This checks and gets a whole number from the input decNumber. */\r
+/* The sign can be determined from dn by the caller when BIGEVEN or */\r
+/* BIGODD is returned. */\r
+/* ------------------------------------------------------------------ */\r
+static Int decGetInt(const decNumber *dn) {\r
+ Int theInt; // result accumulator\r
+ const Unit *up; // work\r
+ Int got; // digits (real or not) processed\r
+ Int ilength=dn->digits+dn->exponent; // integral length\r
+ Flag neg=decNumberIsNegative(dn); // 1 if -ve\r
+\r
+ // The number must be an integer that fits in 10 digits\r
+ // Assert, here, that 10 is enough for any rescale Etiny\r
+ #if DEC_MAX_EMAX > 999999999\r
+ #error GetInt may need updating [for Emax]\r
+ #endif\r
+ #if DEC_MIN_EMIN < -999999999\r
+ #error GetInt may need updating [for Emin]\r
+ #endif\r
+ if (ISZERO(dn)) return 0; // zeros are OK, with any exponent\r
+\r
+ up=dn->lsu; // ready for lsu\r
+ theInt=0; // ready to accumulate\r
+ if (dn->exponent>=0) { // relatively easy\r
+ // no fractional part [usual]; allow for positive exponent\r
+ got=dn->exponent;\r
+ }\r
+ else { // -ve exponent; some fractional part to check and discard\r
+ Int count=-dn->exponent; // digits to discard\r
+ // spin up whole units until reach the Unit with the unit digit\r
+ for (; count>=DECDPUN; up++) {\r
+ if (*up!=0) return BADINT; // non-zero Unit to discard\r
+ count-=DECDPUN;\r
+ }\r
+ if (count==0) got=0; // [a multiple of DECDPUN]\r
+ else { // [not multiple of DECDPUN]\r
+ Int rem; // work\r
+ // slice off fraction digits and check for non-zero\r
+ #if DECDPUN<=4\r
+ theInt=QUOT10(*up, count);\r
+ rem=*up-theInt*powers[count];\r
+ #else\r
+ rem=*up%powers[count]; // slice off discards\r
+ theInt=*up/powers[count];\r
+ #endif\r
+ if (rem!=0) return BADINT; // non-zero fraction\r
+ // it looks good\r
+ got=DECDPUN-count; // number of digits so far\r
+ up++; // ready for next\r
+ }\r
+ }\r
+ // now it's known there's no fractional part\r
+\r
+ // tricky code now, to accumulate up to 9.3 digits\r
+ if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there\r
+\r
+ if (ilength<11) {\r
+ Int save=theInt;\r
+ // collect any remaining unit(s)\r
+ for (; got<ilength; up++) {\r
+ theInt+=*up*powers[got];\r
+ got+=DECDPUN;\r
+ }\r
+ if (ilength==10) { // need to check for wrap\r
+ if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;\r
+ // [that test also disallows the BADINT result case]\r
+ else if (neg && theInt>1999999997) ilength=11;\r
+ else if (!neg && theInt>999999999) ilength=11;\r
+ if (ilength==11) theInt=save; // restore correct low bit\r
+ }\r
+ }\r
+\r
+ if (ilength>10) { // too big\r
+ if (theInt&1) return BIGODD; // bottom bit 1\r
+ return BIGEVEN; // bottom bit 0\r
+ }\r
+\r
+ if (neg) theInt=-theInt; // apply sign\r
+ return theInt;\r
+ } // decGetInt\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decDecap -- decapitate the coefficient of a number */\r
+/* */\r
+/* dn is the number to be decapitated */\r
+/* drop is the number of digits to be removed from the left of dn; */\r
+/* this must be <= dn->digits (if equal, the coefficient is */\r
+/* set to 0) */\r
+/* */\r
+/* Returns dn; dn->digits will be <= the initial digits less drop */\r
+/* (after removing drop digits there may be leading zero digits */\r
+/* which will also be removed). Only dn->lsu and dn->digits change. */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber *decDecap(decNumber *dn, Int drop) {\r
+ Unit *msu; // -> target cut point\r
+ Int cut; // work\r
+ if (drop>=dn->digits) { // losing the whole thing\r
+ #if DECCHECK\r
+ if (drop>dn->digits)\r
+ printf("decDecap called with drop>digits [%ld>%ld]\n",\r
+ (LI)drop, (LI)dn->digits);\r
+ #endif\r
+ dn->lsu[0]=0;\r
+ dn->digits=1;\r
+ return dn;\r
+ }\r
+ msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu\r
+ cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu\r
+ if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits\r
+ // that may have left leading zero digits, so do a proper count...\r
+ dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);\r
+ return dn;\r
+ } // decDecap\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decBiStr -- compare string with pairwise options */\r
+/* */\r
+/* targ is the string to compare */\r
+/* str1 is one of the strings to compare against (length may be 0) */\r
+/* str2 is the other; it must be the same length as str1 */\r
+/* */\r
+/* returns 1 if strings compare equal, (that is, it is the same */\r
+/* length as str1 and str2, and each character of targ is in either */\r
+/* str1 or str2 in the corresponding position), or 0 otherwise */\r
+/* */\r
+/* This is used for generic caseless compare, including the awkward */\r
+/* case of the Turkish dotted and dotless Is. Use as (for example): */\r
+/* if (decBiStr(test, "mike", "MIKE")) ... */\r
+/* ------------------------------------------------------------------ */\r
+static Flag decBiStr(const char *targ, const char *str1, const char *str2) {\r
+ for (;;targ++, str1++, str2++) {\r
+ if (*targ!=*str1 && *targ!=*str2) return 0;\r
+ // *targ has a match in one (or both, if terminator)\r
+ if (*targ=='\0') break;\r
+ } // forever\r
+ return 1;\r
+ } // decBiStr\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decNaNs -- handle NaN operand or operands */\r
+/* */\r
+/* res is the result number */\r
+/* lhs is the first operand */\r
+/* rhs is the second operand, or NULL if none */\r
+/* context is used to limit payload length */\r
+/* status contains the current status */\r
+/* returns res in case convenient */\r
+/* */\r
+/* Called when one or both operands is a NaN, and propagates the */\r
+/* appropriate result to res. When an sNaN is found, it is changed */\r
+/* to a qNaN and Invalid operation is set. */\r
+/* ------------------------------------------------------------------ */\r
+static decNumber * decNaNs(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set,\r
+ uInt *status) {\r
+ // This decision tree ends up with LHS being the source pointer,\r
+ // and status updated if need be\r
+ if (lhs->bits & DECSNAN)\r
+ *status|=DEC_Invalid_operation | DEC_sNaN;\r
+ else if (rhs==NULL);\r
+ else if (rhs->bits & DECSNAN) {\r
+ lhs=rhs;\r
+ *status|=DEC_Invalid_operation | DEC_sNaN;\r
+ }\r
+ else if (lhs->bits & DECNAN);\r
+ else lhs=rhs;\r
+\r
+ // propagate the payload\r
+ if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy\r
+ else { // too long\r
+ const Unit *ul;\r
+ Unit *ur, *uresp1;\r
+ // copy safe number of units, then decapitate\r
+ res->bits=lhs->bits; // need sign etc.\r
+ uresp1=res->lsu+D2U(set->digits);\r
+ for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;\r
+ res->digits=D2U(set->digits)*DECDPUN;\r
+ // maybe still too long\r
+ if (res->digits>set->digits) decDecap(res, res->digits-set->digits);\r
+ }\r
+\r
+ res->bits&=~DECSNAN; // convert any sNaN to NaN, while\r
+ res->bits|=DECNAN; // .. preserving sign\r
+ res->exponent=0; // clean exponent\r
+ // [coefficient was copied/decapitated]\r
+ return res;\r
+ } // decNaNs\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decStatus -- apply non-zero status */\r
+/* */\r
+/* dn is the number to set if error */\r
+/* status contains the current status (not yet in context) */\r
+/* set is the context */\r
+/* */\r
+/* If the status is an error status, the number is set to a NaN, */\r
+/* unless the error was an overflow, divide-by-zero, or underflow, */\r
+/* in which case the number will have already been set. */\r
+/* */\r
+/* The context status is then updated with the new status. Note that */\r
+/* this may raise a signal, so control may never return from this */\r
+/* routine (hence resources must be recovered before it is called). */\r
+/* ------------------------------------------------------------------ */\r
+static void decStatus(decNumber *dn, uInt status, decContext *set) {\r
+ if (status & DEC_NaNs) { // error status -> NaN\r
+ // if cause was an sNaN, clear and propagate [NaN is already set up]\r
+ if (status & DEC_sNaN) status&=~DEC_sNaN;\r
+ else {\r
+ decNumberZero(dn); // other error: clean throughout\r
+ dn->bits=DECNAN; // and make a quiet NaN\r
+ }\r
+ }\r
+ decContextSetStatus(set, status); // [may not return]\r
+ return;\r
+ } // decStatus\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decGetDigits -- count digits in a Units array */\r
+/* */\r
+/* uar is the Unit array holding the number (this is often an */\r
+/* accumulator of some sort) */\r
+/* len is the length of the array in units [>=1] */\r
+/* */\r
+/* returns the number of (significant) digits in the array */\r
+/* */\r
+/* All leading zeros are excluded, except the last if the array has */\r
+/* only zero Units. */\r
+/* ------------------------------------------------------------------ */\r
+// This may be called twice during some operations.\r
+static Int decGetDigits(Unit *uar, Int len) {\r
+ Unit *up=uar+(len-1); // -> msu\r
+ Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu\r
+ #if DECDPUN>4\r
+ uInt const *pow; // work\r
+ #endif\r
+ // (at least 1 in final msu)\r
+ #if DECCHECK\r
+ if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);\r
+ #endif\r
+\r
+ for (; up>=uar; up--) {\r
+ if (*up==0) { // unit is all 0s\r
+ if (digits==1) break; // a zero has one digit\r
+ digits-=DECDPUN; // adjust for 0 unit\r
+ continue;}\r
+ // found the first (most significant) non-zero Unit\r
+ #if DECDPUN>1 // not done yet\r
+ if (*up<10) break; // is 1-9\r
+ digits++;\r
+ #if DECDPUN>2 // not done yet\r
+ if (*up<100) break; // is 10-99\r
+ digits++;\r
+ #if DECDPUN>3 // not done yet\r
+ if (*up<1000) break; // is 100-999\r
+ digits++;\r
+ #if DECDPUN>4 // count the rest ...\r
+ for (pow=&powers[4]; *up>=*pow; pow++) digits++;\r
+ #endif\r
+ #endif\r
+ #endif\r
+ #endif\r
+ break;\r
+ } // up\r
+ return digits;\r
+ } // decGetDigits\r
+\r
+#if DECTRACE | DECCHECK\r
+/* ------------------------------------------------------------------ */\r
+/* decNumberShow -- display a number [debug aid] */\r
+/* dn is the number to show */\r
+/* */\r
+/* Shows: sign, exponent, coefficient (msu first), digits */\r
+/* or: sign, special-value */\r
+/* ------------------------------------------------------------------ */\r
+// this is public so other modules can use it\r
+void decNumberShow(const decNumber *dn) {\r
+ const Unit *up; // work\r
+ uInt u, d; // ..\r
+ Int cut; // ..\r
+ char isign='+'; // main sign\r
+ if (dn==NULL) {\r
+ printf("NULL\n");\r
+ return;}\r
+ if (decNumberIsNegative(dn)) isign='-';\r
+ printf(" >> %c ", isign);\r
+ if (dn->bits&DECSPECIAL) { // Is a special value\r
+ if (decNumberIsInfinite(dn)) printf("Infinity");\r
+ else { // a NaN\r
+ if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN\r
+ else printf("NaN");\r
+ }\r
+ // if coefficient and exponent are 0, no more to do\r
+ if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {\r
+ printf("\n");\r
+ return;}\r
+ // drop through to report other information\r
+ printf(" ");\r
+ }\r
+\r
+ // now carefully display the coefficient\r
+ up=dn->lsu+D2U(dn->digits)-1; // msu\r
+ printf("%ld", (LI)*up);\r
+ for (up=up-1; up>=dn->lsu; up--) {\r
+ u=*up;\r
+ printf(":");\r
+ for (cut=DECDPUN-1; cut>=0; cut--) {\r
+ d=u/powers[cut];\r
+ u-=d*powers[cut];\r
+ printf("%ld", (LI)d);\r
+ } // cut\r
+ } // up\r
+ if (dn->exponent!=0) {\r
+ char esign='+';\r
+ if (dn->exponent<0) esign='-';\r
+ printf(" E%c%ld", esign, (LI)abs(dn->exponent));\r
+ }\r
+ printf(" [%ld]\n", (LI)dn->digits);\r
+ } // decNumberShow\r
+#endif\r
+\r
+#if DECTRACE || DECCHECK\r
+/* ------------------------------------------------------------------ */\r
+/* decDumpAr -- display a unit array [debug/check aid] */\r
+/* name is a single-character tag name */\r
+/* ar is the array to display */\r
+/* len is the length of the array in Units */\r
+/* ------------------------------------------------------------------ */\r
+static void decDumpAr(char name, const Unit *ar, Int len) {\r
+ Int i;\r
+ const char *spec;\r
+ #if DECDPUN==9\r
+ spec="%09d ";\r
+ #elif DECDPUN==8\r
+ spec="%08d ";\r
+ #elif DECDPUN==7\r
+ spec="%07d ";\r
+ #elif DECDPUN==6\r
+ spec="%06d ";\r
+ #elif DECDPUN==5\r
+ spec="%05d ";\r
+ #elif DECDPUN==4\r
+ spec="%04d ";\r
+ #elif DECDPUN==3\r
+ spec="%03d ";\r
+ #elif DECDPUN==2\r
+ spec="%02d ";\r
+ #else\r
+ spec="%d ";\r
+ #endif\r
+ printf(" :%c: ", name);\r
+ for (i=len-1; i>=0; i--) {\r
+ if (i==len-1) printf("%ld ", (LI)ar[i]);\r
+ else printf(spec, ar[i]);\r
+ }\r
+ printf("\n");\r
+ return;}\r
+#endif\r
+\r
+#if DECCHECK\r
+/* ------------------------------------------------------------------ */\r
+/* decCheckOperands -- check operand(s) to a routine */\r
+/* res is the result structure (not checked; it will be set to */\r
+/* quiet NaN if error found (and it is not NULL)) */\r
+/* lhs is the first operand (may be DECUNRESU) */\r
+/* rhs is the second (may be DECUNUSED) */\r
+/* set is the context (may be DECUNCONT) */\r
+/* returns 0 if both operands, and the context are clean, or 1 */\r
+/* otherwise (in which case the context will show an error, */\r
+/* unless NULL). Note that res is not cleaned; caller should */\r
+/* handle this so res=NULL case is safe. */\r
+/* The caller is expected to abandon immediately if 1 is returned. */\r
+/* ------------------------------------------------------------------ */\r
+static Flag decCheckOperands(decNumber *res, const decNumber *lhs,\r
+ const decNumber *rhs, decContext *set) {\r
+ Flag bad=0;\r
+ if (set==NULL) { // oops; hopeless\r
+ #if DECTRACE || DECVERB\r
+ printf("Reference to context is NULL.\n");\r
+ #endif\r
+ bad=1;\r
+ return 1;}\r
+ else if (set!=DECUNCONT\r
+ && (set->digits<1 || set->round>=DEC_ROUND_MAX)) {\r
+ bad=1;\r
+ #if DECTRACE || DECVERB\r
+ printf("Bad context [digits=%ld round=%ld].\n",\r
+ (LI)set->digits, (LI)set->round);\r
+ #endif\r
+ }\r
+ else {\r
+ if (res==NULL) {\r
+ bad=1;\r
+ #if DECTRACE\r
+ // this one not DECVERB as standard tests include NULL\r
+ printf("Reference to result is NULL.\n");\r
+ #endif\r
+ }\r
+ if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));\r
+ if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));\r
+ }\r
+ if (bad) {\r
+ if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);\r
+ if (res!=DECUNRESU && res!=NULL) {\r
+ decNumberZero(res);\r
+ res->bits=DECNAN; // qNaN\r
+ }\r
+ }\r
+ return bad;\r
+ } // decCheckOperands\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCheckNumber -- check a number */\r
+/* dn is the number to check */\r
+/* returns 0 if the number is clean, or 1 otherwise */\r
+/* */\r
+/* The number is considered valid if it could be a result from some */\r
+/* operation in some valid context. */\r
+/* ------------------------------------------------------------------ */\r
+static Flag decCheckNumber(const decNumber *dn) {\r
+ const Unit *up; // work\r
+ uInt maxuint; // ..\r
+ Int ae, d, digits; // ..\r
+ Int emin, emax; // ..\r
+\r
+ if (dn==NULL) { // hopeless\r
+ #if DECTRACE\r
+ // this one not DECVERB as standard tests include NULL\r
+ printf("Reference to decNumber is NULL.\n");\r
+ #endif\r
+ return 1;}\r
+\r
+ // check special values\r
+ if (dn->bits & DECSPECIAL) {\r
+ if (dn->exponent!=0) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Exponent %ld (not 0) for a special value [%02x].\n",\r
+ (LI)dn->exponent, dn->bits);\r
+ #endif\r
+ return 1;}\r
+\r
+ // 2003.09.08: NaNs may now have coefficients, so next tests Inf only\r
+ if (decNumberIsInfinite(dn)) {\r
+ if (dn->digits!=1) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);\r
+ #endif\r
+ return 1;}\r
+ if (*dn->lsu!=0) {\r
+ #if DECTRACE || DECVERB\r
+ printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);\r
+ #endif\r
+ decDumpAr('I', dn->lsu, D2U(dn->digits));\r
+ return 1;}\r
+ } // Inf\r
+ // 2002.12.26: negative NaNs can now appear through proposed IEEE\r
+ // concrete formats (decimal64, etc.).\r
+ return 0;\r
+ }\r
+\r
+ // check the coefficient\r
+ if (dn->digits<1 || dn->digits>DECNUMMAXP) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Digits %ld in number.\n", (LI)dn->digits);\r
+ #endif\r
+ return 1;}\r
+\r
+ d=dn->digits;\r
+\r
+ for (up=dn->lsu; d>0; up++) {\r
+ if (d>DECDPUN) maxuint=DECDPUNMAX;\r
+ else { // reached the msu\r
+ maxuint=powers[d]-1;\r
+ if (dn->digits>1 && *up<powers[d-1]) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Leading 0 in number.\n");\r
+ decNumberShow(dn);\r
+ #endif\r
+ return 1;}\r
+ }\r
+ if (*up>maxuint) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",\r
+ (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);\r
+ #endif\r
+ return 1;}\r
+ d-=DECDPUN;\r
+ }\r
+\r
+ // check the exponent. Note that input operands can have exponents\r
+ // which are out of the set->emin/set->emax and set->digits range\r
+ // (just as they can have more digits than set->digits).\r
+ ae=dn->exponent+dn->digits-1; // adjusted exponent\r
+ emax=DECNUMMAXE;\r
+ emin=DECNUMMINE;\r
+ digits=DECNUMMAXP;\r
+ if (ae<emin-(digits-1)) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Adjusted exponent underflow [%ld].\n", (LI)ae);\r
+ decNumberShow(dn);\r
+ #endif\r
+ return 1;}\r
+ if (ae>+emax) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Adjusted exponent overflow [%ld].\n", (LI)ae);\r
+ decNumberShow(dn);\r
+ #endif\r
+ return 1;}\r
+\r
+ return 0; // it's OK\r
+ } // decCheckNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decCheckInexact -- check a normal finite inexact result has digits */\r
+/* dn is the number to check */\r
+/* set is the context (for status and precision) */\r
+/* sets Invalid operation, etc., if some digits are missing */\r
+/* [this check is not made for DECSUBSET compilation or when */\r
+/* subnormal is not set] */\r
+/* ------------------------------------------------------------------ */\r
+static void decCheckInexact(const decNumber *dn, decContext *set) {\r
+ #if !DECSUBSET && DECEXTFLAG\r
+ if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact\r
+ && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {\r
+ #if DECTRACE || DECVERB\r
+ printf("Insufficient digits [%ld] on normal Inexact result.\n",\r
+ (LI)dn->digits);\r
+ decNumberShow(dn);\r
+ #endif\r
+ decContextSetStatus(set, DEC_Invalid_operation);\r
+ }\r
+ #else\r
+ // next is a noop for quiet compiler\r
+ if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;\r
+ #endif\r
+ return;\r
+ } // decCheckInexact\r
+#endif\r
+\r
+#if DECALLOC\r
+#undef malloc\r
+#undef free\r
+/* ------------------------------------------------------------------ */\r
+/* decMalloc -- accountable allocation routine */\r
+/* n is the number of bytes to allocate */\r
+/* */\r
+/* Semantics is the same as the stdlib malloc routine, but bytes */\r
+/* allocated are accounted for globally, and corruption fences are */\r
+/* added before and after the 'actual' storage. */\r
+/* ------------------------------------------------------------------ */\r
+/* This routine allocates storage with an extra twelve bytes; 8 are */\r
+/* at the start and hold: */\r
+/* 0-3 the original length requested */\r
+/* 4-7 buffer corruption detection fence (DECFENCE, x4) */\r
+/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */\r
+/* ------------------------------------------------------------------ */\r
+static void *decMalloc(size_t n) {\r
+ uInt size=n+12; // true size\r
+ void *alloc; // -> allocated storage\r
+ uByte *b, *b0; // work\r
+ uInt uiwork; // for macros\r
+\r
+ alloc=malloc(size); // -> allocated storage\r
+ if (alloc==NULL) return NULL; // out of strorage\r
+ b0=(uByte *)alloc; // as bytes\r
+ decAllocBytes+=n; // account for storage\r
+ UBFROMUI(alloc, n); // save n\r
+ // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n);\r
+ for (b=b0+4; b<b0+8; b++) *b=DECFENCE;\r
+ for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;\r
+ return b0+8; // -> play area\r
+ } // decMalloc\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decFree -- accountable free routine */\r
+/* alloc is the storage to free */\r
+/* */\r
+/* Semantics is the same as the stdlib malloc routine, except that */\r
+/* the global storage accounting is updated and the fences are */\r
+/* checked to ensure that no routine has written 'out of bounds'. */\r
+/* ------------------------------------------------------------------ */\r
+/* This routine first checks that the fences have not been corrupted. */\r
+/* It then frees the storage using the 'truw' storage address (that */\r
+/* is, offset by 8). */\r
+/* ------------------------------------------------------------------ */\r
+static void decFree(void *alloc) {\r
+ uInt n; // original length\r
+ uByte *b, *b0; // work\r
+ uInt uiwork; // for macros\r
+\r
+ if (alloc==NULL) return; // allowed; it's a nop\r
+ b0=(uByte *)alloc; // as bytes\r
+ b0-=8; // -> true start of storage\r
+ n=UBTOUI(b0); // lift length\r
+ for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)\r
+ printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,\r
+ b-b0-8, (LI)b0);\r
+ for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)\r
+ printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,\r
+ b-b0-8, (LI)b0, (LI)n);\r
+ free(b0); // drop the storage\r
+ decAllocBytes-=n; // account for storage\r
+ // printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n);\r
+ } // decFree\r
+#define malloc(a) decMalloc(a)\r
+#define free(a) decFree(a)\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number arithmetic module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECNUMBER)\r
+ #define DECNUMBER\r
+ #define DECNAME "decNumber" /* Short name */\r
+ #define DECFULLNAME "Decimal Number Module" /* Verbose name */\r
+ #define DECAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ #if !defined(DECCONTEXT)\r
+ #include "decContext.h"\r
+ #endif\r
+\r
+ /* Bit settings for decNumber.bits */\r
+ #define DECNEG 0x80 /* Sign; 1=negative, 0=positive or zero */\r
+ #define DECINF 0x40 /* 1=Infinity */\r
+ #define DECNAN 0x20 /* 1=NaN */\r
+ #define DECSNAN 0x10 /* 1=sNaN */\r
+ /* The remaining bits are reserved; they must be 0 */\r
+ #define DECSPECIAL (DECINF|DECNAN|DECSNAN) /* any special value */\r
+\r
+ /* Define the decNumber data structure. The size and shape of the */\r
+ /* units array in the structure is determined by the following */\r
+ /* constant. This must not be changed without recompiling the */\r
+ /* decNumber library modules. */\r
+\r
+ #define DECDPUN 3 /* DECimal Digits Per UNit [must be >0 */\r
+ /* and <10; 3 or powers of 2 are best]. */\r
+\r
+ /* DECNUMDIGITS is the default number of digits that can be held in */\r
+ /* the structure. If undefined, 1 is assumed and it is assumed */\r
+ /* that the structure will be immediately followed by extra space, */\r
+ /* as required. DECNUMDIGITS is always >0. */\r
+ #if !defined(DECNUMDIGITS)\r
+ #define DECNUMDIGITS 1\r
+ #endif\r
+\r
+ /* The size (integer data type) of each unit is determined by the */\r
+ /* number of digits it will hold. */\r
+ #if DECDPUN<=2\r
+ #define decNumberUnit uint8_t\r
+ #elif DECDPUN<=4\r
+ #define decNumberUnit uint16_t\r
+ #else\r
+ #define decNumberUnit uint32_t\r
+ #endif\r
+ /* The number of units needed is ceil(DECNUMDIGITS/DECDPUN) */\r
+ #define DECNUMUNITS ((DECNUMDIGITS+DECDPUN-1)/DECDPUN)\r
+\r
+ /* The data structure... */\r
+ typedef struct {\r
+ int32_t digits; /* Count of digits in the coefficient; >0 */\r
+ int32_t exponent; /* Unadjusted exponent, unbiased, in */\r
+ /* range: -1999999997 through 999999999 */\r
+ uint8_t bits; /* Indicator bits (see above) */\r
+ /* Coefficient, from least significant unit */\r
+ decNumberUnit lsu[DECNUMUNITS];\r
+ } decNumber;\r
+\r
+ /* Notes: */\r
+ /* 1. If digits is > DECDPUN then there will one or more */\r
+ /* decNumberUnits immediately following the first element of lsu.*/\r
+ /* These contain the remaining (more significant) digits of the */\r
+ /* number, and may be in the lsu array, or may be guaranteed by */\r
+ /* some other mechanism (such as being contained in another */\r
+ /* structure, or being overlaid on dynamically allocated */\r
+ /* storage). */\r
+ /* */\r
+ /* Each integer of the coefficient (except potentially the last) */\r
+ /* contains DECDPUN digits (e.g., a value in the range 0 through */\r
+ /* 99999999 if DECDPUN is 8, or 0 through 999 if DECDPUN is 3). */\r
+ /* */\r
+ /* 2. A decNumber converted to a string may need up to digits+14 */\r
+ /* characters. The worst cases (non-exponential and exponential */\r
+ /* formats) are -0.00000{9...}# and -9.{9...}E+999999999# */\r
+ /* (where # is '\0') */\r
+\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* decNumber public functions and macros */\r
+ /* ---------------------------------------------------------------- */\r
+ /* Conversions */\r
+ decNumber * decNumberFromInt32(decNumber *, int32_t);\r
+ decNumber * decNumberFromUInt32(decNumber *, uint32_t);\r
+ decNumber * decNumberFromString(decNumber *, const char *, decContext *);\r
+ char * decNumberToString(const decNumber *, char *);\r
+ char * decNumberToEngString(const decNumber *, char *);\r
+ uint32_t decNumberToUInt32(const decNumber *, decContext *);\r
+ int32_t decNumberToInt32(const decNumber *, decContext *);\r
+ uint8_t * decNumberGetBCD(const decNumber *, uint8_t *);\r
+ decNumber * decNumberSetBCD(decNumber *, const uint8_t *, uint32_t);\r
+\r
+ /* Operators and elementary functions */\r
+ decNumber * decNumberAbs(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberAdd(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberAnd(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberCompare(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberCompareSignal(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberCompareTotal(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberCompareTotalMag(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberDivide(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberDivideInteger(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberExp(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberFMA(decNumber *, const decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberInvert(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberLn(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberLogB(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberLog10(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberMax(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberMaxMag(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberMin(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberMinMag(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberMinus(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberMultiply(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberNormalize(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberOr(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberPlus(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberPower(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberQuantize(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberReduce(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberRemainder(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberRemainderNear(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberRescale(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberRotate(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberSameQuantum(decNumber *, const decNumber *, const decNumber *);\r
+ decNumber * decNumberScaleB(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberShift(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberSquareRoot(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberSubtract(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberToIntegralExact(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberToIntegralValue(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberXor(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+\r
+ /* Utilities */\r
+ enum decClass decNumberClass(const decNumber *, decContext *);\r
+ const char * decNumberClassToString(enum decClass);\r
+ decNumber * decNumberCopy(decNumber *, const decNumber *);\r
+ decNumber * decNumberCopyAbs(decNumber *, const decNumber *);\r
+ decNumber * decNumberCopyNegate(decNumber *, const decNumber *);\r
+ decNumber * decNumberCopySign(decNumber *, const decNumber *, const decNumber *);\r
+ decNumber * decNumberNextMinus(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberNextPlus(decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberNextToward(decNumber *, const decNumber *, const decNumber *, decContext *);\r
+ decNumber * decNumberTrim(decNumber *);\r
+ const char * decNumberVersion(void);\r
+ decNumber * decNumberZero(decNumber *);\r
+\r
+ /* Functions for testing decNumbers (normality depends on context) */\r
+ int32_t decNumberIsNormal(const decNumber *, decContext *);\r
+ int32_t decNumberIsSubnormal(const decNumber *, decContext *);\r
+\r
+ /* Macros for testing decNumber *dn */\r
+ #define decNumberIsCanonical(dn) (1) /* All decNumbers are saintly */\r
+ #define decNumberIsFinite(dn) (((dn)->bits&DECSPECIAL)==0)\r
+ #define decNumberIsInfinite(dn) (((dn)->bits&DECINF)!=0)\r
+ #define decNumberIsNaN(dn) (((dn)->bits&(DECNAN|DECSNAN))!=0)\r
+ #define decNumberIsNegative(dn) (((dn)->bits&DECNEG)!=0)\r
+ #define decNumberIsQNaN(dn) (((dn)->bits&(DECNAN))!=0)\r
+ #define decNumberIsSNaN(dn) (((dn)->bits&(DECSNAN))!=0)\r
+ #define decNumberIsSpecial(dn) (((dn)->bits&DECSPECIAL)!=0)\r
+ #define decNumberIsZero(dn) (*(dn)->lsu==0 \\r
+ && (dn)->digits==1 \\r
+ && (((dn)->bits&DECSPECIAL)==0))\r
+ #define decNumberRadix(dn) (10)\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decNumber package local type, tuning, and macro definitions */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This header file is included by all modules in the decNumber */\r
+/* library, and contains local type definitions, tuning parameters, */\r
+/* etc. It should not need to be used by application programs. */\r
+/* decNumber.h or one of decDouble (etc.) must be included first. */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECNUMBERLOC)\r
+ #define DECNUMBERLOC\r
+ #define DECVERSION "decNumber 3.68" /* Package Version [16 max.] */\r
+ #define DECNLAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ #include <stdlib.h> /* for abs */\r
+ #include <string.h> /* for memset, strcpy */\r
+\r
+ /* Conditional code flag -- set this to match hardware platform */\r
+ #if !defined(DECLITEND)\r
+ #define DECLITEND 1 /* 1=little-endian, 0=big-endian */\r
+ #endif\r
+\r
+ /* Conditional code flag -- set this to 1 for best performance */\r
+ #if !defined(DECUSE64)\r
+ #define DECUSE64 1 /* 1=use int64s, 0=int32 & smaller only */\r
+ #endif\r
+\r
+ /* Conditional code flag -- set this to 0 to exclude printf calls */\r
+ #if !defined(DECPRINT)\r
+ #define DECPRINT 1 /* 1=allow printf calls; 0=no printf */\r
+ #endif\r
+\r
+ /* Conditional check flags -- set these to 0 for best performance */\r
+ #if !defined(DECCHECK)\r
+ #define DECCHECK 0 /* 1 to enable robust checking */\r
+ #endif\r
+ #if !defined(DECALLOC)\r
+ #define DECALLOC 0 /* 1 to enable memory accounting */\r
+ #endif\r
+ #if !defined(DECTRACE)\r
+ #define DECTRACE 0 /* 1 to trace certain internals, etc. */\r
+ #endif\r
+\r
+ /* Tuning parameter for decNumber (arbitrary precision) module */\r
+ #if !defined(DECBUFFER)\r
+ #define DECBUFFER 36 /* Size basis for local buffers. This */\r
+ /* should be a common maximum precision */\r
+ /* rounded up to a multiple of 4; must */\r
+ /* be zero or positive. */\r
+ #endif\r
+\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Check parameter dependencies */\r
+ /* ---------------------------------------------------------------- */\r
+ #if DECCHECK & !DECPRINT\r
+ #error DECCHECK needs DECPRINT to be useful\r
+ #endif\r
+ #if DECALLOC & !DECPRINT\r
+ #error DECALLOC needs DECPRINT to be useful\r
+ #endif\r
+ #if DECTRACE & !DECPRINT\r
+ #error DECTRACE needs DECPRINT to be useful\r
+ #endif\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Definitions for all modules (general-purpose) */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* Local names for common types -- for safety, decNumber modules do */\r
+ /* not use int or long directly. */\r
+ #define Flag uint8_t\r
+ #define Byte int8_t\r
+ #define uByte uint8_t\r
+ #define Short int16_t\r
+ #define uShort uint16_t\r
+ #define Int int32_t\r
+ #define uInt uint32_t\r
+ #define Unit decNumberUnit\r
+ #if DECUSE64\r
+ #define Long int64_t\r
+ #define uLong uint64_t\r
+ #endif\r
+\r
+ /* Development-use definitions */\r
+ typedef long int LI; /* for printf arguments only */\r
+ #define DECNOINT 0 /* 1 to check no internal use of 'int' */\r
+ /* or stdint types */\r
+ #if DECNOINT\r
+ /* if these interfere with your C includes, do not set DECNOINT */\r
+ #define int ? /* enable to ensure that plain C 'int' */\r
+ #define long ?? /* .. or 'long' types are not used */\r
+ #endif\r
+\r
+ /* Shared lookup tables */\r
+ extern const uByte DECSTICKYTAB[10]; /* re-round digits if sticky */\r
+ extern const uInt DECPOWERS[10]; /* powers of ten table */\r
+ /* The following are included from decDPD.h */\r
+ extern const uShort DPD2BIN[1024]; /* DPD -> 0-999 */\r
+ extern const uShort BIN2DPD[1000]; /* 0-999 -> DPD */\r
+ extern const uInt DPD2BINK[1024]; /* DPD -> 0-999000 */\r
+ extern const uInt DPD2BINM[1024]; /* DPD -> 0-999000000 */\r
+ extern const uByte DPD2BCD8[4096]; /* DPD -> ddd + len */\r
+ extern const uByte BIN2BCD8[4000]; /* 0-999 -> ddd + len */\r
+ extern const uShort BCD2DPD[2458]; /* 0-0x999 -> DPD (0x999=2457)*/\r
+\r
+ /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts */\r
+ /* (that is, sets w to be the high-order word of the 64-bit result; */\r
+ /* the low-order word is simply u*v.) */\r
+ /* This version is derived from Knuth via Hacker's Delight; */\r
+ /* it seems to optimize better than some others tried */\r
+ #define LONGMUL32HI(w, u, v) { \\r
+ uInt u0, u1, v0, v1, w0, w1, w2, t; \\r
+ u0=u & 0xffff; u1=u>>16; \\r
+ v0=v & 0xffff; v1=v>>16; \\r
+ w0=u0*v0; \\r
+ t=u1*v0 + (w0>>16); \\r
+ w1=t & 0xffff; w2=t>>16; \\r
+ w1=u0*v1 + w1; \\r
+ (w)=u1*v1 + w2 + (w1>>16);}\r
+\r
+ /* ROUNDUP -- round an integer up to a multiple of n */\r
+ #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n)\r
+ #define ROUNDUP4(i) (((i)+3)&~3) /* special for n=4 */\r
+\r
+ /* ROUNDDOWN -- round an integer down to a multiple of n */\r
+ #define ROUNDDOWN(i, n) (((i)/n)*n)\r
+ #define ROUNDDOWN4(i) ((i)&~3) /* special for n=4 */\r
+\r
+ /* References to multi-byte sequences under different sizes; these */\r
+ /* require locally declared variables, but do not violate strict */\r
+ /* aliasing or alignment (as did the UINTAT simple cast to uInt). */\r
+ /* Variables needed are uswork, uiwork, etc. [so do not use at same */\r
+ /* level in an expression, e.g., UBTOUI(x)==UBTOUI(y) may fail]. */\r
+\r
+ /* Return a uInt, etc., from bytes starting at a char* or uByte* */\r
+ #define UBTOUS(b) (memcpy((void *)&uswork, b, 2), uswork)\r
+ #define UBTOUI(b) (memcpy((void *)&uiwork, b, 4), uiwork)\r
+\r
+ /* Store a uInt, etc., into bytes starting at a char* or uByte*. */\r
+ /* Returns i, evaluated, for convenience; has to use uiwork because */\r
+ /* i may be an expression. */\r
+ #define UBFROMUS(b, i) (uswork=(i), memcpy(b, (void *)&uswork, 2), uswork)\r
+ #define UBFROMUI(b, i) (uiwork=(i), memcpy(b, (void *)&uiwork, 4), uiwork)\r
+\r
+ /* X10 and X100 -- multiply integer i by 10 or 100 */\r
+ /* [shifts are usually faster than multiply; could be conditional] */\r
+ #define X10(i) (((i)<<1)+((i)<<3))\r
+ #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6))\r
+\r
+ /* MAXI and MINI -- general max & min (not in ANSI) for integers */\r
+ #define MAXI(x,y) ((x)<(y)?(y):(x))\r
+ #define MINI(x,y) ((x)>(y)?(y):(x))\r
+\r
+ /* Useful constants */\r
+ #define BILLION 1000000000 /* 10**9 */\r
+ /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC */\r
+ #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0')\r
+\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Definitions for arbitary-precision modules (only valid after */\r
+ /* decNumber.h has been included) */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* Limits and constants */\r
+ #define DECNUMMAXP 999999999 /* maximum precision code can handle */\r
+ #define DECNUMMAXE 999999999 /* maximum adjusted exponent ditto */\r
+ #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto */\r
+ #if (DECNUMMAXP != DEC_MAX_DIGITS)\r
+ #error Maximum digits mismatch\r
+ #endif\r
+ #if (DECNUMMAXE != DEC_MAX_EMAX)\r
+ #error Maximum exponent mismatch\r
+ #endif\r
+ #if (DECNUMMINE != DEC_MIN_EMIN)\r
+ #error Minimum exponent mismatch\r
+ #endif\r
+\r
+ /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN */\r
+ /* digits, and D2UTABLE -- the initializer for the D2U table */\r
+ #if DECDPUN==1\r
+ #define DECDPUNMAX 9\r
+ #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \\r
+ 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \\r
+ 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \\r
+ 48,49}\r
+ #elif DECDPUN==2\r
+ #define DECDPUNMAX 99\r
+ #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10, \\r
+ 11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \\r
+ 18,19,19,20,20,21,21,22,22,23,23,24,24,25}\r
+ #elif DECDPUN==3\r
+ #define DECDPUNMAX 999\r
+ #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7, \\r
+ 8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \\r
+ 13,14,14,14,15,15,15,16,16,16,17}\r
+ #elif DECDPUN==4\r
+ #define DECDPUNMAX 9999\r
+ #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6, \\r
+ 6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \\r
+ 11,11,11,12,12,12,12,13}\r
+ #elif DECDPUN==5\r
+ #define DECDPUNMAX 99999\r
+ #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5, \\r
+ 5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9, \\r
+ 9,9,10,10,10,10}\r
+ #elif DECDPUN==6\r
+ #define DECDPUNMAX 999999\r
+ #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4, \\r
+ 4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8, \\r
+ 8,8,8,8,8,9}\r
+ #elif DECDPUN==7\r
+ #define DECDPUNMAX 9999999\r
+ #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3, \\r
+ 4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7, \\r
+ 7,7,7,7,7,7}\r
+ #elif DECDPUN==8\r
+ #define DECDPUNMAX 99999999\r
+ #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3, \\r
+ 3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6, \\r
+ 6,6,6,6,6,7}\r
+ #elif DECDPUN==9\r
+ #define DECDPUNMAX 999999999\r
+ #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3, \\r
+ 3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5, \\r
+ 5,5,6,6,6,6}\r
+ #elif defined(DECDPUN)\r
+ #error DECDPUN must be in the range 1-9\r
+ #endif\r
+\r
+ /* ----- Shared data (in decNumber.c) ----- */\r
+ /* Public lookup table used by the D2U macro (see below) */\r
+ #define DECMAXD2U 49\r
+ extern const uByte d2utable[DECMAXD2U+1];\r
+\r
+ /* ----- Macros ----- */\r
+ /* ISZERO -- return true if decNumber dn is a zero */\r
+ /* [performance-critical in some situations] */\r
+ #define ISZERO(dn) decNumberIsZero(dn) /* now just a local name */\r
+\r
+ /* D2U -- return the number of Units needed to hold d digits */\r
+ /* (runtime version, with table lookaside for small d) */\r
+ #if DECDPUN==8\r
+ #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3))\r
+ #elif DECDPUN==4\r
+ #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2))\r
+ #else\r
+ #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN)\r
+ #endif\r
+ /* SD2U -- static D2U macro (for compile-time calculation) */\r
+ #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN)\r
+\r
+ /* MSUDIGITS -- returns digits in msu, from digits, calculated */\r
+ /* using D2U */\r
+ #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN)\r
+\r
+ /* D2N -- return the number of decNumber structs that would be */\r
+ /* needed to contain that number of digits (and the initial */\r
+ /* decNumber struct) safely. Note that one Unit is included in the */\r
+ /* initial structure. Used for allocating space that is aligned on */\r
+ /* a decNumber struct boundary. */\r
+ #define D2N(d) \\r
+ ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber))\r
+\r
+ /* TODIGIT -- macro to remove the leading digit from the unsigned */\r
+ /* integer u at column cut (counting from the right, LSD=0) and */\r
+ /* place it as an ASCII character into the character pointed to by */\r
+ /* c. Note that cut must be <= 9, and the maximum value for u is */\r
+ /* 2,000,000,000 (as is needed for negative exponents of */\r
+ /* subnormals). The unsigned integer pow is used as a temporary */\r
+ /* variable. */\r
+ #define TODIGIT(u, cut, c, pow) { \\r
+ *(c)='0'; \\r
+ pow=DECPOWERS[cut]*2; \\r
+ if ((u)>pow) { \\r
+ pow*=4; \\r
+ if ((u)>=pow) {(u)-=pow; *(c)+=8;} \\r
+ pow/=2; \\r
+ if ((u)>=pow) {(u)-=pow; *(c)+=4;} \\r
+ pow/=2; \\r
+ } \\r
+ if ((u)>=pow) {(u)-=pow; *(c)+=2;} \\r
+ pow/=2; \\r
+ if ((u)>=pow) {(u)-=pow; *(c)+=1;} \\r
+ }\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Definitions for fixed-precision modules (only valid after */\r
+ /* decSingle.h, decDouble.h, or decQuad.h has been included) */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* bcdnum -- a structure describing a format-independent finite */\r
+ /* number, whose coefficient is a string of bcd8 uBytes */\r
+ typedef struct {\r
+ uByte *msd; /* -> most significant digit */\r
+ uByte *lsd; /* -> least ditto */\r
+ uInt sign; /* 0=positive, DECFLOAT_Sign=negative */\r
+ Int exponent; /* Unadjusted signed exponent (q), or */\r
+ /* DECFLOAT_NaN etc. for a special */\r
+ } bcdnum;\r
+\r
+ /* Test if exponent or bcdnum exponent must be a special, etc. */\r
+ #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp)\r
+ #define EXPISINF(exp) (exp==DECFLOAT_Inf)\r
+ #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN)\r
+ #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent))\r
+\r
+ /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian */\r
+ /* (array) notation (the 0 word or byte contains the sign bit), */\r
+ /* automatically adjusting for endianness; similarly address a word */\r
+ /* in the next-wider format (decFloatWider, or dfw) */\r
+ #define DECWORDS (DECBYTES/4)\r
+ #define DECWWORDS (DECWBYTES/4)\r
+ #if DECLITEND\r
+ #define DFBYTE(df, off) ((df)->bytes[DECBYTES-1-(off)])\r
+ #define DFWORD(df, off) ((df)->words[DECWORDS-1-(off)])\r
+ #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)])\r
+ #else\r
+ #define DFBYTE(df, off) ((df)->bytes[off])\r
+ #define DFWORD(df, off) ((df)->words[off])\r
+ #define DFWWORD(dfw, off) ((dfw)->words[off])\r
+ #endif\r
+\r
+ /* Tests for sign or specials, directly on DECFLOATs */\r
+ #define DFISSIGNED(df) ((DFWORD(df, 0)&0x80000000)!=0)\r
+ #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000)\r
+ #define DFISINF(df) ((DFWORD(df, 0)&0x7c000000)==0x78000000)\r
+ #define DFISNAN(df) ((DFWORD(df, 0)&0x7c000000)==0x7c000000)\r
+ #define DFISQNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7c000000)\r
+ #define DFISSNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7e000000)\r
+\r
+ /* Shared lookup tables */\r
+ extern const uInt DECCOMBMSD[64]; /* Combination field -> MSD */\r
+ extern const uInt DECCOMBFROM[48]; /* exp+msd -> Combination */\r
+\r
+ /* Private generic (utility) routine */\r
+ #if DECCHECK || DECTRACE\r
+ extern void decShowNum(const bcdnum *, const char *);\r
+ #endif\r
+\r
+ /* Format-dependent macros and constants */\r
+ #if defined(DECPMAX)\r
+\r
+ /* Useful constants */\r
+ #define DECPMAX9 (ROUNDUP(DECPMAX, 9)/9) /* 'Pmax' in 10**9s */\r
+ /* Top words for a zero */\r
+ #define SINGLEZERO 0x22500000\r
+ #define DOUBLEZERO 0x22380000\r
+ #define QUADZERO 0x22080000\r
+ /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */\r
+\r
+ /* Format-dependent common tests: */\r
+ /* DFISZERO -- test for (any) zero */\r
+ /* DFISCCZERO -- test for coefficient continuation being zero */\r
+ /* DFISCC01 -- test for coefficient contains only 0s and 1s */\r
+ /* DFISINT -- test for finite and exponent q=0 */\r
+ /* DFISUINT01 -- test for sign=0, finite, exponent q=0, and */\r
+ /* MSD=0 or 1 */\r
+ /* ZEROWORD is also defined here. */\r
+ /* */\r
+ /* In DFISZERO the first test checks the least-significant word */\r
+ /* (most likely to be non-zero); the penultimate tests MSD and */\r
+ /* DPDs in the signword, and the final test excludes specials and */\r
+ /* MSD>7. DFISINT similarly has to allow for the two forms of */\r
+ /* MSD codes. DFISUINT01 only has to allow for one form of MSD */\r
+ /* code. */\r
+ #if DECPMAX==7\r
+ #define ZEROWORD SINGLEZERO\r
+ /* [test macros not needed except for Zero] */\r
+ #define DFISZERO(df) ((DFWORD(df, 0)&0x1c0fffff)==0 \\r
+ && (DFWORD(df, 0)&0x60000000)!=0x60000000)\r
+ #elif DECPMAX==16\r
+ #define ZEROWORD DOUBLEZERO\r
+ #define DFISZERO(df) ((DFWORD(df, 1)==0 \\r
+ && (DFWORD(df, 0)&0x1c03ffff)==0 \\r
+ && (DFWORD(df, 0)&0x60000000)!=0x60000000))\r
+ #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000 \\r
+ ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000)\r
+ #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000)\r
+ #define DFISCCZERO(df) (DFWORD(df, 1)==0 \\r
+ && (DFWORD(df, 0)&0x0003ffff)==0)\r
+ #define DFISCC01(df) ((DFWORD(df, 0)&~0xfffc9124)==0 \\r
+ && (DFWORD(df, 1)&~0x49124491)==0)\r
+ #elif DECPMAX==34\r
+ #define ZEROWORD QUADZERO\r
+ #define DFISZERO(df) ((DFWORD(df, 3)==0 \\r
+ && DFWORD(df, 2)==0 \\r
+ && DFWORD(df, 1)==0 \\r
+ && (DFWORD(df, 0)&0x1c003fff)==0 \\r
+ && (DFWORD(df, 0)&0x60000000)!=0x60000000))\r
+ #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000 \\r
+ ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000)\r
+ #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000)\r
+ #define DFISCCZERO(df) (DFWORD(df, 3)==0 \\r
+ && DFWORD(df, 2)==0 \\r
+ && DFWORD(df, 1)==0 \\r
+ && (DFWORD(df, 0)&0x00003fff)==0)\r
+\r
+ #define DFISCC01(df) ((DFWORD(df, 0)&~0xffffc912)==0 \\r
+ && (DFWORD(df, 1)&~0x44912449)==0 \\r
+ && (DFWORD(df, 2)&~0x12449124)==0 \\r
+ && (DFWORD(df, 3)&~0x49124491)==0)\r
+ #endif\r
+\r
+ /* Macros to test if a certain 10 bits of a uInt or pair of uInts */\r
+ /* are a canonical declet [higher or lower bits are ignored]. */\r
+ /* declet is at offset 0 (from the right) in a uInt: */\r
+ #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e)\r
+ /* declet is at offset k (a multiple of 2) in a uInt: */\r
+ #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0 \\r
+ || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))\r
+ /* declet is at offset k (a multiple of 2) in a pair of uInts: */\r
+ /* [the top 2 bits will always be in the more-significant uInt] */\r
+ #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0 \\r
+ || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k))) \\r
+ || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k)))\r
+\r
+ /* Macro to test whether a full-length (length DECPMAX) BCD8 */\r
+ /* coefficient, starting at uByte u, is all zeros */\r
+ /* Test just the LSWord first, then the remainder as a sequence */\r
+ /* of tests in order to avoid same-level use of UBTOUI */\r
+ #if DECPMAX==7\r
+ #define ISCOEFFZERO(u) ( \\r
+ UBTOUI((u)+DECPMAX-4)==0 \\r
+ && UBTOUS((u)+DECPMAX-6)==0 \\r
+ && *(u)==0)\r
+ #elif DECPMAX==16\r
+ #define ISCOEFFZERO(u) ( \\r
+ UBTOUI((u)+DECPMAX-4)==0 \\r
+ && UBTOUI((u)+DECPMAX-8)==0 \\r
+ && UBTOUI((u)+DECPMAX-12)==0 \\r
+ && UBTOUI(u)==0)\r
+ #elif DECPMAX==34\r
+ #define ISCOEFFZERO(u) ( \\r
+ UBTOUI((u)+DECPMAX-4)==0 \\r
+ && UBTOUI((u)+DECPMAX-8)==0 \\r
+ && UBTOUI((u)+DECPMAX-12)==0 \\r
+ && UBTOUI((u)+DECPMAX-16)==0 \\r
+ && UBTOUI((u)+DECPMAX-20)==0 \\r
+ && UBTOUI((u)+DECPMAX-24)==0 \\r
+ && UBTOUI((u)+DECPMAX-28)==0 \\r
+ && UBTOUI((u)+DECPMAX-32)==0 \\r
+ && UBTOUS(u)==0)\r
+ #endif\r
+\r
+ /* Macros and masks for the sign, exponent continuation, and MSD */\r
+ /* Get the sign as DECFLOAT_Sign or 0 */\r
+ #define GETSIGN(df) (DFWORD(df, 0)&0x80000000)\r
+ /* Get the exponent continuation from a decFloat *df as an Int */\r
+ #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL)))\r
+ /* Ditto, from the next-wider format */\r
+ #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL)))\r
+ /* Get the biased exponent similarly */\r
+ #define GETEXP(df) ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df)))\r
+ /* Get the unbiased exponent similarly */\r
+ #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS)\r
+ /* Get the MSD similarly (as uInt) */\r
+ #define GETMSD(df) (DECCOMBMSD[DFWORD((df), 0)>>26])\r
+\r
+ /* Compile-time computes of the exponent continuation field masks */\r
+ /* full exponent continuation field: */\r
+ #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))\r
+ /* same, not including its first digit (the qNaN/sNaN selector): */\r
+ #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL))\r
+\r
+ /* Macros to decode the coefficient in a finite decFloat *df into */\r
+ /* a BCD string (uByte *bcdin) of length DECPMAX uBytes. */\r
+\r
+ /* In-line sequence to convert least significant 10 bits of uInt */\r
+ /* dpd to three BCD8 digits starting at uByte u. Note that an */\r
+ /* extra byte is written to the right of the three digits because */\r
+ /* four bytes are moved at a time for speed; the alternative */\r
+ /* macro moves exactly three bytes (usually slower). */\r
+ #define dpd2bcd8(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4)\r
+ #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3)\r
+\r
+ /* Decode the declets. After extracting each one, it is decoded */\r
+ /* to BCD8 using a table lookup (also used for variable-length */\r
+ /* decode). Each DPD decode is 3 bytes BCD8 plus a one-byte */\r
+ /* length which is not used, here). Fixed-length 4-byte moves */\r
+ /* are fast, however, almost everywhere, and so are used except */\r
+ /* for the final three bytes (to avoid overrun). The code below */\r
+ /* is 36 instructions for Doubles and about 70 for Quads, even */\r
+ /* on IA32. */\r
+\r
+ /* Two macros are defined for each format: */\r
+ /* GETCOEFF extracts the coefficient of the current format */\r
+ /* GETWCOEFF extracts the coefficient of the next-wider format. */\r
+ /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */\r
+\r
+ #if DECPMAX==7\r
+ #define GETCOEFF(df, bcd) { \\r
+ uInt sourhi=DFWORD(df, 0); \\r
+ *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \\r
+ dpd2bcd8(bcd+1, sourhi>>10); \\r
+ dpd2bcd83(bcd+4, sourhi);}\r
+ #define GETWCOEFF(df, bcd) { \\r
+ uInt sourhi=DFWWORD(df, 0); \\r
+ uInt sourlo=DFWWORD(df, 1); \\r
+ *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \\r
+ dpd2bcd8(bcd+1, sourhi>>8); \\r
+ dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \\r
+ dpd2bcd8(bcd+7, sourlo>>20); \\r
+ dpd2bcd8(bcd+10, sourlo>>10); \\r
+ dpd2bcd83(bcd+13, sourlo);}\r
+\r
+ #elif DECPMAX==16\r
+ #define GETCOEFF(df, bcd) { \\r
+ uInt sourhi=DFWORD(df, 0); \\r
+ uInt sourlo=DFWORD(df, 1); \\r
+ *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \\r
+ dpd2bcd8(bcd+1, sourhi>>8); \\r
+ dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \\r
+ dpd2bcd8(bcd+7, sourlo>>20); \\r
+ dpd2bcd8(bcd+10, sourlo>>10); \\r
+ dpd2bcd83(bcd+13, sourlo);}\r
+ #define GETWCOEFF(df, bcd) { \\r
+ uInt sourhi=DFWWORD(df, 0); \\r
+ uInt sourmh=DFWWORD(df, 1); \\r
+ uInt sourml=DFWWORD(df, 2); \\r
+ uInt sourlo=DFWWORD(df, 3); \\r
+ *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \\r
+ dpd2bcd8(bcd+1, sourhi>>4); \\r
+ dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \\r
+ dpd2bcd8(bcd+7, sourmh>>16); \\r
+ dpd2bcd8(bcd+10, sourmh>>6); \\r
+ dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \\r
+ dpd2bcd8(bcd+16, sourml>>18); \\r
+ dpd2bcd8(bcd+19, sourml>>8); \\r
+ dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \\r
+ dpd2bcd8(bcd+25, sourlo>>20); \\r
+ dpd2bcd8(bcd+28, sourlo>>10); \\r
+ dpd2bcd83(bcd+31, sourlo);}\r
+\r
+ #elif DECPMAX==34\r
+ #define GETCOEFF(df, bcd) { \\r
+ uInt sourhi=DFWORD(df, 0); \\r
+ uInt sourmh=DFWORD(df, 1); \\r
+ uInt sourml=DFWORD(df, 2); \\r
+ uInt sourlo=DFWORD(df, 3); \\r
+ *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \\r
+ dpd2bcd8(bcd+1, sourhi>>4); \\r
+ dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \\r
+ dpd2bcd8(bcd+7, sourmh>>16); \\r
+ dpd2bcd8(bcd+10, sourmh>>6); \\r
+ dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \\r
+ dpd2bcd8(bcd+16, sourml>>18); \\r
+ dpd2bcd8(bcd+19, sourml>>8); \\r
+ dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \\r
+ dpd2bcd8(bcd+25, sourlo>>20); \\r
+ dpd2bcd8(bcd+28, sourlo>>10); \\r
+ dpd2bcd83(bcd+31, sourlo);}\r
+\r
+ #define GETWCOEFF(df, bcd) {??} /* [should never be used] */\r
+ #endif\r
+\r
+ /* Macros to decode the coefficient in a finite decFloat *df into */\r
+ /* a base-billion uInt array, with the least-significant */\r
+ /* 0-999999999 'digit' at offset 0. */\r
+\r
+ /* Decode the declets. After extracting each one, it is decoded */\r
+ /* to binary using a table lookup. Three tables are used; one */\r
+ /* the usual DPD to binary, the other two pre-multiplied by 1000 */\r
+ /* and 1000000 to avoid multiplication during decode. These */\r
+ /* tables can also be used for multiplying up the MSD as the DPD */\r
+ /* code for 0 through 9 is the identity. */\r
+ #define DPD2BIN0 DPD2BIN /* for prettier code */\r
+\r
+ #if DECPMAX==7\r
+ #define GETCOEFFBILL(df, buf) { \\r
+ uInt sourhi=DFWORD(df, 0); \\r
+ (buf)[0]=DPD2BIN0[sourhi&0x3ff] \\r
+ +DPD2BINK[(sourhi>>10)&0x3ff] \\r
+ +DPD2BINM[DECCOMBMSD[sourhi>>26]];}\r
+\r
+ #elif DECPMAX==16\r
+ #define GETCOEFFBILL(df, buf) { \\r
+ uInt sourhi, sourlo; \\r
+ sourlo=DFWORD(df, 1); \\r
+ (buf)[0]=DPD2BIN0[sourlo&0x3ff] \\r
+ +DPD2BINK[(sourlo>>10)&0x3ff] \\r
+ +DPD2BINM[(sourlo>>20)&0x3ff]; \\r
+ sourhi=DFWORD(df, 0); \\r
+ (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff] \\r
+ +DPD2BINK[(sourhi>>8)&0x3ff] \\r
+ +DPD2BINM[DECCOMBMSD[sourhi>>26]];}\r
+\r
+ #elif DECPMAX==34\r
+ #define GETCOEFFBILL(df, buf) { \\r
+ uInt sourhi, sourmh, sourml, sourlo; \\r
+ sourlo=DFWORD(df, 3); \\r
+ (buf)[0]=DPD2BIN0[sourlo&0x3ff] \\r
+ +DPD2BINK[(sourlo>>10)&0x3ff] \\r
+ +DPD2BINM[(sourlo>>20)&0x3ff]; \\r
+ sourml=DFWORD(df, 2); \\r
+ (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff] \\r
+ +DPD2BINK[(sourml>>8)&0x3ff] \\r
+ +DPD2BINM[(sourml>>18)&0x3ff]; \\r
+ sourmh=DFWORD(df, 1); \\r
+ (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff] \\r
+ +DPD2BINK[(sourmh>>6)&0x3ff] \\r
+ +DPD2BINM[(sourmh>>16)&0x3ff]; \\r
+ sourhi=DFWORD(df, 0); \\r
+ (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff] \\r
+ +DPD2BINK[(sourhi>>4)&0x3ff] \\r
+ +DPD2BINM[DECCOMBMSD[sourhi>>26]];}\r
+\r
+ #endif\r
+\r
+ /* Macros to decode the coefficient in a finite decFloat *df into */\r
+ /* a base-thousand uInt array (of size DECLETS+1, to allow for */\r
+ /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/\r
+\r
+ /* Decode the declets. After extracting each one, it is decoded */\r
+ /* to binary using a table lookup. */\r
+ #if DECPMAX==7\r
+ #define GETCOEFFTHOU(df, buf) { \\r
+ uInt sourhi=DFWORD(df, 0); \\r
+ (buf)[0]=DPD2BIN[sourhi&0x3ff]; \\r
+ (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff]; \\r
+ (buf)[2]=DECCOMBMSD[sourhi>>26];}\r
+\r
+ #elif DECPMAX==16\r
+ #define GETCOEFFTHOU(df, buf) { \\r
+ uInt sourhi, sourlo; \\r
+ sourlo=DFWORD(df, 1); \\r
+ (buf)[0]=DPD2BIN[sourlo&0x3ff]; \\r
+ (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \\r
+ (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \\r
+ sourhi=DFWORD(df, 0); \\r
+ (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \\r
+ (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff]; \\r
+ (buf)[5]=DECCOMBMSD[sourhi>>26];}\r
+\r
+ #elif DECPMAX==34\r
+ #define GETCOEFFTHOU(df, buf) { \\r
+ uInt sourhi, sourmh, sourml, sourlo; \\r
+ sourlo=DFWORD(df, 3); \\r
+ (buf)[0]=DPD2BIN[sourlo&0x3ff]; \\r
+ (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \\r
+ (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \\r
+ sourml=DFWORD(df, 2); \\r
+ (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \\r
+ (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff]; \\r
+ (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff]; \\r
+ sourmh=DFWORD(df, 1); \\r
+ (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \\r
+ (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff]; \\r
+ (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff]; \\r
+ sourhi=DFWORD(df, 0); \\r
+ (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \\r
+ (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff]; \\r
+ (buf)[11]=DECCOMBMSD[sourhi>>26];}\r
+ #endif\r
+\r
+\r
+ /* Macros to decode the coefficient in a finite decFloat *df and */\r
+ /* add to a base-thousand uInt array (as for GETCOEFFTHOU). */\r
+ /* After the addition then most significant 'digit' in the array */\r
+ /* might have a value larger then 10 (with a maximum of 19). */\r
+ #if DECPMAX==7\r
+ #define ADDCOEFFTHOU(df, buf) { \\r
+ uInt sourhi=DFWORD(df, 0); \\r
+ (buf)[0]+=DPD2BIN[sourhi&0x3ff]; \\r
+ if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \\r
+ (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff]; \\r
+ if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \\r
+ (buf)[2]+=DECCOMBMSD[sourhi>>26];}\r
+\r
+ #elif DECPMAX==16\r
+ #define ADDCOEFFTHOU(df, buf) { \\r
+ uInt sourhi, sourlo; \\r
+ sourlo=DFWORD(df, 1); \\r
+ (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \\r
+ if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \\r
+ (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \\r
+ if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \\r
+ (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \\r
+ if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \\r
+ sourhi=DFWORD(df, 0); \\r
+ (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \\r
+ if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \\r
+ (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff]; \\r
+ if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \\r
+ (buf)[5]+=DECCOMBMSD[sourhi>>26];}\r
+\r
+ #elif DECPMAX==34\r
+ #define ADDCOEFFTHOU(df, buf) { \\r
+ uInt sourhi, sourmh, sourml, sourlo; \\r
+ sourlo=DFWORD(df, 3); \\r
+ (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \\r
+ if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \\r
+ (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \\r
+ if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \\r
+ (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \\r
+ if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \\r
+ sourml=DFWORD(df, 2); \\r
+ (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \\r
+ if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \\r
+ (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff]; \\r
+ if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \\r
+ (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff]; \\r
+ if (buf[5]>999) {buf[5]-=1000; buf[6]++;} \\r
+ sourmh=DFWORD(df, 1); \\r
+ (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \\r
+ if (buf[6]>999) {buf[6]-=1000; buf[7]++;} \\r
+ (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff]; \\r
+ if (buf[7]>999) {buf[7]-=1000; buf[8]++;} \\r
+ (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff]; \\r
+ if (buf[8]>999) {buf[8]-=1000; buf[9]++;} \\r
+ sourhi=DFWORD(df, 0); \\r
+ (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \\r
+ if (buf[9]>999) {buf[9]-=1000; buf[10]++;} \\r
+ (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff]; \\r
+ if (buf[10]>999) {buf[10]-=1000; buf[11]++;} \\r
+ (buf)[11]+=DECCOMBMSD[sourhi>>26];}\r
+ #endif\r
+\r
+\r
+ /* Set a decFloat to the maximum positive finite number (Nmax) */\r
+ #if DECPMAX==7\r
+ #define DFSETNMAX(df) \\r
+ {DFWORD(df, 0)=0x77f3fcff;}\r
+ #elif DECPMAX==16\r
+ #define DFSETNMAX(df) \\r
+ {DFWORD(df, 0)=0x77fcff3f; \\r
+ DFWORD(df, 1)=0xcff3fcff;}\r
+ #elif DECPMAX==34\r
+ #define DFSETNMAX(df) \\r
+ {DFWORD(df, 0)=0x77ffcff3; \\r
+ DFWORD(df, 1)=0xfcff3fcf; \\r
+ DFWORD(df, 2)=0xf3fcff3f; \\r
+ DFWORD(df, 3)=0xcff3fcff;}\r
+ #endif\r
+\r
+ /* [end of format-dependent macros and constants] */\r
+ #endif\r
+\r
+#else\r
+ #error decNumberLocal included more than once\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Packed Decimal conversion module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2002. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises the routines for Packed Decimal format */\r
+/* numbers. Conversions are supplied to and from decNumber, which in */\r
+/* turn supports: */\r
+/* conversions to and from string */\r
+/* arithmetic routines */\r
+/* utilities. */\r
+/* Conversions from decNumber to and from densely packed decimal */\r
+/* formats are provided by the decimal32 through decimal128 modules. */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#include <string.h> // for NULL\r
+#include "decNumber.h" // base number library\r
+#include "decPacked.h" // packed decimal\r
+#include "decNumberLocal.h" // decNumber local types, etc.\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decPackedFromNumber -- convert decNumber to BCD Packed Decimal */\r
+/* */\r
+/* bcd is the BCD bytes */\r
+/* length is the length of the BCD array */\r
+/* scale is the scale result */\r
+/* dn is the decNumber */\r
+/* returns bcd, or NULL if error */\r
+/* */\r
+/* The number is converted to a BCD packed decimal byte array, */\r
+/* right aligned in the bcd array, whose length is indicated by the */\r
+/* second parameter. The final 4-bit nibble in the array will be a */\r
+/* sign nibble, C (1100) for + and D (1101) for -. Unused bytes and */\r
+/* nibbles to the left of the number are set to 0. */\r
+/* */\r
+/* scale is set to the scale of the number (this is the exponent, */\r
+/* negated). To force the number to a specified scale, first use the */\r
+/* decNumberRescale routine, which will round and change the exponent */\r
+/* as necessary. */\r
+/* */\r
+/* If there is an error (that is, the decNumber has too many digits */\r
+/* to fit in length bytes, or it is a NaN or Infinity), NULL is */\r
+/* returned and the bcd and scale results are unchanged. Otherwise */\r
+/* bcd is returned. */\r
+/* ------------------------------------------------------------------ */\r
+uByte * decPackedFromNumber(uByte *bcd, Int length, Int *scale,\r
+ const decNumber *dn) {\r
+ const Unit *up=dn->lsu; // Unit array pointer\r
+ uByte obyte, *out; // current output byte, and where it goes\r
+ Int indigs=dn->digits; // digits processed\r
+ uInt cut=DECDPUN; // downcounter per Unit\r
+ uInt u=*up; // work\r
+ uInt nib; // ..\r
+ #if DECDPUN<=4\r
+ uInt temp; // ..\r
+ #endif\r
+\r
+ if (dn->digits>length*2-1 // too long ..\r
+ ||(dn->bits & DECSPECIAL)) return NULL; // .. or special -- hopeless\r
+\r
+ if (dn->bits&DECNEG) obyte=DECPMINUS; // set the sign ..\r
+ else obyte=DECPPLUS;\r
+ *scale=-dn->exponent; // .. and scale\r
+\r
+ // loop from lowest (rightmost) byte\r
+ out=bcd+length-1; // -> final byte\r
+ for (; out>=bcd; out--) {\r
+ if (indigs>0) {\r
+ if (cut==0) {\r
+ up++;\r
+ u=*up;\r
+ cut=DECDPUN;\r
+ }\r
+ #if DECDPUN<=4\r
+ temp=(u*6554)>>16; // fast /10\r
+ nib=u-X10(temp);\r
+ u=temp;\r
+ #else\r
+ nib=u%10; // cannot use *6554 trick :-(\r
+ u=u/10;\r
+ #endif\r
+ obyte|=(nib<<4);\r
+ indigs--;\r
+ cut--;\r
+ }\r
+ *out=obyte;\r
+ obyte=0; // assume 0\r
+ if (indigs>0) {\r
+ if (cut==0) {\r
+ up++;\r
+ u=*up;\r
+ cut=DECDPUN;\r
+ }\r
+ #if DECDPUN<=4\r
+ temp=(u*6554)>>16; // as above\r
+ obyte=(uByte)(u-X10(temp));\r
+ u=temp;\r
+ #else\r
+ obyte=(uByte)(u%10);\r
+ u=u/10;\r
+ #endif\r
+ indigs--;\r
+ cut--;\r
+ }\r
+ } // loop\r
+\r
+ return bcd;\r
+ } // decPackedFromNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decPackedToNumber -- convert BCD Packed Decimal to a decNumber */\r
+/* */\r
+/* bcd is the BCD bytes */\r
+/* length is the length of the BCD array */\r
+/* scale is the scale associated with the BCD integer */\r
+/* dn is the decNumber [with space for length*2 digits] */\r
+/* returns dn, or NULL if error */\r
+/* */\r
+/* The BCD packed decimal byte array, together with an associated */\r
+/* scale, is converted to a decNumber. The BCD array is assumed full */\r
+/* of digits, and must be ended by a 4-bit sign nibble in the least */\r
+/* significant four bits of the final byte. */\r
+/* */\r
+/* The scale is used (negated) as the exponent of the decNumber. */\r
+/* Note that zeros may have a sign and/or a scale. */\r
+/* */\r
+/* The decNumber structure is assumed to have sufficient space to */\r
+/* hold the converted number (that is, up to length*2-1 digits), so */\r
+/* no error is possible unless the adjusted exponent is out of range, */\r
+/* no sign nibble was found, or a sign nibble was found before the */\r
+/* final nibble. In these error cases, NULL is returned and the */\r
+/* decNumber will be 0. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decPackedToNumber(const uByte *bcd, Int length,\r
+ const Int *scale, decNumber *dn) {\r
+ const uByte *last=bcd+length-1; // -> last byte\r
+ const uByte *first; // -> first non-zero byte\r
+ uInt nib; // work nibble\r
+ Unit *up=dn->lsu; // output pointer\r
+ Int digits; // digits count\r
+ Int cut=0; // phase of output\r
+\r
+ decNumberZero(dn); // default result\r
+ last=&bcd[length-1];\r
+ nib=*last & 0x0f; // get the sign\r
+ if (nib==DECPMINUS || nib==DECPMINUSALT) dn->bits=DECNEG;\r
+ else if (nib<=9) return NULL; // not a sign nibble\r
+\r
+ // skip leading zero bytes [final byte is always non-zero, due to sign]\r
+ for (first=bcd; *first==0;) first++;\r
+ digits=(last-first)*2+1; // calculate digits ..\r
+ if ((*first & 0xf0)==0) digits--; // adjust for leading zero nibble\r
+ if (digits!=0) dn->digits=digits; // count of actual digits [if 0,\r
+ // leave as 1]\r
+\r
+ // check the adjusted exponent; note that scale could be unbounded\r
+ dn->exponent=-*scale; // set the exponent\r
+ if (*scale>=0) { // usual case\r
+ if ((dn->digits-*scale-1)<-DECNUMMAXE) { // underflow\r
+ decNumberZero(dn);\r
+ return NULL;}\r
+ }\r
+ else { // -ve scale; +ve exponent\r
+ // need to be careful to avoid wrap, here, also BADINT case\r
+ if ((*scale<-DECNUMMAXE) // overflow even without digits\r
+ || ((dn->digits-*scale-1)>DECNUMMAXE)) { // overflow\r
+ decNumberZero(dn);\r
+ return NULL;}\r
+ }\r
+ if (digits==0) return dn; // result was zero\r
+\r
+ // copy the digits to the number's units, starting at the lsu\r
+ // [unrolled]\r
+ for (;;) { // forever\r
+ // left nibble first\r
+ nib=(unsigned)(*last & 0xf0)>>4;\r
+ // got a digit, in nib\r
+ if (nib>9) {decNumberZero(dn); return NULL;}\r
+\r
+ if (cut==0) *up=(Unit)nib;\r
+ else *up=(Unit)(*up+nib*DECPOWERS[cut]);\r
+ digits--;\r
+ if (digits==0) break; // got them all\r
+ cut++;\r
+ if (cut==DECDPUN) {\r
+ up++;\r
+ cut=0;\r
+ }\r
+ last--; // ready for next\r
+ nib=*last & 0x0f; // get right nibble\r
+ if (nib>9) {decNumberZero(dn); return NULL;}\r
+\r
+ // got a digit, in nib\r
+ if (cut==0) *up=(Unit)nib;\r
+ else *up=(Unit)(*up+nib*DECPOWERS[cut]);\r
+ digits--;\r
+ if (digits==0) break; // got them all\r
+ cut++;\r
+ if (cut==DECDPUN) {\r
+ up++;\r
+ cut=0;\r
+ }\r
+ } // forever\r
+\r
+ return dn;\r
+ } // decPackedToNumber\r
+\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Packed Decimal conversion module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2005. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECPACKED)\r
+ #define DECPACKED\r
+ #define DECPNAME "decPacked" /* Short name */\r
+ #define DECPFULLNAME "Packed Decimal conversions" /* Verbose name */\r
+ #define DECPAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ #define DECPACKED_DefP 32 /* default precision */\r
+\r
+ #ifndef DECNUMDIGITS\r
+ #define DECNUMDIGITS DECPACKED_DefP /* size if not already defined*/\r
+ #endif\r
+ #include "decNumber.h" /* context and number library */\r
+\r
+ /* Sign nibble constants */\r
+ #if !defined(DECPPLUSALT)\r
+ #define DECPPLUSALT 0x0A /* alternate plus nibble */\r
+ #define DECPMINUSALT 0x0B /* alternate minus nibble */\r
+ #define DECPPLUS 0x0C /* preferred plus nibble */\r
+ #define DECPMINUS 0x0D /* preferred minus nibble */\r
+ #define DECPPLUSALT2 0x0E /* alternate plus nibble */\r
+ #define DECPUNSIGNED 0x0F /* alternate plus nibble (unsigned) */\r
+ #endif\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* decPacked public routines */\r
+ /* ---------------------------------------------------------------- */\r
+ /* Conversions */\r
+ uint8_t * decPackedFromNumber(uint8_t *, int32_t, int32_t *,\r
+ const decNumber *);\r
+ decNumber * decPackedToNumber(const uint8_t *, int32_t, const int32_t *,\r
+ decNumber *);\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decQuad.c -- decQuad operations module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises decQuad operations (including conversions) */\r
+/* ------------------------------------------------------------------ */\r
+\r
+\r
+/* Constant mappings for shared code */\r
+#define DECPMAX DECQUAD_Pmax\r
+#define DECEMIN DECQUAD_Emin\r
+#define DECEMAX DECQUAD_Emax\r
+#define DECEMAXD DECQUAD_EmaxD\r
+#define DECBYTES DECQUAD_Bytes\r
+#define DECSTRING DECQUAD_String\r
+#define DECECONL DECQUAD_EconL\r
+#define DECBIAS DECQUAD_Bias\r
+#define DECLETS DECQUAD_Declets\r
+#define DECQTINY (-DECQUAD_Bias)\r
+\r
+/* Type and function mappings for shared code */\r
+#define decFloat decQuad // Type name\r
+\r
+// Utilities and conversions (binary results, extractors, etc.)\r
+#define decFloatFromBCD decQuadFromBCD\r
+#define decFloatFromInt32 decQuadFromInt32\r
+#define decFloatFromPacked decQuadFromPacked\r
+#define decFloatFromPackedChecked decQuadFromPackedChecked\r
+#define decFloatFromString decQuadFromString\r
+#define decFloatFromUInt32 decQuadFromUInt32\r
+#define decFloatFromWider decQuadFromWider\r
+#define decFloatGetCoefficient decQuadGetCoefficient\r
+#define decFloatGetExponent decQuadGetExponent\r
+#define decFloatSetCoefficient decQuadSetCoefficient\r
+#define decFloatSetExponent decQuadSetExponent\r
+#define decFloatShow decQuadShow\r
+#define decFloatToBCD decQuadToBCD\r
+#define decFloatToEngString decQuadToEngString\r
+#define decFloatToInt32 decQuadToInt32\r
+#define decFloatToInt32Exact decQuadToInt32Exact\r
+#define decFloatToPacked decQuadToPacked\r
+#define decFloatToString decQuadToString\r
+#define decFloatToUInt32 decQuadToUInt32\r
+#define decFloatToUInt32Exact decQuadToUInt32Exact\r
+#define decFloatToWider decQuadToWider\r
+#define decFloatZero decQuadZero\r
+\r
+// Computational (result is a decFloat)\r
+#define decFloatAbs decQuadAbs\r
+#define decFloatAdd decQuadAdd\r
+#define decFloatAnd decQuadAnd\r
+#define decFloatDivide decQuadDivide\r
+#define decFloatDivideInteger decQuadDivideInteger\r
+#define decFloatFMA decQuadFMA\r
+#define decFloatInvert decQuadInvert\r
+#define decFloatLogB decQuadLogB\r
+#define decFloatMax decQuadMax\r
+#define decFloatMaxMag decQuadMaxMag\r
+#define decFloatMin decQuadMin\r
+#define decFloatMinMag decQuadMinMag\r
+#define decFloatMinus decQuadMinus\r
+#define decFloatMultiply decQuadMultiply\r
+#define decFloatNextMinus decQuadNextMinus\r
+#define decFloatNextPlus decQuadNextPlus\r
+#define decFloatNextToward decQuadNextToward\r
+#define decFloatOr decQuadOr\r
+#define decFloatPlus decQuadPlus\r
+#define decFloatQuantize decQuadQuantize\r
+#define decFloatReduce decQuadReduce\r
+#define decFloatRemainder decQuadRemainder\r
+#define decFloatRemainderNear decQuadRemainderNear\r
+#define decFloatRotate decQuadRotate\r
+#define decFloatScaleB decQuadScaleB\r
+#define decFloatShift decQuadShift\r
+#define decFloatSubtract decQuadSubtract\r
+#define decFloatToIntegralValue decQuadToIntegralValue\r
+#define decFloatToIntegralExact decQuadToIntegralExact\r
+#define decFloatXor decQuadXor\r
+\r
+// Comparisons\r
+#define decFloatCompare decQuadCompare\r
+#define decFloatCompareSignal decQuadCompareSignal\r
+#define decFloatCompareTotal decQuadCompareTotal\r
+#define decFloatCompareTotalMag decQuadCompareTotalMag\r
+\r
+// Copies\r
+#define decFloatCanonical decQuadCanonical\r
+#define decFloatCopy decQuadCopy\r
+#define decFloatCopyAbs decQuadCopyAbs\r
+#define decFloatCopyNegate decQuadCopyNegate\r
+#define decFloatCopySign decQuadCopySign\r
+\r
+// Non-computational\r
+#define decFloatClass decQuadClass\r
+#define decFloatClassString decQuadClassString\r
+#define decFloatDigits decQuadDigits\r
+#define decFloatIsCanonical decQuadIsCanonical\r
+#define decFloatIsFinite decQuadIsFinite\r
+#define decFloatIsInfinite decQuadIsInfinite\r
+#define decFloatIsInteger decQuadIsInteger\r
+#define decFloatIsLogical decQuadIsLogical\r
+#define decFloatIsNaN decQuadIsNaN\r
+#define decFloatIsNegative decQuadIsNegative\r
+#define decFloatIsNormal decQuadIsNormal\r
+#define decFloatIsPositive decQuadIsPositive\r
+#define decFloatIsSignaling decQuadIsSignaling\r
+#define decFloatIsSignalling decQuadIsSignalling\r
+#define decFloatIsSigned decQuadIsSigned\r
+#define decFloatIsSubnormal decQuadIsSubnormal\r
+#define decFloatIsZero decQuadIsZero\r
+#define decFloatRadix decQuadRadix\r
+#define decFloatSameQuantum decQuadSameQuantum\r
+#define decFloatVersion decQuadVersion\r
+\r
+/* And now the code itself */\r
+#include "decContext.h" // public includes\r
+#include "decQuad.h" // ..\r
+#include "decNumberLocal.h" // local includes (need DECPMAX)\r
+#include "decCommon.c" // non-arithmetic decFloat routines\r
+#include "decBasic.c" // basic formats routines\r
+\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decQuad.h -- Decimal 128-bit format module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This include file is always included by decSingle and decDouble, */\r
+/* and therefore also holds useful constants used by all three. */\r
+\r
+#if !defined(DECQUAD)\r
+ #define DECQUAD\r
+\r
+ #define DECQUADNAME "decimalQuad" /* Short name */\r
+ #define DECQUADTITLE "Decimal 128-bit datum" /* Verbose name */\r
+ #define DECQUADAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ /* parameters for decQuads */\r
+ #define DECQUAD_Bytes 16 /* length */\r
+ #define DECQUAD_Pmax 34 /* maximum precision (digits) */\r
+ #define DECQUAD_Emin -6143 /* minimum adjusted exponent */\r
+ #define DECQUAD_Emax 6144 /* maximum adjusted exponent */\r
+ #define DECQUAD_EmaxD 4 /* maximum exponent digits */\r
+ #define DECQUAD_Bias 6176 /* bias for the exponent */\r
+ #define DECQUAD_String 43 /* maximum string length, +1 */\r
+ #define DECQUAD_EconL 12 /* exponent continuation length */\r
+ #define DECQUAD_Declets 11 /* count of declets */\r
+ /* highest biased exponent (Elimit-1) */\r
+ #define DECQUAD_Ehigh (DECQUAD_Emax + DECQUAD_Bias - (DECQUAD_Pmax-1))\r
+\r
+ /* Required include */\r
+ #include "decContext.h"\r
+\r
+ /* The decQuad decimal 128-bit type, accessible by all sizes */\r
+ typedef union {\r
+ uint8_t bytes[DECQUAD_Bytes]; /* fields: 1, 5, 12, 110 bits */\r
+ uint16_t shorts[DECQUAD_Bytes/2];\r
+ uint32_t words[DECQUAD_Bytes/4];\r
+ #if DECUSE64\r
+ uint64_t longs[DECQUAD_Bytes/8];\r
+ #endif\r
+ } decQuad;\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Shared constants */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* sign and special values [top 32-bits; last two bits are don't-care\r
+ for Infinity on input, last bit don't-care for NaNs] */\r
+ #define DECFLOAT_Sign 0x80000000 /* 1 00000 00 Sign */\r
+ #define DECFLOAT_NaN 0x7c000000 /* 0 11111 00 NaN generic */\r
+ #define DECFLOAT_qNaN 0x7c000000 /* 0 11111 00 qNaN */\r
+ #define DECFLOAT_sNaN 0x7e000000 /* 0 11111 10 sNaN */\r
+ #define DECFLOAT_Inf 0x78000000 /* 0 11110 00 Infinity */\r
+ #define DECFLOAT_MinSp 0x78000000 /* minimum special value */\r
+ /* [specials are all >=MinSp] */\r
+ /* Sign nibble constants */\r
+ #if !defined(DECPPLUSALT)\r
+ #define DECPPLUSALT 0x0A /* alternate plus nibble */\r
+ #define DECPMINUSALT 0x0B /* alternate minus nibble */\r
+ #define DECPPLUS 0x0C /* preferred plus nibble */\r
+ #define DECPMINUS 0x0D /* preferred minus nibble */\r
+ #define DECPPLUSALT2 0x0E /* alternate plus nibble */\r
+ #define DECPUNSIGNED 0x0F /* alternate plus nibble (unsigned) */\r
+ #endif\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Routines -- implemented as decFloat routines in common files */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* Utilities and conversions, extractors, etc.) */\r
+ extern decQuad * decQuadFromBCD(decQuad *, int32_t, const uint8_t *, int32_t);\r
+ extern decQuad * decQuadFromInt32(decQuad *, int32_t);\r
+ extern decQuad * decQuadFromPacked(decQuad *, int32_t, const uint8_t *);\r
+ extern decQuad * decQuadFromPackedChecked(decQuad *, int32_t, const uint8_t *);\r
+ extern decQuad * decQuadFromString(decQuad *, const char *, decContext *);\r
+ extern decQuad * decQuadFromUInt32(decQuad *, uint32_t);\r
+ extern int32_t decQuadGetCoefficient(const decQuad *, uint8_t *);\r
+ extern int32_t decQuadGetExponent(const decQuad *);\r
+ extern decQuad * decQuadSetCoefficient(decQuad *, const uint8_t *, int32_t);\r
+ extern decQuad * decQuadSetExponent(decQuad *, decContext *, int32_t);\r
+ extern void decQuadShow(const decQuad *, const char *);\r
+ extern int32_t decQuadToBCD(const decQuad *, int32_t *, uint8_t *);\r
+ extern char * decQuadToEngString(const decQuad *, char *);\r
+ extern int32_t decQuadToInt32(const decQuad *, decContext *, enum rounding);\r
+ extern int32_t decQuadToInt32Exact(const decQuad *, decContext *, enum rounding);\r
+ extern int32_t decQuadToPacked(const decQuad *, int32_t *, uint8_t *);\r
+ extern char * decQuadToString(const decQuad *, char *);\r
+ extern uint32_t decQuadToUInt32(const decQuad *, decContext *, enum rounding);\r
+ extern uint32_t decQuadToUInt32Exact(const decQuad *, decContext *, enum rounding);\r
+ extern decQuad * decQuadZero(decQuad *);\r
+\r
+ /* Computational (result is a decQuad) */\r
+ extern decQuad * decQuadAbs(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadAdd(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadAnd(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadDivide(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadDivideInteger(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadFMA(decQuad *, const decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadInvert(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadLogB(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadMax(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadMaxMag(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadMin(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadMinMag(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadMinus(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadMultiply(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadNextMinus(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadNextPlus(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadNextToward(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadOr(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadPlus(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadQuantize(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadReduce(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadRemainder(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadRemainderNear(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadRotate(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadScaleB(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadShift(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadSubtract(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadToIntegralValue(decQuad *, const decQuad *, decContext *, enum rounding);\r
+ extern decQuad * decQuadToIntegralExact(decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadXor(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+\r
+ /* Comparisons */\r
+ extern decQuad * decQuadCompare(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadCompareSignal(decQuad *, const decQuad *, const decQuad *, decContext *);\r
+ extern decQuad * decQuadCompareTotal(decQuad *, const decQuad *, const decQuad *);\r
+ extern decQuad * decQuadCompareTotalMag(decQuad *, const decQuad *, const decQuad *);\r
+\r
+ /* Copies */\r
+ extern decQuad * decQuadCanonical(decQuad *, const decQuad *);\r
+ extern decQuad * decQuadCopy(decQuad *, const decQuad *);\r
+ extern decQuad * decQuadCopyAbs(decQuad *, const decQuad *);\r
+ extern decQuad * decQuadCopyNegate(decQuad *, const decQuad *);\r
+ extern decQuad * decQuadCopySign(decQuad *, const decQuad *, const decQuad *);\r
+\r
+ /* Non-computational */\r
+ extern enum decClass decQuadClass(const decQuad *);\r
+ extern const char * decQuadClassString(const decQuad *);\r
+ extern uint32_t decQuadDigits(const decQuad *);\r
+ extern uint32_t decQuadIsCanonical(const decQuad *);\r
+ extern uint32_t decQuadIsFinite(const decQuad *);\r
+ extern uint32_t decQuadIsInteger(const decQuad *);\r
+ extern uint32_t decQuadIsLogical(const decQuad *);\r
+ extern uint32_t decQuadIsInfinite(const decQuad *);\r
+ extern uint32_t decQuadIsNaN(const decQuad *);\r
+ extern uint32_t decQuadIsNegative(const decQuad *);\r
+ extern uint32_t decQuadIsNormal(const decQuad *);\r
+ extern uint32_t decQuadIsPositive(const decQuad *);\r
+ extern uint32_t decQuadIsSignaling(const decQuad *);\r
+ extern uint32_t decQuadIsSignalling(const decQuad *);\r
+ extern uint32_t decQuadIsSigned(const decQuad *);\r
+ extern uint32_t decQuadIsSubnormal(const decQuad *);\r
+ extern uint32_t decQuadIsZero(const decQuad *);\r
+ extern uint32_t decQuadRadix(const decQuad *);\r
+ extern uint32_t decQuadSameQuantum(const decQuad *, const decQuad *);\r
+ extern const char * decQuadVersion(void);\r
+\r
+ /* decNumber conversions; these are implemented as macros so as not */\r
+ /* to force a dependency on decimal128 and decNumber in decQuad. */\r
+ /* decQuadFromNumber returns a decimal128 * to avoid warnings. */\r
+ #define decQuadToNumber(dq, dn) decimal128ToNumber((decimal128 *)(dq), dn)\r
+ #define decQuadFromNumber(dq, dn, set) decimal128FromNumber((decimal128 *)(dq), dn, set)\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decSingle.c -- decSingle operations module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises decSingle operations (including conversions) */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#include "decContext.h" // public includes\r
+#include "decSingle.h" // public includes\r
+\r
+/* Constant mappings for shared code */\r
+#define DECPMAX DECSINGLE_Pmax\r
+#define DECEMIN DECSINGLE_Emin\r
+#define DECEMAX DECSINGLE_Emax\r
+#define DECEMAXD DECSINGLE_EmaxD\r
+#define DECBYTES DECSINGLE_Bytes\r
+#define DECSTRING DECSINGLE_String\r
+#define DECECONL DECSINGLE_EconL\r
+#define DECBIAS DECSINGLE_Bias\r
+#define DECLETS DECSINGLE_Declets\r
+#define DECQTINY (-DECSINGLE_Bias)\r
+// parameters of next-wider format\r
+#define DECWBYTES DECDOUBLE_Bytes\r
+#define DECWPMAX DECDOUBLE_Pmax\r
+#define DECWECONL DECDOUBLE_EconL\r
+#define DECWBIAS DECDOUBLE_Bias\r
+\r
+/* Type and function mappings for shared code */\r
+#define decFloat decSingle // Type name\r
+#define decFloatWider decDouble // Type name\r
+\r
+// Utility (binary results, extractors, etc.)\r
+#define decFloatFromBCD decSingleFromBCD\r
+#define decFloatFromPacked decSingleFromPacked\r
+#define decFloatFromPackedChecked decSingleFromPackedChecked\r
+#define decFloatFromString decSingleFromString\r
+#define decFloatFromWider decSingleFromWider\r
+#define decFloatGetCoefficient decSingleGetCoefficient\r
+#define decFloatGetExponent decSingleGetExponent\r
+#define decFloatSetCoefficient decSingleSetCoefficient\r
+#define decFloatSetExponent decSingleSetExponent\r
+#define decFloatShow decSingleShow\r
+#define decFloatToBCD decSingleToBCD\r
+#define decFloatToEngString decSingleToEngString\r
+#define decFloatToPacked decSingleToPacked\r
+#define decFloatToString decSingleToString\r
+#define decFloatToWider decSingleToWider\r
+#define decFloatZero decSingleZero\r
+\r
+// Non-computational\r
+#define decFloatRadix decSingleRadix\r
+#define decFloatVersion decSingleVersion\r
+\r
+#include "decNumberLocal.h" // local includes (need DECPMAX)\r
+#include "decCommon.c" // non-basic decFloat routines\r
+// [Do not include decBasic.c for decimal32]\r
+\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* decSingle.h -- Decimal 32-bit format module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is included in the package as decNumber.pdf. This */\r
+/* document is also available in HTML, together with specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECSINGLE)\r
+ #define DECSINGLE\r
+\r
+ #define DECSINGLENAME "decSingle" /* Short name */\r
+ #define DECSINGLETITLE "Decimal 32-bit datum" /* Verbose name */\r
+ #define DECSINGLEAUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ /* parameters for decSingles */\r
+ #define DECSINGLE_Bytes 4 /* length */\r
+ #define DECSINGLE_Pmax 7 /* maximum precision (digits) */\r
+ #define DECSINGLE_Emin -95 /* minimum adjusted exponent */\r
+ #define DECSINGLE_Emax 96 /* maximum adjusted exponent */\r
+ #define DECSINGLE_EmaxD 3 /* maximum exponent digits */\r
+ #define DECSINGLE_Bias 101 /* bias for the exponent */\r
+ #define DECSINGLE_String 16 /* maximum string length, +1 */\r
+ #define DECSINGLE_EconL 6 /* exponent continuation length */\r
+ #define DECSINGLE_Declets 2 /* count of declets */\r
+ /* highest biased exponent (Elimit-1) */\r
+ #define DECSINGLE_Ehigh (DECSINGLE_Emax + DECSINGLE_Bias - (DECSINGLE_Pmax-1))\r
+\r
+ /* Required includes */\r
+ #include "decContext.h"\r
+ #include "decQuad.h"\r
+ #include "decDouble.h"\r
+\r
+ /* The decSingle decimal 32-bit type, accessible by all sizes */\r
+ typedef union {\r
+ uint8_t bytes[DECSINGLE_Bytes]; /* fields: 1, 5, 6, 20 bits */\r
+ uint16_t shorts[DECSINGLE_Bytes/2];\r
+ uint32_t words[DECSINGLE_Bytes/4];\r
+ } decSingle;\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Routines -- implemented as decFloat routines in common files */\r
+ /* ---------------------------------------------------------------- */\r
+\r
+ /* Utilities (binary argument(s) or result, extractors, etc.) */\r
+ extern decSingle * decSingleFromBCD(decSingle *, int32_t, const uint8_t *, int32_t);\r
+ extern decSingle * decSingleFromPacked(decSingle *, int32_t, const uint8_t *);\r
+ extern decSingle * decSingleFromPackedChecked(decSingle *, int32_t, const uint8_t *);\r
+ extern decSingle * decSingleFromString(decSingle *, const char *, decContext *);\r
+ extern decSingle * decSingleFromWider(decSingle *, const decDouble *, decContext *);\r
+ extern int32_t decSingleGetCoefficient(const decSingle *, uint8_t *);\r
+ extern int32_t decSingleGetExponent(const decSingle *);\r
+ extern decSingle * decSingleSetCoefficient(decSingle *, const uint8_t *, int32_t);\r
+ extern decSingle * decSingleSetExponent(decSingle *, decContext *, int32_t);\r
+ extern void decSingleShow(const decSingle *, const char *);\r
+ extern int32_t decSingleToBCD(const decSingle *, int32_t *, uint8_t *);\r
+ extern char * decSingleToEngString(const decSingle *, char *);\r
+ extern int32_t decSingleToPacked(const decSingle *, int32_t *, uint8_t *);\r
+ extern char * decSingleToString(const decSingle *, char *);\r
+ extern decDouble * decSingleToWider(const decSingle *, decDouble *);\r
+ extern decSingle * decSingleZero(decSingle *);\r
+\r
+ /* (No Arithmetic routines for decSingle) */\r
+\r
+ /* Non-computational */\r
+ extern uint32_t decSingleRadix(const decSingle *);\r
+ extern const char * decSingleVersion(void);\r
+\r
+ /* decNumber conversions; these are implemented as macros so as not */\r
+ /* to force a dependency on decimal32 and decNumber in decSingle. */\r
+ /* decSingleFromNumber returns a decimal32 * to avoid warnings. */\r
+ #define decSingleToNumber(dq, dn) decimal32ToNumber((decimal32 *)(dq), dn)\r
+ #define decSingleFromNumber(dq, dn, set) decimal32FromNumber((decimal32 *)(dq), dn, set)\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal 128-bit format module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises the routines for decimal128 format numbers. */\r
+/* Conversions are supplied to and from decNumber and String. */\r
+/* */\r
+/* This is used when decNumber provides operations, either for all */\r
+/* operations or as a proxy between decNumber and decSingle. */\r
+/* */\r
+/* Error handling is the same as decNumber (qv.). */\r
+/* ------------------------------------------------------------------ */\r
+#include <string.h> // [for memset/memcpy]\r
+#include <stdio.h> // [for printf]\r
+\r
+#define DECNUMDIGITS 34 // make decNumbers with space for 34\r
+#include "decNumber.h" // base number library\r
+#include "decNumberLocal.h" // decNumber local types, etc.\r
+#include "decimal128.h" // our primary include\r
+\r
+/* Utility routines and tables [in decimal64.c] */\r
+// DPD2BIN and the reverse are renamed to prevent link-time conflict\r
+// if decQuad is also built in the same executable\r
+#define DPD2BIN DPD2BINx\r
+#define BIN2DPD BIN2DPDx\r
+extern const uInt COMBEXP[32], COMBMSD[32];\r
+extern const uShort DPD2BIN[1024];\r
+extern const uShort BIN2DPD[1000]; // [not used]\r
+extern const uByte BIN2CHAR[4001];\r
+\r
+extern void decDigitsFromDPD(decNumber *, const uInt *, Int);\r
+extern void decDigitsToDPD(const decNumber *, uInt *, Int);\r
+\r
+#if DECTRACE || DECCHECK\r
+void decimal128Show(const decimal128 *); // for debug\r
+extern void decNumberShow(const decNumber *); // ..\r
+#endif\r
+\r
+/* Useful macro */\r
+// Clear a structure (e.g., a decNumber)\r
+#define DEC_clear(d) memset(d, 0, sizeof(*d))\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal128FromNumber -- convert decNumber to decimal128 */\r
+/* */\r
+/* ds is the target decimal128 */\r
+/* dn is the source number (assumed valid) */\r
+/* set is the context, used only for reporting errors */\r
+/* */\r
+/* The set argument is used only for status reporting and for the */\r
+/* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/\r
+/* digits or an overflow is detected). If the exponent is out of the */\r
+/* valid range then Overflow or Underflow will be raised. */\r
+/* After Underflow a subnormal result is possible. */\r
+/* */\r
+/* DEC_Clamped is set if the number has to be 'folded down' to fit, */\r
+/* by reducing its exponent and multiplying the coefficient by a */\r
+/* power of ten, or if the exponent on a zero had to be clamped. */\r
+/* ------------------------------------------------------------------ */\r
+decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn,\r
+ decContext *set) {\r
+ uInt status=0; // status accumulator\r
+ Int ae; // adjusted exponent\r
+ decNumber dw; // work\r
+ decContext dc; // ..\r
+ uInt comb, exp; // ..\r
+ uInt uiwork; // for macros\r
+ uInt targar[4]={0,0,0,0}; // target 128-bit\r
+ #define targhi targar[3] // name the word with the sign\r
+ #define targmh targar[2] // name the words\r
+ #define targml targar[1] // ..\r
+ #define targlo targar[0] // ..\r
+\r
+ // If the number has too many digits, or the exponent could be\r
+ // out of range then reduce the number under the appropriate\r
+ // constraints. This could push the number to Infinity or zero,\r
+ // so this check and rounding must be done before generating the\r
+ // decimal128]\r
+ ae=dn->exponent+dn->digits-1; // [0 if special]\r
+ if (dn->digits>DECIMAL128_Pmax // too many digits\r
+ || ae>DECIMAL128_Emax // likely overflow\r
+ || ae<DECIMAL128_Emin) { // likely underflow\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL128); // [no traps]\r
+ dc.round=set->round; // use supplied rounding\r
+ decNumberPlus(&dw, dn, &dc); // (round and check)\r
+ // [this changes -0 to 0, so enforce the sign...]\r
+ dw.bits|=dn->bits&DECNEG;\r
+ status=dc.status; // save status\r
+ dn=&dw; // use the work number\r
+ } // maybe out of range\r
+\r
+ if (dn->bits&DECSPECIAL) { // a special value\r
+ if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;\r
+ else { // sNaN or qNaN\r
+ if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient\r
+ && (dn->digits<DECIMAL128_Pmax)) { // coefficient fits\r
+ decDigitsToDPD(dn, targar, 0);\r
+ }\r
+ if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;\r
+ else targhi|=DECIMAL_sNaN<<24;\r
+ } // a NaN\r
+ } // special\r
+\r
+ else { // is finite\r
+ if (decNumberIsZero(dn)) { // is a zero\r
+ // set and clamp exponent\r
+ if (dn->exponent<-DECIMAL128_Bias) {\r
+ exp=0; // low clamp\r
+ status|=DEC_Clamped;\r
+ }\r
+ else {\r
+ exp=dn->exponent+DECIMAL128_Bias; // bias exponent\r
+ if (exp>DECIMAL128_Ehigh) { // top clamp\r
+ exp=DECIMAL128_Ehigh;\r
+ status|=DEC_Clamped;\r
+ }\r
+ }\r
+ comb=(exp>>9) & 0x18; // msd=0, exp top 2 bits ..\r
+ }\r
+ else { // non-zero finite number\r
+ uInt msd; // work\r
+ Int pad=0; // coefficient pad digits\r
+\r
+ // the dn is known to fit, but it may need to be padded\r
+ exp=(uInt)(dn->exponent+DECIMAL128_Bias); // bias exponent\r
+ if (exp>DECIMAL128_Ehigh) { // fold-down case\r
+ pad=exp-DECIMAL128_Ehigh;\r
+ exp=DECIMAL128_Ehigh; // [to maximum]\r
+ status|=DEC_Clamped;\r
+ }\r
+\r
+ // [fastpath for common case is not a win, here]\r
+ decDigitsToDPD(dn, targar, pad);\r
+ // save and clear the top digit\r
+ msd=targhi>>14;\r
+ targhi&=0x00003fff;\r
+\r
+ // create the combination field\r
+ if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);\r
+ else comb=((exp>>9) & 0x18) | msd;\r
+ }\r
+ targhi|=comb<<26; // add combination field ..\r
+ targhi|=(exp&0xfff)<<14; // .. and exponent continuation\r
+ } // finite\r
+\r
+ if (dn->bits&DECNEG) targhi|=0x80000000; // add sign bit\r
+\r
+ // now write to storage; this is endian\r
+ if (DECLITEND) {\r
+ // lo -> hi\r
+ UBFROMUI(d128->bytes, targlo);\r
+ UBFROMUI(d128->bytes+4, targml);\r
+ UBFROMUI(d128->bytes+8, targmh);\r
+ UBFROMUI(d128->bytes+12, targhi);\r
+ }\r
+ else {\r
+ // hi -> lo\r
+ UBFROMUI(d128->bytes, targhi);\r
+ UBFROMUI(d128->bytes+4, targmh);\r
+ UBFROMUI(d128->bytes+8, targml);\r
+ UBFROMUI(d128->bytes+12, targlo);\r
+ }\r
+\r
+ if (status!=0) decContextSetStatus(set, status); // pass on status\r
+ // decimal128Show(d128);\r
+ return d128;\r
+ } // decimal128FromNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal128ToNumber -- convert decimal128 to decNumber */\r
+/* d128 is the source decimal128 */\r
+/* dn is the target number, with appropriate space */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) {\r
+ uInt msd; // coefficient MSD\r
+ uInt exp; // exponent top two bits\r
+ uInt comb; // combination field\r
+ Int need; // work\r
+ uInt uiwork; // for macros\r
+ uInt sourar[4]; // source 128-bit\r
+ #define sourhi sourar[3] // name the word with the sign\r
+ #define sourmh sourar[2] // and the mid-high word\r
+ #define sourml sourar[1] // and the mod-low word\r
+ #define sourlo sourar[0] // and the lowest word\r
+\r
+ // load source from storage; this is endian\r
+ if (DECLITEND) {\r
+ sourlo=UBTOUI(d128->bytes ); // directly load the low int\r
+ sourml=UBTOUI(d128->bytes+4 ); // then the mid-low\r
+ sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high\r
+ sourhi=UBTOUI(d128->bytes+12); // then the high int\r
+ }\r
+ else {\r
+ sourhi=UBTOUI(d128->bytes ); // directly load the high int\r
+ sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high\r
+ sourml=UBTOUI(d128->bytes+8 ); // then the mid-low\r
+ sourlo=UBTOUI(d128->bytes+12); // then the low int\r
+ }\r
+\r
+ comb=(sourhi>>26)&0x1f; // combination field\r
+\r
+ decNumberZero(dn); // clean number\r
+ if (sourhi&0x80000000) dn->bits=DECNEG; // set sign if negative\r
+\r
+ msd=COMBMSD[comb]; // decode the combination field\r
+ exp=COMBEXP[comb]; // ..\r
+\r
+ if (exp==3) { // is a special\r
+ if (msd==0) {\r
+ dn->bits|=DECINF;\r
+ return dn; // no coefficient needed\r
+ }\r
+ else if (sourhi&0x02000000) dn->bits|=DECSNAN;\r
+ else dn->bits|=DECNAN;\r
+ msd=0; // no top digit\r
+ }\r
+ else { // is a finite number\r
+ dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased\r
+ }\r
+\r
+ // get the coefficient\r
+ sourhi&=0x00003fff; // clean coefficient continuation\r
+ if (msd) { // non-zero msd\r
+ sourhi|=msd<<14; // prefix to coefficient\r
+ need=12; // process 12 declets\r
+ }\r
+ else { // msd=0\r
+ if (sourhi) need=11; // declets to process\r
+ else if (sourmh) need=10;\r
+ else if (sourml) need=7;\r
+ else if (sourlo) need=4;\r
+ else return dn; // easy: coefficient is 0\r
+ } //msd=0\r
+\r
+ decDigitsFromDPD(dn, sourar, need); // process declets\r
+ // decNumberShow(dn);\r
+ return dn;\r
+ } // decimal128ToNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-scientific-string -- conversion to numeric string */\r
+/* to-engineering-string -- conversion to numeric string */\r
+/* */\r
+/* decimal128ToString(d128, string); */\r
+/* decimal128ToEngString(d128, string); */\r
+/* */\r
+/* d128 is the decimal128 format number to convert */\r
+/* string is the string where the result will be laid out */\r
+/* */\r
+/* string must be at least 24 characters */\r
+/* */\r
+/* No error is possible, and no status can be set. */\r
+/* ------------------------------------------------------------------ */\r
+char * decimal128ToEngString(const decimal128 *d128, char *string){\r
+ decNumber dn; // work\r
+ decimal128ToNumber(d128, &dn);\r
+ decNumberToEngString(&dn, string);\r
+ return string;\r
+ } // decimal128ToEngString\r
+\r
+char * decimal128ToString(const decimal128 *d128, char *string){\r
+ uInt msd; // coefficient MSD\r
+ Int exp; // exponent top two bits or full\r
+ uInt comb; // combination field\r
+ char *cstart; // coefficient start\r
+ char *c; // output pointer in string\r
+ const uByte *u; // work\r
+ char *s, *t; // .. (source, target)\r
+ Int dpd; // ..\r
+ Int pre, e; // ..\r
+ uInt uiwork; // for macros\r
+\r
+ uInt sourar[4]; // source 128-bit\r
+ #define sourhi sourar[3] // name the word with the sign\r
+ #define sourmh sourar[2] // and the mid-high word\r
+ #define sourml sourar[1] // and the mod-low word\r
+ #define sourlo sourar[0] // and the lowest word\r
+\r
+ // load source from storage; this is endian\r
+ if (DECLITEND) {\r
+ sourlo=UBTOUI(d128->bytes ); // directly load the low int\r
+ sourml=UBTOUI(d128->bytes+4 ); // then the mid-low\r
+ sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high\r
+ sourhi=UBTOUI(d128->bytes+12); // then the high int\r
+ }\r
+ else {\r
+ sourhi=UBTOUI(d128->bytes ); // directly load the high int\r
+ sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high\r
+ sourml=UBTOUI(d128->bytes+8 ); // then the mid-low\r
+ sourlo=UBTOUI(d128->bytes+12); // then the low int\r
+ }\r
+\r
+ c=string; // where result will go\r
+ if (((Int)sourhi)<0) *c++='-'; // handle sign\r
+\r
+ comb=(sourhi>>26)&0x1f; // combination field\r
+ msd=COMBMSD[comb]; // decode the combination field\r
+ exp=COMBEXP[comb]; // ..\r
+\r
+ if (exp==3) {\r
+ if (msd==0) { // infinity\r
+ strcpy(c, "Inf");\r
+ strcpy(c+3, "inity");\r
+ return string; // easy\r
+ }\r
+ if (sourhi&0x02000000) *c++='s'; // sNaN\r
+ strcpy(c, "NaN"); // complete word\r
+ c+=3; // step past\r
+ if (sourlo==0 && sourml==0 && sourmh==0\r
+ && (sourhi&0x0003ffff)==0) return string; // zero payload\r
+ // otherwise drop through to add integer; set correct exp\r
+ exp=0; msd=0; // setup for following code\r
+ }\r
+ else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased\r
+\r
+ // convert 34 digits of significand to characters\r
+ cstart=c; // save start of coefficient\r
+ if (msd) *c++='0'+(char)msd; // non-zero most significant digit\r
+\r
+ // Now decode the declets. After extracting each one, it is\r
+ // decoded to binary and then to a 4-char sequence by table lookup;\r
+ // the 4-chars are a 1-char length (significant digits, except 000\r
+ // has length 0). This allows us to left-align the first declet\r
+ // with non-zero content, then remaining ones are full 3-char\r
+ // length. We use fixed-length memcpys because variable-length\r
+ // causes a subroutine call in GCC. (These are length 4 for speed\r
+ // and are safe because the array has an extra terminator byte.)\r
+ #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \\r
+ if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \\r
+ else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}\r
+ dpd=(sourhi>>4)&0x3ff; // declet 1\r
+ dpd2char;\r
+ dpd=((sourhi&0xf)<<6) | (sourmh>>26); // declet 2\r
+ dpd2char;\r
+ dpd=(sourmh>>16)&0x3ff; // declet 3\r
+ dpd2char;\r
+ dpd=(sourmh>>6)&0x3ff; // declet 4\r
+ dpd2char;\r
+ dpd=((sourmh&0x3f)<<4) | (sourml>>28); // declet 5\r
+ dpd2char;\r
+ dpd=(sourml>>18)&0x3ff; // declet 6\r
+ dpd2char;\r
+ dpd=(sourml>>8)&0x3ff; // declet 7\r
+ dpd2char;\r
+ dpd=((sourml&0xff)<<2) | (sourlo>>30); // declet 8\r
+ dpd2char;\r
+ dpd=(sourlo>>20)&0x3ff; // declet 9\r
+ dpd2char;\r
+ dpd=(sourlo>>10)&0x3ff; // declet 10\r
+ dpd2char;\r
+ dpd=(sourlo)&0x3ff; // declet 11\r
+ dpd2char;\r
+\r
+ if (c==cstart) *c++='0'; // all zeros -- make 0\r
+\r
+ if (exp==0) { // integer or NaN case -- easy\r
+ *c='\0'; // terminate\r
+ return string;\r
+ }\r
+\r
+ /* non-0 exponent */\r
+ e=0; // assume no E\r
+ pre=c-cstart+exp;\r
+ // [here, pre-exp is the digits count (==1 for zero)]\r
+ if (exp>0 || pre<-5) { // need exponential form\r
+ e=pre-1; // calculate E value\r
+ pre=1; // assume one digit before '.'\r
+ } // exponential form\r
+\r
+ /* modify the coefficient, adding 0s, '.', and E+nn as needed */\r
+ s=c-1; // source (LSD)\r
+ if (pre>0) { // ddd.ddd (plain), perhaps with E\r
+ char *dotat=cstart+pre;\r
+ if (dotat<c) { // if embedded dot needed...\r
+ t=c; // target\r
+ for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap\r
+ *t='.'; // insert the dot\r
+ c++; // length increased by one\r
+ }\r
+\r
+ // finally add the E-part, if needed; it will never be 0, and has\r
+ // a maximum length of 4 digits\r
+ if (e!=0) {\r
+ *c++='E'; // starts with E\r
+ *c++='+'; // assume positive\r
+ if (e<0) {\r
+ *(c-1)='-'; // oops, need '-'\r
+ e=-e; // uInt, please\r
+ }\r
+ if (e<1000) { // 3 (or fewer) digits case\r
+ u=&BIN2CHAR[e*4]; // -> length byte\r
+ memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe]\r
+ c+=*u; // bump pointer appropriately\r
+ }\r
+ else { // 4-digits\r
+ Int thou=((e>>3)*1049)>>17; // e/1000\r
+ Int rem=e-(1000*thou); // e%1000\r
+ *c++='0'+(char)thou;\r
+ u=&BIN2CHAR[rem*4]; // -> length byte\r
+ memcpy(c, u+1, 4); // copy fixed 3+1 characters [is safe]\r
+ c+=3; // bump pointer, always 3 digits\r
+ }\r
+ }\r
+ *c='\0'; // add terminator\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // pre>0\r
+\r
+ /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */\r
+ t=c+1-pre;\r
+ *(t+1)='\0'; // can add terminator now\r
+ for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right\r
+ c=cstart;\r
+ *c++='0'; // always starts with 0.\r
+ *c++='.';\r
+ for (; pre<0; pre++) *c++='0'; // add any 0's after '.'\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // decimal128ToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-number -- conversion from numeric string */\r
+/* */\r
+/* decimal128FromString(result, string, set); */\r
+/* */\r
+/* result is the decimal128 format number which gets the result of */\r
+/* the conversion */\r
+/* *string is the character string which should contain a valid */\r
+/* number (which may be a special value) */\r
+/* set is the context */\r
+/* */\r
+/* The context is supplied to this routine is used for error handling */\r
+/* (setting of status and traps) and for the rounding mode, only. */\r
+/* If an error occurs, the result will be a valid decimal128 NaN. */\r
+/* ------------------------------------------------------------------ */\r
+decimal128 * decimal128FromString(decimal128 *result, const char *string,\r
+ decContext *set) {\r
+ decContext dc; // work\r
+ decNumber dn; // ..\r
+\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL128); // no traps, please\r
+ dc.round=set->round; // use supplied rounding\r
+\r
+ decNumberFromString(&dn, string, &dc); // will round if needed\r
+ decimal128FromNumber(result, &dn, &dc);\r
+ if (dc.status!=0) { // something happened\r
+ decContextSetStatus(set, dc.status); // .. pass it on\r
+ }\r
+ return result;\r
+ } // decimal128FromString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal128IsCanonical -- test whether encoding is canonical */\r
+/* d128 is the source decimal128 */\r
+/* returns 1 if the encoding of d128 is canonical, 0 otherwise */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decimal128IsCanonical(const decimal128 *d128) {\r
+ decNumber dn; // work\r
+ decimal128 canon; // ..\r
+ decContext dc; // ..\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL128);\r
+ decimal128ToNumber(d128, &dn);\r
+ decimal128FromNumber(&canon, &dn, &dc);// canon will now be canonical\r
+ return memcmp(d128, &canon, DECIMAL128_Bytes)==0;\r
+ } // decimal128IsCanonical\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal128Canonical -- copy an encoding, ensuring it is canonical */\r
+/* d128 is the source decimal128 */\r
+/* result is the target (may be the same decimal128) */\r
+/* returns result */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) {\r
+ decNumber dn; // work\r
+ decContext dc; // ..\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL128);\r
+ decimal128ToNumber(d128, &dn);\r
+ decimal128FromNumber(result, &dn, &dc);// result will now be canonical\r
+ return result;\r
+ } // decimal128Canonical\r
+\r
+#if DECTRACE || DECCHECK\r
+/* Macros for accessing decimal128 fields. These assume the argument\r
+ is a reference (pointer) to the decimal128 structure, and the\r
+ decimal128 is in network byte order (big-endian) */\r
+// Get sign\r
+#define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7)\r
+\r
+// Get combination field\r
+#define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2)\r
+\r
+// Get exponent continuation [does not remove bias]\r
+#define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \\r
+ | ((unsigned)(d)->bytes[1]<<2) \\r
+ | ((unsigned)(d)->bytes[2]>>6))\r
+\r
+// Set sign [this assumes sign previously 0]\r
+#define decimal128SetSign(d, b) { \\r
+ (d)->bytes[0]|=((unsigned)(b)<<7);}\r
+\r
+// Set exponent continuation [does not apply bias]\r
+// This assumes range has been checked and exponent previously 0;\r
+// type of exponent must be unsigned\r
+#define decimal128SetExpCon(d, e) { \\r
+ (d)->bytes[0]|=(uByte)((e)>>10); \\r
+ (d)->bytes[1] =(uByte)(((e)&0x3fc)>>2); \\r
+ (d)->bytes[2]|=(uByte)(((e)&0x03)<<6);}\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */\r
+/* d128 -- the number to show */\r
+/* ------------------------------------------------------------------ */\r
+// Also shows sign/cob/expconfields extracted\r
+void decimal128Show(const decimal128 *d128) {\r
+ char buf[DECIMAL128_Bytes*2+1];\r
+ Int i, j=0;\r
+\r
+ if (DECLITEND) {\r
+ for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {\r
+ sprintf(&buf[j], "%02x", d128->bytes[15-i]);\r
+ }\r
+ printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,\r
+ d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,\r
+ ((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)|\r
+ (d128->bytes[13]>>6));\r
+ }\r
+ else {\r
+ for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {\r
+ sprintf(&buf[j], "%02x", d128->bytes[i]);\r
+ }\r
+ printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,\r
+ decimal128Sign(d128), decimal128Comb(d128),\r
+ decimal128ExpCon(d128));\r
+ }\r
+ } // decimal128Show\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal 128-bit format module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2005. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECIMAL128)\r
+ #define DECIMAL128\r
+ #define DEC128NAME "decimal128" /* Short name */\r
+ #define DEC128FULLNAME "Decimal 128-bit Number" /* Verbose name */\r
+ #define DEC128AUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ /* parameters for decimal128s */\r
+ #define DECIMAL128_Bytes 16 /* length */\r
+ #define DECIMAL128_Pmax 34 /* maximum precision (digits) */\r
+ #define DECIMAL128_Emax 6144 /* maximum adjusted exponent */\r
+ #define DECIMAL128_Emin -6143 /* minimum adjusted exponent */\r
+ #define DECIMAL128_Bias 6176 /* bias for the exponent */\r
+ #define DECIMAL128_String 43 /* maximum string length, +1 */\r
+ #define DECIMAL128_EconL 12 /* exp. continuation length */\r
+ /* highest biased exponent (Elimit-1) */\r
+ #define DECIMAL128_Ehigh (DECIMAL128_Emax+DECIMAL128_Bias-DECIMAL128_Pmax+1)\r
+\r
+ /* check enough digits, if pre-defined */\r
+ #if defined(DECNUMDIGITS)\r
+ #if (DECNUMDIGITS<DECIMAL128_Pmax)\r
+ #error decimal128.h needs pre-defined DECNUMDIGITS>=34 for safe use\r
+ #endif\r
+ #endif\r
+\r
+ #ifndef DECNUMDIGITS\r
+ #define DECNUMDIGITS DECIMAL128_Pmax /* size if not already defined*/\r
+ #endif\r
+ #ifndef DECNUMBER\r
+ #include "decNumber.h" /* context and number library */\r
+ #endif\r
+\r
+ /* Decimal 128-bit type, accessible by bytes */\r
+ typedef struct {\r
+ uint8_t bytes[DECIMAL128_Bytes]; /* decimal128: 1, 5, 12, 110 bits*/\r
+ } decimal128;\r
+\r
+ /* special values [top byte excluding sign bit; last two bits are */\r
+ /* don't-care for Infinity on input, last bit don't-care for NaN] */\r
+ #if !defined(DECIMAL_NaN)\r
+ #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */\r
+ #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */\r
+ #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */\r
+ #endif\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Routines */\r
+ /* ---------------------------------------------------------------- */\r
+ /* String conversions */\r
+ decimal128 * decimal128FromString(decimal128 *, const char *, decContext *);\r
+ char * decimal128ToString(const decimal128 *, char *);\r
+ char * decimal128ToEngString(const decimal128 *, char *);\r
+\r
+ /* decNumber conversions */\r
+ decimal128 * decimal128FromNumber(decimal128 *, const decNumber *,\r
+ decContext *);\r
+ decNumber * decimal128ToNumber(const decimal128 *, decNumber *);\r
+\r
+ /* Format-dependent utilities */\r
+ uint32_t decimal128IsCanonical(const decimal128 *);\r
+ decimal128 * decimal128Canonical(decimal128 *, const decimal128 *);\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal 32-bit format module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2008. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises the routines for decimal32 format numbers. */\r
+/* Conversions are supplied to and from decNumber and String. */\r
+/* */\r
+/* This is used when decNumber provides operations, either for all */\r
+/* operations or as a proxy between decNumber and decSingle. */\r
+/* */\r
+/* Error handling is the same as decNumber (qv.). */\r
+/* ------------------------------------------------------------------ */\r
+#include <string.h> // [for memset/memcpy]\r
+#include <stdio.h> // [for printf]\r
+\r
+#define DECNUMDIGITS 7 // make decNumbers with space for 7\r
+#include "decNumber.h" // base number library\r
+#include "decNumberLocal.h" // decNumber local types, etc.\r
+#include "decimal32.h" // our primary include\r
+\r
+/* Utility tables and routines [in decimal64.c] */\r
+// DPD2BIN and the reverse are renamed to prevent link-time conflict\r
+// if decQuad is also built in the same executable\r
+#define DPD2BIN DPD2BINx\r
+#define BIN2DPD BIN2DPDx\r
+extern const uInt COMBEXP[32], COMBMSD[32];\r
+extern const uShort DPD2BIN[1024];\r
+extern const uShort BIN2DPD[1000];\r
+extern const uByte BIN2CHAR[4001];\r
+\r
+extern void decDigitsToDPD(const decNumber *, uInt *, Int);\r
+extern void decDigitsFromDPD(decNumber *, const uInt *, Int);\r
+\r
+#if DECTRACE || DECCHECK\r
+void decimal32Show(const decimal32 *); // for debug\r
+extern void decNumberShow(const decNumber *); // ..\r
+#endif\r
+\r
+/* Useful macro */\r
+// Clear a structure (e.g., a decNumber)\r
+#define DEC_clear(d) memset(d, 0, sizeof(*d))\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal32FromNumber -- convert decNumber to decimal32 */\r
+/* */\r
+/* ds is the target decimal32 */\r
+/* dn is the source number (assumed valid) */\r
+/* set is the context, used only for reporting errors */\r
+/* */\r
+/* The set argument is used only for status reporting and for the */\r
+/* rounding mode (used if the coefficient is more than DECIMAL32_Pmax */\r
+/* digits or an overflow is detected). If the exponent is out of the */\r
+/* valid range then Overflow or Underflow will be raised. */\r
+/* After Underflow a subnormal result is possible. */\r
+/* */\r
+/* DEC_Clamped is set if the number has to be 'folded down' to fit, */\r
+/* by reducing its exponent and multiplying the coefficient by a */\r
+/* power of ten, or if the exponent on a zero had to be clamped. */\r
+/* ------------------------------------------------------------------ */\r
+decimal32 * decimal32FromNumber(decimal32 *d32, const decNumber *dn,\r
+ decContext *set) {\r
+ uInt status=0; // status accumulator\r
+ Int ae; // adjusted exponent\r
+ decNumber dw; // work\r
+ decContext dc; // ..\r
+ uInt comb, exp; // ..\r
+ uInt uiwork; // for macros\r
+ uInt targ=0; // target 32-bit\r
+\r
+ // If the number has too many digits, or the exponent could be\r
+ // out of range then reduce the number under the appropriate\r
+ // constraints. This could push the number to Infinity or zero,\r
+ // so this check and rounding must be done before generating the\r
+ // decimal32]\r
+ ae=dn->exponent+dn->digits-1; // [0 if special]\r
+ if (dn->digits>DECIMAL32_Pmax // too many digits\r
+ || ae>DECIMAL32_Emax // likely overflow\r
+ || ae<DECIMAL32_Emin) { // likely underflow\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL32); // [no traps]\r
+ dc.round=set->round; // use supplied rounding\r
+ decNumberPlus(&dw, dn, &dc); // (round and check)\r
+ // [this changes -0 to 0, so enforce the sign...]\r
+ dw.bits|=dn->bits&DECNEG;\r
+ status=dc.status; // save status\r
+ dn=&dw; // use the work number\r
+ } // maybe out of range\r
+\r
+ if (dn->bits&DECSPECIAL) { // a special value\r
+ if (dn->bits&DECINF) targ=DECIMAL_Inf<<24;\r
+ else { // sNaN or qNaN\r
+ if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient\r
+ && (dn->digits<DECIMAL32_Pmax)) { // coefficient fits\r
+ decDigitsToDPD(dn, &targ, 0);\r
+ }\r
+ if (dn->bits&DECNAN) targ|=DECIMAL_NaN<<24;\r
+ else targ|=DECIMAL_sNaN<<24;\r
+ } // a NaN\r
+ } // special\r
+\r
+ else { // is finite\r
+ if (decNumberIsZero(dn)) { // is a zero\r
+ // set and clamp exponent\r
+ if (dn->exponent<-DECIMAL32_Bias) {\r
+ exp=0; // low clamp\r
+ status|=DEC_Clamped;\r
+ }\r
+ else {\r
+ exp=dn->exponent+DECIMAL32_Bias; // bias exponent\r
+ if (exp>DECIMAL32_Ehigh) { // top clamp\r
+ exp=DECIMAL32_Ehigh;\r
+ status|=DEC_Clamped;\r
+ }\r
+ }\r
+ comb=(exp>>3) & 0x18; // msd=0, exp top 2 bits ..\r
+ }\r
+ else { // non-zero finite number\r
+ uInt msd; // work\r
+ Int pad=0; // coefficient pad digits\r
+\r
+ // the dn is known to fit, but it may need to be padded\r
+ exp=(uInt)(dn->exponent+DECIMAL32_Bias); // bias exponent\r
+ if (exp>DECIMAL32_Ehigh) { // fold-down case\r
+ pad=exp-DECIMAL32_Ehigh;\r
+ exp=DECIMAL32_Ehigh; // [to maximum]\r
+ status|=DEC_Clamped;\r
+ }\r
+\r
+ // fastpath common case\r
+ if (DECDPUN==3 && pad==0) {\r
+ targ=BIN2DPD[dn->lsu[0]];\r
+ if (dn->digits>3) targ|=(uInt)(BIN2DPD[dn->lsu[1]])<<10;\r
+ msd=(dn->digits==7 ? dn->lsu[2] : 0);\r
+ }\r
+ else { // general case\r
+ decDigitsToDPD(dn, &targ, pad);\r
+ // save and clear the top digit\r
+ msd=targ>>20;\r
+ targ&=0x000fffff;\r
+ }\r
+\r
+ // create the combination field\r
+ if (msd>=8) comb=0x18 | ((exp>>5) & 0x06) | (msd & 0x01);\r
+ else comb=((exp>>3) & 0x18) | msd;\r
+ }\r
+ targ|=comb<<26; // add combination field ..\r
+ targ|=(exp&0x3f)<<20; // .. and exponent continuation\r
+ } // finite\r
+\r
+ if (dn->bits&DECNEG) targ|=0x80000000; // add sign bit\r
+\r
+ // now write to storage; this is endian\r
+ UBFROMUI(d32->bytes, targ); // directly store the int\r
+\r
+ if (status!=0) decContextSetStatus(set, status); // pass on status\r
+ // decimal32Show(d32);\r
+ return d32;\r
+ } // decimal32FromNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal32ToNumber -- convert decimal32 to decNumber */\r
+/* d32 is the source decimal32 */\r
+/* dn is the target number, with appropriate space */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decimal32ToNumber(const decimal32 *d32, decNumber *dn) {\r
+ uInt msd; // coefficient MSD\r
+ uInt exp; // exponent top two bits\r
+ uInt comb; // combination field\r
+ uInt sour; // source 32-bit\r
+ uInt uiwork; // for macros\r
+\r
+ // load source from storage; this is endian\r
+ sour=UBTOUI(d32->bytes); // directly load the int\r
+\r
+ comb=(sour>>26)&0x1f; // combination field\r
+\r
+ decNumberZero(dn); // clean number\r
+ if (sour&0x80000000) dn->bits=DECNEG; // set sign if negative\r
+\r
+ msd=COMBMSD[comb]; // decode the combination field\r
+ exp=COMBEXP[comb]; // ..\r
+\r
+ if (exp==3) { // is a special\r
+ if (msd==0) {\r
+ dn->bits|=DECINF;\r
+ return dn; // no coefficient needed\r
+ }\r
+ else if (sour&0x02000000) dn->bits|=DECSNAN;\r
+ else dn->bits|=DECNAN;\r
+ msd=0; // no top digit\r
+ }\r
+ else { // is a finite number\r
+ dn->exponent=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased\r
+ }\r
+\r
+ // get the coefficient\r
+ sour&=0x000fffff; // clean coefficient continuation\r
+ if (msd) { // non-zero msd\r
+ sour|=msd<<20; // prefix to coefficient\r
+ decDigitsFromDPD(dn, &sour, 3); // process 3 declets\r
+ return dn;\r
+ }\r
+ // msd=0\r
+ if (!sour) return dn; // easy: coefficient is 0\r
+ if (sour&0x000ffc00) // need 2 declets?\r
+ decDigitsFromDPD(dn, &sour, 2); // process 2 declets\r
+ else\r
+ decDigitsFromDPD(dn, &sour, 1); // process 1 declet\r
+ return dn;\r
+ } // decimal32ToNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-scientific-string -- conversion to numeric string */\r
+/* to-engineering-string -- conversion to numeric string */\r
+/* */\r
+/* decimal32ToString(d32, string); */\r
+/* decimal32ToEngString(d32, string); */\r
+/* */\r
+/* d32 is the decimal32 format number to convert */\r
+/* string is the string where the result will be laid out */\r
+/* */\r
+/* string must be at least 24 characters */\r
+/* */\r
+/* No error is possible, and no status can be set. */\r
+/* ------------------------------------------------------------------ */\r
+char * decimal32ToEngString(const decimal32 *d32, char *string){\r
+ decNumber dn; // work\r
+ decimal32ToNumber(d32, &dn);\r
+ decNumberToEngString(&dn, string);\r
+ return string;\r
+ } // decimal32ToEngString\r
+\r
+char * decimal32ToString(const decimal32 *d32, char *string){\r
+ uInt msd; // coefficient MSD\r
+ Int exp; // exponent top two bits or full\r
+ uInt comb; // combination field\r
+ char *cstart; // coefficient start\r
+ char *c; // output pointer in string\r
+ const uByte *u; // work\r
+ char *s, *t; // .. (source, target)\r
+ Int dpd; // ..\r
+ Int pre, e; // ..\r
+ uInt uiwork; // for macros\r
+ uInt sour; // source 32-bit\r
+\r
+ // load source from storage; this is endian\r
+ sour=UBTOUI(d32->bytes); // directly load the int\r
+\r
+ c=string; // where result will go\r
+ if (((Int)sour)<0) *c++='-'; // handle sign\r
+\r
+ comb=(sour>>26)&0x1f; // combination field\r
+ msd=COMBMSD[comb]; // decode the combination field\r
+ exp=COMBEXP[comb]; // ..\r
+\r
+ if (exp==3) {\r
+ if (msd==0) { // infinity\r
+ strcpy(c, "Inf");\r
+ strcpy(c+3, "inity");\r
+ return string; // easy\r
+ }\r
+ if (sour&0x02000000) *c++='s'; // sNaN\r
+ strcpy(c, "NaN"); // complete word\r
+ c+=3; // step past\r
+ if ((sour&0x000fffff)==0) return string; // zero payload\r
+ // otherwise drop through to add integer; set correct exp\r
+ exp=0; msd=0; // setup for following code\r
+ }\r
+ else exp=(exp<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased\r
+\r
+ // convert 7 digits of significand to characters\r
+ cstart=c; // save start of coefficient\r
+ if (msd) *c++='0'+(char)msd; // non-zero most significant digit\r
+\r
+ // Now decode the declets. After extracting each one, it is\r
+ // decoded to binary and then to a 4-char sequence by table lookup;\r
+ // the 4-chars are a 1-char length (significant digits, except 000\r
+ // has length 0). This allows us to left-align the first declet\r
+ // with non-zero content, then remaining ones are full 3-char\r
+ // length. We use fixed-length memcpys because variable-length\r
+ // causes a subroutine call in GCC. (These are length 4 for speed\r
+ // and are safe because the array has an extra terminator byte.)\r
+ #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \\r
+ if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \\r
+ else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}\r
+\r
+ dpd=(sour>>10)&0x3ff; // declet 1\r
+ dpd2char;\r
+ dpd=(sour)&0x3ff; // declet 2\r
+ dpd2char;\r
+\r
+ if (c==cstart) *c++='0'; // all zeros -- make 0\r
+\r
+ if (exp==0) { // integer or NaN case -- easy\r
+ *c='\0'; // terminate\r
+ return string;\r
+ }\r
+\r
+ /* non-0 exponent */\r
+ e=0; // assume no E\r
+ pre=c-cstart+exp;\r
+ // [here, pre-exp is the digits count (==1 for zero)]\r
+ if (exp>0 || pre<-5) { // need exponential form\r
+ e=pre-1; // calculate E value\r
+ pre=1; // assume one digit before '.'\r
+ } // exponential form\r
+\r
+ /* modify the coefficient, adding 0s, '.', and E+nn as needed */\r
+ s=c-1; // source (LSD)\r
+ if (pre>0) { // ddd.ddd (plain), perhaps with E\r
+ char *dotat=cstart+pre;\r
+ if (dotat<c) { // if embedded dot needed...\r
+ t=c; // target\r
+ for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap\r
+ *t='.'; // insert the dot\r
+ c++; // length increased by one\r
+ }\r
+\r
+ // finally add the E-part, if needed; it will never be 0, and has\r
+ // a maximum length of 3 digits (E-101 case)\r
+ if (e!=0) {\r
+ *c++='E'; // starts with E\r
+ *c++='+'; // assume positive\r
+ if (e<0) {\r
+ *(c-1)='-'; // oops, need '-'\r
+ e=-e; // uInt, please\r
+ }\r
+ u=&BIN2CHAR[e*4]; // -> length byte\r
+ memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe]\r
+ c+=*u; // bump pointer appropriately\r
+ }\r
+ *c='\0'; // add terminator\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // pre>0\r
+\r
+ /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */\r
+ t=c+1-pre;\r
+ *(t+1)='\0'; // can add terminator now\r
+ for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right\r
+ c=cstart;\r
+ *c++='0'; // always starts with 0.\r
+ *c++='.';\r
+ for (; pre<0; pre++) *c++='0'; // add any 0's after '.'\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // decimal32ToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-number -- conversion from numeric string */\r
+/* */\r
+/* decimal32FromString(result, string, set); */\r
+/* */\r
+/* result is the decimal32 format number which gets the result of */\r
+/* the conversion */\r
+/* *string is the character string which should contain a valid */\r
+/* number (which may be a special value) */\r
+/* set is the context */\r
+/* */\r
+/* The context is supplied to this routine is used for error handling */\r
+/* (setting of status and traps) and for the rounding mode, only. */\r
+/* If an error occurs, the result will be a valid decimal32 NaN. */\r
+/* ------------------------------------------------------------------ */\r
+decimal32 * decimal32FromString(decimal32 *result, const char *string,\r
+ decContext *set) {\r
+ decContext dc; // work\r
+ decNumber dn; // ..\r
+\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL32); // no traps, please\r
+ dc.round=set->round; // use supplied rounding\r
+\r
+ decNumberFromString(&dn, string, &dc); // will round if needed\r
+ decimal32FromNumber(result, &dn, &dc);\r
+ if (dc.status!=0) { // something happened\r
+ decContextSetStatus(set, dc.status); // .. pass it on\r
+ }\r
+ return result;\r
+ } // decimal32FromString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal32IsCanonical -- test whether encoding is canonical */\r
+/* d32 is the source decimal32 */\r
+/* returns 1 if the encoding of d32 is canonical, 0 otherwise */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decimal32IsCanonical(const decimal32 *d32) {\r
+ decNumber dn; // work\r
+ decimal32 canon; // ..\r
+ decContext dc; // ..\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL32);\r
+ decimal32ToNumber(d32, &dn);\r
+ decimal32FromNumber(&canon, &dn, &dc);// canon will now be canonical\r
+ return memcmp(d32, &canon, DECIMAL32_Bytes)==0;\r
+ } // decimal32IsCanonical\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal32Canonical -- copy an encoding, ensuring it is canonical */\r
+/* d32 is the source decimal32 */\r
+/* result is the target (may be the same decimal32) */\r
+/* returns result */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decimal32 * decimal32Canonical(decimal32 *result, const decimal32 *d32) {\r
+ decNumber dn; // work\r
+ decContext dc; // ..\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL32);\r
+ decimal32ToNumber(d32, &dn);\r
+ decimal32FromNumber(result, &dn, &dc);// result will now be canonical\r
+ return result;\r
+ } // decimal32Canonical\r
+\r
+#if DECTRACE || DECCHECK\r
+/* Macros for accessing decimal32 fields. These assume the argument\r
+ is a reference (pointer) to the decimal32 structure, and the\r
+ decimal32 is in network byte order (big-endian) */\r
+// Get sign\r
+#define decimal32Sign(d) ((unsigned)(d)->bytes[0]>>7)\r
+\r
+// Get combination field\r
+#define decimal32Comb(d) (((d)->bytes[0] & 0x7c)>>2)\r
+\r
+// Get exponent continuation [does not remove bias]\r
+#define decimal32ExpCon(d) ((((d)->bytes[0] & 0x03)<<4) \\r
+ | ((unsigned)(d)->bytes[1]>>4))\r
+\r
+// Set sign [this assumes sign previously 0]\r
+#define decimal32SetSign(d, b) { \\r
+ (d)->bytes[0]|=((unsigned)(b)<<7);}\r
+\r
+// Set exponent continuation [does not apply bias]\r
+// This assumes range has been checked and exponent previously 0;\r
+// type of exponent must be unsigned\r
+#define decimal32SetExpCon(d, e) { \\r
+ (d)->bytes[0]|=(uByte)((e)>>4); \\r
+ (d)->bytes[1]|=(uByte)(((e)&0x0F)<<4);}\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal32Show -- display a decimal32 in hexadecimal [debug aid] */\r
+/* d32 -- the number to show */\r
+/* ------------------------------------------------------------------ */\r
+// Also shows sign/cob/expconfields extracted - valid bigendian only\r
+void decimal32Show(const decimal32 *d32) {\r
+ char buf[DECIMAL32_Bytes*2+1];\r
+ Int i, j=0;\r
+\r
+ if (DECLITEND) {\r
+ for (i=0; i<DECIMAL32_Bytes; i++, j+=2) {\r
+ sprintf(&buf[j], "%02x", d32->bytes[3-i]);\r
+ }\r
+ printf(" D32> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,\r
+ d32->bytes[3]>>7, (d32->bytes[3]>>2)&0x1f,\r
+ ((d32->bytes[3]&0x3)<<4)| (d32->bytes[2]>>4));\r
+ }\r
+ else {\r
+ for (i=0; i<DECIMAL32_Bytes; i++, j+=2) {\r
+ sprintf(&buf[j], "%02x", d32->bytes[i]);\r
+ }\r
+ printf(" D32> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,\r
+ decimal32Sign(d32), decimal32Comb(d32), decimal32ExpCon(d32));\r
+ }\r
+ } // decimal32Show\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal 32-bit format module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2006. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECIMAL32)\r
+ #define DECIMAL32\r
+ #define DEC32NAME "decimal32" /* Short name */\r
+ #define DEC32FULLNAME "Decimal 32-bit Number" /* Verbose name */\r
+ #define DEC32AUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+ /* parameters for decimal32s */\r
+ #define DECIMAL32_Bytes 4 /* length */\r
+ #define DECIMAL32_Pmax 7 /* maximum precision (digits) */\r
+ #define DECIMAL32_Emax 96 /* maximum adjusted exponent */\r
+ #define DECIMAL32_Emin -95 /* minimum adjusted exponent */\r
+ #define DECIMAL32_Bias 101 /* bias for the exponent */\r
+ #define DECIMAL32_String 15 /* maximum string length, +1 */\r
+ #define DECIMAL32_EconL 6 /* exp. continuation length */\r
+ /* highest biased exponent (Elimit-1) */\r
+ #define DECIMAL32_Ehigh (DECIMAL32_Emax+DECIMAL32_Bias-DECIMAL32_Pmax+1)\r
+\r
+ /* check enough digits, if pre-defined */\r
+ #if defined(DECNUMDIGITS)\r
+ #if (DECNUMDIGITS<DECIMAL32_Pmax)\r
+ #error decimal32.h needs pre-defined DECNUMDIGITS>=7 for safe use\r
+ #endif\r
+ #endif\r
+\r
+ #ifndef DECNUMDIGITS\r
+ #define DECNUMDIGITS DECIMAL32_Pmax /* size if not already defined*/\r
+ #endif\r
+ #ifndef DECNUMBER\r
+ #include "decNumber.h" /* context and number library */\r
+ #endif\r
+\r
+ /* Decimal 32-bit type, accessible by bytes */\r
+ typedef struct {\r
+ uint8_t bytes[DECIMAL32_Bytes]; /* decimal32: 1, 5, 6, 20 bits*/\r
+ } decimal32;\r
+\r
+ /* special values [top byte excluding sign bit; last two bits are */\r
+ /* don't-care for Infinity on input, last bit don't-care for NaN] */\r
+ #if !defined(DECIMAL_NaN)\r
+ #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */\r
+ #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */\r
+ #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */\r
+ #endif\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Routines */\r
+ /* ---------------------------------------------------------------- */\r
+ /* String conversions */\r
+ decimal32 * decimal32FromString(decimal32 *, const char *, decContext *);\r
+ char * decimal32ToString(const decimal32 *, char *);\r
+ char * decimal32ToEngString(const decimal32 *, char *);\r
+\r
+ /* decNumber conversions */\r
+ decimal32 * decimal32FromNumber(decimal32 *, const decNumber *,\r
+ decContext *);\r
+ decNumber * decimal32ToNumber(const decimal32 *, decNumber *);\r
+\r
+ /* Format-dependent utilities */\r
+ uint32_t decimal32IsCanonical(const decimal32 *);\r
+ decimal32 * decimal32Canonical(decimal32 *, const decimal32 *);\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal 64-bit format module */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+/* This module comprises the routines for decimal64 format numbers. */\r
+/* Conversions are supplied to and from decNumber and String. */\r
+/* */\r
+/* This is used when decNumber provides operations, either for all */\r
+/* operations or as a proxy between decNumber and decSingle. */\r
+/* */\r
+/* Error handling is the same as decNumber (qv.). */\r
+/* ------------------------------------------------------------------ */\r
+#include <string.h> // [for memset/memcpy]\r
+#include <stdio.h> // [for printf]\r
+\r
+#define DECNUMDIGITS 16 // make decNumbers with space for 16\r
+#include "decNumber.h" // base number library\r
+#include "decNumberLocal.h" // decNumber local types, etc.\r
+#include "decimal64.h" // our primary include\r
+\r
+/* Utility routines and tables [in decimal64.c]; externs for C++ */\r
+// DPD2BIN and the reverse are renamed to prevent link-time conflict\r
+// if decQuad is also built in the same executable\r
+#define DPD2BIN DPD2BINx\r
+#define BIN2DPD BIN2DPDx\r
+extern const uInt COMBEXP[32], COMBMSD[32];\r
+extern const uShort DPD2BIN[1024];\r
+extern const uShort BIN2DPD[1000];\r
+extern const uByte BIN2CHAR[4001];\r
+\r
+extern void decDigitsFromDPD(decNumber *, const uInt *, Int);\r
+extern void decDigitsToDPD(const decNumber *, uInt *, Int);\r
+\r
+#if DECTRACE || DECCHECK\r
+void decimal64Show(const decimal64 *); // for debug\r
+extern void decNumberShow(const decNumber *); // ..\r
+#endif\r
+\r
+/* Useful macro */\r
+// Clear a structure (e.g., a decNumber)\r
+#define DEC_clear(d) memset(d, 0, sizeof(*d))\r
+\r
+/* define and include the tables to use for conversions */\r
+#define DEC_BIN2CHAR 1\r
+#define DEC_DPD2BIN 1\r
+#define DEC_BIN2DPD 1 // used for all sizes\r
+#include "decDPD.h" // lookup tables\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal64FromNumber -- convert decNumber to decimal64 */\r
+/* */\r
+/* ds is the target decimal64 */\r
+/* dn is the source number (assumed valid) */\r
+/* set is the context, used only for reporting errors */\r
+/* */\r
+/* The set argument is used only for status reporting and for the */\r
+/* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */\r
+/* digits or an overflow is detected). If the exponent is out of the */\r
+/* valid range then Overflow or Underflow will be raised. */\r
+/* After Underflow a subnormal result is possible. */\r
+/* */\r
+/* DEC_Clamped is set if the number has to be 'folded down' to fit, */\r
+/* by reducing its exponent and multiplying the coefficient by a */\r
+/* power of ten, or if the exponent on a zero had to be clamped. */\r
+/* ------------------------------------------------------------------ */\r
+decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn,\r
+ decContext *set) {\r
+ uInt status=0; // status accumulator\r
+ Int ae; // adjusted exponent\r
+ decNumber dw; // work\r
+ decContext dc; // ..\r
+ uInt comb, exp; // ..\r
+ uInt uiwork; // for macros\r
+ uInt targar[2]={0, 0}; // target 64-bit\r
+ #define targhi targar[1] // name the word with the sign\r
+ #define targlo targar[0] // and the other\r
+\r
+ // If the number has too many digits, or the exponent could be\r
+ // out of range then reduce the number under the appropriate\r
+ // constraints. This could push the number to Infinity or zero,\r
+ // so this check and rounding must be done before generating the\r
+ // decimal64]\r
+ ae=dn->exponent+dn->digits-1; // [0 if special]\r
+ if (dn->digits>DECIMAL64_Pmax // too many digits\r
+ || ae>DECIMAL64_Emax // likely overflow\r
+ || ae<DECIMAL64_Emin) { // likely underflow\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL64); // [no traps]\r
+ dc.round=set->round; // use supplied rounding\r
+ decNumberPlus(&dw, dn, &dc); // (round and check)\r
+ // [this changes -0 to 0, so enforce the sign...]\r
+ dw.bits|=dn->bits&DECNEG;\r
+ status=dc.status; // save status\r
+ dn=&dw; // use the work number\r
+ } // maybe out of range\r
+\r
+ if (dn->bits&DECSPECIAL) { // a special value\r
+ if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;\r
+ else { // sNaN or qNaN\r
+ if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient\r
+ && (dn->digits<DECIMAL64_Pmax)) { // coefficient fits\r
+ decDigitsToDPD(dn, targar, 0);\r
+ }\r
+ if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;\r
+ else targhi|=DECIMAL_sNaN<<24;\r
+ } // a NaN\r
+ } // special\r
+\r
+ else { // is finite\r
+ if (decNumberIsZero(dn)) { // is a zero\r
+ // set and clamp exponent\r
+ if (dn->exponent<-DECIMAL64_Bias) {\r
+ exp=0; // low clamp\r
+ status|=DEC_Clamped;\r
+ }\r
+ else {\r
+ exp=dn->exponent+DECIMAL64_Bias; // bias exponent\r
+ if (exp>DECIMAL64_Ehigh) { // top clamp\r
+ exp=DECIMAL64_Ehigh;\r
+ status|=DEC_Clamped;\r
+ }\r
+ }\r
+ comb=(exp>>5) & 0x18; // msd=0, exp top 2 bits ..\r
+ }\r
+ else { // non-zero finite number\r
+ uInt msd; // work\r
+ Int pad=0; // coefficient pad digits\r
+\r
+ // the dn is known to fit, but it may need to be padded\r
+ exp=(uInt)(dn->exponent+DECIMAL64_Bias); // bias exponent\r
+ if (exp>DECIMAL64_Ehigh) { // fold-down case\r
+ pad=exp-DECIMAL64_Ehigh;\r
+ exp=DECIMAL64_Ehigh; // [to maximum]\r
+ status|=DEC_Clamped;\r
+ }\r
+\r
+ // fastpath common case\r
+ if (DECDPUN==3 && pad==0) {\r
+ uInt dpd[6]={0,0,0,0,0,0};\r
+ uInt i;\r
+ Int d=dn->digits;\r
+ for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];\r
+ targlo =dpd[0];\r
+ targlo|=dpd[1]<<10;\r
+ targlo|=dpd[2]<<20;\r
+ if (dn->digits>6) {\r
+ targlo|=dpd[3]<<30;\r
+ targhi =dpd[3]>>2;\r
+ targhi|=dpd[4]<<8;\r
+ }\r
+ msd=dpd[5]; // [did not really need conversion]\r
+ }\r
+ else { // general case\r
+ decDigitsToDPD(dn, targar, pad);\r
+ // save and clear the top digit\r
+ msd=targhi>>18;\r
+ targhi&=0x0003ffff;\r
+ }\r
+\r
+ // create the combination field\r
+ if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);\r
+ else comb=((exp>>5) & 0x18) | msd;\r
+ }\r
+ targhi|=comb<<26; // add combination field ..\r
+ targhi|=(exp&0xff)<<18; // .. and exponent continuation\r
+ } // finite\r
+\r
+ if (dn->bits&DECNEG) targhi|=0x80000000; // add sign bit\r
+\r
+ // now write to storage; this is now always endian\r
+ if (DECLITEND) {\r
+ // lo int then hi\r
+ UBFROMUI(d64->bytes, targar[0]);\r
+ UBFROMUI(d64->bytes+4, targar[1]);\r
+ }\r
+ else {\r
+ // hi int then lo\r
+ UBFROMUI(d64->bytes, targar[1]);\r
+ UBFROMUI(d64->bytes+4, targar[0]);\r
+ }\r
+\r
+ if (status!=0) decContextSetStatus(set, status); // pass on status\r
+ // decimal64Show(d64);\r
+ return d64;\r
+ } // decimal64FromNumber\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal64ToNumber -- convert decimal64 to decNumber */\r
+/* d64 is the source decimal64 */\r
+/* dn is the target number, with appropriate space */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) {\r
+ uInt msd; // coefficient MSD\r
+ uInt exp; // exponent top two bits\r
+ uInt comb; // combination field\r
+ Int need; // work\r
+ uInt uiwork; // for macros\r
+ uInt sourar[2]; // source 64-bit\r
+ #define sourhi sourar[1] // name the word with the sign\r
+ #define sourlo sourar[0] // and the lower word\r
+\r
+ // load source from storage; this is endian\r
+ if (DECLITEND) {\r
+ sourlo=UBTOUI(d64->bytes ); // directly load the low int\r
+ sourhi=UBTOUI(d64->bytes+4); // then the high int\r
+ }\r
+ else {\r
+ sourhi=UBTOUI(d64->bytes ); // directly load the high int\r
+ sourlo=UBTOUI(d64->bytes+4); // then the low int\r
+ }\r
+\r
+ comb=(sourhi>>26)&0x1f; // combination field\r
+\r
+ decNumberZero(dn); // clean number\r
+ if (sourhi&0x80000000) dn->bits=DECNEG; // set sign if negative\r
+\r
+ msd=COMBMSD[comb]; // decode the combination field\r
+ exp=COMBEXP[comb]; // ..\r
+\r
+ if (exp==3) { // is a special\r
+ if (msd==0) {\r
+ dn->bits|=DECINF;\r
+ return dn; // no coefficient needed\r
+ }\r
+ else if (sourhi&0x02000000) dn->bits|=DECSNAN;\r
+ else dn->bits|=DECNAN;\r
+ msd=0; // no top digit\r
+ }\r
+ else { // is a finite number\r
+ dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; // unbiased\r
+ }\r
+\r
+ // get the coefficient\r
+ sourhi&=0x0003ffff; // clean coefficient continuation\r
+ if (msd) { // non-zero msd\r
+ sourhi|=msd<<18; // prefix to coefficient\r
+ need=6; // process 6 declets\r
+ }\r
+ else { // msd=0\r
+ if (!sourhi) { // top word 0\r
+ if (!sourlo) return dn; // easy: coefficient is 0\r
+ need=3; // process at least 3 declets\r
+ if (sourlo&0xc0000000) need++; // process 4 declets\r
+ // [could reduce some more, here]\r
+ }\r
+ else { // some bits in top word, msd=0\r
+ need=4; // process at least 4 declets\r
+ if (sourhi&0x0003ff00) need++; // top declet!=0, process 5\r
+ }\r
+ } //msd=0\r
+\r
+ decDigitsFromDPD(dn, sourar, need); // process declets\r
+ return dn;\r
+ } // decimal64ToNumber\r
+\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-scientific-string -- conversion to numeric string */\r
+/* to-engineering-string -- conversion to numeric string */\r
+/* */\r
+/* decimal64ToString(d64, string); */\r
+/* decimal64ToEngString(d64, string); */\r
+/* */\r
+/* d64 is the decimal64 format number to convert */\r
+/* string is the string where the result will be laid out */\r
+/* */\r
+/* string must be at least 24 characters */\r
+/* */\r
+/* No error is possible, and no status can be set. */\r
+/* ------------------------------------------------------------------ */\r
+char * decimal64ToEngString(const decimal64 *d64, char *string){\r
+ decNumber dn; // work\r
+ decimal64ToNumber(d64, &dn);\r
+ decNumberToEngString(&dn, string);\r
+ return string;\r
+ } // decimal64ToEngString\r
+\r
+char * decimal64ToString(const decimal64 *d64, char *string){\r
+ uInt msd; // coefficient MSD\r
+ Int exp; // exponent top two bits or full\r
+ uInt comb; // combination field\r
+ char *cstart; // coefficient start\r
+ char *c; // output pointer in string\r
+ const uByte *u; // work\r
+ char *s, *t; // .. (source, target)\r
+ Int dpd; // ..\r
+ Int pre, e; // ..\r
+ uInt uiwork; // for macros\r
+\r
+ uInt sourar[2]; // source 64-bit\r
+ #define sourhi sourar[1] // name the word with the sign\r
+ #define sourlo sourar[0] // and the lower word\r
+\r
+ // load source from storage; this is endian\r
+ if (DECLITEND) {\r
+ sourlo=UBTOUI(d64->bytes ); // directly load the low int\r
+ sourhi=UBTOUI(d64->bytes+4); // then the high int\r
+ }\r
+ else {\r
+ sourhi=UBTOUI(d64->bytes ); // directly load the high int\r
+ sourlo=UBTOUI(d64->bytes+4); // then the low int\r
+ }\r
+\r
+ c=string; // where result will go\r
+ if (((Int)sourhi)<0) *c++='-'; // handle sign\r
+\r
+ comb=(sourhi>>26)&0x1f; // combination field\r
+ msd=COMBMSD[comb]; // decode the combination field\r
+ exp=COMBEXP[comb]; // ..\r
+\r
+ if (exp==3) {\r
+ if (msd==0) { // infinity\r
+ strcpy(c, "Inf");\r
+ strcpy(c+3, "inity");\r
+ return string; // easy\r
+ }\r
+ if (sourhi&0x02000000) *c++='s'; // sNaN\r
+ strcpy(c, "NaN"); // complete word\r
+ c+=3; // step past\r
+ if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; // zero payload\r
+ // otherwise drop through to add integer; set correct exp\r
+ exp=0; msd=0; // setup for following code\r
+ }\r
+ else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;\r
+\r
+ // convert 16 digits of significand to characters\r
+ cstart=c; // save start of coefficient\r
+ if (msd) *c++='0'+(char)msd; // non-zero most significant digit\r
+\r
+ // Now decode the declets. After extracting each one, it is\r
+ // decoded to binary and then to a 4-char sequence by table lookup;\r
+ // the 4-chars are a 1-char length (significant digits, except 000\r
+ // has length 0). This allows us to left-align the first declet\r
+ // with non-zero content, then remaining ones are full 3-char\r
+ // length. We use fixed-length memcpys because variable-length\r
+ // causes a subroutine call in GCC. (These are length 4 for speed\r
+ // and are safe because the array has an extra terminator byte.)\r
+ #define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \\r
+ if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \\r
+ else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}\r
+\r
+ dpd=(sourhi>>8)&0x3ff; // declet 1\r
+ dpd2char;\r
+ dpd=((sourhi&0xff)<<2) | (sourlo>>30); // declet 2\r
+ dpd2char;\r
+ dpd=(sourlo>>20)&0x3ff; // declet 3\r
+ dpd2char;\r
+ dpd=(sourlo>>10)&0x3ff; // declet 4\r
+ dpd2char;\r
+ dpd=(sourlo)&0x3ff; // declet 5\r
+ dpd2char;\r
+\r
+ if (c==cstart) *c++='0'; // all zeros -- make 0\r
+\r
+ if (exp==0) { // integer or NaN case -- easy\r
+ *c='\0'; // terminate\r
+ return string;\r
+ }\r
+\r
+ /* non-0 exponent */\r
+ e=0; // assume no E\r
+ pre=c-cstart+exp;\r
+ // [here, pre-exp is the digits count (==1 for zero)]\r
+ if (exp>0 || pre<-5) { // need exponential form\r
+ e=pre-1; // calculate E value\r
+ pre=1; // assume one digit before '.'\r
+ } // exponential form\r
+\r
+ /* modify the coefficient, adding 0s, '.', and E+nn as needed */\r
+ s=c-1; // source (LSD)\r
+ if (pre>0) { // ddd.ddd (plain), perhaps with E\r
+ char *dotat=cstart+pre;\r
+ if (dotat<c) { // if embedded dot needed...\r
+ t=c; // target\r
+ for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap\r
+ *t='.'; // insert the dot\r
+ c++; // length increased by one\r
+ }\r
+\r
+ // finally add the E-part, if needed; it will never be 0, and has\r
+ // a maximum length of 3 digits\r
+ if (e!=0) {\r
+ *c++='E'; // starts with E\r
+ *c++='+'; // assume positive\r
+ if (e<0) {\r
+ *(c-1)='-'; // oops, need '-'\r
+ e=-e; // uInt, please\r
+ }\r
+ u=&BIN2CHAR[e*4]; // -> length byte\r
+ memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe]\r
+ c+=*u; // bump pointer appropriately\r
+ }\r
+ *c='\0'; // add terminator\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // pre>0\r
+\r
+ /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */\r
+ t=c+1-pre;\r
+ *(t+1)='\0'; // can add terminator now\r
+ for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right\r
+ c=cstart;\r
+ *c++='0'; // always starts with 0.\r
+ *c++='.';\r
+ for (; pre<0; pre++) *c++='0'; // add any 0's after '.'\r
+ //printf("res %s\n", string);\r
+ return string;\r
+ } // decimal64ToString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* to-number -- conversion from numeric string */\r
+/* */\r
+/* decimal64FromString(result, string, set); */\r
+/* */\r
+/* result is the decimal64 format number which gets the result of */\r
+/* the conversion */\r
+/* *string is the character string which should contain a valid */\r
+/* number (which may be a special value) */\r
+/* set is the context */\r
+/* */\r
+/* The context is supplied to this routine is used for error handling */\r
+/* (setting of status and traps) and for the rounding mode, only. */\r
+/* If an error occurs, the result will be a valid decimal64 NaN. */\r
+/* ------------------------------------------------------------------ */\r
+decimal64 * decimal64FromString(decimal64 *result, const char *string,\r
+ decContext *set) {\r
+ decContext dc; // work\r
+ decNumber dn; // ..\r
+\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL64); // no traps, please\r
+ dc.round=set->round; // use supplied rounding\r
+\r
+ decNumberFromString(&dn, string, &dc); // will round if needed\r
+\r
+ decimal64FromNumber(result, &dn, &dc);\r
+ if (dc.status!=0) { // something happened\r
+ decContextSetStatus(set, dc.status); // .. pass it on\r
+ }\r
+ return result;\r
+ } // decimal64FromString\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal64IsCanonical -- test whether encoding is canonical */\r
+/* d64 is the source decimal64 */\r
+/* returns 1 if the encoding of d64 is canonical, 0 otherwise */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+uInt decimal64IsCanonical(const decimal64 *d64) {\r
+ decNumber dn; // work\r
+ decimal64 canon; // ..\r
+ decContext dc; // ..\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL64);\r
+ decimal64ToNumber(d64, &dn);\r
+ decimal64FromNumber(&canon, &dn, &dc);// canon will now be canonical\r
+ return memcmp(d64, &canon, DECIMAL64_Bytes)==0;\r
+ } // decimal64IsCanonical\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal64Canonical -- copy an encoding, ensuring it is canonical */\r
+/* d64 is the source decimal64 */\r
+/* result is the target (may be the same decimal64) */\r
+/* returns result */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {\r
+ decNumber dn; // work\r
+ decContext dc; // ..\r
+ decContextDefault(&dc, DEC_INIT_DECIMAL64);\r
+ decimal64ToNumber(d64, &dn);\r
+ decimal64FromNumber(result, &dn, &dc);// result will now be canonical\r
+ return result;\r
+ } // decimal64Canonical\r
+\r
+#if DECTRACE || DECCHECK\r
+/* Macros for accessing decimal64 fields. These assume the\r
+ argument is a reference (pointer) to the decimal64 structure,\r
+ and the decimal64 is in network byte order (big-endian) */\r
+// Get sign\r
+#define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7)\r
+\r
+// Get combination field\r
+#define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2)\r
+\r
+// Get exponent continuation [does not remove bias]\r
+#define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \\r
+ | ((unsigned)(d)->bytes[1]>>2))\r
+\r
+// Set sign [this assumes sign previously 0]\r
+#define decimal64SetSign(d, b) { \\r
+ (d)->bytes[0]|=((unsigned)(b)<<7);}\r
+\r
+// Set exponent continuation [does not apply bias]\r
+// This assumes range has been checked and exponent previously 0;\r
+// type of exponent must be unsigned\r
+#define decimal64SetExpCon(d, e) { \\r
+ (d)->bytes[0]|=(uByte)((e)>>6); \\r
+ (d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);}\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */\r
+/* d64 -- the number to show */\r
+/* ------------------------------------------------------------------ */\r
+// Also shows sign/cob/expconfields extracted\r
+void decimal64Show(const decimal64 *d64) {\r
+ char buf[DECIMAL64_Bytes*2+1];\r
+ Int i, j=0;\r
+\r
+ if (DECLITEND) {\r
+ for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {\r
+ sprintf(&buf[j], "%02x", d64->bytes[7-i]);\r
+ }\r
+ printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,\r
+ d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,\r
+ ((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));\r
+ }\r
+ else { // big-endian\r
+ for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {\r
+ sprintf(&buf[j], "%02x", d64->bytes[i]);\r
+ }\r
+ printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,\r
+ decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));\r
+ }\r
+ } // decimal64Show\r
+#endif\r
+\r
+/* ================================================================== */\r
+/* Shared utility routines and tables */\r
+/* ================================================================== */\r
+// define and include the conversion tables to use for shared code\r
+#if DECDPUN==3\r
+ #define DEC_DPD2BIN 1\r
+#else\r
+ #define DEC_DPD2BCD 1\r
+#endif\r
+#include "decDPD.h" // lookup tables\r
+\r
+// The maximum number of decNumberUnits needed for a working copy of\r
+// the units array is the ceiling of digits/DECDPUN, where digits is\r
+// the maximum number of digits in any of the formats for which this\r
+// is used. decimal128.h must not be included in this module, so, as\r
+// a very special case, that number is defined as a literal here.\r
+#define DECMAX754 34\r
+#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* Combination field lookup tables (uInts to save measurable work) */\r
+/* */\r
+/* COMBEXP - 2-bit most-significant-bits of exponent */\r
+/* [11 if an Infinity or NaN] */\r
+/* COMBMSD - 4-bit most-significant-digit */\r
+/* [0=Infinity, 1=NaN if COMBEXP=11] */\r
+/* */\r
+/* Both are indexed by the 5-bit combination field (0-31) */\r
+/* ------------------------------------------------------------------ */\r
+const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,\r
+ 1, 1, 1, 1, 1, 1, 1, 1,\r
+ 2, 2, 2, 2, 2, 2, 2, 2,\r
+ 0, 0, 1, 1, 2, 2, 3, 3};\r
+const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7,\r
+ 0, 1, 2, 3, 4, 5, 6, 7,\r
+ 0, 1, 2, 3, 4, 5, 6, 7,\r
+ 8, 9, 8, 9, 8, 9, 0, 1};\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decDigitsToDPD -- pack coefficient into DPD form */\r
+/* */\r
+/* dn is the source number (assumed valid, max DECMAX754 digits) */\r
+/* targ is 1, 2, or 4-element uInt array, which the caller must */\r
+/* have cleared to zeros */\r
+/* shift is the number of 0 digits to add on the right (normally 0) */\r
+/* */\r
+/* The coefficient must be known small enough to fit. The full */\r
+/* coefficient is copied, including the leading 'odd' digit. This */\r
+/* digit is retrieved and packed into the combination field by the */\r
+/* caller. */\r
+/* */\r
+/* The target uInts are altered only as necessary to receive the */\r
+/* digits of the decNumber. When more than one uInt is needed, they */\r
+/* are filled from left to right (that is, the uInt at offset 0 will */\r
+/* end up with the least-significant digits). */\r
+/* */\r
+/* shift is used for 'fold-down' padding. */\r
+/* */\r
+/* No error is possible. */\r
+/* ------------------------------------------------------------------ */\r
+#if DECDPUN<=4\r
+// Constant multipliers for divide-by-power-of five using reciprocal\r
+// multiply, after removing powers of 2 by shifting, and final shift\r
+// of 17 [we only need up to **4]\r
+static const uInt multies[]={131073, 26215, 5243, 1049, 210};\r
+// QUOT10 -- macro to return the quotient of unit u divided by 10**n\r
+#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)\r
+#endif\r
+void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {\r
+ Int cut; // work\r
+ Int n; // output bunch counter\r
+ Int digits=dn->digits; // digit countdown\r
+ uInt dpd; // densely packed decimal value\r
+ uInt bin; // binary value 0-999\r
+ uInt *uout=targ; // -> current output uInt\r
+ uInt uoff=0; // -> current output offset [from right]\r
+ const Unit *inu=dn->lsu; // -> current input unit\r
+ Unit uar[DECMAXUNITS]; // working copy of units, iff shifted\r
+ #if DECDPUN!=3 // not fast path\r
+ Unit in; // current unit\r
+ #endif\r
+\r
+ if (shift!=0) { // shift towards most significant required\r
+ // shift the units array to the left by pad digits and copy\r
+ // [this code is a special case of decShiftToMost, which could\r
+ // be used instead if exposed and the array were copied first]\r
+ const Unit *source; // ..\r
+ Unit *target, *first; // ..\r
+ uInt next=0; // work\r
+\r
+ source=dn->lsu+D2U(digits)-1; // where msu comes from\r
+ target=uar+D2U(digits)-1+D2U(shift);// where upper part of first cut goes\r
+ cut=DECDPUN-MSUDIGITS(shift); // where to slice\r
+ if (cut==0) { // unit-boundary case\r
+ for (; source>=dn->lsu; source--, target--) *target=*source;\r
+ }\r
+ else {\r
+ first=uar+D2U(digits+shift)-1; // where msu will end up\r
+ for (; source>=dn->lsu; source--, target--) {\r
+ // split the source Unit and accumulate remainder for next\r
+ #if DECDPUN<=4\r
+ uInt quot=QUOT10(*source, cut);\r
+ uInt rem=*source-quot*DECPOWERS[cut];\r
+ next+=quot;\r
+ #else\r
+ uInt rem=*source%DECPOWERS[cut];\r
+ next+=*source/DECPOWERS[cut];\r
+ #endif\r
+ if (target<=first) *target=(Unit)next; // write to target iff valid\r
+ next=rem*DECPOWERS[DECDPUN-cut]; // save remainder for next Unit\r
+ }\r
+ } // shift-move\r
+ // propagate remainder to one below and clear the rest\r
+ for (; target>=uar; target--) {\r
+ *target=(Unit)next;\r
+ next=0;\r
+ }\r
+ digits+=shift; // add count (shift) of zeros added\r
+ inu=uar; // use units in working array\r
+ }\r
+\r
+ /* now densely pack the coefficient into DPD declets */\r
+\r
+ #if DECDPUN!=3 // not fast path\r
+ in=*inu; // current unit\r
+ cut=0; // at lowest digit\r
+ bin=0; // [keep compiler quiet]\r
+ #endif\r
+\r
+ for(n=0; digits>0; n++) { // each output bunch\r
+ #if DECDPUN==3 // fast path, 3-at-a-time\r
+ bin=*inu; // 3 digits ready for convert\r
+ digits-=3; // [may go negative]\r
+ inu++; // may need another\r
+\r
+ #else // must collect digit-by-digit\r
+ Unit dig; // current digit\r
+ Int j; // digit-in-declet count\r
+ for (j=0; j<3; j++) {\r
+ #if DECDPUN<=4\r
+ Unit temp=(Unit)((uInt)(in*6554)>>16);\r
+ dig=(Unit)(in-X10(temp));\r
+ in=temp;\r
+ #else\r
+ dig=in%10;\r
+ in=in/10;\r
+ #endif\r
+ if (j==0) bin=dig;\r
+ else if (j==1) bin+=X10(dig);\r
+ else /* j==2 */ bin+=X100(dig);\r
+ digits--;\r
+ if (digits==0) break; // [also protects *inu below]\r
+ cut++;\r
+ if (cut==DECDPUN) {inu++; in=*inu; cut=0;}\r
+ }\r
+ #endif\r
+ // here there are 3 digits in bin, or have used all input digits\r
+\r
+ dpd=BIN2DPD[bin];\r
+\r
+ // write declet to uInt array\r
+ *uout|=dpd<<uoff;\r
+ uoff+=10;\r
+ if (uoff<32) continue; // no uInt boundary cross\r
+ uout++;\r
+ uoff-=32;\r
+ *uout|=dpd>>(10-uoff); // collect top bits\r
+ } // n declets\r
+ return;\r
+ } // decDigitsToDPD\r
+\r
+/* ------------------------------------------------------------------ */\r
+/* decDigitsFromDPD -- unpack a format's coefficient */\r
+/* */\r
+/* dn is the target number, with 7, 16, or 34-digit space. */\r
+/* sour is a 1, 2, or 4-element uInt array containing only declets */\r
+/* declets is the number of (right-aligned) declets in sour to */\r
+/* be processed. This may be 1 more than the obvious number in */\r
+/* a format, as any top digit is prefixed to the coefficient */\r
+/* continuation field. It also may be as small as 1, as the */\r
+/* caller may pre-process leading zero declets. */\r
+/* */\r
+/* When doing the 'extra declet' case care is taken to avoid writing */\r
+/* extra digits when there are leading zeros, as these could overflow */\r
+/* the units array when DECDPUN is not 3. */\r
+/* */\r
+/* The target uInts are used only as necessary to process declets */\r
+/* declets into the decNumber. When more than one uInt is needed, */\r
+/* they are used from left to right (that is, the uInt at offset 0 */\r
+/* provides the least-significant digits). */\r
+/* */\r
+/* dn->digits is set, but not the sign or exponent. */\r
+/* No error is possible [the redundant 888 codes are allowed]. */\r
+/* ------------------------------------------------------------------ */\r
+void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {\r
+\r
+ uInt dpd; // collector for 10 bits\r
+ Int n; // counter\r
+ Unit *uout=dn->lsu; // -> current output unit\r
+ Unit *last=uout; // will be unit containing msd\r
+ const uInt *uin=sour; // -> current input uInt\r
+ uInt uoff=0; // -> current input offset [from right]\r
+\r
+ #if DECDPUN!=3\r
+ uInt bcd; // BCD result\r
+ uInt nibble; // work\r
+ Unit out=0; // accumulator\r
+ Int cut=0; // power of ten in current unit\r
+ #endif\r
+ #if DECDPUN>4\r
+ uInt const *pow; // work\r
+ #endif\r
+\r
+ // Expand the densely-packed integer, right to left\r
+ for (n=declets-1; n>=0; n--) { // count down declets of 10 bits\r
+ dpd=*uin>>uoff;\r
+ uoff+=10;\r
+ if (uoff>32) { // crossed uInt boundary\r
+ uin++;\r
+ uoff-=32; // [if using this code for wider, check this]\r
+ dpd|=*uin<<(10-uoff); // get waiting bits\r
+ }\r
+ dpd&=0x3ff; // clear uninteresting bits\r
+\r
+ #if DECDPUN==3\r
+ if (dpd==0) *uout=0;\r
+ else {\r
+ *uout=DPD2BIN[dpd]; // convert 10 bits to binary 0-999\r
+ last=uout; // record most significant unit\r
+ }\r
+ uout++;\r
+ } // n\r
+\r
+ #else // DECDPUN!=3\r
+ if (dpd==0) { // fastpath [e.g., leading zeros]\r
+ // write out three 0 digits (nibbles); out may have digit(s)\r
+ cut++;\r
+ if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}\r
+ if (n==0) break; // [as below, works even if MSD=0]\r
+ cut++;\r
+ if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}\r
+ cut++;\r
+ if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}\r
+ continue;\r
+ }\r
+\r
+ bcd=DPD2BCD[dpd]; // convert 10 bits to 12 bits BCD\r
+\r
+ // now accumulate the 3 BCD nibbles into units\r
+ nibble=bcd & 0x00f;\r
+ if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);\r
+ cut++;\r
+ if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}\r
+ bcd>>=4;\r
+\r
+ // if this is the last declet and the remaining nibbles in bcd\r
+ // are 00 then process no more nibbles, because this could be\r
+ // the 'odd' MSD declet and writing any more Units would then\r
+ // overflow the unit array\r
+ if (n==0 && !bcd) break;\r
+\r
+ nibble=bcd & 0x00f;\r
+ if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);\r
+ cut++;\r
+ if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}\r
+ bcd>>=4;\r
+\r
+ nibble=bcd & 0x00f;\r
+ if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);\r
+ cut++;\r
+ if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}\r
+ } // n\r
+ if (cut!=0) { // some more left over\r
+ *uout=out; // write out final unit\r
+ if (out) last=uout; // and note if non-zero\r
+ }\r
+ #endif\r
+\r
+ // here, last points to the most significant unit with digits;\r
+ // inspect it to get the final digits count -- this is essentially\r
+ // the same code as decGetDigits in decNumber.c\r
+ dn->digits=(last-dn->lsu)*DECDPUN+1; // floor of digits, plus\r
+ // must be at least 1 digit\r
+ #if DECDPUN>1\r
+ if (*last<10) return; // common odd digit or 0\r
+ dn->digits++; // must be 2 at least\r
+ #if DECDPUN>2\r
+ if (*last<100) return; // 10-99\r
+ dn->digits++; // must be 3 at least\r
+ #if DECDPUN>3\r
+ if (*last<1000) return; // 100-999\r
+ dn->digits++; // must be 4 at least\r
+ #if DECDPUN>4\r
+ for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;\r
+ #endif\r
+ #endif\r
+ #endif\r
+ #endif\r
+ return;\r
+ } //decDigitsFromDPD\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal 64-bit format module header */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2000, 2005. All rights reserved. */\r
+/* */\r
+/* This software is made available under the terms of the */\r
+/* ICU License -- ICU 1.8.1 and later. */\r
+/* */\r
+/* The description and User's Guide ("The decNumber C Library") for */\r
+/* this software is called decNumber.pdf. This document is */\r
+/* available, together with arithmetic and format specifications, */\r
+/* testcases, and Web links, on the General Decimal Arithmetic page. */\r
+/* */\r
+/* Please send comments, suggestions, and corrections to the author: */\r
+/* mfc@uk.ibm.com */\r
+/* Mike Cowlishaw, IBM Fellow */\r
+/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */\r
+/* ------------------------------------------------------------------ */\r
+\r
+#if !defined(DECIMAL64)\r
+ #define DECIMAL64\r
+ #define DEC64NAME "decimal64" /* Short name */\r
+ #define DEC64FULLNAME "Decimal 64-bit Number" /* Verbose name */\r
+ #define DEC64AUTHOR "Mike Cowlishaw" /* Who to blame */\r
+\r
+\r
+ /* parameters for decimal64s */\r
+ #define DECIMAL64_Bytes 8 /* length */\r
+ #define DECIMAL64_Pmax 16 /* maximum precision (digits) */\r
+ #define DECIMAL64_Emax 384 /* maximum adjusted exponent */\r
+ #define DECIMAL64_Emin -383 /* minimum adjusted exponent */\r
+ #define DECIMAL64_Bias 398 /* bias for the exponent */\r
+ #define DECIMAL64_String 24 /* maximum string length, +1 */\r
+ #define DECIMAL64_EconL 8 /* exp. continuation length */\r
+ /* highest biased exponent (Elimit-1) */\r
+ #define DECIMAL64_Ehigh (DECIMAL64_Emax+DECIMAL64_Bias-DECIMAL64_Pmax+1)\r
+\r
+ /* check enough digits, if pre-defined */\r
+ #if defined(DECNUMDIGITS)\r
+ #if (DECNUMDIGITS<DECIMAL64_Pmax)\r
+ #error decimal64.h needs pre-defined DECNUMDIGITS>=16 for safe use\r
+ #endif\r
+ #endif\r
+\r
+\r
+ #ifndef DECNUMDIGITS\r
+ #define DECNUMDIGITS DECIMAL64_Pmax /* size if not already defined*/\r
+ #endif\r
+ #ifndef DECNUMBER\r
+ #include "decNumber.h" /* context and number library */\r
+ #endif\r
+\r
+ /* Decimal 64-bit type, accessible by bytes */\r
+ typedef struct {\r
+ uint8_t bytes[DECIMAL64_Bytes]; /* decimal64: 1, 5, 8, 50 bits*/\r
+ } decimal64;\r
+\r
+ /* special values [top byte excluding sign bit; last two bits are */\r
+ /* don't-care for Infinity on input, last bit don't-care for NaN] */\r
+ #if !defined(DECIMAL_NaN)\r
+ #define DECIMAL_NaN 0x7c /* 0 11111 00 NaN */\r
+ #define DECIMAL_sNaN 0x7e /* 0 11111 10 sNaN */\r
+ #define DECIMAL_Inf 0x78 /* 0 11110 00 Infinity */\r
+ #endif\r
+\r
+ /* ---------------------------------------------------------------- */\r
+ /* Routines */\r
+ /* ---------------------------------------------------------------- */\r
+ /* String conversions */\r
+ decimal64 * decimal64FromString(decimal64 *, const char *, decContext *);\r
+ char * decimal64ToString(const decimal64 *, char *);\r
+ char * decimal64ToEngString(const decimal64 *, char *);\r
+\r
+ /* decNumber conversions */\r
+ decimal64 * decimal64FromNumber(decimal64 *, const decNumber *,\r
+ decContext *);\r
+ decNumber * decimal64ToNumber(const decimal64 *, decNumber *);\r
+\r
+ /* Format-dependent utilities */\r
+ uint32_t decimal64IsCanonical(const decimal64 *);\r
+ decimal64 * decimal64Canonical(decimal64 *, const decimal64 *);\r
+\r
+#endif\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001, 2007. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example1.c -- convert the first two argument words to decNumber,\r
+// add them together, and display the result\r
+\r
+#define DECNUMDIGITS 34 // work with up to 34 digits\r
+#include "decNumber.h" // base number library\r
+#include <stdio.h> // for printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ decNumber a, b; // working numbers\r
+ decContext set; // working context\r
+ char string[DECNUMDIGITS+14]; // conversion buffer\r
+\r
+ decContextTestEndian(0); // warn if DECLITEND is wrong\r
+\r
+ if (argc<3) { // not enough words\r
+ printf("Please supply two numbers to add.\n");\r
+ return 1;\r
+ }\r
+ decContextDefault(&set, DEC_INIT_BASE); // initialize\r
+ set.traps=0; // no traps, thank you\r
+ set.digits=DECNUMDIGITS; // set precision\r
+\r
+ decNumberFromString(&a, argv[1], &set);\r
+ decNumberFromString(&b, argv[2], &set);\r
+\r
+ decNumberAdd(&a, &a, &b, &set); // a=a+b\r
+ decNumberToString(&a, string);\r
+\r
+ printf("%s + %s => %s\n", argv[1], argv[2], string);\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example2.c -- calculate compound interest\r
+// Arguments are investment, rate (%), and years\r
+\r
+#define DECNUMDIGITS 38 // work with up to 38 digits\r
+#include "decNumber.h" // base number library\r
+#include <stdio.h> // for printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ int need=3;\r
+ if (argc<need+1) { // not enough words\r
+ printf("Please supply %d number(s).\n", need);\r
+ return 1;\r
+ }\r
+\r
+ { // excerpt for User's Guide starts here--------------------------|\r
+ decNumber one, mtwo, hundred; // constants\r
+ decNumber start, rate, years; // parameters\r
+ decNumber total; // result\r
+ decContext set; // working context\r
+ char string[DECNUMDIGITS+14]; // conversion buffer\r
+\r
+ decContextDefault(&set, DEC_INIT_BASE); // initialize\r
+ set.traps=0; // no traps\r
+ set.digits=25; // precision 25\r
+ decNumberFromString(&one, "1", &set); // set constants\r
+ decNumberFromString(&mtwo, "-2", &set);\r
+ decNumberFromString(&hundred, "100", &set);\r
+\r
+ decNumberFromString(&start, argv[1], &set); // parameter words\r
+ decNumberFromString(&rate, argv[2], &set);\r
+ decNumberFromString(&years, argv[3], &set);\r
+\r
+ decNumberDivide(&rate, &rate, &hundred, &set); // rate=rate/100\r
+ decNumberAdd(&rate, &rate, &one, &set); // rate=rate+1\r
+ decNumberPower(&rate, &rate, &years, &set); // rate=rate^years\r
+ decNumberMultiply(&total, &rate, &start, &set); // total=rate*start\r
+ decNumberRescale(&total, &total, &mtwo, &set); // two digits please\r
+\r
+ decNumberToString(&total, string);\r
+ printf("%s at %s%% for %s years => %s\n",\r
+ argv[1], argv[2], argv[3], string);\r
+\r
+ } //---------------------------------------------------------------|\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example3.c -- calculate compound interest, passive checking\r
+// Arguments are investment, rate (%), and years\r
+\r
+#define DECNUMDIGITS 38 // work with up to 38 digits\r
+#include "decNumber.h" // base number library\r
+#include <stdio.h> // for printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ int need=3;\r
+ if (argc<need+1) { // not enough words\r
+ printf("Please supply %d number(s).\n", need);\r
+ return 1;\r
+ }\r
+\r
+ { // start of Example 2 segment\r
+ decNumber one, mtwo, hundred; // constants\r
+ decNumber start, rate, years; // parameters\r
+ decNumber total; // result\r
+ decContext set; // working context\r
+ char string[DECNUMDIGITS+14]; // conversion buffer\r
+\r
+ decContextDefault(&set, DEC_INIT_BASE); // initialize\r
+ set.traps=0; // no traps\r
+ set.digits=25; // precision 25\r
+ decNumberFromString(&one, "1", &set); // set constants\r
+ decNumberFromString(&mtwo, "-2", &set);\r
+ decNumberFromString(&hundred, "100", &set);\r
+\r
+// [snip...\r
+ decNumberFromString(&start, argv[1], &set); // parameter words\r
+ decNumberFromString(&rate, argv[2], &set);\r
+ decNumberFromString(&years, argv[3], &set);\r
+ if (set.status & DEC_Errors) {\r
+ printf("An input argument word was invalid [%s]\n",\r
+ decContextStatusToString(&set));\r
+ return 1;\r
+ }\r
+ decNumberDivide(&rate, &rate, &hundred, &set); // rate=rate/100\r
+ decNumberAdd(&rate, &rate, &one, &set); // rate=rate+1\r
+ decNumberPower(&rate, &rate, &years, &set); // rate=rate^years\r
+ decNumberMultiply(&total, &rate, &start, &set); // total=rate*start\r
+ decNumberRescale(&total, &total, &mtwo, &set); // two digits please\r
+ if (set.status & DEC_Errors) {\r
+ set.status &= DEC_Errors; // keep only errors\r
+ printf("Result could not be calculated [%s]\n",\r
+ decContextStatusToString(&set));\r
+ return 1;\r
+ }\r
+// ...snip]\r
+\r
+ decNumberToString(&total, string);\r
+ printf("%s at %s%% for %s years => %s\n",\r
+ argv[1], argv[2], argv[3], string);\r
+\r
+ } //---------------------------------------------------------------|\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example4.c -- add two numbers, active error handling\r
+// Arguments are two numbers\r
+\r
+#define DECNUMDIGITS 38 // work with up to 38 digits\r
+#include "decNumber.h" // base number library\r
+#include <stdio.h> // for printf\r
+\r
+// [snip...\r
+#include <signal.h> // signal handling\r
+#include <setjmp.h> // setjmp/longjmp\r
+\r
+jmp_buf preserve; // stack snapshot\r
+\r
+void signalHandler(int); // prototype for GCC\r
+void signalHandler(int sig) {\r
+ signal(SIGFPE, signalHandler); // re-enable\r
+ longjmp(preserve, sig); // branch to preserved point\r
+ }\r
+// ...snip]\r
+int main(int argc, char *argv[]) {\r
+ decNumber a, b; // working numbers\r
+ decContext set; // working context\r
+ char string[DECNUMDIGITS+14]; // conversion buffer\r
+ int value; // work variable\r
+\r
+ if (argc<3) { // not enough words\r
+ printf("Please supply two numbers to add.\n");\r
+ return 1;\r
+ }\r
+ decContextDefault(&set, DEC_INIT_BASE); // initialize\r
+\r
+// [snip...\r
+ signal(SIGFPE, signalHandler); // set up signal handler\r
+ value=setjmp(preserve); // preserve and test environment\r
+ if (value) { // (non-0 after longjmp)\r
+ set.status &= DEC_Errors; // keep only errors\r
+ printf("Signal trapped [%s].\n", decContextStatusToString(&set));\r
+ return 1;\r
+ }\r
+// ...snip]\r
+\r
+// [change from Example 1, here]\r
+ // leave traps enabled\r
+ set.digits=DECNUMDIGITS; // set precision\r
+\r
+ decNumberFromString(&a, argv[1], &set);\r
+ decNumberFromString(&b, argv[2], &set);\r
+\r
+ decNumberAdd(&a, &a, &b, &set); // A=A+B\r
+ decNumberToString(&a, string);\r
+\r
+ printf("%s + %s => %s\n", argv[1], argv[2], string);\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001, 2007. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example5.c -- decimal64 conversions\r
+\r
+#include "decimal64.h" // decimal64 and decNumber library\r
+#include <stdio.h> // for (s)printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ decimal64 a; // working decimal64 number\r
+ decNumber d; // working number\r
+ decContext set; // working context\r
+ char string[DECIMAL64_String]; // number->string buffer\r
+ char hexes[25]; // decimal64->hex buffer\r
+ int i; // counter\r
+\r
+ if (argc<2) { // not enough words\r
+ printf("Please supply a number.\n");\r
+ return 1;\r
+ }\r
+ decContextDefault(&set, DEC_INIT_DECIMAL64); // initialize\r
+\r
+ decimal64FromString(&a, argv[1], &set);\r
+ // lay out the decimal64 as eight hexadecimal pairs\r
+ for (i=0; i<8; i++) {\r
+ sprintf(&hexes[i*3], "%02x ", a.bytes[i]);\r
+ }\r
+ decimal64ToNumber(&a, &d);\r
+ decNumberToString(&d, string);\r
+ printf("%s => %s=> %s\n", argv[1], hexes, string);\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example6.c -- calculate compound interest, using Packed Decimal\r
+// Values are investment, rate (%), and years\r
+\r
+#include "decPacked.h" // base number library\r
+#include <stdio.h> // for printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ { // excerpt for User's Guide starts here--------------------------|\r
+ decNumber one, mtwo, hundred; // constants\r
+ decNumber start, rate, years; // parameters\r
+ decNumber total; // result\r
+ decContext set; // working context\r
+\r
+ uint8_t startpack[]={0x01, 0x00, 0x00, 0x0C}; // investment=100000\r
+ int32_t startscale=0;\r
+ uint8_t ratepack[]={0x06, 0x5C}; // rate=6.5%\r
+ int32_t ratescale=1;\r
+ uint8_t yearspack[]={0x02, 0x0C}; // years=20\r
+ int32_t yearsscale=0;\r
+ uint8_t respack[16]; // result, packed\r
+ int32_t resscale; // ..\r
+ char hexes[49]; // for packed->hex\r
+ int i; // counter\r
+\r
+ if (argc<0) printf("%s", argv[1]); // noop for warning\r
+\r
+ decContextDefault(&set, DEC_INIT_BASE); // initialize\r
+ set.traps=0; // no traps\r
+ set.digits=25; // precision 25\r
+ decNumberFromString(&one, "1", &set); // set constants\r
+ decNumberFromString(&mtwo, "-2", &set);\r
+ decNumberFromString(&hundred, "100", &set);\r
+\r
+ decPackedToNumber(startpack, sizeof(startpack), &startscale, &start);\r
+ decPackedToNumber(ratepack, sizeof(ratepack), &ratescale, &rate);\r
+ decPackedToNumber(yearspack, sizeof(yearspack), &yearsscale, &years);\r
+\r
+ decNumberDivide(&rate, &rate, &hundred, &set); // rate=rate/100\r
+ decNumberAdd(&rate, &rate, &one, &set); // rate=rate+1\r
+ decNumberPower(&rate, &rate, &years, &set); // rate=rate^years\r
+ decNumberMultiply(&total, &rate, &start, &set); // total=rate*start\r
+ decNumberRescale(&total, &total, &mtwo, &set); // two digits please\r
+\r
+ decPackedFromNumber(respack, sizeof(respack), &resscale, &total);\r
+\r
+ // lay out the total as sixteen hexadecimal pairs\r
+ for (i=0; i<16; i++) {\r
+ sprintf(&hexes[i*3], "%02x ", respack[i]);\r
+ }\r
+ printf("Result: %s (scale=%ld)\n", hexes, (long int)resscale);\r
+\r
+ } //---------------------------------------------------------------|\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001, 2008. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example7.c -- using decQuad to add two numbers together\r
+\r
+// compile: example7.c decContext.c decQuad.c\r
+\r
+#include "decQuad.h" // decQuad library\r
+#include <stdio.h> // for printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ decQuad a, b; // working decQuads\r
+ decContext set; // working context\r
+ char string[DECQUAD_String]; // number->string buffer\r
+\r
+ decContextTestEndian(0); // warn if DECLITEND is wrong\r
+\r
+ if (argc<3) { // not enough words\r
+ printf("Please supply two numbers to add.\n");\r
+ return 1;\r
+ }\r
+ decContextDefault(&set, DEC_INIT_DECQUAD); // initialize\r
+\r
+ decQuadFromString(&a, argv[1], &set);\r
+ decQuadFromString(&b, argv[2], &set);\r
+ decQuadAdd(&a, &a, &b, &set); // a=a+b\r
+ decQuadToString(&a, string);\r
+\r
+ printf("%s + %s => %s\n", argv[1], argv[2], string);\r
+ return 0;\r
+ } // main\r
--- /dev/null
+/* ------------------------------------------------------------------ */\r
+/* Decimal Number Library Demonstration program */\r
+/* ------------------------------------------------------------------ */\r
+/* Copyright (c) IBM Corporation, 2001, 2007. All rights reserved. */\r
+/* ----------------------------------------------------------------+- */\r
+/* right margin -->| */\r
+\r
+// example8.c -- using decQuad with the decNumber module\r
+\r
+// compile: example8.c decContext.c decQuad.c\r
+// and: decNumber.c decimal128.c decimal64.c\r
+\r
+#include "decQuad.h" // decQuad library\r
+#include "decimal128.h" // interface to decNumber\r
+#include <stdio.h> // for printf\r
+\r
+int main(int argc, char *argv[]) {\r
+ decQuad a; // working decQuad\r
+ decNumber numa, numb; // working decNumbers\r
+ decContext set; // working context\r
+ char string[DECQUAD_String]; // number->string buffer\r
+\r
+ if (argc<3) { // not enough words\r
+ printf("Please supply two numbers for power(2*a, b).\n");\r
+ return 1;\r
+ }\r
+ decContextDefault(&set, DEC_INIT_DECQUAD); // initialize\r
+\r
+ decQuadFromString(&a, argv[1], &set); // get a\r
+ decQuadAdd(&a, &a, &a, &set); // double a\r
+ decQuadToNumber(&a, &numa); // convert to decNumber\r
+ decNumberFromString(&numb, argv[2], &set);\r
+ decNumberPower(&numa, &numa, &numb, &set); // numa=numa**numb\r
+ decQuadFromNumber(&a, &numa, &set); // back via a Quad\r
+ decQuadToString(&a, string); // ..\r
+\r
+ printf("power(2*%s, %s) => %s\n", argv[1], argv[2], string);\r
+ return 0;\r
+ } // main\r
--- /dev/null
+This is the readme.txt for the decNumber package. It includes\r
+instructions for compiling and testing the package; please read them.\r
+---------------------------------------------------------------------\r
+\r
+decNumber is distributed in two forms; as a complete package from\r
+the International Components for Unicode (ICU) site (under an as-is\r
+license), or as a collection of Open Source files from the GCC source\r
+repository (under the GPL license).\r
+\r
+If you are using the GCC files, you can obtain the documentation, the\r
+example files mentioned below, and this readme from the General\r
+Decimal Arithmetic web page -- http://speleotrove.com/decimal/ (the\r
+URL for the open source files is also linked from there).\r
+\r
+\r
+The ICU package\r
+---------------\r
+\r
+The ICU package includes the files:\r
+\r
+ * readme.txt (this file)\r
+\r
+ * ICU-license.html\r
+\r
+ * decNumber.pdf (documentation)\r
+\r
+ * The .c and .h file for each module in the package (see the\r
+ decNumber documentation), together with other included files.\r
+\r
+ * The .c files for each of the examples (example1.c through\r
+ example8.c).\r
+\r
+The ICU package is made available under the terms of the ICU License\r
+(ICU 1.8.1 and later) included in the package as ICU-license.html.\r
+Your use of that package indicates your acceptance of the terms and\r
+conditions of that Agreement.\r
+\r
+\r
+To use and check decNumber\r
+--------------------------\r
+\r
+ Please read the appropriate license and documentation before using\r
+ this package. If you are upgrading an existing use of decNumber\r
+ (with version <= 3.37) please read the Changes Appendix for later\r
+ versions -- you may need to change the DECLITEND flag.\r
+\r
+ 1. Compile and link example1.c, decNumber.c, and decContext.c\r
+ For instance, use:\r
+\r
+ gcc -o example1 example1.c decNumber.c decContext.c\r
+\r
+ Note: If your compiler does not provide stdint.h or if your C\r
+ compiler does not handle line comments (// ...), then see the\r
+ User's Guide section in the documentation for further information\r
+ (including a sample minimal stdint.h).\r
+\r
+ The use of compiler optimization is strongly recommended (e.g.,\r
+ -O3 for GCC or /O2 for Visual Studio).\r
+\r
+ 2. Run example1 with two numeric arguments, for example:\r
+\r
+ example1 1.23 1.27\r
+\r
+ this should display:\r
+\r
+ 1.23 + 1.27 => 2.50\r
+\r
+ 3. Similarly, try the other examples, at will.\r
+\r
+ Examples 2->4 require three files to be compiled, like Example 1.\r
+\r
+ Example 5 requires decimal64.c in addition to the core modules.\r
+\r
+ Example 6 requires decPacked.c in addition to the core modules.\r
+\r
+ Example 7 requires only example7.c decContext.c and decQuad.c\r
+\r
+ Example 8 requires example8.c, decContext.c, and decQuad.c, plus\r
+ decNumber.c, decimal128.c, and decimal64.c (the latter\r
+ for shared tables and code)\r
+\r
--- /dev/null
+Skipped 9 tests
+Testing '.[0]' at line number 37
+Hit the number of tests limit (1), breaking
+1 of 1 tests passed (0 malformed)
+==9681== 17 bytes in 1 blocks are definitely lost in loss record 4 of 45
+==9681== at 0x100180545: malloc (vg_replace_malloc.c:302)
+==9681== by 0x1000240D8: jv_mem_alloc (jv_alloc.c:122)
+==9681== by 0x10001F425: jv_number_with_literal (jv.c:193)
+==9681== by 0x10002F9C8: check_literal (jv_parse.c:508)
+==9681== by 0x10002EAA4: jv_parser_next (jv_parse.c:797)
+==9681== by 0x10002FBF2: jv_parse_sized (jv_parse.c:830)
+==9681== by 0x10003544B: jq_yylex (lexer.l:90)
+==9681== by 0x100036FB4: yylex (parser.y:153)
+==9681== by 0x100037352: yyparse (parser.c:2292)
+==9681== by 0x10003B0FD: jq_parse (parser.y:967)
+==9681== by 0x100032CD4: load_program (linker.c:374)
+==9681== by 0x10001C5B3: jq_compile_args (execute.c:1172)
+==9681==
+
+
+Skipped 10 tests
+Testing '.[2]' at line number 41
+Hit the number of tests limit (1), breaking
+1 of 1 tests passed (0 malformed)
+==9690== 17 bytes in 1 blocks are definitely lost in loss record 4 of 45
+==9690== at 0x100180545: malloc (vg_replace_malloc.c:302)
+==9690== by 0x1000240D8: jv_mem_alloc (jv_alloc.c:122)
+==9690== by 0x10001F425: jv_number_with_literal (jv.c:193)
+==9690== by 0x10002F9C8: check_literal (jv_parse.c:508)
+==9690== by 0x10002EAA4: jv_parser_next (jv_parse.c:797)
+==9690== by 0x10002FBF2: jv_parse_sized (jv_parse.c:830)
+==9690== by 0x10003544B: jq_yylex (lexer.l:90)
+==9690== by 0x100036FB4: yylex (parser.y:153)
+==9690== by 0x100037352: yyparse (parser.c:2292)
+==9690== by 0x10003B0FD: jq_parse (parser.y:967)
+==9690== by 0x100032CD4: load_program (linker.c:374)
+==9690== by 0x10001C5B3: jq_compile_args (execute.c:1172)
+==9690==
+
+Skipped 12 tests
+Testing '.[2:4]' at line number 49
+Hit the number of tests limit (1), breaking
+1 of 1 tests passed (0 malformed)
+==9713== 34 bytes in 2 blocks are definitely lost in loss record 15 of 45
+==9713== at 0x100180545: malloc (vg_replace_malloc.c:302)
+==9713== by 0x1000240D8: jv_mem_alloc (jv_alloc.c:122)
+==9713== by 0x10001F425: jv_number_with_literal (jv.c:193)
+==9713== by 0x10002F9C8: check_literal (jv_parse.c:508)
+==9713== by 0x10002EAA4: jv_parser_next (jv_parse.c:797)
+==9713== by 0x10002FBF2: jv_parse_sized (jv_parse.c:830)
+==9713== by 0x10003544B: jq_yylex (lexer.l:90)
+==9713== by 0x100036FB4: yylex (parser.y:153)
+==9713== by 0x100037352: yyparse (parser.c:2292)
+==9713== by 0x10003B0FD: jq_parse (parser.y:967)
+==9713== by 0x100032CD4: load_program (linker.c:374)
+==9713== by 0x10001C5B3: jq_compile_args (execute.c:1172)
+==9713==
+
+Skipped 13 tests
+Testing '.[2:4]' at line number 53
+Hit the number of tests limit (1), breaking
+1 of 1 tests passed (0 malformed)
+==9714== 34 bytes in 2 blocks are definitely lost in loss record 15 of 45
+==9714== at 0x100180545: malloc (vg_replace_malloc.c:302)
+==9714== by 0x1000240D8: jv_mem_alloc (jv_alloc.c:122)
+==9714== by 0x10001F425: jv_number_with_literal (jv.c:193)
+==9714== by 0x10002F9C8: check_literal (jv_parse.c:508)
+==9714== by 0x10002EAA4: jv_parser_next (jv_parse.c:797)
+==9714== by 0x10002FBF2: jv_parse_sized (jv_parse.c:830)
+==9714== by 0x10003544B: jq_yylex (lexer.l:90)
+==9714== by 0x100036FB4: yylex (parser.y:153)
+==9714== by 0x100037352: yyparse (parser.c:2292)
+==9714== by 0x10003B0FD: jq_parse (parser.y:967)
+==9714== by 0x100032CD4: load_program (linker.c:374)
+==9714== by 0x10001C5B3: jq_compile_args (execute.c:1172)
+==9714==
+
+Skipped 14 tests
+Testing '.[:3]' at line number 57
+Hit the number of tests limit (1), breaking
+1 of 1 tests passed (0 malformed)
+==9715== 17 bytes in 1 blocks are definitely lost in loss record 4 of 45
+==9715== at 0x100180545: malloc (vg_replace_malloc.c:302)
+==9715== by 0x1000240D8: jv_mem_alloc (jv_alloc.c:122)
+==9715== by 0x10001F425: jv_number_with_literal (jv.c:193)
+==9715== by 0x10002F9C8: check_literal (jv_parse.c:508)
+==9715== by 0x10002EAA4: jv_parser_next (jv_parse.c:797)
+==9715== by 0x10002FBF2: jv_parse_sized (jv_parse.c:830)
+==9715== by 0x10003544B: jq_yylex (lexer.l:90)
+==9715== by 0x100036FB4: yylex (parser.y:153)
+==9715== by 0x100037352: yyparse (parser.c:2292)
+==9715== by 0x10003B0FD: jq_parse (parser.y:967)
+==9715== by 0x100032CD4: load_program (linker.c:374)
+==9715== by 0x10001C5B3: jq_compile_args (execute.c:1172)
+==9715==
+
+Skipped 19 tests
+Testing '.foo, .bar' at line number 78
+Hit the number of tests limit (1), breaking
+1 of 1 tests passed (0 malformed)
+
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