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 #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
_bc_simp_mul(bc_num n1,int n1len,bc_num n2,int n2len,bc_num * prod,int full_scale)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
_bc_shift_addsub(bc_num accum,bc_num val,int shift,int sub)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
_bc_rec_mul(bc_num u,int ulen,bc_num v,int vlen,bc_num * prod,int full_scale)182 _bc_rec_mul (bc_num u, int ulen, bc_num v, int vlen, bc_num *prod,
183 int full_scale)
184 {
185 bc_num u0, u1, v0, v1;
186 bc_num m1, m2, m3, d1, d2;
187 int n, prodlen, m1zero;
188 int d1len, d2len;
189
190 /* Base case? */
191 if ((ulen+vlen) < mul_base_digits
192 || ulen < MUL_SMALL_DIGITS
193 || vlen < MUL_SMALL_DIGITS ) {
194 _bc_simp_mul (u, ulen, v, vlen, prod, full_scale);
195 return;
196 }
197
198 /* Calculate n -- the u and v split point in digits. */
199 n = (MAX(ulen, vlen)+1) / 2;
200
201 /* Split u and v. */
202 if (ulen < n) {
203 u1 = bc_copy_num (BCG(_zero_));
204 u0 = new_sub_num (ulen,0, u->n_value);
205 } else {
206 u1 = new_sub_num (ulen-n, 0, u->n_value);
207 u0 = new_sub_num (n, 0, u->n_value+ulen-n);
208 }
209 if (vlen < n) {
210 v1 = bc_copy_num (BCG(_zero_));
211 v0 = new_sub_num (vlen,0, v->n_value);
212 } else {
213 v1 = new_sub_num (vlen-n, 0, v->n_value);
214 v0 = new_sub_num (n, 0, v->n_value+vlen-n);
215 }
216 _bc_rm_leading_zeros (u1);
217 _bc_rm_leading_zeros (u0);
218 _bc_rm_leading_zeros (v1);
219 _bc_rm_leading_zeros (v0);
220
221 m1zero = bc_is_zero(u1) || bc_is_zero(v1);
222
223 /* Calculate sub results ... */
224
225 bc_init_num(&d1);
226 bc_init_num(&d2);
227 bc_sub (u1, u0, &d1, 0);
228 d1len = d1->n_len;
229 bc_sub (v0, v1, &d2, 0);
230 d2len = d2->n_len;
231
232
233 /* Do recursive multiplies and shifted adds. */
234 if (m1zero)
235 m1 = bc_copy_num (BCG(_zero_));
236 else
237 _bc_rec_mul (u1, u1->n_len, v1, v1->n_len, &m1, 0);
238
239 if (bc_is_zero(d1) || bc_is_zero(d2))
240 m2 = bc_copy_num (BCG(_zero_));
241 else
242 _bc_rec_mul (d1, d1len, d2, d2len, &m2, 0);
243
244 if (bc_is_zero(u0) || bc_is_zero(v0))
245 m3 = bc_copy_num (BCG(_zero_));
246 else
247 _bc_rec_mul (u0, u0->n_len, v0, v0->n_len, &m3, 0);
248
249 /* Initialize product */
250 prodlen = ulen+vlen+1;
251 *prod = bc_new_num(prodlen, 0);
252
253 if (!m1zero) {
254 _bc_shift_addsub (*prod, m1, 2*n, 0);
255 _bc_shift_addsub (*prod, m1, n, 0);
256 }
257 _bc_shift_addsub (*prod, m3, n, 0);
258 _bc_shift_addsub (*prod, m3, 0, 0);
259 _bc_shift_addsub (*prod, m2, n, d1->n_sign != d2->n_sign);
260
261 /* Now clean up! */
262 bc_free_num (&u1);
263 bc_free_num (&u0);
264 bc_free_num (&v1);
265 bc_free_num (&m1);
266 bc_free_num (&v0);
267 bc_free_num (&m2);
268 bc_free_num (&m3);
269 bc_free_num (&d1);
270 bc_free_num (&d2);
271 }
272
273 /* The multiply routine. N2 times N1 is put int PROD with the scale of
274 the result being MIN(N2 scale+N1 scale, MAX (SCALE, N2 scale, N1 scale)).
275 */
276
277 void
bc_multiply(bc_num n1,bc_num n2,bc_num * prod,int scale)278 bc_multiply (bc_num n1, bc_num n2, bc_num *prod, int scale)
279 {
280 bc_num pval;
281 int len1, len2;
282 int full_scale, prod_scale;
283
284 /* Initialize things. */
285 len1 = n1->n_len + n1->n_scale;
286 len2 = n2->n_len + n2->n_scale;
287 full_scale = n1->n_scale + n2->n_scale;
288 prod_scale = MIN(full_scale,MAX(scale,MAX(n1->n_scale,n2->n_scale)));
289
290 /* Do the multiply */
291 _bc_rec_mul (n1, len1, n2, len2, &pval, full_scale);
292
293 /* Assign to prod and clean up the number. */
294 pval->n_sign = ( n1->n_sign == n2->n_sign ? PLUS : MINUS );
295 pval->n_value = pval->n_ptr;
296 pval->n_len = len2 + len1 + 1 - full_scale;
297 pval->n_scale = prod_scale;
298 _bc_rm_leading_zeros (pval);
299 if (bc_is_zero (pval))
300 pval->n_sign = PLUS;
301 bc_free_num (prod);
302 *prod = pval;
303 }
304
