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postgres/src/backend/utils/adt/numeric.c
Tom Lane 08195a43f3 Fix bugs in NUMERIC ceil() and floor() functions. ceil(0) returned 1, 
and both would insert random junk digits if given an input that was an
exact multiple of 10.
2000-01-20 02:21:44 +00:00

3485 lines
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/* ----------
* 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 1.24 2000/01/20 02:21:44 tgl Exp $
*
* ----------
*/
#include "postgres.h"
#include <ctype.h>
#include <float.h>
#include <math.h>
#include <errno.h>
#include <sys/types.h>
#include "utils/builtins.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
* ----------
*/
Numeric
numeric_in(char *str, int dummy, int32 typmod)
{
NumericVar value;
Numeric res;
/* ----------
* Check for NULL
* ----------
*/
if (str == NULL)
return NULL;
if (strcmp(str, "NULL") == 0)
return NULL;
/* ----------
* Check for NaN
* ----------
*/
if (strcmp(str, "NaN") == 0)
return 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);
return res;
}
/* ----------
* numeric_out() -
*
* Output function for numeric data type
* ----------
*/
char *
numeric_out(Numeric num)
{
NumericVar x;
char *str;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return pstrdup("NULL");
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return 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.
* ----------
*/
Numeric
numeric(Numeric num, int32 typmod)
{
Numeric new;
int32 tmp_typmod;
int precision;
int scale;
int maxweight;
NumericVar var;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return 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);
return 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);
return new;
}
/* ----------------------------------------------------------------------
*
* Rounding and the like
*
* ----------------------------------------------------------------------
*/
Numeric
numeric_abs(Numeric num)
{
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
Numeric
numeric_sign(Numeric num)
{
Numeric res;
NumericVar result;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------
* numeric_round() -
*
* Modify rscale and dscale of a number and round it if required.
* ----------
*/
Numeric
numeric_round(Numeric num, int32 scale)
{
int32 typmod;
int precision;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return make_result(&const_nan);
/* ----------
* Check that the requested scale is valid
* ----------
*/
if (scale < 0 || scale > NUMERIC_MAX_DISPLAY_SCALE)
elog(ERROR, "illegal numeric scale %d - must be between 0 and %d",
scale, NUMERIC_MAX_DISPLAY_SCALE);
/* ----------
* Let numeric() and in turn apply_typmod() do the job
* ----------
*/
precision = MAX(0, num->n_weight) + scale;
typmod = (((precision + 2) << 16) | scale) + VARHDRSZ;
return numeric(num, typmod);
}
/* ----------
* numeric_trunc() -
*
* Modify rscale and dscale of a number and cut it if required.
* ----------
*/
Numeric
numeric_trunc(Numeric num, int32 scale)
{
Numeric res;
NumericVar arg;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return make_result(&const_nan);
/* ----------
* Check that the requested scale is valid
* ----------
*/
if (scale < 0 || scale > NUMERIC_MAX_DISPLAY_SCALE)
elog(ERROR, "illegal numeric scale %d - must be between 0 and %d",
scale, NUMERIC_MAX_DISPLAY_SCALE);
/* ----------
* Unpack the argument and truncate it
* ----------
*/
init_var(&arg);
set_var_from_num(num, &arg);
arg.rscale = scale;
arg.dscale = scale;
arg.ndigits = MIN(arg.ndigits, MAX(0, arg.weight + scale + 1));
/* ----------
* Return the truncated result
* ----------
*/
res = make_result(&arg);
free_var(&arg);
return res;
}
/* ----------
* numeric_ceil() -
*
* Return the smallest integer greater than or equal to the argument
* ----------
*/
Numeric
numeric_ceil(Numeric num)
{
Numeric res;
NumericVar result;
if (num == NULL)
return NULL;
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------
* numeric_floor() -
*
* Return the largest integer equal to or less than the argument
* ----------
*/
Numeric
numeric_floor(Numeric num)
{
Numeric res;
NumericVar result;
if (num == NULL)
return NULL;
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------------------------------------------------------------------
*
* Comparison functions
*
* ----------------------------------------------------------------------
*/
int32
numeric_cmp(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return (int32)0;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return (int32)0;
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);
return (int32)((result == 0) ? 0 : ((result < 0) ? -1 : 1));
}
bool
numeric_eq(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return FALSE;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return FALSE;
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);
return (result == 0);
}
bool
numeric_ne(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return FALSE;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return FALSE;
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);
return (result != 0);
}
bool
numeric_gt(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return FALSE;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return FALSE;
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);
return (result > 0);
}
bool
numeric_ge(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return FALSE;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return FALSE;
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);
return (result >= 0);
}
bool
numeric_lt(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return FALSE;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return FALSE;
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);
return (result < 0);
}
bool
numeric_le(Numeric num1, Numeric num2)
{
int result;
NumericVar arg1;
NumericVar arg2;
if (num1 == NULL || num2 == NULL)
return FALSE;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return FALSE;
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);
return (result <= 0);
}
/* ----------------------------------------------------------------------
*
* Arithmetic base functions
*
* ----------------------------------------------------------------------
*/
/* ----------
* numeric_add() -
*
* Add two numerics
* ----------
*/
Numeric
numeric_add(Numeric num1, Numeric num2)
{
NumericVar arg1;
NumericVar arg2;
NumericVar result;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_sub() -
*
* Subtract one numeric from another
* ----------
*/
Numeric
numeric_sub(Numeric num1, Numeric num2)
{
NumericVar arg1;
NumericVar arg2;
NumericVar result;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_mul() -
*
* Calculate the product of two numerics
* ----------
*/
Numeric
numeric_mul(Numeric num1, Numeric num2)
{
NumericVar arg1;
NumericVar arg2;
NumericVar result;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_div() -
*
* Divide one numeric into another
* ----------
*/
Numeric
numeric_div(Numeric num1, Numeric num2)
{
NumericVar arg1;
NumericVar arg2;
NumericVar result;
Numeric res;
int res_dscale;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_mod() -
*
* Calculate the modulo of two numerics
* ----------
*/
Numeric
numeric_mod(Numeric num1, Numeric num2)
{
Numeric res;
NumericVar arg1;
NumericVar arg2;
NumericVar result;
if (num1 == NULL || num2 == NULL)
return NULL;
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_inc() -
*
* Increment a number by one
* ----------
*/
Numeric
numeric_inc(Numeric num)
{
NumericVar arg;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------
* numeric_dec() -
*
* Decrement a number by one
* ----------
*/
Numeric
numeric_dec(Numeric num)
{
NumericVar arg;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return make_result(&const_nan);
/* ----------
* Compute the result and return it
* ----------
*/
init_var(&arg);
set_var_from_num(num, &arg);
sub_var(&arg, &const_one, &arg);
res = make_result(&arg);
free_var(&arg);
return res;
}
/* ----------
* numeric_smaller() -
*
* Return the smaller of two numbers
* ----------
*/
Numeric
numeric_smaller(Numeric num1, Numeric num2)
{
NumericVar arg1;
NumericVar arg2;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_larger() -
*
* Return the larger of two numbers
* ----------
*/
Numeric
numeric_larger(Numeric num1, Numeric num2)
{
NumericVar arg1;
NumericVar arg2;
Numeric res;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------------------------------------------------------------------
*
* Complex math functions
*
* ----------------------------------------------------------------------
*/
/* ----------
* numeric_sqrt() -
*
* Compute the square root of a numeric.
* ----------
*/
Numeric
numeric_sqrt(Numeric num)
{
Numeric res;
NumericVar arg;
NumericVar result;
int res_dscale;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------
* numeric_exp() -
*
* Raise e to the power of x
* ----------
*/
Numeric
numeric_exp(Numeric num)
{
Numeric res;
NumericVar arg;
NumericVar result;
int res_dscale;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------
* numeric_ln() -
*
* Compute the natural logarithm of x
* ----------
*/
Numeric
numeric_ln(Numeric num)
{
Numeric res;
NumericVar arg;
NumericVar result;
int res_dscale;
/* ----------
* Handle NULL
* ----------
*/
if (num == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num))
return 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);
return res;
}
/* ----------
* numeric_ln() -
*
* Compute the logarithm of x in a given base
* ----------
*/
Numeric
numeric_log(Numeric num1, Numeric num2)
{
Numeric res;
NumericVar arg1;
NumericVar arg2;
NumericVar result;
int res_dscale;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------
* numeric_power() -
*
* Raise m to the power of x
* ----------
*/
Numeric
numeric_power(Numeric num1, Numeric num2)
{
Numeric res;
NumericVar arg1;
NumericVar arg2;
NumericVar result;
int res_dscale;
/* ----------
* Handle NULL
* ----------
*/
if (num1 == NULL || num2 == NULL)
return NULL;
/* ----------
* Handle NaN
* ----------
*/
if (NUMERIC_IS_NAN(num1) || NUMERIC_IS_NAN(num2))
return 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);
return res;
}
/* ----------------------------------------------------------------------
*
* Type conversion functions
*
* ----------------------------------------------------------------------
*/
Numeric
int4_numeric(int32 val)
{
Numeric res;
NumericVar result;
char *tmp;
init_var(&result);
tmp = int4out(val);
set_var_from_str(tmp, &result);
res = make_result(&result);
free_var(&result);
pfree(tmp);
return res;
}
int32
numeric_int4(Numeric num)
{
NumericVar x;
char *str;
int32 result;
if (num == NULL)
return 0;
if (NUMERIC_IS_NAN(num))
return 0;
/* ----------
* 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 = int4in(str);
pfree(str);
return result;
}
Numeric
float8_numeric(float64 val)
{
Numeric res;
NumericVar result;
char buf[DBL_DIG + 100];
if (val == NULL)
return NULL;
if (isnan(*val))
return 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);
return res;
}
float64
numeric_float8(Numeric num)
{
char *tmp;
float64 result;
if (num == NULL)
return NULL;
if (NUMERIC_IS_NAN(num))
{
result = (float64) palloc(sizeof(float64data));
*result = NAN;
return result;
}
tmp = numeric_out(num);
result = float8in(tmp);
pfree(tmp);
return result;
}
Numeric
float4_numeric(float32 val)
{
Numeric res;
NumericVar result;
char buf[FLT_DIG + 100];
if (val == NULL)
return NULL;
if (isnan(*val))
return 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);
return res;
}
float32
numeric_float4(Numeric num)
{
char *tmp;
float32 result;
if (num == NULL)
return NULL;
if (NUMERIC_IS_NAN(num))
{
result = (float32) palloc(sizeof(float32data));
*result = NAN;
return result;
}
tmp = numeric_out(num);
result = float4in(tmp);
pfree(tmp);
return result;
}
/* ----------------------------------------------------------------------
*
* 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(*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(*cp))
elog(ERROR, "Bad numeric input format '%s'", str);
while (*cp)
{
if (isdigit(*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(*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 = 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(&dividend);
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(&dividend, &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(&dividend, &divisor[guess], &dividend);
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; TRUE; 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; TRUE; 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;
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 < var1->ndigits)
carry += var1->digits[i1];
if (i2 >= 0 && i2 < var2->ndigits)
carry += var2->digits[i2];
res_digits[i] = carry % 10;
carry /= 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_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;
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 < var1->ndigits)
borrow += var1->digits[i1];
if (i2 >= 0 && i2 < var2->ndigits)
borrow -= var2->digits[i2];
if (borrow < 0)
{
res_digits[i] = borrow + 10;
borrow = -1;
}
else
{
res_digits[i] = borrow;
borrow = 0;
}
}
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;
}
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