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
new_sub_num(length,scale,value)54 new_sub_num (length, scale, value)
55 int length, scale;
56 char *value;
57 {
58 bc_num temp;
59
60 temp = (bc_num) emalloc (sizeof(bc_struct));
61
62 temp->n_sign = PLUS;
63 temp->n_len = length;
64 temp->n_scale = scale;
65 temp->n_refs = 1;
66 temp->n_ptr = NULL;
67 temp->n_value = value;
68 return temp;
69 }
70
71 static void
_bc_simp_mul(bc_num n1,int n1len,bc_num n2,int n2len,bc_num * prod,int full_scale)72 _bc_simp_mul (bc_num n1, int n1len, bc_num n2, int n2len, bc_num *prod,
73 int full_scale)
74 {
75 char *n1ptr, *n2ptr, *pvptr;
76 char *n1end, *n2end; /* To the end of n1 and n2. */
77 int indx, sum, prodlen;
78
79 prodlen = n1len+n2len+1;
80
81 *prod = bc_new_num (prodlen, 0);
82
83 n1end = (char *) (n1->n_value + n1len - 1);
84 n2end = (char *) (n2->n_value + n2len - 1);
85 pvptr = (char *) ((*prod)->n_value + prodlen - 1);
86 sum = 0;
87
88 /* Here is the loop... */
89 for (indx = 0; indx < prodlen-1; indx++)
90 {
91 n1ptr = (char *) (n1end - MAX(0, indx-n2len+1));
92 n2ptr = (char *) (n2end - MIN(indx, n2len-1));
93 while ((n1ptr >= n1->n_value) && (n2ptr <= n2end))
94 sum += *n1ptr-- * *n2ptr++;
95 *pvptr-- = sum % BASE;
96 sum = sum / BASE;
97 }
98 *pvptr = sum;
99 }
100
101
102 /* A special adder/subtractor for the recursive divide and conquer
103 multiply algorithm. Note: if sub is called, accum must
104 be larger that what is being subtracted. Also, accum and val
105 must have n_scale = 0. (e.g. they must look like integers. *) */
106 static void
_bc_shift_addsub(bc_num accum,bc_num val,int shift,int sub)107 _bc_shift_addsub (bc_num accum, bc_num val, int shift, int sub)
108 {
109 signed char *accp, *valp;
110 int count, carry;
111
112 count = val->n_len;
113 if (val->n_value[0] == 0)
114 count--;
115 assert (accum->n_len+accum->n_scale >= shift+count);
116
117 /* Set up pointers and others */
118 accp = (signed char *)(accum->n_value +
119 accum->n_len + accum->n_scale - shift - 1);
120 valp = (signed char *)(val->n_value + val->n_len - 1);
121 carry = 0;
122
123 if (sub) {
124 /* Subtraction, carry is really borrow. */
125 while (count--) {
126 *accp -= *valp-- + carry;
127 if (*accp < 0) {
128 carry = 1;
129 *accp-- += BASE;
130 } else {
131 carry = 0;
132 accp--;
133 }
134 }
135 while (carry) {
136 *accp -= carry;
137 if (*accp < 0)
138 *accp-- += BASE;
139 else
140 carry = 0;
141 }
142 } else {
143 /* Addition */
144 while (count--) {
145 *accp += *valp-- + carry;
146 if (*accp > (BASE-1)) {
147 carry = 1;
148 *accp-- -= BASE;
149 } else {
150 carry = 0;
151 accp--;
152 }
153 }
154 while (carry) {
155 *accp += carry;
156 if (*accp > (BASE-1))
157 *accp-- -= BASE;
158 else
159 carry = 0;
160 }
161 }
162 }
163
164 /* Recursive divide and conquer multiply algorithm.
165 Based on
166 Let u = u0 + u1*(b^n)
167 Let v = v0 + v1*(b^n)
168 Then uv = (B^2n+B^n)*u1*v1 + B^n*(u1-u0)*(v0-v1) + (B^n+1)*u0*v0
169
170 B is the base of storage, number of digits in u1,u0 close to equal.
171 */
172 static void
_bc_rec_mul(bc_num u,int ulen,bc_num v,int vlen,bc_num * prod,int full_scale)173 _bc_rec_mul (bc_num u, int ulen, bc_num v, int vlen, bc_num *prod,
174 int full_scale)
175 {
176 bc_num u0, u1, v0, v1;
177 bc_num m1, m2, m3, d1, d2;
178 int n, prodlen, m1zero;
179 int d1len, d2len;
180
181 /* Base case? */
182 if ((ulen+vlen) < mul_base_digits
183 || ulen < MUL_SMALL_DIGITS
184 || vlen < MUL_SMALL_DIGITS ) {
185 _bc_simp_mul (u, ulen, v, vlen, prod, full_scale);
186 return;
187 }
188
189 /* Calculate n -- the u and v split point in digits. */
190 n = (MAX(ulen, vlen)+1) / 2;
191
192 /* Split u and v. */
193 if (ulen < n) {
194 u1 = bc_copy_num (BCG(_zero_));
195 u0 = new_sub_num (ulen,0, u->n_value);
196 } else {
197 u1 = new_sub_num (ulen-n, 0, u->n_value);
198 u0 = new_sub_num (n, 0, u->n_value+ulen-n);
199 }
200 if (vlen < n) {
201 v1 = bc_copy_num (BCG(_zero_));
202 v0 = new_sub_num (vlen,0, v->n_value);
203 } else {
204 v1 = new_sub_num (vlen-n, 0, v->n_value);
205 v0 = new_sub_num (n, 0, v->n_value+vlen-n);
206 }
207 _bc_rm_leading_zeros (u1);
208 _bc_rm_leading_zeros (u0);
209 _bc_rm_leading_zeros (v1);
210 _bc_rm_leading_zeros (v0);
211
212 m1zero = bc_is_zero(u1) || bc_is_zero(v1);
213
214 /* Calculate sub results ... */
215
216 bc_init_num(&d1);
217 bc_init_num(&d2);
218 bc_sub (u1, u0, &d1, 0);
219 d1len = d1->n_len;
220 bc_sub (v0, v1, &d2, 0);
221 d2len = d2->n_len;
222
223
224 /* Do recursive multiplies and shifted adds. */
225 if (m1zero)
226 m1 = bc_copy_num (BCG(_zero_));
227 else
228 _bc_rec_mul (u1, u1->n_len, v1, v1->n_len, &m1, 0);
229
230 if (bc_is_zero(d1) || bc_is_zero(d2))
231 m2 = bc_copy_num (BCG(_zero_));
232 else
233 _bc_rec_mul (d1, d1len, d2, d2len, &m2, 0);
234
235 if (bc_is_zero(u0) || bc_is_zero(v0))
236 m3 = bc_copy_num (BCG(_zero_));
237 else
238 _bc_rec_mul (u0, u0->n_len, v0, v0->n_len, &m3, 0);
239
240 /* Initialize product */
241 prodlen = ulen+vlen+1;
242 *prod = bc_new_num(prodlen, 0);
243
244 if (!m1zero) {
245 _bc_shift_addsub (*prod, m1, 2*n, 0);
246 _bc_shift_addsub (*prod, m1, n, 0);
247 }
248 _bc_shift_addsub (*prod, m3, n, 0);
249 _bc_shift_addsub (*prod, m3, 0, 0);
250 _bc_shift_addsub (*prod, m2, n, d1->n_sign != d2->n_sign);
251
252 /* Now clean up! */
253 bc_free_num (&u1);
254 bc_free_num (&u0);
255 bc_free_num (&v1);
256 bc_free_num (&m1);
257 bc_free_num (&v0);
258 bc_free_num (&m2);
259 bc_free_num (&m3);
260 bc_free_num (&d1);
261 bc_free_num (&d2);
262 }
263
264 /* The multiply routine. N2 times N1 is put int PROD with the scale of
265 the result being MIN(N2 scale+N1 scale, MAX (SCALE, N2 scale, N1 scale)).
266 */
267
268 void
bc_multiply(bc_num n1,bc_num n2,bc_num * prod,int scale)269 bc_multiply (bc_num n1, bc_num n2, bc_num *prod, int scale)
270 {
271 bc_num pval;
272 int len1, len2;
273 int full_scale, prod_scale;
274
275 /* Initialize things. */
276 len1 = n1->n_len + n1->n_scale;
277 len2 = n2->n_len + n2->n_scale;
278 full_scale = n1->n_scale + n2->n_scale;
279 prod_scale = MIN(full_scale,MAX(scale,MAX(n1->n_scale,n2->n_scale)));
280
281 /* Do the multiply */
282 _bc_rec_mul (n1, len1, n2, len2, &pval, full_scale);
283
284 /* Assign to prod and clean up the number. */
285 pval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
286 pval->n_value = pval->n_ptr;
287 pval->n_len = len2 + len1 + 1 - full_scale;
288 pval->n_scale = prod_scale;
289 _bc_rm_leading_zeros (pval);
290 if (bc_is_zero (pval))
291 pval->n_sign = PLUS;
292 bc_free_num (prod);
293 *prod = pval;
294 }
295
