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DEFINITIONS
This source file includes following definitions.
- new_sub_num
- _bc_simp_mul
- _bc_shift_addsub
- _bc_rec_mul
- bc_multiply
/* recmul.c: bcmath library file. */
/*
Copyright (C) 1991, 1992, 1993, 1994, 1997 Free Software Foundation, Inc.
Copyright (C) 2000 Philip A. Nelson
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2 of the License, or (at your option) any later version.
This library 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
Lesser General Public License for more details. (COPYING.LIB)
You should have received a copy of the GNU Lesser General Public
License along with this library; 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 <config.h>
#include <stdio.h>
#include <assert.h>
#include <stdlib.h>
#include <ctype.h>
#include <stdarg.h>
#include "bcmath.h"
#include "private.h"
/* 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;
#ifdef SANDER_0
if (_bc_Free_list != NULL) {
temp = _bc_Free_list;
_bc_Free_list = temp->n_next;
} else {
#endif
temp = (bc_num) emalloc (sizeof(bc_struct));
#ifdef SANDER_0
if (temp == NULL) bc_out_of_memory ();
}
#endif
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 TSRMLS_DC)
{
bc_num u0, u1, v0, v1;
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 (BCG(_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 (BCG(_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);
_bc_rm_leading_zeros (v1);
_bc_rm_leading_zeros (v0);
m1zero = bc_is_zero(u1 TSRMLS_CC) || bc_is_zero(v1 TSRMLS_CC);
/* Calculate sub results ... */
bc_init_num(&d1 TSRMLS_CC);
bc_init_num(&d2 TSRMLS_CC);
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 (BCG(_zero_));
else
_bc_rec_mul (u1, u1->n_len, v1, v1->n_len, &m1, 0 TSRMLS_CC);
if (bc_is_zero(d1 TSRMLS_CC) || bc_is_zero(d2 TSRMLS_CC))
m2 = bc_copy_num (BCG(_zero_));
else
_bc_rec_mul (d1, d1len, d2, d2len, &m2, 0 TSRMLS_CC);
if (bc_is_zero(u0 TSRMLS_CC) || bc_is_zero(v0 TSRMLS_CC))
m3 = bc_copy_num (BCG(_zero_));
else
_bc_rec_mul (u0, u0->n_len, v0, v0->n_len, &m3, 0 TSRMLS_CC);
/* 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 (bc_num n1, bc_num n2, bc_num *prod, int scale TSRMLS_DC)
{
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 TSRMLS_CC);
/* 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 TSRMLS_CC))
pval->n_sign = PLUS;
bc_free_num (prod);
*prod = pval;
}