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. (LICENSE)
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 "bcmath.h"
33 #include <stddef.h>
34 #include <assert.h>
35 #include <stdbool.h>
36 #include "private.h" /* For _bc_rm_leading_zeros() */
37 #include "zend_alloc.h"
38
39 /* Recursive vs non-recursive multiply crossover ranges. */
40 #if defined(MULDIGITS)
41 #include "muldigits.h"
42 #else
43 #define MUL_BASE_DIGITS 80
44 #endif
45
46 int mul_base_digits = MUL_BASE_DIGITS;
47 #define MUL_SMALL_DIGITS mul_base_digits/4
48
49 /* Multiply utility routines */
50
new_sub_num(size_t length,size_t scale,char * value)51 static bc_num new_sub_num(size_t length, size_t scale, char *value)
52 {
53 bc_num temp = (bc_num) emalloc(sizeof(bc_struct));
54
55 temp->n_sign = PLUS;
56 temp->n_len = length;
57 temp->n_scale = scale;
58 temp->n_refs = 1;
59 temp->n_ptr = NULL;
60 temp->n_value = value;
61 return temp;
62 }
63
_bc_simp_mul(bc_num n1,size_t n1len,bc_num n2,int n2len,bc_num * prod)64 static void _bc_simp_mul(bc_num n1, size_t n1len, bc_num n2, int n2len, bc_num *prod)
65 {
66 char *n1ptr, *n2ptr, *pvptr;
67 char *n1end, *n2end; /* To the end of n1 and n2. */
68 int sum = 0;
69
70 int prodlen = n1len + n2len + 1;
71
72 *prod = bc_new_num (prodlen, 0);
73
74 n1end = (char *) (n1->n_value + n1len - 1);
75 n2end = (char *) (n2->n_value + n2len - 1);
76 pvptr = (char *) ((*prod)->n_value + prodlen - 1);
77
78 /* Here is the loop... */
79 for (int index = 0; index < prodlen - 1; index++) {
80 n1ptr = (char *) (n1end - MAX(0, index - n2len + 1));
81 n2ptr = (char *) (n2end - MIN(index, n2len - 1));
82 while ((n1ptr >= n1->n_value) && (n2ptr <= n2end)) {
83 sum += *n1ptr * *n2ptr;
84 n1ptr--;
85 n2ptr++;
86 }
87 *pvptr-- = sum % BASE;
88 sum = sum / BASE;
89 }
90 *pvptr = sum;
91 }
92
93
94 /* A special adder/subtractor for the recursive divide and conquer
95 multiply algorithm. Note: if sub is called, accum must
96 be larger that what is being subtracted. Also, accum and val
97 must have n_scale = 0. (e.g. they must look like integers. *) */
_bc_shift_addsub(bc_num accum,bc_num val,int shift,bool sub)98 static void _bc_shift_addsub(bc_num accum, bc_num val, int shift, bool sub)
99 {
100 signed char *accp, *valp;
101 unsigned int carry = 0;
102 size_t count = val->n_len;
103
104 if (val->n_value[0] == 0) {
105 count--;
106 }
107 assert(accum->n_len + accum->n_scale >= shift + count);
108
109 /* Set up pointers and others */
110 accp = (signed char *) (accum->n_value + accum->n_len + accum->n_scale - shift - 1);
111 valp = (signed char *) (val->n_value + val->n_len - 1);
112
113 if (sub) {
114 /* Subtraction, carry is really borrow. */
115 while (count--) {
116 *accp -= *valp-- + carry;
117 if (*accp < 0) {
118 carry = 1;
119 *accp-- += BASE;
120 } else {
121 carry = 0;
122 accp--;
123 }
124 }
125 while (carry) {
126 *accp -= carry;
127 if (*accp < 0) {
128 *accp-- += BASE;
129 } else {
130 carry = 0;
131 }
132 }
133 } else {
134 /* Addition */
135 while (count--) {
136 *accp += *valp-- + carry;
137 if (*accp > (BASE - 1)) {
138 carry = 1;
139 *accp-- -= BASE;
140 } else {
141 carry = 0;
142 accp--;
143 }
144 }
145 while (carry) {
146 *accp += carry;
147 if (*accp > (BASE - 1)) {
148 *accp-- -= BASE;
149 } else {
150 carry = 0;
151 }
152 }
153 }
154 }
155
156 /* Recursive divide and conquer multiply algorithm.
157 Based on
158 Let u = u0 + u1*(b^n)
159 Let v = v0 + v1*(b^n)
160 Then uv = (B^2n+B^n)*u1*v1 + B^n*(u1-u0)*(v0-v1) + (B^n+1)*u0*v0
161
162 B is the base of storage, number of digits in u1,u0 close to equal.
163 */
_bc_rec_mul(bc_num u,size_t ulen,bc_num v,size_t vlen,bc_num * prod)164 static void _bc_rec_mul(bc_num u, size_t ulen, bc_num v, size_t vlen, bc_num *prod)
165 {
166 bc_num u0, u1, v0, v1;
167 bc_num m1, m2, m3, d1, d2;
168 size_t n;
169 bool m1zero;
170
171 /* Base case? */
172 if ((ulen + vlen) < mul_base_digits
173 || ulen < MUL_SMALL_DIGITS
174 || vlen < MUL_SMALL_DIGITS
175 ) {
176 _bc_simp_mul(u, ulen, v, vlen, prod);
177 return;
178 }
179
180 /* Calculate n -- the u and v split point in digits. */
181 n = (MAX(ulen, vlen) + 1) / 2;
182
183 /* Split u and v. */
184 if (ulen < n) {
185 u1 = bc_copy_num(BCG(_zero_));
186 u0 = new_sub_num(ulen, 0, u->n_value);
187 } else {
188 u1 = new_sub_num(ulen - n, 0, u->n_value);
189 u0 = new_sub_num(n, 0, u->n_value + ulen - n);
190 }
191 if (vlen < n) {
192 v1 = bc_copy_num(BCG(_zero_));
193 v0 = new_sub_num(vlen, 0, v->n_value);
194 } else {
195 v1 = new_sub_num(vlen - n, 0, v->n_value);
196 v0 = new_sub_num(n, 0, v->n_value + vlen - n);
197 }
198 _bc_rm_leading_zeros(u1);
199 _bc_rm_leading_zeros(u0);
200 _bc_rm_leading_zeros(v1);
201 _bc_rm_leading_zeros(v0);
202
203 m1zero = bc_is_zero(u1) || bc_is_zero(v1);
204
205 /* Calculate sub results ... */
206
207 bc_init_num(&d1);
208 bc_init_num(&d2);
209 bc_sub(u1, u0, &d1, 0);
210 bc_sub(v0, v1, &d2, 0);
211
212
213 /* Do recursive multiplies and shifted adds. */
214 if (m1zero) {
215 m1 = bc_copy_num(BCG(_zero_));
216 } else {
217 _bc_rec_mul(u1, u1->n_len, v1, v1->n_len, &m1);
218 }
219
220 if (bc_is_zero(d1) || bc_is_zero(d2)) {
221 m2 = bc_copy_num(BCG(_zero_));
222 } else {
223 _bc_rec_mul(d1, d1->n_len, d2, d2->n_len, &m2);
224 }
225
226 if (bc_is_zero(u0) || bc_is_zero(v0)) {
227 m3 = bc_copy_num(BCG(_zero_));
228 } else {
229 _bc_rec_mul(u0, u0->n_len, v0, v0->n_len, &m3);
230 }
231
232 /* Initialize product */
233 *prod = bc_new_num(ulen + vlen + 1, 0);
234
235 if (!m1zero) {
236 _bc_shift_addsub(*prod, m1, 2 * n, false);
237 _bc_shift_addsub(*prod, m1, n, false);
238 }
239 _bc_shift_addsub(*prod, m3, n, false);
240 _bc_shift_addsub(*prod, m3, 0, false);
241 _bc_shift_addsub(*prod, m2, n, d1->n_sign != d2->n_sign);
242
243 /* Now clean up! */
244 bc_free_num (&u1);
245 bc_free_num (&u0);
246 bc_free_num (&v1);
247 bc_free_num (&m1);
248 bc_free_num (&v0);
249 bc_free_num (&m2);
250 bc_free_num (&m3);
251 bc_free_num (&d1);
252 bc_free_num (&d2);
253 }
254
255 /* The multiply routine. N2 times N1 is put int PROD with the scale of
256 the result being MIN(N2 scale+N1 scale, MAX (SCALE, N2 scale, N1 scale)).
257 */
258
bc_multiply(bc_num n1,bc_num n2,bc_num * prod,size_t scale)259 void bc_multiply(bc_num n1, bc_num n2, bc_num *prod, size_t scale)
260 {
261 bc_num pval;
262 size_t len1, len2;
263 size_t full_scale, prod_scale;
264
265 /* Initialize things. */
266 len1 = n1->n_len + n1->n_scale;
267 len2 = n2->n_len + n2->n_scale;
268 full_scale = n1->n_scale + n2->n_scale;
269 prod_scale = MIN(full_scale, MAX(scale, MAX(n1->n_scale, n2->n_scale)));
270
271 /* Do the multiply */
272 _bc_rec_mul(n1, len1, n2, len2, &pval);
273
274 /* Assign to prod and clean up the number. */
275 pval->n_sign = (n1->n_sign == n2->n_sign ? PLUS : MINUS);
276 pval->n_value = pval->n_ptr;
277 pval->n_len = len2 + len1 + 1 - full_scale;
278 pval->n_scale = prod_scale;
279 _bc_rm_leading_zeros(pval);
280 if (bc_is_zero(pval)) {
281 pval->n_sign = PLUS;
282 }
283 bc_free_num(prod);
284 *prod = pval;
285 }
286
