* Transactions on Mathematical Software, Vol. 24, No. 4, December 1998,
* pages 359-367.
*
- * Copyright (c) 1998-2007, PostgreSQL Global Development Group
+ * Copyright (c) 1998-2010, PostgreSQL Global Development Group
*
* IDENTIFICATION
- * $PostgreSQL: pgsql/src/backend/utils/adt/numeric.c,v 1.101 2007/02/27 23:48:08 tgl Exp $
+ * $PostgreSQL: pgsql/src/backend/utils/adt/numeric.c,v 1.121 2010/01/07 04:53:34 tgl Exp $
*
*-------------------------------------------------------------------------
*/
#include <limits.h>
#include <math.h>
+#include "access/hash.h"
#include "catalog/pg_type.h"
#include "libpq/pqformat.h"
+#include "miscadmin.h"
#include "utils/array.h"
#include "utils/builtins.h"
#include "utils/int8.h"
* NBASE that's less than sqrt(INT_MAX), in practice we are only interested
* in NBASE a power of ten, so that I/O conversions and decimal rounding
* are easy. Also, it's actually more efficient if NBASE is rather less than
- * sqrt(INT_MAX), so that there is "headroom" for mul_var and div_var to
+ * sqrt(INT_MAX), so that there is "headroom" for mul_var and div_var_fast to
* postpone processing carries.
* ----------
*/
/* ----------
+ * NumericVar is the format we use for arithmetic. The digit-array part
+ * is the same as the NumericData storage format, but the header is more
+ * complex.
+ *
* The value represented by a NumericVar is determined by the sign, weight,
* ndigits, and digits[] array.
* Note: the first digit of a NumericVar's value is assumed to be multiplied
* NumericVar. digits points at the first digit in actual use (the one
* with the specified weight). We normally leave an unused digit or two
* (preset to zeroes) between buf and digits, so that there is room to store
- * a carry out of the top digit without special pushups. We just need to
+ * a carry out of the top digit without reallocating space. We just need to
* decrement digits (and increment weight) to make room for the carry digit.
* (There is no such extra space in a numeric value stored in the database,
* only in a NumericVar in memory.)
static void free_var(NumericVar *var);
static void zero_var(NumericVar *var);
-static void set_var_from_str(const char *str, NumericVar *dest);
+static const char *set_var_from_str(const char *str, const char *cp,
+ NumericVar *dest);
static void set_var_from_num(Numeric value, NumericVar *dest);
static void set_var_from_var(NumericVar *value, NumericVar *dest);
static char *get_str_from_var(NumericVar *var, int dscale);
+static char *get_str_from_var_sci(NumericVar *var, int rscale);
static Numeric make_result(NumericVar *var);
int rscale);
static void div_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
int rscale, bool round);
+static void div_var_fast(NumericVar *var1, NumericVar *var2, NumericVar *result,
+ int rscale, bool round);
static int select_div_scale(NumericVar *var1, NumericVar *var2);
static void mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void ceil_var(NumericVar *var, NumericVar *result);
Oid typelem = PG_GETARG_OID(1);
#endif
int32 typmod = PG_GETARG_INT32(2);
- NumericVar value;
Numeric res;
+ const char *cp;
+
+ /* Skip leading spaces */
+ cp = str;
+ while (*cp)
+ {
+ if (!isspace((unsigned char) *cp))
+ break;
+ cp++;
+ }
/*
* Check for NaN
*/
- if (pg_strcasecmp(str, "NaN") == 0)
- PG_RETURN_NUMERIC(make_result(&const_nan));
+ if (pg_strncasecmp(cp, "NaN", 3) == 0)
+ {
+ res = make_result(&const_nan);
- /*
- * Use set_var_from_str() to parse the input string and return it in the
- * packed DB storage format
- */
- init_var(&value);
- set_var_from_str(str, &value);
+ /* Should be nothing left but spaces */
+ cp += 3;
+ while (*cp)
+ {
+ if (!isspace((unsigned char) *cp))
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+ errmsg("invalid input syntax for type numeric: \"%s\"",
+ str)));
+ cp++;
+ }
+ }
+ else
+ {
+ /*
+ * Use set_var_from_str() to parse a normal numeric value
+ */
+ NumericVar value;
- apply_typmod(&value, typmod);
+ init_var(&value);
- res = make_result(&value);
- free_var(&value);
+ cp = set_var_from_str(str, cp, &value);
+
+ /*
+ * We duplicate a few lines of code here because we would like to
+ * throw any trailing-junk syntax error before any semantic error
+ * resulting from apply_typmod. We can't easily fold the two cases
+ * together because we mustn't apply apply_typmod to a NaN.
+ */
+ while (*cp)
+ {
+ if (!isspace((unsigned char) *cp))
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+ errmsg("invalid input syntax for type numeric: \"%s\"",
+ str)));
+ cp++;
+ }
+
+ apply_typmod(&value, typmod);
+
+ res = make_result(&value);
+ free_var(&value);
+ }
PG_RETURN_NUMERIC(res);
}
PG_RETURN_CSTRING(str);
}
+/*
+ * numeric_out_sci() -
+ *
+ * Output function for numeric data type in scientific notation.
+ */
+char *
+numeric_out_sci(Numeric num, int scale)
+{
+ NumericVar x;
+ char *str;
+
+ /*
+ * Handle NaN
+ */
+ if (NUMERIC_IS_NAN(num))
+ return pstrdup("NaN");
+
+ init_var(&x);
+ set_var_from_num(num, &x);
+
+ str = get_str_from_var_sci(&x, scale);
+
+ free_var(&x);
+ return str;
+}
+
/*
* numeric_recv - converts external binary format to numeric
*
* scale of the attribute have to be applied on the value.
*/
Datum
-numeric(PG_FUNCTION_ARGS)
+numeric (PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
int32 typmod = PG_GETARG_INT32(1);
Datum
numerictypmodin(PG_FUNCTION_ARGS)
{
- ArrayType *ta = PG_GETARG_ARRAYTYPE_P(0);
- int32 *tl;
+ ArrayType *ta = PG_GETARG_ARRAYTYPE_P(0);
+ int32 *tl;
int n;
int32 typmod;
- tl = ArrayGetTypmods(ta, &n);
+ tl = ArrayGetIntegerTypmods(ta, &n);
if (n == 2)
{
if (tl[1] < 0 || tl[1] > tl[0])
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
- errmsg("NUMERIC scale %d must be between 0 and precision %d",
- tl[1], tl[0])));
+ errmsg("NUMERIC scale %d must be between 0 and precision %d",
+ tl[1], tl[0])));
typmod = ((tl[0] << 16) | tl[1]) + VARHDRSZ;
}
else if (n == 1)
{
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
- errmsg("invalid NUMERIC type modifier")));
+ errmsg("invalid NUMERIC type modifier")));
typmod = 0; /* keep compiler quiet */
}
Datum
numerictypmodout(PG_FUNCTION_ARGS)
{
- int32 typmod = PG_GETARG_INT32(0);
- char *res = (char *) palloc(64);
+ int32 typmod = PG_GETARG_INT32(0);
+ char *res = (char *) palloc(64);
if (typmod >= 0)
snprintf(res, 64, "(%d,%d)",
NUMERIC_IS_NAN(bound2))
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
- errmsg("operand, lower bound and upper bound cannot be NaN")));
+ errmsg("operand, lower bound and upper bound cannot be NaN")));
init_var(&result_var);
init_var(&count_var);
return result;
}
+Datum
+hash_numeric(PG_FUNCTION_ARGS)
+{
+ Numeric key = PG_GETARG_NUMERIC(0);
+ Datum digit_hash;
+ Datum result;
+ int weight;
+ int start_offset;
+ int end_offset;
+ int i;
+ int hash_len;
+
+ /* If it's NaN, don't try to hash the rest of the fields */
+ if (NUMERIC_IS_NAN(key))
+ PG_RETURN_UINT32(0);
+
+ weight = key->n_weight;
+ start_offset = 0;
+ end_offset = 0;
+
+ /*
+ * Omit any leading or trailing zeros from the input to the hash. The
+ * numeric implementation *should* guarantee that leading and trailing
+ * zeros are suppressed, but we're paranoid. Note that we measure the
+ * starting and ending offsets in units of NumericDigits, not bytes.
+ */
+ for (i = 0; i < NUMERIC_NDIGITS(key); i++)
+ {
+ if (NUMERIC_DIGITS(key)[i] != (NumericDigit) 0)
+ break;
+
+ start_offset++;
+
+ /*
+ * The weight is effectively the # of digits before the decimal point,
+ * so decrement it for each leading zero we skip.
+ */
+ weight--;
+ }
+
+ /*
+ * If there are no non-zero digits, then the value of the number is zero,
+ * regardless of any other fields.
+ */
+ if (NUMERIC_NDIGITS(key) == start_offset)
+ PG_RETURN_UINT32(-1);
+
+ for (i = NUMERIC_NDIGITS(key) - 1; i >= 0; i--)
+ {
+ if (NUMERIC_DIGITS(key)[i] != (NumericDigit) 0)
+ break;
+
+ end_offset++;
+ }
+
+ /* If we get here, there should be at least one non-zero digit */
+ Assert(start_offset + end_offset < NUMERIC_NDIGITS(key));
+
+ /*
+ * Note that we don't hash on the Numeric's scale, since two numerics can
+ * compare equal but have different scales. We also don't hash on the
+ * sign, although we could: since a sign difference implies inequality,
+ * this shouldn't affect correctness.
+ */
+ hash_len = NUMERIC_NDIGITS(key) - start_offset - end_offset;
+ digit_hash = hash_any((unsigned char *) (NUMERIC_DIGITS(key) + start_offset),
+ hash_len * sizeof(NumericDigit));
+
+ /* Mix in the weight, via XOR */
+ result = digit_hash ^ weight;
+
+ PG_RETURN_DATUM(result);
+}
+
/* ----------------------------------------------------------------------
*
}
+/*
+ * numeric_div_trunc() -
+ *
+ * Divide one numeric into another, truncating the result to an integer
+ */
+Datum
+numeric_div_trunc(PG_FUNCTION_ARGS)
+{
+ Numeric num1 = PG_GETARG_NUMERIC(0);
+ Numeric num2 = PG_GETARG_NUMERIC(1);
+ NumericVar arg1;
+ NumericVar arg2;
+ NumericVar result;
+ Numeric res;
+
+ /*
+ * Handle NaN
+ */
+ if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
+ PG_RETURN_NUMERIC(make_result(&const_nan));
+
+ /*
+ * Unpack the arguments
+ */
+ init_var(&arg1);
+ init_var(&arg2);
+ init_var(&result);
+
+ set_var_from_num(num1, &arg1);
+ set_var_from_num(num2, &arg2);
+
+ /*
+ * Do the divide and return the result
+ */
+ div_var(&arg1, &arg2, &result, 0, false);
+
+ res = make_result(&result);
+
+ free_var(&arg1);
+ free_var(&arg2);
+ free_var(&result);
+
+ PG_RETURN_NUMERIC(res);
+}
+
+
/*
* numeric_mod() -
*
res = make_result(&const_one);
PG_RETURN_NUMERIC(res);
}
+ /* Fail immediately if the result would overflow */
+ if (num > 32177)
+ ereport(ERROR,
+ (errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+ errmsg("value overflows numeric format")));
init_var(&fact);
init_var(&result);
for (num = num - 1; num > 1; num--)
{
+ /* this loop can take awhile, so allow it to be interrupted */
+ CHECK_FOR_INTERRUPTS();
+
int8_to_numericvar(num, &fact);
mul_var(&result, &fact, &result, 0);
trunc_var(&arg2_trunc, 0);
/*
- * Return special SQLSTATE error codes for a few conditions mandated by
- * the standard.
+ * The SQL spec requires that we emit a particular SQLSTATE error code for
+ * certain error conditions. Specifically, we don't return a
+ * divide-by-zero error code for 0 ^ -1.
*/
- if ((cmp_var(&arg1, &const_zero) == 0 &&
- cmp_var(&arg2, &const_zero) < 0) ||
- (cmp_var(&arg1, &const_zero) < 0 &&
- cmp_var(&arg2, &arg2_trunc) != 0))
+ if (cmp_var(&arg1, &const_zero) == 0 &&
+ cmp_var(&arg2, &const_zero) < 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
+ errmsg("zero raised to a negative power is undefined")));
+
+ if (cmp_var(&arg1, &const_zero) < 0 &&
+ cmp_var(&arg2, &arg2_trunc) != 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
- errmsg("invalid argument for power function")));
+ errmsg("a negative number raised to a non-integer power yields a complex result")));
/*
* Call power_var() to compute and return the result; note it handles
init_var(&result);
- set_var_from_str(buf, &result);
+ /* Assume we need not worry about leading/trailing spaces */
+ (void) set_var_from_str(buf, buf, &result);
+
res = make_result(&result);
free_var(&result);
init_var(&result);
- set_var_from_str(buf, &result);
+ /* Assume we need not worry about leading/trailing spaces */
+ (void) set_var_from_str(buf, buf, &result);
+
res = make_result(&result);
free_var(&result);
}
-Datum
-text_numeric(PG_FUNCTION_ARGS)
-{
- text *str = PG_GETARG_TEXT_P(0);
- int len;
- char *s;
- Datum result;
-
- len = (VARSIZE(str) - VARHDRSZ);
- s = palloc(len + 1);
- memcpy(s, VARDATA(str), len);
- *(s + len) = '\0';
-
- result = DirectFunctionCall3(numeric_in, CStringGetDatum(s),
- ObjectIdGetDatum(0), Int32GetDatum(-1));
-
- pfree(s);
-
- return result;
-}
-
-Datum
-numeric_text(PG_FUNCTION_ARGS)
-{
- /* val is numeric, but easier to leave it as Datum */
- Datum val = PG_GETARG_DATUM(0);
- char *s;
- int len;
- text *result;
-
- s = DatumGetCString(DirectFunctionCall1(numeric_out, val));
- len = strlen(s);
-
- result = (text *) palloc(VARHDRSZ + len);
-
- SET_VARSIZE(result, VARHDRSZ + len);
- memcpy(VARDATA(result), s, len);
-
- pfree(s);
-
- PG_RETURN_TEXT_P(result);
-}
-
-
/* ----------------------------------------------------------------------
*
* Aggregate functions
}
else
{
- mul_var(&vN, &vNminus1, &vNminus1, 0); /* N * (N - 1) */
+ if (sample)
+ mul_var(&vN, &vNminus1, &vNminus1, 0); /* N * (N - 1) */
+ else
+ mul_var(&vN, &vN, &vNminus1, 0); /* N * N */
rscale = select_div_scale(&vsumX2, &vNminus1);
div_var(&vsumX2, &vNminus1, &vsumX, rscale, true); /* variance */
if (!variance)
}
/*
- * If we're invoked by nodeAgg, we can cheat and modify out first
+ * If we're invoked by nodeAgg, we can cheat and modify our first
* parameter in-place to avoid palloc overhead. If not, we need to return
- * the new value of the transition variable.
+ * the new value of the transition variable. (If int8 is pass-by-value,
+ * then of course this is useless as well as incorrect, so just ifdef it
+ * out.)
*/
- if (fcinfo->context && IsA(fcinfo->context, AggState))
+#ifndef USE_FLOAT8_BYVAL /* controls int8 too */
+ if (fcinfo->context &&
+ (IsA(fcinfo->context, AggState) ||
+ IsA(fcinfo->context, WindowAggState)))
{
int64 *oldsum = (int64 *) PG_GETARG_POINTER(0);
PG_RETURN_POINTER(oldsum);
}
else
+#endif
{
int64 oldsum = PG_GETARG_INT64(0);
}
/*
- * If we're invoked by nodeAgg, we can cheat and modify out first
+ * If we're invoked by nodeAgg, we can cheat and modify our first
* parameter in-place to avoid palloc overhead. If not, we need to return
- * the new value of the transition variable.
+ * the new value of the transition variable. (If int8 is pass-by-value,
+ * then of course this is useless as well as incorrect, so just ifdef it
+ * out.)
*/
- if (fcinfo->context && IsA(fcinfo->context, AggState))
+#ifndef USE_FLOAT8_BYVAL /* controls int8 too */
+ if (fcinfo->context &&
+ (IsA(fcinfo->context, AggState) ||
+ IsA(fcinfo->context, WindowAggState)))
{
int64 *oldsum = (int64 *) PG_GETARG_POINTER(0);
PG_RETURN_POINTER(oldsum);
}
else
+#endif
{
int64 oldsum = PG_GETARG_INT64(0);
typedef struct Int8TransTypeData
{
-#ifndef INT64_IS_BUSTED
int64 count;
int64 sum;
-#else
- /* "int64" isn't really 64 bits, so fake up properly-aligned fields */
- int32 count;
- int32 pad1;
- int32 sum;
- int32 pad2;
-#endif
} Int8TransTypeData;
Datum
* parameter in-place to reduce palloc overhead. Otherwise we need to make
* a copy of it before scribbling on it.
*/
- if (fcinfo->context && IsA(fcinfo->context, AggState))
+ if (fcinfo->context &&
+ (IsA(fcinfo->context, AggState) ||
+ IsA(fcinfo->context, WindowAggState)))
transarray = PG_GETARG_ARRAYTYPE_P(0);
else
transarray = PG_GETARG_ARRAYTYPE_P_COPY(0);
* parameter in-place to reduce palloc overhead. Otherwise we need to make
* a copy of it before scribbling on it.
*/
- if (fcinfo->context && IsA(fcinfo->context, AggState))
+ if (fcinfo->context &&
+ (IsA(fcinfo->context, AggState) ||
+ IsA(fcinfo->context, WindowAggState)))
transarray = PG_GETARG_ARRAYTYPE_P(0);
else
transarray = PG_GETARG_ARRAYTYPE_P_COPY(0);
* set_var_from_str()
*
* Parse a string and put the number into a variable
+ *
+ * This function does not handle leading or trailing spaces, and it doesn't
+ * accept "NaN" either. It returns the end+1 position so that caller can
+ * check for trailing spaces/garbage if deemed necessary.
+ *
+ * cp is the place to actually start parsing; str is what to use in error
+ * reports. (Typically cp would be the same except advanced over spaces.)
*/
-static void
-set_var_from_str(const char *str, NumericVar *dest)
+static const char *
+set_var_from_str(const char *str, const char *cp, NumericVar *dest)
{
- const char *cp = str;
bool have_dp = FALSE;
int i;
unsigned char *decdigits;
* We first parse the string to extract decimal digits and determine the
* correct decimal weight. Then convert to NBASE representation.
*/
-
- /* skip leading spaces */
- while (*cp)
- {
- if (!isspace((unsigned char) *cp))
- break;
- cp++;
- }
-
switch (*cp)
{
case '+':
dscale = 0;
}
- /* Should be nothing left but spaces */
- while (*cp)
- {
- if (!isspace((unsigned char) *cp))
- ereport(ERROR,
- (errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
- errmsg("invalid input syntax for type numeric: \"%s\"",
- str)));
- cp++;
- }
-
/*
* Okay, convert pure-decimal representation to base NBASE. First we need
* to determine the converted weight and ndigits. offset is the number of
/* Strip any leading/trailing zeroes, and normalize weight if zero */
strip_var(dest);
+
+ /* Return end+1 position for caller */
+ return cp;
}
return str;
}
+/*
+ * get_str_from_var_sci() -
+ *
+ * Convert a var to a normalised scientific notation text representation.
+ * This function does the heavy lifting for numeric_out_sci().
+ *
+ * This notation has the general form a * 10^b, where a is known as the
+ * "significand" and b is known as the "exponent".
+ *
+ * Because we can't do superscript in ASCII (and because we want to copy
+ * printf's behaviour) we display the exponent using E notation, with a
+ * minimum of two exponent digits.
+ *
+ * For example, the value 1234 could be output as 1.2e+03.
+ *
+ * We assume that the exponent can fit into an int32.
+ *
+ * rscale is the number of decimal digits desired after the decimal point in
+ * the output, negative values will be treated as meaning zero.
+ *
+ * CAUTION: var's contents may be modified by rounding!
+ *
+ * Returns a palloc'd string.
+ */
+static char *
+get_str_from_var_sci(NumericVar *var, int rscale)
+{
+ int32 exponent;
+ NumericVar denominator;
+ NumericVar significand;
+ int denom_scale;
+ size_t len;
+ char *str;
+ char *sig_out;
+
+ if (rscale < 0)
+ rscale = 0;
+
+ /*
+ * Determine the exponent of this number in normalised form.
+ *
+ * This is the exponent required to represent the number with only one
+ * significant digit before the decimal place.
+ */
+ if (var->ndigits > 0)
+ {
+ exponent = (var->weight + 1) * DEC_DIGITS;
+
+ /*
+ * Compensate for leading decimal zeroes in the first numeric digit by
+ * decrementing the exponent.
+ */
+ exponent -= DEC_DIGITS - (int) log10(var->digits[0]);
+ }
+ else
+ {
+ /*
+ * If var has no digits, then it must be zero.
+ *
+ * Zero doesn't technically have a meaningful exponent in normalised
+ * notation, but we just display the exponent as zero for consistency
+ * of output.
+ */
+ exponent = 0;
+ }
+
+ /*
+ * The denominator is set to 10 raised to the power of the exponent.
+ *
+ * We then divide var by the denominator to get the significand, rounding
+ * to rscale decimal digits in the process.
+ */
+ if (exponent < 0)
+ denom_scale = -exponent;
+ else
+ denom_scale = 0;
+
+ init_var(&denominator);
+ init_var(&significand);
+
+ int8_to_numericvar((int64) 10, &denominator);
+ power_var_int(&denominator, exponent, &denominator, denom_scale);
+ div_var(var, &denominator, &significand, rscale, true);
+ sig_out = get_str_from_var(&significand, rscale);
+
+ free_var(&denominator);
+ free_var(&significand);
+
+ /*
+ * Allocate space for the result.
+ *
+ * In addition to the significand, we need room for the exponent decoration
+ * ("e"), the sign of the exponent, up to 10 digits for the exponent
+ * itself, and of course the null terminator.
+ */
+ len = strlen(sig_out) + 13;
+ str = palloc(len);
+ snprintf(str, len, "%se%+03d", sig_out, exponent);
+
+ pfree(sig_out);
+
+ return str;
+}
+
/*
* make_result() -
/*
* div_var() -
*
- * Division on variable level. Quotient of var1 / var2 is stored
- * in result. Result is rounded to no more than rscale fractional digits.
+ * Division on variable level. Quotient of var1 / var2 is stored in result.
+ * The quotient is figured to exactly rscale fractional digits.
+ * If round is true, it is rounded at the rscale'th digit; if false, it
+ * is truncated (towards zero) at that digit.
*/
static void
div_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
int rscale, bool round)
+{
+ int div_ndigits;
+ int res_ndigits;
+ int res_sign;
+ int res_weight;
+ int carry;
+ int borrow;
+ int divisor1;
+ int divisor2;
+ NumericDigit *dividend;
+ NumericDigit *divisor;
+ NumericDigit *res_digits;
+ int i;
+ int j;
+
+ /* copy these values into local vars for speed in inner loop */
+ int var1ndigits = var1->ndigits;
+ int var2ndigits = var2->ndigits;
+
+ /*
+ * First of all division by zero check; we must not be handed an
+ * unnormalized divisor.
+ */
+ if (var2ndigits == 0 || var2->digits[0] == 0)
+ ereport(ERROR,
+ (errcode(ERRCODE_DIVISION_BY_ZERO),
+ errmsg("division by zero")));
+
+ /*
+ * Now result zero check
+ */
+ if (var1ndigits == 0)
+ {
+ zero_var(result);
+ result->dscale = rscale;
+ return;
+ }
+
+ /*
+ * Determine the result sign, weight and number of digits to calculate.
+ * The weight figured here is correct if the emitted quotient has no
+ * leading zero digits; otherwise strip_var() will fix things up.
+ */
+ if (var1->sign == var2->sign)
+ res_sign = NUMERIC_POS;
+ else
+ res_sign = NUMERIC_NEG;
+ res_weight = var1->weight - var2->weight;
+ /* The number of accurate result digits we need to produce: */
+ res_ndigits = res_weight + 1 + (rscale + DEC_DIGITS - 1) / DEC_DIGITS;
+ /* ... but always at least 1 */
+ res_ndigits = Max(res_ndigits, 1);
+ /* If rounding needed, figure one more digit to ensure correct result */
+ if (round)
+ res_ndigits++;
+
+ /*
+ * The working dividend normally requires res_ndigits + var2ndigits
+ * digits, but make it at least var1ndigits so we can load all of var1
+ * into it. (There will be an additional digit dividend[0] in the
+ * dividend space, but for consistency with Knuth's notation we don't
+ * count that in div_ndigits.)
+ */
+ div_ndigits = res_ndigits + var2ndigits;
+ div_ndigits = Max(div_ndigits, var1ndigits);
+
+ /*
+ * We need a workspace with room for the working dividend (div_ndigits+1
+ * digits) plus room for the possibly-normalized divisor (var2ndigits
+ * digits). It is convenient also to have a zero at divisor[0] with the
+ * actual divisor data in divisor[1 .. var2ndigits]. Transferring the
+ * digits into the workspace also allows us to realloc the result (which
+ * might be the same as either input var) before we begin the main loop.
+ * Note that we use palloc0 to ensure that divisor[0], dividend[0], and
+ * any additional dividend positions beyond var1ndigits, start out 0.
+ */
+ dividend = (NumericDigit *)
+ palloc0((div_ndigits + var2ndigits + 2) * sizeof(NumericDigit));
+ divisor = dividend + (div_ndigits + 1);
+ memcpy(dividend + 1, var1->digits, var1ndigits * sizeof(NumericDigit));
+ memcpy(divisor + 1, var2->digits, var2ndigits * sizeof(NumericDigit));
+
+ /*
+ * Now we can realloc the result to hold the generated quotient digits.
+ */
+ alloc_var(result, res_ndigits);
+ res_digits = result->digits;
+
+ if (var2ndigits == 1)
+ {
+ /*
+ * If there's only a single divisor digit, we can use a fast path (cf.
+ * Knuth section 4.3.1 exercise 16).
+ */
+ divisor1 = divisor[1];
+ carry = 0;
+ for (i = 0; i < res_ndigits; i++)
+ {
+ carry = carry * NBASE + dividend[i + 1];
+ res_digits[i] = carry / divisor1;
+ carry = carry % divisor1;
+ }
+ }
+ else
+ {
+ /*
+ * The full multiple-place algorithm is taken from Knuth volume 2,
+ * Algorithm 4.3.1D.
+ *
+ * We need the first divisor digit to be >= NBASE/2. If it isn't,
+ * make it so by scaling up both the divisor and dividend by the
+ * factor "d". (The reason for allocating dividend[0] above is to
+ * leave room for possible carry here.)
+ */
+ if (divisor[1] < HALF_NBASE)
+ {
+ int d = NBASE / (divisor[1] + 1);
+
+ carry = 0;
+ for (i = var2ndigits; i > 0; i--)
+ {
+ carry += divisor[i] * d;
+ divisor[i] = carry % NBASE;
+ carry = carry / NBASE;
+ }
+ Assert(carry == 0);
+ carry = 0;
+ /* at this point only var1ndigits of dividend can be nonzero */
+ for (i = var1ndigits; i >= 0; i--)
+ {
+ carry += dividend[i] * d;
+ dividend[i] = carry % NBASE;
+ carry = carry / NBASE;
+ }
+ Assert(carry == 0);
+ Assert(divisor[1] >= HALF_NBASE);
+ }
+ /* First 2 divisor digits are used repeatedly in main loop */
+ divisor1 = divisor[1];
+ divisor2 = divisor[2];
+
+ /*
+ * Begin the main loop. Each iteration of this loop produces the j'th
+ * quotient digit by dividing dividend[j .. j + var2ndigits] by the
+ * divisor; this is essentially the same as the common manual
+ * procedure for long division.
+ */
+ for (j = 0; j < res_ndigits; j++)
+ {
+ /* Estimate quotient digit from the first two dividend digits */
+ int next2digits = dividend[j] * NBASE + dividend[j + 1];
+ int qhat;
+
+ /*
+ * If next2digits are 0, then quotient digit must be 0 and there's
+ * no need to adjust the working dividend. It's worth testing
+ * here to fall out ASAP when processing trailing zeroes in a
+ * dividend.
+ */
+ if (next2digits == 0)
+ {
+ res_digits[j] = 0;
+ continue;
+ }
+
+ if (dividend[j] == divisor1)
+ qhat = NBASE - 1;
+ else
+ qhat = next2digits / divisor1;
+
+ /*
+ * Adjust quotient digit if it's too large. Knuth proves that
+ * after this step, the quotient digit will be either correct or
+ * just one too large. (Note: it's OK to use dividend[j+2] here
+ * because we know the divisor length is at least 2.)
+ */
+ while (divisor2 * qhat >
+ (next2digits - qhat * divisor1) * NBASE + dividend[j + 2])
+ qhat--;
+
+ /* As above, need do nothing more when quotient digit is 0 */
+ if (qhat > 0)
+ {
+ /*
+ * Multiply the divisor by qhat, and subtract that from the
+ * working dividend. "carry" tracks the multiplication,
+ * "borrow" the subtraction (could we fold these together?)
+ */
+ carry = 0;
+ borrow = 0;
+ for (i = var2ndigits; i >= 0; i--)
+ {
+ carry += divisor[i] * qhat;
+ borrow -= carry % NBASE;
+ carry = carry / NBASE;
+ borrow += dividend[j + i];
+ if (borrow < 0)
+ {
+ dividend[j + i] = borrow + NBASE;
+ borrow = -1;
+ }
+ else
+ {
+ dividend[j + i] = borrow;
+ borrow = 0;
+ }
+ }
+ Assert(carry == 0);
+
+ /*
+ * If we got a borrow out of the top dividend digit, then
+ * indeed qhat was one too large. Fix it, and add back the
+ * divisor to correct the working dividend. (Knuth proves
+ * that this will occur only about 3/NBASE of the time; hence,
+ * it's a good idea to test this code with small NBASE to be
+ * sure this section gets exercised.)
+ */
+ if (borrow)
+ {
+ qhat--;
+ carry = 0;
+ for (i = var2ndigits; i >= 0; i--)
+ {
+ carry += dividend[j + i] + divisor[i];
+ if (carry >= NBASE)
+ {
+ dividend[j + i] = carry - NBASE;
+ carry = 1;
+ }
+ else
+ {
+ dividend[j + i] = carry;
+ carry = 0;
+ }
+ }
+ /* A carry should occur here to cancel the borrow above */
+ Assert(carry == 1);
+ }
+ }
+
+ /* And we're done with this quotient digit */
+ res_digits[j] = qhat;
+ }
+ }
+
+ pfree(dividend);
+
+ /*
+ * Finally, round or truncate the result to the requested precision.
+ */
+ result->weight = res_weight;
+ result->sign = res_sign;
+
+ /* Round or truncate to target rscale (and set result->dscale) */
+ if (round)
+ round_var(result, rscale);
+ else
+ trunc_var(result, rscale);
+
+ /* Strip leading and trailing zeroes */
+ strip_var(result);
+}
+
+
+/*
+ * div_var_fast() -
+ *
+ * This has the same API as div_var, but is implemented using the division
+ * algorithm from the "FM" library, rather than Knuth's schoolbook-division
+ * approach. This is significantly faster but can produce inaccurate
+ * results, because it sometimes has to propagate rounding to the left,
+ * and so we can never be entirely sure that we know the requested digits
+ * exactly. We compute DIV_GUARD_DIGITS extra digits, but there is
+ * no certainty that that's enough. We use this only in the transcendental
+ * function calculation routines, where everything is approximate anyway.
+ */
+static void
+div_var_fast(NumericVar *var1, NumericVar *var2, NumericVar *result,
+ int rscale, bool round)
{
int div_ndigits;
int res_sign;
mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericVar tmp;
- int rscale;
init_var(&tmp);
/* ---------
* We do this using the equation
* mod(x,y) = x - trunc(x/y)*y
- * We set rscale the same way numeric_div and numeric_mul do
- * to get the right answer from the equation. The final result,
- * however, need not be displayed to more precision than the inputs.
+ * div_var can be persuaded to give us trunc(x/y) directly.
* ----------
*/
- rscale = select_div_scale(var1, var2);
-
- div_var(var1, var2, &tmp, rscale, false);
+ div_var(var1, var2, &tmp, 0, false);
- trunc_var(&tmp, 0);
-
- mul_var(var2, &tmp, &tmp, var2->dscale + tmp.dscale);
+ mul_var(var2, &tmp, &tmp, var2->dscale);
sub_var(var1, &tmp, result);
- round_var(result, Max(var1->dscale, var2->dscale));
-
free_var(&tmp);
}
for (;;)
{
- div_var(&tmp_arg, result, &tmp_val, local_rscale, true);
+ div_var_fast(&tmp_arg, result, &tmp_val, local_rscale, true);
add_var(result, &tmp_val, result);
mul_var(result, &const_zero_point_five, result, local_rscale);
/* Compensate for input sign, and round to requested rscale */
if (xneg)
- div_var(&const_one, result, result, rscale, true);
+ div_var_fast(&const_one, result, result, rscale, true);
else
round_var(result, rscale);
add_var(&ni, &const_one, &ni);
mul_var(&xpow, &x, &xpow, local_rscale);
mul_var(&ifac, &ni, &ifac, 0);
- div_var(&xpow, &ifac, &elem, local_rscale, true);
+ div_var_fast(&xpow, &ifac, &elem, local_rscale, true);
if (elem.ndigits == 0)
break;
*/
sub_var(&x, &const_one, result);
add_var(&x, &const_one, &elem);
- div_var(result, &elem, result, local_rscale, true);
+ div_var_fast(result, &elem, result, local_rscale, true);
set_var_from_var(result, &xx);
mul_var(result, result, &x, local_rscale);
{
add_var(&ni, &const_two, &ni);
mul_var(&xx, &x, &xx, local_rscale);
- div_var(&xx, &ni, &elem, local_rscale, true);
+ div_var_fast(&xx, &ni, &elem, local_rscale, true);
if (elem.ndigits == 0)
break;
/* Select scale for division result */
rscale = select_div_scale(&ln_num, &ln_base);
- div_var(&ln_num, &ln_base, result, rscale, true);
+ div_var_fast(&ln_num, &ln_base, result, rscale, true);
free_var(&ln_num);
free_var(&ln_base);
free_var(&x);
}
+ /*
+ * This avoids log(0) for cases of 0 raised to a non-integer. 0 ^ 0
+ * handled by power_var_int().
+ */
+ if (cmp_var(base, &const_zero) == 0)
+ {
+ set_var_from_var(&const_zero, result);
+ result->dscale = NUMERIC_MIN_SIG_DIGITS; /* no need to round */
+ return;
+ }
+
init_var(&ln_base);
init_var(&ln_num);
NumericVar base_prod;
int local_rscale;
- /* Detect some special cases, particularly 0^0. */
-
switch (exp)
{
case 0:
- if (base->ndigits == 0)
- ereport(ERROR,
- (errcode(ERRCODE_FLOATING_POINT_EXCEPTION),
- errmsg("zero raised to zero is undefined")));
+
+ /*
+ * While 0 ^ 0 can be either 1 or indeterminate (error), we treat
+ * it as 1 because most programming languages do this. SQL:2003
+ * also requires a return value of 1.
+ * http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_pow
+ * er
+ */
set_var_from_var(&const_one, result);
result->dscale = rscale; /* no need to round */
return;
/* Compensate for input sign, and round to requested rscale */
if (neg)
- div_var(&const_one, result, result, rscale, true);
+ div_var_fast(&const_one, result, result, rscale, true);
else
round_var(result, rscale);
}
/*
* trunc_var
*
- * Truncate the value of a variable at rscale decimal digits after the
- * decimal point. NOTE: we allow rscale < 0 here, implying
+ * Truncate (towards zero) the value of a variable at rscale decimal digits
+ * after the decimal point. NOTE: we allow rscale < 0 here, implying
* truncation before the decimal point.
*/
static void
projects / postgresql / blobdiff