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authorLorry Tar Creator <lorry-tar-importer@baserock.org>2013-03-14 05:42:27 +0000
committer <>2013-04-03 16:25:08 +0000
commitc4dd7a1a684490673e25aaf4fabec5df138854c4 (patch)
tree4d57c44caae4480efff02b90b9be86f44bf25409 /ext/bcmath/libbcmath/src/recmul.c
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+/* 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;
+ 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 (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);
+ u0len = u0->n_len;
+ _bc_rm_leading_zeros (v1);
+ _bc_rm_leading_zeros (v0);
+ v0len = v0->n_len;
+
+ 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;
+}