/* ----------
* numeric.c
*
* An exact numeric data type for the Postgres database system
*
* 1998 Jan Wieck
*
* $Header: /cvsroot/pgsql/src/backend/utils/adt/numeric.c,v 1.36 2000/12/07 02:47:35 tgl Exp $
*
* ----------
*/
#include "postgres.h"
#include <ctype.h>
#include <float.h>
#include <math.h>
#include <errno.h>
#include <sys/types.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 definitions
* ----------
*/
#ifndef MIN
#define MIN(a,b) (((a)<(b)) ? (a) : (b))
#endif
#ifndef MAX
#define MAX(a,b) (((a)>(b)) ? (a) : (b))
#endif
#ifndef NAN
#define NAN (0.0/0.0)
#endif
/* ----------
* Local data types
*
* Note: the first digit of a NumericVar's value is assumed to be multiplied
* by 10 ** weight. Another way to say it is that there are weight+1 digits
* before the decimal point. It is possible to have weight < 0.
*
* The value represented by a NumericVar is determined by the sign, weight,
* ndigits, and digits[] array. The rscale and dscale are carried along,
* but they are just auxiliary information until rounding is done before
* final storage or display. (Scales are the number of digits wanted
* *after* the decimal point. Scales are always >= 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 byte or two
* (preset to zeroes) between buf and digits, so that there is room to store
* a carry out of the top digit without special pushups. We just need to
* decrement digits (and increment weight) to make room for the carry digit.
*
* 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.
*
* 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 unsigned char NumericDigit;
typedef struct NumericVar
{
int ndigits; /* number of digits in digits[] - can be
* 0! */
int weight; /* weight of first digit */
int rscale; /* result scale */
int dscale; /* display scale */
int sign; /* NUMERIC_POS, NUMERIC_NEG, or
* NUMERIC_NAN */
NumericDigit *buf; /* start of palloc'd space for digits[] */
NumericDigit *digits; /* decimal digits */
} NumericVar;
/* ----------
* Local data
* ----------
*/
static int global_rscale = NUMERIC_MIN_RESULT_SCALE;
/* ----------
* Some preinitialized variables we need often
* ----------
*/
static NumericDigit const_zero_data[1] = {0};
static NumericVar const_zero =
{0, 0, 0, 0, NUMERIC_POS, NULL, const_zero_data};
static NumericDigit const_one_data[1] = {1};
static NumericVar const_one =
{1, 0, 0, 0, NUMERIC_POS, NULL, const_one_data};
static NumericDigit const_two_data[1] = {2};
static NumericVar const_two =
{1, 0, 0, 0, NUMERIC_POS, NULL, const_two_data};
static NumericVar const_nan =
{0, 0, 0, 0, NUMERIC_NAN, NULL, NULL};
/* ----------
* Local functions
* ----------
*/
#ifdef NUMERIC_DEBUG
static void dump_numeric(char *str, Numeric num);
static void dump_var(char *str, NumericVar *var);
#else
#define dump_numeric(s,n)
#define dump_var(s,v)
#endif
#define digitbuf_alloc(size) ((NumericDigit *) palloc(size))
#define digitbuf_free(buf) \
do { \
if ((buf) != NULL) \
pfree(buf); \
} while (0)
#define init_var(v) memset(v,0,sizeof(NumericVar))
static void alloc_var(NumericVar *var, int ndigits);
static void free_var(NumericVar *var);
static void zero_var(NumericVar *var);
static void set_var_from_str(char *str, NumericVar *dest);
static void set_var_from_num(Numeric value, NumericVar *dest);
static void set_var_from_var(NumericVar *value, NumericVar *dest);
static char *get_str_from_var(NumericVar *var, int dscale);
static Numeric make_result(NumericVar *var);
static void apply_typmod(NumericVar *var, int32 typmod);
static int cmp_var(NumericVar *var1, NumericVar *var2);
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);
static void div_var(NumericVar *var1, NumericVar *var2, NumericVar *result);
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);
static void exp_var(NumericVar *arg, NumericVar *result);
static void ln_var(NumericVar *arg, NumericVar *result);
static void log_var(NumericVar *base, NumericVar *num, NumericVar *result);
static void power_var(NumericVar *base, NumericVar *exp, NumericVar *result);
static int cmp_abs(NumericVar *var1, NumericVar *var2);
static void add_abs(NumericVar *var1, NumericVar *var2, NumericVar *result);
static void sub_abs(NumericVar *var1, NumericVar *var2, NumericVar *result);
/* ----------------------------------------------------------------------
*
* 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);
NumericVar value;
Numeric res;
/* ----------
* Check for NaN
* ----------
*/
if (strcmp(str, "NaN") == 0)
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Use set_var_from_str() to parse the input string
* and return it in the packed DB storage format
* ----------
*/
init_var(&value);
set_var_from_str(str, &value);
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.
*
* Even if we didn't need to change format, we'd still need to copy
* the value to have a modifiable copy for rounding. set_var_from_num()
* also guarantees there is extra digit space in case we produce a
* carry out from rounding.
* ----------
*/
init_var(&x);
set_var_from_num(num, &x);
str = get_str_from_var(&x, x.dscale);
free_var(&x);
PG_RETURN_CSTRING(str);
}
/* ----------
* numeric() -
*
* This is a special function called by the Postgres database system
* before a value is stored in a tuples 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 maxweight;
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(num->varlen);
memcpy(new, num, num->varlen);
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;
maxweight = precision - scale;
/* ----------
* If the number is in bounds and due to the present result scale
* no rounding could be necessary, just make a copy of the input
* and modify its scale fields.
* ----------
*/
if (num->n_weight < maxweight && scale >= num->n_rscale)
{
new = (Numeric) palloc(num->varlen);
memcpy(new, num, num->varlen);
new->n_rscale = scale;
new->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);
}
/* ----------------------------------------------------------------------
*
* 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(num->varlen);
memcpy(res, num, num->varlen);
res->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(num->varlen);
memcpy(res, num, num->varlen);
/* ----------
* 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 (num->varlen != NUMERIC_HDRSZ)
{
/* Else, flip the sign */
if (NUMERIC_SIGN(num) == NUMERIC_POS)
res->n_sign_dscale = NUMERIC_NEG | NUMERIC_DSCALE(num);
else
res->n_sign_dscale = NUMERIC_POS | NUMERIC_DSCALE(num);
}
PG_RETURN_NUMERIC(res);
}
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 (num->varlen == NUMERIC_HDRSZ)
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;
int i;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Limit the scale value to avoid possible overflow in calculations below.
* ----------
*/
scale = MIN(NUMERIC_MAX_RESULT_SCALE,
MAX(-NUMERIC_MAX_RESULT_SCALE, scale));
/* ----------
* Unpack the argument and round it at the proper digit position
* ----------
*/
init_var(&arg);
set_var_from_num(num, &arg);
i = arg.weight + scale + 1;
if (i < arg.ndigits)
{
/*
* If i = 0, the value loses all digits, but could round up if its
* first digit is more than 4. If i < 0 the result must be 0.
*/
if (i < 0)
arg.ndigits = 0;
else
{
int carry = (arg.digits[i] > 4) ? 1 : 0;
arg.ndigits = i;
while (carry)
{
carry += arg.digits[--i];
arg.digits[i] = carry % 10;
carry /= 10;
}
if (i < 0)
{
Assert(i == -1);/* better not have added more than 1 digit */
Assert(arg.digits > arg.buf);
arg.digits--;
arg.ndigits++;
arg.weight++;
}
}
}
/* ----------
* Set result's scale to something reasonable.
* ----------
*/
scale = MIN(NUMERIC_MAX_DISPLAY_SCALE, MAX(0, scale));
arg.rscale = scale;
arg.dscale = scale;
/* ----------
* 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 below.
* ----------
*/
scale = MIN(NUMERIC_MAX_RESULT_SCALE,
MAX(-NUMERIC_MAX_RESULT_SCALE, scale));
/* ----------
* Unpack the argument and truncate it at the proper digit position
* ----------
*/
init_var(&arg);
set_var_from_num(num, &arg);
arg.ndigits = MIN(arg.ndigits, MAX(0, arg.weight + scale + 1));
/* ----------
* Set result's scale to something reasonable.
* ----------
*/
scale = MIN(NUMERIC_MAX_DISPLAY_SCALE, MAX(0, scale));
arg.rscale = scale;
arg.dscale = scale;
/* ----------
* 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(&result);
set_var_from_num(num, &result);
ceil_var(&result, &result);
result.dscale = 0;
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(&result);
set_var_from_num(num, &result);
floor_var(&result, &result);
result.dscale = 0;
res = make_result(&result);
free_var(&result);
PG_RETURN_NUMERIC(res);
}
/* ----------------------------------------------------------------------
*
* 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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = 0;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2);
free_var(&arg1);
free_var(&arg2);
}
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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = false;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2) == 0;
free_var(&arg1);
free_var(&arg2);
}
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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = false;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2) != 0;
free_var(&arg1);
free_var(&arg2);
}
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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = false;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2) > 0;
free_var(&arg1);
free_var(&arg2);
}
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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = false;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2) >= 0;
free_var(&arg1);
free_var(&arg2);
}
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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = false;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2) < 0;
free_var(&arg1);
free_var(&arg2);
}
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;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
result = false;
else
{
NumericVar arg1;
NumericVar arg2;
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
result = cmp_var(&arg1, &arg2) <= 0;
free_var(&arg1);
free_var(&arg2);
}
PG_FREE_IF_COPY(num1, 0);
PG_FREE_IF_COPY(num2, 1);
PG_RETURN_BOOL(result);
}
/* ----------------------------------------------------------------------
*
* Arithmetic base 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. The internals of add_var() will automatically
* set the correct result and display scales in the result.
* ----------
*/
init_var(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
add_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&arg1);
free_var(&arg2);
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 two arguments, let sub_var() compute the
* result and return it.
* ----------
*/
init_var(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
sub_var(&arg1, &arg2, &result);
res = make_result(&result);
free_var(&arg1);
free_var(&arg2);
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 arguments, let mul_var() compute the result
* and return it. Unlike add_var() and sub_var(), mul_var()
* will round the result to the scale stored in global_rscale.
* In the case of numeric_mul(), which is invoked for the *
* operator on numerics, we set it to the exact representation
* for the product (rscale = sum(rscale of arg1, rscale of arg2)
* and the same for the dscale).
* ----------
*/
init_var(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
global_rscale = arg1.rscale + arg2.rscale;
mul_var(&arg1, &arg2, &result);
result.dscale = arg1.dscale + arg2.dscale;
res = make_result(&result);
free_var(&arg1);
free_var(&arg2);
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 res_dscale;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Unpack the arguments
* ----------
*/
init_var(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
/* ----------
* The result scale of a division isn't specified in any
* SQL standard. For Postgres it is the following (where
* SR, DR are the result- and display-scales of the returned
* value, S1, D1, S2 and D2 are the scales of the two arguments,
* The minimum and maximum scales are compile time options from
* numeric.h):
*
* DR = MIN(MAX(D1 + D2, MIN_DISPLAY_SCALE), MAX_DISPLAY_SCALE)
* SR = MIN(MAX(MAX(S1 + S2, MIN_RESULT_SCALE), DR + 4), MAX_RESULT_SCALE)
*
* By default, any result is computed with a minimum of 34 digits
* after the decimal point or at least with 4 digits more than
* displayed.
* ----------
*/
res_dscale = MAX(arg1.dscale + arg2.dscale, NUMERIC_MIN_DISPLAY_SCALE);
res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
global_rscale = MAX(arg1.rscale + arg2.rscale,
NUMERIC_MIN_RESULT_SCALE);
global_rscale = MAX(global_rscale, res_dscale + 4);
global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
/* ----------
* Do the divide, set the display scale and return the result
* ----------
*/
div_var(&arg1, &arg2, &result);
result.dscale = res_dscale;
res = make_result(&result);
free_var(&arg1);
free_var(&arg2);
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(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
mod_var(&arg1, &arg2, &result);
result.dscale = result.rscale;
res = make_result(&result);
free_var(&result);
free_var(&arg2);
free_var(&arg1);
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(&arg);
set_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);
NumericVar arg1;
NumericVar arg2;
Numeric res;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Unpack the values, and decide which is the smaller one
* ----------
*/
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
if (cmp_var(&arg1, &arg2) <= 0)
res = make_result(&arg1);
else
res = make_result(&arg2);
free_var(&arg1);
free_var(&arg2);
PG_RETURN_NUMERIC(res);
}
/* ----------
* 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);
NumericVar arg1;
NumericVar arg2;
Numeric res;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Unpack the values, and decide which is the larger one
* ----------
*/
init_var(&arg1);
init_var(&arg2);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
if (cmp_var(&arg1, &arg2) >= 0)
res = make_result(&arg1);
else
res = make_result(&arg2);
free_var(&arg1);
free_var(&arg2);
PG_RETURN_NUMERIC(res);
}
/* ----------------------------------------------------------------------
*
* Complex math functions
*
* ----------------------------------------------------------------------
*/
/* ----------
* 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 res_dscale;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Unpack the argument, determine the scales like for divide,
* let sqrt_var() do the calculation and return the result.
* ----------
*/
init_var(&arg);
init_var(&result);
set_var_from_num(num, &arg);
res_dscale = MAX(arg.dscale, NUMERIC_MIN_DISPLAY_SCALE);
res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
global_rscale = MAX(arg.rscale, NUMERIC_MIN_RESULT_SCALE);
global_rscale = MAX(global_rscale, res_dscale + 4);
global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
sqrt_var(&arg, &result);
result.dscale = res_dscale;
res = make_result(&result);
free_var(&result);
free_var(&arg);
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 res_dscale;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Same procedure like for sqrt().
* ----------
*/
init_var(&arg);
init_var(&result);
set_var_from_num(num, &arg);
res_dscale = MAX(arg.dscale, NUMERIC_MIN_DISPLAY_SCALE);
res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
global_rscale = MAX(arg.rscale, NUMERIC_MIN_RESULT_SCALE);
global_rscale = MAX(global_rscale, res_dscale + 4);
global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
exp_var(&arg, &result);
result.dscale = res_dscale;
res = make_result(&result);
free_var(&result);
free_var(&arg);
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 res_dscale;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Same procedure like for sqrt()
* ----------
*/
init_var(&arg);
init_var(&result);
set_var_from_num(num, &arg);
res_dscale = MAX(arg.dscale, NUMERIC_MIN_DISPLAY_SCALE);
res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
global_rscale = MAX(arg.rscale, NUMERIC_MIN_RESULT_SCALE);
global_rscale = MAX(global_rscale, res_dscale + 4);
global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
ln_var(&arg, &result);
result.dscale = res_dscale;
res = make_result(&result);
free_var(&result);
free_var(&arg);
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;
int res_dscale;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Initialize things and calculate scales
* ----------
*/
init_var(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
res_dscale = MAX(arg1.dscale + arg2.dscale, NUMERIC_MIN_DISPLAY_SCALE);
res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
global_rscale = MAX(arg1.rscale + arg2.rscale, NUMERIC_MIN_RESULT_SCALE);
global_rscale = MAX(global_rscale, res_dscale + 4);
global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
/* ----------
* Call log_var() to compute and return the result
* ----------
*/
log_var(&arg1, &arg2, &result);
result.dscale = res_dscale;
res = make_result(&result);
free_var(&result);
free_var(&arg2);
free_var(&arg1);
PG_RETURN_NUMERIC(res);
}
/* ----------
* numeric_power() -
*
* Raise m 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 result;
int res_dscale;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* ----------
* Initialize things and calculate scales
* ----------
*/
init_var(&arg1);
init_var(&arg2);
init_var(&result);
set_var_from_num(num1, &arg1);
set_var_from_num(num2, &arg2);
res_dscale = MAX(arg1.dscale + arg2.dscale, NUMERIC_MIN_DISPLAY_SCALE);
res_dscale = MIN(res_dscale, NUMERIC_MAX_DISPLAY_SCALE);
global_rscale = MAX(arg1.rscale + arg2.rscale, NUMERIC_MIN_RESULT_SCALE);
global_rscale = MAX(global_rscale, res_dscale + 4);
global_rscale = MIN(global_rscale, NUMERIC_MAX_RESULT_SCALE);
/* ----------
* Call log_var() to compute and return the result
* ----------
*/
power_var(&arg1, &arg2, &result);
result.dscale = res_dscale;
res = make_result(&result);
free_var(&result);
free_var(&arg2);
free_var(&arg1);
PG_RETURN_NUMERIC(res);
}
/* ----------------------------------------------------------------------
*
* Type conversion functions
*
* ----------------------------------------------------------------------
*/
Datum
int4_numeric(PG_FUNCTION_ARGS)
{
int32 val = PG_GETARG_INT32(0);
Numeric res;
NumericVar result;
char *tmp;
init_var(&result);
tmp = DatumGetCString(DirectFunctionCall1(int4out,
Int32GetDatum(val)));
set_var_from_str(tmp, &result);
res = make_result(&result);
free_var(&result);
pfree(tmp);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_int4(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
char *str;
Datum result;
/* XXX would it be better to return NULL? */
if (NUMERIC_IS_NAN(num))
elog(ERROR, "Cannot convert NaN to int4");
/* ----------
* Get the number in the variable format so we can round to integer.
* ----------
*/
init_var(&x);
set_var_from_num(num, &x);
str = get_str_from_var(&x, 0); /* dscale = 0 produces rounding */
free_var(&x);
result = DirectFunctionCall1(int4in, CStringGetDatum(str));
pfree(str);
PG_RETURN_DATUM(result);
}
Datum
int8_numeric(PG_FUNCTION_ARGS)
{
Datum val = PG_GETARG_DATUM(0);
Numeric res;
NumericVar result;
char *tmp;
init_var(&result);
tmp = DatumGetCString(DirectFunctionCall1(int8out, val));
set_var_from_str(tmp, &result);
res = make_result(&result);
free_var(&result);
pfree(tmp);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_int8(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
char *str;
Datum result;
/* XXX would it be better to return NULL? */
if (NUMERIC_IS_NAN(num))
elog(ERROR, "Cannot convert NaN to int8");
/* ----------
* Get the number in the variable format so we can round to integer.
* ----------
*/
init_var(&x);
set_var_from_num(num, &x);
str = get_str_from_var(&x, 0); /* dscale = 0 produces rounding */
free_var(&x);
result = DirectFunctionCall1(int8in, CStringGetDatum(str));
pfree(str);
PG_RETURN_DATUM(result);
}
Datum
int2_numeric(PG_FUNCTION_ARGS)
{
int16 val = PG_GETARG_INT16(0);
Numeric res;
NumericVar result;
char *tmp;
init_var(&result);
tmp = DatumGetCString(DirectFunctionCall1(int2out,
Int16GetDatum(val)));
set_var_from_str(tmp, &result);
res = make_result(&result);
free_var(&result);
pfree(tmp);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_int2(PG_FUNCTION_ARGS)
{
Numeric num = PG_GETARG_NUMERIC(0);
NumericVar x;
char *str;
Datum result;
if (NUMERIC_IS_NAN(num))
elog(ERROR, "Cannot convert NaN to int2");
/* ----------
* Get the number in the variable format so we can round to integer.
* ----------
*/
init_var(&x);
set_var_from_num(num, &x);
str = get_str_from_var(&x, 0); /* dscale = 0 produces rounding */
free_var(&x);
result = DirectFunctionCall1(int2in, CStringGetDatum(str));
pfree(str);
return 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);
set_var_from_str(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(NAN);
tmp = DatumGetCString(DirectFunctionCall1(numeric_out,
NumericGetDatum(num)));
result = DirectFunctionCall1(float8in, CStringGetDatum(tmp));
pfree(tmp);
PG_RETURN_DATUM(result);
}
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);
set_var_from_str(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((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 a 3-element array
* of Numeric, holding the values N, sum(X), sum(X*X) in that order.
*
* We represent N as a numeric mainly to avoid having to build a special
* datatype; it's unlikely it'd overflow an int4, but ...
*
* ----------------------------------------------------------------------
*/
static ArrayType *
do_numeric_accum(ArrayType *transarray, Numeric newval)
{
Datum *transdatums;
int ndatums;
Datum N,
sumX,
sumX2;
ArrayType *result;
/* We assume the input is array of numeric */
deconstruct_array(transarray,
false, -1, 'i',
&transdatums, &ndatums);
if (ndatums != 3)
elog(ERROR, "do_numeric_accum: expected 3-element numeric array");
N = transdatums[0];
sumX = transdatums[1];
sumX2 = transdatums[2];
N = DirectFunctionCall1(numeric_inc, N);
sumX = DirectFunctionCall2(numeric_add, sumX,
NumericGetDatum(newval));
sumX2 = DirectFunctionCall2(numeric_add, sumX2,
DirectFunctionCall2(numeric_mul,
NumericGetDatum(newval),
NumericGetDatum(newval)));
transdatums[0] = N;
transdatums[1] = sumX;
transdatums[2] = sumX2;
result = construct_array(transdatums, 3,
false, -1, 'i');
return result;
}
Datum
numeric_accum(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Numeric newval = PG_GETARG_NUMERIC(1);
PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
}
/*
* Integer data types all use Numeric accumulators to share code and
* avoid risk of overflow.
*/
Datum
int2_accum(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Datum newval2 = PG_GETARG_DATUM(1);
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int2_numeric, newval2));
PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
}
Datum
int4_accum(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Datum newval4 = PG_GETARG_DATUM(1);
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int4_numeric, newval4));
PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
}
Datum
int8_accum(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Datum newval8 = PG_GETARG_DATUM(1);
Numeric newval;
newval = DatumGetNumeric(DirectFunctionCall1(int8_numeric, newval8));
PG_RETURN_ARRAYTYPE_P(do_numeric_accum(transarray, newval));
}
Datum
numeric_avg(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Datum *transdatums;
int ndatums;
Numeric N,
sumX;
/* We assume the input is array of numeric */
deconstruct_array(transarray,
false, -1, 'i',
&transdatums, &ndatums);
if (ndatums != 3)
elog(ERROR, "numeric_avg: expected 3-element numeric array");
N = DatumGetNumeric(transdatums[0]);
sumX = DatumGetNumeric(transdatums[1]);
/* ignore sumX2 */
/* SQL92 defines AVG of no values to be NULL */
/* N is zero iff no digits (cf. numeric_uminus) */
if (N->varlen == NUMERIC_HDRSZ)
PG_RETURN_NULL();
PG_RETURN_DATUM(DirectFunctionCall2(numeric_div,
NumericGetDatum(sumX),
NumericGetDatum(N)));
}
Datum
numeric_variance(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Datum *transdatums;
int ndatums;
Numeric N,
sumX,
sumX2,
res;
NumericVar vN,
vsumX,
vsumX2,
vNminus1;
/* We assume the input is array of numeric */
deconstruct_array(transarray,
false, -1, 'i',
&transdatums, &ndatums);
if (ndatums != 3)
elog(ERROR, "numeric_variance: expected 3-element numeric array");
N = DatumGetNumeric(transdatums[0]);
sumX = DatumGetNumeric(transdatums[1]);
sumX2 = DatumGetNumeric(transdatums[2]);
if (NUMERIC_IS_NAN(N) || NUMERIC_IS_NAN(sumX) || NUMERIC_IS_NAN(sumX2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* We define VARIANCE of no values to be NULL, of 1 value to be 0 */
/* N is zero iff no digits (cf. numeric_uminus) */
if (N->varlen == NUMERIC_HDRSZ)
PG_RETURN_NULL();
init_var(&vN);
set_var_from_num(N, &vN);
init_var(&vNminus1);
sub_var(&vN, &const_one, &vNminus1);
if (cmp_var(&vNminus1, &const_zero) <= 0)
{
free_var(&vN);
free_var(&vNminus1);
PG_RETURN_NUMERIC(make_result(&const_zero));
}
init_var(&vsumX);
set_var_from_num(sumX, &vsumX);
init_var(&vsumX2);
set_var_from_num(sumX2, &vsumX2);
mul_var(&vsumX, &vsumX, &vsumX); /* now vsumX contains sumX * sumX */
mul_var(&vN, &vsumX2, &vsumX2); /* now vsumX2 contains N * sumX2 */
sub_var(&vsumX2, &vsumX, &vsumX2); /* N * sumX2 - sumX * sumX */
mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
div_var(&vsumX2, &vNminus1, &vsumX); /* variance */
res = make_result(&vsumX);
free_var(&vN);
free_var(&vNminus1);
free_var(&vsumX);
free_var(&vsumX2);
PG_RETURN_NUMERIC(res);
}
Datum
numeric_stddev(PG_FUNCTION_ARGS)
{
ArrayType *transarray = PG_GETARG_ARRAYTYPE_P(0);
Datum *transdatums;
int ndatums;
Numeric N,
sumX,
sumX2,
res;
NumericVar vN,
vsumX,
vsumX2,
vNminus1;
/* We assume the input is array of numeric */
deconstruct_array(transarray,
false, -1, 'i',
&transdatums, &ndatums);
if (ndatums != 3)
elog(ERROR, "numeric_stddev: expected 3-element numeric array");
N = DatumGetNumeric(transdatums[0]);
sumX = DatumGetNumeric(transdatums[1]);
sumX2 = DatumGetNumeric(transdatums[2]);
if (NUMERIC_IS_NAN(N) || NUMERIC_IS_NAN(sumX) || NUMERIC_IS_NAN(sumX2))
PG_RETURN_NUMERIC(make_result(&const_nan));
/* We define STDDEV of no values to be NULL, of 1 value to be 0 */
/* N is zero iff no digits (cf. numeric_uminus) */
if (N->varlen == NUMERIC_HDRSZ)
PG_RETURN_NULL();
init_var(&vN);
set_var_from_num(N, &vN);
init_var(&vNminus1);
sub_var(&vN, &const_one, &vNminus1);
if (cmp_var(&vNminus1, &const_zero) <= 0)
{
free_var(&vN);
free_var(&vNminus1);
PG_RETURN_NUMERIC(make_result(&const_zero));
}
init_var(&vsumX);
set_var_from_num(sumX, &vsumX);
init_var(&vsumX2);
set_var_from_num(sumX2, &vsumX2);
mul_var(&vsumX, &vsumX, &vsumX); /* now vsumX contains sumX * sumX */
mul_var(&vN, &vsumX2, &vsumX2); /* now vsumX2 contains N * sumX2 */
sub_var(&vsumX2, &vsumX, &vsumX2); /* N * sumX2 - sumX * sumX */
mul_var(&vN, &vNminus1, &vNminus1); /* N * (N - 1) */
div_var(&vsumX2, &vNminus1, &vsumX); /* variance */
sqrt_var(&vsumX, &vsumX); /* stddev */
res = make_result(&vsumX);
free_var(&vN);
free_var(&vNminus1);
free_var(&vsumX);
free_var(&vsumX2);
PG_RETURN_NUMERIC(res);
}
/*
* SUM transition functions for integer datatypes.
*
* We use a Numeric accumulator to avoid overflow. Because SQL92 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)
{
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(int2_numeric, PG_GETARG_DATUM(1));
PG_RETURN_DATUM(newval);
}
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(int2_numeric, PG_GETARG_DATUM(1));
PG_RETURN_DATUM(DirectFunctionCall2(numeric_add,
NumericGetDatum(oldsum), newval));
}
Datum
int4_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(int4_numeric, PG_GETARG_DATUM(1));
PG_RETURN_DATUM(newval);
}
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(int4_numeric, PG_GETARG_DATUM(1));
PG_RETURN_DATUM(DirectFunctionCall2(numeric_add,
NumericGetDatum(oldsum), newval));
}
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);
}
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));
}
/* ----------------------------------------------------------------------
*
* Local functions follow
*
* ----------------------------------------------------------------------
*/
#ifdef NUMERIC_DEBUG
/* ----------
* dump_numeric() - Dump a value in the db storage format for debugging
* ----------
*/
static void
dump_numeric(char *str, Numeric num)
{
int i;
printf("%s: NUMERIC w=%d r=%d d=%d ", str, num->n_weight, num->n_rscale,
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 < num->varlen - NUMERIC_HDRSZ; i++)
printf(" %d %d", (num->n_data[i] >> 4) & 0x0f, num->n_data[i] & 0x0f);
printf("\n");
}
/* ----------
* dump_var() - Dump a value in the variable format for debugging
* ----------
*/
static void
dump_var(char *str, NumericVar *var)
{
int i;
printf("%s: VAR w=%d r=%d d=%d ", str, var->weight, var->rscale,
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(" %d", var->digits[i]);
printf("\n");
}
#endif /* NUMERIC_DEBUG */
/* ----------
* 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;
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: rscale and dscale are 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
* ----------
*/
static void
set_var_from_str(char *str, NumericVar *dest)
{
char *cp = str;
bool have_dp = FALSE;
int i = 0;
while (*cp)
{
if (!isspace((unsigned char) *cp))
break;
cp++;
}
alloc_var(dest, strlen(cp));
dest->weight = -1;
dest->dscale = 0;
dest->sign = NUMERIC_POS;
switch (*cp)
{
case '+':
dest->sign = NUMERIC_POS;
cp++;
break;
case '-':
dest->sign = NUMERIC_NEG;
cp++;
break;
}
if (*cp == '.')
{
have_dp = TRUE;
cp++;
}
if (!isdigit((unsigned char) *cp))
elog(ERROR, "Bad numeric input format '%s'", str);
while (*cp)
{
if (isdigit((unsigned char) *cp))
{
dest->digits[i++] = *cp++ - '0';
if (!have_dp)
dest->weight++;
else
dest->dscale++;
}
else if (*cp == '.')
{
if (have_dp)
elog(ERROR, "Bad numeric input format '%s'", str);
have_dp = TRUE;
cp++;
}
else
break;
}
dest->ndigits = i;
/* Handle exponent, if any */
if (*cp == 'e' || *cp == 'E')
{
long exponent;
char *endptr;
cp++;
exponent = strtol(cp, &endptr, 10);
if (endptr == cp)
elog(ERROR, "Bad numeric input format '%s'", str);
cp = endptr;
if (exponent > NUMERIC_MAX_PRECISION ||
exponent < -NUMERIC_MAX_PRECISION)
elog(ERROR, "Bad numeric input format '%s'", str);
dest->weight += (int) exponent;
dest->dscale -= (int) exponent;
if (dest->dscale < 0)
dest->dscale = 0;
}
/* Should be nothing left but spaces */
while (*cp)
{
if (!isspace((unsigned char) *cp))
elog(ERROR, "Bad numeric input format '%s'", str);
cp++;
}
/* Strip any leading zeroes */
while (dest->ndigits > 0 && *(dest->digits) == 0)
{
(dest->digits)++;
(dest->weight)--;
(dest->ndigits)--;
}
if (dest->ndigits == 0)
dest->weight = 0;
dest->rscale = dest->dscale;
}
/*
* set_var_from_num() -
*
* Parse back the packed db format into a variable
*
*/
static void
set_var_from_num(Numeric num, NumericVar *dest)
{
NumericDigit *digit;
int i;
int n;
n = num->varlen - NUMERIC_HDRSZ; /* number of digit-pairs in packed
* fmt */
alloc_var(dest, n * 2);
dest->weight = num->n_weight;
dest->rscale = num->n_rscale;
dest->dscale = NUMERIC_DSCALE(num);
dest->sign = NUMERIC_SIGN(num);
digit = dest->digits;
for (i = 0; i < n; i++)
{
unsigned char digitpair = num->n_data[i];
*digit++ = (digitpair >> 4) & 0x0f;
*digit++ = digitpair & 0x0f;
}
}
/* ----------
* 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);
digitbuf_free(dest->buf);
memcpy(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).
* CAUTION: var's contents may be modified by rounding!
* Caller must have checked for NaN case.
* Returns a palloc'd string.
* ----------
*/
static char *
get_str_from_var(NumericVar *var, int dscale)
{
char *str;
char *cp;
int i;
int d;
/* ----------
* Check if we must round up before printing the value and
* do so.
* ----------
*/
i = dscale + var->weight + 1;
if (i >= 0 && var->ndigits > i)
{
int carry = (var->digits[i] > 4) ? 1 : 0;
var->ndigits = i;
while (carry)
{
carry += var->digits[--i];
var->digits[i] = carry % 10;
carry /= 10;
}
if (i < 0)
{
Assert(i == -1); /* better not have added more than 1 digit */
Assert(var->digits > var->buf);
var->digits--;
var->ndigits++;
var->weight++;
}
}
else
var->ndigits = MAX(0, MIN(i, var->ndigits));
/* ----------
* Allocate space for the result
* ----------
*/
str = palloc(MAX(0, dscale) + MAX(0, var->weight) + 4);
cp = str;
/* ----------
* Output a dash for negative values
* ----------
*/
if (var->sign == NUMERIC_NEG)
*cp++ = '-';
/* ----------
* Output all digits before the decimal point
* ----------
*/
i = MAX(var->weight, 0);
d = 0;
while (i >= 0)
{
if (i <= var->weight && d < var->ndigits)
*cp++ = var->digits[d++] + '0';
else
*cp++ = '0';
i--;
}
/* ----------
* If requested, output a decimal point and all the digits
* that follow it.
* ----------
*/
if (dscale > 0)
{
*cp++ = '.';
while (i >= -dscale)
{
if (i <= var->weight && d < var->ndigits)
*cp++ = var->digits[d++] + '0';
else
*cp++ = '0';
i--;
}
}
/* ----------
* terminate the string and return it
* ----------
*/
*cp = '\0';
return str;
}
/* ----------
* make_result() -
*
* Create the packed db numeric format in palloc()'d memory from
* a variable. The var's rscale determines the number of digits kept.
* ----------
*/
static Numeric
make_result(NumericVar *var)
{
Numeric result;
NumericDigit *digit = var->digits;
int weight = var->weight;
int sign = var->sign;
int n;
int i,
j;
if (sign == NUMERIC_NAN)
{
result = (Numeric) palloc(NUMERIC_HDRSZ);
result->varlen = NUMERIC_HDRSZ;
result->n_weight = 0;
result->n_rscale = 0;
result->n_sign_dscale = NUMERIC_NAN;
dump_numeric("make_result()", result);
return result;
}
n = MAX(0, MIN(var->ndigits, var->weight + var->rscale + 1));
/* truncate leading zeroes */
while (n > 0 && *digit == 0)
{
digit++;
weight--;
n--;
}
/* truncate trailing zeroes */
while (n > 0 && digit[n - 1] == 0)
n--;
/* If zero result, force to weight=0 and positive sign */
if (n == 0)
{
weight = 0;
sign = NUMERIC_POS;
}
result = (Numeric) palloc(NUMERIC_HDRSZ + (n + 1) / 2);
result->varlen = NUMERIC_HDRSZ + (n + 1) / 2;
result->n_weight = weight;
result->n_rscale = var->rscale;
result->n_sign_dscale = sign |
((uint16) var->dscale & NUMERIC_DSCALE_MASK);
i = 0;
j = 0;
while (j < n)
{
unsigned char digitpair = digit[j++] << 4;
if (j < n)
digitpair |= digit[j++];
result->n_data[i++] = digitpair;
}
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 maxweight;
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;
maxweight = precision - scale;
/* Round to target scale */
i = scale + var->weight + 1;
if (i >= 0 && var->ndigits > i)
{
int carry = (var->digits[i] > 4) ? 1 : 0;
var->ndigits = i;
while (carry)
{
carry += var->digits[--i];
var->digits[i] = carry % 10;
carry /= 10;
}
if (i < 0)
{
Assert(i == -1); /* better not have added more than 1 digit */
Assert(var->digits > var->buf);
var->digits--;
var->ndigits++;
var->weight++;
}
}
else
var->ndigits = MAX(0, MIN(i, var->ndigits));
/* ----------
* 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.
* ----------
*/
if (var->weight >= maxweight)
{
/* Determine true weight; and check for all-zero result */
int tweight = var->weight;
for (i = 0; i < var->ndigits; i++)
{
if (var->digits[i])
break;
tweight--;
}
if (tweight >= maxweight && i < var->ndigits)
elog(ERROR, "overflow on numeric "
"ABS(value) >= 10^%d for field with precision %d scale %d",
tweight, precision, scale);
}
var->rscale = scale;
var->dscale = scale;
}
/* ----------
* cmp_var() -
*
* Compare two values on variable level
* ----------
*/
static int
cmp_var(NumericVar *var1, NumericVar *var2)
{
if (var1->ndigits == 0)
{
if (var2->ndigits == 0)
return 0;
if (var2->sign == NUMERIC_NEG)
return 1;
return -1;
}
if (var2->ndigits == 0)
{
if (var1->sign == NUMERIC_POS)
return 1;
return -1;
}
if (var1->sign == NUMERIC_POS)
{
if (var2->sign == NUMERIC_NEG)
return 1;
return cmp_abs(var1, var2);
}
if (var2->sign == NUMERIC_POS)
return -1;
return cmp_abs(var2, var1);
}
/* ----------
* 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->rscale = MAX(var1->rscale, var2->rscale);
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->rscale = MAX(var1->rscale, var2->rscale);
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->rscale = MAX(var1->rscale, var2->rscale);
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->rscale = MAX(var1->rscale, var2->rscale);
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.
* ----------
*/
static void
mul_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericDigit *res_buf;
NumericDigit *res_digits;
int res_ndigits;
int res_weight;
int res_sign;
int i,
ri,
i1,
i2;
long sum = 0;
res_weight = var1->weight + var2->weight + 2;
res_ndigits = var1->ndigits + var2->ndigits + 1;
if (var1->sign == var2->sign)
res_sign = NUMERIC_POS;
else
res_sign = NUMERIC_NEG;
res_buf = digitbuf_alloc(res_ndigits);
res_digits = res_buf;
memset(res_digits, 0, res_ndigits);
ri = res_ndigits;
for (i1 = var1->ndigits - 1; i1 >= 0; i1--)
{
sum = 0;
i = --ri;
for (i2 = var2->ndigits - 1; i2 >= 0; i2--)
{
sum += res_digits[i] + var1->digits[i1] * var2->digits[i2];
res_digits[i--] = sum % 10;
sum /= 10;
}
res_digits[i] = sum;
}
i = res_weight + global_rscale + 2;
if (i >= 0 && i < res_ndigits)
{
sum = (res_digits[i] > 4) ? 1 : 0;
res_ndigits = i;
i--;
while (sum)
{
sum += res_digits[i];
res_digits[i--] = sum % 10;
sum /= 10;
}
}
while (res_ndigits > 0 && *res_digits == 0)
{
res_digits++;
res_weight--;
res_ndigits--;
}
while (res_ndigits > 0 && res_digits[res_ndigits - 1] == 0)
res_ndigits--;
if (res_ndigits == 0)
{
res_sign = NUMERIC_POS;
res_weight = 0;
}
digitbuf_free(result->buf);
result->buf = res_buf;
result->digits = res_digits;
result->ndigits = res_ndigits;
result->weight = res_weight;
result->rscale = global_rscale;
result->sign = res_sign;
}
/* ----------
* div_var() -
*
* Division on variable level.
* ----------
*/
static void
div_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericDigit *res_digits;
int res_ndigits;
int res_sign;
int res_weight;
NumericVar dividend;
NumericVar divisor[10];
int ndigits_tmp;
int weight_tmp;
int rscale_tmp;
int ri;
int i;
long guess;
long first_have;
long first_div;
int first_nextdigit;
int stat = 0;
/* ----------
* First of all division by zero check
* ----------
*/
ndigits_tmp = var2->ndigits + 1;
if (ndigits_tmp == 1)
elog(ERROR, "division by zero on numeric");
/* ----------
* 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;
res_ndigits = global_rscale + res_weight;
if (res_ndigits <= 0)
res_ndigits = 1;
/* ----------
* Now result zero check
* ----------
*/
if (var1->ndigits == 0)
{
zero_var(result);
result->rscale = global_rscale;
return;
}
/* ----------
* Initialize local variables
* ----------
*/
init_var(÷nd);
for (i = 1; i < 10; i++)
init_var(&divisor[i]);
/* ----------
* Make a copy of the divisor which has one leading zero digit
* ----------
*/
divisor[1].ndigits = ndigits_tmp;
divisor[1].rscale = var2->ndigits;
divisor[1].sign = NUMERIC_POS;
divisor[1].buf = digitbuf_alloc(ndigits_tmp);
divisor[1].digits = divisor[1].buf;
divisor[1].digits[0] = 0;
memcpy(&(divisor[1].digits[1]), var2->digits, ndigits_tmp - 1);
/* ----------
* Make a copy of the dividend
* ----------
*/
dividend.ndigits = var1->ndigits;
dividend.weight = 0;
dividend.rscale = var1->ndigits;
dividend.sign = NUMERIC_POS;
dividend.buf = digitbuf_alloc(var1->ndigits);
dividend.digits = dividend.buf;
memcpy(dividend.digits, var1->digits, var1->ndigits);
/* ----------
* Setup the result
* ----------
*/
digitbuf_free(result->buf);
result->buf = digitbuf_alloc(res_ndigits + 2);
res_digits = result->buf;
result->digits = res_digits;
result->ndigits = res_ndigits;
result->weight = res_weight;
result->rscale = global_rscale;
result->sign = res_sign;
res_digits[0] = 0;
first_div = divisor[1].digits[1] * 10;
if (ndigits_tmp > 2)
first_div += divisor[1].digits[2];
first_have = 0;
first_nextdigit = 0;
weight_tmp = 1;
rscale_tmp = divisor[1].rscale;
for (ri = 0; ri <= res_ndigits; ri++)
{
first_have = first_have * 10;
if (first_nextdigit >= 0 && first_nextdigit < dividend.ndigits)
first_have += dividend.digits[first_nextdigit];
first_nextdigit++;
guess = (first_have * 10) / first_div + 1;
if (guess > 9)
guess = 9;
while (guess > 0)
{
if (divisor[guess].buf == NULL)
{
int i;
long sum = 0;
memcpy(&divisor[guess], &divisor[1], sizeof(NumericVar));
divisor[guess].buf = digitbuf_alloc(divisor[guess].ndigits);
divisor[guess].digits = divisor[guess].buf;
for (i = divisor[1].ndigits - 1; i >= 0; i--)
{
sum += divisor[1].digits[i] * guess;
divisor[guess].digits[i] = sum % 10;
sum /= 10;
}
}
divisor[guess].weight = weight_tmp;
divisor[guess].rscale = rscale_tmp;
stat = cmp_abs(÷nd, &divisor[guess]);
if (stat >= 0)
break;
guess--;
}
res_digits[ri + 1] = guess;
if (stat == 0)
{
ri++;
break;
}
weight_tmp--;
rscale_tmp++;
if (guess == 0)
continue;
sub_abs(÷nd, &divisor[guess], ÷nd);
first_nextdigit = dividend.weight - weight_tmp;
first_have = 0;
if (first_nextdigit >= 0 && first_nextdigit < dividend.ndigits)
first_have = dividend.digits[first_nextdigit];
first_nextdigit++;
}
result->ndigits = ri + 1;
if (ri == res_ndigits + 1)
{
int carry = (res_digits[ri] > 4) ? 1 : 0;
result->ndigits = ri;
res_digits[ri] = 0;
while (carry && ri > 0)
{
carry += res_digits[--ri];
res_digits[ri] = carry % 10;
carry /= 10;
}
}
while (result->ndigits > 0 && *(result->digits) == 0)
{
(result->digits)++;
(result->weight)--;
(result->ndigits)--;
}
while (result->ndigits > 0 && result->digits[result->ndigits - 1] == 0)
(result->ndigits)--;
if (result->ndigits == 0)
result->sign = NUMERIC_POS;
/*
* Tidy up
*/
digitbuf_free(dividend.buf);
for (i = 1; i < 10; i++)
digitbuf_free(divisor[i].buf);
}
/* ----------
* mod_var() -
*
* Calculate the modulo of two numerics at variable level
* ----------
*/
static void
mod_var(NumericVar *var1, NumericVar *var2, NumericVar *result)
{
NumericVar tmp;
int save_global_rscale;
init_var(&tmp);
/* ----------
* We do it by fiddling around with global_rscale and truncating
* the result of the division.
* ----------
*/
save_global_rscale = global_rscale;
global_rscale = var2->rscale + 2;
div_var(var1, var2, &tmp);
tmp.rscale = var2->rscale;
tmp.ndigits = MAX(0, MIN(tmp.ndigits, tmp.weight + tmp.rscale + 1));
global_rscale = var2->rscale;
mul_var(var2, &tmp, &tmp);
sub_var(var1, &tmp, result);
global_rscale = save_global_rscale;
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);
tmp.rscale = 0;
tmp.ndigits = MIN(tmp.ndigits, MAX(0, tmp.weight + 1));
if (tmp.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);
tmp.rscale = 0;
tmp.ndigits = MIN(tmp.ndigits, MAX(0, tmp.weight + 1));
if (tmp.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 Newtons algorithm
* ----------
*/
static void
sqrt_var(NumericVar *arg, NumericVar *result)
{
NumericVar tmp_arg;
NumericVar tmp_val;
NumericVar last_val;
int res_rscale;
int save_global_rscale;
int stat;
save_global_rscale = global_rscale;
global_rscale += 8;
res_rscale = global_rscale;
stat = cmp_var(arg, &const_zero);
if (stat == 0)
{
set_var_from_var(&const_zero, result);
result->rscale = res_rscale;
result->sign = NUMERIC_POS;
return;
}
if (stat < 0)
elog(ERROR, "math error on numeric - cannot compute SQRT of negative value");
init_var(&tmp_arg);
init_var(&tmp_val);
init_var(&last_val);
set_var_from_var(arg, &tmp_arg);
set_var_from_var(result, &last_val);
/* ----------
* Initialize the result to the first guess
* ----------
*/
digitbuf_free(result->buf);
result->buf = digitbuf_alloc(1);
result->digits = result->buf;
result->digits[0] = tmp_arg.digits[0] / 2;
if (result->digits[0] == 0)
result->digits[0] = 1;
result->ndigits = 1;
result->weight = tmp_arg.weight / 2;
result->rscale = res_rscale;
result->sign = NUMERIC_POS;
for (;;)
{
div_var(&tmp_arg, result, &tmp_val);
add_var(result, &tmp_val, result);
div_var(result, &const_two, result);
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);
global_rscale = save_global_rscale;
div_var(result, &const_one, result);
}
/* ----------
* exp_var() -
*
* Raise e to the power of x
* ----------
*/
static void
exp_var(NumericVar *arg, NumericVar *result)
{
NumericVar x;
NumericVar xpow;
NumericVar ifac;
NumericVar elem;
NumericVar ni;
int d;
int i;
int ndiv2 = 0;
bool xneg = FALSE;
int save_global_rscale;
init_var(&x);
init_var(&xpow);
init_var(&ifac);
init_var(&elem);
init_var(&ni);
set_var_from_var(arg, &x);
if (x.sign == NUMERIC_NEG)
{
xneg = TRUE;
x.sign = NUMERIC_POS;
}
save_global_rscale = global_rscale;
global_rscale = 0;
for (i = x.weight, d = 0; i >= 0; i--, d++)
{
global_rscale *= 10;
if (d < x.ndigits)
global_rscale += x.digits[d];
if (global_rscale >= 1000)
elog(ERROR, "argument for EXP() too big");
}
global_rscale = global_rscale / 2 + save_global_rscale + 8;
while (cmp_var(&x, &const_one) > 0)
{
ndiv2++;
global_rscale++;
div_var(&x, &const_two, &x);
}
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 (i = 2; ; i++)
{
add_var(&ni, &const_one, &ni);
mul_var(&xpow, &x, &xpow);
mul_var(&ifac, &ni, &ifac);
div_var(&xpow, &ifac, &elem);
if (elem.ndigits == 0)
break;
add_var(result, &elem, result);
}
while (ndiv2-- > 0)
mul_var(result, result, result);
global_rscale = save_global_rscale;
if (xneg)
div_var(&const_one, result, result);
else
div_var(result, &const_one, result);
result->sign = NUMERIC_POS;
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)
{
NumericVar x;
NumericVar xx;
NumericVar ni;
NumericVar elem;
NumericVar fact;
int i;
int save_global_rscale;
if (cmp_var(arg, &const_zero) <= 0)
elog(ERROR, "math error on numeric - cannot compute LN of value <= zero");
save_global_rscale = global_rscale;
global_rscale += 8;
init_var(&x);
init_var(&xx);
init_var(&ni);
init_var(&elem);
init_var(&fact);
set_var_from_var(&const_two, &fact);
set_var_from_var(arg, &x);
while (cmp_var(&x, &const_two) >= 0)
{
sqrt_var(&x, &x);
mul_var(&fact, &const_two, &fact);
}
set_var_from_str("0.5", &elem);
while (cmp_var(&x, &elem) <= 0)
{
sqrt_var(&x, &x);
mul_var(&fact, &const_two, &fact);
}
sub_var(&x, &const_one, result);
add_var(&x, &const_one, &elem);
div_var(result, &elem, result);
set_var_from_var(result, &xx);
mul_var(result, result, &x);
set_var_from_var(&const_one, &ni);
for (i = 2; ; i++)
{
add_var(&ni, &const_two, &ni);
mul_var(&xx, &x, &xx);
div_var(&xx, &ni, &elem);
if (cmp_var(&elem, &const_zero) == 0)
break;
add_var(result, &elem, result);
}
global_rscale = save_global_rscale;
mul_var(result, &fact, result);
free_var(&x);
free_var(&xx);
free_var(&ni);
free_var(&elem);
free_var(&fact);
}
/* ----------
* log_var() -
*
* Compute the logarithm of x in a given base
* ----------
*/
static void
log_var(NumericVar *base, NumericVar *num, NumericVar *result)
{
NumericVar ln_base;
NumericVar ln_num;
global_rscale += 8;
init_var(&ln_base);
init_var(&ln_num);
ln_var(base, &ln_base);
ln_var(num, &ln_num);
global_rscale -= 8;
div_var(&ln_num, &ln_base, result);
free_var(&ln_num);
free_var(&ln_base);
}
/* ----------
* power_var() -
*
* Raise base to the power of exp
* ----------
*/
static void
power_var(NumericVar *base, NumericVar *exp, NumericVar *result)
{
NumericVar ln_base;
NumericVar ln_num;
int save_global_rscale;
save_global_rscale = global_rscale;
global_rscale += global_rscale / 3 + 8;
init_var(&ln_base);
init_var(&ln_num);
ln_var(base, &ln_base);
mul_var(&ln_base, exp, &ln_num);
global_rscale = save_global_rscale;
exp_var(&ln_num, result);
free_var(&ln_num);
free_var(&ln_base);
}
/* ----------------------------------------------------------------------
*
* 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)
{
int i1 = 0;
int i2 = 0;
int w1 = var1->weight;
int w2 = var2->weight;
int stat;
while (w1 > w2 && i1 < var1->ndigits)
{
if (var1->digits[i1++] != 0)
return 1;
w1--;
}
while (w2 > w1 && i2 < var2->ndigits)
{
if (var2->digits[i2++] != 0)
return -1;
w2--;
}
if (w1 == w2)
{
while (i1 < var1->ndigits && i2 < var2->ndigits)
{
stat = var1->digits[i1++] - var2->digits[i2++];
if (stat)
{
if (stat > 0)
return 1;
return -1;
}
}
}
while (i1 < var1->ndigits)
{
if (var1->digits[i1++] != 0)
return 1;
}
while (i2 < var2->ndigits)
{
if (var2->digits[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;
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_rscale = MAX(var1->rscale, var2->rscale);
res_dscale = MAX(var1->dscale, var2->dscale);
res_ndigits = res_rscale + res_weight + 1;
if (res_ndigits <= 0)
res_ndigits = 1;
res_buf = digitbuf_alloc(res_ndigits);
res_digits = res_buf;
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 >= 10)
{
res_digits[i] = carry - 10;
carry = 1;
}
else
{
res_digits[i] = carry;
carry = 0;
}
}
Assert(carry == 0); /* else we failed to allow for carry out */
while (res_ndigits > 0 && *res_digits == 0)
{
res_digits++;
res_weight--;
res_ndigits--;
}
while (res_ndigits > 0 && res_digits[res_ndigits - 1] == 0)
res_ndigits--;
if (res_ndigits == 0)
res_weight = 0;
digitbuf_free(result->buf);
result->ndigits = res_ndigits;
result->buf = res_buf;
result->digits = res_digits;
result->weight = res_weight;
result->rscale = res_rscale;
result->dscale = res_dscale;
}
/* ----------
* 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;
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_rscale = MAX(var1->rscale, var2->rscale);
res_dscale = MAX(var1->dscale, var2->dscale);
res_ndigits = res_rscale + res_weight + 1;
if (res_ndigits <= 0)
res_ndigits = 1;
res_buf = digitbuf_alloc(res_ndigits);
res_digits = res_buf;
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 + 10;
borrow = -1;
}
else
{
res_digits[i] = borrow;
borrow = 0;
}
}
Assert(borrow == 0); /* else caller gave us var1 < var2 */
while (res_ndigits > 0 && *res_digits == 0)
{
res_digits++;
res_weight--;
res_ndigits--;
}
while (res_ndigits > 0 && res_digits[res_ndigits - 1] == 0)
res_ndigits--;
if (res_ndigits == 0)
res_weight = 0;
digitbuf_free(result->buf);
result->ndigits = res_ndigits;
result->buf = res_buf;
result->digits = res_digits;
result->weight = res_weight;
result->rscale = res_rscale;
result->dscale = res_dscale;
}