--- /dev/null
+/****************************************************************
+ *
+ * The author of this software is David M. Gay.
+ *
+ * Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
+ *
+ * Permission to use, copy, modify, and distribute this software for any
+ * purpose without fee is hereby granted, provided that this entire notice
+ * is included in all copies of any software which is or includes a copy
+ * or modification of this software and in all copies of the supporting
+ * documentation for such software.
+ *
+ * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
+ * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
+ * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
+ *
+ ***************************************************************/
+
+/* Please send bug reports to David M. Gay (dmg at acm dot org,
+ * with " at " changed at "@" and " dot " changed to "."). */
+
+/* On a machine with IEEE extended-precision registers, it is
+ * necessary to specify double-precision (53-bit) rounding precision
+ * before invoking strtod or dtoa. If the machine uses (the equivalent
+ * of) Intel 80x87 arithmetic, the call
+ * _control87(PC_53, MCW_PC);
+ * does this with many compilers. Whether this or another call is
+ * appropriate depends on the compiler; for this to work, it may be
+ * necessary to #include "float.h" or another system-dependent header
+ * file.
+ */
+
+/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
+ * (Note that IEEE arithmetic is disabled by gcc's -ffast-math flag.)
+ *
+ * This strtod returns a nearest machine number to the input decimal
+ * string (or sets errno to ERANGE). With IEEE arithmetic, ties are
+ * broken by the IEEE round-even rule. Otherwise ties are broken by
+ * biased rounding (add half and chop).
+ *
+ * Inspired loosely by William D. Clinger's paper "How to Read Floating
+ * Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
+ *
+ * Modifications:
+ *
+ * 1. We only require IEEE, IBM, or VAX double-precision
+ * arithmetic (not IEEE double-extended).
+ * 2. We get by with floating-point arithmetic in a case that
+ * Clinger missed -- when we're computing d * 10^n
+ * for a small integer d and the integer n is not too
+ * much larger than 22 (the maximum integer k for which
+ * we can represent 10^k exactly), we may be able to
+ * compute (d*10^k) * 10^(e-k) with just one roundoff.
+ * 3. Rather than a bit-at-a-time adjustment of the binary
+ * result in the hard case, we use floating-point
+ * arithmetic to determine the adjustment to within
+ * one bit; only in really hard cases do we need to
+ * compute a second residual.
+ * 4. Because of 3., we don't need a large table of powers of 10
+ * for ten-to-e (just some small tables, e.g. of 10^k
+ * for 0 <= k <= 22).
+ */
+
+/*
+ * #define IEEE_8087 for IEEE-arithmetic machines where the least
+ * significant byte has the lowest address.
+ * #define IEEE_MC68k for IEEE-arithmetic machines where the most
+ * significant byte has the lowest address.
+ * #define Long int on machines with 32-bit ints and 64-bit longs.
+ * #define IBM for IBM mainframe-style floating-point arithmetic.
+ * #define VAX for VAX-style floating-point arithmetic (D_floating).
+ * #define No_leftright to omit left-right logic in fast floating-point
+ * computation of dtoa. This will cause dtoa modes 4 and 5 to be
+ * treated the same as modes 2 and 3 for some inputs.
+ * #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+ * and strtod and dtoa should round accordingly. Unless Trust_FLT_ROUNDS
+ * is also #defined, fegetround() will be queried for the rounding mode.
+ * Note that both FLT_ROUNDS and fegetround() are specified by the C99
+ * standard (and are specified to be consistent, with fesetround()
+ * affecting the value of FLT_ROUNDS), but that some (Linux) systems
+ * do not work correctly in this regard, so using fegetround() is more
+ * portable than using FLT_ROUNDS directly.
+ * #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
+ * and Honor_FLT_ROUNDS is not #defined.
+ * #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
+ * that use extended-precision instructions to compute rounded
+ * products and quotients) with IBM.
+ * #define ROUND_BIASED for IEEE-format with biased rounding and arithmetic
+ * that rounds toward +Infinity.
+ * #define ROUND_BIASED_without_Round_Up for IEEE-format with biased
+ * rounding when the underlying floating-point arithmetic uses
+ * unbiased rounding. This prevent using ordinary floating-point
+ * arithmetic when the result could be computed with one rounding error.
+ * #define Inaccurate_Divide for IEEE-format with correctly rounded
+ * products but inaccurate quotients, e.g., for Intel i860.
+ * #define NO_LONG_LONG on machines that do not have a "long long"
+ * integer type (of >= 64 bits). On such machines, you can
+ * #define Just_16 to store 16 bits per 32-bit Long when doing
+ * high-precision integer arithmetic. Whether this speeds things
+ * up or slows things down depends on the machine and the number
+ * being converted. If long long is available and the name is
+ * something other than "long long", #define Llong to be the name,
+ * and if "unsigned Llong" does not work as an unsigned version of
+ * Llong, #define #ULLong to be the corresponding unsigned type.
+ * #define KR_headers for old-style C function headers.
+ * #define Bad_float_h if your system lacks a float.h or if it does not
+ * define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
+ * FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
+ * #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
+ * if memory is available and otherwise does something you deem
+ * appropriate. If MALLOC is undefined, malloc will be invoked
+ * directly -- and assumed always to succeed. Similarly, if you
+ * want something other than the system's free() to be called to
+ * recycle memory acquired from MALLOC, #define FREE to be the
+ * name of the alternate routine. (FREE or free is only called in
+ * pathological cases, e.g., in a dtoa call after a dtoa return in
+ * mode 3 with thousands of digits requested.)
+ * #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
+ * memory allocations from a private pool of memory when possible.
+ * When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
+ * unless #defined to be a different length. This default length
+ * suffices to get rid of MALLOC calls except for unusual cases,
+ * such as decimal-to-binary conversion of a very long string of
+ * digits. The longest string dtoa can return is about 751 bytes
+ * long. For conversions by strtod of strings of 800 digits and
+ * all dtoa conversions in single-threaded executions with 8-byte
+ * pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
+ * pointers, PRIVATE_MEM >= 7112 appears adequate.
+ * #define NO_INFNAN_CHECK if you do not wish to have INFNAN_CHECK
+ * #defined automatically on IEEE systems. On such systems,
+ * when INFNAN_CHECK is #defined, strtod checks
+ * for Infinity and NaN (case insensitively). On some systems
+ * (e.g., some HP systems), it may be necessary to #define NAN_WORD0
+ * appropriately -- to the most significant word of a quiet NaN.
+ * (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
+ * When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
+ * strtod also accepts (case insensitively) strings of the form
+ * NaN(x), where x is a string of hexadecimal digits and spaces;
+ * if there is only one string of hexadecimal digits, it is taken
+ * for the 52 fraction bits of the resulting NaN; if there are two
+ * or more strings of hex digits, the first is for the high 20 bits,
+ * the second and subsequent for the low 32 bits, with intervening
+ * white space ignored; but if this results in none of the 52
+ * fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
+ * and NAN_WORD1 are used instead.
+ * #define MULTIPLE_THREADS if the system offers preemptively scheduled
+ * multiple threads. In this case, you must provide (or suitably
+ * #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
+ * by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
+ * in pow5mult, ensures lazy evaluation of only one copy of high
+ * powers of 5; omitting this lock would introduce a small
+ * probability of wasting memory, but would otherwise be harmless.)
+ * You must also invoke freedtoa(s) to free the value s returned by
+ * dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
+ * #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
+ * avoids underflows on inputs whose result does not underflow.
+ * If you #define NO_IEEE_Scale on a machine that uses IEEE-format
+ * floating-point numbers and flushes underflows to zero rather
+ * than implementing gradual underflow, then you must also #define
+ * Sudden_Underflow.
+ * #define USE_LOCALE to use the current locale's decimal_point value.
+ * #define SET_INEXACT if IEEE arithmetic is being used and extra
+ * computation should be done to set the inexact flag when the
+ * result is inexact and avoid setting inexact when the result
+ * is exact. In this case, dtoa.c must be compiled in
+ * an environment, perhaps provided by #include "dtoa.c" in a
+ * suitable wrapper, that defines two functions,
+ * int get_inexact(void);
+ * void clear_inexact(void);
+ * such that get_inexact() returns a nonzero value if the
+ * inexact bit is already set, and clear_inexact() sets the
+ * inexact bit to 0. When SET_INEXACT is #defined, strtod
+ * also does extra computations to set the underflow and overflow
+ * flags when appropriate (i.e., when the result is tiny and
+ * inexact or when it is a numeric value rounded to +-infinity).
+ * #define NO_ERRNO if strtod should not assign errno = ERANGE when
+ * the result overflows to +-Infinity or underflows to 0.
+ * #define NO_HEX_FP to omit recognition of hexadecimal floating-point
+ * values by strtod.
+ * #define NO_STRTOD_BIGCOMP (on IEEE-arithmetic systems only for now)
+ * to disable logic for "fast" testing of very long input strings
+ * to strtod. This testing proceeds by initially truncating the
+ * input string, then if necessary comparing the whole string with
+ * a decimal expansion to decide close cases. This logic is only
+ * used for input more than STRTOD_DIGLIM digits long (default 40).
+ */
+
+#ifndef Long
+#define Long long
+#endif
+#ifndef ULong
+typedef unsigned Long ULong;
+#endif
+
+#ifdef DEBUG
+#include "stdio.h"
+#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
+#endif
+
+#include "stdlib.h"
+#include "string.h"
+
+#ifdef USE_LOCALE
+#include "locale.h"
+#endif
+
+#ifdef Honor_FLT_ROUNDS
+#ifndef Trust_FLT_ROUNDS
+#include <fenv.h>
+#endif
+#endif
+
+#ifdef MALLOC
+#ifdef KR_headers
+extern char *MALLOC();
+#else
+extern void *MALLOC(size_t);
+#endif
+#else
+#define MALLOC malloc
+#endif
+
+#ifndef Omit_Private_Memory
+#ifndef PRIVATE_MEM
+#define PRIVATE_MEM 2304
+#endif
+#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
+static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
+#endif
+
+#undef IEEE_Arith
+#undef Avoid_Underflow
+#ifdef IEEE_MC68k
+#define IEEE_Arith
+#endif
+#ifdef IEEE_8087
+#define IEEE_Arith
+#endif
+
+#ifdef IEEE_Arith
+#ifndef NO_INFNAN_CHECK
+#undef INFNAN_CHECK
+#define INFNAN_CHECK
+#endif
+#else
+#undef INFNAN_CHECK
+#define NO_STRTOD_BIGCOMP
+#endif
+
+#include "errno.h"
+
+#ifdef Bad_float_h
+
+#ifdef IEEE_Arith
+#define DBL_DIG 15
+#define DBL_MAX_10_EXP 308
+#define DBL_MAX_EXP 1024
+#define FLT_RADIX 2
+#endif /*IEEE_Arith*/
+
+#ifdef IBM
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 75
+#define DBL_MAX_EXP 63
+#define FLT_RADIX 16
+#define DBL_MAX 7.2370055773322621e+75
+#endif
+
+#ifdef VAX
+#define DBL_DIG 16
+#define DBL_MAX_10_EXP 38
+#define DBL_MAX_EXP 127
+#define FLT_RADIX 2
+#define DBL_MAX 1.7014118346046923e+38
+#endif
+
+#ifndef LONG_MAX
+#define LONG_MAX 2147483647
+#endif
+
+#else /* ifndef Bad_float_h */
+#include "float.h"
+#endif /* Bad_float_h */
+
+#ifndef __MATH_H__
+#include "math.h"
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#ifndef CONST
+#ifdef KR_headers
+#define CONST /* blank */
+#else
+#define CONST const
+#endif
+#endif
+
+#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1
+Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.
+#endif
+
+typedef union { double d; ULong L[2]; } U;
+
+#ifdef IEEE_8087
+#define word0(x) (x)->L[1]
+#define word1(x) (x)->L[0]
+#else
+#define word0(x) (x)->L[0]
+#define word1(x) (x)->L[1]
+#endif
+#define dval(x) (x)->d
+
+#ifndef STRTOD_DIGLIM
+#define STRTOD_DIGLIM 40
+#endif
+
+#ifdef DIGLIM_DEBUG
+extern int strtod_diglim;
+#else
+#define strtod_diglim STRTOD_DIGLIM
+#endif
+
+/* The following definition of Storeinc is appropriate for MIPS processors.
+ * An alternative that might be better on some machines is
+ * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
+ */
+#if defined(IEEE_8087) + defined(VAX)
+#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
+((unsigned short *)a)[0] = (unsigned short)c, a++)
+#else
+#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
+((unsigned short *)a)[1] = (unsigned short)c, a++)
+#endif
+
+/* #define P DBL_MANT_DIG */
+/* Ten_pmax = floor(P*log(2)/log(5)) */
+/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
+/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
+/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
+
+#ifdef IEEE_Arith
+#define Exp_shift 20
+#define Exp_shift1 20
+#define Exp_msk1 0x100000
+#define Exp_msk11 0x100000
+#define Exp_mask 0x7ff00000
+#define P 53
+#define Nbits 53
+#define Bias 1023
+#define Emax 1023
+#define Emin (-1022)
+#define Exp_1 0x3ff00000
+#define Exp_11 0x3ff00000
+#define Ebits 11
+#define Frac_mask 0xfffff
+#define Frac_mask1 0xfffff
+#define Ten_pmax 22
+#define Bletch 0x10
+#define Bndry_mask 0xfffff
+#define Bndry_mask1 0xfffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 1
+#define Tiny0 0
+#define Tiny1 1
+#define Quick_max 14
+#define Int_max 14
+#ifndef NO_IEEE_Scale
+#define Avoid_Underflow
+#ifdef Flush_Denorm /* debugging option */
+#undef Sudden_Underflow
+#endif
+#endif
+
+#ifndef Flt_Rounds
+#ifdef FLT_ROUNDS
+#define Flt_Rounds FLT_ROUNDS
+#else
+#define Flt_Rounds 1
+#endif
+#endif /*Flt_Rounds*/
+
+#ifdef Honor_FLT_ROUNDS
+#undef Check_FLT_ROUNDS
+#define Check_FLT_ROUNDS
+#else
+#define Rounding Flt_Rounds
+#endif
+
+#else /* ifndef IEEE_Arith */
+#undef Check_FLT_ROUNDS
+#undef Honor_FLT_ROUNDS
+#undef SET_INEXACT
+#undef Sudden_Underflow
+#define Sudden_Underflow
+#ifdef IBM
+#undef Flt_Rounds
+#define Flt_Rounds 0
+#define Exp_shift 24
+#define Exp_shift1 24
+#define Exp_msk1 0x1000000
+#define Exp_msk11 0x1000000
+#define Exp_mask 0x7f000000
+#define P 14
+#define Nbits 56
+#define Bias 65
+#define Emax 248
+#define Emin (-260)
+#define Exp_1 0x41000000
+#define Exp_11 0x41000000
+#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
+#define Frac_mask 0xffffff
+#define Frac_mask1 0xffffff
+#define Bletch 4
+#define Ten_pmax 22
+#define Bndry_mask 0xefffff
+#define Bndry_mask1 0xffffff
+#define LSB 1
+#define Sign_bit 0x80000000
+#define Log2P 4
+#define Tiny0 0x100000
+#define Tiny1 0
+#define Quick_max 14
+#define Int_max 15
+#else /* VAX */
+#undef Flt_Rounds
+#define Flt_Rounds 1
+#define Exp_shift 23
+#define Exp_shift1 7
+#define Exp_msk1 0x80
+#define Exp_msk11 0x800000
+#define Exp_mask 0x7f80
+#define P 56
+#define Nbits 56
+#define Bias 129
+#define Emax 126
+#define Emin (-129)
+#define Exp_1 0x40800000
+#define Exp_11 0x4080
+#define Ebits 8
+#define Frac_mask 0x7fffff
+#define Frac_mask1 0xffff007f
+#define Ten_pmax 24
+#define Bletch 2
+#define Bndry_mask 0xffff007f
+#define Bndry_mask1 0xffff007f
+#define LSB 0x10000
+#define Sign_bit 0x8000
+#define Log2P 1
+#define Tiny0 0x80
+#define Tiny1 0
+#define Quick_max 15
+#define Int_max 15
+#endif /* IBM, VAX */
+#endif /* IEEE_Arith */
+
+#ifndef IEEE_Arith
+#define ROUND_BIASED
+#else
+#ifdef ROUND_BIASED_without_Round_Up
+#undef ROUND_BIASED
+#define ROUND_BIASED
+#endif
+#endif
+
+#ifdef RND_PRODQUOT
+#define rounded_product(a,b) a = rnd_prod(a, b)
+#define rounded_quotient(a,b) a = rnd_quot(a, b)
+#ifdef KR_headers
+extern double rnd_prod(), rnd_quot();
+#else
+extern double rnd_prod(double, double), rnd_quot(double, double);
+#endif
+#else
+#define rounded_product(a,b) a *= b
+#define rounded_quotient(a,b) a /= b
+#endif
+
+#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
+#define Big1 0xffffffff
+
+#ifndef Pack_32
+#define Pack_32
+#endif
+
+typedef struct BCinfo BCinfo;
+ struct
+BCinfo { int dp0, dp1, dplen, dsign, e0, inexact, nd, nd0, rounding, scale, uflchk; };
+
+#ifdef KR_headers
+#define FFFFFFFF ((((unsigned long)0xffff)<<16)|(unsigned long)0xffff)
+#else
+#define FFFFFFFF 0xffffffffUL
+#endif
+
+#ifdef NO_LONG_LONG
+#undef ULLong
+#ifdef Just_16
+#undef Pack_32
+/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
+ * This makes some inner loops simpler and sometimes saves work
+ * during multiplications, but it often seems to make things slightly
+ * slower. Hence the default is now to store 32 bits per Long.
+ */
+#endif
+#else /* long long available */
+#ifndef Llong
+#define Llong long long
+#endif
+#ifndef ULLong
+#define ULLong unsigned Llong
+#endif
+#endif /* NO_LONG_LONG */
+
+#ifndef MULTIPLE_THREADS
+#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
+#define FREE_DTOA_LOCK(n) /*nothing*/
+#endif
+
+#define Kmax 7
+
+#ifdef __cplusplus
+extern "C" double strtod(const char *s00, char **se);
+extern "C" char *dtoa(double d, int mode, int ndigits,
+ int *decpt, int *sign, char **rve);
+#endif
+
+ struct
+Bigint {
+ struct Bigint *next;
+ int k, maxwds, sign, wds;
+ ULong x[1];
+ };
+
+ typedef struct Bigint Bigint;
+
+ static Bigint *freelist[Kmax+1];
+
+ static Bigint *
+Balloc
+#ifdef KR_headers
+ (k) int k;
+#else
+ (int k)
+#endif
+{
+ int x;
+ Bigint *rv;
+#ifndef Omit_Private_Memory
+ unsigned int len;
+#endif
+
+ ACQUIRE_DTOA_LOCK(0);
+ /* The k > Kmax case does not need ACQUIRE_DTOA_LOCK(0), */
+ /* but this case seems very unlikely. */
+ if (k <= Kmax && (rv = freelist[k]))
+ freelist[k] = rv->next;
+ else {
+ x = 1 << k;
+#ifdef Omit_Private_Memory
+ rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
+#else
+ len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
+ /sizeof(double);
+ if (k <= Kmax && pmem_next - private_mem + len <= PRIVATE_mem) {
+ rv = (Bigint*)pmem_next;
+ pmem_next += len;
+ }
+ else
+ rv = (Bigint*)MALLOC(len*sizeof(double));
+#endif
+ rv->k = k;
+ rv->maxwds = x;
+ }
+ FREE_DTOA_LOCK(0);
+ rv->sign = rv->wds = 0;
+ return rv;
+ }
+
+ static void
+Bfree
+#ifdef KR_headers
+ (v) Bigint *v;
+#else
+ (Bigint *v)
+#endif
+{
+ if (v) {
+ if (v->k > Kmax)
+#ifdef FREE
+ FREE((void*)v);
+#else
+ free((void*)v);
+#endif
+ else {
+ ACQUIRE_DTOA_LOCK(0);
+ v->next = freelist[v->k];
+ freelist[v->k] = v;
+ FREE_DTOA_LOCK(0);
+ }
+ }
+ }
+
+#define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
+y->wds*sizeof(Long) + 2*sizeof(int))
+
+ static Bigint *
+multadd
+#ifdef KR_headers
+ (b, m, a) Bigint *b; int m, a;
+#else
+ (Bigint *b, int m, int a) /* multiply by m and add a */
+#endif
+{
+ int i, wds;
+#ifdef ULLong
+ ULong *x;
+ ULLong carry, y;
+#else
+ ULong carry, *x, y;
+#ifdef Pack_32
+ ULong xi, z;
+#endif
+#endif
+ Bigint *b1;
+
+ wds = b->wds;
+ x = b->x;
+ i = 0;
+ carry = a;
+ do {
+#ifdef ULLong
+ y = *x * (ULLong)m + carry;
+ carry = y >> 32;
+ *x++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+ xi = *x;
+ y = (xi & 0xffff) * m + carry;
+ z = (xi >> 16) * m + (y >> 16);
+ carry = z >> 16;
+ *x++ = (z << 16) + (y & 0xffff);
+#else
+ y = *x * m + carry;
+ carry = y >> 16;
+ *x++ = y & 0xffff;
+#endif
+#endif
+ }
+ while(++i < wds);
+ if (carry) {
+ if (wds >= b->maxwds) {
+ b1 = Balloc(b->k+1);
+ Bcopy(b1, b);
+ Bfree(b);
+ b = b1;
+ }
+ b->x[wds++] = carry;
+ b->wds = wds;
+ }
+ return b;
+ }
+
+ static Bigint *
+s2b
+#ifdef KR_headers
+ (s, nd0, nd, y9, dplen) CONST char *s; int nd0, nd, dplen; ULong y9;
+#else
+ (const char *s, int nd0, int nd, ULong y9, int dplen)
+#endif
+{
+ Bigint *b;
+ int i, k;
+ Long x, y;
+
+ x = (nd + 8) / 9;
+ for(k = 0, y = 1; x > y; y <<= 1, k++) ;
+#ifdef Pack_32
+ b = Balloc(k);
+ b->x[0] = y9;
+ b->wds = 1;
+#else
+ b = Balloc(k+1);
+ b->x[0] = y9 & 0xffff;
+ b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
+#endif
+
+ i = 9;
+ if (9 < nd0) {
+ s += 9;
+ do b = multadd(b, 10, *s++ - '0');
+ while(++i < nd0);
+ s += dplen;
+ }
+ else
+ s += dplen + 9;
+ for(; i < nd; i++)
+ b = multadd(b, 10, *s++ - '0');
+ return b;
+ }
+
+ static int
+hi0bits
+#ifdef KR_headers
+ (x) ULong x;
+#else
+ (ULong x)
+#endif
+{
+ int k = 0;
+
+ if (!(x & 0xffff0000)) {
+ k = 16;
+ x <<= 16;
+ }
+ if (!(x & 0xff000000)) {
+ k += 8;
+ x <<= 8;
+ }
+ if (!(x & 0xf0000000)) {
+ k += 4;
+ x <<= 4;
+ }
+ if (!(x & 0xc0000000)) {
+ k += 2;
+ x <<= 2;
+ }
+ if (!(x & 0x80000000)) {
+ k++;
+ if (!(x & 0x40000000))
+ return 32;
+ }
+ return k;
+ }
+
+ static int
+lo0bits
+#ifdef KR_headers
+ (y) ULong *y;
+#else
+ (ULong *y)
+#endif
+{
+ int k;
+ ULong x = *y;
+
+ if (x & 7) {
+ if (x & 1)
+ return 0;
+ if (x & 2) {
+ *y = x >> 1;
+ return 1;
+ }
+ *y = x >> 2;
+ return 2;
+ }
+ k = 0;
+ if (!(x & 0xffff)) {
+ k = 16;
+ x >>= 16;
+ }
+ if (!(x & 0xff)) {
+ k += 8;
+ x >>= 8;
+ }
+ if (!(x & 0xf)) {
+ k += 4;
+ x >>= 4;
+ }
+ if (!(x & 0x3)) {
+ k += 2;
+ x >>= 2;
+ }
+ if (!(x & 1)) {
+ k++;
+ x >>= 1;
+ if (!x)
+ return 32;
+ }
+ *y = x;
+ return k;
+ }
+
+ static Bigint *
+i2b
+#ifdef KR_headers
+ (i) int i;
+#else
+ (int i)
+#endif
+{
+ Bigint *b;
+
+ b = Balloc(1);
+ b->x[0] = i;
+ b->wds = 1;
+ return b;
+ }
+
+ static Bigint *
+mult
+#ifdef KR_headers
+ (a, b) Bigint *a, *b;
+#else
+ (Bigint *a, Bigint *b)
+#endif
+{
+ Bigint *c;
+ int k, wa, wb, wc;
+ ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
+ ULong y;
+#ifdef ULLong
+ ULLong carry, z;
+#else
+ ULong carry, z;
+#ifdef Pack_32
+ ULong z2;
+#endif
+#endif
+
+ if (a->wds < b->wds) {
+ c = a;
+ a = b;
+ b = c;
+ }
+ k = a->k;
+ wa = a->wds;
+ wb = b->wds;
+ wc = wa + wb;
+ if (wc > a->maxwds)
+ k++;
+ c = Balloc(k);
+ for(x = c->x, xa = x + wc; x < xa; x++)
+ *x = 0;
+ xa = a->x;
+ xae = xa + wa;
+ xb = b->x;
+ xbe = xb + wb;
+ xc0 = c->x;
+#ifdef ULLong
+ for(; xb < xbe; xc0++) {
+ if ((y = *xb++)) {
+ x = xa;
+ xc = xc0;
+ carry = 0;
+ do {
+ z = *x++ * (ULLong)y + *xc + carry;
+ carry = z >> 32;
+ *xc++ = z & FFFFFFFF;
+ }
+ while(x < xae);
+ *xc = carry;
+ }
+ }
+#else
+#ifdef Pack_32
+ for(; xb < xbe; xb++, xc0++) {
+ if (y = *xb & 0xffff) {
+ x = xa;
+ xc = xc0;
+ carry = 0;
+ do {
+ z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
+ carry = z >> 16;
+ z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
+ carry = z2 >> 16;
+ Storeinc(xc, z2, z);
+ }
+ while(x < xae);
+ *xc = carry;
+ }
+ if (y = *xb >> 16) {
+ x = xa;
+ xc = xc0;
+ carry = 0;
+ z2 = *xc;
+ do {
+ z = (*x & 0xffff) * y + (*xc >> 16) + carry;
+ carry = z >> 16;
+ Storeinc(xc, z, z2);
+ z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
+ carry = z2 >> 16;
+ }
+ while(x < xae);
+ *xc = z2;
+ }
+ }
+#else
+ for(; xb < xbe; xc0++) {
+ if (y = *xb++) {
+ x = xa;
+ xc = xc0;
+ carry = 0;
+ do {
+ z = *x++ * y + *xc + carry;
+ carry = z >> 16;
+ *xc++ = z & 0xffff;
+ }
+ while(x < xae);
+ *xc = carry;
+ }
+ }
+#endif
+#endif
+ for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
+ c->wds = wc;
+ return c;
+ }
+
+ static Bigint *p5s;
+
+ static Bigint *
+pow5mult
+#ifdef KR_headers
+ (b, k) Bigint *b; int k;
+#else
+ (Bigint *b, int k)
+#endif
+{
+ Bigint *b1, *p5, *p51;
+ int i;
+ static int p05[3] = { 5, 25, 125 };
+
+ if ((i = k & 3))
+ b = multadd(b, p05[i-1], 0);
+
+ if (!(k >>= 2))
+ return b;
+ if (!(p5 = p5s)) {
+ /* first time */
+#ifdef MULTIPLE_THREADS
+ ACQUIRE_DTOA_LOCK(1);
+ if (!(p5 = p5s)) {
+ p5 = p5s = i2b(625);
+ p5->next = 0;
+ }
+ FREE_DTOA_LOCK(1);
+#else
+ p5 = p5s = i2b(625);
+ p5->next = 0;
+#endif
+ }
+ for(;;) {
+ if (k & 1) {
+ b1 = mult(b, p5);
+ Bfree(b);
+ b = b1;
+ }
+ if (!(k >>= 1))
+ break;
+ if (!(p51 = p5->next)) {
+#ifdef MULTIPLE_THREADS
+ ACQUIRE_DTOA_LOCK(1);
+ if (!(p51 = p5->next)) {
+ p51 = p5->next = mult(p5,p5);
+ p51->next = 0;
+ }
+ FREE_DTOA_LOCK(1);
+#else
+ p51 = p5->next = mult(p5,p5);
+ p51->next = 0;
+#endif
+ }
+ p5 = p51;
+ }
+ return b;
+ }
+
+ static Bigint *
+lshift
+#ifdef KR_headers
+ (b, k) Bigint *b; int k;
+#else
+ (Bigint *b, int k)
+#endif
+{
+ int i, k1, n, n1;
+ Bigint *b1;
+ ULong *x, *x1, *xe, z;
+
+#ifdef Pack_32
+ n = k >> 5;
+#else
+ n = k >> 4;
+#endif
+ k1 = b->k;
+ n1 = n + b->wds + 1;
+ for(i = b->maxwds; n1 > i; i <<= 1)
+ k1++;
+ b1 = Balloc(k1);
+ x1 = b1->x;
+ for(i = 0; i < n; i++)
+ *x1++ = 0;
+ x = b->x;
+ xe = x + b->wds;
+#ifdef Pack_32
+ if (k &= 0x1f) {
+ k1 = 32 - k;
+ z = 0;
+ do {
+ *x1++ = *x << k | z;
+ z = *x++ >> k1;
+ }
+ while(x < xe);
+ if ((*x1 = z))
+ ++n1;
+ }
+#else
+ if (k &= 0xf) {
+ k1 = 16 - k;
+ z = 0;
+ do {
+ *x1++ = *x << k & 0xffff | z;
+ z = *x++ >> k1;
+ }
+ while(x < xe);
+ if (*x1 = z)
+ ++n1;
+ }
+#endif
+ else do
+ *x1++ = *x++;
+ while(x < xe);
+ b1->wds = n1 - 1;
+ Bfree(b);
+ return b1;
+ }
+
+ static int
+cmp
+#ifdef KR_headers
+ (a, b) Bigint *a, *b;
+#else
+ (Bigint *a, Bigint *b)
+#endif
+{
+ ULong *xa, *xa0, *xb, *xb0;
+ int i, j;
+
+ i = a->wds;
+ j = b->wds;
+#ifdef DEBUG
+ if (i > 1 && !a->x[i-1])
+ Bug("cmp called with a->x[a->wds-1] == 0");
+ if (j > 1 && !b->x[j-1])
+ Bug("cmp called with b->x[b->wds-1] == 0");
+#endif
+ if (i -= j)
+ return i;
+ xa0 = a->x;
+ xa = xa0 + j;
+ xb0 = b->x;
+ xb = xb0 + j;
+ for(;;) {
+ if (*--xa != *--xb)
+ return *xa < *xb ? -1 : 1;
+ if (xa <= xa0)
+ break;
+ }
+ return 0;
+ }
+
+ static Bigint *
+diff
+#ifdef KR_headers
+ (a, b) Bigint *a, *b;
+#else
+ (Bigint *a, Bigint *b)
+#endif
+{
+ Bigint *c;
+ int i, wa, wb;
+ ULong *xa, *xae, *xb, *xbe, *xc;
+#ifdef ULLong
+ ULLong borrow, y;
+#else
+ ULong borrow, y;
+#ifdef Pack_32
+ ULong z;
+#endif
+#endif
+
+ i = cmp(a,b);
+ if (!i) {
+ c = Balloc(0);
+ c->wds = 1;
+ c->x[0] = 0;
+ return c;
+ }
+ if (i < 0) {
+ c = a;
+ a = b;
+ b = c;
+ i = 1;
+ }
+ else
+ i = 0;
+ c = Balloc(a->k);
+ c->sign = i;
+ wa = a->wds;
+ xa = a->x;
+ xae = xa + wa;
+ wb = b->wds;
+ xb = b->x;
+ xbe = xb + wb;
+ xc = c->x;
+ borrow = 0;
+#ifdef ULLong
+ do {
+ y = (ULLong)*xa++ - *xb++ - borrow;
+ borrow = y >> 32 & (ULong)1;
+ *xc++ = y & FFFFFFFF;
+ }
+ while(xb < xbe);
+ while(xa < xae) {
+ y = *xa++ - borrow;
+ borrow = y >> 32 & (ULong)1;
+ *xc++ = y & FFFFFFFF;
+ }
+#else
+#ifdef Pack_32
+ do {
+ y = (*xa & 0xffff) - (*xb & 0xffff) - borrow;
+ borrow = (y & 0x10000) >> 16;
+ z = (*xa++ >> 16) - (*xb++ >> 16) - borrow;
+ borrow = (z & 0x10000) >> 16;
+ Storeinc(xc, z, y);
+ }
+ while(xb < xbe);
+ while(xa < xae) {
+ y = (*xa & 0xffff) - borrow;
+ borrow = (y & 0x10000) >> 16;
+ z = (*xa++ >> 16) - borrow;
+ borrow = (z & 0x10000) >> 16;
+ Storeinc(xc, z, y);
+ }
+#else
+ do {
+ y = *xa++ - *xb++ - borrow;
+ borrow = (y & 0x10000) >> 16;
+ *xc++ = y & 0xffff;
+ }
+ while(xb < xbe);
+ while(xa < xae) {
+ y = *xa++ - borrow;
+ borrow = (y & 0x10000) >> 16;
+ *xc++ = y & 0xffff;
+ }
+#endif
+#endif
+ while(!*--xc)
+ wa--;
+ c->wds = wa;
+ return c;
+ }
+
+ static double
+ulp
+#ifdef KR_headers
+ (x) U *x;
+#else
+ (U *x)
+#endif
+{
+ Long L;
+ U u;
+
+ L = (word0(x) & Exp_mask) - (P-1)*Exp_msk1;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+ if (L > 0) {
+#endif
+#endif
+#ifdef IBM
+ L |= Exp_msk1 >> 4;
+#endif
+ word0(&u) = L;
+ word1(&u) = 0;
+#ifndef Avoid_Underflow
+#ifndef Sudden_Underflow
+ }
+ else {
+ L = -L >> Exp_shift;
+ if (L < Exp_shift) {
+ word0(&u) = 0x80000 >> L;
+ word1(&u) = 0;
+ }
+ else {
+ word0(&u) = 0;
+ L -= Exp_shift;
+ word1(&u) = L >= 31 ? 1 : 1 << 31 - L;
+ }
+ }
+#endif
+#endif
+ return dval(&u);
+ }
+
+ static double
+b2d
+#ifdef KR_headers
+ (a, e) Bigint *a; int *e;
+#else
+ (Bigint *a, int *e)
+#endif
+{
+ ULong *xa, *xa0, w, y, z;
+ int k;
+ U d;
+#ifdef VAX
+ ULong d0, d1;
+#else
+#define d0 word0(&d)
+#define d1 word1(&d)
+#endif
+
+ xa0 = a->x;
+ xa = xa0 + a->wds;
+ y = *--xa;
+#ifdef DEBUG
+ if (!y) Bug("zero y in b2d");
+#endif
+ k = hi0bits(y);
+ *e = 32 - k;
+#ifdef Pack_32
+ if (k < Ebits) {
+ d0 = Exp_1 | y >> (Ebits - k);
+ w = xa > xa0 ? *--xa : 0;
+ d1 = y << ((32-Ebits) + k) | w >> (Ebits - k);
+ goto ret_d;
+ }
+ z = xa > xa0 ? *--xa : 0;
+ if (k -= Ebits) {
+ d0 = Exp_1 | y << k | z >> (32 - k);
+ y = xa > xa0 ? *--xa : 0;
+ d1 = z << k | y >> (32 - k);
+ }
+ else {
+ d0 = Exp_1 | y;
+ d1 = z;
+ }
+#else
+ if (k < Ebits + 16) {
+ z = xa > xa0 ? *--xa : 0;
+ d0 = Exp_1 | y << k - Ebits | z >> Ebits + 16 - k;
+ w = xa > xa0 ? *--xa : 0;
+ y = xa > xa0 ? *--xa : 0;
+ d1 = z << k + 16 - Ebits | w << k - Ebits | y >> 16 + Ebits - k;
+ goto ret_d;
+ }
+ z = xa > xa0 ? *--xa : 0;
+ w = xa > xa0 ? *--xa : 0;
+ k -= Ebits + 16;
+ d0 = Exp_1 | y << k + 16 | z << k | w >> 16 - k;
+ y = xa > xa0 ? *--xa : 0;
+ d1 = w << k + 16 | y << k;
+#endif
+ ret_d:
+#ifdef VAX
+ word0(&d) = d0 >> 16 | d0 << 16;
+ word1(&d) = d1 >> 16 | d1 << 16;
+#else
+#undef d0
+#undef d1
+#endif
+ return dval(&d);
+ }
+
+ static Bigint *
+d2b
+#ifdef KR_headers
+ (d, e, bits) U *d; int *e, *bits;
+#else
+ (U *d, int *e, int *bits)
+#endif
+{
+ Bigint *b;
+ int de, k;
+ ULong *x, y, z;
+#ifndef Sudden_Underflow
+ int i;
+#endif
+#ifdef VAX
+ ULong d0, d1;
+ d0 = word0(d) >> 16 | word0(d) << 16;
+ d1 = word1(d) >> 16 | word1(d) << 16;
+#else
+#define d0 word0(d)
+#define d1 word1(d)
+#endif
+
+#ifdef Pack_32
+ b = Balloc(1);
+#else
+ b = Balloc(2);
+#endif
+ x = b->x;
+
+ z = d0 & Frac_mask;
+ d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
+#ifdef Sudden_Underflow
+ de = (int)(d0 >> Exp_shift);
+#ifndef IBM
+ z |= Exp_msk11;
+#endif
+#else
+ if ((de = (int)(d0 >> Exp_shift)))
+ z |= Exp_msk1;
+#endif
+#ifdef Pack_32
+ if ((y = d1)) {
+ if ((k = lo0bits(&y))) {
+ x[0] = y | z << (32 - k);
+ z >>= k;
+ }
+ else
+ x[0] = y;
+#ifndef Sudden_Underflow
+ i =
+#endif
+ b->wds = (x[1] = z) ? 2 : 1;
+ }
+ else {
+ k = lo0bits(&z);
+ x[0] = z;
+#ifndef Sudden_Underflow
+ i =
+#endif
+ b->wds = 1;
+ k += 32;
+ }
+#else
+ if (y = d1) {
+ if (k = lo0bits(&y))
+ if (k >= 16) {
+ x[0] = y | z << 32 - k & 0xffff;
+ x[1] = z >> k - 16 & 0xffff;
+ x[2] = z >> k;
+ i = 2;
+ }
+ else {
+ x[0] = y & 0xffff;
+ x[1] = y >> 16 | z << 16 - k & 0xffff;
+ x[2] = z >> k & 0xffff;
+ x[3] = z >> k+16;
+ i = 3;
+ }
+ else {
+ x[0] = y & 0xffff;
+ x[1] = y >> 16;
+ x[2] = z & 0xffff;
+ x[3] = z >> 16;
+ i = 3;
+ }
+ }
+ else {
+#ifdef DEBUG
+ if (!z)
+ Bug("Zero passed to d2b");
+#endif
+ k = lo0bits(&z);
+ if (k >= 16) {
+ x[0] = z;
+ i = 0;
+ }
+ else {
+ x[0] = z & 0xffff;
+ x[1] = z >> 16;
+ i = 1;
+ }
+ k += 32;
+ }
+ while(!x[i])
+ --i;
+ b->wds = i + 1;
+#endif
+#ifndef Sudden_Underflow
+ if (de) {
+#endif
+#ifdef IBM
+ *e = (de - Bias - (P-1) << 2) + k;
+ *bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
+#else
+ *e = de - Bias - (P-1) + k;
+ *bits = P - k;
+#endif
+#ifndef Sudden_Underflow
+ }
+ else {
+ *e = de - Bias - (P-1) + 1 + k;
+#ifdef Pack_32
+ *bits = 32*i - hi0bits(x[i-1]);
+#else
+ *bits = (i+2)*16 - hi0bits(x[i]);
+#endif
+ }
+#endif
+ return b;
+ }
+#undef d0
+#undef d1
+
+ static double
+ratio
+#ifdef KR_headers
+ (a, b) Bigint *a, *b;
+#else
+ (Bigint *a, Bigint *b)
+#endif
+{
+ U da, db;
+ int k, ka, kb;
+
+ dval(&da) = b2d(a, &ka);
+ dval(&db) = b2d(b, &kb);
+#ifdef Pack_32
+ k = ka - kb + 32*(a->wds - b->wds);
+#else
+ k = ka - kb + 16*(a->wds - b->wds);
+#endif
+#ifdef IBM
+ if (k > 0) {
+ word0(&da) += (k >> 2)*Exp_msk1;
+ if (k &= 3)
+ dval(&da) *= 1 << k;
+ }
+ else {
+ k = -k;
+ word0(&db) += (k >> 2)*Exp_msk1;
+ if (k &= 3)
+ dval(&db) *= 1 << k;
+ }
+#else
+ if (k > 0)
+ word0(&da) += k*Exp_msk1;
+ else {
+ k = -k;
+ word0(&db) += k*Exp_msk1;
+ }
+#endif
+ return dval(&da) / dval(&db);
+ }
+
+ static CONST double
+tens[] = {
+ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+ 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
+ 1e20, 1e21, 1e22
+#ifdef VAX
+ , 1e23, 1e24
+#endif
+ };
+
+ static CONST double
+#ifdef IEEE_Arith
+bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128,
+#ifdef Avoid_Underflow
+ 9007199254740992.*9007199254740992.e-256
+ /* = 2^106 * 1e-256 */
+#else
+ 1e-256
+#endif
+ };
+/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */
+/* flag unnecessarily. It leads to a song and dance at the end of strtod. */
+#define Scale_Bit 0x10
+#define n_bigtens 5
+#else
+#ifdef IBM
+bigtens[] = { 1e16, 1e32, 1e64 };
+static CONST double tinytens[] = { 1e-16, 1e-32, 1e-64 };
+#define n_bigtens 3
+#else
+bigtens[] = { 1e16, 1e32 };
+static CONST double tinytens[] = { 1e-16, 1e-32 };
+#define n_bigtens 2
+#endif
+#endif
+
+#undef Need_Hexdig
+#ifdef INFNAN_CHECK
+#ifndef No_Hex_NaN
+#define Need_Hexdig
+#endif
+#endif
+
+#ifndef Need_Hexdig
+#ifndef NO_HEX_FP
+#define Need_Hexdig
+#endif
+#endif
+
+#ifdef Need_Hexdig /*{*/
+static unsigned char hexdig[256];
+
+ static void
+#ifdef KR_headers
+htinit(h, s, inc) unsigned char *h; unsigned char *s; int inc;
+#else
+htinit(unsigned char *h, unsigned char *s, int inc)
+#endif
+{
+ int i, j;
+ for(i = 0; (j = s[i]) !=0; i++)
+ h[j] = i + inc;
+ }
+
+ static void
+#ifdef KR_headers
+hexdig_init()
+#else
+hexdig_init(void)
+#endif
+{
+#define USC (unsigned char *)
+ htinit(hexdig, USC "0123456789", 0x10);
+ htinit(hexdig, USC "abcdef", 0x10 + 10);
+ htinit(hexdig, USC "ABCDEF", 0x10 + 10);
+ }
+#endif /* } Need_Hexdig */
+
+#ifdef INFNAN_CHECK
+
+#ifndef NAN_WORD0
+#define NAN_WORD0 0x7ff80000
+#endif
+
+#ifndef NAN_WORD1
+#define NAN_WORD1 0
+#endif
+
+ static int
+match
+#ifdef KR_headers
+ (sp, t) char **sp, *t;
+#else
+ (const char **sp, const char *t)
+#endif
+{
+ int c, d;
+ CONST char *s = *sp;
+
+ while((d = *t++)) {
+ if ((c = *++s) >= 'A' && c <= 'Z')
+ c += 'a' - 'A';
+ if (c != d)
+ return 0;
+ }
+ *sp = s + 1;
+ return 1;
+ }
+
+#ifndef No_Hex_NaN
+ static void
+hexnan
+#ifdef KR_headers
+ (rvp, sp) U *rvp; CONST char **sp;
+#else
+ (U *rvp, const char **sp)
+#endif
+{
+ ULong c, x[2];
+ CONST char *s;
+ int c1, havedig, udx0, xshift;
+
+ if (!hexdig['0'])
+ hexdig_init();
+ x[0] = x[1] = 0;
+ havedig = xshift = 0;
+ udx0 = 1;
+ s = *sp;
+ /* allow optional initial 0x or 0X */
+ while((c = *(CONST unsigned char*)(s+1)) && c <= ' ')
+ ++s;
+ if (s[1] == '0' && (s[2] == 'x' || s[2] == 'X'))
+ s += 2;
+ while((c = *(CONST unsigned char*)++s)) {
+ if ((c1 = hexdig[c]))
+ c = c1 & 0xf;
+ else if (c <= ' ') {
+ if (udx0 && havedig) {
+ udx0 = 0;
+ xshift = 1;
+ }
+ continue;
+ }
+#ifdef GDTOA_NON_PEDANTIC_NANCHECK
+ else if (/*(*/ c == ')' && havedig) {
+ *sp = s + 1;
+ break;
+ }
+ else
+ return; /* invalid form: don't change *sp */
+#else
+ else {
+ do {
+ if (/*(*/ c == ')') {
+ *sp = s + 1;
+ break;
+ }
+ } while((c = *++s));
+ break;
+ }
+#endif
+ havedig = 1;
+ if (xshift) {
+ xshift = 0;
+ x[0] = x[1];
+ x[1] = 0;
+ }
+ if (udx0)
+ x[0] = (x[0] << 4) | (x[1] >> 28);
+ x[1] = (x[1] << 4) | c;
+ }
+ if ((x[0] &= 0xfffff) || x[1]) {
+ word0(rvp) = Exp_mask | x[0];
+ word1(rvp) = x[1];
+ }
+ }
+#endif /*No_Hex_NaN*/
+#endif /* INFNAN_CHECK */
+
+#ifdef Pack_32
+#define ULbits 32
+#define kshift 5
+#define kmask 31
+#else
+#define ULbits 16
+#define kshift 4
+#define kmask 15
+#endif
+
+#if !defined(NO_HEX_FP) || defined(Honor_FLT_ROUNDS) /*{*/
+ static Bigint *
+#ifdef KR_headers
+increment(b) Bigint *b;
+#else
+increment(Bigint *b)
+#endif
+{
+ ULong *x, *xe;
+ Bigint *b1;
+
+ x = b->x;
+ xe = x + b->wds;
+ do {
+ if (*x < (ULong)0xffffffffL) {
+ ++*x;
+ return b;
+ }
+ *x++ = 0;
+ } while(x < xe);
+ {
+ if (b->wds >= b->maxwds) {
+ b1 = Balloc(b->k+1);
+ Bcopy(b1,b);
+ Bfree(b);
+ b = b1;
+ }
+ b->x[b->wds++] = 1;
+ }
+ return b;
+ }
+
+#endif /*}*/
+
+#ifndef NO_HEX_FP /*{*/
+
+ static void
+#ifdef KR_headers
+rshift(b, k) Bigint *b; int k;
+#else
+rshift(Bigint *b, int k)
+#endif
+{
+ ULong *x, *x1, *xe, y;
+ int n;
+
+ x = x1 = b->x;
+ n = k >> kshift;
+ if (n < b->wds) {
+ xe = x + b->wds;
+ x += n;
+ if (k &= kmask) {
+ n = 32 - k;
+ y = *x++ >> k;
+ while(x < xe) {
+ *x1++ = (y | (*x << n)) & 0xffffffff;
+ y = *x++ >> k;
+ }
+ if ((*x1 = y) !=0)
+ x1++;
+ }
+ else
+ while(x < xe)
+ *x1++ = *x++;
+ }
+ if ((b->wds = x1 - b->x) == 0)
+ b->x[0] = 0;
+ }
+
+ static ULong
+#ifdef KR_headers
+any_on(b, k) Bigint *b; int k;
+#else
+any_on(Bigint *b, int k)
+#endif
+{
+ int n, nwds;
+ ULong *x, *x0, x1, x2;
+
+ x = b->x;
+ nwds = b->wds;
+ n = k >> kshift;
+ if (n > nwds)
+ n = nwds;
+ else if (n < nwds && (k &= kmask)) {
+ x1 = x2 = x[n];
+ x1 >>= k;
+ x1 <<= k;
+ if (x1 != x2)
+ return 1;
+ }
+ x0 = x;
+ x += n;
+ while(x > x0)
+ if (*--x)
+ return 1;
+ return 0;
+ }
+
+enum { /* rounding values: same as FLT_ROUNDS */
+ Round_zero = 0,
+ Round_near = 1,
+ Round_up = 2,
+ Round_down = 3
+ };
+
+ void
+#ifdef KR_headers
+gethex(sp, rvp, rounding, sign)
+ CONST char **sp; U *rvp; int rounding, sign;
+#else
+gethex( CONST char **sp, U *rvp, int rounding, int sign)
+#endif
+{
+ Bigint *b;
+ CONST unsigned char *decpt, *s0, *s, *s1;
+ Long e, e1;
+ ULong L, lostbits, *x;
+ int big, denorm, esign, havedig, k, n, nbits, up, zret;
+#ifdef IBM
+ int j;
+#endif
+ enum {
+#ifdef IEEE_Arith /*{{*/
+ emax = 0x7fe - Bias - P + 1,
+ emin = Emin - P + 1
+#else /*}{*/
+ emin = Emin - P,
+#ifdef VAX
+ emax = 0x7ff - Bias - P + 1
+#endif
+#ifdef IBM
+ emax = 0x7f - Bias - P
+#endif
+#endif /*}}*/
+ };
+#ifdef USE_LOCALE
+ int i;
+#ifdef NO_LOCALE_CACHE
+ const unsigned char *decimalpoint = (unsigned char*)
+ localeconv()->decimal_point;
+#else
+ const unsigned char *decimalpoint;
+ static unsigned char *decimalpoint_cache;
+ if (!(s0 = decimalpoint_cache)) {
+ s0 = (unsigned char*)localeconv()->decimal_point;
+ if ((decimalpoint_cache = (unsigned char*)
+ MALLOC(strlen((CONST char*)s0) + 1))) {
+ strcpy((char*)decimalpoint_cache, (CONST char*)s0);
+ s0 = decimalpoint_cache;
+ }
+ }
+ decimalpoint = s0;
+#endif
+#endif
+
+ if (!hexdig['0'])
+ hexdig_init();
+ havedig = 0;
+ s0 = *(CONST unsigned char **)sp + 2;
+ while(s0[havedig] == '0')
+ havedig++;
+ s0 += havedig;
+ s = s0;
+ decpt = 0;
+ zret = 0;
+ e = 0;
+ if (hexdig[*s])
+ havedig++;
+ else {
+ zret = 1;
+#ifdef USE_LOCALE
+ for(i = 0; decimalpoint[i]; ++i) {
+ if (s[i] != decimalpoint[i])
+ goto pcheck;
+ }
+ decpt = s += i;
+#else
+ if (*s != '.')
+ goto pcheck;
+ decpt = ++s;
+#endif
+ if (!hexdig[*s])
+ goto pcheck;
+ while(*s == '0')
+ s++;
+ if (hexdig[*s])
+ zret = 0;
+ havedig = 1;
+ s0 = s;
+ }
+ while(hexdig[*s])
+ s++;
+#ifdef USE_LOCALE
+ if (*s == *decimalpoint && !decpt) {
+ for(i = 1; decimalpoint[i]; ++i) {
+ if (s[i] != decimalpoint[i])
+ goto pcheck;
+ }
+ decpt = s += i;
+#else
+ if (*s == '.' && !decpt) {
+ decpt = ++s;
+#endif
+ while(hexdig[*s])
+ s++;
+ }/*}*/
+ if (decpt)
+ e = -(((Long)(s-decpt)) << 2);
+ pcheck:
+ s1 = s;
+ big = esign = 0;
+ switch(*s) {
+ case 'p':
+ case 'P':
+ switch(*++s) {
+ case '-':
+ esign = 1;
+ /* no break */
+ case '+':
+ s++;
+ }
+ if ((n = hexdig[*s]) == 0 || n > 0x19) {
+ s = s1;
+ break;
+ }
+ e1 = n - 0x10;
+ while((n = hexdig[*++s]) !=0 && n <= 0x19) {
+ if (e1 & 0xf8000000)
+ big = 1;
+ e1 = 10*e1 + n - 0x10;
+ }
+ if (esign)
+ e1 = -e1;
+ e += e1;
+ }
+ *sp = (char*)s;
+ if (!havedig)
+ *sp = (char*)s0 - 1;
+ if (zret)
+ goto retz1;
+ if (big) {
+ if (esign) {
+#ifdef IEEE_Arith
+ switch(rounding) {
+ case Round_up:
+ if (sign)
+ break;
+ goto ret_tiny;
+ case Round_down:
+ if (!sign)
+ break;
+ goto ret_tiny;
+ }
+#endif
+ goto retz;
+#ifdef IEEE_Arith
+ ret_tiny:
+#ifndef NO_ERRNO
+ errno = ERANGE;
+#endif
+ word0(rvp) = 0;
+ word1(rvp) = 1;
+ return;
+#endif /* IEEE_Arith */
+ }
+ switch(rounding) {
+ case Round_near:
+ goto ovfl1;
+ case Round_up:
+ if (!sign)
+ goto ovfl1;
+ goto ret_big;
+ case Round_down:
+ if (sign)
+ goto ovfl1;
+ goto ret_big;
+ }
+ ret_big:
+ word0(rvp) = Big0;
+ word1(rvp) = Big1;
+ return;
+ }
+ n = s1 - s0 - 1;
+ for(k = 0; n > (1 << (kshift-2)) - 1; n >>= 1)
+ k++;
+ b = Balloc(k);
+ x = b->x;
+ n = 0;
+ L = 0;
+#ifdef USE_LOCALE
+ for(i = 0; decimalpoint[i+1]; ++i);
+#endif
+ while(s1 > s0) {
+#ifdef USE_LOCALE
+ if (*--s1 == decimalpoint[i]) {
+ s1 -= i;
+ continue;
+ }
+#else
+ if (*--s1 == '.')
+ continue;
+#endif
+ if (n == ULbits) {
+ *x++ = L;
+ L = 0;
+ n = 0;
+ }
+ L |= (hexdig[*s1] & 0x0f) << n;
+ n += 4;
+ }
+ *x++ = L;
+ b->wds = n = x - b->x;
+ n = ULbits*n - hi0bits(L);
+ nbits = Nbits;
+ lostbits = 0;
+ x = b->x;
+ if (n > nbits) {
+ n -= nbits;
+ if (any_on(b,n)) {
+ lostbits = 1;
+ k = n - 1;
+ if (x[k>>kshift] & 1 << (k & kmask)) {
+ lostbits = 2;
+ if (k > 0 && any_on(b,k))
+ lostbits = 3;
+ }
+ }
+ rshift(b, n);
+ e += n;
+ }
+ else if (n < nbits) {
+ n = nbits - n;
+ b = lshift(b, n);
+ e -= n;
+ x = b->x;
+ }
+ if (e > Emax) {
+ ovfl:
+ Bfree(b);
+ ovfl1:
+#ifndef NO_ERRNO
+ errno = ERANGE;
+#endif
+ word0(rvp) = Exp_mask;
+ word1(rvp) = 0;
+ return;
+ }
+ denorm = 0;
+ if (e < emin) {
+ denorm = 1;
+ n = emin - e;
+ if (n >= nbits) {
+#ifdef IEEE_Arith /*{*/
+ switch (rounding) {
+ case Round_near:
+ if (n == nbits && (n < 2 || any_on(b,n-1)))
+ goto ret_tiny;
+ break;
+ case Round_up:
+ if (!sign)
+ goto ret_tiny;
+ break;
+ case Round_down:
+ if (sign)
+ goto ret_tiny;
+ }
+#endif /* } IEEE_Arith */
+ Bfree(b);
+ retz:
+#ifndef NO_ERRNO
+ errno = ERANGE;
+#endif
+ retz1:
+ rvp->d = 0.;
+ return;
+ }
+ k = n - 1;
+ if (lostbits)
+ lostbits = 1;
+ else if (k > 0)
+ lostbits = any_on(b,k);
+ if (x[k>>kshift] & 1 << (k & kmask))
+ lostbits |= 2;
+ nbits -= n;
+ rshift(b,n);
+ e = emin;
+ }
+ if (lostbits) {
+ up = 0;
+ switch(rounding) {
+ case Round_zero:
+ break;
+ case Round_near:
+ if (lostbits & 2
+ && (lostbits & 1) | (x[0] & 1))
+ up = 1;
+ break;
+ case Round_up:
+ up = 1 - sign;
+ break;
+ case Round_down:
+ up = sign;
+ }
+ if (up) {
+ k = b->wds;
+ b = increment(b);
+ x = b->x;
+ if (denorm) {
+#if 0
+ if (nbits == Nbits - 1
+ && x[nbits >> kshift] & 1 << (nbits & kmask))
+ denorm = 0; /* not currently used */
+#endif
+ }
+ else if (b->wds > k
+ || ((n = nbits & kmask) !=0
+ && hi0bits(x[k-1]) < 32-n)) {
+ rshift(b,1);
+ if (++e > Emax)
+ goto ovfl;
+ }
+ }
+ }
+#ifdef IEEE_Arith
+ if (denorm)
+ word0(rvp) = b->wds > 1 ? b->x[1] & ~0x100000 : 0;
+ else
+ word0(rvp) = (b->x[1] & ~0x100000) | ((e + 0x3ff + 52) << 20);
+ word1(rvp) = b->x[0];
+#endif
+#ifdef IBM
+ if ((j = e & 3)) {
+ k = b->x[0] & ((1 << j) - 1);
+ rshift(b,j);
+ if (k) {
+ switch(rounding) {
+ case Round_up:
+ if (!sign)
+ increment(b);
+ break;
+ case Round_down:
+ if (sign)
+ increment(b);
+ break;
+ case Round_near:
+ j = 1 << (j-1);
+ if (k & j && ((k & (j-1)) | lostbits))
+ increment(b);
+ }
+ }
+ }
+ e >>= 2;
+ word0(rvp) = b->x[1] | ((e + 65 + 13) << 24);
+ word1(rvp) = b->x[0];
+#endif
+#ifdef VAX
+ /* The next two lines ignore swap of low- and high-order 2 bytes. */
+ /* word0(rvp) = (b->x[1] & ~0x800000) | ((e + 129 + 55) << 23); */
+ /* word1(rvp) = b->x[0]; */
+ word0(rvp) = ((b->x[1] & ~0x800000) >> 16) | ((e + 129 + 55) << 7) | (b->x[1] << 16);
+ word1(rvp) = (b->x[0] >> 16) | (b->x[0] << 16);
+#endif
+ Bfree(b);
+ }
+#endif /*!NO_HEX_FP}*/
+
+ static int
+#ifdef KR_headers
+dshift(b, p2) Bigint *b; int p2;
+#else
+dshift(Bigint *b, int p2)
+#endif
+{
+ int rv = hi0bits(b->x[b->wds-1]) - 4;
+ if (p2 > 0)
+ rv -= p2;
+ return rv & kmask;
+ }
+
+ static int
+quorem
+#ifdef KR_headers
+ (b, S) Bigint *b, *S;
+#else
+ (Bigint *b, Bigint *S)
+#endif
+{
+ int n;
+ ULong *bx, *bxe, q, *sx, *sxe;
+#ifdef ULLong
+ ULLong borrow, carry, y, ys;
+#else
+ ULong borrow, carry, y, ys;
+#ifdef Pack_32
+ ULong si, z, zs;
+#endif
+#endif
+
+ n = S->wds;
+#ifdef DEBUG
+ /*debug*/ if (b->wds > n)
+ /*debug*/ Bug("oversize b in quorem");
+#endif
+ if (b->wds < n)
+ return 0;
+ sx = S->x;
+ sxe = sx + --n;
+ bx = b->x;
+ bxe = bx + n;
+ q = *bxe / (*sxe + 1); /* ensure q <= true quotient */
+#ifdef DEBUG
+#ifdef NO_STRTOD_BIGCOMP
+ /*debug*/ if (q > 9)
+#else
+ /* An oversized q is possible when quorem is called from bigcomp and */
+ /* the input is near, e.g., twice the smallest denormalized number. */
+ /*debug*/ if (q > 15)
+#endif
+ /*debug*/ Bug("oversized quotient in quorem");
+#endif
+ if (q) {
+ borrow = 0;
+ carry = 0;
+ do {
+#ifdef ULLong
+ ys = *sx++ * (ULLong)q + carry;
+ carry = ys >> 32;
+ y = *bx - (ys & FFFFFFFF) - borrow;
+ borrow = y >> 32 & (ULong)1;
+ *bx++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+ si = *sx++;
+ ys = (si & 0xffff) * q + carry;
+ zs = (si >> 16) * q + (ys >> 16);
+ carry = zs >> 16;
+ y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
+ borrow = (y & 0x10000) >> 16;
+ z = (*bx >> 16) - (zs & 0xffff) - borrow;
+ borrow = (z & 0x10000) >> 16;
+ Storeinc(bx, z, y);
+#else
+ ys = *sx++ * q + carry;
+ carry = ys >> 16;
+ y = *bx - (ys & 0xffff) - borrow;
+ borrow = (y & 0x10000) >> 16;
+ *bx++ = y & 0xffff;
+#endif
+#endif
+ }
+ while(sx <= sxe);
+ if (!*bxe) {
+ bx = b->x;
+ while(--bxe > bx && !*bxe)
+ --n;
+ b->wds = n;
+ }
+ }
+ if (cmp(b, S) >= 0) {
+ q++;
+ borrow = 0;
+ carry = 0;
+ bx = b->x;
+ sx = S->x;
+ do {
+#ifdef ULLong
+ ys = *sx++ + carry;
+ carry = ys >> 32;
+ y = *bx - (ys & FFFFFFFF) - borrow;
+ borrow = y >> 32 & (ULong)1;
+ *bx++ = y & FFFFFFFF;
+#else
+#ifdef Pack_32
+ si = *sx++;
+ ys = (si & 0xffff) + carry;
+ zs = (si >> 16) + (ys >> 16);
+ carry = zs >> 16;
+ y = (*bx & 0xffff) - (ys & 0xffff) - borrow;
+ borrow = (y & 0x10000) >> 16;
+ z = (*bx >> 16) - (zs & 0xffff) - borrow;
+ borrow = (z & 0x10000) >> 16;
+ Storeinc(bx, z, y);
+#else
+ ys = *sx++ + carry;
+ carry = ys >> 16;
+ y = *bx - (ys & 0xffff) - borrow;
+ borrow = (y & 0x10000) >> 16;
+ *bx++ = y & 0xffff;
+#endif
+#endif
+ }
+ while(sx <= sxe);
+ bx = b->x;
+ bxe = bx + n;
+ if (!*bxe) {
+ while(--bxe > bx && !*bxe)
+ --n;
+ b->wds = n;
+ }
+ }
+ return q;
+ }
+
+#if defined(Avoid_Underflow) || !defined(NO_STRTOD_BIGCOMP) /*{*/
+ static double
+sulp
+#ifdef KR_headers
+ (x, bc) U *x; BCinfo *bc;
+#else
+ (U *x, BCinfo *bc)
+#endif
+{
+ U u;
+ double rv;
+ int i;
+
+ rv = ulp(x);
+ if (!bc->scale || (i = 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift)) <= 0)
+ return rv; /* Is there an example where i <= 0 ? */
+ word0(&u) = Exp_1 + (i << Exp_shift);
+ word1(&u) = 0;
+ return rv * u.d;
+ }
+#endif /*}*/
+
+#ifndef NO_STRTOD_BIGCOMP
+ static void
+bigcomp
+#ifdef KR_headers
+ (rv, s0, bc)
+ U *rv; CONST char *s0; BCinfo *bc;
+#else
+ (U *rv, const char *s0, BCinfo *bc)
+#endif
+{
+ Bigint *b, *d;
+ int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
+
+ dsign = bc->dsign;
+ nd = bc->nd;
+ nd0 = bc->nd0;
+ p5 = nd + bc->e0 - 1;
+ speccase = 0;
+#ifndef Sudden_Underflow
+ if (rv->d == 0.) { /* special case: value near underflow-to-zero */
+ /* threshold was rounded to zero */
+ b = i2b(1);
+ p2 = Emin - P + 1;
+ bbits = 1;
+#ifdef Avoid_Underflow
+ word0(rv) = (P+2) << Exp_shift;
+#else
+ word1(rv) = 1;
+#endif
+ i = 0;
+#ifdef Honor_FLT_ROUNDS
+ if (bc->rounding == 1)
+#endif
+ {
+ speccase = 1;
+ --p2;
+ dsign = 0;
+ goto have_i;
+ }
+ }
+ else
+#endif
+ b = d2b(rv, &p2, &bbits);
+#ifdef Avoid_Underflow
+ p2 -= bc->scale;
+#endif
+ /* floor(log2(rv)) == bbits - 1 + p2 */
+ /* Check for denormal case. */
+ i = P - bbits;
+ if (i > (j = P - Emin - 1 + p2)) {
+#ifdef Sudden_Underflow
+ Bfree(b);
+ b = i2b(1);
+ p2 = Emin;
+ i = P - 1;
+#ifdef Avoid_Underflow
+ word0(rv) = (1 + bc->scale) << Exp_shift;
+#else
+ word0(rv) = Exp_msk1;
+#endif
+ word1(rv) = 0;
+#else
+ i = j;
+#endif
+ }
+#ifdef Honor_FLT_ROUNDS
+ if (bc->rounding != 1) {
+ if (i > 0)
+ b = lshift(b, i);
+ if (dsign)
+ b = increment(b);
+ }
+ else
+#endif
+ {
+ b = lshift(b, ++i);
+ b->x[0] |= 1;
+ }
+#ifndef Sudden_Underflow
+ have_i:
+#endif
+ p2 -= p5 + i;
+ d = i2b(1);
+ /* Arrange for convenient computation of quotients:
+ * shift left if necessary so divisor has 4 leading 0 bits.
+ */
+ if (p5 > 0)
+ d = pow5mult(d, p5);
+ else if (p5 < 0)
+ b = pow5mult(b, -p5);
+ if (p2 > 0) {
+ b2 = p2;
+ d2 = 0;
+ }
+ else {
+ b2 = 0;
+ d2 = -p2;
+ }
+ i = dshift(d, d2);
+ if ((b2 += i) > 0)
+ b = lshift(b, b2);
+ if ((d2 += i) > 0)
+ d = lshift(d, d2);
+
+ /* Now b/d = exactly half-way between the two floating-point values */
+ /* on either side of the input string. Compute first digit of b/d. */
+
+ if (!(dig = quorem(b,d))) {
+ b = multadd(b, 10, 0); /* very unlikely */
+ dig = quorem(b,d);
+ }
+
+ /* Compare b/d with s0 */
+
+ for(i = 0; i < nd0; ) {
+ if ((dd = s0[i++] - '0' - dig))
+ goto ret;
+ if (!b->x[0] && b->wds == 1) {
+ if (i < nd)
+ dd = 1;
+ goto ret;
+ }
+ b = multadd(b, 10, 0);
+ dig = quorem(b,d);
+ }
+ for(j = bc->dp1; i++ < nd;) {
+ if ((dd = s0[j++] - '0' - dig))
+ goto ret;
+ if (!b->x[0] && b->wds == 1) {
+ if (i < nd)
+ dd = 1;
+ goto ret;
+ }
+ b = multadd(b, 10, 0);
+ dig = quorem(b,d);
+ }
+ if (dig > 0 || b->x[0] || b->wds > 1)
+ dd = -1;
+ ret:
+ Bfree(b);
+ Bfree(d);
+#ifdef Honor_FLT_ROUNDS
+ if (bc->rounding != 1) {
+ if (dd < 0) {
+ if (bc->rounding == 0) {
+ if (!dsign)
+ goto retlow1;
+ }
+ else if (dsign)
+ goto rethi1;
+ }
+ else if (dd > 0) {
+ if (bc->rounding == 0) {
+ if (dsign)
+ goto rethi1;
+ goto ret1;
+ }
+ if (!dsign)
+ goto rethi1;
+ dval(rv) += 2.*sulp(rv,bc);
+ }
+ else {
+ bc->inexact = 0;
+ if (dsign)
+ goto rethi1;
+ }
+ }
+ else
+#endif
+ if (speccase) {
+ if (dd <= 0)
+ rv->d = 0.;
+ }
+ else if (dd < 0) {
+ if (!dsign) /* does not happen for round-near */
+retlow1:
+ dval(rv) -= sulp(rv,bc);
+ }
+ else if (dd > 0) {
+ if (dsign) {
+ rethi1:
+ dval(rv) += sulp(rv,bc);
+ }
+ }
+ else {
+ /* Exact half-way case: apply round-even rule. */
+ if ((j = ((word0(rv) & Exp_mask) >> Exp_shift) - bc->scale) <= 0) {
+ i = 1 - j;
+ if (i <= 31) {
+ if (word1(rv) & (0x1 << i))
+ goto odd;
+ }
+ else if (word0(rv) & (0x1 << (i-32)))
+ goto odd;
+ }
+ else if (word1(rv) & 1) {
+ odd:
+ if (dsign)
+ goto rethi1;
+ goto retlow1;
+ }
+ }
+
+#ifdef Honor_FLT_ROUNDS
+ ret1:
+#endif
+ return;
+ }
+#endif /* NO_STRTOD_BIGCOMP */
+
+ double
+strtod
+#ifdef KR_headers
+ (s00, se) CONST char *s00; char **se;
+#else
+ (const char *s00, char **se)
+#endif
+{
+ int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1;
+ int esign, i, j, k, nd, nd0, nf, nz, nz0, nz1, sign;
+ CONST char *s, *s0, *s1;
+ double aadj, aadj1;
+ Long L;
+ U aadj2, adj, rv, rv0;
+ ULong y, z;
+ BCinfo bc;
+ Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
+#ifdef Avoid_Underflow
+ ULong Lsb, Lsb1;
+#endif
+#ifdef SET_INEXACT
+ int oldinexact;
+#endif
+#ifndef NO_STRTOD_BIGCOMP
+ int req_bigcomp = 0;
+#endif
+#ifdef Honor_FLT_ROUNDS /*{*/
+#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
+ bc.rounding = Flt_Rounds;
+#else /*}{*/
+ bc.rounding = 1;
+ switch(fegetround()) {
+ case FE_TOWARDZERO: bc.rounding = 0; break;
+ case FE_UPWARD: bc.rounding = 2; break;
+ case FE_DOWNWARD: bc.rounding = 3;
+ }
+#endif /*}}*/
+#endif /*}*/
+#ifdef USE_LOCALE
+ CONST char *s2;
+#endif
+
+ sign = nz0 = nz1 = nz = bc.dplen = bc.uflchk = 0;
+ dval(&rv) = 0.;
+ for(s = s00;;s++) switch(*s) {
+ case '-':
+ sign = 1;
+ /* no break */
+ case '+':
+ if (*++s)
+ goto break2;
+ /* no break */
+ case 0:
+ goto ret0;
+ case '\t':
+ case '\n':
+ case '\v':
+ case '\f':
+ case '\r':
+ case ' ':
+ continue;
+ default:
+ goto break2;
+ }
+ break2:
+ if (*s == '0') {
+#ifndef NO_HEX_FP /*{*/
+ switch(s[1]) {
+ case 'x':
+ case 'X':
+#ifdef Honor_FLT_ROUNDS
+ gethex(&s, &rv, bc.rounding, sign);
+#else
+ gethex(&s, &rv, 1, sign);
+#endif
+ goto ret;
+ }
+#endif /*}*/
+ nz0 = 1;
+ while(*++s == '0') ;
+ if (!*s)
+ goto ret;
+ }
+ s0 = s;
+ y = z = 0;
+ for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
+ if (nd < 9)
+ y = 10*y + c - '0';
+ else if (nd < 16)
+ z = 10*z + c - '0';
+ nd0 = nd;
+ bc.dp0 = bc.dp1 = s - s0;
+ for(s1 = s; s1 > s0 && *--s1 == '0'; )
+ ++nz1;
+#ifdef USE_LOCALE
+ s1 = localeconv()->decimal_point;
+ if (c == *s1) {
+ c = '.';
+ if (*++s1) {
+ s2 = s;
+ for(;;) {
+ if (*++s2 != *s1) {
+ c = 0;
+ break;
+ }
+ if (!*++s1) {
+ s = s2;
+ break;
+ }
+ }
+ }
+ }
+#endif
+ if (c == '.') {
+ c = *++s;
+ bc.dp1 = s - s0;
+ bc.dplen = bc.dp1 - bc.dp0;
+ if (!nd) {
+ for(; c == '0'; c = *++s)
+ nz++;
+ if (c > '0' && c <= '9') {
+ bc.dp0 = s0 - s;
+ bc.dp1 = bc.dp0 + bc.dplen;
+ s0 = s;
+ nf += nz;
+ nz = 0;
+ goto have_dig;
+ }
+ goto dig_done;
+ }
+ for(; c >= '0' && c <= '9'; c = *++s) {
+ have_dig:
+ nz++;
+ if (c -= '0') {
+ nf += nz;
+ for(i = 1; i < nz; i++)
+ if (nd++ < 9)
+ y *= 10;
+ else if (nd <= DBL_DIG + 1)
+ z *= 10;
+ if (nd++ < 9)
+ y = 10*y + c;
+ else if (nd <= DBL_DIG + 1)
+ z = 10*z + c;
+ nz = nz1 = 0;
+ }
+ }
+ }
+ dig_done:
+ e = 0;
+ if (c == 'e' || c == 'E') {
+ if (!nd && !nz && !nz0) {
+ goto ret0;
+ }
+ s00 = s;
+ esign = 0;
+ switch(c = *++s) {
+ case '-':
+ esign = 1;
+ case '+':
+ c = *++s;
+ }
+ if (c >= '0' && c <= '9') {
+ while(c == '0')
+ c = *++s;
+ if (c > '0' && c <= '9') {
+ L = c - '0';
+ s1 = s;
+ while((c = *++s) >= '0' && c <= '9')
+ L = 10*L + c - '0';
+ if (s - s1 > 8 || L > 19999)
+ /* Avoid confusion from exponents
+ * so large that e might overflow.
+ */
+ e = 19999; /* safe for 16 bit ints */
+ else
+ e = (int)L;
+ if (esign)
+ e = -e;
+ }
+ else
+ e = 0;
+ }
+ else
+ s = s00;
+ }
+ if (!nd) {
+ if (!nz && !nz0) {
+#ifdef INFNAN_CHECK
+ /* Check for Nan and Infinity */
+ if (!bc.dplen)
+ switch(c) {
+ case 'i':
+ case 'I':
+ if (match(&s,"nf")) {
+ --s;
+ if (!match(&s,"inity"))
+ ++s;
+ word0(&rv) = 0x7ff00000;
+ word1(&rv) = 0;
+ goto ret;
+ }
+ break;
+ case 'n':
+ case 'N':
+ if (match(&s, "an")) {
+ word0(&rv) = NAN_WORD0;
+ word1(&rv) = NAN_WORD1;
+#ifndef No_Hex_NaN
+ if (*s == '(') /*)*/
+ hexnan(&rv, &s);
+#endif
+ goto ret;
+ }
+ }
+#endif /* INFNAN_CHECK */
+ ret0:
+ s = s00;
+ sign = 0;
+ }
+ goto ret;
+ }
+ bc.e0 = e1 = e -= nf;
+
+ /* Now we have nd0 digits, starting at s0, followed by a
+ * decimal point, followed by nd-nd0 digits. The number we're
+ * after is the integer represented by those digits times
+ * 10**e */
+
+ if (!nd0)
+ nd0 = nd;
+ k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
+ dval(&rv) = y;
+ if (k > 9) {
+#ifdef SET_INEXACT
+ if (k > DBL_DIG)
+ oldinexact = get_inexact();
+#endif
+ dval(&rv) = tens[k - 9] * dval(&rv) + z;
+ }
+ bd0 = 0;
+ if (nd <= DBL_DIG
+#ifndef RND_PRODQUOT
+#ifndef Honor_FLT_ROUNDS
+ && Flt_Rounds == 1
+#endif
+#endif
+ ) {
+ if (!e)
+ goto ret;
+#ifndef ROUND_BIASED_without_Round_Up
+ if (e > 0) {
+ if (e <= Ten_pmax) {
+#ifdef VAX
+ goto vax_ovfl_check;
+#else
+#ifdef Honor_FLT_ROUNDS
+ /* round correctly FLT_ROUNDS = 2 or 3 */
+ if (sign) {
+ rv.d = -rv.d;
+ sign = 0;
+ }
+#endif
+ /* rv = */ rounded_product(dval(&rv), tens[e]);
+ goto ret;
+#endif
+ }
+ i = DBL_DIG - nd;
+ if (e <= Ten_pmax + i) {
+ /* A fancier test would sometimes let us do
+ * this for larger i values.
+ */
+#ifdef Honor_FLT_ROUNDS
+ /* round correctly FLT_ROUNDS = 2 or 3 */
+ if (sign) {
+ rv.d = -rv.d;
+ sign = 0;
+ }
+#endif
+ e -= i;
+ dval(&rv) *= tens[i];
+#ifdef VAX
+ /* VAX exponent range is so narrow we must
+ * worry about overflow here...
+ */
+ vax_ovfl_check:
+ word0(&rv) -= P*Exp_msk1;
+ /* rv = */ rounded_product(dval(&rv), tens[e]);
+ if ((word0(&rv) & Exp_mask)
+ > Exp_msk1*(DBL_MAX_EXP+Bias-1-P))
+ goto ovfl;
+ word0(&rv) += P*Exp_msk1;
+#else
+ /* rv = */ rounded_product(dval(&rv), tens[e]);
+#endif
+ goto ret;
+ }
+ }
+#ifndef Inaccurate_Divide
+ else if (e >= -Ten_pmax) {
+#ifdef Honor_FLT_ROUNDS
+ /* round correctly FLT_ROUNDS = 2 or 3 */
+ if (sign) {
+ rv.d = -rv.d;
+ sign = 0;
+ }
+#endif
+ /* rv = */ rounded_quotient(dval(&rv), tens[-e]);
+ goto ret;
+ }
+#endif
+#endif /* ROUND_BIASED_without_Round_Up */
+ }
+ e1 += nd - k;
+
+#ifdef IEEE_Arith
+#ifdef SET_INEXACT
+ bc.inexact = 1;
+ if (k <= DBL_DIG)
+ oldinexact = get_inexact();
+#endif
+#ifdef Avoid_Underflow
+ bc.scale = 0;
+#endif
+#ifdef Honor_FLT_ROUNDS
+ if (bc.rounding >= 2) {
+ if (sign)
+ bc.rounding = bc.rounding == 2 ? 0 : 2;
+ else
+ if (bc.rounding != 2)
+ bc.rounding = 0;
+ }
+#endif
+#endif /*IEEE_Arith*/
+
+ /* Get starting approximation = rv * 10**e1 */
+
+ if (e1 > 0) {
+ if ((i = e1 & 15))
+ dval(&rv) *= tens[i];
+ if (e1 &= ~15) {
+ if (e1 > DBL_MAX_10_EXP) {
+ ovfl:
+ /* Can't trust HUGE_VAL */
+#ifdef IEEE_Arith
+#ifdef Honor_FLT_ROUNDS
+ switch(bc.rounding) {
+ case 0: /* toward 0 */
+ case 3: /* toward -infinity */
+ word0(&rv) = Big0;
+ word1(&rv) = Big1;
+ break;
+ default:
+ word0(&rv) = Exp_mask;
+ word1(&rv) = 0;
+ }
+#else /*Honor_FLT_ROUNDS*/
+ word0(&rv) = Exp_mask;
+ word1(&rv) = 0;
+#endif /*Honor_FLT_ROUNDS*/
+#ifdef SET_INEXACT
+ /* set overflow bit */
+ dval(&rv0) = 1e300;
+ dval(&rv0) *= dval(&rv0);
+#endif
+#else /*IEEE_Arith*/
+ word0(&rv) = Big0;
+ word1(&rv) = Big1;
+#endif /*IEEE_Arith*/
+ range_err:
+ if (bd0) {
+ Bfree(bb);
+ Bfree(bd);
+ Bfree(bs);
+ Bfree(bd0);
+ Bfree(delta);
+ }
+#ifndef NO_ERRNO
+ errno = ERANGE;
+#endif
+ goto ret;
+ }
+ e1 >>= 4;
+ for(j = 0; e1 > 1; j++, e1 >>= 1)
+ if (e1 & 1)
+ dval(&rv) *= bigtens[j];
+ /* The last multiplication could overflow. */
+ word0(&rv) -= P*Exp_msk1;
+ dval(&rv) *= bigtens[j];
+ if ((z = word0(&rv) & Exp_mask)
+ > Exp_msk1*(DBL_MAX_EXP+Bias-P))
+ goto ovfl;
+ if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) {
+ /* set to largest number */
+ /* (Can't trust DBL_MAX) */
+ word0(&rv) = Big0;
+ word1(&rv) = Big1;
+ }
+ else
+ word0(&rv) += P*Exp_msk1;
+ }
+ }
+ else if (e1 < 0) {
+ e1 = -e1;
+ if ((i = e1 & 15))
+ dval(&rv) /= tens[i];
+ if (e1 >>= 4) {
+ if (e1 >= 1 << n_bigtens)
+ goto undfl;
+#ifdef Avoid_Underflow
+ if (e1 & Scale_Bit)
+ bc.scale = 2*P;
+ for(j = 0; e1 > 0; j++, e1 >>= 1)
+ if (e1 & 1)
+ dval(&rv) *= tinytens[j];
+ if (bc.scale && (j = 2*P + 1 - ((word0(&rv) & Exp_mask)
+ >> Exp_shift)) > 0) {
+ /* scaled rv is denormal; clear j low bits */
+ if (j >= 32) {
+ if (j > 54)
+ goto undfl;
+ word1(&rv) = 0;
+ if (j >= 53)
+ word0(&rv) = (P+2)*Exp_msk1;
+ else
+ word0(&rv) &= 0xffffffff << (j-32);
+ }
+ else
+ word1(&rv) &= 0xffffffff << j;
+ }
+#else
+ for(j = 0; e1 > 1; j++, e1 >>= 1)
+ if (e1 & 1)
+ dval(&rv) *= tinytens[j];
+ /* The last multiplication could underflow. */
+ dval(&rv0) = dval(&rv);
+ dval(&rv) *= tinytens[j];
+ if (!dval(&rv)) {
+ dval(&rv) = 2.*dval(&rv0);
+ dval(&rv) *= tinytens[j];
+#endif
+ if (!dval(&rv)) {
+ undfl:
+ dval(&rv) = 0.;
+ goto range_err;
+ }
+#ifndef Avoid_Underflow
+ word0(&rv) = Tiny0;
+ word1(&rv) = Tiny1;
+ /* The refinement below will clean
+ * this approximation up.
+ */
+ }
+#endif
+ }
+ }
+
+ /* Now the hard part -- adjusting rv to the correct value.*/
+
+ /* Put digits into bd: true value = bd * 10^e */
+
+ bc.nd = nd - nz1;
+#ifndef NO_STRTOD_BIGCOMP
+ bc.nd0 = nd0; /* Only needed if nd > strtod_diglim, but done here */
+ /* to silence an erroneous warning about bc.nd0 */
+ /* possibly not being initialized. */
+ if (nd > strtod_diglim) {
+ /* ASSERT(strtod_diglim >= 18); 18 == one more than the */
+ /* minimum number of decimal digits to distinguish double values */
+ /* in IEEE arithmetic. */
+ i = j = 18;
+ if (i > nd0)
+ j += bc.dplen;
+ for(;;) {
+ if (--j < bc.dp1 && j >= bc.dp0)
+ j = bc.dp0 - 1;
+ if (s0[j] != '0')
+ break;
+ --i;
+ }
+ e += nd - i;
+ nd = i;
+ if (nd0 > nd)
+ nd0 = nd;
+ if (nd < 9) { /* must recompute y */
+ y = 0;
+ for(i = 0; i < nd0; ++i)
+ y = 10*y + s0[i] - '0';
+ for(j = bc.dp1; i < nd; ++i)
+ y = 10*y + s0[j++] - '0';
+ }
+ }
+#endif
+ bd0 = s2b(s0, nd0, nd, y, bc.dplen);
+
+ for(;;) {
+ bd = Balloc(bd0->k);
+ Bcopy(bd, bd0);
+ bb = d2b(&rv, &bbe, &bbbits); /* rv = bb * 2^bbe */
+ bs = i2b(1);
+
+ if (e >= 0) {
+ bb2 = bb5 = 0;
+ bd2 = bd5 = e;
+ }
+ else {
+ bb2 = bb5 = -e;
+ bd2 = bd5 = 0;
+ }
+ if (bbe >= 0)
+ bb2 += bbe;
+ else
+ bd2 -= bbe;
+ bs2 = bb2;
+#ifdef Honor_FLT_ROUNDS
+ if (bc.rounding != 1)
+ bs2++;
+#endif
+#ifdef Avoid_Underflow
+ Lsb = LSB;
+ Lsb1 = 0;
+ j = bbe - bc.scale;
+ i = j + bbbits - 1; /* logb(rv) */
+ j = P + 1 - bbbits;
+ if (i < Emin) { /* denormal */
+ i = Emin - i;
+ j -= i;
+ if (i < 32)
+ Lsb <<= i;
+ else if (i < 52)
+ Lsb1 = Lsb << (i-32);
+ else
+ Lsb1 = Exp_mask;
+ }
+#else /*Avoid_Underflow*/
+#ifdef Sudden_Underflow
+#ifdef IBM
+ j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
+#else
+ j = P + 1 - bbbits;
+#endif
+#else /*Sudden_Underflow*/
+ j = bbe;
+ i = j + bbbits - 1; /* logb(rv) */
+ if (i < Emin) /* denormal */
+ j += P - Emin;
+ else
+ j = P + 1 - bbbits;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+ bb2 += j;
+ bd2 += j;
+#ifdef Avoid_Underflow
+ bd2 += bc.scale;
+#endif
+ i = bb2 < bd2 ? bb2 : bd2;
+ if (i > bs2)
+ i = bs2;
+ if (i > 0) {
+ bb2 -= i;
+ bd2 -= i;
+ bs2 -= i;
+ }
+ if (bb5 > 0) {
+ bs = pow5mult(bs, bb5);
+ bb1 = mult(bs, bb);
+ Bfree(bb);
+ bb = bb1;
+ }
+ if (bb2 > 0)
+ bb = lshift(bb, bb2);
+ if (bd5 > 0)
+ bd = pow5mult(bd, bd5);
+ if (bd2 > 0)
+ bd = lshift(bd, bd2);
+ if (bs2 > 0)
+ bs = lshift(bs, bs2);
+ delta = diff(bb, bd);
+ bc.dsign = delta->sign;
+ delta->sign = 0;
+ i = cmp(delta, bs);
+#ifndef NO_STRTOD_BIGCOMP /*{*/
+ if (bc.nd > nd && i <= 0) {
+ if (bc.dsign) {
+ /* Must use bigcomp(). */
+ req_bigcomp = 1;
+ break;
+ }
+#ifdef Honor_FLT_ROUNDS
+ if (bc.rounding != 1) {
+ if (i < 0) {
+ req_bigcomp = 1;
+ break;
+ }
+ }
+ else
+#endif
+ i = -1; /* Discarded digits make delta smaller. */
+ }
+#endif /*}*/
+#ifdef Honor_FLT_ROUNDS /*{*/
+ if (bc.rounding != 1) {
+ if (i < 0) {
+ /* Error is less than an ulp */
+ if (!delta->x[0] && delta->wds <= 1) {
+ /* exact */
+#ifdef SET_INEXACT
+ bc.inexact = 0;
+#endif
+ break;
+ }
+ if (bc.rounding) {
+ if (bc.dsign) {
+ adj.d = 1.;
+ goto apply_adj;
+ }
+ }
+ else if (!bc.dsign) {
+ adj.d = -1.;
+ if (!word1(&rv)
+ && !(word0(&rv) & Frac_mask)) {
+ y = word0(&rv) & Exp_mask;
+#ifdef Avoid_Underflow
+ if (!bc.scale || y > 2*P*Exp_msk1)
+#else
+ if (y)
+#endif
+ {
+ delta = lshift(delta,Log2P);
+ if (cmp(delta, bs) <= 0)
+ adj.d = -0.5;
+ }
+ }
+ apply_adj:
+#ifdef Avoid_Underflow /*{*/
+ if (bc.scale && (y = word0(&rv) & Exp_mask)
+ <= 2*P*Exp_msk1)
+ word0(&adj) += (2*P+1)*Exp_msk1 - y;
+#else
+#ifdef Sudden_Underflow
+ if ((word0(&rv) & Exp_mask) <=
+ P*Exp_msk1) {
+ word0(&rv) += P*Exp_msk1;
+ dval(&rv) += adj.d*ulp(dval(&rv));
+ word0(&rv) -= P*Exp_msk1;
+ }
+ else
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow}*/
+ dval(&rv) += adj.d*ulp(&rv);
+ }
+ break;
+ }
+ adj.d = ratio(delta, bs);
+ if (adj.d < 1.)
+ adj.d = 1.;
+ if (adj.d <= 0x7ffffffe) {
+ /* adj = rounding ? ceil(adj) : floor(adj); */
+ y = adj.d;
+ if (y != adj.d) {
+ if (!((bc.rounding>>1) ^ bc.dsign))
+ y++;
+ adj.d = y;
+ }
+ }
+#ifdef Avoid_Underflow /*{*/
+ if (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
+ word0(&adj) += (2*P+1)*Exp_msk1 - y;
+#else
+#ifdef Sudden_Underflow
+ if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
+ word0(&rv) += P*Exp_msk1;
+ adj.d *= ulp(dval(&rv));
+ if (bc.dsign)
+ dval(&rv) += adj.d;
+ else
+ dval(&rv) -= adj.d;
+ word0(&rv) -= P*Exp_msk1;
+ goto cont;
+ }
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow}*/
+ adj.d *= ulp(&rv);
+ if (bc.dsign) {
+ if (word0(&rv) == Big0 && word1(&rv) == Big1)
+ goto ovfl;
+ dval(&rv) += adj.d;
+ }
+ else
+ dval(&rv) -= adj.d;
+ goto cont;
+ }
+#endif /*}Honor_FLT_ROUNDS*/
+
+ if (i < 0) {
+ /* Error is less than half an ulp -- check for
+ * special case of mantissa a power of two.
+ */
+ if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask
+#ifdef IEEE_Arith /*{*/
+#ifdef Avoid_Underflow
+ || (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
+#else
+ || (word0(&rv) & Exp_mask) <= Exp_msk1
+#endif
+#endif /*}*/
+ ) {
+#ifdef SET_INEXACT
+ if (!delta->x[0] && delta->wds <= 1)
+ bc.inexact = 0;
+#endif
+ break;
+ }
+ if (!delta->x[0] && delta->wds <= 1) {
+ /* exact result */
+#ifdef SET_INEXACT
+ bc.inexact = 0;
+#endif
+ break;
+ }
+ delta = lshift(delta,Log2P);
+ if (cmp(delta, bs) > 0)
+ goto drop_down;
+ break;
+ }
+ if (i == 0) {
+ /* exactly half-way between */
+ if (bc.dsign) {
+ if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
+ && word1(&rv) == (
+#ifdef Avoid_Underflow
+ (bc.scale && (y = word0(&rv) & Exp_mask) <= 2*P*Exp_msk1)
+ ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) :
+#endif
+ 0xffffffff)) {
+ /*boundary case -- increment exponent*/
+ if (word0(&rv) == Big0 && word1(&rv) == Big1)
+ goto ovfl;
+ word0(&rv) = (word0(&rv) & Exp_mask)
+ + Exp_msk1
+#ifdef IBM
+ | Exp_msk1 >> 4
+#endif
+ ;
+ word1(&rv) = 0;
+#ifdef Avoid_Underflow
+ bc.dsign = 0;
+#endif
+ break;
+ }
+ }
+ else if (!(word0(&rv) & Bndry_mask) && !word1(&rv)) {
+ drop_down:
+ /* boundary case -- decrement exponent */
+#ifdef Sudden_Underflow /*{{*/
+ L = word0(&rv) & Exp_mask;
+#ifdef IBM
+ if (L < Exp_msk1)
+#else
+#ifdef Avoid_Underflow
+ if (L <= (bc.scale ? (2*P+1)*Exp_msk1 : Exp_msk1))
+#else
+ if (L <= Exp_msk1)
+#endif /*Avoid_Underflow*/
+#endif /*IBM*/
+ {
+ if (bc.nd >nd) {
+ bc.uflchk = 1;
+ break;
+ }
+ goto undfl;
+ }
+ L -= Exp_msk1;
+#else /*Sudden_Underflow}{*/
+#ifdef Avoid_Underflow
+ if (bc.scale) {
+ L = word0(&rv) & Exp_mask;
+ if (L <= (2*P+1)*Exp_msk1) {
+ if (L > (P+2)*Exp_msk1)
+ /* round even ==> */
+ /* accept rv */
+ break;
+ /* rv = smallest denormal */
+ if (bc.nd >nd) {
+ bc.uflchk = 1;
+ break;
+ }
+ goto undfl;
+ }
+ }
+#endif /*Avoid_Underflow*/
+ L = (word0(&rv) & Exp_mask) - Exp_msk1;
+#endif /*Sudden_Underflow}}*/
+ word0(&rv) = L | Bndry_mask1;
+ word1(&rv) = 0xffffffff;
+#ifdef IBM
+ goto cont;
+#else
+#ifndef NO_STRTOD_BIGCOMP
+ if (bc.nd > nd)
+ goto cont;
+#endif
+ break;
+#endif
+ }
+#ifndef ROUND_BIASED
+#ifdef Avoid_Underflow
+ if (Lsb1) {
+ if (!(word0(&rv) & Lsb1))
+ break;
+ }
+ else if (!(word1(&rv) & Lsb))
+ break;
+#else
+ if (!(word1(&rv) & LSB))
+ break;
+#endif
+#endif
+ if (bc.dsign)
+#ifdef Avoid_Underflow
+ dval(&rv) += sulp(&rv, &bc);
+#else
+ dval(&rv) += ulp(&rv);
+#endif
+#ifndef ROUND_BIASED
+ else {
+#ifdef Avoid_Underflow
+ dval(&rv) -= sulp(&rv, &bc);
+#else
+ dval(&rv) -= ulp(&rv);
+#endif
+#ifndef Sudden_Underflow
+ if (!dval(&rv)) {
+ if (bc.nd >nd) {
+ bc.uflchk = 1;
+ break;
+ }
+ goto undfl;
+ }
+#endif
+ }
+#ifdef Avoid_Underflow
+ bc.dsign = 1 - bc.dsign;
+#endif
+#endif
+ break;
+ }
+ if ((aadj = ratio(delta, bs)) <= 2.) {
+ if (bc.dsign)
+ aadj = aadj1 = 1.;
+ else if (word1(&rv) || word0(&rv) & Bndry_mask) {
+#ifndef Sudden_Underflow
+ if (word1(&rv) == Tiny1 && !word0(&rv)) {
+ if (bc.nd >nd) {
+ bc.uflchk = 1;
+ break;
+ }
+ goto undfl;
+ }
+#endif
+ aadj = 1.;
+ aadj1 = -1.;
+ }
+ else {
+ /* special case -- power of FLT_RADIX to be */
+ /* rounded down... */
+
+ if (aadj < 2./FLT_RADIX)
+ aadj = 1./FLT_RADIX;
+ else
+ aadj *= 0.5;
+ aadj1 = -aadj;
+ }
+ }
+ else {
+ aadj *= 0.5;
+ aadj1 = bc.dsign ? aadj : -aadj;
+#ifdef Check_FLT_ROUNDS
+ switch(bc.rounding) {
+ case 2: /* towards +infinity */
+ aadj1 -= 0.5;
+ break;
+ case 0: /* towards 0 */
+ case 3: /* towards -infinity */
+ aadj1 += 0.5;
+ }
+#else
+ if (Flt_Rounds == 0)
+ aadj1 += 0.5;
+#endif /*Check_FLT_ROUNDS*/
+ }
+ y = word0(&rv) & Exp_mask;
+
+ /* Check for overflow */
+
+ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) {
+ dval(&rv0) = dval(&rv);
+ word0(&rv) -= P*Exp_msk1;
+ adj.d = aadj1 * ulp(&rv);
+ dval(&rv) += adj.d;
+ if ((word0(&rv) & Exp_mask) >=
+ Exp_msk1*(DBL_MAX_EXP+Bias-P)) {
+ if (word0(&rv0) == Big0 && word1(&rv0) == Big1)
+ goto ovfl;
+ word0(&rv) = Big0;
+ word1(&rv) = Big1;
+ goto cont;
+ }
+ else
+ word0(&rv) += P*Exp_msk1;
+ }
+ else {
+#ifdef Avoid_Underflow
+ if (bc.scale && y <= 2*P*Exp_msk1) {
+ if (aadj <= 0x7fffffff) {
+ if ((z = aadj) <= 0)
+ z = 1;
+ aadj = z;
+ aadj1 = bc.dsign ? aadj : -aadj;
+ }
+ dval(&aadj2) = aadj1;
+ word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
+ aadj1 = dval(&aadj2);
+ adj.d = aadj1 * ulp(&rv);
+ dval(&rv) += adj.d;
+ if (rv.d == 0.)
+#ifdef NO_STRTOD_BIGCOMP
+ goto undfl;
+#else
+ {
+ if (bc.nd > nd)
+ bc.dsign = 1;
+ break;
+ }
+#endif
+ }
+ else {
+ adj.d = aadj1 * ulp(&rv);
+ dval(&rv) += adj.d;
+ }
+#else
+#ifdef Sudden_Underflow
+ if ((word0(&rv) & Exp_mask) <= P*Exp_msk1) {
+ dval(&rv0) = dval(&rv);
+ word0(&rv) += P*Exp_msk1;
+ adj.d = aadj1 * ulp(&rv);
+ dval(&rv) += adj.d;
+#ifdef IBM
+ if ((word0(&rv) & Exp_mask) < P*Exp_msk1)
+#else
+ if ((word0(&rv) & Exp_mask) <= P*Exp_msk1)
+#endif
+ {
+ if (word0(&rv0) == Tiny0
+ && word1(&rv0) == Tiny1) {
+ if (bc.nd >nd) {
+ bc.uflchk = 1;
+ break;
+ }
+ goto undfl;
+ }
+ word0(&rv) = Tiny0;
+ word1(&rv) = Tiny1;
+ goto cont;
+ }
+ else
+ word0(&rv) -= P*Exp_msk1;
+ }
+ else {
+ adj.d = aadj1 * ulp(&rv);
+ dval(&rv) += adj.d;
+ }
+#else /*Sudden_Underflow*/
+ /* Compute adj so that the IEEE rounding rules will
+ * correctly round rv + adj in some half-way cases.
+ * If rv * ulp(rv) is denormalized (i.e.,
+ * y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
+ * trouble from bits lost to denormalization;
+ * example: 1.2e-307 .
+ */
+ if (y <= (P-1)*Exp_msk1 && aadj > 1.) {
+ aadj1 = (double)(int)(aadj + 0.5);
+ if (!bc.dsign)
+ aadj1 = -aadj1;
+ }
+ adj.d = aadj1 * ulp(&rv);
+ dval(&rv) += adj.d;
+#endif /*Sudden_Underflow*/
+#endif /*Avoid_Underflow*/
+ }
+ z = word0(&rv) & Exp_mask;
+#ifndef SET_INEXACT
+ if (bc.nd == nd) {
+#ifdef Avoid_Underflow
+ if (!bc.scale)
+#endif
+ if (y == z) {
+ /* Can we stop now? */
+ L = (Long)aadj;
+ aadj -= L;
+ /* The tolerances below are conservative. */
+ if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
+ if (aadj < .4999999 || aadj > .5000001)
+ break;
+ }
+ else if (aadj < .4999999/FLT_RADIX)
+ break;
+ }
+ }
+#endif
+ cont:
+ Bfree(bb);
+ Bfree(bd);
+ Bfree(bs);
+ Bfree(delta);
+ }
+ Bfree(bb);
+ Bfree(bd);
+ Bfree(bs);
+ Bfree(bd0);
+ Bfree(delta);
+#ifndef NO_STRTOD_BIGCOMP
+ if (req_bigcomp) {
+ bd0 = 0;
+ bc.e0 += nz1;
+ bigcomp(&rv, s0, &bc);
+ y = word0(&rv) & Exp_mask;
+ if (y == Exp_mask)
+ goto ovfl;
+ if (y == 0 && rv.d == 0.)
+ goto undfl;
+ }
+#endif
+#ifdef SET_INEXACT
+ if (bc.inexact) {
+ if (!oldinexact) {
+ word0(&rv0) = Exp_1 + (70 << Exp_shift);
+ word1(&rv0) = 0;
+ dval(&rv0) += 1.;
+ }
+ }
+ else if (!oldinexact)
+ clear_inexact();
+#endif
+#ifdef Avoid_Underflow
+ if (bc.scale) {
+ word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
+ word1(&rv0) = 0;
+ dval(&rv) *= dval(&rv0);
+#ifndef NO_ERRNO
+ /* try to avoid the bug of testing an 8087 register value */
+#ifdef IEEE_Arith
+ if (!(word0(&rv) & Exp_mask))
+#else
+ if (word0(&rv) == 0 && word1(&rv) == 0)
+#endif
+ errno = ERANGE;
+#endif
+ }
+#endif /* Avoid_Underflow */
+#ifdef SET_INEXACT
+ if (bc.inexact && !(word0(&rv) & Exp_mask)) {
+ /* set underflow bit */
+ dval(&rv0) = 1e-300;
+ dval(&rv0) *= dval(&rv0);
+ }
+#endif
+ ret:
+ if (se)
+ *se = (char *)s;
+ return sign ? -dval(&rv) : dval(&rv);
+ }
+
+#ifndef MULTIPLE_THREADS
+ static char *dtoa_result;
+#endif
+
+ static char *
+#ifdef KR_headers
+rv_alloc(i) int i;
+#else
+rv_alloc(int i)
+#endif
+{
+ int j, k, *r;
+
+ j = sizeof(ULong);
+ for(k = 0;
+ sizeof(Bigint) - sizeof(ULong) - sizeof(int) + j <= i;
+ j <<= 1)
+ k++;
+ r = (int*)Balloc(k);
+ *r = k;
+ return
+#ifndef MULTIPLE_THREADS
+ dtoa_result =
+#endif
+ (char *)(r+1);
+ }
+
+ static char *
+#ifdef KR_headers
+nrv_alloc(s, rve, n) char *s, **rve; int n;
+#else
+nrv_alloc(const char *s, char **rve, int n)
+#endif
+{
+ char *rv, *t;
+
+ t = rv = rv_alloc(n);
+ while((*t = *s++)) t++;
+ if (rve)
+ *rve = t;
+ return rv;
+ }
+
+/* freedtoa(s) must be used to free values s returned by dtoa
+ * when MULTIPLE_THREADS is #defined. It should be used in all cases,
+ * but for consistency with earlier versions of dtoa, it is optional
+ * when MULTIPLE_THREADS is not defined.
+ */
+
+ void
+#ifdef KR_headers
+freedtoa(s) char *s;
+#else
+freedtoa(char *s)
+#endif
+{
+ Bigint *b = (Bigint *)((int *)s - 1);
+ b->maxwds = 1 << (b->k = *(int*)b);
+ Bfree(b);
+#ifndef MULTIPLE_THREADS
+ if (s == dtoa_result)
+ dtoa_result = 0;
+#endif
+ }
+
+/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
+ *
+ * Inspired by "How to Print Floating-Point Numbers Accurately" by
+ * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
+ *
+ * Modifications:
+ * 1. Rather than iterating, we use a simple numeric overestimate
+ * to determine k = floor(log10(d)). We scale relevant
+ * quantities using O(log2(k)) rather than O(k) multiplications.
+ * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
+ * try to generate digits strictly left to right. Instead, we
+ * compute with fewer bits and propagate the carry if necessary
+ * when rounding the final digit up. This is often faster.
+ * 3. Under the assumption that input will be rounded nearest,
+ * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
+ * That is, we allow equality in stopping tests when the
+ * round-nearest rule will give the same floating-point value
+ * as would satisfaction of the stopping test with strict
+ * inequality.
+ * 4. We remove common factors of powers of 2 from relevant
+ * quantities.
+ * 5. When converting floating-point integers less than 1e16,
+ * we use floating-point arithmetic rather than resorting
+ * to multiple-precision integers.
+ * 6. When asked to produce fewer than 15 digits, we first try
+ * to get by with floating-point arithmetic; we resort to
+ * multiple-precision integer arithmetic only if we cannot
+ * guarantee that the floating-point calculation has given
+ * the correctly rounded result. For k requested digits and
+ * "uniformly" distributed input, the probability is
+ * something like 10^(k-15) that we must resort to the Long
+ * calculation.
+ */
+
+ char *
+dtoa
+#ifdef KR_headers
+ (dd, mode, ndigits, decpt, sign, rve)
+ double dd; int mode, ndigits, *decpt, *sign; char **rve;
+#else
+ (double dd, int mode, int ndigits, int *decpt, int *sign, char **rve)
+#endif
+{
+ /* Arguments ndigits, decpt, sign are similar to those
+ of ecvt and fcvt; trailing zeros are suppressed from
+ the returned string. If not null, *rve is set to point
+ to the end of the return value. If d is +-Infinity or NaN,
+ then *decpt is set to 9999.
+
+ mode:
+ 0 ==> shortest string that yields d when read in
+ and rounded to nearest.
+ 1 ==> like 0, but with Steele & White stopping rule;
+ e.g. with IEEE P754 arithmetic , mode 0 gives
+ 1e23 whereas mode 1 gives 9.999999999999999e22.
+ 2 ==> max(1,ndigits) significant digits. This gives a
+ return value similar to that of ecvt, except
+ that trailing zeros are suppressed.
+ 3 ==> through ndigits past the decimal point. This
+ gives a return value similar to that from fcvt,
+ except that trailing zeros are suppressed, and
+ ndigits can be negative.
+ 4,5 ==> similar to 2 and 3, respectively, but (in
+ round-nearest mode) with the tests of mode 0 to
+ possibly return a shorter string that rounds to d.
+ With IEEE arithmetic and compilation with
+ -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
+ as modes 2 and 3 when FLT_ROUNDS != 1.
+ 6-9 ==> Debugging modes similar to mode - 4: don't try
+ fast floating-point estimate (if applicable).
+
+ Values of mode other than 0-9 are treated as mode 0.
+
+ Sufficient space is allocated to the return value
+ to hold the suppressed trailing zeros.
+ */
+
+ int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
+ j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
+ spec_case, try_quick;
+ Long L;
+#ifndef Sudden_Underflow
+ int denorm;
+ ULong x;
+#endif
+ Bigint *b, *b1, *delta, *mlo, *mhi, *S;
+ U d2, eps, u;
+ double ds;
+ char *s, *s0;
+#ifndef No_leftright
+#ifdef IEEE_Arith
+ U eps1;
+#endif
+#endif
+#ifdef SET_INEXACT
+ int inexact, oldinexact;
+#endif
+#ifdef Honor_FLT_ROUNDS /*{*/
+ int Rounding;
+#ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */
+ Rounding = Flt_Rounds;
+#else /*}{*/
+ Rounding = 1;
+ switch(fegetround()) {
+ case FE_TOWARDZERO: Rounding = 0; break;
+ case FE_UPWARD: Rounding = 2; break;
+ case FE_DOWNWARD: Rounding = 3;
+ }
+#endif /*}}*/
+#endif /*}*/
+
+#ifndef MULTIPLE_THREADS
+ if (dtoa_result) {
+ freedtoa(dtoa_result);
+ dtoa_result = 0;
+ }
+#endif
+
+ u.d = dd;
+ if (word0(&u) & Sign_bit) {
+ /* set sign for everything, including 0's and NaNs */
+ *sign = 1;
+ word0(&u) &= ~Sign_bit; /* clear sign bit */
+ }
+ else
+ *sign = 0;
+
+#if defined(IEEE_Arith) + defined(VAX)
+#ifdef IEEE_Arith
+ if ((word0(&u) & Exp_mask) == Exp_mask)
+#else
+ if (word0(&u) == 0x8000)
+#endif
+ {
+ /* Infinity or NaN */
+ *decpt = 9999;
+#ifdef IEEE_Arith
+ if (!word1(&u) && !(word0(&u) & 0xfffff))
+ return nrv_alloc("Infinity", rve, 8);
+#endif
+ return nrv_alloc("NaN", rve, 3);
+ }
+#endif
+#ifdef IBM
+ dval(&u) += 0; /* normalize */
+#endif
+ if (!dval(&u)) {
+ *decpt = 1;
+ return nrv_alloc("0", rve, 1);
+ }
+
+#ifdef SET_INEXACT
+ try_quick = oldinexact = get_inexact();
+ inexact = 1;
+#endif
+#ifdef Honor_FLT_ROUNDS
+ if (Rounding >= 2) {
+ if (*sign)
+ Rounding = Rounding == 2 ? 0 : 2;
+ else
+ if (Rounding != 2)
+ Rounding = 0;
+ }
+#endif
+
+ b = d2b(&u, &be, &bbits);
+#ifdef Sudden_Underflow
+ i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
+#else
+ if ((i = (int)(word0(&u) >> Exp_shift1 & (Exp_mask>>Exp_shift1)))) {
+#endif
+ dval(&d2) = dval(&u);
+ word0(&d2) &= Frac_mask1;
+ word0(&d2) |= Exp_11;
+#ifdef IBM
+ if (j = 11 - hi0bits(word0(&d2) & Frac_mask))
+ dval(&d2) /= 1 << j;
+#endif
+
+ /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
+ * log10(x) = log(x) / log(10)
+ * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
+ * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
+ *
+ * This suggests computing an approximation k to log10(d) by
+ *
+ * k = (i - Bias)*0.301029995663981
+ * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
+ *
+ * We want k to be too large rather than too small.
+ * The error in the first-order Taylor series approximation
+ * is in our favor, so we just round up the constant enough
+ * to compensate for any error in the multiplication of
+ * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
+ * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
+ * adding 1e-13 to the constant term more than suffices.
+ * Hence we adjust the constant term to 0.1760912590558.
+ * (We could get a more accurate k by invoking log10,
+ * but this is probably not worthwhile.)
+ */
+
+ i -= Bias;
+#ifdef IBM
+ i <<= 2;
+ i += j;
+#endif
+#ifndef Sudden_Underflow
+ denorm = 0;
+ }
+ else {
+ /* d is denormalized */
+
+ i = bbits + be + (Bias + (P-1) - 1);
+ x = i > 32 ? word0(&u) << (64 - i) | word1(&u) >> (i - 32)
+ : word1(&u) << (32 - i);
+ dval(&d2) = x;
+ word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
+ i -= (Bias + (P-1) - 1) + 1;
+ denorm = 1;
+ }
+#endif
+ ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
+ k = (int)ds;
+ if (ds < 0. && ds != k)
+ k--; /* want k = floor(ds) */
+ k_check = 1;
+ if (k >= 0 && k <= Ten_pmax) {
+ if (dval(&u) < tens[k])
+ k--;
+ k_check = 0;
+ }
+ j = bbits - i - 1;
+ if (j >= 0) {
+ b2 = 0;
+ s2 = j;
+ }
+ else {
+ b2 = -j;
+ s2 = 0;
+ }
+ if (k >= 0) {
+ b5 = 0;
+ s5 = k;
+ s2 += k;
+ }
+ else {
+ b2 -= k;
+ b5 = -k;
+ s5 = 0;
+ }
+ if (mode < 0 || mode > 9)
+ mode = 0;
+
+#ifndef SET_INEXACT
+#ifdef Check_FLT_ROUNDS
+ try_quick = Rounding == 1;
+#else
+ try_quick = 1;
+#endif
+#endif /*SET_INEXACT*/
+
+ if (mode > 5) {
+ mode -= 4;
+ try_quick = 0;
+ }
+ leftright = 1;
+ ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
+ /* silence erroneous "gcc -Wall" warning. */
+ switch(mode) {
+ case 0:
+ case 1:
+ i = 18;
+ ndigits = 0;
+ break;
+ case 2:
+ leftright = 0;
+ /* no break */
+ case 4:
+ if (ndigits <= 0)
+ ndigits = 1;
+ ilim = ilim1 = i = ndigits;
+ break;
+ case 3:
+ leftright = 0;
+ /* no break */
+ case 5:
+ i = ndigits + k + 1;
+ ilim = i;
+ ilim1 = i - 1;
+ if (i <= 0)
+ i = 1;
+ }
+ s = s0 = rv_alloc(i);
+
+#ifdef Honor_FLT_ROUNDS
+ if (mode > 1 && Rounding != 1)
+ leftright = 0;
+#endif
+
+ if (ilim >= 0 && ilim <= Quick_max && try_quick) {
+
+ /* Try to get by with floating-point arithmetic. */
+
+ i = 0;
+ dval(&d2) = dval(&u);
+ k0 = k;
+ ilim0 = ilim;
+ ieps = 2; /* conservative */
+ if (k > 0) {
+ ds = tens[k&0xf];
+ j = k >> 4;
+ if (j & Bletch) {
+ /* prevent overflows */
+ j &= Bletch - 1;
+ dval(&u) /= bigtens[n_bigtens-1];
+ ieps++;
+ }
+ for(; j; j >>= 1, i++)
+ if (j & 1) {
+ ieps++;
+ ds *= bigtens[i];
+ }
+ dval(&u) /= ds;
+ }
+ else if ((j1 = -k)) {
+ dval(&u) *= tens[j1 & 0xf];
+ for(j = j1 >> 4; j; j >>= 1, i++)
+ if (j & 1) {
+ ieps++;
+ dval(&u) *= bigtens[i];
+ }
+ }
+ if (k_check && dval(&u) < 1. && ilim > 0) {
+ if (ilim1 <= 0)
+ goto fast_failed;
+ ilim = ilim1;
+ k--;
+ dval(&u) *= 10.;
+ ieps++;
+ }
+ dval(&eps) = ieps*dval(&u) + 7.;
+ word0(&eps) -= (P-1)*Exp_msk1;
+ if (ilim == 0) {
+ S = mhi = 0;
+ dval(&u) -= 5.;
+ if (dval(&u) > dval(&eps))
+ goto one_digit;
+ if (dval(&u) < -dval(&eps))
+ goto no_digits;
+ goto fast_failed;
+ }
+#ifndef No_leftright
+ if (leftright) {
+ /* Use Steele & White method of only
+ * generating digits needed.
+ */
+ dval(&eps) = 0.5/tens[ilim-1] - dval(&eps);
+#ifdef IEEE_Arith
+ if (k0 < 0 && j1 >= 307) {
+ eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */
+ word0(&eps1) -= Exp_msk1 * (Bias+P-1);
+ dval(&eps1) *= tens[j1 & 0xf];
+ for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++)
+ if (j & 1)
+ dval(&eps1) *= bigtens[i];
+ if (eps.d < eps1.d)
+ eps.d = eps1.d;
+ }
+#endif
+ for(i = 0;;) {
+ L = dval(&u);
+ dval(&u) -= L;
+ *s++ = '0' + (int)L;
+ if (1. - dval(&u) < dval(&eps))
+ goto bump_up;
+ if (dval(&u) < dval(&eps))
+ goto ret1;
+ if (++i >= ilim)
+ break;
+ dval(&eps) *= 10.;
+ dval(&u) *= 10.;
+ }
+ }
+ else {
+#endif
+ /* Generate ilim digits, then fix them up. */
+ dval(&eps) *= tens[ilim-1];
+ for(i = 1;; i++, dval(&u) *= 10.) {
+ L = (Long)(dval(&u));
+ if (!(dval(&u) -= L))
+ ilim = i;
+ *s++ = '0' + (int)L;
+ if (i == ilim) {
+ if (dval(&u) > 0.5 + dval(&eps))
+ goto bump_up;
+ else if (dval(&u) < 0.5 - dval(&eps)) {
+ while(*--s == '0');
+ s++;
+ goto ret1;
+ }
+ break;
+ }
+ }
+#ifndef No_leftright
+ }
+#endif
+ fast_failed:
+ s = s0;
+ dval(&u) = dval(&d2);
+ k = k0;
+ ilim = ilim0;
+ }
+
+ /* Do we have a "small" integer? */
+
+ if (be >= 0 && k <= Int_max) {
+ /* Yes. */
+ ds = tens[k];
+ if (ndigits < 0 && ilim <= 0) {
+ S = mhi = 0;
+ if (ilim < 0 || dval(&u) <= 5*ds)
+ goto no_digits;
+ goto one_digit;
+ }
+ for(i = 1;; i++, dval(&u) *= 10.) {
+ L = (Long)(dval(&u) / ds);
+ dval(&u) -= L*ds;
+#ifdef Check_FLT_ROUNDS
+ /* If FLT_ROUNDS == 2, L will usually be high by 1 */
+ if (dval(&u) < 0) {
+ L--;
+ dval(&u) += ds;
+ }
+#endif
+ *s++ = '0' + (int)L;
+ if (!dval(&u)) {
+#ifdef SET_INEXACT
+ inexact = 0;
+#endif
+ break;
+ }
+ if (i == ilim) {
+#ifdef Honor_FLT_ROUNDS
+ if (mode > 1)
+ switch(Rounding) {
+ case 0: goto ret1;
+ case 2: goto bump_up;
+ }
+#endif
+ dval(&u) += dval(&u);
+#ifdef ROUND_BIASED
+ if (dval(&u) >= ds)
+#else
+ if (dval(&u) > ds || (dval(&u) == ds && L & 1))
+#endif
+ {
+ bump_up:
+ while(*--s == '9')
+ if (s == s0) {
+ k++;
+ *s = '0';
+ break;
+ }
+ ++*s++;
+ }
+ break;
+ }
+ }
+ goto ret1;
+ }
+
+ m2 = b2;
+ m5 = b5;
+ mhi = mlo = 0;
+ if (leftright) {
+ i =
+#ifndef Sudden_Underflow
+ denorm ? be + (Bias + (P-1) - 1 + 1) :
+#endif
+#ifdef IBM
+ 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
+#else
+ 1 + P - bbits;
+#endif
+ b2 += i;
+ s2 += i;
+ mhi = i2b(1);
+ }
+ if (m2 > 0 && s2 > 0) {
+ i = m2 < s2 ? m2 : s2;
+ b2 -= i;
+ m2 -= i;
+ s2 -= i;
+ }
+ if (b5 > 0) {
+ if (leftright) {
+ if (m5 > 0) {
+ mhi = pow5mult(mhi, m5);
+ b1 = mult(mhi, b);
+ Bfree(b);
+ b = b1;
+ }
+ if ((j = b5 - m5))
+ b = pow5mult(b, j);
+ }
+ else
+ b = pow5mult(b, b5);
+ }
+ S = i2b(1);
+ if (s5 > 0)
+ S = pow5mult(S, s5);
+
+ /* Check for special case that d is a normalized power of 2. */
+
+ spec_case = 0;
+ if ((mode < 2 || leftright)
+#ifdef Honor_FLT_ROUNDS
+ && Rounding == 1
+#endif
+ ) {
+ if (!word1(&u) && !(word0(&u) & Bndry_mask)
+#ifndef Sudden_Underflow
+ && word0(&u) & (Exp_mask & ~Exp_msk1)
+#endif
+ ) {
+ /* The special case */
+ b2 += Log2P;
+ s2 += Log2P;
+ spec_case = 1;
+ }
+ }
+
+ /* Arrange for convenient computation of quotients:
+ * shift left if necessary so divisor has 4 leading 0 bits.
+ *
+ * Perhaps we should just compute leading 28 bits of S once
+ * and for all and pass them and a shift to quorem, so it
+ * can do shifts and ors to compute the numerator for q.
+ */
+ i = dshift(S, s2);
+ b2 += i;
+ m2 += i;
+ s2 += i;
+ if (b2 > 0)
+ b = lshift(b, b2);
+ if (s2 > 0)
+ S = lshift(S, s2);
+ if (k_check) {
+ if (cmp(b,S) < 0) {
+ k--;
+ b = multadd(b, 10, 0); /* we botched the k estimate */
+ if (leftright)
+ mhi = multadd(mhi, 10, 0);
+ ilim = ilim1;
+ }
+ }
+ if (ilim <= 0 && (mode == 3 || mode == 5)) {
+ if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
+ /* no digits, fcvt style */
+ no_digits:
+ k = -1 - ndigits;
+ goto ret;
+ }
+ one_digit:
+ *s++ = '1';
+ k++;
+ goto ret;
+ }
+ if (leftright) {
+ if (m2 > 0)
+ mhi = lshift(mhi, m2);
+
+ /* Compute mlo -- check for special case
+ * that d is a normalized power of 2.
+ */
+
+ mlo = mhi;
+ if (spec_case) {
+ mhi = Balloc(mhi->k);
+ Bcopy(mhi, mlo);
+ mhi = lshift(mhi, Log2P);
+ }
+
+ for(i = 1;;i++) {
+ dig = quorem(b,S) + '0';
+ /* Do we yet have the shortest decimal string
+ * that will round to d?
+ */
+ j = cmp(b, mlo);
+ delta = diff(S, mhi);
+ j1 = delta->sign ? 1 : cmp(b, delta);
+ Bfree(delta);
+#ifndef ROUND_BIASED
+ if (j1 == 0 && mode != 1 && !(word1(&u) & 1)
+#ifdef Honor_FLT_ROUNDS
+ && Rounding >= 1
+#endif
+ ) {
+ if (dig == '9')
+ goto round_9_up;
+ if (j > 0)
+ dig++;
+#ifdef SET_INEXACT
+ else if (!b->x[0] && b->wds <= 1)
+ inexact = 0;
+#endif
+ *s++ = dig;
+ goto ret;
+ }
+#endif
+ if (j < 0 || (j == 0 && mode != 1
+#ifndef ROUND_BIASED
+ && !(word1(&u) & 1)
+#endif
+ )) {
+ if (!b->x[0] && b->wds <= 1) {
+#ifdef SET_INEXACT
+ inexact = 0;
+#endif
+ goto accept_dig;
+ }
+#ifdef Honor_FLT_ROUNDS
+ if (mode > 1)
+ switch(Rounding) {
+ case 0: goto accept_dig;
+ case 2: goto keep_dig;
+ }
+#endif /*Honor_FLT_ROUNDS*/
+ if (j1 > 0) {
+ b = lshift(b, 1);
+ j1 = cmp(b, S);
+#ifdef ROUND_BIASED
+ if (j1 >= 0 /*)*/
+#else
+ if ((j1 > 0 || (j1 == 0 && dig & 1))
+#endif
+ && dig++ == '9')
+ goto round_9_up;
+ }
+ accept_dig:
+ *s++ = dig;
+ goto ret;
+ }
+ if (j1 > 0) {
+#ifdef Honor_FLT_ROUNDS
+ if (!Rounding)
+ goto accept_dig;
+#endif
+ if (dig == '9') { /* possible if i == 1 */
+ round_9_up:
+ *s++ = '9';
+ goto roundoff;
+ }
+ *s++ = dig + 1;
+ goto ret;
+ }
+#ifdef Honor_FLT_ROUNDS
+ keep_dig:
+#endif
+ *s++ = dig;
+ if (i == ilim)
+ break;
+ b = multadd(b, 10, 0);
+ if (mlo == mhi)
+ mlo = mhi = multadd(mhi, 10, 0);
+ else {
+ mlo = multadd(mlo, 10, 0);
+ mhi = multadd(mhi, 10, 0);
+ }
+ }
+ }
+ else
+ for(i = 1;; i++) {
+ *s++ = dig = quorem(b,S) + '0';
+ if (!b->x[0] && b->wds <= 1) {
+#ifdef SET_INEXACT
+ inexact = 0;
+#endif
+ goto ret;
+ }
+ if (i >= ilim)
+ break;
+ b = multadd(b, 10, 0);
+ }
+
+ /* Round off last digit */
+
+#ifdef Honor_FLT_ROUNDS
+ switch(Rounding) {
+ case 0: goto trimzeros;
+ case 2: goto roundoff;
+ }
+#endif
+ b = lshift(b, 1);
+ j = cmp(b, S);
+#ifdef ROUND_BIASED
+ if (j >= 0)
+#else
+ if (j > 0 || (j == 0 && dig & 1))
+#endif
+ {
+ roundoff:
+ while(*--s == '9')
+ if (s == s0) {
+ k++;
+ *s++ = '1';
+ goto ret;
+ }
+ ++*s++;
+ }
+ else {
+#ifdef Honor_FLT_ROUNDS
+ trimzeros:
+#endif
+ while(*--s == '0');
+ s++;
+ }
+ ret:
+ Bfree(S);
+ if (mhi) {
+ if (mlo && mlo != mhi)
+ Bfree(mlo);
+ Bfree(mhi);
+ }
+ ret1:
+#ifdef SET_INEXACT
+ if (inexact) {
+ if (!oldinexact) {
+ word0(&u) = Exp_1 + (70 << Exp_shift);
+ word1(&u) = 0;
+ dval(&u) += 1.;
+ }
+ }
+ else if (!oldinexact)
+ clear_inexact();
+#endif
+ Bfree(b);
+ *s = 0;
+ *decpt = k + 1;
+ if (rve)
+ *rve = s;
+ return s0;
+ }
+#ifdef __cplusplus
+}
+#endif
projects / jq / commitdiff