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Rename Karatsuba constants now that we have @gfx_kmul@ too.
[u/mdw/catacomb] / mp-arith.c
1 /* -*-c-*-
2 *
3 * $Id: mp-arith.c,v 1.9 2000/10/08 15:48:35 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 1.9 2000/10/08 15:48:35 mdw
34 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
35 *
36 * Revision 1.8 2000/10/08 12:02:21 mdw
37 * Use @MP_EQ@ instead of @MP_CMP@.
38 *
39 * Revision 1.7 2000/06/22 19:02:53 mdw
40 * New function @mp_odd@ to extract powers of two from an integer. This is
41 * common code from the Rabin-Miller test, RSA key recovery and modular
42 * square-root extraction.
43 *
44 * Revision 1.6 2000/06/17 11:45:09 mdw
45 * Major memory management overhaul. Added arena support. Use the secure
46 * arena for secret integers. Replace and improve the MP management macros
47 * (e.g., replace MP_MODIFY by MP_DEST).
48 *
49 * Revision 1.5 1999/12/22 15:54:41 mdw
50 * Adjust Karatsuba parameters. Calculate destination size better.
51 *
52 * Revision 1.4 1999/12/13 15:35:16 mdw
53 * Slightly different rules on memory allocation.
54 *
55 * Revision 1.3 1999/12/11 10:57:43 mdw
56 * Karatsuba squaring algorithm.
57 *
58 * Revision 1.2 1999/12/10 23:18:39 mdw
59 * Change interface for suggested destinations.
60 *
61 * Revision 1.1 1999/11/17 18:02:16 mdw
62 * New multiprecision integer arithmetic suite.
63 *
64 */
65
66 /*----- Header files ------------------------------------------------------*/
67
68 #include "mp.h"
69
70 /*----- Macros ------------------------------------------------------------*/
71
72 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
73
74 /*----- Main code ---------------------------------------------------------*/
75
76 /* --- @mp_2c@ --- *
77 *
78 * Arguments: @mp *a@ = source
79 *
80 * Returns: Result, @a@ converted to two's complement notation.
81 */
82
83 mp *mp_2c(mp *d, mp *a)
84 {
85 if (!(a->f & MP_NEG))
86 return (MP_COPY(a));
87
88 MP_DEST(d, MP_LEN(a), a->f);
89 mpx_2c(d->v, d->vl, a->v, a->vl);
90 d->f = a->f & MP_BURN;
91 MP_SHRINK(d);
92 return (d);
93 }
94
95 /* --- @mp_sm@ --- *
96 *
97 * Arguments: @mp *d@ = destination
98 * @mp *a@ = source
99 *
100 * Returns: Result, @a@ converted to the native signed-magnitude
101 * notation.
102 */
103
104 mp *mp_sm(mp *d, mp *a)
105 {
106 if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2)
107 return (MP_COPY(a));
108
109 MP_DEST(d, MP_LEN(a), a->f);
110 mpx_2c(d->v, d->vl, a->v, a->vl);
111 d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG;
112 MP_SHRINK(d);
113 return (d);
114 }
115
116 /* --- @mp_lsl@ --- *
117 *
118 * Arguments: @mp *d@ = destination
119 * @mp *a@ = source
120 * @size_t n@ = number of bits to move
121 *
122 * Returns: Result, @a@ shifted left by @n@.
123 */
124
125 mp *mp_lsl(mp *d, mp *a, size_t n)
126 {
127 MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
128 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
129 d->f = a->f & (MP_NEG | MP_BURN);
130 MP_SHRINK(d);
131 return (d);
132 }
133
134 /* --- @mp_lsr@ --- *
135 *
136 * Arguments: @mp *d@ = destination
137 * @mp *a@ = source
138 * @size_t n@ = number of bits to move
139 *
140 * Returns: Result, @a@ shifted left by @n@.
141 */
142
143 mp *mp_lsr(mp *d, mp *a, size_t n)
144 {
145 MP_DEST(d, MP_LEN(a), a->f);
146 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
147 d->f = a->f & (MP_NEG | MP_BURN);
148 MP_SHRINK(d);
149 return (d);
150 }
151
152 /* --- @mp_eq@ --- *
153 *
154 * Arguments: @const mp *a, *b@ = two numbers
155 *
156 * Returns: Nonzero if the numbers are equal.
157 */
158
159 int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); }
160
161 /* --- @mp_cmp@ --- *
162 *
163 * Arguments: @const mp *a, *b@ = two numbers
164 *
165 * Returns: Less than, equal to or greater than zero, according to
166 * whether @a@ is less than, equal to or greater than @b@.
167 */
168
169 int mp_cmp(const mp *a, const mp *b)
170 {
171 if (!((a->f ^ b->f) & MP_NEG))
172 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
173 else if (a->f & MP_NEG)
174 return (-1);
175 else
176 return (+1);
177 }
178
179 /* --- @mp_add@ --- *
180 *
181 * Arguments: @mp *d@ = destination
182 * @mp *a, *b@ = sources
183 *
184 * Returns: Result, @a@ added to @b@.
185 */
186
187 mp *mp_add(mp *d, mp *a, mp *b)
188 {
189 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
190 if (!((a->f ^ b->f) & MP_NEG))
191 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
192 else {
193 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
194 mp *t = a; a = b; b = t;
195 }
196 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
197 }
198 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
199 MP_SHRINK(d);
200 return (d);
201 }
202
203 /* --- @mp_sub@ --- *
204 *
205 * Arguments: @mp *d@ = destination
206 * @mp *a, *b@ = sources
207 *
208 * Returns: Result, @b@ subtracted from @a@.
209 */
210
211 mp *mp_sub(mp *d, mp *a, mp *b)
212 {
213 unsigned sgn = 0;
214 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
215 if ((a->f ^ b->f) & MP_NEG)
216 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
217 else {
218 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
219 mp *t = a; a = b; b = t;
220 sgn = MP_NEG;
221 }
222 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
223 }
224 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
225 MP_SHRINK(d);
226 return (d);
227 }
228
229 /* --- @mp_mul@ --- *
230 *
231 * Arguments: @mp *d@ = destination
232 * @mp *a, *b@ = sources
233 *
234 * Returns: Result, @a@ multiplied by @b@.
235 */
236
237 mp *mp_mul(mp *d, mp *a, mp *b)
238 {
239 a = MP_COPY(a);
240 b = MP_COPY(b);
241
242 if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) {
243 MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
244 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
245 } else {
246 size_t m = 2 * MAX(MP_LEN(a), MP_LEN(b)) + 2;
247 mpw *s;
248 MP_DEST(d, m, a->f | b->f | MP_UNDEF);
249 m += MPK_SLOP;
250 s = mpalloc(d->a, m);
251 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m);
252 mpfree(d->a, s);
253 }
254
255 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
256 MP_SHRINK(d);
257 MP_DROP(a);
258 MP_DROP(b);
259 return (d);
260 }
261
262 /* --- @mp_sqr@ --- *
263 *
264 * Arguments: @mp *d@ = destination
265 * @mp *a@ = source
266 *
267 * Returns: Result, @a@ squared.
268 */
269
270 mp *mp_sqr(mp *d, mp *a)
271 {
272 size_t m = MP_LEN(a);
273
274 a = MP_COPY(a);
275 MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
276 if (m > MPK_THRESH) {
277 mpw *s;
278 m = 2 * (m + 1) + MPK_SLOP;
279 s = mpalloc(d->a, m);
280 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m);
281 mpfree(d->a, s);
282 } else
283 mpx_usqr(d->v, d->vl, a->v, a->vl);
284 d->f = a->f & MP_BURN;
285 MP_SHRINK(d);
286 MP_DROP(a);
287 return (d);
288 }
289
290 /* --- @mp_div@ --- *
291 *
292 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
293 * @mp *a, *b@ = sources
294 *
295 * Use: Calculates the quotient and remainder when @a@ is divided by
296 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
297 * Either of @qq@ or @rr@ may be null to indicate that the
298 * result is irrelevant. (Discarding both results is silly.)
299 * There is a performance advantage if @a == *rr@.
300 *
301 * The behaviour when @a@ and @b@ have the same sign is
302 * straightforward. When the signs differ, this implementation
303 * chooses @r@ to have the same sign as @b@, rather than the
304 * more normal choice that the remainder has the same sign as
305 * the dividend. This makes modular arithmetic a little more
306 * straightforward.
307 */
308
309 void mp_div(mp **qq, mp **rr, mp *a, mp *b)
310 {
311 mp *r = rr ? *rr : MP_NEW;
312 mp *q = qq ? *qq : MP_NEW;
313 mpw *sv, *svl;
314
315 /* --- Set the remainder up right --- *
316 *
317 * Just in case the divisor is larger, be able to cope with this. It's not
318 * important in @mpx_udiv@, but it is here because of the sign correction.
319 */
320
321 b = MP_COPY(b);
322 a = MP_COPY(a);
323 if (r)
324 MP_DROP(r);
325 r = a;
326 MP_DEST(r, MP_LEN(a) + 2, a->f | b->f);
327
328 /* --- Fix up the quotient too --- */
329
330 r = MP_COPY(r);
331 MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
332 MP_DROP(r);
333
334 /* --- Set up some temporary workspace --- */
335
336 {
337 size_t rq = MP_LEN(b) + 1;
338 sv = mpalloc(r->a, rq);
339 svl = sv + rq;
340 }
341
342 /* --- Perform the calculation --- */
343
344 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
345
346 /* --- Sort out the sign of the results --- *
347 *
348 * If the signs of the arguments differ, and the remainder is nonzero, I
349 * must add one to the absolute value of the quotient and subtract the
350 * remainder from @b@.
351 */
352
353 q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG);
354 if (q->f & MP_NEG) {
355 mpw *v;
356 for (v = r->v; v < r->vl; v++) {
357 if (*v) {
358 MPX_UADDN(q->v, q->vl, 1);
359 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
360 break;
361 }
362 }
363 }
364
365 r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG);
366
367 /* --- Store the return values --- */
368
369 mpfree(r->a, sv);
370 MP_DROP(b);
371
372 if (!qq)
373 MP_DROP(q);
374 else {
375 MP_SHRINK(q);
376 *qq = q;
377 }
378
379 if (!rr)
380 MP_DROP(r);
381 else {
382 MP_SHRINK(r);
383 *rr = r;
384 }
385 }
386
387 /* --- @mp_odd@ --- *
388 *
389 * Arguments: @mp *d@ = pointer to destination integer
390 * @mp *m@ = pointer to source integer
391 * @size_t *s@ = where to store the power of 2
392 *
393 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
394 *
395 * Use: Computes a power of two and an odd integer which, when
396 * multiplied, give a specified result. This sort of thing is
397 * useful in number theory quite often.
398 */
399
400 mp *mp_odd(mp *d, mp *m, size_t *s)
401 {
402 size_t ss = 0;
403 const mpw *v, *vl;
404
405 v = m->v;
406 vl = m->vl;
407 for (; !*v && v < vl; v++)
408 ss += MPW_BITS;
409 if (v >= vl)
410 ss = 0;
411 else {
412 mpw x = *v;
413 mpw mask = MPW_MAX;
414 unsigned z = MPW_BITS / 2;
415
416 while (z) {
417 mask >>= z;
418 if (!(x & mask)) {
419 x >>= z;
420 ss += z;
421 }
422 z >>= 1;
423 }
424 }
425
426 *s = ss;
427 return (mp_lsr(d, m, ss));
428 }
429
430 /*----- Test rig ----------------------------------------------------------*/
431
432 #ifdef TEST_RIG
433
434 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
435 {
436 if (!MP_EQ(expect, result)) {
437 fprintf(stderr, "\n*** %s failed", op);
438 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
439 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
440 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
441 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
442 fputc('\n', stderr);
443 return (0);
444 }
445 return (1);
446 }
447
448 #define RIG(name, op) \
449 static int t##name(dstr *v) \
450 { \
451 mp *a = *(mp **)v[0].buf; \
452 mpw n = *(int *)v[1].buf; \
453 mp b; \
454 mp *r = *(mp **)v[2].buf; \
455 mp *c = op(MP_NEW, a, n); \
456 int ok; \
457 mp_build(&b, &n, &n + 1); \
458 ok = verify(#name, r, c, a, &b); \
459 mp_drop(a); mp_drop(c); mp_drop(r); \
460 assert(mparena_count(MPARENA_GLOBAL) == 0); \
461 return (ok); \
462 }
463
464 RIG(lsl, mp_lsl)
465 RIG(lsr, mp_lsr)
466
467 #undef RIG
468
469 #define RIG(name, op) \
470 static int t##name(dstr *v) \
471 { \
472 mp *a = *(mp **)v[0].buf; \
473 mp *b = *(mp **)v[1].buf; \
474 mp *r = *(mp **)v[2].buf; \
475 mp *c = op(MP_NEW, a, b); \
476 int ok = verify(#name, r, c, a, b); \
477 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
478 assert(mparena_count(MPARENA_GLOBAL) == 0); \
479 return (ok); \
480 }
481
482 RIG(add, mp_add)
483 RIG(sub, mp_sub)
484 RIG(mul, mp_mul)
485
486 #undef RIG
487
488 static int tdiv(dstr *v)
489 {
490 mp *a = *(mp **)v[0].buf;
491 mp *b = *(mp **)v[1].buf;
492 mp *q = *(mp **)v[2].buf;
493 mp *r = *(mp **)v[3].buf;
494 mp *c = MP_NEW, *d = MP_NEW;
495 int ok = 1;
496 mp_div(&c, &d, a, b);
497 ok &= verify("div(quotient)", q, c, a, b);
498 ok &= verify("div(remainder)", r, d, a, b);
499 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
500 assert(mparena_count(MPARENA_GLOBAL) == 0);
501 return (ok);
502 }
503
504 static int todd(dstr *v)
505 {
506 mp *a = *(mp **)v[0].buf;
507 size_t rs = *(uint32 *)v[1].buf;
508 mp *rt = *(mp **)v[2].buf;
509 int ok = 1;
510 mp *t;
511 size_t s;
512 t = mp_odd(MP_NEW, a, &s);
513 if (s != rs || !MP_EQ(t, rt)) {
514 ok = 0;
515 fprintf(stderr, "\n*** odd failed");
516 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
517 fprintf(stderr, "\n*** s = %lu", (unsigned long)s);
518 fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10);
519 fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs);
520 fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10);
521 fputc('\n', stderr);
522 }
523 mp_drop(a);
524 mp_drop(rt);
525 mp_drop(t);
526 return (ok);
527 }
528
529 static test_chunk tests[] = {
530 { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } },
531 { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } },
532 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
533 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
534 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
535 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
536 { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } },
537 { 0, 0, { 0 } },
538 };
539
540 int main(int argc, char *argv[])
541 {
542 sub_init();
543 test_run(argc, argv, tests, SRCDIR "/tests/mp");
544 return (0);
545 }
546
547 #endif
548
549 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)