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[u/mdw/catacomb] / mp-arith.c
1 /* -*-c-*-
2 *
3 * $Id: mp-arith.c,v 1.3 1999/12/11 10:57:43 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 1.3 1999/12/11 10:57:43 mdw
34 * Karatsuba squaring algorithm.
35 *
36 * Revision 1.2 1999/12/10 23:18:39 mdw
37 * Change interface for suggested destinations.
38 *
39 * Revision 1.1 1999/11/17 18:02:16 mdw
40 * New multiprecision integer arithmetic suite.
41 *
42 */
43
44 /*----- Header files ------------------------------------------------------*/
45
46 #include "mp.h"
47
48 /*----- Macros ------------------------------------------------------------*/
49
50 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
51
52 /*----- Main code ---------------------------------------------------------*/
53
54 /* --- @mp_2c@ --- *
55 *
56 * Arguments: @mp *a@ = source
57 *
58 * Returns: Result, @a@ converted to two's complement notation.
59 */
60
61 mp *mp_2c(mp *d, mp *a)
62 {
63 if (!(a->f & MP_NEG))
64 return (MP_COPY(a));
65
66 MP_MODIFY(d, MP_LEN(a));
67 mpx_2c(d->v, d->vl, a->v, a->vl);
68 d->f = a->f & MP_BURN;
69 MP_SHRINK(d);
70 return (d);
71 }
72
73 /* --- @mp_sm@ --- *
74 *
75 * Arguments: @mp *d@ = destination
76 * @mp *a@ = source
77 *
78 * Returns: Result, @a@ converted to the native signed-magnitude
79 * notation.
80 */
81
82 mp *mp_sm(mp *d, mp *a)
83 {
84 if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2)
85 return (MP_COPY(a));
86
87 MP_MODIFY(d, MP_LEN(a));
88 mpx_2c(d->v, d->vl, a->v, a->vl);
89 d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG;
90 MP_SHRINK(d);
91 return (d);
92 }
93
94 /* --- @mp_lsl@ --- *
95 *
96 * Arguments: @mp *d@ = destination
97 * @mp *a@ = source
98 * @size_t n@ = number of bits to move
99 *
100 * Returns: Result, @a@ shifted left by @n@.
101 */
102
103 mp *mp_lsl(mp *d, mp *a, size_t n)
104 {
105 MP_MODIFY(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS);
106 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
107 d->f = a->f & (MP_NEG | MP_BURN);
108 MP_SHRINK(d);
109 return (d);
110 }
111
112 /* --- @mp_lsr@ --- *
113 *
114 * Arguments: @mp *d@ = destination
115 * @mp *a@ = source
116 * @size_t n@ = number of bits to move
117 *
118 * Returns: Result, @a@ shifted left by @n@.
119 */
120
121 mp *mp_lsr(mp *d, mp *a, size_t n)
122 {
123 MP_MODIFY(d, MP_LEN(a));
124 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
125 d->f = a->f & (MP_NEG | MP_BURN);
126 MP_SHRINK(d);
127 return (d);
128 }
129
130 /* --- @mp_cmp@ --- *
131 *
132 * Arguments: @const mp *a, *b@ = two numbers
133 *
134 * Returns: Less than, equal to or greater than zero, according to
135 * whether @a@ is less than, equal to or greater than @b@.
136 */
137
138 int mp_cmp(const mp *a, const mp *b)
139 {
140 if (!((a->f ^ b->f) & MP_NEG))
141 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
142 else if (a->f & MP_NEG)
143 return (-1);
144 else
145 return (+1);
146 }
147
148 /* --- @mp_add@ --- *
149 *
150 * Arguments: @mp *d@ = destination
151 * @mp *a, *b@ = sources
152 *
153 * Returns: Result, @a@ added to @b@.
154 */
155
156 mp *mp_add(mp *d, mp *a, mp *b)
157 {
158 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
159 if (!((a->f ^ b->f) & MP_NEG))
160 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
161 else {
162 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
163 mp *t = a; a = b; b = t;
164 }
165 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
166 }
167 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
168 MP_SHRINK(d);
169 return (d);
170 }
171
172 /* --- @mp_sub@ --- *
173 *
174 * Arguments: @mp *d@ = destination
175 * @mp *a, *b@ = sources
176 *
177 * Returns: Result, @b@ subtracted from @a@.
178 */
179
180 mp *mp_sub(mp *d, mp *a, mp *b)
181 {
182 unsigned sgn = 0;
183 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
184 if ((a->f ^ b->f) & MP_NEG)
185 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
186 else {
187 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
188 mp *t = a; a = b; b = t;
189 sgn = MP_NEG;
190 }
191 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
192 }
193 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
194 MP_SHRINK(d);
195 return (d);
196 }
197
198 /* --- @mp_mul@ --- *
199 *
200 * Arguments: @mp *d@ = destination
201 * @mp *a, *b@ = sources
202 *
203 * Returns: Result, @a@ multiplied by @b@.
204 */
205
206 mp *mp_mul(mp *d, mp *a, mp *b)
207 {
208 a = MP_COPY(a);
209 b = MP_COPY(b);
210
211 MP_MODIFY(d, MP_LEN(a) + MP_LEN(b));
212 if (MP_LEN(a) <= KARATSUBA_CUTOFF || MP_LEN(b) <= KARATSUBA_CUTOFF)
213 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
214 else {
215 size_t m = MAX(MP_LEN(a), MP_LEN(b)) * 2 + KARATSUBA_SLOP;
216 mpw *s;
217 m += 32;
218 s = MP_ALLOC(m);
219 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m);
220 MP_FREE(s);
221 }
222
223 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
224 MP_SHRINK(d);
225 MP_DROP(a);
226 MP_DROP(b);
227 return (d);
228 }
229
230 /* --- @mp_sqr@ --- *
231 *
232 * Arguments: @mp *d@ = destination
233 * @mp *a@ = source
234 *
235 * Returns: Result, @a@ squared.
236 */
237
238 mp *mp_sqr(mp *d, mp *a)
239 {
240 size_t m = MP_LEN(a);
241
242 a = MP_COPY(a);
243 MP_MODIFY(d, 2 * m);
244 if (m > KARATSUBA_CUTOFF) {
245 mpw *s;
246 m = 2 * (m + 1) + 32;
247 s = MP_ALLOC(m);
248 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m);
249 MP_FREE(s);
250 } else
251 mpx_usqr(d->v, d->vl, a->v, a->vl);
252 d->f = a->f & MP_BURN;
253 MP_SHRINK(d);
254 MP_DROP(a);
255 return (d);
256 }
257
258 /* --- @mp_div@ --- *
259 *
260 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
261 * @mp *a, *b@ = sources
262 *
263 * Use: Calculates the quotient and remainder when @a@ is divided by
264 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
265 * Either of @qq@ or @rr@ may be null to indicate that the
266 * result is irrelevant. (Discarding both results is silly.)
267 * There is a performance advantage if @a == *rr@.
268 *
269 * The behaviour when @a@ and @b@ have the same sign is
270 * straightforward. When the signs differ, this implementation
271 * chooses @r@ to have the same sign as @b@, rather than the
272 * more normal choice that the remainder has the same sign as
273 * the dividend. This makes modular arithmetic a little more
274 * straightforward.
275 */
276
277 void mp_div(mp **qq, mp **rr, mp *a, mp *b)
278 {
279 mp *r = rr ? *rr : MP_NEW;
280 mp *q = qq ? *qq : MP_NEW;
281 mpw *sv, *svl;
282
283 /* --- Set up some temporary workspace --- */
284
285 {
286 size_t rq = MP_LEN(b) + 1;
287 sv = MP_ALLOC(rq);
288 svl = sv + rq;
289 }
290
291 /* --- Set the remainder up right --- *
292 *
293 * Just in case the divisor is larger, be able to cope with this. It's not
294 * important in @mpx_udiv@, but it is here because of the sign correction.
295 */
296
297 {
298 size_t rq = MP_LEN(a) + 2;
299 if (MP_LEN(b) > rq)
300 rq = MP_LEN(b);
301
302 b = MP_COPY(b);
303 if (r == a) {
304 MP_SPLIT(a);
305 a = r = MP_COPY(a);
306 MP_ENSURE(r, MP_LEN(r) + 2);
307 } else {
308 a = MP_COPY(a);
309 MP_MODIFY(r, MP_LEN(a) + 2);
310 memcpy(r->v, a->v, MPWS(MP_LEN(a)));
311 memset(r->v + MP_LEN(a), 0, MPWS(2));
312 }
313 }
314
315 /* --- Fix up the quotient too --- */
316
317 MP_MODIFY(q, MP_LEN(a));
318
319 /* --- Perform the calculation --- */
320
321 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
322
323 /* --- Sort out the sign of the results --- *
324 *
325 * If the signs of the arguments differ, and the remainder is nonzero, I
326 * must add one to the absolute value of the quotient and subtract the
327 * remainder from @b@.
328 */
329
330 q->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
331 if (q->f & MP_NEG) {
332 mpw *v;
333 for (v = r->v; v < r->vl; v++) {
334 if (*v) {
335 MPX_UADDN(q->v, q->vl, 1);
336 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
337 break;
338 }
339 }
340 }
341
342 r->f = ((a->f | b->f) & MP_BURN) | (b->f & MP_NEG);
343
344 /* --- Store the return values --- */
345
346 if (!qq)
347 MP_DROP(q);
348 else {
349 MP_SHRINK(q);
350 *qq = q;
351 }
352
353 if (!rr)
354 MP_DROP(r);
355 else {
356 MP_SHRINK(r);
357 *rr = r;
358 }
359
360 MP_DROP(a);
361 MP_DROP(b);
362 MP_FREE(sv);
363 }
364
365 /*----- Test rig ----------------------------------------------------------*/
366
367 #ifdef TEST_RIG
368
369 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
370 {
371 if (MP_CMP(expect, !=, result)) {
372 fprintf(stderr, "\n*** %s failed", op);
373 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
374 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
375 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
376 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
377 fputc('\n', stderr);
378 return (0);
379 }
380 return (1);
381 }
382
383 #define RIG(name, op) \
384 static int t##name(dstr *v) \
385 { \
386 mp *a = *(mp **)v[0].buf; \
387 mpw n = *(int *)v[1].buf; \
388 mp b; \
389 mp *r = *(mp **)v[2].buf; \
390 mp *c = op(MP_NEW, a, n); \
391 int ok; \
392 mp_build(&b, &n, &n + 1); \
393 ok = verify(#name, r, c, a, &b); \
394 mp_drop(a); mp_drop(c); mp_drop(r); \
395 assert(mparena_count(MPARENA_GLOBAL) == 0); \
396 return (ok); \
397 }
398
399 RIG(lsl, mp_lsl)
400 RIG(lsr, mp_lsr)
401
402 #undef RIG
403
404 #define RIG(name, op) \
405 static int t##name(dstr *v) \
406 { \
407 mp *a = *(mp **)v[0].buf; \
408 mp *b = *(mp **)v[1].buf; \
409 mp *r = *(mp **)v[2].buf; \
410 mp *c = op(MP_NEW, a, b); \
411 int ok = verify(#name, r, c, a, b); \
412 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
413 assert(mparena_count(MPARENA_GLOBAL) == 0); \
414 return (ok); \
415 }
416
417 RIG(add, mp_add)
418 RIG(sub, mp_sub)
419 RIG(mul, mp_mul)
420
421 #undef RIG
422
423 static int tdiv(dstr *v)
424 {
425 mp *a = *(mp **)v[0].buf;
426 mp *b = *(mp **)v[1].buf;
427 mp *q = *(mp **)v[2].buf;
428 mp *r = *(mp **)v[3].buf;
429 mp *c = MP_NEW, *d = MP_NEW;
430 int ok = 1;
431 mp_div(&c, &d, a, b);
432 ok &= verify("div(quotient)", q, c, a, b);
433 ok &= verify("div(remainder)", r, d, a, b);
434 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
435 assert(mparena_count(MPARENA_GLOBAL) == 0);
436 return (ok);
437 }
438
439 static test_chunk tests[] = {
440 { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } },
441 { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } },
442 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
443 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
444 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
445 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
446 { 0, 0, { 0 } },
447 };
448
449 int main(int argc, char *argv[])
450 {
451 sub_init();
452 test_run(argc, argv, tests, SRCDIR "/tests/mp");
453 return (0);
454 }
455
456 #endif
457
458 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)