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postgresql/src/backend/utils/adt/numeric.c

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/*-------------------------------------------------------------------------
*
* numeric.c
* An exact numeric data type for the Postgres database system
*
* Original coding 1998, Jan Wieck. Heavily revised 2003, Tom Lane.
*
* Many of the algorithmic ideas are borrowed from David M. Smith's "FM"
* multiple-precision math library, most recently published as Algorithm
* 786: Multiple-Precision Complex Arithmetic and Functions, ACM
* Transactions on Mathematical Software, Vol. 24, No. 4, December 1998,
* pages 359-367.
*
* Copyright (c) 1998-2014, PostgreSQL Global Development Group
*
* IDENTIFICATION
* src/backend/utils/adt/numeric.c
*
*-------------------------------------------------------------------------
*/
#include "postgres.h"
#include <ctype.h>
#include <float.h>
#include <limits.h>
#include <math.h>
#include "access/hash.h"
#include "catalog/pg_type.h"
#include "libpq/pqformat.h"
#include "miscadmin.h"
#include "nodes/nodeFuncs.h"
#include "utils/array.h"
#include "utils/builtins.h"
#include "utils/int8.h"
#include "utils/numeric.h"
/* ----------
* Uncomment the following to enable compilation of dump_numeric()
* and dump_var() and to get a dump of any result produced by make_result().
* ----------
#define NUMERIC_DEBUG
*/
/* ----------
* Local data types
*
* Numeric values are represented in a base-NBASE floating point format.
* Each "digit" ranges from 0 to NBASE-1. The type NumericDigit is signed
* and wide enough to store a digit. We assume that NBASE*NBASE can fit in
* an int. Although the purely calculational routines could handle any even
* 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_fast to
* postpone processing carries.
* ----------
*/
#if 0
#define NBASE 10
#define HALF_NBASE 5
#define DEC_DIGITS 1 /* decimal digits per NBASE digit */
#define MUL_GUARD_DIGITS 4 /* these are measured in NBASE digits */
#define DIV_GUARD_DIGITS 8
typedef signed char NumericDigit;
#endif
#if 0
#define NBASE 100
#define HALF_NBASE 50
#define DEC_DIGITS 2 /* decimal digits per NBASE digit */
#define MUL_GUARD_DIGITS 3 /* these are measured in NBASE digits */
#define DIV_GUARD_DIGITS 6
typedef signed char NumericDigit;
#endif
#if 1
#define NBASE 10000
#define HALF_NBASE 5000
#define DEC_DIGITS 4 /* decimal digits per NBASE digit */
#define MUL_GUARD_DIGITS 2 /* these are measured in NBASE digits */
#define DIV_GUARD_DIGITS 4
typedef int16 NumericDigit;
#endif
/*
* The Numeric type as stored on disk.
*
* If the high bits of the first word of a NumericChoice (n_header, or
* n_short.n_header, or n_long.n_sign_dscale) are NUMERIC_SHORT, then the
* numeric follows the NumericShort format; if they are NUMERIC_POS or
* NUMERIC_NEG, it follows the NumericLong format. If they are NUMERIC_NAN,
* it is a NaN. We currently always store a NaN using just two bytes (i.e.
* only n_header), but previous releases used only the NumericLong format,
* so we might find 4-byte NaNs on disk if a database has been migrated using
* pg_upgrade. In either case, when the high bits indicate a NaN, the
* remaining bits are never examined. Currently, we always initialize these
* to zero, but it might be possible to use them for some other purpose in
* the future.
*
* In the NumericShort format, the remaining 14 bits of the header word
* (n_short.n_header) are allocated as follows: 1 for sign (positive or
* negative), 6 for dynamic scale, and 7 for weight. In practice, most
* commonly-encountered values can be represented this way.
*
* In the NumericLong format, the remaining 14 bits of the header word
* (n_long.n_sign_dscale) represent the display scale; and the weight is
* stored separately in n_weight.
*
* NOTE: by convention, values in the packed form have been stripped of
* all leading and trailing zero digits (where a "digit" is of base NBASE).
* In particular, if the value is zero, there will be no digits at all!
* The weight is arbitrary in that case, but we normally set it to zero.
*/
struct NumericShort
{
uint16 n_header; /* Sign + display scale + weight */
NumericDigit n_data[1]; /* Digits */
};
struct NumericLong
{
uint16 n_sign_dscale; /* Sign + display scale */
int16 n_weight; /* Weight of 1st digit */
NumericDigit n_data[1]; /* Digits */
};
union NumericChoice
{
uint16 n_header; /* Header word */
struct NumericLong n_long; /* Long form (4-byte header) */
struct NumericShort n_short; /* Short form (2-byte header) */
};
struct NumericData
{
int32 vl_len_; /* varlena header (do not touch directly!) */
union NumericChoice choice; /* choice of format */
};
/*
* Interpretation of high bits.
*/
#define NUMERIC_SIGN_MASK 0xC000
#define NUMERIC_POS 0x0000
#define NUMERIC_NEG 0x4000
#define NUMERIC_SHORT 0x8000
#define NUMERIC_NAN 0xC000
#define NUMERIC_FLAGBITS(n) ((n)->choice.n_header & NUMERIC_SIGN_MASK)
#define NUMERIC_IS_NAN(n) (NUMERIC_FLAGBITS(n) == NUMERIC_NAN)
#define NUMERIC_IS_SHORT(n) (NUMERIC_FLAGBITS(n) == NUMERIC_SHORT)
#define NUMERIC_HDRSZ (VARHDRSZ + sizeof(uint16) + sizeof(int16))
#define NUMERIC_HDRSZ_SHORT (VARHDRSZ + sizeof(uint16))
/*
* If the flag bits are NUMERIC_SHORT or NUMERIC_NAN, we want the short header;
* otherwise, we want the long one. Instead of testing against each value, we
* can just look at the high bit, for a slight efficiency gain.
*/
#define NUMERIC_HEADER_SIZE(n) \
(VARHDRSZ + sizeof(uint16) + \
(((NUMERIC_FLAGBITS(n) & 0x8000) == 0) ? sizeof(int16) : 0))
/*
* Short format definitions.
*/
#define NUMERIC_SHORT_SIGN_MASK 0x2000
#define NUMERIC_SHORT_DSCALE_MASK 0x1F80
#define NUMERIC_SHORT_DSCALE_SHIFT 7
#define NUMERIC_SHORT_DSCALE_MAX \
(NUMERIC_SHORT_DSCALE_MASK >> NUMERIC_SHORT_DSCALE_SHIFT)
#define NUMERIC_SHORT_WEIGHT_SIGN_MASK 0x0040
#define NUMERIC_SHORT_WEIGHT_MASK 0x003F
#define NUMERIC_SHORT_WEIGHT_MAX NUMERIC_SHORT_WEIGHT_MASK
#define NUMERIC_SHORT_WEIGHT_MIN (-(NUMERIC_SHORT_WEIGHT_MASK+1))
/*
* Extract sign, display scale, weight.
*/
#define NUMERIC_DSCALE_MASK 0x3FFF
#define NUMERIC_SIGN(n) \
(NUMERIC_IS_SHORT(n) ? \
(((n)->choice.n_short.n_header & NUMERIC_SHORT_SIGN_MASK) ? \
NUMERIC_NEG : NUMERIC_POS) : NUMERIC_FLAGBITS(n))
#define NUMERIC_DSCALE(n) (NUMERIC_IS_SHORT((n)) ? \
((n)->choice.n_short.n_header & NUMERIC_SHORT_DSCALE_MASK) \
>> NUMERIC_SHORT_DSCALE_SHIFT \
: ((n)->choice.n_long.n_sign_dscale & NUMERIC_DSCALE_MASK))
#define NUMERIC_WEIGHT(n) (NUMERIC_IS_SHORT((n)) ? \
(((n)->choice.n_short.n_header & NUMERIC_SHORT_WEIGHT_SIGN_MASK ? \
~NUMERIC_SHORT_WEIGHT_MASK : 0) \
| ((n)->choice.n_short.n_header & NUMERIC_SHORT_WEIGHT_MASK)) \
: ((n)->choice.n_long.n_weight))
/* ----------
* 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
* by NBASE ** weight. Another way to say it is that there are weight+1
* digits before the decimal point. It is possible to have weight < 0.
*
* buf points at the physical start of the palloc'd digit buffer for the
* 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 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.)
*
* If buf is NULL then the digit buffer isn't actually palloc'd and should
* not be freed --- see the constants below for an example.
*
* dscale, or display scale, is the nominal precision expressed as number
* of digits after the decimal point (it must always be >= 0 at present).
* dscale may be more than the number of physically stored fractional digits,
* implying that we have suppressed storage of significant trailing zeroes.
* It should never be less than the number of stored digits, since that would
* imply hiding digits that are present. NOTE that dscale is always expressed
* in *decimal* digits, and so it may correspond to a fractional number of
* base-NBASE digits --- divide by DEC_DIGITS to convert to NBASE digits.
*
* rscale, or result scale, is the target precision for a computation.
* Like dscale it is expressed as number of *decimal* digits after the decimal
* point, and is always >= 0 at present.
* Note that rscale is not stored in variables --- it's figured on-the-fly
* from the dscales of the inputs.
*
* NB: All the variable-level functions are written in a style that makes it
* possible to give one and the same variable as argument and destination.
* This is feasible because the digit buffer is separate from the variable.
* ----------
*/
typedef struct NumericVar
{
int ndigits; /* # of digits in digits[] - can be 0! */
int weight; /* weight of first digit */
int sign; /* NUMERIC_POS, NUMERIC_NEG, or NUMERIC_NAN */
int dscale; /* display scale */
NumericDigit *buf; /* start of palloc'd space for digits[] */
NumericDigit *digits; /* base-NBASE digits */
} NumericVar;
/* ----------
* Some preinitialized constants
* ----------
*/
static NumericDigit const_zero_data[1] = {0};
static NumericVar const_zero =
{0, 0, NUMERIC_POS, 0, NULL, const_zero_data};
static NumericDigit const_one_data[1] = {1};
static NumericVar const_one =
{1, 0, NUMERIC_POS, 0, NULL, const_one_data};
static NumericDigit const_two_data[1] = {2};
static NumericVar const_two =
{1, 0, NUMERIC_POS, 0, NULL, const_two_data};
#if DEC_DIGITS == 4 || DEC_DIGITS == 2
static NumericDigit const_ten_data[1] = {10};
static NumericVar const_ten =
{1, 0, NUMERIC_POS, 0, NULL, const_ten_data};
#elif DEC_DIGITS == 1
static NumericDigit const_ten_data[1] = {1};
static NumericVar const_ten =
{1, 1, NUMERIC_POS, 0, NULL, const_ten_data};
#endif
#if DEC_DIGITS == 4
static NumericDigit const_zero_point_five_data[1] = {5000};
#elif DEC_DIGITS == 2
static NumericDigit const_zero_point_five_data[1] = {50};
#elif DEC_DIGITS == 1
static NumericDigit const_zero_point_five_data[1] = {5};
#endif
static NumericVar const_zero_point_five =
{1, -1, NUMERIC_POS, 1, NULL, const_zero_point_five_data};
#if DEC_DIGITS == 4
static NumericDigit const_zero_point_nine_data[1] = {9000};
#elif DEC_DIGITS == 2
static NumericDigit const_zero_point_nine_data[1] = {90};
#elif DEC_DIGITS == 1
static NumericDigit const_zero_point_nine_data[1] = {9};
#endif
static NumericVar const_zero_point_nine =
{1, -1, NUMERIC_POS, 1, NULL, const_zero_point_nine_data};
#if DEC_DIGITS == 4
static NumericDigit const_zero_point_01_data[1] = {100};
static NumericVar const_zero_point_01 =
{1, -1, NUMERIC_POS, 2, NULL, const_zero_point_01_data};
#elif DEC_DIGITS == 2
static NumericDigit const_zero_point_01_data[1] = {1};
static NumericVar const_zero_point_01 =
{1, -1, NUMERIC_POS, 2, NULL, const_zero_point_01_data};
#elif DEC_DIGITS == 1
static NumericDigit const_zero_point_01_data[1] = {1};
static NumericVar const_zero_point_01 =
{1, -2, NUMERIC_POS, 2, NULL, const_zero_point_01_data};
#endif
#if DEC_DIGITS == 4
static NumericDigit const_one_point_one_data[2] = {1, 1000};
#elif DEC_DIGITS == 2
static NumericDigit const_one_point_one_data[2] = {1, 10};
#elif DEC_DIGITS == 1
static NumericDigit const_one_point_one_data[2] = {1, 1};
#endif
static NumericVar const_one_point_one =
{2, 0, NUMERIC_POS, 1, NULL, const_one_point_one_data};
static NumericVar const_nan =
{0, 0, NUMERIC_NAN, 0, NULL, NULL};
#if DEC_DIGITS == 4
static const int round_powers[4] = {0, 1000, 100, 10};
#endif
/* ----------
* Local functions
* ----------
*/
#ifdef NUMERIC_DEBUG
static void dump_numeric(const char *str, Numeric num);
static void dump_var(const char *str, NumericVar *var);
#else
#define dump_numeric(s,n)
#define dump_var(s,v)
#endif
#define digitbuf_alloc(ndigits) \
((NumericDigit *) palloc((ndigits) * sizeof(NumericDigit)))
#define digitbuf_free(buf) \
do { \
if ((buf) != NULL) \
pfree(buf); \
} while (0)
#define init_var(v) MemSetAligned(v, 0, sizeof(NumericVar))
#define NUMERIC_DIGITS(num) (NUMERIC_IS_SHORT(num) ? \
(num)->choice.n_short.n_data : (num)->choice.n_long.n_data)
#define NUMERIC_NDIGITS(num) \
((VARSIZE(num) - NUMERIC_HEADER_SIZE(num)) / sizeof(NumericDigit))
#define NUMERIC_CAN_BE_SHORT(scale,weight) \
((scale) <= NUMERIC_SHORT_DSCALE_MAX && \
(weight) <= NUMERIC_SHORT_WEIGHT_MAX && \
(weight) >= NUMERIC_SHORT_WEIGHT_MIN)
static void alloc_var(NumericVar *var, int ndigits);
static void free_var(NumericVar *var);
static void zero_var(NumericVar *var);
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 init_var_from_num(Numeric num, NumericVar *dest);
static void set_var_from_var(NumericVar *value, NumericVar *dest);
static char *get_str_from_var(NumericVar *var);
static char *get_str_from_var_sci(NumericVar *var, int rscale);
static Numeric make_result(NumericVar *var);
static void apply_typmod(NumericVar *var, int32 typmod);
static int32 numericvar_to_int4(NumericVar *var);
static bool numericvar_to_int8(NumericVar *var, int64 *result);
static void int8_to_numericvar(int64 val, NumericVar *var);
static double numeric_to_double_no_overflow(Numeric num);
static double numericvar_to_double_no_overflow(NumericVar *var);
static int cmp_numerics(Numeric num1, Numeric num2);
static int cmp_var(NumericVar *var1, NumericVar *var2);
static int cmp_var_common(const NumericDigit *var1digits, int var1ndigits,
int var1weight, int var1sign,
const NumericDigit *var2digits, int var2ndigits,
int var2weight, int var2sign);
static void add_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
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);
static void floor_var(NumericVar *var, NumericVar *result);
static void sqrt_var(NumericVar *arg, NumericVar *result, int rscale);
static void exp_var(NumericVar *arg, NumericVar *result, int rscale);
static void exp_var_internal(NumericVar *arg, NumericVar *result, int rscale);
static void ln_var(NumericVar *arg, NumericVar *result, int rscale);
static void log_var(NumericVar *base, NumericVar *num, NumericVar *result);
static void power_var(NumericVar *base, NumericVar *exp, NumericVar *result);
static void power_var_int(NumericVar *base, int exp, NumericVar *result,
int rscale);
static int cmp_abs(NumericVar *var1, NumericVar *var2);
static int cmp_abs_common(const NumericDigit *var1digits, int var1ndigits,
int var1weight,
const NumericDigit *var2digits, int var2ndigits,
int var2weight);
static void add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void round_var(NumericVar *var, int rscale);
static void trunc_var(NumericVar *var, int rscale);
static void strip_var(NumericVar *var);
static void compute_bucket(Numeric operand, Numeric bound1, Numeric bound2,
NumericVar *count_var, NumericVar *result_var);
/* ----------------------------------------------------------------------
*
* Input-, output- and rounding-functions
*
* ----------------------------------------------------------------------
*/
/*
* numeric_in() -
*
* Input function for numeric data type
*/
Datum
numeric_in(PG_FUNCTION_ARGS)
{
char *str = PG_GETARG_CSTRING(0);
#ifdef NOT_USED
Oid typelem = PG_GETARG_OID(1);
#endif
int32 typmod = PG_GETARG_INT32(2);
Numeric res;
const char *cp;
/* Skip leading spaces */
cp = str;
while (*cp)
{
if (!isspace((unsigned char) *cp))
break;
cp++;
}
/*
* Check for NaN
*/
if (pg_strncasecmp(cp, "NaN", 3) == 0)
{
res = make_result(&const_nan);
/* 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;
init_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);
}
/*
* numeric_out() -
*
* Output function for numeric data type
*/
Datum
numeric_out(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
char *str;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_CSTRING(pstrdup("NaN"));
/*
* Get the number in the variable format.
*/
init_var_from_num(num, &x);
str = get_str_from_var(&x);
PG_RETURN_CSTRING(str);
}
/*
* numeric_is_nan() -
*
* Is Numeric value a NaN?
*/
bool
numeric_is_nan(Numeric num)
{
return NUMERIC_IS_NAN(num);
}
/*
* numeric_maximum_size() -
*
* Maximum size of a numeric with given typmod, or -1 if unlimited/unknown.
*/
int32
numeric_maximum_size(int32 typmod)
{
int precision;
int numeric_digits;
if (typmod < (int32) (VARHDRSZ))
return -1;
/* precision (ie, max # of digits) is in upper bits of typmod */
precision = ((typmod - VARHDRSZ) >> 16) & 0xffff;
/*
* This formula computes the maximum number of NumericDigits we could need
* in order to store the specified number of decimal digits. Because the
* weight is stored as a number of NumericDigits rather than a number of
* decimal digits, it's possible that the first NumericDigit will contain
* only a single decimal digit. Thus, the first two decimal digits can
* require two NumericDigits to store, but it isn't until we reach
* DEC_DIGITS + 2 decimal digits that we potentially need a third
* NumericDigit.
*/
numeric_digits = (precision + 2 * (DEC_DIGITS - 1)) / DEC_DIGITS;
/*
* In most cases, the size of a numeric will be smaller than the value
* computed below, because the varlena header will typically get toasted
* down to a single byte before being stored on disk, and it may also be
* possible to use a short numeric header. But our job here is to compute
* the worst case.
*/
return NUMERIC_HDRSZ + (numeric_digits * sizeof(NumericDigit));
}
/*
* 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_from_num(num, &x);
str = get_str_from_var_sci(&x, scale);
return str;
}
/*
* numeric_normalize() -
*
* Output function for numeric data type without trailing zeroes.
*/
char *
numeric_normalize(Numeric num)
{
NumericVar x;
char *str;
int orig, last;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
return pstrdup("NaN");
init_var_from_num(num, &x);
str = get_str_from_var(&x);
orig = last = strlen(str) - 1;
for (;;)
{
if (last == 0 || str[last] != '0')
break;
last--;
}
if (last > 0 && last != orig)
str[last] = '\0';
return str;
}
/*
* numeric_recv - converts external binary format to numeric
*
* External format is a sequence of int16's:
* ndigits, weight, sign, dscale, NumericDigits.
*/
Datum
numeric_recv(PG_FUNCTION_ARGS)
{
StringInfo buf = (StringInfo) PG_GETARG_POINTER(0);
#ifdef NOT_USED
Oid typelem = PG_GETARG_OID(1);
#endif
int32 typmod = PG_GETARG_INT32(2);
NumericVar value;
Numeric res;
int len,
i;
init_var(&value);
len = (uint16) pq_getmsgint(buf, sizeof(uint16));
if (len < 0 || len > NUMERIC_MAX_PRECISION + NUMERIC_MAX_RESULT_SCALE)
ereport(ERROR,
(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
errmsg("invalid length in external \"numeric\" value")));
alloc_var(&value, len);
value.weight = (int16) pq_getmsgint(buf, sizeof(int16));
value.sign = (uint16) pq_getmsgint(buf, sizeof(uint16));
if (!(value.sign == NUMERIC_POS ||
value.sign == NUMERIC_NEG ||
value.sign == NUMERIC_NAN))
ereport(ERROR,
(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
errmsg("invalid sign in external \"numeric\" value")));
value.dscale = (uint16) pq_getmsgint(buf, sizeof(uint16));
for (i = 0; i < len; i++)
{
NumericDigit d = pq_getmsgint(buf, sizeof(NumericDigit));
if (d < 0 || d >= NBASE)
ereport(ERROR,
(errcode(ERRCODE_INVALID_BINARY_REPRESENTATION),
errmsg("invalid digit in external \"numeric\" value")));
value.digits[i] = d;
}
apply_typmod(&value, typmod);
res = make_result(&value);
free_var(&value);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_send - converts numeric to binary format
*/
Datum
numeric_send(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
StringInfoData buf;
int i;
init_var_from_num(num, &x);
pq_begintypsend(&buf);
pq_sendint(&buf, x.ndigits, sizeof(int16));
pq_sendint(&buf, x.weight, sizeof(int16));
pq_sendint(&buf, x.sign, sizeof(int16));
pq_sendint(&buf, x.dscale, sizeof(int16));
for (i = 0; i < x.ndigits; i++)
pq_sendint(&buf, x.digits[i], sizeof(NumericDigit));
PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
}
/*
* numeric_transform() -
*
* Flatten calls to numeric's length coercion function that solely represent
* increases in allowable precision. Scale changes mutate every datum, so
* they are unoptimizable. Some values, e.g. 1E-1001, can only fit into an
* unconstrained numeric, so a change from an unconstrained numeric to any
* constrained numeric is also unoptimizable.
*/
Datum
numeric_transform(PG_FUNCTION_ARGS)
{
FuncExpr *expr = (FuncExpr *) PG_GETARG_POINTER(0);
Node *ret = NULL;
Node *typmod;
Assert(IsA(expr, FuncExpr));
Assert(list_length(expr->args) >= 2);
typmod = (Node *) lsecond(expr->args);
if (IsA(typmod, Const) &&!((Const *) typmod)->constisnull)
{
Node *source = (Node *) linitial(expr->args);
int32 old_typmod = exprTypmod(source);
int32 new_typmod = DatumGetInt32(((Const *) typmod)->constvalue);
int32 old_scale = (old_typmod - VARHDRSZ) & 0xffff;
int32 new_scale = (new_typmod - VARHDRSZ) & 0xffff;
int32 old_precision = (old_typmod - VARHDRSZ) >> 16 & 0xffff;
int32 new_precision = (new_typmod - VARHDRSZ) >> 16 & 0xffff;
/*
* If new_typmod < VARHDRSZ, the destination is unconstrained; that's
* always OK. If old_typmod >= VARHDRSZ, the source is constrained,
* and we're OK if the scale is unchanged and the precision is not
* decreasing. See further notes in function header comment.
*/
if (new_typmod < (int32) VARHDRSZ ||
(old_typmod >= (int32) VARHDRSZ &&
new_scale == old_scale && new_precision >= old_precision))
ret = relabel_to_typmod(source, new_typmod);
}
PG_RETURN_POINTER(ret);
}
/*
* numeric() -
*
* This is a special function called by the Postgres database system
* before a value is stored in a tuple's attribute. The precision and
* scale of the attribute have to be applied on the value.
*/
Datum
numeric (PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
int32 typmod = PG_GETARG_INT32(1);
Numeric new;
int32 tmp_typmod;
int precision;
int scale;
int ddigits;
int maxdigits;
NumericVar var;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* If the value isn't a valid type modifier, simply return a copy of the
* input value
*/
if (typmod < (int32) (VARHDRSZ))
{
new = (Numeric) palloc(VARSIZE(num));
memcpy(new, num, VARSIZE(num));
PG_RETURN_NUMERIC(new);
}
/*
* Get the precision and scale out of the typmod value
*/
tmp_typmod = typmod - VARHDRSZ;
precision = (tmp_typmod >> 16) & 0xffff;
scale = tmp_typmod & 0xffff;
maxdigits = precision - scale;
/*
* If the number is certainly in bounds and due to the target scale no
* rounding could be necessary, just make a copy of the input and modify
* its scale fields, unless the larger scale forces us to abandon the
* short representation. (Note we assume the existing dscale is
* honest...)
*/
ddigits = (NUMERIC_WEIGHT(num) + 1) * DEC_DIGITS;
if (ddigits <= maxdigits && scale >= NUMERIC_DSCALE(num)
&& (NUMERIC_CAN_BE_SHORT(scale, NUMERIC_WEIGHT(num))
|| !NUMERIC_IS_SHORT(num)))
{
new = (Numeric) palloc(VARSIZE(num));
memcpy(new, num, VARSIZE(num));
if (NUMERIC_IS_SHORT(num))
new->choice.n_short.n_header =
(num->choice.n_short.n_header & ~NUMERIC_SHORT_DSCALE_MASK)
| (scale << NUMERIC_SHORT_DSCALE_SHIFT);
else
new->choice.n_long.n_sign_dscale = NUMERIC_SIGN(new) |
((uint16) scale & NUMERIC_DSCALE_MASK);
PG_RETURN_NUMERIC(new);
}
/*
* We really need to fiddle with things - unpack the number into a
* variable and let apply_typmod() do it.
*/
init_var(&var);
set_var_from_num(num, &var);
apply_typmod(&var, typmod);
new = make_result(&var);
free_var(&var);
PG_RETURN_NUMERIC(new);
}
Datum
numerictypmodin(PG_FUNCTION_ARGS)
{
ArrayType *ta = PG_GETARG_ARRAYTYPE_P(0);
int32 *tl;
int n;
int32 typmod;
tl = ArrayGetIntegerTypmods(ta, &n);
if (n == 2)
{
if (tl[0] < 1 || tl[0] > NUMERIC_MAX_PRECISION)
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
errmsg("NUMERIC precision %d must be between 1 and %d",
tl[0], NUMERIC_MAX_PRECISION)));
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])));
typmod = ((tl[0] << 16) | tl[1]) + VARHDRSZ;
}
else if (n == 1)
{
if (tl[0] < 1 || tl[0] > NUMERIC_MAX_PRECISION)
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
errmsg("NUMERIC precision %d must be between 1 and %d",
tl[0], NUMERIC_MAX_PRECISION)));
/* scale defaults to zero */
typmod = (tl[0] << 16) + VARHDRSZ;
}
else
{
ereport(ERROR,
(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
errmsg("invalid NUMERIC type modifier")));
typmod = 0; /* keep compiler quiet */
}
PG_RETURN_INT32(typmod);
}
Datum
numerictypmodout(PG_FUNCTION_ARGS)
{
int32 typmod = PG_GETARG_INT32(0);
char *res = (char *) palloc(64);
if (typmod >= 0)
snprintf(res, 64, "(%d,%d)",
((typmod - VARHDRSZ) >> 16) & 0xffff,
(typmod - VARHDRSZ) & 0xffff);
else
*res = '\0';
PG_RETURN_CSTRING(res);
}
/* ----------------------------------------------------------------------
*
* Sign manipulation, rounding and the like
*
* ----------------------------------------------------------------------
*/
Datum
numeric_abs(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Do it the easy way directly on the packed format
*/
res = (Numeric) palloc(VARSIZE(num));
memcpy(res, num, VARSIZE(num));
if (NUMERIC_IS_SHORT(num))
res->choice.n_short.n_header =
num->choice.n_short.n_header & ~NUMERIC_SHORT_SIGN_MASK;
else
res->choice.n_long.n_sign_dscale = NUMERIC_POS | NUMERIC_DSCALE(num);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_uminus(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Do it the easy way directly on the packed format
*/
res = (Numeric) palloc(VARSIZE(num));
memcpy(res, num, VARSIZE(num));
/*
* The packed format is known to be totally zero digit trimmed always. So
* we can identify a ZERO by the fact that there are no digits at all. Do
* nothing to a zero.
*/
if (NUMERIC_NDIGITS(num) != 0)
{
/* Else, flip the sign */
if (NUMERIC_IS_SHORT(num))
res->choice.n_short.n_header =
num->choice.n_short.n_header ^ NUMERIC_SHORT_SIGN_MASK;
else if (NUMERIC_SIGN(num) == NUMERIC_POS)
res->choice.n_long.n_sign_dscale =
NUMERIC_NEG | NUMERIC_DSCALE(num);
else
res->choice.n_long.n_sign_dscale =
NUMERIC_POS | NUMERIC_DSCALE(num);
}
PG_RETURN_NUMERIC(res);
}
Datum
numeric_uplus(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
res = (Numeric) palloc(VARSIZE(num));
memcpy(res, num, VARSIZE(num));
PG_RETURN_NUMERIC(res);
}
/*
* numeric_sign() -
*
* returns -1 if the argument is less than 0, 0 if the argument is equal
* to 0, and 1 if the argument is greater than zero.
*/
Datum
numeric_sign(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
NumericVar result;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
init_var(&result);
/*
* The packed format is known to be totally zero digit trimmed always. So
* we can identify a ZERO by the fact that there are no digits at all.
*/
if (NUMERIC_NDIGITS(num) == 0)
set_var_from_var(&const_zero, &result);
else
{
/*
* And if there are some, we return a copy of ONE with the sign of our
* argument
*/
set_var_from_var(&const_one, &result);
result.sign = NUMERIC_SIGN(num);
}
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_round() -
*
* Round a value to have 'scale' digits after the decimal point.
* We allow negative 'scale', implying rounding before the decimal
* point --- Oracle interprets rounding that way.
*/
Datum
numeric_round(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
int32 scale = PG_GETARG_INT32(1);
Numeric res;
NumericVar arg;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Limit the scale value to avoid possible overflow in calculations
*/
scale = Max(scale, -NUMERIC_MAX_RESULT_SCALE);
scale = Min(scale, NUMERIC_MAX_RESULT_SCALE);
/*
* Unpack the argument and round it at the proper digit position
*/
init_var(&arg);
set_var_from_num(num, &arg);
round_var(&arg, scale);
/* We don't allow negative output dscale */
if (scale < 0)
arg.dscale = 0;
/*
* Return the rounded result
*/
res = make_result(&arg);
free_var(&arg);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_trunc() -
*
* Truncate a value to have 'scale' digits after the decimal point.
* We allow negative 'scale', implying a truncation before the decimal
* point --- Oracle interprets truncation that way.
*/
Datum
numeric_trunc(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
int32 scale = PG_GETARG_INT32(1);
Numeric res;
NumericVar arg;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Limit the scale value to avoid possible overflow in calculations
*/
scale = Max(scale, -NUMERIC_MAX_RESULT_SCALE);
scale = Min(scale, NUMERIC_MAX_RESULT_SCALE);
/*
* Unpack the argument and truncate it at the proper digit position
*/
init_var(&arg);
set_var_from_num(num, &arg);
trunc_var(&arg, scale);
/* We don't allow negative output dscale */
if (scale < 0)
arg.dscale = 0;
/*
* Return the truncated result
*/
res = make_result(&arg);
free_var(&arg);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_ceil() -
*
* Return the smallest integer greater than or equal to the argument
*/
Datum
numeric_ceil(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
NumericVar result;
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
init_var_from_num(num, &result);
ceil_var(&result, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_floor() -
*
* Return the largest integer equal to or less than the argument
*/
Datum
numeric_floor(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
NumericVar result;
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
init_var_from_num(num, &result);
floor_var(&result, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* Implements the numeric version of the width_bucket() function
* defined by SQL2003. See also width_bucket_float8().
*
* 'bound1' and 'bound2' are the lower and upper bounds of the
* histogram's range, respectively. 'count' is the number of buckets
* in the histogram. width_bucket() returns an integer indicating the
* bucket number that 'operand' belongs to in an equiwidth histogram
* with the specified characteristics. An operand smaller than the
* lower bound is assigned to bucket 0. An operand greater than the
* upper bound is assigned to an additional bucket (with number
* count+1). We don't allow "NaN" for any of the numeric arguments.
*/
Datum
width_bucket_numeric(PG_FUNCTION_ARGS)
{
Numeric operand = PG_GETARG_NUMERIC(0);
Numeric bound1 = PG_GETARG_NUMERIC(1);
Numeric bound2 = PG_GETARG_NUMERIC(2);
int32 count = PG_GETARG_INT32(3);
NumericVar count_var;
NumericVar result_var;
int32 result;
if (count <= 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
errmsg("count must be greater than zero")));
if (NUMERIC_IS_NAN(operand) ||
NUMERIC_IS_NAN(bound1) ||
NUMERIC_IS_NAN(bound2))
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
errmsg("operand, lower bound, and upper bound cannot be NaN")));
init_var(&result_var);
init_var(&count_var);
/* Convert 'count' to a numeric, for ease of use later */
int8_to_numericvar((int64) count, &count_var);
switch (cmp_numerics(bound1, bound2))
{
case 0:
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_WIDTH_BUCKET_FUNCTION),
errmsg("lower bound cannot equal upper bound")));
/* bound1 < bound2 */
case -1:
if (cmp_numerics(operand, bound1) < 0)
set_var_from_var(&const_zero, &result_var);
else if (cmp_numerics(operand, bound2) >= 0)
add_var(&count_var, &const_one, &result_var);
else
compute_bucket(operand, bound1, bound2,
&count_var, &result_var);
break;
/* bound1 > bound2 */
case 1:
if (cmp_numerics(operand, bound1) > 0)
set_var_from_var(&const_zero, &result_var);
else if (cmp_numerics(operand, bound2) <= 0)
add_var(&count_var, &const_one, &result_var);
else
compute_bucket(operand, bound1, bound2,
&count_var, &result_var);
break;
}
/* if result exceeds the range of a legal int4, we ereport here */
result = numericvar_to_int4(&result_var);
free_var(&count_var);
free_var(&result_var);
PG_RETURN_INT32(result);
}
/*
* If 'operand' is not outside the bucket range, determine the correct
* bucket for it to go. The calculations performed by this function
* are derived directly from the SQL2003 spec.
*/
static void
compute_bucket(Numeric operand, Numeric bound1, Numeric bound2,
NumericVar *count_var, NumericVar *result_var)
{
NumericVar bound1_var;
NumericVar bound2_var;
NumericVar operand_var;
init_var_from_num(bound1, &bound1_var);
init_var_from_num(bound2, &bound2_var);
init_var_from_num(operand, &operand_var);
if (cmp_var(&bound1_var, &bound2_var) < 0)
{
sub_var(&operand_var, &bound1_var, &operand_var);
sub_var(&bound2_var, &bound1_var, &bound2_var);
div_var(&operand_var, &bound2_var, result_var,
select_div_scale(&operand_var, &bound2_var), true);
}
else
{
sub_var(&bound1_var, &operand_var, &operand_var);
sub_var(&bound1_var, &bound2_var, &bound1_var);
div_var(&operand_var, &bound1_var, result_var,
select_div_scale(&operand_var, &bound1_var), true);
}
mul_var(result_var, count_var, result_var,
result_var->dscale + count_var->dscale);
add_var(result_var, &const_one, result_var);
floor_var(result_var, result_var);
free_var(&bound1_var);
free_var(&bound2_var);
free_var(&operand_var);
}
/* ----------------------------------------------------------------------
*
* Comparison functions
*
* Note: btree indexes need these routines not to leak memory; therefore,
* be careful to free working copies of toasted datums. Most places don't
* need to be so careful.
* ----------------------------------------------------------------------
*/
Datum
numeric_cmp(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
int result;
result = cmp_numerics(num1, num2);
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_INT32(result);
}
Datum
numeric_eq(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
bool result;
result = cmp_numerics(num1, num2) == 0;
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
Datum
numeric_ne(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
bool result;
result = cmp_numerics(num1, num2) != 0;
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
Datum
numeric_gt(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
bool result;
result = cmp_numerics(num1, num2) > 0;
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
Datum
numeric_ge(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
bool result;
result = cmp_numerics(num1, num2) >= 0;
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
Datum
numeric_lt(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
bool result;
result = cmp_numerics(num1, num2) < 0;
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
Datum
numeric_le(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
bool result;
result = cmp_numerics(num1, num2) <= 0;
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
static int
cmp_numerics(Numeric num1, Numeric num2)
{
int result;
/*
* We consider all NANs to be equal and larger than any non-NAN. This is
* somewhat arbitrary; the important thing is to have a consistent sort
* order.
*/
if (NUMERIC_IS_NAN(num1))
{
if (NUMERIC_IS_NAN(num2))
result = 0; /* NAN = NAN */
else
result = 1; /* NAN > non-NAN */
}
else if (NUMERIC_IS_NAN(num2))
{
result = -1; /* non-NAN < NAN */
}
else
{
result = cmp_var_common(NUMERIC_DIGITS(num1), NUMERIC_NDIGITS(num1),
NUMERIC_WEIGHT(num1), NUMERIC_SIGN(num1),
NUMERIC_DIGITS(num2), NUMERIC_NDIGITS(num2),
NUMERIC_WEIGHT(num2), NUMERIC_SIGN(num2));
}
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;
NumericDigit *digits;
/* If it's NaN, don't try to hash the rest of the fields */
if (NUMERIC_IS_NAN(key))
PG_RETURN_UINT32(0);
weight = NUMERIC_WEIGHT(key);
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.
*/
digits = NUMERIC_DIGITS(key);
for (i = 0; i < NUMERIC_NDIGITS(key); i++)
{
if (digits[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 (digits[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);
}
/* ----------------------------------------------------------------------
*
* Basic arithmetic functions
*
* ----------------------------------------------------------------------
*/
/*
* numeric_add() -
*
* Add two numerics
*/
Datum
numeric_add(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 values, let add_var() compute the result and return it.
*/
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
add_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_sub() -
*
* Subtract one numeric from another
*/
Datum
numeric_sub(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 values, let sub_var() compute the result and return it.
*/
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
sub_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_mul() -
*
* Calculate the product of two numerics
*/
Datum
numeric_mul(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 values, let mul_var() compute the result and return it.
* Unlike add_var() and sub_var(), mul_var() will round its result. In the
* case of numeric_mul(), which is invoked for the * operator on numerics,
* we request exact representation for the product (rscale = sum(dscale of
* arg1, dscale of arg2)).
*/
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
mul_var(&arg1, &arg2, &result, arg1.dscale + arg2.dscale);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_div() -
*
* Divide one numeric into another
*/
Datum
numeric_div(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
NumericVar arg1;
NumericVar arg2;
NumericVar result;
Numeric res;
int rscale;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Unpack the arguments
*/
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
/*
* Select scale for division result
*/
rscale = select_div_scale(&arg1, &arg2);
/*
* Do the divide and return the result
*/
div_var(&arg1, &arg2, &result, rscale, true);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* 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_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
/*
* Do the divide and return the result
*/
div_var(&arg1, &arg2, &result, 0, false);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_mod() -
*
* Calculate the modulo of two numerics
*/
Datum
numeric_mod(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
Numeric res;
NumericVar arg1;
NumericVar arg2;
NumericVar result;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
mod_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_inc() -
*
* Increment a number by one
*/
Datum
numeric_inc(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar arg;
Numeric res;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Compute the result and return it
*/
init_var_from_num(num, &arg);
add_var(&arg, &const_one, &arg);
res = make_result(&arg);
free_var(&arg);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_smaller() -
*
* Return the smaller of two numbers
*/
Datum
numeric_smaller(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
/*
* Use cmp_numerics so that this will agree with the comparison operators,
* particularly as regards comparisons involving NaN.
*/
if (cmp_numerics(num1, num2) < 0)
PG_RETURN_NUMERIC(num1);
else
PG_RETURN_NUMERIC(num2);
}
/*
* numeric_larger() -
*
* Return the larger of two numbers
*/
Datum
numeric_larger(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
/*
* Use cmp_numerics so that this will agree with the comparison operators,
* particularly as regards comparisons involving NaN.
*/
if (cmp_numerics(num1, num2) > 0)
PG_RETURN_NUMERIC(num1);
else
PG_RETURN_NUMERIC(num2);
}
/* ----------------------------------------------------------------------
*
* Advanced math functions
*
* ----------------------------------------------------------------------
*/
/*
* numeric_fac()
*
* Compute factorial
*/
Datum
numeric_fac(PG_FUNCTION_ARGS)
{
int64 num = PG_GETARG_INT64(0);
Numeric res;
NumericVar fact;
NumericVar result;
if (num <= 1)
{
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);
int8_to_numericvar(num, &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);
}
res = make_result(&result);
free_var(&fact);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_sqrt() -
*
* Compute the square root of a numeric.
*/
Datum
numeric_sqrt(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
NumericVar arg;
NumericVar result;
int sweight;
int rscale;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Unpack the argument and determine the result scale. We choose a scale
* to give at least NUMERIC_MIN_SIG_DIGITS significant digits; but in any
* case not less than the input's dscale.
*/
init_var_from_num(num, &arg);
init_var(&result);
/* Assume the input was normalized, so arg.weight is accurate */
sweight = (arg.weight + 1) * DEC_DIGITS / 2 - 1;
rscale = NUMERIC_MIN_SIG_DIGITS - sweight;
rscale = Max(rscale, arg.dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
/*
* Let sqrt_var() do the calculation and return the result.
*/
sqrt_var(&arg, &result, rscale);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_exp() -
*
* Raise e to the power of x
*/
Datum
numeric_exp(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
NumericVar arg;
NumericVar result;
int rscale;
double val;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Unpack the argument and determine the result scale. We choose a scale
* to give at least NUMERIC_MIN_SIG_DIGITS significant digits; but in any
* case not less than the input's dscale.
*/
init_var_from_num(num, &arg);
init_var(&result);
/* convert input to float8, ignoring overflow */
val = numericvar_to_double_no_overflow(&arg);
/*
* log10(result) = num * log10(e), so this is approximately the decimal
* weight of the result:
*/
val *= 0.434294481903252;
/* limit to something that won't cause integer overflow */
val = Max(val, -NUMERIC_MAX_RESULT_SCALE);
val = Min(val, NUMERIC_MAX_RESULT_SCALE);
rscale = NUMERIC_MIN_SIG_DIGITS - (int) val;
rscale = Max(rscale, arg.dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
/*
* Let exp_var() do the calculation and return the result.
*/
exp_var(&arg, &result, rscale);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_ln() -
*
* Compute the natural logarithm of x
*/
Datum
numeric_ln(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
Numeric res;
NumericVar arg;
NumericVar result;
int dec_digits;
int rscale;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
init_var_from_num(num, &arg);
init_var(&result);
/* Approx decimal digits before decimal point */
dec_digits = (arg.weight + 1) * DEC_DIGITS;
if (dec_digits > 1)
rscale = NUMERIC_MIN_SIG_DIGITS - (int) log10(dec_digits - 1);
else if (dec_digits < 1)
rscale = NUMERIC_MIN_SIG_DIGITS - (int) log10(1 - dec_digits);
else
rscale = NUMERIC_MIN_SIG_DIGITS;
rscale = Max(rscale, arg.dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
ln_var(&arg, &result, rscale);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_log() -
*
* Compute the logarithm of x in a given base
*/
Datum
numeric_log(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
Numeric res;
NumericVar arg1;
NumericVar arg2;
NumericVar result;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Initialize things
*/
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
init_var(&result);
/*
* Call log_var() to compute and return the result; note it handles scale
* selection itself.
*/
log_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/*
* numeric_power() -
*
* Raise b to the power of x
*/
Datum
numeric_power(PG_FUNCTION_ARGS)
{
Numeric num1 = PG_GETARG_NUMERIC(0);
Numeric num2 = PG_GETARG_NUMERIC(1);
Numeric res;
NumericVar arg1;
NumericVar arg2;
NumericVar arg2_trunc;
NumericVar result;
/*
* Handle NaN
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/*
* Initialize things
*/
init_var(&arg2_trunc);
init_var(&result);
init_var_from_num(num1, &arg1);
init_var_from_num(num2, &arg2);
set_var_from_var(&arg2, &arg2_trunc);
trunc_var(&arg2_trunc, 0);
/*
* 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)
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("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
* scale selection itself.
*/
power_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&result);
free_var(&arg2_trunc);
PG_RETURN_NUMERIC(res);
}
/* ----------------------------------------------------------------------
*
* Type conversion functions
*
* ----------------------------------------------------------------------
*/
Datum
int4_numeric(PG_FUNCTION_ARGS)
{
int32 val = PG_GETARG_INT32(0);
Numeric res;
NumericVar result;
init_var(&result);
int8_to_numericvar((int64) val, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_int4(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
int32 result;
/* XXX would it be better to return NULL? */
if (NUMERIC_IS_NAN(num))
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("cannot convert NaN to integer")));
/* Convert to variable format, then convert to int4 */
init_var_from_num(num, &x);
result = numericvar_to_int4(&x);
PG_RETURN_INT32(result);
}
/*
* Given a NumericVar, convert it to an int32. If the NumericVar
* exceeds the range of an int32, raise the appropriate error via
* ereport(). The input NumericVar is *not* free'd.
*/
static int32
numericvar_to_int4(NumericVar *var)
{
int32 result;
int64 val;
if (!numericvar_to_int8(var, &val))
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("integer out of range")));
/* Down-convert to int4 */
result = (int32) val;
/* Test for overflow by reverse-conversion. */
if ((int64) result != val)
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("integer out of range")));
return result;
}
Datum
int8_numeric(PG_FUNCTION_ARGS)
{
int64 val = PG_GETARG_INT64(0);
Numeric res;
NumericVar result;
init_var(&result);
int8_to_numericvar(val, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_int8(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
int64 result;
/* XXX would it be better to return NULL? */
if (NUMERIC_IS_NAN(num))
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("cannot convert NaN to bigint")));
/* Convert to variable format and thence to int8 */
init_var_from_num(num, &x);
if (!numericvar_to_int8(&x, &result))
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("bigint out of range")));
PG_RETURN_INT64(result);
}
Datum
int2_numeric(PG_FUNCTION_ARGS)
{
int16 val = PG_GETARG_INT16(0);
Numeric res;
NumericVar result;
init_var(&result);
int8_to_numericvar((int64) val, &result);
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_int2(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
int64 val;
int16 result;
/* XXX would it be better to return NULL? */
if (NUMERIC_IS_NAN(num))
ereport(ERROR,
(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
errmsg("cannot convert NaN to smallint")));
/* Convert to variable format and thence to int8 */
init_var_from_num(num, &x);
if (!numericvar_to_int8(&x, &val))
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("smallint out of range")));
/* Down-convert to int2 */
result = (int16) val;
/* Test for overflow by reverse-conversion. */
if ((int64) result != val)
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("smallint out of range")));
PG_RETURN_INT16(result);
}
Datum
float8_numeric(PG_FUNCTION_ARGS)
{
float8 val = PG_GETARG_FLOAT8(0);
Numeric res;
NumericVar result;
char buf[DBL_DIG + 100];
if (isnan(val))
PG_RETURN_NUMERIC(make_result(&const_nan));
sprintf(buf, "%.*g", DBL_DIG, val);
init_var(&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);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_float8(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
char *tmp;
Datum result;
if (NUMERIC_IS_NAN(num))
PG_RETURN_FLOAT8(get_float8_nan());
tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
NumericGetDatum(num)));
result = DirectFunctionCall1(float8in, CStringGetDatum(tmp));
pfree(tmp);
PG_RETURN_DATUM(result);
}
/* Convert numeric to float8; if out of range, return +/- HUGE_VAL */
Datum
numeric_float8_no_overflow(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
double val;
if (NUMERIC_IS_NAN(num))
PG_RETURN_FLOAT8(get_float8_nan());
val = numeric_to_double_no_overflow(num);
PG_RETURN_FLOAT8(val);
}
Datum
float4_numeric(PG_FUNCTION_ARGS)
{
float4 val = PG_GETARG_FLOAT4(0);
Numeric res;
NumericVar result;
char buf[FLT_DIG + 100];
if (isnan(val))
PG_RETURN_NUMERIC(make_result(&const_nan));
sprintf(buf, "%.*g", FLT_DIG, val);
init_var(&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);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_float4(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
char *tmp;
Datum result;
if (NUMERIC_IS_NAN(num))
PG_RETURN_FLOAT4(get_float4_nan());
tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
NumericGetDatum(num)));
result = DirectFunctionCall1(float4in, CStringGetDatum(tmp));
pfree(tmp);
PG_RETURN_DATUM(result);
}
/* ----------------------------------------------------------------------
*
* Aggregate functions
*
* The transition datatype for all these aggregates is declared as INTERNAL.
* Actually, it's a pointer to a NumericAggState allocated in the aggregate
* context. The digit buffers for the NumericVars will be there too.
*
* Note that the transition functions don't bother to create a NumericAggState
* until they see the first non-null input value; therefore, the final
* functions will never see N == 0. (The case is represented as a NULL
* state pointer, instead.)
*
* ----------------------------------------------------------------------
*/
typedef struct NumericAggState
{
bool calcSumX2; /* if true, calculate sumX2 */
bool isNaN; /* true if any processed number was NaN */
MemoryContext agg_context; /* context we're calculating in */
int64 N; /* count of processed numbers */
NumericVar sumX; /* sum of processed numbers */
NumericVar sumX2; /* sum of squares of processed numbers */
} NumericAggState;
/*
* Prepare state data for a numeric aggregate function that needs to compute
* sum, count and optionally sum of squares of the input.
*/
static NumericAggState *
makeNumericAggState(FunctionCallInfo fcinfo, bool calcSumX2)
{
NumericAggState *state;
MemoryContext agg_context;
MemoryContext old_context;
if (!AggCheckCallContext(fcinfo, &agg_context))
elog(ERROR, "aggregate function called in non-aggregate context");
old_context = MemoryContextSwitchTo(agg_context);
state = (NumericAggState *) palloc0(sizeof(NumericAggState));
state->calcSumX2 = calcSumX2;
state->agg_context = agg_context;
MemoryContextSwitchTo(old_context);
return state;
}
/*
* Accumulate a new input value for numeric aggregate functions.
*/
static void
do_numeric_accum(NumericAggState *state, Numeric newval)
{
NumericVar X;
NumericVar X2;
MemoryContext old_context;
/* result is NaN if any processed number is NaN */
if (state->isNaN || NUMERIC_IS_NAN(newval))
{
state->isNaN = true;
return;
}
/* load processed number in short-lived context */
init_var_from_num(newval, &X);
/* if we need X^2, calculate that in short-lived context */
if (state->calcSumX2)
{
init_var(&X2);
mul_var(&X, &X, &X2, X.dscale * 2);
}
/* The rest of this needs to work in the aggregate context */
old_context = MemoryContextSwitchTo(state->agg_context);
if (state->N++ > 0)
{
/* Accumulate sums */
add_var(&X, &(state->sumX), &(state->sumX));
if (state->calcSumX2)
add_var(&X2, &(state->sumX2), &(state->sumX2));
}
else
{
/* First input, so initialize sums */
set_var_from_var(&X, &(state->sumX));
if (state->calcSumX2)
set_var_from_var(&X2, &(state->sumX2));
}
MemoryContextSwitchTo(old_context);
}
/*
* Generic transition function for numeric aggregates that require sumX2.
*/
Datum
numeric_accum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (!PG_ARGISNULL(1))
{
/* Create the state data when we see the first non-null input. */
if (state == NULL)
state = makeNumericAggState(fcinfo, true);
do_numeric_accum(state, PG_GETARG_NUMERIC(1));
}
PG_RETURN_POINTER(state);
}
/*
* Generic transition function for numeric aggregates that don't require sumX2.
*/
Datum
numeric_avg_accum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (!PG_ARGISNULL(1))
{
/* Create the state data when we see the first non-null input. */
if (state == NULL)
state = makeNumericAggState(fcinfo, false);
do_numeric_accum(state, PG_GETARG_NUMERIC(1));
}
PG_RETURN_POINTER(state);
}
/*
* Integer data types all use Numeric accumulators to share code and
* avoid risk of overflow. For int2 and int4 inputs, Numeric accumulation
* is overkill for the N and sum(X) values, but definitely not overkill
* for the sum(X*X) value. Hence, we use int2_accum and int4_accum only
* for stddev/variance --- there are faster special-purpose accumulator
* routines for SUM and AVG of these datatypes.
*/
Datum
int2_accum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (!PG_ARGISNULL(1))
{
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int2_numeric,
PG_GETARG_DATUM(1)));
/* Create the state data when we see the first non-null input. */
if (state == NULL)
state = makeNumericAggState(fcinfo, true);
do_numeric_accum(state, newval);
}
PG_RETURN_POINTER(state);
}
Datum
int4_accum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (!PG_ARGISNULL(1))
{
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int4_numeric,
PG_GETARG_DATUM(1)));
/* Create the state data when we see the first non-null input. */
if (state == NULL)
state = makeNumericAggState(fcinfo, true);
do_numeric_accum(state, newval);
}
PG_RETURN_POINTER(state);
}
Datum
int8_accum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (!PG_ARGISNULL(1))
{
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric,
PG_GETARG_DATUM(1)));
/* Create the state data when we see the first non-null input. */
if (state == NULL)
state = makeNumericAggState(fcinfo, true);
do_numeric_accum(state, newval);
}
PG_RETURN_POINTER(state);
}
/*
* Transition function for int8 input when we don't need sumX2.
*/
Datum
int8_avg_accum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (!PG_ARGISNULL(1))
{
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric,
PG_GETARG_DATUM(1)));
/* Create the state data when we see the first non-null input. */
if (state == NULL)
state = makeNumericAggState(fcinfo, false);
do_numeric_accum(state, newval);
}
PG_RETURN_POINTER(state);
}
Datum
numeric_avg(PG_FUNCTION_ARGS)
{
NumericAggState *state;
Datum N_datum;
Datum sumX_datum;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (state == NULL) /* there were no non-null inputs */
PG_RETURN_NULL();
if (state->isNaN) /* there was at least one NaN input */
PG_RETURN_NUMERIC(make_result(&const_nan));
N_datum = DirectFunctionCall1(int8_numeric, Int64GetDatum(state->N));
sumX_datum = NumericGetDatum(make_result(&state->sumX));
PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumX_datum, N_datum));
}
Datum
numeric_sum(PG_FUNCTION_ARGS)
{
NumericAggState *state;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
if (state == NULL) /* there were no non-null inputs */
PG_RETURN_NULL();
if (state->isNaN) /* there was at least one NaN input */
PG_RETURN_NUMERIC(make_result(&const_nan));
PG_RETURN_NUMERIC(make_result(&(state->sumX)));
}
/*
* Workhorse routine for the standard deviance and variance
* aggregates. 'state' is aggregate's transition state.
* 'variance' specifies whether we should calculate the
* variance or the standard deviation. 'sample' indicates whether the
* caller is interested in the sample or the population
* variance/stddev.
*
* If appropriate variance statistic is undefined for the input,
* *is_null is set to true and NULL is returned.
*/
static Numeric
numeric_stddev_internal(NumericAggState *state,
bool variance, bool sample,
bool *is_null)
{
Numeric res;
NumericVar vN,
vsumX,
vsumX2,
vNminus1;
NumericVar *comp;
int rscale;
/* Deal with empty input and NaN-input cases */
if (state == NULL)
{
*is_null = true;
return NULL;
}
*is_null = false;
if (state->isNaN)
return make_result(&const_nan);
init_var(&vN);
init_var(&vsumX);
init_var(&vsumX2);
int8_to_numericvar(state->N, &vN);
set_var_from_var(&(state->sumX), &vsumX);
set_var_from_var(&(state->sumX2), &vsumX2);
/*
* Sample stddev and variance are undefined when N <= 1; population stddev
* is undefined when N == 0. Return NULL in either case.
*/
if (sample)
comp = &const_one;
else
comp = &const_zero;
if (cmp_var(&vN, comp) <= 0)
{
*is_null = true;
return NULL;
}
init_var(&vNminus1);
sub_var(&vN, &const_one, &vNminus1);
/* compute rscale for mul_var calls */
rscale = vsumX.dscale * 2;
mul_var(&vsumX, &vsumX, &vsumX, rscale); /* vsumX = sumX * sumX */
mul_var(&vN, &vsumX2, &vsumX2, rscale); /* vsumX2 = N * sumX2 */
sub_var(&vsumX2, &vsumX, &vsumX2); /* N * sumX2 - sumX * sumX */
if (cmp_var(&vsumX2, &const_zero) <= 0)
{
/* Watch out for roundoff error producing a negative numerator */
res = make_result(&const_zero);
}
else
{
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)
sqrt_var(&vsumX, &vsumX, rscale); /* stddev */
res = make_result(&vsumX);
}
free_var(&vNminus1);
free_var(&vsumX);
free_var(&vsumX2);
return res;
}
Datum
numeric_var_samp(PG_FUNCTION_ARGS)
{
NumericAggState *state;
Numeric res;
bool is_null;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
res = numeric_stddev_internal(state, true, true, &is_null);
if (is_null)
PG_RETURN_NULL();
else
PG_RETURN_NUMERIC(res);
}
Datum
numeric_stddev_samp(PG_FUNCTION_ARGS)
{
NumericAggState *state;
Numeric res;
bool is_null;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
res = numeric_stddev_internal(state, false, true, &is_null);
if (is_null)
PG_RETURN_NULL();
else
PG_RETURN_NUMERIC(res);
}
Datum
numeric_var_pop(PG_FUNCTION_ARGS)
{
NumericAggState *state;
Numeric res;
bool is_null;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
res = numeric_stddev_internal(state, true, false, &is_null);
if (is_null)
PG_RETURN_NULL();
else
PG_RETURN_NUMERIC(res);
}
Datum
numeric_stddev_pop(PG_FUNCTION_ARGS)
{
NumericAggState *state;
Numeric res;
bool is_null;
state = PG_ARGISNULL(0) ? NULL : (NumericAggState *) PG_GETARG_POINTER(0);
res = numeric_stddev_internal(state, false, false, &is_null);
if (is_null)
PG_RETURN_NULL();
else
PG_RETURN_NUMERIC(res);
}
/*
* SUM transition functions for integer datatypes.
*
* To avoid overflow, we use accumulators wider than the input datatype.
* A Numeric accumulator is needed for int8 input; for int4 and int2
* inputs, we use int8 accumulators which should be sufficient for practical
* purposes. (The latter two therefore don't really belong in this file,
* but we keep them here anyway.)
*
* Because SQL defines the SUM() of no values to be NULL, not zero,
* the initial condition of the transition data value needs to be NULL. This
* means we can't rely on ExecAgg to automatically insert the first non-null
* data value into the transition data: it doesn't know how to do the type
* conversion. The upshot is that these routines have to be marked non-strict
* and handle substitution of the first non-null input themselves.
*/
Datum
int2_sum(PG_FUNCTION_ARGS)
{
int64 newval;
if (PG_ARGISNULL(0))
{
/* No non-null input seen so far... */
if (PG_ARGISNULL(1))
PG_RETURN_NULL(); /* still no non-null */
/* This is the first non-null input. */
newval = (int64) PG_GETARG_INT16(1);
PG_RETURN_INT64(newval);
}
/*
* If we're invoked as an aggregate, 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. (If int8 is pass-by-value,
* then of course this is useless as well as incorrect, so just ifdef it
* out.)
*/
#ifndef USE_FLOAT8_BYVAL /* controls int8 too */
if (AggCheckCallContext(fcinfo, NULL))
{
int64 *oldsum = (int64 *) PG_GETARG_POINTER(0);
/* Leave the running sum unchanged in the new input is null */
if (!PG_ARGISNULL(1))
*oldsum = *oldsum + (int64) PG_GETARG_INT16(1);
PG_RETURN_POINTER(oldsum);
}
else
#endif
{
int64 oldsum = PG_GETARG_INT64(0);
/* Leave sum unchanged if new input is null. */
if (PG_ARGISNULL(1))
PG_RETURN_INT64(oldsum);
/* OK to do the addition. */
newval = oldsum + (int64) PG_GETARG_INT16(1);
PG_RETURN_INT64(newval);
}
}
Datum
int4_sum(PG_FUNCTION_ARGS)
{
int64 newval;
if (PG_ARGISNULL(0))
{
/* No non-null input seen so far... */
if (PG_ARGISNULL(1))
PG_RETURN_NULL(); /* still no non-null */
/* This is the first non-null input. */
newval = (int64) PG_GETARG_INT32(1);
PG_RETURN_INT64(newval);
}
/*
* If we're invoked as an aggregate, 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. (If int8 is pass-by-value,
* then of course this is useless as well as incorrect, so just ifdef it
* out.)
*/
#ifndef USE_FLOAT8_BYVAL /* controls int8 too */
if (AggCheckCallContext(fcinfo, NULL))
{
int64 *oldsum = (int64 *) PG_GETARG_POINTER(0);
/* Leave the running sum unchanged in the new input is null */
if (!PG_ARGISNULL(1))
*oldsum = *oldsum + (int64) PG_GETARG_INT32(1);
PG_RETURN_POINTER(oldsum);
}
else
#endif
{
int64 oldsum = PG_GETARG_INT64(0);
/* Leave sum unchanged if new input is null. */
if (PG_ARGISNULL(1))
PG_RETURN_INT64(oldsum);
/* OK to do the addition. */
newval = oldsum + (int64) PG_GETARG_INT32(1);
PG_RETURN_INT64(newval);
}
}
/*
* Note: this function is obsolete, it's no longer used for SUM(int8).
*/
Datum
int8_sum(PG_FUNCTION_ARGS)
{
Numeric oldsum;
Datum newval;
if (PG_ARGISNULL(0))
{
/* No non-null input seen so far... */
if (PG_ARGISNULL(1))
PG_RETURN_NULL(); /* still no non-null */
/* This is the first non-null input. */
newval = DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1));
PG_RETURN_DATUM(newval);
}
/*
* Note that we cannot special-case the aggregate case here, as we do for
* int2_sum and int4_sum: numeric is of variable size, so we cannot modify
* our first parameter in-place.
*/
oldsum = PG_GETARG_NUMERIC(0);
/* Leave sum unchanged if new input is null. */
if (PG_ARGISNULL(1))
PG_RETURN_NUMERIC(oldsum);
/* OK to do the addition. */
newval = DirectFunctionCall1(int8_numeric, PG_GETARG_DATUM(1));
PG_RETURN_DATUM(DirectFunctionCall2(numeric_add,
NumericGetDatum(oldsum), newval));
}
/*
* Routines for avg(int2) and avg(int4). The transition datatype
* is a two-element int8 array, holding count and sum.
*/
typedef struct Int8TransTypeData
{
int64 count;
int64 sum;
} Int8TransTypeData;
Datum
int2_avg_accum(PG_FUNCTION_ARGS)
{
ArrayType *transarray;
int16 newval = PG_GETARG_INT16(1);
Int8TransTypeData *transdata;
/*
* If we're invoked as an aggregate, we can cheat and modify our first
* parameter in-place to reduce palloc overhead. Otherwise we need to make
* a copy of it before scribbling on it.
*/
if (AggCheckCallContext(fcinfo, NULL))
transarray = PG_GETARG_ARRAYTYPE_P(0);
else
transarray = PG_GETARG_ARRAYTYPE_P_COPY(0);
if (ARR_HASNULL(transarray) ||
ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData))
elog(ERROR, "expected 2-element int8 array");
transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray);
transdata->count++;
transdata->sum += newval;
PG_RETURN_ARRAYTYPE_P(transarray);
}
Datum
int4_avg_accum(PG_FUNCTION_ARGS)
{
ArrayType *transarray;
int32 newval = PG_GETARG_INT32(1);
Int8TransTypeData *transdata;
/*
* If we're invoked as an aggregate, we can cheat and modify our first
* parameter in-place to reduce palloc overhead. Otherwise we need to make
* a copy of it before scribbling on it.
*/
if (AggCheckCallContext(fcinfo, NULL))
transarray = PG_GETARG_ARRAYTYPE_P(0);
else
transarray = PG_GETARG_ARRAYTYPE_P_COPY(0);
if (ARR_HASNULL(transarray) ||
ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData))
elog(ERROR, "expected 2-element int8 array");
transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray);
transdata->count++;
transdata->sum += newval;
PG_RETURN_ARRAYTYPE_P(transarray);
}
Datum
int8_avg(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Int8TransTypeData *transdata;
Datum countd,
sumd;
if (ARR_HASNULL(transarray) ||
ARR_SIZE(transarray) != ARR_OVERHEAD_NONULLS(1) + sizeof(Int8TransTypeData))
elog(ERROR, "expected 2-element int8 array");
transdata = (Int8TransTypeData *) ARR_DATA_PTR(transarray);
/* SQL defines AVG of no values to be NULL */
if (transdata->count == 0)
PG_RETURN_NULL();
countd = DirectFunctionCall1(int8_numeric,
Int64GetDatumFast(transdata->count));
sumd = DirectFunctionCall1(int8_numeric,
Int64GetDatumFast(transdata->sum));
PG_RETURN_DATUM(DirectFunctionCall2(numeric_div, sumd, countd));
}
/* ----------------------------------------------------------------------
*
* Debug support
*
* ----------------------------------------------------------------------
*/
#ifdef NUMERIC_DEBUG
/*
* dump_numeric() - Dump a value in the db storage format for debugging
*/
static void
dump_numeric(const char *str, Numeric num)
{
NumericDigit *digits = NUMERIC_DIGITS(num);
int ndigits;
int i;
ndigits = NUMERIC_NDIGITS(num);
printf("%s: NUMERIC w=%d d=%d ", str,
NUMERIC_WEIGHT(num), NUMERIC_DSCALE(num));
switch (NUMERIC_SIGN(num))
{
case NUMERIC_POS:
printf("POS");
break;
case NUMERIC_NEG:
printf("NEG");
break;
case NUMERIC_NAN:
printf("NaN");
break;
default:
printf("SIGN=0x%x", NUMERIC_SIGN(num));
break;
}
for (i = 0; i < ndigits; i++)
printf(" %0*d", DEC_DIGITS, digits[i]);
printf("\n");
}
/*
* dump_var() - Dump a value in the variable format for debugging
*/
static void
dump_var(const char *str, NumericVar *var)
{
int i;
printf("%s: VAR w=%d d=%d ", str, var->weight, var->dscale);
switch (var->sign)
{
case NUMERIC_POS:
printf("POS");
break;
case NUMERIC_NEG:
printf("NEG");
break;
case NUMERIC_NAN:
printf("NaN");
break;
default:
printf("SIGN=0x%x", var->sign);
break;
}
for (i = 0; i < var->ndigits; i++)
printf(" %0*d", DEC_DIGITS, var->digits[i]);
printf("\n");
}
#endif /* NUMERIC_DEBUG */
/* ----------------------------------------------------------------------
*
* Local functions follow
*
* In general, these do not support NaNs --- callers must eliminate
* the possibility of NaN first. (make_result() is an exception.)
*
* ----------------------------------------------------------------------
*/
/*
* alloc_var() -
*
* Allocate a digit buffer of ndigits digits (plus a spare digit for rounding)
*/
static void
alloc_var(NumericVar *var, int ndigits)
{
digitbuf_free(var->buf);
var->buf = digitbuf_alloc(ndigits + 1);
var->buf[0] = 0; /* spare digit for rounding */
var->digits = var->buf + 1;
var->ndigits = ndigits;
}
/*
* free_var() -
*
* Return the digit buffer of a variable to the free pool
*/
static void
free_var(NumericVar *var)
{
digitbuf_free(var->buf);
var->buf = NULL;
var->digits = NULL;
var->sign = NUMERIC_NAN;
}
/*
* zero_var() -
*
* Set a variable to ZERO.
* Note: its dscale is not touched.
*/
static void
zero_var(NumericVar *var)
{
digitbuf_free(var->buf);
var->buf = NULL;
var->digits = NULL;
var->ndigits = 0;
var->weight = 0; /* by convention; doesn't really matter */
var->sign = NUMERIC_POS; /* anything but NAN... */
}
/*
* 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 const char *
set_var_from_str(const char *str, const char *cp, NumericVar *dest)
{
bool have_dp = FALSE;
int i;
unsigned char *decdigits;
int sign = NUMERIC_POS;
int dweight = -1;
int ddigits;
int dscale = 0;
int weight;
int ndigits;
int offset;
NumericDigit *digits;
/*
* We first parse the string to extract decimal digits and determine the
* correct decimal weight. Then convert to NBASE representation.
*/
switch (*cp)
{
case '+':
sign = NUMERIC_POS;
cp++;
break;
case '-':
sign = NUMERIC_NEG;
cp++;
break;
}
if (*cp == '.')
{
have_dp = TRUE;
cp++;
}
if (!isdigit((unsigned char) *cp))
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type numeric: \"%s\"", str)));
decdigits = (unsigned char *) palloc(strlen(cp) + DEC_DIGITS * 2);
/* leading padding for digit alignment later */
memset(decdigits, 0, DEC_DIGITS);
i = DEC_DIGITS;
while (*cp)
{
if (isdigit((unsigned char) *cp))
{
decdigits[i++] = *cp++ - '0';
if (!have_dp)
dweight++;
else
dscale++;
}
else if (*cp == '.')
{
if (have_dp)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type numeric: \"%s\"",
str)));
have_dp = TRUE;
cp++;
}
else
break;
}
ddigits = i - DEC_DIGITS;
/* trailing padding for digit alignment later */
memset(decdigits + i, 0, DEC_DIGITS - 1);
/* Handle exponent, if any */
if (*cp == 'e' || *cp == 'E')
{
long exponent;
char *endptr;
cp++;
exponent = strtol(cp, &endptr, 10);
if (endptr == cp)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type numeric: \"%s\"",
str)));
cp = endptr;
if (exponent > NUMERIC_MAX_PRECISION ||
exponent < -NUMERIC_MAX_PRECISION)
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type numeric: \"%s\"",
str)));
dweight += (int) exponent;
dscale -= (int) exponent;
if (dscale < 0)
dscale = 0;
}
/*
* Okay, convert pure-decimal representation to base NBASE. First we need
* to determine the converted weight and ndigits. offset is the number of
* decimal zeroes to insert before the first given digit to have a
* correctly aligned first NBASE digit.
*/
if (dweight >= 0)
weight = (dweight + 1 + DEC_DIGITS - 1) / DEC_DIGITS - 1;
else
weight = -((-dweight - 1) / DEC_DIGITS + 1);
offset = (weight + 1) * DEC_DIGITS - (dweight + 1);
ndigits = (ddigits + offset + DEC_DIGITS - 1) / DEC_DIGITS;
alloc_var(dest, ndigits);
dest->sign = sign;
dest->weight = weight;
dest->dscale = dscale;
i = DEC_DIGITS - offset;
digits = dest->digits;
while (ndigits-- > 0)
{
#if DEC_DIGITS == 4
*digits++ = ((decdigits[i] * 10 + decdigits[i + 1]) * 10 +
decdigits[i + 2]) * 10 + decdigits[i + 3];
#elif DEC_DIGITS == 2
*digits++ = decdigits[i] * 10 + decdigits[i + 1];
#elif DEC_DIGITS == 1
*digits++ = decdigits[i];
#else
#error unsupported NBASE
#endif
i += DEC_DIGITS;
}
pfree(decdigits);
/* Strip any leading/trailing zeroes, and normalize weight if zero */
strip_var(dest);
/* Return end+1 position for caller */
return cp;
}
/*
* set_var_from_num() -
*
* Convert the packed db format into a variable
*/
static void
set_var_from_num(Numeric num, NumericVar *dest)
{
int ndigits;
ndigits = NUMERIC_NDIGITS(num);
alloc_var(dest, ndigits);
dest->weight = NUMERIC_WEIGHT(num);
dest->sign = NUMERIC_SIGN(num);
dest->dscale = NUMERIC_DSCALE(num);
memcpy(dest->digits, NUMERIC_DIGITS(num), ndigits * sizeof(NumericDigit));
}
/*
* init_var_from_num() -
*
* Initialize a variable from packed db format. The digits array is not
* copied, which saves some cycles when the resulting var is not modified.
* Also, there's no need to call free_var(), as long as you don't assign any
* other value to it (with set_var_* functions, or by using the var as the
* destination of a function like add_var())
*
* CAUTION: Do not modify the digits buffer of a var initialized with this
* function, e.g by calling round_var() or trunc_var(), as the changes will
* propagate to the original Numeric! It's OK to use it as the destination
* argument of one of the calculational functions, though.
*/
static void
init_var_from_num(Numeric num, NumericVar *dest)
{
dest->ndigits = NUMERIC_NDIGITS(num);
dest->weight = NUMERIC_WEIGHT(num);
dest->sign = NUMERIC_SIGN(num);
dest->dscale = NUMERIC_DSCALE(num);
dest->digits = NUMERIC_DIGITS(num);
dest->buf = NULL; /* digits array is not palloc'd */
}
/*
* set_var_from_var() -
*
* Copy one variable into another
*/
static void
set_var_from_var(NumericVar *value, NumericVar *dest)
{
NumericDigit *newbuf;
newbuf = digitbuf_alloc(value->ndigits + 1);
newbuf[0] = 0; /* spare digit for rounding */
memcpy(newbuf + 1, value->digits, value->ndigits * sizeof(NumericDigit));
digitbuf_free(dest->buf);
memmove(dest, value, sizeof(NumericVar));
dest->buf = newbuf;
dest->digits = newbuf + 1;
}
/*
* get_str_from_var() -
*
* Convert a var to text representation (guts of numeric_out).
* The var is displayed to the number of digits indicated by its dscale.
* Returns a palloc'd string.
*/
static char *
get_str_from_var(NumericVar *var)
{
int dscale;
char *str;
char *cp;
char *endcp;
int i;
int d;
NumericDigit dig;
#if DEC_DIGITS > 1
NumericDigit d1;
#endif
dscale = var->dscale;
/*
* Allocate space for the result.
*
* i is set to the # of decimal digits before decimal point. dscale is the
* # of decimal digits we will print after decimal point. We may generate
* as many as DEC_DIGITS-1 excess digits at the end, and in addition we
* need room for sign, decimal point, null terminator.
*/
i = (var->weight + 1) * DEC_DIGITS;
if (i <= 0)
i = 1;
str = palloc(i + dscale + DEC_DIGITS + 2);
cp = str;
/*
* Output a dash for negative values
*/
if (var->sign == NUMERIC_NEG)
*cp++ = '-';
/*
* Output all digits before the decimal point
*/
if (var->weight < 0)
{
d = var->weight + 1;
*cp++ = '0';
}
else
{
for (d = 0; d <= var->weight; d++)
{
dig = (d < var->ndigits) ? var->digits[d] : 0;
/* In the first digit, suppress extra leading decimal zeroes */
#if DEC_DIGITS == 4
{
bool putit = (d > 0);
d1 = dig / 1000;
dig -= d1 * 1000;
putit |= (d1 > 0);
if (putit)
*cp++ = d1 + '0';
d1 = dig / 100;
dig -= d1 * 100;
putit |= (d1 > 0);
if (putit)
*cp++ = d1 + '0';
d1 = dig / 10;
dig -= d1 * 10;
putit |= (d1 > 0);
if (putit)
*cp++ = d1 + '0';
*cp++ = dig + '0';
}
#elif DEC_DIGITS == 2
d1 = dig / 10;
dig -= d1 * 10;
if (d1 > 0 || d > 0)
*cp++ = d1 + '0';
*cp++ = dig + '0';
#elif DEC_DIGITS == 1
*cp++ = dig + '0';
#else
#error unsupported NBASE
#endif
}
}
/*
* If requested, output a decimal point and all the digits that follow it.
* We initially put out a multiple of DEC_DIGITS digits, then truncate if
* needed.
*/
if (dscale > 0)
{
*cp++ = '.';
endcp = cp + dscale;
for (i = 0; i < dscale; d++, i += DEC_DIGITS)
{
dig = (d >= 0 && d < var->ndigits) ? var->digits[d] : 0;
#if DEC_DIGITS == 4
d1 = dig / 1000;
dig -= d1 * 1000;
*cp++ = d1 + '0';
d1 = dig / 100;
dig -= d1 * 100;
*cp++ = d1 + '0';
d1 = dig / 10;
dig -= d1 * 10;
*cp++ = d1 + '0';
*cp++ = dig + '0';
#elif DEC_DIGITS == 2
d1 = dig / 10;
dig -= d1 * 10;
*cp++ = d1 + '0';
*cp++ = dig + '0';
#elif DEC_DIGITS == 1
*cp++ = dig + '0';
#else
#error unsupported NBASE
#endif
}
cp = endcp;
}
/*
* terminate the string and return it
*/
*cp = '\0';
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.
*
* 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);
power_var_int(&const_ten, exponent, &denominator, denom_scale);
div_var(var, &denominator, &significand, rscale, true);
sig_out = get_str_from_var(&significand);
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() -
*
* Create the packed db numeric format in palloc()'d memory from
* a variable.
*/
static Numeric
make_result(NumericVar *var)
{
Numeric result;
NumericDigit *digits = var->digits;
int weight = var->weight;
int sign = var->sign;
int n;
Size len;
if (sign == NUMERIC_NAN)
{
result = (Numeric) palloc(NUMERIC_HDRSZ_SHORT);
SET_VARSIZE(result, NUMERIC_HDRSZ_SHORT);
result->choice.n_header = NUMERIC_NAN;
/* the header word is all we need */
dump_numeric("make_result()", result);
return result;
}
n = var->ndigits;
/* truncate leading zeroes */
while (n > 0 && *digits == 0)
{
digits++;
weight--;
n--;
}
/* truncate trailing zeroes */
while (n > 0 && digits[n - 1] == 0)
n--;
/* If zero result, force to weight=0 and positive sign */
if (n == 0)
{
weight = 0;
sign = NUMERIC_POS;
}
/* Build the result */
if (NUMERIC_CAN_BE_SHORT(var->dscale, weight))
{
len = NUMERIC_HDRSZ_SHORT + n * sizeof(NumericDigit);
result = (Numeric) palloc(len);
SET_VARSIZE(result, len);
result->choice.n_short.n_header =
(sign == NUMERIC_NEG ? (NUMERIC_SHORT | NUMERIC_SHORT_SIGN_MASK)
: NUMERIC_SHORT)
| (var->dscale << NUMERIC_SHORT_DSCALE_SHIFT)
| (weight < 0 ? NUMERIC_SHORT_WEIGHT_SIGN_MASK : 0)
| (weight & NUMERIC_SHORT_WEIGHT_MASK);
}
else
{
len = NUMERIC_HDRSZ + n * sizeof(NumericDigit);
result = (Numeric) palloc(len);
SET_VARSIZE(result, len);
result->choice.n_long.n_sign_dscale =
sign | (var->dscale & NUMERIC_DSCALE_MASK);
result->choice.n_long.n_weight = weight;
}
memcpy(NUMERIC_DIGITS(result), digits, n * sizeof(NumericDigit));
Assert(NUMERIC_NDIGITS(result) == n);
/* Check for overflow of int16 fields */
if (NUMERIC_WEIGHT(result) != weight ||
NUMERIC_DSCALE(result) != var->dscale)
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("value overflows numeric format")));
dump_numeric("make_result()", result);
return result;
}
/*
* apply_typmod() -
*
* Do bounds checking and rounding according to the attributes
* typmod field.
*/
static void
apply_typmod(NumericVar *var, int32 typmod)
{
int precision;
int scale;
int maxdigits;
int ddigits;
int i;
/* Do nothing if we have a default typmod (-1) */
if (typmod < (int32) (VARHDRSZ))
return;
typmod -= VARHDRSZ;
precision = (typmod >> 16) & 0xffff;
scale = typmod & 0xffff;
maxdigits = precision - scale;
/* Round to target scale (and set var->dscale) */
round_var(var, scale);
/*
* Check for overflow - note we can't do this before rounding, because
* rounding could raise the weight. Also note that the var's weight could
* be inflated by leading zeroes, which will be stripped before storage
* but perhaps might not have been yet. In any case, we must recognize a
* true zero, whose weight doesn't mean anything.
*/
ddigits = (var->weight + 1) * DEC_DIGITS;
if (ddigits > maxdigits)
{
/* Determine true weight; and check for all-zero result */
for (i = 0; i < var->ndigits; i++)
{
NumericDigit dig = var->digits[i];
if (dig)
{
/* Adjust for any high-order decimal zero digits */
#if DEC_DIGITS == 4
if (dig < 10)
ddigits -= 3;
else if (dig < 100)
ddigits -= 2;
else if (dig < 1000)
ddigits -= 1;
#elif DEC_DIGITS == 2
if (dig < 10)
ddigits -= 1;
#elif DEC_DIGITS == 1
/* no adjustment */
#else
#error unsupported NBASE
#endif
if (ddigits > maxdigits)
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("numeric field overflow"),
errdetail("A field with precision %d, scale %d must round to an absolute value less than %s%d.",
precision, scale,
/* Display 10^0 as 1 */
maxdigits ? "10^" : "",
maxdigits ? maxdigits : 1
)));
break;
}
ddigits -= DEC_DIGITS;
}
}
}
/*
* Convert numeric to int8, rounding if needed.
*
* If overflow, return FALSE (no error is raised). Return TRUE if okay.
*/
static bool
numericvar_to_int8(NumericVar *var, int64 *result)
{
NumericDigit *digits;
int ndigits;
int weight;
int i;
int64 val,
oldval;
bool neg;
NumericVar rounded;
/* Round to nearest integer */
init_var(&rounded);
set_var_from_var(var, &rounded);
round_var(&rounded, 0);
/* Check for zero input */
strip_var(&rounded);
ndigits = rounded.ndigits;
if (ndigits == 0)
{
*result = 0;
free_var(&rounded);
return true;
}
/*
* For input like 10000000000, we must treat stripped digits as real. So
* the loop assumes there are weight+1 digits before the decimal point.
*/
weight = rounded.weight;
Assert(weight >= 0 && ndigits <= weight + 1);
/* Construct the result */
digits = rounded.digits;
neg = (rounded.sign == NUMERIC_NEG);
val = digits[0];
for (i = 1; i <= weight; i++)
{
oldval = val;
val *= NBASE;
if (i < ndigits)
val += digits[i];
/*
* The overflow check is a bit tricky because we want to accept
* INT64_MIN, which will overflow the positive accumulator. We can
* detect this case easily though because INT64_MIN is the only
* nonzero value for which -val == val (on a two's complement machine,
* anyway).
*/
if ((val / NBASE) != oldval) /* possible overflow? */
{
if (!neg || (-val) != val || val == 0 || oldval < 0)
{
free_var(&rounded);
return false;
}
}
}
free_var(&rounded);
*result = neg ? -val : val;
return true;
}
/*
* Convert int8 value to numeric.
*/
static void
int8_to_numericvar(int64 val, NumericVar *var)
{
uint64 uval,
newuval;
NumericDigit *ptr;
int ndigits;
/* int8 can require at most 19 decimal digits; add one for safety */
alloc_var(var, 20 / DEC_DIGITS);
if (val < 0)
{
var->sign = NUMERIC_NEG;
uval = -val;
}
else
{
var->sign = NUMERIC_POS;
uval = val;
}
var->dscale = 0;
if (val == 0)
{
var->ndigits = 0;
var->weight = 0;
return;
}
ptr = var->digits + var->ndigits;
ndigits = 0;
do
{
ptr--;
ndigits++;
newuval = uval / NBASE;
*ptr = uval - newuval * NBASE;
uval = newuval;
} while (uval);
var->digits = ptr;
var->ndigits = ndigits;
var->weight = ndigits - 1;
}
/*
* Convert numeric to float8; if out of range, return +/- HUGE_VAL
*/
static double
numeric_to_double_no_overflow(Numeric num)
{
char *tmp;
double val;
char *endptr;
tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
NumericGetDatum(num)));
/* unlike float8in, we ignore ERANGE from strtod */
val = strtod(tmp, &endptr);
if (*endptr != '\0')
{
/* shouldn't happen ... */
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type double precision: \"%s\"",
tmp)));
}
pfree(tmp);
return val;
}
/* As above, but work from a NumericVar */
static double
numericvar_to_double_no_overflow(NumericVar *var)
{
char *tmp;
double val;
char *endptr;
tmp = get_str_from_var(var);
/* unlike float8in, we ignore ERANGE from strtod */
val = strtod(tmp, &endptr);
if (*endptr != '\0')
{
/* shouldn't happen ... */
ereport(ERROR,
(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
errmsg("invalid input syntax for type double precision: \"%s\"",
tmp)));
}
pfree(tmp);
return val;
}
/*
* cmp_var() -
*
* Compare two values on variable level. We assume zeroes have been
* truncated to no digits.
*/
static int
cmp_var(NumericVar *var1, NumericVar *var2)
{
return cmp_var_common(var1->digits, var1->ndigits,
var1->weight, var1->sign,
var2->digits, var2->ndigits,
var2->weight, var2->sign);
}
/*
* cmp_var_common() -
*
* Main routine of cmp_var(). This function can be used by both
* NumericVar and Numeric.
*/
static int
cmp_var_common(const NumericDigit *var1digits, int var1ndigits,
int var1weight, int var1sign,
const NumericDigit *var2digits, int var2ndigits,
int var2weight, int var2sign)
{
if (var1ndigits == 0)
{
if (var2ndigits == 0)
return 0;
if (var2sign == NUMERIC_NEG)
return 1;
return -1;
}
if (var2ndigits == 0)
{
if (var1sign == NUMERIC_POS)
return 1;
return -1;
}
if (var1sign == NUMERIC_POS)
{
if (var2sign == NUMERIC_NEG)
return 1;
return cmp_abs_common(var1digits, var1ndigits, var1weight,
var2digits, var2ndigits, var2weight);
}
if (var2sign == NUMERIC_POS)
return -1;
return cmp_abs_common(var2digits, var2ndigits, var2weight,
var1digits, var1ndigits, var1weight);
}
/*
* add_var() -
*
* Full version of add functionality on variable level (handling signs).
* result might point to one of the operands too without danger.
*/
static void
add_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
/*
* Decide on the signs of the two variables what to do
*/
if (var1->sign == NUMERIC_POS)
{
if (var2->sign == NUMERIC_POS)
{
/*
* Both are positive result = +(ABS(var1) + ABS(var2))
*/
add_abs(var1, var2, result);
result->sign = NUMERIC_POS;
}
else
{
/*
* var1 is positive, var2 is negative Must compare absolute values
*/
switch (cmp_abs(var1, var2))
{
case 0:
/* ----------
* ABS(var1) == ABS(var2)
* result = ZERO
* ----------
*/
zero_var(result);
result->dscale = Max(var1->dscale, var2->dscale);
break;
case 1:
/* ----------
* ABS(var1) > ABS(var2)
* result = +(ABS(var1) - ABS(var2))
* ----------
*/
sub_abs(var1, var2, result);
result->sign = NUMERIC_POS;
break;
case -1:
/* ----------
* ABS(var1) < ABS(var2)
* result = -(ABS(var2) - ABS(var1))
* ----------
*/
sub_abs(var2, var1, result);
result->sign = NUMERIC_NEG;
break;
}
}
}
else
{
if (var2->sign == NUMERIC_POS)
{
/* ----------
* var1 is negative, var2 is positive
* Must compare absolute values
* ----------
*/
switch (cmp_abs(var1, var2))
{
case 0:
/* ----------
* ABS(var1) == ABS(var2)
* result = ZERO
* ----------
*/
zero_var(result);
result->dscale = Max(var1->dscale, var2->dscale);
break;
case 1:
/* ----------
* ABS(var1) > ABS(var2)
* result = -(ABS(var1) - ABS(var2))
* ----------
*/
sub_abs(var1, var2, result);
result->sign = NUMERIC_NEG;
break;
case -1:
/* ----------
* ABS(var1) < ABS(var2)
* result = +(ABS(var2) - ABS(var1))
* ----------
*/
sub_abs(var2, var1, result);
result->sign = NUMERIC_POS;
break;
}
}
else
{
/* ----------
* Both are negative
* result = -(ABS(var1) + ABS(var2))
* ----------
*/
add_abs(var1, var2, result);
result->sign = NUMERIC_NEG;
}
}
}
/*
* sub_var() -
*
* Full version of sub functionality on variable level (handling signs).
* result might point to one of the operands too without danger.
*/
static void
sub_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
/*
* Decide on the signs of the two variables what to do
*/
if (var1->sign == NUMERIC_POS)
{
if (var2->sign == NUMERIC_NEG)
{
/* ----------
* var1 is positive, var2 is negative
* result = +(ABS(var1) + ABS(var2))
* ----------
*/
add_abs(var1, var2, result);
result->sign = NUMERIC_POS;
}
else
{
/* ----------
* Both are positive
* Must compare absolute values
* ----------
*/
switch (cmp_abs(var1, var2))
{
case 0:
/* ----------
* ABS(var1) == ABS(var2)
* result = ZERO
* ----------
*/
zero_var(result);
result->dscale = Max(var1->dscale, var2->dscale);
break;
case 1:
/* ----------
* ABS(var1) > ABS(var2)
* result = +(ABS(var1) - ABS(var2))
* ----------
*/
sub_abs(var1, var2, result);
result->sign = NUMERIC_POS;
break;
case -1:
/* ----------
* ABS(var1) < ABS(var2)
* result = -(ABS(var2) - ABS(var1))
* ----------
*/
sub_abs(var2, var1, result);
result->sign = NUMERIC_NEG;
break;
}
}
}
else
{
if (var2->sign == NUMERIC_NEG)
{
/* ----------
* Both are negative
* Must compare absolute values
* ----------
*/
switch (cmp_abs(var1, var2))
{
case 0:
/* ----------
* ABS(var1) == ABS(var2)
* result = ZERO
* ----------
*/
zero_var(result);
result->dscale = Max(var1->dscale, var2->dscale);
break;
case 1:
/* ----------
* ABS(var1) > ABS(var2)
* result = -(ABS(var1) - ABS(var2))
* ----------
*/
sub_abs(var1, var2, result);
result->sign = NUMERIC_NEG;
break;
case -1:
/* ----------
* ABS(var1) < ABS(var2)
* result = +(ABS(var2) - ABS(var1))
* ----------
*/
sub_abs(var2, var1, result);
result->sign = NUMERIC_POS;
break;
}
}
else
{
/* ----------
* var1 is negative, var2 is positive
* result = -(ABS(var1) + ABS(var2))
* ----------
*/
add_abs(var1, var2, result);
result->sign = NUMERIC_NEG;
}
}
}
/*
* mul_var() -
*
* Multiplication on variable level. Product of var1 * var2 is stored
* in result. Result is rounded to no more than rscale fractional digits.
*/
static void
mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result,
int rscale)
{
int res_ndigits;
int res_sign;
int res_weight;
int maxdigits;
int *dig;
int carry;
int maxdig;
int newdig;
NumericDigit *res_digits;
int i,
ri,
i1,
i2;
/* copy these values into local vars for speed in inner loop */
int var1ndigits = var1->ndigits;
int var2ndigits = var2->ndigits;
NumericDigit *var1digits = var1->digits;
NumericDigit *var2digits = var2->digits;
if (var1ndigits == 0 || var2ndigits == 0)
{
/* one or both inputs is zero; so is result */
zero_var(result);
result->dscale = rscale;
return;
}
/* Determine result sign and (maximum possible) weight */
if (var1->sign == var2->sign)
res_sign = NUMERIC_POS;
else
res_sign = NUMERIC_NEG;
res_weight = var1->weight + var2->weight + 2;
/*
* Determine number of result digits to compute. If the exact result
* would have more than rscale fractional digits, truncate the computation
* with MUL_GUARD_DIGITS guard digits. We do that by pretending that one
* or both inputs have fewer digits than they really do.
*/
res_ndigits = var1ndigits + var2ndigits + 1;
maxdigits = res_weight + 1 + (rscale * DEC_DIGITS) + MUL_GUARD_DIGITS;
if (res_ndigits > maxdigits)
{
if (maxdigits < 3)
{
/* no useful precision at all in the result... */
zero_var(result);
result->dscale = rscale;
return;
}
/* force maxdigits odd so that input ndigits can be equal */
if ((maxdigits & 1) == 0)
maxdigits++;
if (var1ndigits > var2ndigits)
{
var1ndigits -= res_ndigits - maxdigits;
if (var1ndigits < var2ndigits)
var1ndigits = var2ndigits = (var1ndigits + var2ndigits) / 2;
}
else
{
var2ndigits -= res_ndigits - maxdigits;
if (var2ndigits < var1ndigits)
var1ndigits = var2ndigits = (var1ndigits + var2ndigits) / 2;
}
res_ndigits = maxdigits;
Assert(res_ndigits == var1ndigits + var2ndigits + 1);
}
/*
* We do the arithmetic in an array "dig[]" of signed int's. Since
* INT_MAX is noticeably larger than NBASE*NBASE, this gives us headroom
* to avoid normalizing carries immediately.
*
* maxdig tracks the maximum possible value of any dig[] entry; when this
* threatens to exceed INT_MAX, we take the time to propagate carries. To
* avoid overflow in maxdig itself, it actually represents the max
* possible value divided by NBASE-1.
*/
dig = (int *) palloc0(res_ndigits * sizeof(int));
maxdig = 0;
ri = res_ndigits - 1;
for (i1 = var1ndigits - 1; i1 >= 0; ri--, i1--)
{
int var1digit = var1digits[i1];
if (var1digit == 0)
continue;
/* Time to normalize? */
maxdig += var1digit;
if (maxdig > INT_MAX / (NBASE - 1))
{
/* Yes, do it */
carry = 0;
for (i = res_ndigits - 1; i >= 0; i--)
{
newdig = dig[i] + carry;
if (newdig >= NBASE)
{
carry = newdig / NBASE;
newdig -= carry * NBASE;
}
else
carry = 0;
dig[i] = newdig;
}
Assert(carry == 0);
/* Reset maxdig to indicate new worst-case */
maxdig = 1 + var1digit;
}
/* Add appropriate multiple of var2 into the accumulator */
i = ri;
for (i2 = var2ndigits - 1; i2 >= 0; i2--)
dig[i--] += var1digit * var2digits[i2];
}
/*
* Now we do a final carry propagation pass to normalize the result, which
* we combine with storing the result digits into the output. Note that
* this is still done at full precision w/guard digits.
*/
alloc_var(result, res_ndigits);
res_digits = result->digits;
carry = 0;
for (i = res_ndigits - 1; i >= 0; i--)
{
newdig = dig[i] + carry;
if (newdig >= NBASE)
{
carry = newdig / NBASE;
newdig -= carry * NBASE;
}
else
carry = 0;
res_digits[i] = newdig;
}
Assert(carry == 0);
pfree(dig);
/*
* Finally, round the result to the requested precision.
*/
result->weight = res_weight;
result->sign = res_sign;
/* Round to target rscale (and set result->dscale) */
round_var(result, rscale);
/* Strip leading and trailing zeroes */
strip_var(result);
}
/*
* div_var() -
*
* 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;
int res_weight;
int *div;
int qdigit;
int carry;
int maxdiv;
int newdig;
NumericDigit *res_digits;
double fdividend,
fdivisor,
fdivisorinverse,
fquotient;
int qi;
int i;
/* copy these values into local vars for speed in inner loop */
int var1ndigits = var1->ndigits;
int var2ndigits = var2->ndigits;
NumericDigit *var1digits = var1->digits;
NumericDigit *var2digits = var2->digits;
/*
* First of all division by zero check; we must not be handed an
* unnormalized divisor.
*/
if (var2ndigits == 0 || var2digits[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
*/
if (var1->sign == var2->sign)
res_sign = NUMERIC_POS;
else
res_sign = NUMERIC_NEG;
res_weight = var1->weight - var2->weight + 1;
/* The number of accurate result digits we need to produce: */
div_ndigits = res_weight + 1 + (rscale + DEC_DIGITS - 1) / DEC_DIGITS;
/* Add guard digits for roundoff error */
div_ndigits += DIV_GUARD_DIGITS;
if (div_ndigits < DIV_GUARD_DIGITS)
div_ndigits = DIV_GUARD_DIGITS;
/* Must be at least var1ndigits, too, to simplify data-loading loop */
if (div_ndigits < var1ndigits)
div_ndigits = var1ndigits;
/*
* We do the arithmetic in an array "div[]" of signed int's. Since
* INT_MAX is noticeably larger than NBASE*NBASE, this gives us headroom
* to avoid normalizing carries immediately.
*
* We start with div[] containing one zero digit followed by the
* dividend's digits (plus appended zeroes to reach the desired precision
* including guard digits). Each step of the main loop computes an
* (approximate) quotient digit and stores it into div[], removing one
* position of dividend space. A final pass of carry propagation takes
* care of any mistaken quotient digits.
*/
div = (int *) palloc0((div_ndigits + 1) * sizeof(int));
for (i = 0; i < var1ndigits; i++)
div[i + 1] = var1digits[i];
/*
* We estimate each quotient digit using floating-point arithmetic, taking
* the first four digits of the (current) dividend and divisor. This must
* be float to avoid overflow.
*/
fdivisor = (double) var2digits[0];
for (i = 1; i < 4; i++)
{
fdivisor *= NBASE;
if (i < var2ndigits)
fdivisor += (double) var2digits[i];
}
fdivisorinverse = 1.0 / fdivisor;
/*
* maxdiv tracks the maximum possible absolute value of any div[] entry;
* when this threatens to exceed INT_MAX, we take the time to propagate
* carries. To avoid overflow in maxdiv itself, it actually represents
* the max possible abs. value divided by NBASE-1.
*/
maxdiv = 1;
/*
* Outer loop computes next quotient digit, which will go into div[qi]
*/
for (qi = 0; qi < div_ndigits; qi++)
{
/* Approximate the current dividend value */
fdividend = (double) div[qi];
for (i = 1; i < 4; i++)
{
fdividend *= NBASE;
if (qi + i <= div_ndigits)
fdividend += (double) div[qi + i];
}
/* Compute the (approximate) quotient digit */
fquotient = fdividend * fdivisorinverse;
qdigit = (fquotient >= 0.0) ? ((int) fquotient) :
(((int) fquotient) - 1); /* truncate towards -infinity */
if (qdigit != 0)
{
/* Do we need to normalize now? */
maxdiv += Abs(qdigit);
if (maxdiv > INT_MAX / (NBASE - 1))
{
/* Yes, do it */
carry = 0;
for (i = div_ndigits; i > qi; i--)
{
newdig = div[i] + carry;
if (newdig < 0)
{
carry = -((-newdig - 1) / NBASE) - 1;
newdig -= carry * NBASE;
}
else if (newdig >= NBASE)
{
carry = newdig / NBASE;
newdig -= carry * NBASE;
}
else
carry = 0;
div[i] = newdig;
}
newdig = div[qi] + carry;
div[qi] = newdig;
/*
* All the div[] digits except possibly div[qi] are now in the
* range 0..NBASE-1.
*/
maxdiv = Abs(newdig) / (NBASE - 1);
maxdiv = Max(maxdiv, 1);
/*
* Recompute the quotient digit since new info may have
* propagated into the top four dividend digits
*/
fdividend = (double) div[qi];
for (i = 1; i < 4; i++)
{
fdividend *= NBASE;
if (qi + i <= div_ndigits)
fdividend += (double) div[qi + i];
}
/* Compute the (approximate) quotient digit */
fquotient = fdividend * fdivisorinverse;
qdigit = (fquotient >= 0.0) ? ((int) fquotient) :
(((int) fquotient) - 1); /* truncate towards -infinity */
maxdiv += Abs(qdigit);
}
/* Subtract off the appropriate multiple of the divisor */
if (qdigit != 0)
{
int istop = Min(var2ndigits, div_ndigits - qi + 1);
for (i = 0; i < istop; i++)
div[qi + i] -= qdigit * var2digits[i];
}
}
/*
* The dividend digit we are about to replace might still be nonzero.
* Fold it into the next digit position. We don't need to worry about
* overflow here since this should nearly cancel with the subtraction
* of the divisor.
*/
div[qi + 1] += div[qi] * NBASE;
div[qi] = qdigit;
}
/*
* Approximate and store the last quotient digit (div[div_ndigits])
*/
fdividend = (double) div[qi];
for (i = 1; i < 4; i++)
fdividend *= NBASE;
fquotient = fdividend * fdivisorinverse;
qdigit = (fquotient >= 0.0) ? ((int) fquotient) :
(((int) fquotient) - 1); /* truncate towards -infinity */
div[qi] = qdigit;
/*
* Now we do a final carry propagation pass to normalize the result, which
* we combine with storing the result digits into the output. Note that
* this is still done at full precision w/guard digits.
*/
alloc_var(result, div_ndigits + 1);
res_digits = result->digits;
carry = 0;
for (i = div_ndigits; i >= 0; i--)
{
newdig = div[i] + carry;
if (newdig < 0)
{
carry = -((-newdig - 1) / NBASE) - 1;
newdig -= carry * NBASE;
}
else if (newdig >= NBASE)
{
carry = newdig / NBASE;
newdig -= carry * NBASE;
}
else
carry = 0;
res_digits[i] = newdig;
}
Assert(carry == 0);
pfree(div);
/*
* Finally, round the result to the requested precision.
*/
result->weight = res_weight;
result->sign = res_sign;
/* Round 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);
}
/*
* Default scale selection for division
*
* Returns the appropriate result scale for the division result.
*/
static int
select_div_scale(NumericVar *var1, NumericVar *var2)
{
int weight1,
weight2,
qweight,
i;
NumericDigit firstdigit1,
firstdigit2;
int rscale;
/*
* The result scale of a division isn't specified in any SQL standard. For
* PostgreSQL we select a result scale that will give at least
* NUMERIC_MIN_SIG_DIGITS significant digits, so that numeric gives a
* result no less accurate than float8; but use a scale not less than
* either input's display scale.
*/
/* Get the actual (normalized) weight and first digit of each input */
weight1 = 0; /* values to use if var1 is zero */
firstdigit1 = 0;
for (i = 0; i < var1->ndigits; i++)
{
firstdigit1 = var1->digits[i];
if (firstdigit1 != 0)
{
weight1 = var1->weight - i;
break;
}
}
weight2 = 0; /* values to use if var2 is zero */
firstdigit2 = 0;
for (i = 0; i < var2->ndigits; i++)
{
firstdigit2 = var2->digits[i];
if (firstdigit2 != 0)
{
weight2 = var2->weight - i;
break;
}
}
/*
* Estimate weight of quotient. If the two first digits are equal, we
* can't be sure, but assume that var1 is less than var2.
*/
qweight = weight1 - weight2;
if (firstdigit1 <= firstdigit2)
qweight--;
/* Select result scale */
rscale = NUMERIC_MIN_SIG_DIGITS - qweight * DEC_DIGITS;
rscale = Max(rscale, var1->dscale);
rscale = Max(rscale, var2->dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
return rscale;
}
/*
* mod_var() -
*
* Calculate the modulo of two numerics at variable level
*/
static void
mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericVar tmp;
init_var(&tmp);
/* ---------
* We do this using the equation
* mod(x,y) = x - trunc(x/y)*y
* div_var can be persuaded to give us trunc(x/y) directly.
* ----------
*/
div_var(var1, var2, &tmp, 0, false);
mul_var(var2, &tmp, &tmp, var2->dscale);
sub_var(var1, &tmp, result);
free_var(&tmp);
}
/*
* ceil_var() -
*
* Return the smallest integer greater than or equal to the argument
* on variable level
*/
static void
ceil_var(NumericVar *var, NumericVar *result)
{
NumericVar tmp;
init_var(&tmp);
set_var_from_var(var, &tmp);
trunc_var(&tmp, 0);
if (var->sign == NUMERIC_POS && cmp_var(var, &tmp) != 0)
add_var(&tmp, &const_one, &tmp);
set_var_from_var(&tmp, result);
free_var(&tmp);
}
/*
* floor_var() -
*
* Return the largest integer equal to or less than the argument
* on variable level
*/
static void
floor_var(NumericVar *var, NumericVar *result)
{
NumericVar tmp;
init_var(&tmp);
set_var_from_var(var, &tmp);
trunc_var(&tmp, 0);
if (var->sign == NUMERIC_NEG && cmp_var(var, &tmp) != 0)
sub_var(&tmp, &const_one, &tmp);
set_var_from_var(&tmp, result);
free_var(&tmp);
}
/*
* sqrt_var() -
*
* Compute the square root of x using Newton's algorithm
*/
static void
sqrt_var(NumericVar *arg, NumericVar *result, int rscale)
{
NumericVar tmp_arg;
NumericVar tmp_val;
NumericVar last_val;
int local_rscale;
int stat;
local_rscale = rscale + 8;
stat = cmp_var(arg, &const_zero);
if (stat == 0)
{
zero_var(result);
result->dscale = rscale;
return;
}
/*
* SQL2003 defines sqrt() in terms of power, so we need to emit the right
* SQLSTATE error code if the operand is negative.
*/
if (stat < 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_POWER_FUNCTION),
errmsg("cannot take square root of a negative number")));
init_var(&tmp_arg);
init_var(&tmp_val);
init_var(&last_val);
/* Copy arg in case it is the same var as result */
set_var_from_var(arg, &tmp_arg);
/*
* Initialize the result to the first guess
*/
alloc_var(result, 1);
result->digits[0] = tmp_arg.digits[0] / 2;
if (result->digits[0] == 0)
result->digits[0] = 1;
result->weight = tmp_arg.weight / 2;
result->sign = NUMERIC_POS;
set_var_from_var(result, &last_val);
for (;;)
{
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);
if (cmp_var(&last_val, result) == 0)
break;
set_var_from_var(result, &last_val);
}
free_var(&last_val);
free_var(&tmp_val);
free_var(&tmp_arg);
/* Round to requested precision */
round_var(result, rscale);
}
/*
* exp_var() -
*
* Raise e to the power of x
*/
static void
exp_var(NumericVar *arg, NumericVar *result, int rscale)
{
NumericVar x;
int xintval;
bool xneg = FALSE;
int local_rscale;
/*----------
* We separate the integral and fraction parts of x, then compute
* e^x = e^xint * e^xfrac
* where e = exp(1) and e^xfrac = exp(xfrac) are computed by
* exp_var_internal; the limited range of inputs allows that routine
* to do a good job with a simple Taylor series. Raising e^xint is
* done by repeated multiplications in power_var_int.
*----------
*/
init_var(&x);
set_var_from_var(arg, &x);
if (x.sign == NUMERIC_NEG)
{
xneg = TRUE;
x.sign = NUMERIC_POS;
}
/* Extract the integer part, remove it from x */
xintval = 0;
while (x.weight >= 0)
{
xintval *= NBASE;
if (x.ndigits > 0)
{
xintval += x.digits[0];
x.digits++;
x.ndigits--;
}
x.weight--;
/* Guard against overflow */
if (xintval >= NUMERIC_MAX_RESULT_SCALE * 3)
ereport(ERROR,
(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
errmsg("argument for function \"exp\" too big")));
}
/* Select an appropriate scale for internal calculation */
local_rscale = rscale + MUL_GUARD_DIGITS * 2;
/* Compute e^xfrac */
exp_var_internal(&x, result, local_rscale);
/* If there's an integer part, multiply by e^xint */
if (xintval > 0)
{
NumericVar e;
init_var(&e);
exp_var_internal(&const_one, &e, local_rscale);
power_var_int(&e, xintval, &e, local_rscale);
mul_var(&e, result, result, local_rscale);
free_var(&e);
}
/* Compensate for input sign, and round to requested rscale */
if (xneg)
div_var_fast(&const_one, result, result, rscale, true);
else
round_var(result, rscale);
free_var(&x);
}
/*
* exp_var_internal() -
*
* Raise e to the power of x, where 0 <= x <= 1
*
* NB: the result should be good to at least rscale digits, but it has
* *not* been rounded off; the caller must do that if wanted.
*/
static void
exp_var_internal(NumericVar *arg, NumericVar *result, int rscale)
{
NumericVar x;
NumericVar xpow;
NumericVar ifac;
NumericVar elem;
NumericVar ni;
int ndiv2 = 0;
int local_rscale;
init_var(&x);
init_var(&xpow);
init_var(&ifac);
init_var(&elem);
init_var(&ni);
set_var_from_var(arg, &x);
Assert(x.sign == NUMERIC_POS);
local_rscale = rscale + 8;
/* Reduce input into range 0 <= x <= 0.01 */
while (cmp_var(&x, &const_zero_point_01) > 0)
{
ndiv2++;
local_rscale++;
mul_var(&x, &const_zero_point_five, &x, x.dscale + 1);
}
/*
* Use the Taylor series
*
* exp(x) = 1 + x + x^2/2! + x^3/3! + ...
*
* Given the limited range of x, this should converge reasonably quickly.
* We run the series until the terms fall below the local_rscale limit.
*/
add_var(&const_one, &x, result);
set_var_from_var(&x, &xpow);
set_var_from_var(&const_one, &ifac);
set_var_from_var(&const_one, &ni);
for (;;)
{
add_var(&ni, &const_one, &ni);
mul_var(&xpow, &x, &xpow, local_rscale);
mul_var(&ifac, &ni, &ifac, 0);
div_var_fast(&xpow, &ifac, &elem, local_rscale, true);
if (elem.ndigits == 0)
break;
add_var(result, &elem, result);
}
/* Compensate for argument range reduction */
while (ndiv2-- > 0)
mul_var(result, result, result, local_rscale);
free_var(&x);
free_var(&xpow);
free_var(&ifac);
free_var(&elem);
free_var(&ni);
}
/*
* ln_var() -
*
* Compute the natural log of x
*/
static void
ln_var(NumericVar *arg, NumericVar *result, int rscale)
{
NumericVar x;
NumericVar xx;
NumericVar ni;
NumericVar elem;
NumericVar fact;
int local_rscale;
int cmp;
cmp = cmp_var(arg, &const_zero);
if (cmp == 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
errmsg("cannot take logarithm of zero")));
else if (cmp < 0)
ereport(ERROR,
(errcode(ERRCODE_INVALID_ARGUMENT_FOR_LOG),
errmsg("cannot take logarithm of a negative number")));
local_rscale = rscale + 8;
init_var(&x);
init_var(&xx);
init_var(&ni);
init_var(&elem);
init_var(&fact);
set_var_from_var(arg, &x);
set_var_from_var(&const_two, &fact);
/* Reduce input into range 0.9 < x < 1.1 */
while (cmp_var(&x, &const_zero_point_nine) <= 0)
{
local_rscale++;
sqrt_var(&x, &x, local_rscale);
mul_var(&fact, &const_two, &fact, 0);
}
while (cmp_var(&x, &const_one_point_one) >= 0)
{
local_rscale++;
sqrt_var(&x, &x, local_rscale);
mul_var(&fact, &const_two, &fact, 0);
}
/*
* We use the Taylor series for 0.5 * ln((1+z)/(1-z)),
*
* z + z^3/3 + z^5/5 + ...
*
* where z = (x-1)/(x+1) is in the range (approximately) -0.053 .. 0.048
* due to the above range-reduction of x.
*
* The convergence of this is not as fast as one would like, but is
* tolerable given that z is small.
*/
sub_var(&x, &const_one, result);
add_var(&x, &const_one, &elem);
div_var_fast(result, &elem, result, local_rscale, true);
set_var_from_var(result, &xx);
mul_var(result, result, &x, local_rscale);
set_var_from_var(&const_one, &ni);
for (;;)
{
add_var(&ni, &const_two, &ni);
mul_var(&xx, &x, &xx, local_rscale);
div_var_fast(&xx, &ni, &elem, local_rscale, true);
if (elem.ndigits == 0)
break;
add_var(result, &elem, result);
if (elem.weight < (result->weight - local_rscale * 2 / DEC_DIGITS))
break;
}
/* Compensate for argument range reduction, round to requested rscale */
mul_var(result, &fact, result, rscale);
free_var(&x);
free_var(&xx);
free_var(&ni);
free_var(&elem);
free_var(&fact);
}
/*
* log_var() -
*
* Compute the logarithm of num in a given base.
*
* Note: this routine chooses dscale of the result.
*/
static void
log_var(NumericVar *base, NumericVar *num, NumericVar *result)
{
NumericVar ln_base;
NumericVar ln_num;
int dec_digits;
int rscale;
int local_rscale;
init_var(&ln_base);
init_var(&ln_num);
/* Set scale for ln() calculations --- compare numeric_ln() */
/* Approx decimal digits before decimal point */
dec_digits = (num->weight + 1) * DEC_DIGITS;
if (dec_digits > 1)
rscale = NUMERIC_MIN_SIG_DIGITS - (int) log10(dec_digits - 1);
else if (dec_digits < 1)
rscale = NUMERIC_MIN_SIG_DIGITS - (int) log10(1 - dec_digits);
else
rscale = NUMERIC_MIN_SIG_DIGITS;
rscale = Max(rscale, base->dscale);
rscale = Max(rscale, num->dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
local_rscale = rscale + 8;
/* Form natural logarithms */
ln_var(base, &ln_base, local_rscale);
ln_var(num, &ln_num, local_rscale);
ln_base.dscale = rscale;
ln_num.dscale = rscale;
/* Select scale for division result */
rscale = select_div_scale(&ln_num, &ln_base);
div_var_fast(&ln_num, &ln_base, result, rscale, true);
free_var(&ln_num);
free_var(&ln_base);
}
/*
* power_var() -
*
* Raise base to the power of exp
*
* Note: this routine chooses dscale of the result.
*/
static void
power_var(NumericVar *base, NumericVar *exp, NumericVar *result)
{
NumericVar ln_base;
NumericVar ln_num;
int dec_digits;
int rscale;
int local_rscale;
double val;
/* If exp can be represented as an integer, use power_var_int */
if (exp->ndigits == 0 || exp->ndigits <= exp->weight + 1)
{
/* exact integer, but does it fit in int? */
int64 expval64;
if (numericvar_to_int8(exp, &expval64))
{
int expval = (int) expval64;
/* Test for overflow by reverse-conversion. */
if ((int64) expval == expval64)
{
/* Okay, select rscale */
rscale = NUMERIC_MIN_SIG_DIGITS;
rscale = Max(rscale, base->dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
power_var_int(base, expval, result, rscale);
return;
}
}
}
/*
* 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);
/* Set scale for ln() calculation --- need extra accuracy here */
/* Approx decimal digits before decimal point */
dec_digits = (base->weight + 1) * DEC_DIGITS;
if (dec_digits > 1)
rscale = NUMERIC_MIN_SIG_DIGITS * 2 - (int) log10(dec_digits - 1);
else if (dec_digits < 1)
rscale = NUMERIC_MIN_SIG_DIGITS * 2 - (int) log10(1 - dec_digits);
else
rscale = NUMERIC_MIN_SIG_DIGITS * 2;
rscale = Max(rscale, base->dscale * 2);
rscale = Max(rscale, exp->dscale * 2);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE * 2);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE * 2);
local_rscale = rscale + 8;
ln_var(base, &ln_base, local_rscale);
mul_var(&ln_base, exp, &ln_num, local_rscale);
/* Set scale for exp() -- compare numeric_exp() */
/* convert input to float8, ignoring overflow */
val = numericvar_to_double_no_overflow(&ln_num);
/*
* log10(result) = num * log10(e), so this is approximately the weight:
*/
val *= 0.434294481903252;
/* limit to something that won't cause integer overflow */
val = Max(val, -NUMERIC_MAX_RESULT_SCALE);
val = Min(val, NUMERIC_MAX_RESULT_SCALE);
rscale = NUMERIC_MIN_SIG_DIGITS - (int) val;
rscale = Max(rscale, base->dscale);
rscale = Max(rscale, exp->dscale);
rscale = Max(rscale, NUMERIC_MIN_DISPLAY_SCALE);
rscale = Min(rscale, NUMERIC_MAX_DISPLAY_SCALE);
exp_var(&ln_num, result, rscale);
free_var(&ln_num);
free_var(&ln_base);
}
/*
* power_var_int() -
*
* Raise base to the power of exp, where exp is an integer.
*/
static void
power_var_int(NumericVar *base, int exp, NumericVar *result, int rscale)
{
bool neg;
NumericVar base_prod;
int local_rscale;
switch (exp)
{
case 0:
/*
* 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;
case 1:
set_var_from_var(base, result);
round_var(result, rscale);
return;
case -1:
div_var(&const_one, base, result, rscale, true);
return;
case 2:
mul_var(base, base, result, rscale);
return;
default:
break;
}
/*
* The general case repeatedly multiplies base according to the bit
* pattern of exp. We do the multiplications with some extra precision.
*/
neg = (exp < 0);
exp = Abs(exp);
local_rscale = rscale + MUL_GUARD_DIGITS * 2;
init_var(&base_prod);
set_var_from_var(base, &base_prod);
if (exp & 1)
set_var_from_var(base, result);
else
set_var_from_var(&const_one, result);
while ((exp >>= 1) > 0)
{
mul_var(&base_prod, &base_prod, &base_prod, local_rscale);
if (exp & 1)
mul_var(&base_prod, result, result, local_rscale);
}
free_var(&base_prod);
/* Compensate for input sign, and round to requested rscale */
if (neg)
div_var_fast(&const_one, result, result, rscale, true);
else
round_var(result, rscale);
}
/* ----------------------------------------------------------------------
*
* Following are the lowest level functions that operate unsigned
* on the variable level
*
* ----------------------------------------------------------------------
*/
/* ----------
* cmp_abs() -
*
* Compare the absolute values of var1 and var2
* Returns: -1 for ABS(var1) < ABS(var2)
* 0 for ABS(var1) == ABS(var2)
* 1 for ABS(var1) > ABS(var2)
* ----------
*/
static int
cmp_abs(NumericVar *var1, NumericVar *var2)
{
return cmp_abs_common(var1->digits, var1->ndigits, var1->weight,
var2->digits, var2->ndigits, var2->weight);
}
/* ----------
* cmp_abs_common() -
*
* Main routine of cmp_abs(). This function can be used by both
* NumericVar and Numeric.
* ----------
*/
static int
cmp_abs_common(const NumericDigit *var1digits, int var1ndigits, int var1weight,
const NumericDigit *var2digits, int var2ndigits, int var2weight)
{
int i1 = 0;
int i2 = 0;
/* Check any digits before the first common digit */
while (var1weight > var2weight && i1 < var1ndigits)
{
if (var1digits[i1++] != 0)
return 1;
var1weight--;
}
while (var2weight > var1weight && i2 < var2ndigits)
{
if (var2digits[i2++] != 0)
return -1;
var2weight--;
}
/* At this point, either w1 == w2 or we've run out of digits */
if (var1weight == var2weight)
{
while (i1 < var1ndigits && i2 < var2ndigits)
{
int stat = var1digits[i1++] - var2digits[i2++];
if (stat)
{
if (stat > 0)
return 1;
return -1;
}
}
}
/*
* At this point, we've run out of digits on one side or the other; so any
* remaining nonzero digits imply that side is larger
*/
while (i1 < var1ndigits)
{
if (var1digits[i1++] != 0)
return 1;
}
while (i2 < var2ndigits)
{
if (var2digits[i2++] != 0)
return -1;
}
return 0;
}
/*
* add_abs() -
*
* Add the absolute values of two variables into result.
* result might point to one of the operands without danger.
*/
static void
add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericDigit *res_buf;
NumericDigit *res_digits;
int res_ndigits;
int res_weight;
int res_rscale,
rscale1,
rscale2;
int res_dscale;
int i,
i1,
i2;
int carry = 0;
/* copy these values into local vars for speed in inner loop */
int var1ndigits = var1->ndigits;
int var2ndigits = var2->ndigits;
NumericDigit *var1digits = var1->digits;
NumericDigit *var2digits = var2->digits;
res_weight = Max(var1->weight, var2->weight) + 1;
res_dscale = Max(var1->dscale, var2->dscale);
/* Note: here we are figuring rscale in base-NBASE digits */
rscale1 = var1->ndigits - var1->weight - 1;
rscale2 = var2->ndigits - var2->weight - 1;
res_rscale = Max(rscale1, rscale2);
res_ndigits = res_rscale + res_weight + 1;
if (res_ndigits <= 0)
res_ndigits = 1;
res_buf = digitbuf_alloc(res_ndigits + 1);
res_buf[0] = 0; /* spare digit for later rounding */
res_digits = res_buf + 1;
i1 = res_rscale + var1->weight + 1;
i2 = res_rscale + var2->weight + 1;
for (i = res_ndigits - 1; i >= 0; i--)
{
i1--;
i2--;
if (i1 >= 0 && i1 < var1ndigits)
carry += var1digits[i1];
if (i2 >= 0 && i2 < var2ndigits)
carry += var2digits[i2];
if (carry >= NBASE)
{
res_digits[i] = carry - NBASE;
carry = 1;
}
else
{
res_digits[i] = carry;
carry = 0;
}
}
Assert(carry == 0); /* else we failed to allow for carry out */
digitbuf_free(result->buf);
result->ndigits = res_ndigits;
result->buf = res_buf;
result->digits = res_digits;
result->weight = res_weight;
result->dscale = res_dscale;
/* Remove leading/trailing zeroes */
strip_var(result);
}
/*
* sub_abs()
*
* Subtract the absolute value of var2 from the absolute value of var1
* and store in result. result might point to one of the operands
* without danger.
*
* ABS(var1) MUST BE GREATER OR EQUAL ABS(var2) !!!
*/
static void
sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericDigit *res_buf;
NumericDigit *res_digits;
int res_ndigits;
int res_weight;
int res_rscale,
rscale1,
rscale2;
int res_dscale;
int i,
i1,
i2;
int borrow = 0;
/* copy these values into local vars for speed in inner loop */
int var1ndigits = var1->ndigits;
int var2ndigits = var2->ndigits;
NumericDigit *var1digits = var1->digits;
NumericDigit *var2digits = var2->digits;
res_weight = var1->weight;
res_dscale = Max(var1->dscale, var2->dscale);
/* Note: here we are figuring rscale in base-NBASE digits */
rscale1 = var1->ndigits - var1->weight - 1;
rscale2 = var2->ndigits - var2->weight - 1;
res_rscale = Max(rscale1, rscale2);
res_ndigits = res_rscale + res_weight + 1;
if (res_ndigits <= 0)
res_ndigits = 1;
res_buf = digitbuf_alloc(res_ndigits + 1);
res_buf[0] = 0; /* spare digit for later rounding */
res_digits = res_buf + 1;
i1 = res_rscale + var1->weight + 1;
i2 = res_rscale + var2->weight + 1;
for (i = res_ndigits - 1; i >= 0; i--)
{
i1--;
i2--;
if (i1 >= 0 && i1 < var1ndigits)
borrow += var1digits[i1];
if (i2 >= 0 && i2 < var2ndigits)
borrow -= var2digits[i2];
if (borrow < 0)
{
res_digits[i] = borrow + NBASE;
borrow = -1;
}
else
{
res_digits[i] = borrow;
borrow = 0;
}
}
Assert(borrow == 0); /* else caller gave us var1 < var2 */
digitbuf_free(result->buf);
result->ndigits = res_ndigits;
result->buf = res_buf;
result->digits = res_digits;
result->weight = res_weight;
result->dscale = res_dscale;
/* Remove leading/trailing zeroes */
strip_var(result);
}
/*
* round_var
*
* Round the value of a variable to no more than rscale decimal digits
* after the decimal point. NOTE: we allow rscale < 0 here, implying
* rounding before the decimal point.
*/
static void
round_var(NumericVar *var, int rscale)
{
NumericDigit *digits = var->digits;
int di;
int ndigits;
int carry;
var->dscale = rscale;
/* decimal digits wanted */
di = (var->weight + 1) * DEC_DIGITS + rscale;
/*
* If di = 0, the value loses all digits, but could round up to 1 if its
* first extra digit is >= 5. If di < 0 the result must be 0.
*/
if (di < 0)
{
var->ndigits = 0;
var->weight = 0;
var->sign = NUMERIC_POS;
}
else
{
/* NBASE digits wanted */
ndigits = (di + DEC_DIGITS - 1) / DEC_DIGITS;
/* 0, or number of decimal digits to keep in last NBASE digit */
di %= DEC_DIGITS;
if (ndigits < var->ndigits ||
(ndigits == var->ndigits && di > 0))
{
var->ndigits = ndigits;
#if DEC_DIGITS == 1
/* di must be zero */
carry = (digits[ndigits] >= HALF_NBASE) ? 1 : 0;
#else
if (di == 0)
carry = (digits[ndigits] >= HALF_NBASE) ? 1 : 0;
else
{
/* Must round within last NBASE digit */
int extra,
pow10;
#if DEC_DIGITS == 4
pow10 = round_powers[di];
#elif DEC_DIGITS == 2
pow10 = 10;
#else
#error unsupported NBASE
#endif
extra = digits[--ndigits] % pow10;
digits[ndigits] -= extra;
carry = 0;
if (extra >= pow10 / 2)
{
pow10 += digits[ndigits];
if (pow10 >= NBASE)
{
pow10 -= NBASE;
carry = 1;
}
digits[ndigits] = pow10;
}
}
#endif
/* Propagate carry if needed */
while (carry)
{
carry += digits[--ndigits];
if (carry >= NBASE)
{
digits[ndigits] = carry - NBASE;
carry = 1;
}
else
{
digits[ndigits] = carry;
carry = 0;
}
}
if (ndigits < 0)
{
Assert(ndigits == -1); /* better not have added > 1 digit */
Assert(var->digits > var->buf);
var->digits--;
var->ndigits++;
var->weight++;
}
}
}
}
/*
* trunc_var
*
* 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
trunc_var(NumericVar *var, int rscale)
{
int di;
int ndigits;
var->dscale = rscale;
/* decimal digits wanted */
di = (var->weight + 1) * DEC_DIGITS + rscale;
/*
* If di <= 0, the value loses all digits.
*/
if (di <= 0)
{
var->ndigits = 0;
var->weight = 0;
var->sign = NUMERIC_POS;
}
else
{
/* NBASE digits wanted */
ndigits = (di + DEC_DIGITS - 1) / DEC_DIGITS;
if (ndigits <= var->ndigits)
{
var->ndigits = ndigits;
#if DEC_DIGITS == 1
/* no within-digit stuff to worry about */
#else
/* 0, or number of decimal digits to keep in last NBASE digit */
di %= DEC_DIGITS;
if (di > 0)
{
/* Must truncate within last NBASE digit */
NumericDigit *digits = var->digits;
int extra,
pow10;
#if DEC_DIGITS == 4
pow10 = round_powers[di];
#elif DEC_DIGITS == 2
pow10 = 10;
#else
#error unsupported NBASE
#endif
extra = digits[--ndigits] % pow10;
digits[ndigits] -= extra;
}
#endif
}
}
}
/*
* strip_var
*
* Strip any leading and trailing zeroes from a numeric variable
*/
static void
strip_var(NumericVar *var)
{
NumericDigit *digits = var->digits;
int ndigits = var->ndigits;
/* Strip leading zeroes */
while (ndigits > 0 && *digits == 0)
{
digits++;
var->weight--;
ndigits--;
}
/* Strip trailing zeroes */
while (ndigits > 0 && digits[ndigits - 1] == 0)
ndigits--;
/* If it's zero, normalize the sign and weight */
if (ndigits == 0)
{
var->sign = NUMERIC_POS;
var->weight = 0;
}
var->digits = digits;
var->ndigits = ndigits;
}
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