Annotation of embedaddon/php/ext/bcmath/libbcmath/src/recmul.c, revision 1.1.1.1
1.1 misho 1: /* recmul.c: bcmath library file. */
2: /*
3: Copyright (C) 1991, 1992, 1993, 1994, 1997 Free Software Foundation, Inc.
4: Copyright (C) 2000 Philip A. Nelson
5:
6: This library is free software; you can redistribute it and/or
7: modify it under the terms of the GNU Lesser General Public
8: License as published by the Free Software Foundation; either
9: version 2 of the License, or (at your option) any later version.
10:
11: This library is distributed in the hope that it will be useful,
12: but WITHOUT ANY WARRANTY; without even the implied warranty of
13: MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14: Lesser General Public License for more details. (COPYING.LIB)
15:
16: You should have received a copy of the GNU Lesser General Public
17: License along with this library; if not, write to:
18:
19: The Free Software Foundation, Inc.
20: 59 Temple Place, Suite 330
21: Boston, MA 02111-1307 USA.
22:
23: You may contact the author by:
24: e-mail: philnelson@acm.org
25: us-mail: Philip A. Nelson
26: Computer Science Department, 9062
27: Western Washington University
28: Bellingham, WA 98226-9062
29:
30: *************************************************************************/
31:
32: #include <config.h>
33: #include <stdio.h>
34: #include <assert.h>
35: #include <stdlib.h>
36: #include <ctype.h>
37: #include <stdarg.h>
38: #include "bcmath.h"
39: #include "private.h"
40:
41: /* Recursive vs non-recursive multiply crossover ranges. */
42: #if defined(MULDIGITS)
43: #include "muldigits.h"
44: #else
45: #define MUL_BASE_DIGITS 80
46: #endif
47:
48: int mul_base_digits = MUL_BASE_DIGITS;
49: #define MUL_SMALL_DIGITS mul_base_digits/4
50:
51: /* Multiply utility routines */
52:
53: static bc_num
54: new_sub_num (length, scale, value)
55: int length, scale;
56: char *value;
57: {
58: bc_num temp;
59:
60: #ifdef SANDER_0
61: if (_bc_Free_list != NULL) {
62: temp = _bc_Free_list;
63: _bc_Free_list = temp->n_next;
64: } else {
65: #endif
66: temp = (bc_num) emalloc (sizeof(bc_struct));
67: #ifdef SANDER_0
68: if (temp == NULL) bc_out_of_memory ();
69: }
70: #endif
71: temp->n_sign = PLUS;
72: temp->n_len = length;
73: temp->n_scale = scale;
74: temp->n_refs = 1;
75: temp->n_ptr = NULL;
76: temp->n_value = value;
77: return temp;
78: }
79:
80: static void
81: _bc_simp_mul (bc_num n1, int n1len, bc_num n2, int n2len, bc_num *prod,
82: int full_scale)
83: {
84: char *n1ptr, *n2ptr, *pvptr;
85: char *n1end, *n2end; /* To the end of n1 and n2. */
86: int indx, sum, prodlen;
87:
88: prodlen = n1len+n2len+1;
89:
90: *prod = bc_new_num (prodlen, 0);
91:
92: n1end = (char *) (n1->n_value + n1len - 1);
93: n2end = (char *) (n2->n_value + n2len - 1);
94: pvptr = (char *) ((*prod)->n_value + prodlen - 1);
95: sum = 0;
96:
97: /* Here is the loop... */
98: for (indx = 0; indx < prodlen-1; indx++)
99: {
100: n1ptr = (char *) (n1end - MAX(0, indx-n2len+1));
101: n2ptr = (char *) (n2end - MIN(indx, n2len-1));
102: while ((n1ptr >= n1->n_value) && (n2ptr <= n2end))
103: sum += *n1ptr-- * *n2ptr++;
104: *pvptr-- = sum % BASE;
105: sum = sum / BASE;
106: }
107: *pvptr = sum;
108: }
109:
110:
111: /* A special adder/subtractor for the recursive divide and conquer
112: multiply algorithm. Note: if sub is called, accum must
113: be larger that what is being subtracted. Also, accum and val
114: must have n_scale = 0. (e.g. they must look like integers. *) */
115: static void
116: _bc_shift_addsub (bc_num accum, bc_num val, int shift, int sub)
117: {
118: signed char *accp, *valp;
119: int count, carry;
120:
121: count = val->n_len;
122: if (val->n_value[0] == 0)
123: count--;
124: assert (accum->n_len+accum->n_scale >= shift+count);
125:
126: /* Set up pointers and others */
127: accp = (signed char *)(accum->n_value +
128: accum->n_len + accum->n_scale - shift - 1);
129: valp = (signed char *)(val->n_value + val->n_len - 1);
130: carry = 0;
131:
132: if (sub) {
133: /* Subtraction, carry is really borrow. */
134: while (count--) {
135: *accp -= *valp-- + carry;
136: if (*accp < 0) {
137: carry = 1;
138: *accp-- += BASE;
139: } else {
140: carry = 0;
141: accp--;
142: }
143: }
144: while (carry) {
145: *accp -= carry;
146: if (*accp < 0)
147: *accp-- += BASE;
148: else
149: carry = 0;
150: }
151: } else {
152: /* Addition */
153: while (count--) {
154: *accp += *valp-- + carry;
155: if (*accp > (BASE-1)) {
156: carry = 1;
157: *accp-- -= BASE;
158: } else {
159: carry = 0;
160: accp--;
161: }
162: }
163: while (carry) {
164: *accp += carry;
165: if (*accp > (BASE-1))
166: *accp-- -= BASE;
167: else
168: carry = 0;
169: }
170: }
171: }
172:
173: /* Recursive divide and conquer multiply algorithm.
174: Based on
175: Let u = u0 + u1*(b^n)
176: Let v = v0 + v1*(b^n)
177: Then uv = (B^2n+B^n)*u1*v1 + B^n*(u1-u0)*(v0-v1) + (B^n+1)*u0*v0
178:
179: B is the base of storage, number of digits in u1,u0 close to equal.
180: */
181: static void
182: _bc_rec_mul (bc_num u, int ulen, bc_num v, int vlen, bc_num *prod,
183: int full_scale TSRMLS_DC)
184: {
185: bc_num u0, u1, v0, v1;
186: int u0len, v0len;
187: bc_num m1, m2, m3, d1, d2;
188: int n, prodlen, m1zero;
189: int d1len, d2len;
190:
191: /* Base case? */
192: if ((ulen+vlen) < mul_base_digits
193: || ulen < MUL_SMALL_DIGITS
194: || vlen < MUL_SMALL_DIGITS ) {
195: _bc_simp_mul (u, ulen, v, vlen, prod, full_scale);
196: return;
197: }
198:
199: /* Calculate n -- the u and v split point in digits. */
200: n = (MAX(ulen, vlen)+1) / 2;
201:
202: /* Split u and v. */
203: if (ulen < n) {
204: u1 = bc_copy_num (BCG(_zero_));
205: u0 = new_sub_num (ulen,0, u->n_value);
206: } else {
207: u1 = new_sub_num (ulen-n, 0, u->n_value);
208: u0 = new_sub_num (n, 0, u->n_value+ulen-n);
209: }
210: if (vlen < n) {
211: v1 = bc_copy_num (BCG(_zero_));
212: v0 = new_sub_num (vlen,0, v->n_value);
213: } else {
214: v1 = new_sub_num (vlen-n, 0, v->n_value);
215: v0 = new_sub_num (n, 0, v->n_value+vlen-n);
216: }
217: _bc_rm_leading_zeros (u1);
218: _bc_rm_leading_zeros (u0);
219: u0len = u0->n_len;
220: _bc_rm_leading_zeros (v1);
221: _bc_rm_leading_zeros (v0);
222: v0len = v0->n_len;
223:
224: m1zero = bc_is_zero(u1 TSRMLS_CC) || bc_is_zero(v1 TSRMLS_CC);
225:
226: /* Calculate sub results ... */
227:
228: bc_init_num(&d1 TSRMLS_CC);
229: bc_init_num(&d2 TSRMLS_CC);
230: bc_sub (u1, u0, &d1, 0);
231: d1len = d1->n_len;
232: bc_sub (v0, v1, &d2, 0);
233: d2len = d2->n_len;
234:
235:
236: /* Do recursive multiplies and shifted adds. */
237: if (m1zero)
238: m1 = bc_copy_num (BCG(_zero_));
239: else
240: _bc_rec_mul (u1, u1->n_len, v1, v1->n_len, &m1, 0 TSRMLS_CC);
241:
242: if (bc_is_zero(d1 TSRMLS_CC) || bc_is_zero(d2 TSRMLS_CC))
243: m2 = bc_copy_num (BCG(_zero_));
244: else
245: _bc_rec_mul (d1, d1len, d2, d2len, &m2, 0 TSRMLS_CC);
246:
247: if (bc_is_zero(u0 TSRMLS_CC) || bc_is_zero(v0 TSRMLS_CC))
248: m3 = bc_copy_num (BCG(_zero_));
249: else
250: _bc_rec_mul (u0, u0->n_len, v0, v0->n_len, &m3, 0 TSRMLS_CC);
251:
252: /* Initialize product */
253: prodlen = ulen+vlen+1;
254: *prod = bc_new_num(prodlen, 0);
255:
256: if (!m1zero) {
257: _bc_shift_addsub (*prod, m1, 2*n, 0);
258: _bc_shift_addsub (*prod, m1, n, 0);
259: }
260: _bc_shift_addsub (*prod, m3, n, 0);
261: _bc_shift_addsub (*prod, m3, 0, 0);
262: _bc_shift_addsub (*prod, m2, n, d1->n_sign != d2->n_sign);
263:
264: /* Now clean up! */
265: bc_free_num (&u1);
266: bc_free_num (&u0);
267: bc_free_num (&v1);
268: bc_free_num (&m1);
269: bc_free_num (&v0);
270: bc_free_num (&m2);
271: bc_free_num (&m3);
272: bc_free_num (&d1);
273: bc_free_num (&d2);
274: }
275:
276: /* The multiply routine. N2 times N1 is put int PROD with the scale of
277: the result being MIN(N2 scale+N1 scale, MAX (SCALE, N2 scale, N1 scale)).
278: */
279:
280: void
281: bc_multiply (bc_num n1, bc_num n2, bc_num *prod, int scale TSRMLS_DC)
282: {
283: bc_num pval;
284: int len1, len2;
285: int full_scale, prod_scale;
286:
287: /* Initialize things. */
288: len1 = n1->n_len + n1->n_scale;
289: len2 = n2->n_len + n2->n_scale;
290: full_scale = n1->n_scale + n2->n_scale;
291: prod_scale = MIN(full_scale,MAX(scale,MAX(n1->n_scale,n2->n_scale)));
292:
293: /* Do the multiply */
294: _bc_rec_mul (n1, len1, n2, len2, &pval, full_scale TSRMLS_CC);
295:
296: /* Assign to prod and clean up the number. */
297: pval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
298: pval->n_value = pval->n_ptr;
299: pval->n_len = len2 + len1 + 1 - full_scale;
300: pval->n_scale = prod_scale;
301: _bc_rm_leading_zeros (pval);
302: if (bc_is_zero (pval TSRMLS_CC))
303: pval->n_sign = PLUS;
304: bc_free_num (prod);
305: *prod = pval;
306: }
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