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More changes. Still embryonic.
[u/mdw/catacomb] / mp-arith.c
1 /* -*-c-*-
2 *
3 * $Id: mp-arith.c,v 1.4 1999/12/13 15:35:16 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 1.4 1999/12/13 15:35:16 mdw
34 * Slightly different rules on memory allocation.
35 *
36 * Revision 1.3 1999/12/11 10:57:43 mdw
37 * Karatsuba squaring algorithm.
38 *
39 * Revision 1.2 1999/12/10 23:18:39 mdw
40 * Change interface for suggested destinations.
41 *
42 * Revision 1.1 1999/11/17 18:02:16 mdw
43 * New multiprecision integer arithmetic suite.
44 *
45 */
46
47 /*----- Header files ------------------------------------------------------*/
48
49 #include "mp.h"
50
51 /*----- Macros ------------------------------------------------------------*/
52
53 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
54
55 /*----- Main code ---------------------------------------------------------*/
56
57 /* --- @mp_2c@ --- *
58 *
59 * Arguments: @mp *a@ = source
60 *
61 * Returns: Result, @a@ converted to two's complement notation.
62 */
63
64 mp *mp_2c(mp *d, mp *a)
65 {
66 if (!(a->f & MP_NEG))
67 return (MP_COPY(a));
68
69 MP_MODIFY(d, MP_LEN(a));
70 mpx_2c(d->v, d->vl, a->v, a->vl);
71 d->f = a->f & MP_BURN;
72 MP_SHRINK(d);
73 return (d);
74 }
75
76 /* --- @mp_sm@ --- *
77 *
78 * Arguments: @mp *d@ = destination
79 * @mp *a@ = source
80 *
81 * Returns: Result, @a@ converted to the native signed-magnitude
82 * notation.
83 */
84
85 mp *mp_sm(mp *d, mp *a)
86 {
87 if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2)
88 return (MP_COPY(a));
89
90 MP_MODIFY(d, MP_LEN(a));
91 mpx_2c(d->v, d->vl, a->v, a->vl);
92 d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG;
93 MP_SHRINK(d);
94 return (d);
95 }
96
97 /* --- @mp_lsl@ --- *
98 *
99 * Arguments: @mp *d@ = destination
100 * @mp *a@ = source
101 * @size_t n@ = number of bits to move
102 *
103 * Returns: Result, @a@ shifted left by @n@.
104 */
105
106 mp *mp_lsl(mp *d, mp *a, size_t n)
107 {
108 MP_MODIFY(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS);
109 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
110 d->f = a->f & (MP_NEG | MP_BURN);
111 MP_SHRINK(d);
112 return (d);
113 }
114
115 /* --- @mp_lsr@ --- *
116 *
117 * Arguments: @mp *d@ = destination
118 * @mp *a@ = source
119 * @size_t n@ = number of bits to move
120 *
121 * Returns: Result, @a@ shifted left by @n@.
122 */
123
124 mp *mp_lsr(mp *d, mp *a, size_t n)
125 {
126 MP_MODIFY(d, MP_LEN(a));
127 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
128 d->f = a->f & (MP_NEG | MP_BURN);
129 MP_SHRINK(d);
130 return (d);
131 }
132
133 /* --- @mp_cmp@ --- *
134 *
135 * Arguments: @const mp *a, *b@ = two numbers
136 *
137 * Returns: Less than, equal to or greater than zero, according to
138 * whether @a@ is less than, equal to or greater than @b@.
139 */
140
141 int mp_cmp(const mp *a, const mp *b)
142 {
143 if (!((a->f ^ b->f) & MP_NEG))
144 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
145 else if (a->f & MP_NEG)
146 return (-1);
147 else
148 return (+1);
149 }
150
151 /* --- @mp_add@ --- *
152 *
153 * Arguments: @mp *d@ = destination
154 * @mp *a, *b@ = sources
155 *
156 * Returns: Result, @a@ added to @b@.
157 */
158
159 mp *mp_add(mp *d, mp *a, mp *b)
160 {
161 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
162 if (!((a->f ^ b->f) & MP_NEG))
163 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
164 else {
165 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
166 mp *t = a; a = b; b = t;
167 }
168 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
169 }
170 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
171 MP_SHRINK(d);
172 return (d);
173 }
174
175 /* --- @mp_sub@ --- *
176 *
177 * Arguments: @mp *d@ = destination
178 * @mp *a, *b@ = sources
179 *
180 * Returns: Result, @b@ subtracted from @a@.
181 */
182
183 mp *mp_sub(mp *d, mp *a, mp *b)
184 {
185 unsigned sgn = 0;
186 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
187 if ((a->f ^ b->f) & MP_NEG)
188 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
189 else {
190 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
191 mp *t = a; a = b; b = t;
192 sgn = MP_NEG;
193 }
194 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
195 }
196 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
197 MP_SHRINK(d);
198 return (d);
199 }
200
201 /* --- @mp_mul@ --- *
202 *
203 * Arguments: @mp *d@ = destination
204 * @mp *a, *b@ = sources
205 *
206 * Returns: Result, @a@ multiplied by @b@.
207 */
208
209 mp *mp_mul(mp *d, mp *a, mp *b)
210 {
211 size_t m = MAX(MP_LEN(a), MP_LEN(b)) * 2 + KARATSUBA_SLOP;
212
213 a = MP_COPY(a);
214 b = MP_COPY(b);
215
216 if (MP_LEN(a) <= KARATSUBA_CUTOFF || MP_LEN(b) <= KARATSUBA_CUTOFF) {
217 MP_MODIFY(d, MP_LEN(a) + MP_LEN(b));
218 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
219 } else {
220 mpw *s;
221 m += 32;
222 s = MP_ALLOC(m);
223 MP_MODIFY(d, 2 * m + 2);
224 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m);
225 MP_FREE(s);
226 }
227
228 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
229 MP_SHRINK(d);
230 MP_DROP(a);
231 MP_DROP(b);
232 return (d);
233 }
234
235 /* --- @mp_sqr@ --- *
236 *
237 * Arguments: @mp *d@ = destination
238 * @mp *a@ = source
239 *
240 * Returns: Result, @a@ squared.
241 */
242
243 mp *mp_sqr(mp *d, mp *a)
244 {
245 size_t m = MP_LEN(a);
246
247 a = MP_COPY(a);
248 MP_MODIFY(d, 2 * m + 2);
249 if (m > KARATSUBA_CUTOFF) {
250 mpw *s;
251 m = 2 * (m + 1) + 32;
252 s = MP_ALLOC(m);
253 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m);
254 MP_FREE(s);
255 } else
256 mpx_usqr(d->v, d->vl, a->v, a->vl);
257 d->f = a->f & MP_BURN;
258 MP_SHRINK(d);
259 MP_DROP(a);
260 return (d);
261 }
262
263 /* --- @mp_div@ --- *
264 *
265 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
266 * @mp *a, *b@ = sources
267 *
268 * Use: Calculates the quotient and remainder when @a@ is divided by
269 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
270 * Either of @qq@ or @rr@ may be null to indicate that the
271 * result is irrelevant. (Discarding both results is silly.)
272 * There is a performance advantage if @a == *rr@.
273 *
274 * The behaviour when @a@ and @b@ have the same sign is
275 * straightforward. When the signs differ, this implementation
276 * chooses @r@ to have the same sign as @b@, rather than the
277 * more normal choice that the remainder has the same sign as
278 * the dividend. This makes modular arithmetic a little more
279 * straightforward.
280 */
281
282 void mp_div(mp **qq, mp **rr, mp *a, mp *b)
283 {
284 mp *r = rr ? *rr : MP_NEW;
285 mp *q = qq ? *qq : MP_NEW;
286 mpw *sv, *svl;
287
288 /* --- Set up some temporary workspace --- */
289
290 {
291 size_t rq = MP_LEN(b) + 1;
292 sv = MP_ALLOC(rq);
293 svl = sv + rq;
294 }
295
296 /* --- Set the remainder up right --- *
297 *
298 * Just in case the divisor is larger, be able to cope with this. It's not
299 * important in @mpx_udiv@, but it is here because of the sign correction.
300 */
301
302 {
303 size_t rq = MP_LEN(a) + 2;
304 if (MP_LEN(b) > rq)
305 rq = MP_LEN(b);
306
307 b = MP_COPY(b);
308 if (r == a) {
309 MP_SPLIT(a);
310 a = r = MP_COPY(a);
311 MP_ENSURE(r, MP_LEN(r) + 2);
312 } else {
313 a = MP_COPY(a);
314 MP_MODIFY(r, MP_LEN(a) + 2);
315 memcpy(r->v, a->v, MPWS(MP_LEN(a)));
316 memset(r->v + MP_LEN(a), 0, MPWS(2));
317 }
318 }
319
320 /* --- Fix up the quotient too --- */
321
322 MP_MODIFY(q, MP_LEN(a));
323
324 /* --- Perform the calculation --- */
325
326 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
327
328 /* --- Sort out the sign of the results --- *
329 *
330 * If the signs of the arguments differ, and the remainder is nonzero, I
331 * must add one to the absolute value of the quotient and subtract the
332 * remainder from @b@.
333 */
334
335 q->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
336 if (q->f & MP_NEG) {
337 mpw *v;
338 for (v = r->v; v < r->vl; v++) {
339 if (*v) {
340 MPX_UADDN(q->v, q->vl, 1);
341 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
342 break;
343 }
344 }
345 }
346
347 r->f = ((a->f | b->f) & MP_BURN) | (b->f & MP_NEG);
348
349 /* --- Store the return values --- */
350
351 if (!qq)
352 MP_DROP(q);
353 else {
354 MP_SHRINK(q);
355 *qq = q;
356 }
357
358 if (!rr)
359 MP_DROP(r);
360 else {
361 MP_SHRINK(r);
362 *rr = r;
363 }
364
365 MP_DROP(a);
366 MP_DROP(b);
367 MP_FREE(sv);
368 }
369
370 /*----- Test rig ----------------------------------------------------------*/
371
372 #ifdef TEST_RIG
373
374 static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
375 {
376 if (MP_CMP(expect, !=, result)) {
377 fprintf(stderr, "\n*** %s failed", op);
378 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
379 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
380 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
381 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
382 fputc('\n', stderr);
383 return (0);
384 }
385 return (1);
386 }
387
388 #define RIG(name, op) \
389 static int t##name(dstr *v) \
390 { \
391 mp *a = *(mp **)v[0].buf; \
392 mpw n = *(int *)v[1].buf; \
393 mp b; \
394 mp *r = *(mp **)v[2].buf; \
395 mp *c = op(MP_NEW, a, n); \
396 int ok; \
397 mp_build(&b, &n, &n + 1); \
398 ok = verify(#name, r, c, a, &b); \
399 mp_drop(a); mp_drop(c); mp_drop(r); \
400 assert(mparena_count(MPARENA_GLOBAL) == 0); \
401 return (ok); \
402 }
403
404 RIG(lsl, mp_lsl)
405 RIG(lsr, mp_lsr)
406
407 #undef RIG
408
409 #define RIG(name, op) \
410 static int t##name(dstr *v) \
411 { \
412 mp *a = *(mp **)v[0].buf; \
413 mp *b = *(mp **)v[1].buf; \
414 mp *r = *(mp **)v[2].buf; \
415 mp *c = op(MP_NEW, a, b); \
416 int ok = verify(#name, r, c, a, b); \
417 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
418 assert(mparena_count(MPARENA_GLOBAL) == 0); \
419 return (ok); \
420 }
421
422 RIG(add, mp_add)
423 RIG(sub, mp_sub)
424 RIG(mul, mp_mul)
425
426 #undef RIG
427
428 static int tdiv(dstr *v)
429 {
430 mp *a = *(mp **)v[0].buf;
431 mp *b = *(mp **)v[1].buf;
432 mp *q = *(mp **)v[2].buf;
433 mp *r = *(mp **)v[3].buf;
434 mp *c = MP_NEW, *d = MP_NEW;
435 int ok = 1;
436 mp_div(&c, &d, a, b);
437 ok &= verify("div(quotient)", q, c, a, b);
438 ok &= verify("div(remainder)", r, d, a, b);
439 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
440 assert(mparena_count(MPARENA_GLOBAL) == 0);
441 return (ok);
442 }
443
444 static test_chunk tests[] = {
445 { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } },
446 { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } },
447 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
448 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
449 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
450 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
451 { 0, 0, { 0 } },
452 };
453
454 int main(int argc, char *argv[])
455 {
456 sub_init();
457 test_run(argc, argv, tests, SRCDIR "/tests/mp");
458 return (0);
459 }
460
461 #endif
462
463 /*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)