New multiprecision integer arithmetic suite.
[u/mdw/catacomb] / mp-arith.c
1 /* -*-c-*-
2 *
3 * $Id: mp-arith.c,v 1.1 1999/11/17 18:02:16 mdw Exp $
4 *
5 * Basic arithmetic on multiprecision integers
6 *
7 * (c) 1999 Straylight/Edgeware
8 */
9
10 /*----- Licensing notice --------------------------------------------------*
11 *
12 * This file is part of Catacomb.
13 *
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
18 *
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
23 *
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
27 * MA 02111-1307, USA.
28 */
29
30 /*----- Revision history --------------------------------------------------*
31 *
32 * $Log: mp-arith.c,v $
33 * Revision 1.1 1999/11/17 18:02:16 mdw
34 * New multiprecision integer arithmetic suite.
35 *
36 */
37
38 /*----- Header files ------------------------------------------------------*/
39
40 #include "mp.h"
41
42 /*----- Main code ---------------------------------------------------------*/
43
44 /* --- @mp_2c@ --- *
45 *
46 * Arguments: @mp *a@ = source
47 *
48 * Returns: Result, @a@ converted to two's complement notation.
49 */
50
51 mp *mp_2c(mp *d, mp *a)
52 {
53 if (!(a->f & MP_NEG))
54 return (MP_COPY(a));
55
56 MP_MODIFY(d, MP_LEN(a));
57 mpx_2c(d->v, d->vl, a->v, a->vl);
58 d->f = a->f & MP_BURN;
59 MP_SHRINK(d);
60 return (d);
61 }
62
63 /* --- @mp_sm@ --- *
64 *
65 * Arguments: @mp *d@ = destination
66 * @mp *a@ = source
67 *
68 * Returns: Result, @a@ converted to the native signed-magnitude
69 * notation.
70 */
71
72 mp *mp_sm(mp *d, mp *a)
73 {
74 if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2)
75 return (MP_COPY(a));
76
77 MP_MODIFY(d, MP_LEN(a));
78 mpx_2c(d->v, d->vl, a->v, a->vl);
79 d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG;
80 MP_SHRINK(d);
81 return (d);
82 }
83
84 /* --- @mp_lsl@ --- *
85 *
86 * Arguments: @mp *d@ = destination
87 * @const mp *a@ = source
88 * @size_t n@ = number of bits to move
89 *
90 * Returns: Result, @a@ shifted left by @n@.
91 */
92
93 mp *mp_lsl(mp *d, const mp *a, size_t n)
94 {
95 MP_MODIFY(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS);
96 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
97 d->f = a->f & (MP_NEG | MP_BURN);
98 MP_SHRINK(d);
99 return (d);
100 }
101
102 /* --- @mp_lsr@ --- *
103 *
104 * Arguments: @mp *d@ = destination
105 * @const mp *a@ = source
106 * @size_t n@ = number of bits to move
107 *
108 * Returns: Result, @a@ shifted left by @n@.
109 */
110
111 mp *mp_lsr(mp *d, const mp *a, size_t n)
112 {
113 MP_MODIFY(d, MP_LEN(a));
114 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
115 d->f = a->f & (MP_NEG | MP_BURN);
116 MP_SHRINK(d);
117 return (d);
118 }
119
120 /* --- @mp_cmp@ --- *
121 *
122 * Arguments: @const mp *a, *b@ = two numbers
123 *
124 * Returns: Less than, equal to or greater than zero, according to
125 * whether @a@ is less than, equal to or greater than @b@.
126 */
127
128 int mp_cmp(const mp *a, const mp *b)
129 {
130 if (!((a->f ^ b->f) & MP_NEG))
131 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
132 else if (a->f & MP_NEG)
133 return (-1);
134 else
135 return (+1);
136 }
137
138 /* --- @mp_add@ --- *
139 *
140 * Arguments: @mp *d@ = destination
141 * @const mp *a, *b@ = sources
142 *
143 * Returns: Result, @a@ added to @b@.
144 */
145
146 mp *mp_add(mp *d, const mp *a, const mp *b)
147 {
148 MP_MODIFY(d, (MP_LEN(a) > MP_LEN(b) ? MP_LEN(a) : MP_LEN(b)) + 1);
149 if (!((a->f ^ b->f) & MP_NEG))
150 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
151 else {
152 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
153 const mp *t = a; a = b; b = t;
154 }
155 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
156 }
157 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
158 MP_SHRINK(d);
159 return (d);
160 }
161
162 /* --- @mp_sub@ --- *
163 *
164 * Arguments: @mp *d@ = destination
165 * @const mp *a, *b@ = sources
166 *
167 * Returns: Result, @b@ subtracted from @a@.
168 */
169
170 mp *mp_sub(mp *d, const mp *a, const mp *b)
171 {
172 unsigned sgn = 0;
173 MP_MODIFY(d, (MP_LEN(a) > MP_LEN(b) ? MP_LEN(a) : MP_LEN(b)) + 1);
174 if ((a->f ^ b->f) & MP_NEG)
175 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
176 else {
177 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
178 const mp *t = a; a = b; b = t;
179 sgn = MP_NEG;
180 }
181 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
182 }
183 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
184 MP_SHRINK(d);
185 return (d);
186 }
187
188 /* --- @mp_mul@ --- *
189 *
190 * Arguments: @mp *d@ = destination
191 * @const mp *a, *b@ = sources
192 *
193 * Returns: Result, @a@ multiplied by @b@.
194 */
195
196 mp *mp_mul(mp *d, const mp *a, const mp *b)
197 {
198 if (d == a || d == b)
199 d = MP_NEW;
200 MP_MODIFY(d, MP_LEN(a) + MP_LEN(b));
201 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
202 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
203 MP_SHRINK(d);
204 return (d);
205 }
206
207 /* --- @mp_sqr@ --- *
208 *
209 * Arguments: @mp *d@ = destination
210 * @const mp *a@ = source
211 *
212 * Returns: Result, @a@ squared.
213 */
214
215 mp *mp_sqr(mp *d, const mp *a)
216 {
217 if (d == a)
218 d = MP_NEW;
219 MP_MODIFY(d, 2 * MP_LEN(a));
220 mpx_usqr(d->v, d->vl, a->v, a->vl);
221 d->f = a->f & MP_BURN;
222 MP_SHRINK(d);
223 return (d);
224 }
225
226 /* --- @mp_div@ --- *
227 *
228 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
229 * @const mp *a, *b@ = sources
230 *
231 * Use: Calculates the quotient and remainder when @a@ is divided by
232 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
233 * Either of @qq@ or @rr@ may be null to indicate that the
234 * result is irrelevant. (Discarding both results is silly.)
235 * There is a performance advantage if @a == *rr@.
236 *
237 * The behaviour when @a@ and @b@ have the same sign is
238 * straightforward. When the signs differ, this implementation
239 * chooses @r@ to have the same sign as @b@, rather than the
240 * more normal choice that the remainder has the same sign as
241 * the dividend. This makes modular arithmetic a little more
242 * straightforward.
243 */
244
245 void mp_div(mp **qq, mp **rr, const mp *a, const mp *b)
246 {
247 mp *r = rr ? *rr : MP_NEW;
248 mp *q = qq ? *qq : MP_NEW;
249 mpw *sv, *svl;
250
251 /* --- Set up some temporary workspace --- */
252
253 {
254 size_t rq = MP_LEN(b) + 1;
255 sv = MP_ALLOC(rq);
256 svl = sv + rq;
257 }
258
259 /* --- Set the remainder up right --- *
260 *
261 * Just in case the divisor is larger, be able to cope with this. It's not
262 * important in @mpx_udiv@, but it is here because of the sign correction.
263 */
264
265 {
266 size_t rq = MP_LEN(a) + 2;
267 if (MP_LEN(b) > rq)
268 rq = MP_LEN(b);
269
270 if (r == a) {
271 MP_SPLIT(r);
272 MP_ENSURE(r, MP_LEN(r) + 2);
273 } else {
274 if (r == b)
275 r = MP_NEW;
276 MP_MODIFY(r, MP_LEN(a) + 2);
277 memcpy(r->v, a->v, MPWS(MP_LEN(a)));
278 memset(r->v + MP_LEN(a), 0, MPWS(2));
279 }
280 }
281
282 /* --- Fix up the quotient too --- */
283
284 if (q == a || q == b)
285 q = MP_NEW;
286 MP_MODIFY(q, MP_LEN(a));
287
288 /* --- Perform the calculation --- */
289
290 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
291
292 /* --- Sort out the sign of the results --- *
293 *
294 * If the signs of the arguments differ, and the remainder is nonzero, I
295 * must add one to the absolute value of the quotient and subtract the
296 * remainder from @b@.
297 */
298
299 q->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
300 if (q->f & MP_NEG) {
301 mpw *v = r->v;
302 while (v < r->vl) {
303 if (*v) {
304 MPX_UADDN(q->v, q->vl, 1);
305 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
306 break;
307 }
308 }
309 }
310
311 r->f = ((a->f | b->f) & MP_BURN) | (b->f & MP_NEG);
312
313 /* --- Store the return values --- */
314
315 if (!qq)
316 MP_DROP(q);
317 else {
318 MP_SHRINK(q);
319 *qq = q;
320 }
321
322 if (!rr)
323 MP_DROP(r);
324 else {
325 MP_SHRINK(r);
326 *rr = r;
327 }
328
329 MP_FREE(sv);
330 }
331
332 /*----- Test rig ----------------------------------------------------------*/
333
334 #ifdef TEST_RIG
335
336 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
337 {
338 if (MP_CMP(expect, !=, result)) {
339 fprintf(stderr, "\n*** %s failed", op);
340 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
341 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
342 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
343 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
344 fputc('\n', stderr);
345 return (0);
346 }
347 return (1);
348 }
349
350 #define RIG(name, op) \
351 static int t ## name(dstr *v) \
352 { \
353 mp *a = *(mp **)v[0].buf; \
354 mpw n = *(int *)v[1].buf; \
355 mp b; \
356 mp *r = *(mp **)v[2].buf; \
357 mp *c = op(MP_NEW, a, n); \
358 int ok; \
359 mp_build(&b, &n, &n + 1); \
360 ok = verify(#name, r, c, a, &b); \
361 mp_drop(a); mp_drop(c); mp_drop(r); \
362 return (ok); \
363 }
364
365 RIG(lsl, mp_lsl)
366 RIG(lsr, mp_lsr)
367
368 #undef RIG
369
370 #define RIG(name, op) \
371 static int t ## name(dstr *v) \
372 { \
373 mp *a = *(mp **)v[0].buf; \
374 mp *b = *(mp **)v[1].buf; \
375 mp *r = *(mp **)v[2].buf; \
376 mp *c = op(MP_NEW, a, b); \
377 int ok = verify(#name, r, c, a, b); \
378 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
379 return (ok); \
380 }
381
382 RIG(add, mp_add)
383 RIG(sub, mp_sub)
384 RIG(mul, mp_mul)
385
386 #undef RIG
387
388 static int tdiv(dstr *v)
389 {
390 mp *a = *(mp **)v[0].buf;
391 mp *b = *(mp **)v[1].buf;
392 mp *q = *(mp **)v[2].buf;
393 mp *r = *(mp **)v[3].buf;
394 mp *c = MP_NEW, *d = MP_NEW;
395 int ok = 1;
396 mp_div(&c, &d, a, b);
397 ok &= verify("div(quotient)", q, c, a, b);
398 ok &= verify("div(remainder)", r, d, a, b);
399 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
400 return (ok);
401 }
402
403 static test_chunk tests[] = {
404 { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } },
405 { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } },
406 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
407 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
408 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
409 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
410 { 0, 0, { 0 } },
411 };
412
413 int main(int argc, char *argv[])
414 {
415 sub_init();
416 test_run(argc, argv, tests, SRCDIR "/tests/mp");
417 return (0);
418 }
419
420 #endif
421
422 /*----- That's all, folks -------------------------------------------------*/