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number.c
1816 lines (1574 loc) · 41.2 KB
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number.c
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// pragmas added by Nick Gammon
#pragma warning( disable : 4131) // uses old-style declarator
#pragma warning( disable : 4244) // conversion from 'int' to 'unsigned short', possible loss of data
#pragma warning( disable : 4100) // unreferenced formal parameter
/* number.c: Implements arbitrary precision numbers. */
/*
Copyright (C) 1991, 1992, 1993, 1994, 1997, 2000 Free Software Foundation, Inc.
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; see the file COPYING. If not, write to:
The Free Software Foundation, Inc.
59 Temple Place, Suite 330
Boston, MA 02111-1307 USA.
You may contact the author by:
e-mail: philnelson@acm.org
us-mail: Philip A. Nelson
Computer Science Department, 9062
Western Washington University
Bellingham, WA 98226-9062
*************************************************************************/
#include <stdio.h>
#include "bcconfig.h"
#include <assert.h>
#include <stdlib.h>
#include <ctype.h>/* Prototypes needed for external utility routines. */
#include "number.h"
#define bc_rt_warn rt_warn
#define bc_rt_error rt_error
#define bc_out_of_memory out_of_memory
_PROTOTYPE(void rt_warn, (char *mesg ,...));
_PROTOTYPE(void rt_error, (char *mesg ,...));
_PROTOTYPE(void out_of_memory, (void));
/* Storage used for special numbers. */
bc_num _zero_;
bc_num _one_;
bc_num _two_;
static bc_num _bc_Free_list = NULL;
/* new_num allocates a number and sets fields to known values. */
bc_num
bc_new_num (length, scale)
int length, scale;
{
bc_num temp;
if (_bc_Free_list != NULL) {
temp = _bc_Free_list;
_bc_Free_list = temp->n_next;
} else {
temp = (bc_num) malloc (sizeof(bc_struct));
if (temp == NULL) bc_out_of_memory ();
}
temp->n_sign = PLUS;
temp->n_len = length;
temp->n_scale = scale;
temp->n_refs = 1;
temp->n_ptr = (char *) malloc (length+scale);
if (temp->n_ptr == NULL) bc_out_of_memory();
temp->n_value = temp->n_ptr;
memset (temp->n_ptr, 0, length+scale);
return temp;
}
/* "Frees" a bc_num NUM. Actually decreases reference count and only
frees the storage if reference count is zero. */
void
bc_free_num (num)
bc_num *num;
{
if (*num == NULL) return;
(*num)->n_refs--;
if ((*num)->n_refs == 0) {
if ((*num)->n_ptr)
free ((*num)->n_ptr);
(*num)->n_next = _bc_Free_list;
_bc_Free_list = *num;
}
*num = NULL;
}
/* Frees the memory allocated in the memory-recycling list.
* Primary use is to deafen memory leak warnings. -JW */
void
bc_free_freed_list ()
{
while (_bc_Free_list != NULL)
{
bc_num next = _bc_Free_list->n_next;
free(_bc_Free_list);
_bc_Free_list = next;
}
}
/* Intitialize the number package! */
void
bc_init_numbers ()
{
_zero_ = bc_new_num (1,0);
_one_ = bc_new_num (1,0);
_one_->n_value[0] = 1;
_two_ = bc_new_num (1,0);
_two_->n_value[0] = 2;
}
/* Added by NJG to remove a memory leak */
void
bc_free_numbers ()
{
bc_free_num (&_zero_);
bc_free_num (&_one_);
bc_free_num (&_two_);
bc_free_freed_list();
}
/* Make a copy of a number! Just increments the reference count! */
bc_num
bc_copy_num (num)
bc_num num;
{
num->n_refs++;
return num;
}
/* Initialize a number NUM by making it a copy of zero. */
void
bc_init_num (num)
bc_num *num;
{
*num = bc_copy_num (_zero_);
}
/* For many things, we may have leading zeros in a number NUM.
_bc_rm_leading_zeros just moves the data "value" pointer to the
correct place and adjusts the length. */
static void
_bc_rm_leading_zeros (num)
bc_num num;
{
/* We can move n_value to point to the first non zero digit! */
while (*num->n_value == 0 && num->n_len > 1) {
num->n_value++;
num->n_len--;
}
}
/* Compare two bc numbers. Return value is 0 if equal, -1 if N1 is less
than N2 and +1 if N1 is greater than N2. If USE_SIGN is false, just
compare the magnitudes. */
static int
_bc_do_compare (n1, n2, use_sign, ignore_last)
bc_num n1, n2;
int use_sign;
int ignore_last;
{
char *n1ptr, *n2ptr;
int count;
/* First, compare signs. */
if (use_sign && n1->n_sign != n2->n_sign)
{
if (n1->n_sign == PLUS)
return (1); /* Positive N1 > Negative N2 */
else
return (-1); /* Negative N1 < Positive N1 */
}
/* Now compare the magnitude. */
if (n1->n_len != n2->n_len)
{
if (n1->n_len > n2->n_len)
{
/* Magnitude of n1 > n2. */
if (!use_sign || n1->n_sign == PLUS)
return (1);
else
return (-1);
}
else
{
/* Magnitude of n1 < n2. */
if (!use_sign || n1->n_sign == PLUS)
return (-1);
else
return (1);
}
}
/* If we get here, they have the same number of integer digits.
check the integer part and the equal length part of the fraction. */
count = n1->n_len + MIN (n1->n_scale, n2->n_scale);
n1ptr = n1->n_value;
n2ptr = n2->n_value;
while ((count > 0) && (*n1ptr == *n2ptr))
{
n1ptr++;
n2ptr++;
count--;
}
if (ignore_last && count == 1 && n1->n_scale == n2->n_scale)
return (0);
if (count != 0)
{
if (*n1ptr > *n2ptr)
{
/* Magnitude of n1 > n2. */
if (!use_sign || n1->n_sign == PLUS)
return (1);
else
return (-1);
}
else
{
/* Magnitude of n1 < n2. */
if (!use_sign || n1->n_sign == PLUS)
return (-1);
else
return (1);
}
}
/* They are equal up to the last part of the equal part of the fraction. */
if (n1->n_scale != n2->n_scale)
{
if (n1->n_scale > n2->n_scale)
{
for (count = n1->n_scale-n2->n_scale; count>0; count--)
if (*n1ptr++ != 0)
{
/* Magnitude of n1 > n2. */
if (!use_sign || n1->n_sign == PLUS)
return (1);
else
return (-1);
}
}
else
{
for (count = n2->n_scale-n1->n_scale; count>0; count--)
if (*n2ptr++ != 0)
{
/* Magnitude of n1 < n2. */
if (!use_sign || n1->n_sign == PLUS)
return (-1);
else
return (1);
}
}
}
/* They must be equal! */
return (0);
}
/* This is the "user callable" routine to compare numbers N1 and N2. */
int
bc_compare (n1, n2)
bc_num n1, n2;
{
return _bc_do_compare (n1, n2, TRUE, FALSE);
}
/* In some places we need to check if the number is negative. */
char
bc_is_neg (num)
bc_num num;
{
return num->n_sign == MINUS;
}
/* In some places we need to check if the number NUM is zero. */
char
bc_is_zero (num)
bc_num num;
{
int count;
char *nptr;
/* Quick check. */
if (num == _zero_) return TRUE;
/* Initialize */
count = num->n_len + num->n_scale;
nptr = num->n_value;
/* The check */
while ((count > 0) && (*nptr++ == 0)) count--;
if (count != 0)
return FALSE;
else
return TRUE;
}
/* In some places we need to check if the number NUM is almost zero.
Specifically, all but the last digit is 0 and the last digit is 1.
Last digit is defined by scale. */
char
bc_is_near_zero (num, scale)
bc_num num;
int scale;
{
int count;
char *nptr;
/* Error checking */
if (scale > num->n_scale)
scale = num->n_scale;
/* Initialize */
count = num->n_len + scale;
nptr = num->n_value;
/* The check */
while ((count > 0) && (*nptr++ == 0)) count--;
if (count != 0 && (count != 1 || *--nptr != 1))
return FALSE;
else
return TRUE;
}
/* Perform addition: N1 is added to N2 and the value is
returned. The signs of N1 and N2 are ignored.
SCALE_MIN is to set the minimum scale of the result. */
static bc_num
_bc_do_add (n1, n2, scale_min)
bc_num n1, n2;
int scale_min;
{
bc_num sum;
int sum_scale, sum_digits;
char *n1ptr, *n2ptr, *sumptr;
int carry, n1bytes, n2bytes;
int count;
/* Prepare sum. */
sum_scale = MAX (n1->n_scale, n2->n_scale);
sum_digits = MAX (n1->n_len, n2->n_len) + 1;
sum = bc_new_num (sum_digits, MAX(sum_scale, scale_min));
/* Zero extra digits made by scale_min. */
if (scale_min > sum_scale)
{
sumptr = (char *) (sum->n_value + sum_scale + sum_digits);
for (count = scale_min - sum_scale; count > 0; count--)
*sumptr++ = 0;
}
/* Start with the fraction part. Initialize the pointers. */
n1bytes = n1->n_scale;
n2bytes = n2->n_scale;
n1ptr = (char *) (n1->n_value + n1->n_len + n1bytes - 1);
n2ptr = (char *) (n2->n_value + n2->n_len + n2bytes - 1);
sumptr = (char *) (sum->n_value + sum_scale + sum_digits - 1);
/* Add the fraction part. First copy the longer fraction.*/
if (n1bytes != n2bytes)
{
if (n1bytes > n2bytes)
while (n1bytes>n2bytes)
{ *sumptr-- = *n1ptr--; n1bytes--;}
else
while (n2bytes>n1bytes)
{ *sumptr-- = *n2ptr--; n2bytes--;}
}
/* Now add the remaining fraction part and equal size integer parts. */
n1bytes += n1->n_len;
n2bytes += n2->n_len;
carry = 0;
while ((n1bytes > 0) && (n2bytes > 0))
{
*sumptr = *n1ptr-- + *n2ptr-- + carry;
if (*sumptr > (BASE-1))
{
carry = 1;
*sumptr -= BASE;
}
else
carry = 0;
sumptr--;
n1bytes--;
n2bytes--;
}
/* Now add carry the longer integer part. */
if (n1bytes == 0)
{ n1bytes = n2bytes; n1ptr = n2ptr; }
while (n1bytes-- > 0)
{
*sumptr = *n1ptr-- + carry;
if (*sumptr > (BASE-1))
{
carry = 1;
*sumptr -= BASE;
}
else
carry = 0;
sumptr--;
}
/* Set final carry. */
if (carry == 1)
*sumptr += 1;
/* Adjust sum and return. */
_bc_rm_leading_zeros (sum);
return sum;
}
/* Perform subtraction: N2 is subtracted from N1 and the value is
returned. The signs of N1 and N2 are ignored. Also, N1 is
assumed to be larger than N2. SCALE_MIN is the minimum scale
of the result. */
static bc_num
_bc_do_sub (n1, n2, scale_min)
bc_num n1, n2;
int scale_min;
{
bc_num diff;
int diff_scale, diff_len;
int min_scale, min_len;
char *n1ptr, *n2ptr, *diffptr;
int borrow, count, val;
/* Allocate temporary storage. */
diff_len = MAX (n1->n_len, n2->n_len);
diff_scale = MAX (n1->n_scale, n2->n_scale);
min_len = MIN (n1->n_len, n2->n_len);
min_scale = MIN (n1->n_scale, n2->n_scale);
diff = bc_new_num (diff_len, MAX(diff_scale, scale_min));
/* Zero extra digits made by scale_min. */
if (scale_min > diff_scale)
{
diffptr = (char *) (diff->n_value + diff_len + diff_scale);
for (count = scale_min - diff_scale; count > 0; count--)
*diffptr++ = 0;
}
/* Initialize the subtract. */
n1ptr = (char *) (n1->n_value + n1->n_len + n1->n_scale -1);
n2ptr = (char *) (n2->n_value + n2->n_len + n2->n_scale -1);
diffptr = (char *) (diff->n_value + diff_len + diff_scale -1);
/* Subtract the numbers. */
borrow = 0;
/* Take care of the longer scaled number. */
if (n1->n_scale != min_scale)
{
/* n1 has the longer scale */
for (count = n1->n_scale - min_scale; count > 0; count--)
*diffptr-- = *n1ptr--;
}
else
{
/* n2 has the longer scale */
for (count = n2->n_scale - min_scale; count > 0; count--)
{
val = - *n2ptr-- - borrow;
if (val < 0)
{
val += BASE;
borrow = 1;
}
else
borrow = 0;
*diffptr-- = val;
}
}
/* Now do the equal length scale and integer parts. */
for (count = 0; count < min_len + min_scale; count++)
{
val = *n1ptr-- - *n2ptr-- - borrow;
if (val < 0)
{
val += BASE;
borrow = 1;
}
else
borrow = 0;
*diffptr-- = val;
}
/* If n1 has more digits then n2, we now do that subtract. */
if (diff_len != min_len)
{
for (count = diff_len - min_len; count > 0; count--)
{
val = *n1ptr-- - borrow;
if (val < 0)
{
val += BASE;
borrow = 1;
}
else
borrow = 0;
*diffptr-- = val;
}
}
/* Clean up and return. */
_bc_rm_leading_zeros (diff);
return diff;
}
/* Here is the full subtract routine that takes care of negative numbers.
N2 is subtracted from N1 and the result placed in RESULT. SCALE_MIN
is the minimum scale for the result. */
void
bc_sub (n1, n2, result, scale_min)
bc_num n1, n2, *result;
int scale_min;
{
bc_num diff = NULL;
int cmp_res;
int res_scale;
if (n1->n_sign != n2->n_sign)
{
diff = _bc_do_add (n1, n2, scale_min);
diff->n_sign = n1->n_sign;
}
else
{
/* subtraction must be done. */
/* Compare magnitudes. */
cmp_res = _bc_do_compare (n1, n2, FALSE, FALSE);
switch (cmp_res)
{
case -1:
/* n1 is less than n2, subtract n1 from n2. */
diff = _bc_do_sub (n2, n1, scale_min);
diff->n_sign = (n2->n_sign == PLUS ? MINUS : PLUS);
break;
case 0:
/* They are equal! return zero! */
res_scale = MAX (scale_min, MAX(n1->n_scale, n2->n_scale));
diff = bc_new_num (1, res_scale);
memset (diff->n_value, 0, res_scale+1);
break;
case 1:
/* n2 is less than n1, subtract n2 from n1. */
diff = _bc_do_sub (n1, n2, scale_min);
diff->n_sign = n1->n_sign;
break;
}
}
/* Clean up and return. */
bc_free_num (result);
*result = diff;
}
/* Here is the full add routine that takes care of negative numbers.
N1 is added to N2 and the result placed into RESULT. SCALE_MIN
is the minimum scale for the result. */
void
bc_add (bc_num n1, bc_num n2, bc_num *result, int scale_min)
{
bc_num sum = NULL;
int cmp_res;
int res_scale;
if (n1->n_sign == n2->n_sign)
{
sum = _bc_do_add (n1, n2, scale_min);
sum->n_sign = n1->n_sign;
}
else
{
/* subtraction must be done. */
cmp_res = _bc_do_compare (n1, n2, FALSE, FALSE); /* Compare magnitudes. */
switch (cmp_res)
{
case -1:
/* n1 is less than n2, subtract n1 from n2. */
sum = _bc_do_sub (n2, n1, scale_min);
sum->n_sign = n2->n_sign;
break;
case 0:
/* They are equal! return zero with the correct scale! */
res_scale = MAX (scale_min, MAX(n1->n_scale, n2->n_scale));
sum = bc_new_num (1, res_scale);
memset (sum->n_value, 0, res_scale+1);
break;
case 1:
/* n2 is less than n1, subtract n2 from n1. */
sum = _bc_do_sub (n1, n2, scale_min);
sum->n_sign = n1->n_sign;
}
}
/* Clean up and return. */
bc_free_num (result);
*result = sum;
}
/* Recursive vs non-recursive multiply crossover ranges. */
#if defined(MULDIGITS)
#include "muldigits.h"
#else
#define MUL_BASE_DIGITS 80
#endif
int mul_base_digits = MUL_BASE_DIGITS;
#define MUL_SMALL_DIGITS mul_base_digits/4
/* Multiply utility routines */
static bc_num
new_sub_num (length, scale, value)
int length, scale;
char *value;
{
bc_num temp;
if (_bc_Free_list != NULL) {
temp = _bc_Free_list;
_bc_Free_list = temp->n_next;
} else {
temp = (bc_num) malloc (sizeof(bc_struct));
if (temp == NULL) bc_out_of_memory ();
}
temp->n_sign = PLUS;
temp->n_len = length;
temp->n_scale = scale;
temp->n_refs = 1;
temp->n_ptr = NULL;
temp->n_value = value;
return temp;
}
static void
_bc_simp_mul (bc_num n1, int n1len, bc_num n2, int n2len, bc_num *prod,
int full_scale)
{
char *n1ptr, *n2ptr, *pvptr;
char *n1end, *n2end; /* To the end of n1 and n2. */
int indx, sum, prodlen;
prodlen = n1len+n2len+1;
*prod = bc_new_num (prodlen, 0);
n1end = (char *) (n1->n_value + n1len - 1);
n2end = (char *) (n2->n_value + n2len - 1);
pvptr = (char *) ((*prod)->n_value + prodlen - 1);
sum = 0;
/* Here is the loop... */
for (indx = 0; indx < prodlen-1; indx++)
{
n1ptr = (char *) (n1end - MAX(0, indx-n2len+1));
n2ptr = (char *) (n2end - MIN(indx, n2len-1));
while ((n1ptr >= n1->n_value) && (n2ptr <= n2end))
sum += *n1ptr-- * *n2ptr++;
*pvptr-- = sum % BASE;
sum = sum / BASE;
}
*pvptr = sum;
}
/* A special adder/subtractor for the recursive divide and conquer
multiply algorithm. Note: if sub is called, accum must
be larger that what is being subtracted. Also, accum and val
must have n_scale = 0. (e.g. they must look like integers. *) */
static void
_bc_shift_addsub (bc_num accum, bc_num val, int shift, int sub)
{
signed char *accp, *valp;
int count, carry;
count = val->n_len;
if (val->n_value[0] == 0)
count--;
assert (accum->n_len+accum->n_scale >= shift+count);
/* Set up pointers and others */
accp = (signed char *)(accum->n_value +
accum->n_len + accum->n_scale - shift - 1);
valp = (signed char *)(val->n_value + val->n_len - 1);
carry = 0;
if (sub) {
/* Subtraction, carry is really borrow. */
while (count--) {
*accp -= *valp-- + carry;
if (*accp < 0) {
carry = 1;
*accp-- += BASE;
} else {
carry = 0;
accp--;
}
}
while (carry) {
*accp -= carry;
if (*accp < 0)
*accp-- += BASE;
else
carry = 0;
}
} else {
/* Addition */
while (count--) {
*accp += *valp-- + carry;
if (*accp > (BASE-1)) {
carry = 1;
*accp-- -= BASE;
} else {
carry = 0;
accp--;
}
}
while (carry) {
*accp += carry;
if (*accp > (BASE-1))
*accp-- -= BASE;
else
carry = 0;
}
}
}
/* Recursive divide and conquer multiply algorithm.
Based on
Let u = u0 + u1*(b^n)
Let v = v0 + v1*(b^n)
Then uv = (B^2n+B^n)*u1*v1 + B^n*(u1-u0)*(v0-v1) + (B^n+1)*u0*v0
B is the base of storage, number of digits in u1,u0 close to equal.
*/
static void
_bc_rec_mul (bc_num u, int ulen, bc_num v, int vlen, bc_num *prod,
int full_scale)
{
bc_num u0, u1, v0, v1;
int u0len, v0len;
bc_num m1, m2, m3, d1, d2;
int n, prodlen, m1zero;
int d1len, d2len;
/* Base case? */
if ((ulen+vlen) < mul_base_digits
|| ulen < MUL_SMALL_DIGITS
|| vlen < MUL_SMALL_DIGITS ) {
_bc_simp_mul (u, ulen, v, vlen, prod, full_scale);
return;
}
/* Calculate n -- the u and v split point in digits. */
n = (MAX(ulen, vlen)+1) / 2;
/* Split u and v. */
if (ulen < n) {
u1 = bc_copy_num (_zero_);
u0 = new_sub_num (ulen,0, u->n_value);
} else {
u1 = new_sub_num (ulen-n, 0, u->n_value);
u0 = new_sub_num (n, 0, u->n_value+ulen-n);
}
if (vlen < n) {
v1 = bc_copy_num (_zero_);
v0 = new_sub_num (vlen,0, v->n_value);
} else {
v1 = new_sub_num (vlen-n, 0, v->n_value);
v0 = new_sub_num (n, 0, v->n_value+vlen-n);
}
_bc_rm_leading_zeros (u1);
_bc_rm_leading_zeros (u0);
u0len = u0->n_len;
_bc_rm_leading_zeros (v1);
_bc_rm_leading_zeros (v0);
v0len = v0->n_len;
m1zero = bc_is_zero(u1) || bc_is_zero(v1);
/* Calculate sub results ... */
bc_init_num(&d1);
bc_init_num(&d2);
bc_sub (u1, u0, &d1, 0);
d1len = d1->n_len;
bc_sub (v0, v1, &d2, 0);
d2len = d2->n_len;
/* Do recursive multiplies and shifted adds. */
if (m1zero)
m1 = bc_copy_num (_zero_);
else
_bc_rec_mul (u1, u1->n_len, v1, v1->n_len, &m1, 0);
if (bc_is_zero(d1) || bc_is_zero(d2))
m2 = bc_copy_num (_zero_);
else
_bc_rec_mul (d1, d1len, d2, d2len, &m2, 0);
if (bc_is_zero(u0) || bc_is_zero(v0))
m3 = bc_copy_num (_zero_);
else
_bc_rec_mul (u0, u0->n_len, v0, v0->n_len, &m3, 0);
/* Initialize product */
prodlen = ulen+vlen+1;
*prod = bc_new_num(prodlen, 0);
if (!m1zero) {
_bc_shift_addsub (*prod, m1, 2*n, 0);
_bc_shift_addsub (*prod, m1, n, 0);
}
_bc_shift_addsub (*prod, m3, n, 0);
_bc_shift_addsub (*prod, m3, 0, 0);
_bc_shift_addsub (*prod, m2, n, d1->n_sign != d2->n_sign);
/* Now clean up! */
bc_free_num (&u1);
bc_free_num (&u0);
bc_free_num (&v1);
bc_free_num (&m1);
bc_free_num (&v0);
bc_free_num (&m2);
bc_free_num (&m3);
bc_free_num (&d1);
bc_free_num (&d2);
}
/* The multiply routine. N2 times N1 is put int PROD with the scale of
the result being MIN(N2 scale+N1 scale, MAX (SCALE, N2 scale, N1 scale)).
*/
void
bc_multiply (n1, n2, prod, scale)
bc_num n1, n2, *prod;
int scale;
{
bc_num pval;
int len1, len2;
int full_scale, prod_scale;
/* Initialize things. */
len1 = n1->n_len + n1->n_scale;
len2 = n2->n_len + n2->n_scale;
full_scale = n1->n_scale + n2->n_scale;
prod_scale = MIN(full_scale,MAX(scale,MAX(n1->n_scale,n2->n_scale)));
/* Do the multiply */
_bc_rec_mul (n1, len1, n2, len2, &pval, full_scale);
/* Assign to prod and clean up the number. */
pval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
pval->n_value = pval->n_ptr;
pval->n_len = len2 + len1 + 1 - full_scale;
pval->n_scale = prod_scale;
_bc_rm_leading_zeros (pval);
if (bc_is_zero (pval))
pval->n_sign = PLUS;
bc_free_num (prod);
*prod = pval;
}
/* Some utility routines for the divide: First a one digit multiply.
NUM (with SIZE digits) is multiplied by DIGIT and the result is
placed into RESULT. It is written so that NUM and RESULT can be
the same pointers. */
static void
_one_mult (num, size, digit, result)
unsigned char *num;
int size, digit;
unsigned char *result;
{
int carry, value;
unsigned char *nptr, *rptr;
if (digit == 0)
memset (result, 0, size);
else
{
if (digit == 1)
memcpy (result, num, size);
else
{
/* Initialize */
nptr = (unsigned char *) (num+size-1);
rptr = (unsigned char *) (result+size-1);
carry = 0;
while (size-- > 0)
{
value = *nptr-- * digit + carry;
*rptr-- = value % BASE;
carry = value / BASE;
}
if (carry != 0) *rptr = carry;
}
}
}
/* The full division routine. This computes N1 / N2. It returns
0 if the division is ok and the result is in QUOT. The number of
digits after the decimal point is SCALE. It returns -1 if division
by zero is tried. The algorithm is found in Knuth Vol 2. p237. */
int
bc_divide (n1, n2, quot, scale)
bc_num n1, n2, *quot;
int scale;
{
bc_num qval;
unsigned char *num1, *num2;
unsigned char *ptr1, *ptr2, *n2ptr, *qptr;
int scale1, val;
unsigned int len1, len2, scale2, qdigits, extra, count;
unsigned int qdig, qguess, borrow, carry;
unsigned char *mval;
char zero;
unsigned int norm;
/* Test for divide by zero. */
if (bc_is_zero (n2)) return -1;
/* Test for divide by 1. If it is we must truncate. */
if (n2->n_scale == 0)
{
if (n2->n_len == 1 && *n2->n_value == 1)
{
qval = bc_new_num (n1->n_len, scale);
qval->n_sign = (n1->n_sign == n2->n_sign ? PLUS : MINUS);
memset (&qval->n_value[n1->n_len],0,scale);
memcpy (qval->n_value, n1->n_value,
n1->n_len + MIN(n1->n_scale,scale));
bc_free_num (quot);
*quot = qval;
}
}
/* Set up the divide. Move the decimal point on n1 by n2's scale.
Remember, zeros on the end of num2 are wasted effort for dividing. */
scale2 = n2->n_scale;
n2ptr = (unsigned char *) n2->n_value+n2->n_len+scale2-1;
while ((scale2 > 0) && (*n2ptr-- == 0)) scale2--;
len1 = n1->n_len + scale2;
scale1 = n1->n_scale - scale2;
if (scale1 < scale)
extra = scale - scale1;