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/********************************************************************
* gnc-numeric.c -- an exact-number library for accounting use *
* Copyright (C) 2000 Bill Gribble *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of *
* the License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License*
* along with this program; if not, contact: *
* *
* Free Software Foundation Voice: +1-617-542-5942 *
* 59 Temple Place - Suite 330 Fax: +1-617-542-2652 *
* Boston, MA 02111-1307, USA gnu@gnu.org *
* *
*******************************************************************/
#define _GNU_SOURCE
#include "config.h"
#include <glib.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "gnc-numeric.h"
/* TODO
* - use longer intermediate values to make operations
* 64-bit-overflow-proof
*/
/* static short module = MOD_ENGINE; */
#if 0
static const char * _numeric_error_strings[] =
{
"No error",
"Argument is not a valid number",
"Intermediate result overflow",
"Argument denominators differ in GNC_DENOM_FIXED operation",
"Remainder part in GNC_RND_NEVER operation"
};
#endif
static gint64 gnc_numeric_lcd(gnc_numeric a, gnc_numeric b);
/********************************************************************
* gnc_numeric_zero_p
********************************************************************/
int
gnc_numeric_zero_p(gnc_numeric a) {
if(gnc_numeric_check(a)) {
return 0;
}
else {
if((a.num == 0) && (a.denom != 0)) {
return 1;
}
else {
return 0;
}
}
}
/********************************************************************
* gnc_numeric_negative_p
********************************************************************/
int
gnc_numeric_negative_p(gnc_numeric a) {
if(gnc_numeric_check(a)) {
return 0;
}
else {
if((a.num < 0) && (a.denom != 0)) {
return 1;
}
else {
return 0;
}
}
}
/********************************************************************
* gnc_numeric_positive_p
********************************************************************/
int
gnc_numeric_positive_p(gnc_numeric a) {
if(gnc_numeric_check(a)) {
return 0;
}
else {
if((a.num > 0) && (a.denom != 0)) {
return 1;
}
else {
return 0;
}
}
}
/********************************************************************
* gnc_numeric_compare
* returns 1 if a>b, -1 if b>a, 0 if a == b
********************************************************************/
int
gnc_numeric_compare(gnc_numeric a, gnc_numeric b) {
gint64 ab, ba;
if(gnc_numeric_check(a) || gnc_numeric_check(b)) {
return 0;
}
ab = a.num * b.denom;
ba = b.num * a.denom;
if(ab == ba) {
return 0;
}
else if(ab > ba) {
return 1;
}
else {
return -1;
}
}
/********************************************************************
* gnc_numeric_eq
********************************************************************/
int
gnc_numeric_eq(gnc_numeric a, gnc_numeric b) {
return ((a.num == b.num) && (a.denom == b.denom));
}
/********************************************************************
* gnc_numeric_equal
********************************************************************/
int
gnc_numeric_equal(gnc_numeric a, gnc_numeric b) {
if(((a.denom > 0) && (b.denom > 0)) ||
((a.denom < 0) && (b.denom < 0))) {
return ((a.num * b.denom) == (a.denom * b.num));
}
else {
return 0;
}
}
/********************************************************************
* gnc_numeric_same
* would a and b be equal() if they were both converted to the same
* denominator?
********************************************************************/
int
gnc_numeric_same(gnc_numeric a, gnc_numeric b, gint64 denom,
gint how) {
gnc_numeric aconv, bconv;
aconv = gnc_numeric_convert(a, denom, how);
bconv = gnc_numeric_convert(b, denom, how);
return(gnc_numeric_equal(aconv, bconv));
}
/********************************************************************
* gnc_numeric_add
********************************************************************/
gnc_numeric
gnc_numeric_add(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how) {
gnc_numeric sum;
gint64 lcd;
if(gnc_numeric_check(a) || gnc_numeric_check(b)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
if((denom == GNC_DENOM_AUTO) &&
(how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_FIXED) {
if(a.denom == b.denom) {
denom = a.denom;
}
else if(b.num == 0) {
denom = a.denom;
}
else if(a.num == 0) {
denom = b.denom;
}
else {
return gnc_numeric_error(GNC_ERROR_DENOM_DIFF);
}
}
if(a.denom < 0) {
a.num *= a.denom;
a.denom = 1;
}
if(b.denom < 0) {
b.num *= b.denom;
b.denom = 1;
}
/* get an exact answer.. same denominator is the common case. */
if(a.denom == b.denom) {
sum.num = a.num + b.num;
sum.denom = a.denom;
}
else {
/* ok, convert to the lcd and compute from there... */
lcd = gnc_numeric_lcd(a,b);
sum.num = a.num*(lcd/a.denom) + b.num*(lcd/b.denom);
sum.denom = lcd;
// sum.num = a.num*b.denom + b.num*a.denom;
// sum.denom = a.denom*b.denom;
}
if((denom == GNC_DENOM_AUTO) &&
((how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_LCD)) {
denom = gnc_numeric_lcd(a, b);
how = how & GNC_NUMERIC_RND_MASK;
}
return gnc_numeric_convert(sum, denom, how);
}
/********************************************************************
* gnc_numeric_add_fixed
********************************************************************/
gnc_numeric
gnc_numeric_add_fixed(gnc_numeric a, gnc_numeric b) {
return gnc_numeric_add(a, b, GNC_DENOM_AUTO,
GNC_DENOM_FIXED | GNC_RND_NEVER);
}
/********************************************************************
* gnc_numeric_sub
********************************************************************/
gnc_numeric
gnc_numeric_sub(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how) {
gnc_numeric diff;
gint64 lcd;
if(gnc_numeric_check(a) || gnc_numeric_check(b)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
if((denom == GNC_DENOM_AUTO) &&
(how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_FIXED) {
if(a.denom == b.denom) {
denom = a.denom;
}
else if(b.num == 0) {
denom = a.denom;
}
else if(a.num == 0) {
denom = b.denom;
}
else {
return gnc_numeric_error(GNC_ERROR_DENOM_DIFF);
}
}
if(a.denom < 0) {
a.num *= a.denom;
a.denom = 1;
}
if(b.denom < 0) {
b.num *= b.denom;
b.denom = 1;
}
/* get an exact answer.. same denominator is the common case. */
if(a.denom == b.denom) {
diff.num = a.num - b.num;
diff.denom = a.denom;
}
else {
/* ok, convert to the lcd and compute from there... */
lcd = gnc_numeric_lcd(a,b);
diff.num = a.num*(lcd/a.denom) - b.num*(lcd/b.denom);
diff.denom = lcd;
// diff.num = a.num*b.denom - b.num*a.denom;
// diff.denom = a.denom*b.denom;
}
if((denom == GNC_DENOM_AUTO) &&
((how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_LCD)) {
denom = gnc_numeric_lcd(a, b);
how = how & GNC_NUMERIC_RND_MASK;
}
return gnc_numeric_convert(diff, denom, how);
}
/********************************************************************
* gnc_numeric_sub_fixed
********************************************************************/
gnc_numeric
gnc_numeric_sub_fixed(gnc_numeric a, gnc_numeric b) {
return gnc_numeric_sub(a, b, GNC_DENOM_AUTO,
GNC_DENOM_FIXED | GNC_RND_NEVER);
}
/********************************************************************
* gnc_numeric_mul
********************************************************************/
gnc_numeric
gnc_numeric_mul(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how)
{
gnc_numeric product, result;
if(gnc_numeric_check(a) || gnc_numeric_check(b)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
if((denom == GNC_DENOM_AUTO) &&
(how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_FIXED) {
if(a.denom == b.denom) {
denom = a.denom;
}
else if(b.num == 0) {
denom = a.denom;
}
else if(a.num == 0) {
denom = b.denom;
}
else {
return gnc_numeric_error(GNC_ERROR_DENOM_DIFF);
}
}
if(a.denom < 0) {
a.num *= a.denom;
a.denom = 1;
}
if(b.denom < 0) {
b.num *= b.denom;
b.denom = 1;
}
product.num = a.num*b.num;
product.denom = a.denom*b.denom;
if(product.denom < 0) {
product.num = -product.num;
product.denom = -product.denom;
}
if((denom == GNC_DENOM_AUTO) &&
((how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_LCD))
{
denom = gnc_numeric_lcd(a, b);
how = how & GNC_NUMERIC_RND_MASK;
}
result = gnc_numeric_convert(product, denom, how);
return result;
}
/********************************************************************
* gnc_numeric_div
********************************************************************/
gnc_numeric
gnc_numeric_div(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how) {
gnc_numeric quotient;
gint64 lcd;
if(gnc_numeric_check(a) || gnc_numeric_check(b)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
if((denom == GNC_DENOM_AUTO) &&
(how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_FIXED) {
if(a.denom == b.denom) {
denom = a.denom;
}
else if(a.denom == 0) {
denom = b.denom;
}
else {
return gnc_numeric_error(GNC_ERROR_DENOM_DIFF);
}
}
if(a.denom < 0) {
a.num *= a.denom;
a.denom = 1;
}
if(b.denom < 0) {
b.num *= b.denom;
b.denom = 1;
}
if(a.denom == b.denom) {
quotient.num = a.num;
quotient.denom = b.num;
}
else {
/* ok, convert to the lcd and compute from there... */
lcd = gnc_numeric_lcd(a,b);
quotient.num = a.num*(lcd/a.denom);
quotient.denom = b.num*(lcd/b.denom);
// quotient.num = a.num*b.denom;
// quotient.denom = a.denom*b.num;
}
if(quotient.denom < 0) {
quotient.num = -quotient.num;
quotient.denom = -quotient.denom;
}
if((denom == GNC_DENOM_AUTO) &&
((how & GNC_NUMERIC_DENOM_MASK) == GNC_DENOM_LCD)) {
denom = gnc_numeric_lcd(a, b);
how = how & GNC_NUMERIC_RND_MASK;
}
return gnc_numeric_convert(quotient, denom, how);
}
/********************************************************************
* gnc_numeric_neg
* negate the argument
********************************************************************/
gnc_numeric
gnc_numeric_neg(gnc_numeric a) {
if(gnc_numeric_check(a)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
return gnc_numeric_create(- a.num, a.denom);
}
/********************************************************************
* gnc_numeric_neg
* return the absolute value of the argument
********************************************************************/
gnc_numeric
gnc_numeric_abs(gnc_numeric a) {
if(gnc_numeric_check(a)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
return gnc_numeric_create(ABS(a.num), a.denom);
}
/********************************************************************
* gnc_numeric_convert
********************************************************************/
gnc_numeric
gnc_numeric_convert(gnc_numeric in, gint64 denom, gint how)
{
gnc_numeric out;
gnc_numeric temp;
gint64 temp_bc;
gint64 temp_a;
gint64 remainder;
gint64 sign;
gint denom_neg=0;
double ratio, logratio;
double sigfigs;
if(gnc_numeric_check(in)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
if(denom == GNC_DENOM_AUTO)
{
switch(how & GNC_NUMERIC_DENOM_MASK)
{
default:
case GNC_DENOM_LCD: /* LCD is meaningless with AUTO in here */
case GNC_DENOM_EXACT:
return in;
break;
case GNC_DENOM_REDUCE:
/* reduce the input to a relatively-prime fraction */
return gnc_numeric_reduce(in);
break;
case GNC_DENOM_FIXED:
if(in.denom != denom) {
return gnc_numeric_error(GNC_ERROR_DENOM_DIFF);
}
else {
return in;
}
break;
case GNC_DENOM_SIGFIG:
ratio = fabs(gnc_numeric_to_double(in));
if(ratio < 10e-20) {
logratio = 0;
}
else {
logratio = log10(ratio);
logratio = ((logratio > 0.0) ?
(floor(logratio)+1.0) : (ceil(logratio)));
}
sigfigs = GNC_NUMERIC_GET_SIGFIGS(how);
if(sigfigs-logratio >= 0) {
denom = (gint64)(pow(10, sigfigs-logratio));
}
else {
denom = -((gint64)(pow(10, logratio-sigfigs)));
}
how = how & ~GNC_DENOM_SIGFIG & ~GNC_NUMERIC_SIGFIGS_MASK;
break;
}
}
/* Make sure we need to do the work */
if(in.denom == denom) {
return in;
}
/* If the denominator of the input value is negative, get rid of that. */
if(in.denom < 0) {
in.num = in.num * (- in.denom);
in.denom = 1;
}
sign = (in.num < 0) ? -1 : 1;
/* If the denominator is less than zero, we are to interpret it as
* the reciprocal of its magnitude. */
if(denom < 0)
{
denom = - denom;
denom_neg = 1;
temp_a = (in.num < 0) ? -in.num : in.num;
temp_bc = in.denom * denom;
remainder = in.num % temp_bc;
out.num = in.num / temp_bc;
out.denom = - denom;
}
else
{
/* Do all the modulo and int division on positive values to make
* things a little clearer. Reduce the fraction denom/in.denom to
* help with range errors (FIXME : need bigger intermediate rep) */
temp.num = denom;
temp.denom = in.denom;
temp = gnc_numeric_reduce(temp);
out.num = in.num * temp.num;
out.num = (out.num < 0) ? -out.num : out.num;
remainder = out.num % temp.denom;
out.num = out.num / temp.denom;
out.denom = denom;
}
if(remainder > 0)
{
switch(how) {
case GNC_RND_FLOOR:
if(sign < 0) {
out.num = out.num + 1;
}
break;
case GNC_RND_CEIL:
if(sign > 0) {
out.num = out.num + 1;
}
break;
case GNC_RND_TRUNC:
break;
case GNC_RND_PROMOTE:
out.num = out.num + 1;
break;
case GNC_RND_ROUND_HALF_DOWN:
if(denom_neg) {
if((2 * remainder) > in.denom*denom) {
out.num = out.num + 1;
}
}
else if((2 * remainder) > temp.denom) {
out.num = out.num + 1;
}
break;
case GNC_RND_ROUND_HALF_UP:
if(denom_neg) {
if((2 * remainder) >= in.denom*denom) {
out.num = out.num + 1;
}
}
else if((2 * remainder ) >= temp.denom) {
out.num = out.num + 1;
}
break;
case GNC_RND_ROUND:
if(denom_neg) {
if((2 * remainder) > in.denom*denom) {
out.num = out.num + 1;
}
else if((2 * remainder) == in.denom*denom) {
if(out.num % 2) {
out.num = out.num + 1;
}
}
}
else {
if((2 * remainder ) > temp.denom) {
out.num = out.num + 1;
}
else if((2 * remainder) == temp.denom) {
if(out.num % 2) {
out.num = out.num + 1;
}
}
}
break;
case GNC_RND_NEVER:
return gnc_numeric_error(GNC_ERROR_REMAINDER);
break;
}
}
out.num = (sign > 0) ? out.num : (-out.num);
return out;
}
/********************************************************************
* gnc_numeric_lcd
* Find the least common multiple of the denominators of
* a and b
********************************************************************/
gint64
gnc_numeric_lcd(gnc_numeric a, gnc_numeric b) {
gint64 current_divisor = 2;
gint64 max_square;
gint64 three_count = 0;
gint64 small_denom;
gint64 big_denom;
if(gnc_numeric_check(a) || gnc_numeric_check(b)) {
return GNC_ERROR_ARG;
}
if(b.denom < a.denom) {
small_denom = b.denom;
big_denom = a.denom;
}
else {
small_denom = a.denom;
big_denom = b.denom;
}
/* special case: smaller divides smoothly into larger */
if((big_denom % small_denom) == 0) {
return big_denom;
}
max_square = small_denom;
/* the LCM algorithm : factor out the union of the prime factors of the
* two args and then multiply the remainders together.
*
* To do this, we find the successive prime factors of the smaller
* denominator and eliminate them from both the smaller and larger
* denominator (so we only count factors on a one-on-one basis),
* then multiply the original smaller by the remains of the larger.
*
* I.e. LCM 100,96875 == 2*2*5*5,31*5*5*5*5 = 2*2,31*5*5
* answer: multiply 100 by 31*5*5 == 387500
*/
while(current_divisor * current_divisor <= max_square) {
if(((small_denom % current_divisor) == 0) &&
((big_denom % current_divisor) == 0)) {
big_denom = big_denom / current_divisor;
small_denom = small_denom / current_divisor;
}
else {
if(current_divisor == 2) {
current_divisor++;
}
else if(three_count == 3) {
current_divisor += 4;
three_count = 1;
}
else {
current_divisor += 2;
three_count++;
}
}
if((current_divisor > small_denom) ||
(current_divisor > big_denom)) {
break;
}
}
/* max_sqaure is the original small_denom */
return max_square * big_denom;
}
/********************************************************************
* gnc_numeric_reduce
* reduce a fraction by GCF elimination. This is NOT done as a
* part of the arithmetic API unless GNC_DENOM_REDUCE is specified
* as the output denominator.
********************************************************************/
#if 1
gnc_numeric
gnc_numeric_reduce(gnc_numeric in) {
gint64 t;
gint64 num = (in.num < 0) ? (- in.num) : in.num ;
gint64 denom = in.denom;
gnc_numeric out;
if(gnc_numeric_check(in)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
/* the strategy is to use euclid's algorithm */
while (denom > 0) {
t = num % denom;
num = denom;
denom = t;
}
/* num = gcd */
/* all calculations are done on positive num, since it's not
* well defined what % does for negative values */
out.num = in.num / num;
out.denom = in.denom / num;
return out;
}
#else
gnc_numeric
gnc_numeric_reduce(gnc_numeric in) {
gint64 current_divisor = 2;
gint64 max_square;
gint64 num = (in.num < 0) ? (- in.num) : in.num ;
gint64 denom = in.denom;
int three_count = 0;
gnc_numeric out;
if(gnc_numeric_check(in)) {
return gnc_numeric_error(GNC_ERROR_ARG);
}
/* the strategy is to eliminate common factors from
* 2 up to 'max', where max is the smaller of the smaller
* part of the fraction and the sqrt of the larger part of
* the fraction. There's also the special case of the
* smaller of fraction parts being a common factor.
*
* we test for 2 and 3 first, and thereafter skip all even numbers
* and all odd multiples of 3 (that's every third odd number,
* i.e. 9, 15, 21), thus the three_count stuff. */
/* special case: one side divides evenly by the other */
if (num == 0) {
denom = 1;
}
else if((num > denom) && (num % denom == 0)) {
num = num / denom;
denom = 1;
}
else if ((num <= denom) && (denom % num == 0)) {
denom = denom / num;
num = 1;
}
max_square = (num > denom) ? denom : num;
/* normal case: test 2, then 3, 5, 7, 11, etc.
* (skip multiples of 2 and 3) */
while(current_divisor * current_divisor <= max_square) {
if((num % current_divisor == 0) &&
(denom % current_divisor == 0)) {
num = num / current_divisor;
denom = denom / current_divisor;
}
else {
if(current_divisor == 2) {
current_divisor++;
}
else if(three_count == 3) {
current_divisor += 4;
three_count = 1;
}
else {
current_divisor += 2;
three_count++;
}
}
if((current_divisor > num) ||
(current_divisor > denom)) {
break;
}
}
/* all calculations are done on positive num, since it's not
* well defined what % does for negative values */
out.num = (in.num < 0) ? (- num) : num;
out.denom = denom;
return out;
}
#endif
/********************************************************************
* double_to_gnc_numeric
********************************************************************/
gnc_numeric
double_to_gnc_numeric(double in, gint64 denom, gint how) {
gnc_numeric out;
gint64 int_part=0;
double frac_part;
gint64 frac_int=0;
double logval;
double sigfigs;
if((denom == GNC_DENOM_AUTO) && (how & GNC_DENOM_SIGFIG)) {
if(fabs(in) < 10e-20) {
logval = 0;
}
else {
logval = log10(fabs(in));
logval = ((logval > 0.0) ?
(floor(logval)+1.0) : (ceil(logval)));
}
sigfigs = GNC_NUMERIC_GET_SIGFIGS(how);
if(sigfigs-logval >= 0) {
denom = (gint64)(pow(10, sigfigs-logval));
}
else {
denom = -((gint64)(pow(10, logval-sigfigs)));
}
how = how & ~GNC_DENOM_SIGFIG & ~GNC_NUMERIC_SIGFIGS_MASK;
}
int_part = (gint64)(floor(fabs(in)));
frac_part = in - (double)int_part;
int_part = int_part * denom;
frac_part = frac_part * (double)denom;
switch(how & GNC_NUMERIC_RND_MASK) {
case GNC_RND_FLOOR:
frac_int = (gint64)floor(frac_part);
break;
case GNC_RND_CEIL:
frac_int = (gint64)ceil(frac_part);
break;
case GNC_RND_TRUNC:
frac_int = (gint64)frac_part;
break;
case GNC_RND_ROUND:
case GNC_RND_ROUND_HALF_UP:
frac_int = (gint64)rint(frac_part);
break;
case GNC_RND_NEVER:
frac_int = (gint64)floor(frac_part);
if(frac_part != (double) frac_int) {
/* signal an error */
}
break;
}
out.num = int_part + frac_int;
out.denom = denom;
return out;
}
/********************************************************************
* gnc_numeric_to_double
********************************************************************/
double
gnc_numeric_to_double(gnc_numeric in) {
if(in.denom >= 0) {
return (double)in.num/(double)in.denom;
}
else {
return (double)(in.num * in.denom);
}
}
/********************************************************************
* gnc_numeric_create
********************************************************************/
gnc_numeric
gnc_numeric_create(gint64 num, gint64 denom) {
gnc_numeric out;
out.num = num;
out.denom = denom;
return out;
}
/********************************************************************
* gnc_numeric_error
********************************************************************/
gnc_numeric
gnc_numeric_error(int error_code) {
if(abs(error_code) < 5) {
/* PERR("%s", _numeric_error_strings[ - error_code]); */
}
return gnc_numeric_create(error_code, 0LL);
}
/********************************************************************
* gnc_numeric_zero
********************************************************************/
gnc_numeric
gnc_numeric_zero(void) {
return gnc_numeric_create(0LL, 1LL);
}
/********************************************************************
* gnc_numeric_num
********************************************************************/
gint64
gnc_numeric_num(gnc_numeric a) {
return a.num;
}
/********************************************************************
* gnc_numeric_denom
********************************************************************/
gint64
gnc_numeric_denom(gnc_numeric a) {
return a.denom;
}
/********************************************************************
* gnc_numeric_add_with_error
********************************************************************/
gnc_numeric
gnc_numeric_add_with_error(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how,
gnc_numeric * error) {
gnc_numeric sum = gnc_numeric_add(a, b, denom, how);
gnc_numeric exact = gnc_numeric_add(a, b, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
gnc_numeric err = gnc_numeric_sub(sum, exact, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
if(error) {
*error = err;
}
return sum;
}
/********************************************************************
* gnc_numeric_sub_with_error
********************************************************************/
gnc_numeric
gnc_numeric_sub_with_error(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how,
gnc_numeric * error) {
gnc_numeric diff = gnc_numeric_sub(a, b, denom, how);
gnc_numeric exact = gnc_numeric_sub(a, b, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
gnc_numeric err = gnc_numeric_sub(diff, exact, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
if(error) {
*error = err;
}
return diff;
}
/********************************************************************
* gnc_numeric_mul_with_error
********************************************************************/
gnc_numeric
gnc_numeric_mul_with_error(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how,
gnc_numeric * error) {
gnc_numeric prod = gnc_numeric_mul(a, b, denom, how);
gnc_numeric exact = gnc_numeric_mul(a, b, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
gnc_numeric err = gnc_numeric_sub(prod, exact, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
if(error) {
*error = err;
}
return prod;
}
/********************************************************************
* gnc_numeric_div_with_error
********************************************************************/
gnc_numeric
gnc_numeric_div_with_error(gnc_numeric a, gnc_numeric b,
gint64 denom, gint how,
gnc_numeric * error) {
gnc_numeric quot = gnc_numeric_div(a, b, denom, how);
gnc_numeric exact = gnc_numeric_div(a, b, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE);
gnc_numeric err = gnc_numeric_sub(quot, exact,
GNC_DENOM_AUTO, GNC_DENOM_REDUCE);
if(error) {
*error = err;
}
return quot;
}
int
gnc_numeric_check(gnc_numeric in) {
if(in.denom != 0) {
return GNC_ERROR_OK;
}
else if(in.num) {
return in.num;
}
else {
return GNC_ERROR_ARG;
}
}
/********************************************************************
* gnc_numeric text IO
********************************************************************/
gchar *
gnc_numeric_to_string(gnc_numeric n) {
gchar *result;
long long int tmpnum = n.num;
long long int tmpdenom = n.denom;
result = g_strdup_printf("%lld/%lld", tmpnum, tmpdenom);
return result;
}
const gchar *
string_to_gnc_numeric(const gchar* str, gnc_numeric *n) {
size_t num_read;
long long int tmpnum;
long long int tmpdenom;
if(!str) return NULL;
#ifdef GNC_DEPRECATED
/* must use "<" here because %n's effects aren't well defined */
if(sscanf(str, " " GNC_SCANF_LLD "/" GNC_SCANF_LLD "%n",
&tmpnum, &tmpdenom, &num_read) < 2) {
return(NULL);
}
#else
tmpnum = strtoll (str, NULL, 0);
str = strchr (str, '/');
if (!str) return NULL;
str ++;
tmpdenom = strtoll (str, NULL, 0);
num_read = strspn (str, "0123456789");
#endif
n->num = tmpnum;
n->denom = tmpdenom;
return(str + num_read);
}
#ifdef _GNC_NUMERIC_TEST
static char *
gnc_numeric_print(gnc_numeric in) {
char * retval;
if(gnc_numeric_check(in)) {
retval = g_strdup_printf("<ERROR> [%lld / %lld]",
(long long int) in.num,
(long long int) in.denom);
}
else {
retval = g_strdup_printf("[%lld / %lld]",
(long long int) in.num,
(long long int) in.denom);
}
return retval;
}
int
main(int argc, char ** argv) {
gnc_numeric a = gnc_numeric_create(1, 3);
gnc_numeric b = gnc_numeric_create(1, 4);
gnc_numeric c;
gnc_numeric d = gnc_numeric_create(1, 2);
gnc_numeric err;
int i;
printf("add exact : %s + %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_add(a, b,
GNC_DENOM_AUTO,
GNC_DENOM_EXACT)));
printf("add least : %s + %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_add(a, b,
GNC_DENOM_AUTO,
GNC_DENOM_REDUCE)));
printf("add 100ths (banker's): %s + %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_add(a, b, 100,
GNC_RND_ROUND)));
c = gnc_numeric_add_with_error(a, b, 100, GNC_RND_ROUND, &err);
printf("add 100ths/error : %s + %s = %s + (error) %s\n\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(c),
gnc_numeric_print(err));
printf("sub exact : %s - %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_sub(a, b, GNC_DENOM_AUTO,
GNC_DENOM_EXACT)));
printf("sub least : %s - %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_sub(a, b,
GNC_DENOM_AUTO,
GNC_DENOM_REDUCE)));
printf("sub 100ths : %s - %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_sub(a, b, 100,
GNC_RND_ROUND)));
c = gnc_numeric_sub_with_error(a, b, 100, GNC_RND_FLOOR, &err);
printf("sub 100ths/error : %s - %s = %s + (error) %s\n\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(c),
gnc_numeric_print(err));
printf("mul exact : %s * %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_mul(a, b, GNC_DENOM_AUTO,
GNC_DENOM_EXACT)));
printf("mul least : %s * %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_mul(a, b, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE)));
printf("mul 100ths : %s * %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_mul(a, b, 100,
GNC_RND_ROUND)));
c = gnc_numeric_mul_with_error(a, b, 100, GNC_RND_ROUND, &err);
printf("mul 100ths/error : %s * %s = %s + (error) %s\n\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(c),
gnc_numeric_print(err));
printf("div exact : %s / %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_div(a, b, GNC_DENOM_AUTO,
GNC_DENOM_EXACT)));
printf("div least : %s / %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_div(a, b, GNC_DENOM_AUTO,
GNC_DENOM_REDUCE)));
printf("div 100ths : %s / %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_div(a, b, 100,
GNC_RND_ROUND)));
c = gnc_numeric_div_with_error(a, b, 100, GNC_RND_ROUND, &err);
printf("div 100ths/error : %s / %s = %s + (error) %s\n\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(c),
gnc_numeric_print(err));
printf("7/16 as float: %e\n",
gnc_numeric_to_double(gnc_numeric_create(7, 16)));
printf("7/16 as 100ths (floor): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(7, 16),
100, GNC_RND_FLOOR)));
printf("7/16 as 100ths (ceil): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(7, 16),
100, GNC_RND_CEIL)));
printf("7/16 as 100ths (trunc): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(7, 16),
100, GNC_RND_TRUNC)));
printf("7/16 as 100ths (round): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(7, 16),
100, GNC_RND_ROUND)));
printf("1511/1000 as 1/100 (round): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(1511, 1000),
100, GNC_RND_ROUND)));
printf("1516/1000 as 1/100 (round): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(1516, 1000),
100, GNC_RND_ROUND)));
printf("1515/1000 as 1/100 (round): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(1515, 1000),
100, GNC_RND_ROUND)));
printf("1525/1000 as 1/100 (round): %s\n",
gnc_numeric_print(gnc_numeric_convert(gnc_numeric_create(1525, 1000),
100, GNC_RND_ROUND)));
printf("100023234 / 334216654 reduced: %s\n",
gnc_numeric_print(gnc_numeric_reduce(gnc_numeric_create(10023234LL,
334216654LL))));
printf("2^10*3^10*17^2 / 2^8*3^12 reduced: %s\n",
gnc_numeric_print
(gnc_numeric_reduce(gnc_numeric_create(17474724864LL,
136048896LL))));
printf("1024 / 1024^4 reduced: %s\n",
gnc_numeric_print
(gnc_numeric_reduce(gnc_numeric_create(1024LL,
1099511627776LL))));
printf("reducing 100,000 times:\n\n");
for(i = 0; i < 100000; i++) {
gnc_numeric_reduce(gnc_numeric_create(17474724864LL,
136048896LL));
}
printf("add LCM: %s + %s = %s\n",
gnc_numeric_print(b), gnc_numeric_print(d),
gnc_numeric_print(gnc_numeric_add(b, d, GNC_DENOM_AUTO,
GNC_DENOM_LCD)));
printf("float to 6 sigfigs: %s\n",
gnc_numeric_print(double_to_gnc_numeric(1.1234567890123,
GNC_DENOM_AUTO,
GNC_DENOM_SIGFIGS(6) |
GNC_RND_ROUND)));
printf("float to 6 sigfigs: %s\n",
gnc_numeric_print(double_to_gnc_numeric(.011234567890123,
GNC_DENOM_AUTO,
GNC_DENOM_SIGFIGS(6) |
GNC_RND_ROUND)));
printf("float to 6 sigfigs: %s\n",
gnc_numeric_print(double_to_gnc_numeric(1123.4567890123,
GNC_DENOM_AUTO,
GNC_DENOM_SIGFIGS(6) |
GNC_RND_ROUND)));
printf("float to 6 sigfigs: %s\n",
gnc_numeric_print(double_to_gnc_numeric(1.1234567890123e-5,
GNC_DENOM_AUTO,
GNC_DENOM_SIGFIGS(6) |
GNC_RND_ROUND)));
printf("add to 4 sigfigs: %s + %s = %s\n",
gnc_numeric_print(a), gnc_numeric_print(b),
gnc_numeric_print(gnc_numeric_add(a, b,
GNC_DENOM_AUTO,
GNC_DENOM_SIGFIGS(4) |
GNC_RND_ROUND)));
return 0;
}
#endif
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