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Table for driving key data extraction.
[u/mdw/catacomb] / mp-arith.c
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d3409d5e 1/* -*-c-*-
2 *
bba03f55 3 * $Id: mp-arith.c,v 1.5 1999/12/22 15:54:41 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 $
bba03f55 33 * Revision 1.5 1999/12/22 15:54:41 mdw
34 * Adjust Karatsuba parameters. Calculate destination size better.
35 *
8017495b 36 * Revision 1.4 1999/12/13 15:35:16 mdw
37 * Slightly different rules on memory allocation.
38 *
5bf74dea 39 * Revision 1.3 1999/12/11 10:57:43 mdw
40 * Karatsuba squaring algorithm.
41 *
ef5f4810 42 * Revision 1.2 1999/12/10 23:18:39 mdw
43 * Change interface for suggested destinations.
44 *
d3409d5e 45 * Revision 1.1 1999/11/17 18:02:16 mdw
46 * New multiprecision integer arithmetic suite.
47 *
48 */
49
50/*----- Header files ------------------------------------------------------*/
51
52#include "mp.h"
53
ef5f4810 54/*----- Macros ------------------------------------------------------------*/
55
56#define MAX(x, y) ((x) >= (y) ? (x) : (y))
57
d3409d5e 58/*----- Main code ---------------------------------------------------------*/
59
60/* --- @mp_2c@ --- *
61 *
62 * Arguments: @mp *a@ = source
63 *
64 * Returns: Result, @a@ converted to two's complement notation.
65 */
66
67mp *mp_2c(mp *d, mp *a)
68{
69 if (!(a->f & MP_NEG))
70 return (MP_COPY(a));
71
72 MP_MODIFY(d, MP_LEN(a));
73 mpx_2c(d->v, d->vl, a->v, a->vl);
74 d->f = a->f & MP_BURN;
75 MP_SHRINK(d);
76 return (d);
77}
78
79/* --- @mp_sm@ --- *
80 *
81 * Arguments: @mp *d@ = destination
82 * @mp *a@ = source
83 *
84 * Returns: Result, @a@ converted to the native signed-magnitude
85 * notation.
86 */
87
88mp *mp_sm(mp *d, mp *a)
89{
90 if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2)
91 return (MP_COPY(a));
92
93 MP_MODIFY(d, MP_LEN(a));
94 mpx_2c(d->v, d->vl, a->v, a->vl);
95 d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG;
96 MP_SHRINK(d);
97 return (d);
98}
99
100/* --- @mp_lsl@ --- *
101 *
102 * Arguments: @mp *d@ = destination
ef5f4810 103 * @mp *a@ = source
d3409d5e 104 * @size_t n@ = number of bits to move
105 *
106 * Returns: Result, @a@ shifted left by @n@.
107 */
108
ef5f4810 109mp *mp_lsl(mp *d, mp *a, size_t n)
d3409d5e 110{
111 MP_MODIFY(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS);
112 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
113 d->f = a->f & (MP_NEG | MP_BURN);
114 MP_SHRINK(d);
115 return (d);
116}
117
118/* --- @mp_lsr@ --- *
119 *
120 * Arguments: @mp *d@ = destination
ef5f4810 121 * @mp *a@ = source
d3409d5e 122 * @size_t n@ = number of bits to move
123 *
124 * Returns: Result, @a@ shifted left by @n@.
125 */
126
ef5f4810 127mp *mp_lsr(mp *d, mp *a, size_t n)
d3409d5e 128{
129 MP_MODIFY(d, MP_LEN(a));
130 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
131 d->f = a->f & (MP_NEG | MP_BURN);
132 MP_SHRINK(d);
133 return (d);
134}
135
136/* --- @mp_cmp@ --- *
137 *
138 * Arguments: @const mp *a, *b@ = two numbers
139 *
140 * Returns: Less than, equal to or greater than zero, according to
141 * whether @a@ is less than, equal to or greater than @b@.
142 */
143
144int mp_cmp(const mp *a, const mp *b)
145{
146 if (!((a->f ^ b->f) & MP_NEG))
147 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
148 else if (a->f & MP_NEG)
149 return (-1);
150 else
151 return (+1);
152}
153
154/* --- @mp_add@ --- *
155 *
156 * Arguments: @mp *d@ = destination
ef5f4810 157 * @mp *a, *b@ = sources
d3409d5e 158 *
159 * Returns: Result, @a@ added to @b@.
160 */
161
ef5f4810 162mp *mp_add(mp *d, mp *a, mp *b)
d3409d5e 163{
ef5f4810 164 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
d3409d5e 165 if (!((a->f ^ b->f) & MP_NEG))
166 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
167 else {
168 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 169 mp *t = a; a = b; b = t;
d3409d5e 170 }
171 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
172 }
173 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
174 MP_SHRINK(d);
175 return (d);
176}
177
178/* --- @mp_sub@ --- *
179 *
180 * Arguments: @mp *d@ = destination
ef5f4810 181 * @mp *a, *b@ = sources
d3409d5e 182 *
183 * Returns: Result, @b@ subtracted from @a@.
184 */
185
ef5f4810 186mp *mp_sub(mp *d, mp *a, mp *b)
d3409d5e 187{
188 unsigned sgn = 0;
ef5f4810 189 MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1);
d3409d5e 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)) {
ef5f4810 194 mp *t = a; a = b; b = t;
d3409d5e 195 sgn = MP_NEG;
196 }
197 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
198 }
199 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
200 MP_SHRINK(d);
201 return (d);
202}
203
204/* --- @mp_mul@ --- *
205 *
206 * Arguments: @mp *d@ = destination
ef5f4810 207 * @mp *a, *b@ = sources
d3409d5e 208 *
209 * Returns: Result, @a@ multiplied by @b@.
210 */
211
ef5f4810 212mp *mp_mul(mp *d, mp *a, mp *b)
d3409d5e 213{
ef5f4810 214 a = MP_COPY(a);
215 b = MP_COPY(b);
216
8017495b 217 if (MP_LEN(a) <= KARATSUBA_CUTOFF || MP_LEN(b) <= KARATSUBA_CUTOFF) {
218 MP_MODIFY(d, MP_LEN(a) + MP_LEN(b));
ef5f4810 219 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
8017495b 220 } else {
bba03f55 221 size_t m = 2 * MAX(MP_LEN(a), MP_LEN(b)) + 2;
ef5f4810 222 mpw *s;
bba03f55 223 MP_MODIFY(d, m);
224 m += KARATSUBA_SLOP;
ef5f4810 225 s = MP_ALLOC(m);
226 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m);
227 MP_FREE(s);
228 }
229
d3409d5e 230 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
231 MP_SHRINK(d);
ef5f4810 232 MP_DROP(a);
233 MP_DROP(b);
d3409d5e 234 return (d);
235}
236
237/* --- @mp_sqr@ --- *
238 *
239 * Arguments: @mp *d@ = destination
ef5f4810 240 * @mp *a@ = source
d3409d5e 241 *
242 * Returns: Result, @a@ squared.
243 */
244
ef5f4810 245mp *mp_sqr(mp *d, mp *a)
d3409d5e 246{
ef5f4810 247 size_t m = MP_LEN(a);
248
249 a = MP_COPY(a);
8017495b 250 MP_MODIFY(d, 2 * m + 2);
ef5f4810 251 if (m > KARATSUBA_CUTOFF) {
252 mpw *s;
bba03f55 253 m = 2 * (m + 1) + KARATSUBA_SLOP;
ef5f4810 254 s = MP_ALLOC(m);
5bf74dea 255 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m);
ef5f4810 256 MP_FREE(s);
257 } else
258 mpx_usqr(d->v, d->vl, a->v, a->vl);
d3409d5e 259 d->f = a->f & MP_BURN;
260 MP_SHRINK(d);
ef5f4810 261 MP_DROP(a);
d3409d5e 262 return (d);
263}
264
265/* --- @mp_div@ --- *
266 *
267 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
ef5f4810 268 * @mp *a, *b@ = sources
d3409d5e 269 *
270 * Use: Calculates the quotient and remainder when @a@ is divided by
271 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
272 * Either of @qq@ or @rr@ may be null to indicate that the
273 * result is irrelevant. (Discarding both results is silly.)
274 * There is a performance advantage if @a == *rr@.
275 *
276 * The behaviour when @a@ and @b@ have the same sign is
277 * straightforward. When the signs differ, this implementation
278 * chooses @r@ to have the same sign as @b@, rather than the
279 * more normal choice that the remainder has the same sign as
280 * the dividend. This makes modular arithmetic a little more
281 * straightforward.
282 */
283
ef5f4810 284void mp_div(mp **qq, mp **rr, mp *a, mp *b)
d3409d5e 285 {
286 mp *r = rr ? *rr : MP_NEW;
287 mp *q = qq ? *qq : MP_NEW;
288 mpw *sv, *svl;
289
290 /* --- Set up some temporary workspace --- */
291
292 {
293 size_t rq = MP_LEN(b) + 1;
294 sv = MP_ALLOC(rq);
295 svl = sv + rq;
296 }
297
298 /* --- Set the remainder up right --- *
299 *
300 * Just in case the divisor is larger, be able to cope with this. It's not
301 * important in @mpx_udiv@, but it is here because of the sign correction.
302 */
303
304 {
305 size_t rq = MP_LEN(a) + 2;
306 if (MP_LEN(b) > rq)
307 rq = MP_LEN(b);
308
ef5f4810 309 b = MP_COPY(b);
d3409d5e 310 if (r == a) {
ef5f4810 311 MP_SPLIT(a);
312 a = r = MP_COPY(a);
d3409d5e 313 MP_ENSURE(r, MP_LEN(r) + 2);
314 } else {
ef5f4810 315 a = MP_COPY(a);
d3409d5e 316 MP_MODIFY(r, MP_LEN(a) + 2);
317 memcpy(r->v, a->v, MPWS(MP_LEN(a)));
318 memset(r->v + MP_LEN(a), 0, MPWS(2));
319 }
320 }
321
322 /* --- Fix up the quotient too --- */
323
d3409d5e 324 MP_MODIFY(q, MP_LEN(a));
325
326 /* --- Perform the calculation --- */
327
328 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
329
330 /* --- Sort out the sign of the results --- *
331 *
332 * If the signs of the arguments differ, and the remainder is nonzero, I
333 * must add one to the absolute value of the quotient and subtract the
334 * remainder from @b@.
335 */
336
337 q->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
338 if (q->f & MP_NEG) {
ef5f4810 339 mpw *v;
340 for (v = r->v; v < r->vl; v++) {
d3409d5e 341 if (*v) {
342 MPX_UADDN(q->v, q->vl, 1);
343 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
344 break;
345 }
346 }
347 }
348
349 r->f = ((a->f | b->f) & MP_BURN) | (b->f & MP_NEG);
350
351 /* --- Store the return values --- */
352
353 if (!qq)
354 MP_DROP(q);
355 else {
356 MP_SHRINK(q);
357 *qq = q;
358 }
359
360 if (!rr)
361 MP_DROP(r);
362 else {
363 MP_SHRINK(r);
364 *rr = r;
365 }
366
ef5f4810 367 MP_DROP(a);
368 MP_DROP(b);
d3409d5e 369 MP_FREE(sv);
370}
371
372/*----- Test rig ----------------------------------------------------------*/
373
374#ifdef TEST_RIG
375
376static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
377{
378 if (MP_CMP(expect, !=, result)) {
379 fprintf(stderr, "\n*** %s failed", op);
380 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
381 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
382 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
383 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
384 fputc('\n', stderr);
385 return (0);
386 }
387 return (1);
388}
389
390#define RIG(name, op) \
ef5f4810 391 static int t##name(dstr *v) \
d3409d5e 392 { \
393 mp *a = *(mp **)v[0].buf; \
394 mpw n = *(int *)v[1].buf; \
395 mp b; \
396 mp *r = *(mp **)v[2].buf; \
397 mp *c = op(MP_NEW, a, n); \
398 int ok; \
399 mp_build(&b, &n, &n + 1); \
400 ok = verify(#name, r, c, a, &b); \
401 mp_drop(a); mp_drop(c); mp_drop(r); \
ef5f4810 402 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 403 return (ok); \
404 }
405
406RIG(lsl, mp_lsl)
407RIG(lsr, mp_lsr)
408
409#undef RIG
410
411#define RIG(name, op) \
ef5f4810 412 static int t##name(dstr *v) \
d3409d5e 413 { \
414 mp *a = *(mp **)v[0].buf; \
415 mp *b = *(mp **)v[1].buf; \
416 mp *r = *(mp **)v[2].buf; \
417 mp *c = op(MP_NEW, a, b); \
418 int ok = verify(#name, r, c, a, b); \
419 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
ef5f4810 420 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 421 return (ok); \
422 }
423
424RIG(add, mp_add)
425RIG(sub, mp_sub)
426RIG(mul, mp_mul)
427
428#undef RIG
429
430static int tdiv(dstr *v)
431{
432 mp *a = *(mp **)v[0].buf;
433 mp *b = *(mp **)v[1].buf;
434 mp *q = *(mp **)v[2].buf;
435 mp *r = *(mp **)v[3].buf;
436 mp *c = MP_NEW, *d = MP_NEW;
437 int ok = 1;
438 mp_div(&c, &d, a, b);
439 ok &= verify("div(quotient)", q, c, a, b);
440 ok &= verify("div(remainder)", r, d, a, b);
441 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
ef5f4810 442 assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e 443 return (ok);
444}
445
446static test_chunk tests[] = {
447 { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } },
448 { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } },
449 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
450 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
451 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
452 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
453 { 0, 0, { 0 } },
454};
455
456int main(int argc, char *argv[])
457{
458 sub_init();
459 test_run(argc, argv, tests, SRCDIR "/tests/mp");
460 return (0);
461}
462
463#endif
464
465/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)