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Change Karatsuba parameters slightly.
[u/mdw/catacomb] / mp-arith.c
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d3409d5e 1/* -*-c-*-
2 *
ef5f4810 3 * $Id: mp-arith.c,v 1.2 1999/12/10 23:18:39 mdw Exp $
d3409d5e 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 $
ef5f4810 33 * Revision 1.2 1999/12/10 23:18:39 mdw
34 * Change interface for suggested destinations.
35 *
d3409d5e 36 * Revision 1.1 1999/11/17 18:02:16 mdw
37 * New multiprecision integer arithmetic suite.
38 *
39 */
40
41/*----- Header files ------------------------------------------------------*/
42
43#include "mp.h"
44
ef5f4810 45/*----- Macros ------------------------------------------------------------*/
46
47#define MAX(x, y) ((x) >= (y) ? (x) : (y))
48
d3409d5e 49/*----- Main code ---------------------------------------------------------*/
50
51/* --- @mp_2c@ --- *
52 *
53 * Arguments: @mp *a@ = source
54 *
55 * Returns: Result, @a@ converted to two's complement notation.
56 */
57
58mp *mp_2c(mp *d, mp *a)
59{
60 if (!(a->f & MP_NEG))
61 return (MP_COPY(a));
62
63 MP_MODIFY(d, MP_LEN(a));
64 mpx_2c(d->v, d->vl, a->v, a->vl);
65 d->f = a->f & MP_BURN;
66 MP_SHRINK(d);
67 return (d);
68}
69
70/* --- @mp_sm@ --- *
71 *
72 * Arguments: @mp *d@ = destination
73 * @mp *a@ = source
74 *
75 * Returns: Result, @a@ converted to the native signed-magnitude
76 * notation.
77 */
78
79mp *mp_sm(mp *d, mp *a)
80{
81 if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2)
82 return (MP_COPY(a));
83
84 MP_MODIFY(d, MP_LEN(a));
85 mpx_2c(d->v, d->vl, a->v, a->vl);
86 d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG;
87 MP_SHRINK(d);
88 return (d);
89}
90
91/* --- @mp_lsl@ --- *
92 *
93 * Arguments: @mp *d@ = destination
ef5f4810 94 * @mp *a@ = source
d3409d5e 95 * @size_t n@ = number of bits to move
96 *
97 * Returns: Result, @a@ shifted left by @n@.
98 */
99
ef5f4810 100mp *mp_lsl(mp *d, mp *a, size_t n)
d3409d5e 101{
102 MP_MODIFY(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS);
103 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
104 d->f = a->f & (MP_NEG | MP_BURN);
105 MP_SHRINK(d);
106 return (d);
107}
108
109/* --- @mp_lsr@ --- *
110 *
111 * Arguments: @mp *d@ = destination
ef5f4810 112 * @mp *a@ = source
d3409d5e 113 * @size_t n@ = number of bits to move
114 *
115 * Returns: Result, @a@ shifted left by @n@.
116 */
117
ef5f4810 118mp *mp_lsr(mp *d, mp *a, size_t n)
d3409d5e 119{
120 MP_MODIFY(d, MP_LEN(a));
121 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
122 d->f = a->f & (MP_NEG | MP_BURN);
123 MP_SHRINK(d);
124 return (d);
125}
126
127/* --- @mp_cmp@ --- *
128 *
129 * Arguments: @const mp *a, *b@ = two numbers
130 *
131 * Returns: Less than, equal to or greater than zero, according to
132 * whether @a@ is less than, equal to or greater than @b@.
133 */
134
135int mp_cmp(const mp *a, const mp *b)
136{
137 if (!((a->f ^ b->f) & MP_NEG))
138 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
139 else if (a->f & MP_NEG)
140 return (-1);
141 else
142 return (+1);
143}
144
145/* --- @mp_add@ --- *
146 *
147 * Arguments: @mp *d@ = destination
ef5f4810 148 * @mp *a, *b@ = sources
d3409d5e 149 *
150 * Returns: Result, @a@ added to @b@.
151 */
152
ef5f4810 153mp *mp_add(mp *d, mp *a, mp *b)
d3409d5e 154{
ef5f4810 155 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
d3409d5e 156 if (!((a->f ^ b->f) & MP_NEG))
157 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
158 else {
159 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 160 mp *t = a; a = b; b = t;
d3409d5e 161 }
162 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
163 }
164 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
165 MP_SHRINK(d);
166 return (d);
167}
168
169/* --- @mp_sub@ --- *
170 *
171 * Arguments: @mp *d@ = destination
ef5f4810 172 * @mp *a, *b@ = sources
d3409d5e 173 *
174 * Returns: Result, @b@ subtracted from @a@.
175 */
176
ef5f4810 177mp *mp_sub(mp *d, mp *a, mp *b)
d3409d5e 178{
179 unsigned sgn = 0;
ef5f4810 180 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
d3409d5e 181 if ((a->f ^ b->f) & MP_NEG)
182 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
183 else {
184 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 185 mp *t = a; a = b; b = t;
d3409d5e 186 sgn = MP_NEG;
187 }
188 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
189 }
190 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
191 MP_SHRINK(d);
192 return (d);
193}
194
195/* --- @mp_mul@ --- *
196 *
197 * Arguments: @mp *d@ = destination
ef5f4810 198 * @mp *a, *b@ = sources
d3409d5e 199 *
200 * Returns: Result, @a@ multiplied by @b@.
201 */
202
ef5f4810 203mp *mp_mul(mp *d, mp *a, mp *b)
d3409d5e 204{
ef5f4810 205 a = MP_COPY(a);
206 b = MP_COPY(b);
207
d3409d5e 208 MP_MODIFY(d, MP_LEN(a) + MP_LEN(b));
ef5f4810 209 if (MP_LEN(a) <= KARATSUBA_CUTOFF || MP_LEN(b) <= KARATSUBA_CUTOFF)
210 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
211 else {
212 size_t m = MAX(MP_LEN(a), MP_LEN(b)) * 2 + KARATSUBA_SLOP;
213 mpw *s;
214 m += 32;
215 s = MP_ALLOC(m);
216 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m);
217 MP_FREE(s);
218 }
219
d3409d5e 220 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
221 MP_SHRINK(d);
ef5f4810 222 MP_DROP(a);
223 MP_DROP(b);
d3409d5e 224 return (d);
225}
226
227/* --- @mp_sqr@ --- *
228 *
229 * Arguments: @mp *d@ = destination
ef5f4810 230 * @mp *a@ = source
d3409d5e 231 *
232 * Returns: Result, @a@ squared.
233 */
234
ef5f4810 235mp *mp_sqr(mp *d, mp *a)
d3409d5e 236{
ef5f4810 237 size_t m = MP_LEN(a);
238
239 a = MP_COPY(a);
240 MP_MODIFY(d, 2 * m);
241 if (m > KARATSUBA_CUTOFF) {
242 mpw *s;
243 m = 2 * (m + 1) + 32;
244 s = MP_ALLOC(m);
245 mpx_kmul(d->v, d->vl, a->v, a->vl, a->v, a->vl, s, s + m);
246 MP_FREE(s);
247 } else
248 mpx_usqr(d->v, d->vl, a->v, a->vl);
d3409d5e 249 d->f = a->f & MP_BURN;
250 MP_SHRINK(d);
ef5f4810 251 MP_DROP(a);
d3409d5e 252 return (d);
253}
254
255/* --- @mp_div@ --- *
256 *
257 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
ef5f4810 258 * @mp *a, *b@ = sources
d3409d5e 259 *
260 * Use: Calculates the quotient and remainder when @a@ is divided by
261 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
262 * Either of @qq@ or @rr@ may be null to indicate that the
263 * result is irrelevant. (Discarding both results is silly.)
264 * There is a performance advantage if @a == *rr@.
265 *
266 * The behaviour when @a@ and @b@ have the same sign is
267 * straightforward. When the signs differ, this implementation
268 * chooses @r@ to have the same sign as @b@, rather than the
269 * more normal choice that the remainder has the same sign as
270 * the dividend. This makes modular arithmetic a little more
271 * straightforward.
272 */
273
ef5f4810 274void mp_div(mp **qq, mp **rr, mp *a, mp *b)
d3409d5e 275 {
276 mp *r = rr ? *rr : MP_NEW;
277 mp *q = qq ? *qq : MP_NEW;
278 mpw *sv, *svl;
279
280 /* --- Set up some temporary workspace --- */
281
282 {
283 size_t rq = MP_LEN(b) + 1;
284 sv = MP_ALLOC(rq);
285 svl = sv + rq;
286 }
287
288 /* --- Set the remainder up right --- *
289 *
290 * Just in case the divisor is larger, be able to cope with this. It's not
291 * important in @mpx_udiv@, but it is here because of the sign correction.
292 */
293
294 {
295 size_t rq = MP_LEN(a) + 2;
296 if (MP_LEN(b) > rq)
297 rq = MP_LEN(b);
298
ef5f4810 299 b = MP_COPY(b);
d3409d5e 300 if (r == a) {
ef5f4810 301 MP_SPLIT(a);
302 a = r = MP_COPY(a);
d3409d5e 303 MP_ENSURE(r, MP_LEN(r) + 2);
304 } else {
ef5f4810 305 a = MP_COPY(a);
d3409d5e 306 MP_MODIFY(r, MP_LEN(a) + 2);
307 memcpy(r->v, a->v, MPWS(MP_LEN(a)));
308 memset(r->v + MP_LEN(a), 0, MPWS(2));
309 }
310 }
311
312 /* --- Fix up the quotient too --- */
313
d3409d5e 314 MP_MODIFY(q, MP_LEN(a));
315
316 /* --- Perform the calculation --- */
317
318 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
319
320 /* --- Sort out the sign of the results --- *
321 *
322 * If the signs of the arguments differ, and the remainder is nonzero, I
323 * must add one to the absolute value of the quotient and subtract the
324 * remainder from @b@.
325 */
326
327 q->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
328 if (q->f & MP_NEG) {
ef5f4810 329 mpw *v;
330 for (v = r->v; v < r->vl; v++) {
d3409d5e 331 if (*v) {
332 MPX_UADDN(q->v, q->vl, 1);
333 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
334 break;
335 }
336 }
337 }
338
339 r->f = ((a->f | b->f) & MP_BURN) | (b->f & MP_NEG);
340
341 /* --- Store the return values --- */
342
343 if (!qq)
344 MP_DROP(q);
345 else {
346 MP_SHRINK(q);
347 *qq = q;
348 }
349
350 if (!rr)
351 MP_DROP(r);
352 else {
353 MP_SHRINK(r);
354 *rr = r;
355 }
356
ef5f4810 357 MP_DROP(a);
358 MP_DROP(b);
d3409d5e 359 MP_FREE(sv);
360}
361
362/*----- Test rig ----------------------------------------------------------*/
363
364#ifdef TEST_RIG
365
366static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
367{
368 if (MP_CMP(expect, !=, result)) {
369 fprintf(stderr, "\n*** %s failed", op);
370 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
371 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
372 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
373 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
374 fputc('\n', stderr);
375 return (0);
376 }
377 return (1);
378}
379
380#define RIG(name, op) \
ef5f4810 381 static int t##name(dstr *v) \
d3409d5e 382 { \
383 mp *a = *(mp **)v[0].buf; \
384 mpw n = *(int *)v[1].buf; \
385 mp b; \
386 mp *r = *(mp **)v[2].buf; \
387 mp *c = op(MP_NEW, a, n); \
388 int ok; \
389 mp_build(&b, &n, &n + 1); \
390 ok = verify(#name, r, c, a, &b); \
391 mp_drop(a); mp_drop(c); mp_drop(r); \
ef5f4810 392 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 393 return (ok); \
394 }
395
396RIG(lsl, mp_lsl)
397RIG(lsr, mp_lsr)
398
399#undef RIG
400
401#define RIG(name, op) \
ef5f4810 402 static int t##name(dstr *v) \
d3409d5e 403 { \
404 mp *a = *(mp **)v[0].buf; \
405 mp *b = *(mp **)v[1].buf; \
406 mp *r = *(mp **)v[2].buf; \
407 mp *c = op(MP_NEW, a, b); \
408 int ok = verify(#name, r, c, a, b); \
409 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
ef5f4810 410 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 411 return (ok); \
412 }
413
414RIG(add, mp_add)
415RIG(sub, mp_sub)
416RIG(mul, mp_mul)
417
418#undef RIG
419
420static int tdiv(dstr *v)
421{
422 mp *a = *(mp **)v[0].buf;
423 mp *b = *(mp **)v[1].buf;
424 mp *q = *(mp **)v[2].buf;
425 mp *r = *(mp **)v[3].buf;
426 mp *c = MP_NEW, *d = MP_NEW;
427 int ok = 1;
428 mp_div(&c, &d, a, b);
429 ok &= verify("div(quotient)", q, c, a, b);
430 ok &= verify("div(remainder)", r, d, a, b);
431 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
ef5f4810 432 assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e 433 return (ok);
434}
435
436static test_chunk tests[] = {
437 { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } },
438 { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } },
439 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
440 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
441 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
442 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
443 { 0, 0, { 0 } },
444};
445
446int main(int argc, char *argv[])
447{
448 sub_init();
449 test_run(argc, argv, tests, SRCDIR "/tests/mp");
450 return (0);
451}
452
453#endif
454
455/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)