d3409d5e |
1 | /* -*-c-*- |
2 | * |
f1713c63 |
3 | * $Id: mp-arith.c,v 1.7 2000/06/22 19:02:53 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 $ |
f1713c63 |
33 | * Revision 1.7 2000/06/22 19:02:53 mdw |
34 | * New function @mp_odd@ to extract powers of two from an integer. This is |
35 | * common code from the Rabin-Miller test, RSA key recovery and modular |
36 | * square-root extraction. |
37 | * |
d34decd2 |
38 | * Revision 1.6 2000/06/17 11:45:09 mdw |
39 | * Major memory management overhaul. Added arena support. Use the secure |
40 | * arena for secret integers. Replace and improve the MP management macros |
41 | * (e.g., replace MP_MODIFY by MP_DEST). |
42 | * |
bba03f55 |
43 | * Revision 1.5 1999/12/22 15:54:41 mdw |
44 | * Adjust Karatsuba parameters. Calculate destination size better. |
45 | * |
8017495b |
46 | * Revision 1.4 1999/12/13 15:35:16 mdw |
47 | * Slightly different rules on memory allocation. |
48 | * |
5bf74dea |
49 | * Revision 1.3 1999/12/11 10:57:43 mdw |
50 | * Karatsuba squaring algorithm. |
51 | * |
ef5f4810 |
52 | * Revision 1.2 1999/12/10 23:18:39 mdw |
53 | * Change interface for suggested destinations. |
54 | * |
d3409d5e |
55 | * Revision 1.1 1999/11/17 18:02:16 mdw |
56 | * New multiprecision integer arithmetic suite. |
57 | * |
58 | */ |
59 | |
60 | /*----- Header files ------------------------------------------------------*/ |
61 | |
62 | #include "mp.h" |
63 | |
ef5f4810 |
64 | /*----- Macros ------------------------------------------------------------*/ |
65 | |
66 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
67 | |
d3409d5e |
68 | /*----- Main code ---------------------------------------------------------*/ |
69 | |
70 | /* --- @mp_2c@ --- * |
71 | * |
72 | * Arguments: @mp *a@ = source |
73 | * |
74 | * Returns: Result, @a@ converted to two's complement notation. |
75 | */ |
76 | |
77 | mp *mp_2c(mp *d, mp *a) |
78 | { |
79 | if (!(a->f & MP_NEG)) |
80 | return (MP_COPY(a)); |
81 | |
d34decd2 |
82 | MP_DEST(d, MP_LEN(a), a->f); |
d3409d5e |
83 | mpx_2c(d->v, d->vl, a->v, a->vl); |
84 | d->f = a->f & MP_BURN; |
85 | MP_SHRINK(d); |
86 | return (d); |
87 | } |
88 | |
89 | /* --- @mp_sm@ --- * |
90 | * |
91 | * Arguments: @mp *d@ = destination |
92 | * @mp *a@ = source |
93 | * |
94 | * Returns: Result, @a@ converted to the native signed-magnitude |
95 | * notation. |
96 | */ |
97 | |
98 | mp *mp_sm(mp *d, mp *a) |
99 | { |
100 | if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2) |
101 | return (MP_COPY(a)); |
102 | |
d34decd2 |
103 | MP_DEST(d, MP_LEN(a), a->f); |
d3409d5e |
104 | mpx_2c(d->v, d->vl, a->v, a->vl); |
105 | d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG; |
106 | MP_SHRINK(d); |
107 | return (d); |
108 | } |
109 | |
110 | /* --- @mp_lsl@ --- * |
111 | * |
112 | * Arguments: @mp *d@ = destination |
ef5f4810 |
113 | * @mp *a@ = source |
d3409d5e |
114 | * @size_t n@ = number of bits to move |
115 | * |
116 | * Returns: Result, @a@ shifted left by @n@. |
117 | */ |
118 | |
ef5f4810 |
119 | mp *mp_lsl(mp *d, mp *a, size_t n) |
d3409d5e |
120 | { |
d34decd2 |
121 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
d3409d5e |
122 | mpx_lsl(d->v, d->vl, a->v, a->vl, n); |
123 | d->f = a->f & (MP_NEG | MP_BURN); |
124 | MP_SHRINK(d); |
125 | return (d); |
126 | } |
127 | |
128 | /* --- @mp_lsr@ --- * |
129 | * |
130 | * Arguments: @mp *d@ = destination |
ef5f4810 |
131 | * @mp *a@ = source |
d3409d5e |
132 | * @size_t n@ = number of bits to move |
133 | * |
134 | * Returns: Result, @a@ shifted left by @n@. |
135 | */ |
136 | |
ef5f4810 |
137 | mp *mp_lsr(mp *d, mp *a, size_t n) |
d3409d5e |
138 | { |
d34decd2 |
139 | MP_DEST(d, MP_LEN(a), a->f); |
d3409d5e |
140 | mpx_lsr(d->v, d->vl, a->v, a->vl, n); |
141 | d->f = a->f & (MP_NEG | MP_BURN); |
142 | MP_SHRINK(d); |
143 | return (d); |
144 | } |
145 | |
146 | /* --- @mp_cmp@ --- * |
147 | * |
148 | * Arguments: @const mp *a, *b@ = two numbers |
149 | * |
150 | * Returns: Less than, equal to or greater than zero, according to |
151 | * whether @a@ is less than, equal to or greater than @b@. |
152 | */ |
153 | |
154 | int mp_cmp(const mp *a, const mp *b) |
155 | { |
156 | if (!((a->f ^ b->f) & MP_NEG)) |
157 | return (mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
158 | else if (a->f & MP_NEG) |
159 | return (-1); |
160 | else |
161 | return (+1); |
162 | } |
163 | |
164 | /* --- @mp_add@ --- * |
165 | * |
166 | * Arguments: @mp *d@ = destination |
ef5f4810 |
167 | * @mp *a, *b@ = sources |
d3409d5e |
168 | * |
169 | * Returns: Result, @a@ added to @b@. |
170 | */ |
171 | |
ef5f4810 |
172 | mp *mp_add(mp *d, mp *a, mp *b) |
d3409d5e |
173 | { |
d34decd2 |
174 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
175 | if (!((a->f ^ b->f) & MP_NEG)) |
176 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
177 | else { |
178 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
179 | mp *t = a; a = b; b = t; |
d3409d5e |
180 | } |
181 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
182 | } |
183 | d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG); |
184 | MP_SHRINK(d); |
185 | return (d); |
186 | } |
187 | |
188 | /* --- @mp_sub@ --- * |
189 | * |
190 | * Arguments: @mp *d@ = destination |
ef5f4810 |
191 | * @mp *a, *b@ = sources |
d3409d5e |
192 | * |
193 | * Returns: Result, @b@ subtracted from @a@. |
194 | */ |
195 | |
ef5f4810 |
196 | mp *mp_sub(mp *d, mp *a, mp *b) |
d3409d5e |
197 | { |
198 | unsigned sgn = 0; |
d34decd2 |
199 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
200 | if ((a->f ^ b->f) & MP_NEG) |
201 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
202 | else { |
203 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
204 | mp *t = a; a = b; b = t; |
d3409d5e |
205 | sgn = MP_NEG; |
206 | } |
207 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
208 | } |
209 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG); |
210 | MP_SHRINK(d); |
211 | return (d); |
212 | } |
213 | |
214 | /* --- @mp_mul@ --- * |
215 | * |
216 | * Arguments: @mp *d@ = destination |
ef5f4810 |
217 | * @mp *a, *b@ = sources |
d3409d5e |
218 | * |
219 | * Returns: Result, @a@ multiplied by @b@. |
220 | */ |
221 | |
ef5f4810 |
222 | mp *mp_mul(mp *d, mp *a, mp *b) |
d3409d5e |
223 | { |
ef5f4810 |
224 | a = MP_COPY(a); |
225 | b = MP_COPY(b); |
226 | |
8017495b |
227 | if (MP_LEN(a) <= KARATSUBA_CUTOFF || MP_LEN(b) <= KARATSUBA_CUTOFF) { |
d34decd2 |
228 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); |
ef5f4810 |
229 | mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
8017495b |
230 | } else { |
bba03f55 |
231 | size_t m = 2 * MAX(MP_LEN(a), MP_LEN(b)) + 2; |
ef5f4810 |
232 | mpw *s; |
d34decd2 |
233 | MP_DEST(d, m, a->f | b->f | MP_UNDEF); |
bba03f55 |
234 | m += KARATSUBA_SLOP; |
d34decd2 |
235 | s = mpalloc(d->a, m); |
ef5f4810 |
236 | mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m); |
d34decd2 |
237 | mpfree(d->a, s); |
ef5f4810 |
238 | } |
239 | |
d3409d5e |
240 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
241 | MP_SHRINK(d); |
ef5f4810 |
242 | MP_DROP(a); |
243 | MP_DROP(b); |
d3409d5e |
244 | return (d); |
245 | } |
246 | |
247 | /* --- @mp_sqr@ --- * |
248 | * |
249 | * Arguments: @mp *d@ = destination |
ef5f4810 |
250 | * @mp *a@ = source |
d3409d5e |
251 | * |
252 | * Returns: Result, @a@ squared. |
253 | */ |
254 | |
ef5f4810 |
255 | mp *mp_sqr(mp *d, mp *a) |
d3409d5e |
256 | { |
ef5f4810 |
257 | size_t m = MP_LEN(a); |
258 | |
259 | a = MP_COPY(a); |
d34decd2 |
260 | MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF); |
ef5f4810 |
261 | if (m > KARATSUBA_CUTOFF) { |
262 | mpw *s; |
bba03f55 |
263 | m = 2 * (m + 1) + KARATSUBA_SLOP; |
d34decd2 |
264 | s = mpalloc(d->a, m); |
5bf74dea |
265 | mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m); |
d34decd2 |
266 | mpfree(d->a, s); |
ef5f4810 |
267 | } else |
268 | mpx_usqr(d->v, d->vl, a->v, a->vl); |
d3409d5e |
269 | d->f = a->f & MP_BURN; |
270 | MP_SHRINK(d); |
ef5f4810 |
271 | MP_DROP(a); |
d3409d5e |
272 | return (d); |
273 | } |
274 | |
275 | /* --- @mp_div@ --- * |
276 | * |
277 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
ef5f4810 |
278 | * @mp *a, *b@ = sources |
d3409d5e |
279 | * |
280 | * Use: Calculates the quotient and remainder when @a@ is divided by |
281 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
282 | * Either of @qq@ or @rr@ may be null to indicate that the |
283 | * result is irrelevant. (Discarding both results is silly.) |
284 | * There is a performance advantage if @a == *rr@. |
285 | * |
286 | * The behaviour when @a@ and @b@ have the same sign is |
287 | * straightforward. When the signs differ, this implementation |
288 | * chooses @r@ to have the same sign as @b@, rather than the |
289 | * more normal choice that the remainder has the same sign as |
290 | * the dividend. This makes modular arithmetic a little more |
291 | * straightforward. |
292 | */ |
293 | |
ef5f4810 |
294 | void mp_div(mp **qq, mp **rr, mp *a, mp *b) |
d3409d5e |
295 | { |
296 | mp *r = rr ? *rr : MP_NEW; |
297 | mp *q = qq ? *qq : MP_NEW; |
298 | mpw *sv, *svl; |
299 | |
d3409d5e |
300 | /* --- Set the remainder up right --- * |
301 | * |
302 | * Just in case the divisor is larger, be able to cope with this. It's not |
303 | * important in @mpx_udiv@, but it is here because of the sign correction. |
304 | */ |
305 | |
d34decd2 |
306 | b = MP_COPY(b); |
307 | a = MP_COPY(a); |
308 | if (r) |
309 | MP_DROP(r); |
310 | r = a; |
311 | MP_DEST(r, MP_LEN(a) + 2, a->f | b->f); |
d3409d5e |
312 | |
313 | /* --- Fix up the quotient too --- */ |
314 | |
d34decd2 |
315 | r = MP_COPY(r); |
316 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); |
317 | MP_DROP(r); |
318 | |
319 | /* --- Set up some temporary workspace --- */ |
320 | |
321 | { |
322 | size_t rq = MP_LEN(b) + 1; |
323 | sv = mpalloc(r->a, rq); |
324 | svl = sv + rq; |
325 | } |
d3409d5e |
326 | |
327 | /* --- Perform the calculation --- */ |
328 | |
329 | mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl); |
330 | |
331 | /* --- Sort out the sign of the results --- * |
332 | * |
333 | * If the signs of the arguments differ, and the remainder is nonzero, I |
334 | * must add one to the absolute value of the quotient and subtract the |
335 | * remainder from @b@. |
336 | */ |
337 | |
d34decd2 |
338 | q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG); |
d3409d5e |
339 | if (q->f & MP_NEG) { |
ef5f4810 |
340 | mpw *v; |
341 | for (v = r->v; v < r->vl; v++) { |
d3409d5e |
342 | if (*v) { |
343 | MPX_UADDN(q->v, q->vl, 1); |
344 | mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl); |
345 | break; |
346 | } |
347 | } |
348 | } |
349 | |
d34decd2 |
350 | r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG); |
d3409d5e |
351 | |
352 | /* --- Store the return values --- */ |
353 | |
d34decd2 |
354 | mpfree(r->a, sv); |
355 | MP_DROP(b); |
356 | |
d3409d5e |
357 | if (!qq) |
358 | MP_DROP(q); |
359 | else { |
360 | MP_SHRINK(q); |
361 | *qq = q; |
362 | } |
363 | |
364 | if (!rr) |
365 | MP_DROP(r); |
366 | else { |
367 | MP_SHRINK(r); |
368 | *rr = r; |
369 | } |
d3409d5e |
370 | } |
371 | |
f1713c63 |
372 | /* --- @mp_odd@ --- * |
373 | * |
374 | * Arguments: @mp *d@ = pointer to destination integer |
375 | * @mp *m@ = pointer to source integer |
376 | * @size_t *s@ = where to store the power of 2 |
377 | * |
378 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
379 | * |
380 | * Use: Computes a power of two and an odd integer which, when |
381 | * multiplied, give a specified result. This sort of thing is |
382 | * useful in number theory quite often. |
383 | */ |
384 | |
385 | mp *mp_odd(mp *d, mp *m, size_t *s) |
386 | { |
387 | size_t ss = 0; |
388 | const mpw *v, *vl; |
389 | |
390 | v = m->v; |
391 | vl = m->vl; |
392 | for (; !*v && v < vl; v++) |
393 | ss += MPW_BITS; |
394 | if (v >= vl) |
395 | ss = 0; |
396 | else { |
397 | mpw x = *v; |
398 | mpw mask = MPW_MAX; |
399 | unsigned z = MPW_BITS / 2; |
400 | |
401 | while (z) { |
402 | mask >>= z; |
403 | if (!(x & mask)) { |
404 | x >>= z; |
405 | ss += z; |
406 | } |
407 | z >>= 1; |
408 | } |
409 | } |
410 | |
411 | *s = ss; |
412 | return (mp_lsr(d, m, ss)); |
413 | } |
414 | |
d3409d5e |
415 | /*----- Test rig ----------------------------------------------------------*/ |
416 | |
417 | #ifdef TEST_RIG |
418 | |
419 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
420 | { |
421 | if (MP_CMP(expect, !=, result)) { |
422 | fprintf(stderr, "\n*** %s failed", op); |
423 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
424 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10); |
425 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10); |
426 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10); |
427 | fputc('\n', stderr); |
428 | return (0); |
429 | } |
430 | return (1); |
431 | } |
432 | |
433 | #define RIG(name, op) \ |
ef5f4810 |
434 | static int t##name(dstr *v) \ |
d3409d5e |
435 | { \ |
436 | mp *a = *(mp **)v[0].buf; \ |
437 | mpw n = *(int *)v[1].buf; \ |
438 | mp b; \ |
439 | mp *r = *(mp **)v[2].buf; \ |
440 | mp *c = op(MP_NEW, a, n); \ |
441 | int ok; \ |
442 | mp_build(&b, &n, &n + 1); \ |
443 | ok = verify(#name, r, c, a, &b); \ |
444 | mp_drop(a); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
445 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
446 | return (ok); \ |
447 | } |
448 | |
449 | RIG(lsl, mp_lsl) |
450 | RIG(lsr, mp_lsr) |
451 | |
452 | #undef RIG |
453 | |
454 | #define RIG(name, op) \ |
ef5f4810 |
455 | static int t##name(dstr *v) \ |
d3409d5e |
456 | { \ |
457 | mp *a = *(mp **)v[0].buf; \ |
458 | mp *b = *(mp **)v[1].buf; \ |
459 | mp *r = *(mp **)v[2].buf; \ |
460 | mp *c = op(MP_NEW, a, b); \ |
461 | int ok = verify(#name, r, c, a, b); \ |
462 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
463 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
464 | return (ok); \ |
465 | } |
466 | |
467 | RIG(add, mp_add) |
468 | RIG(sub, mp_sub) |
469 | RIG(mul, mp_mul) |
470 | |
471 | #undef RIG |
472 | |
473 | static int tdiv(dstr *v) |
474 | { |
475 | mp *a = *(mp **)v[0].buf; |
476 | mp *b = *(mp **)v[1].buf; |
477 | mp *q = *(mp **)v[2].buf; |
478 | mp *r = *(mp **)v[3].buf; |
479 | mp *c = MP_NEW, *d = MP_NEW; |
480 | int ok = 1; |
481 | mp_div(&c, &d, a, b); |
482 | ok &= verify("div(quotient)", q, c, a, b); |
483 | ok &= verify("div(remainder)", r, d, a, b); |
484 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
ef5f4810 |
485 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
486 | return (ok); |
487 | } |
488 | |
f1713c63 |
489 | static int todd(dstr *v) |
490 | { |
491 | mp *a = *(mp **)v[0].buf; |
492 | size_t rs = *(uint32 *)v[1].buf; |
493 | mp *rt = *(mp **)v[2].buf; |
494 | int ok = 1; |
495 | mp *t; |
496 | size_t s; |
497 | t = mp_odd(MP_NEW, a, &s); |
498 | if (s != rs || MP_CMP(t, !=, rt)) { |
499 | ok = 0; |
500 | fprintf(stderr, "\n*** odd failed"); |
501 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
502 | fprintf(stderr, "\n*** s = %lu", (unsigned long)s); |
503 | fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10); |
504 | fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs); |
505 | fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10); |
506 | fputc('\n', stderr); |
507 | } |
508 | mp_drop(a); |
509 | mp_drop(rt); |
510 | mp_drop(t); |
511 | return (ok); |
512 | } |
513 | |
d3409d5e |
514 | static test_chunk tests[] = { |
515 | { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } }, |
516 | { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } }, |
517 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
518 | { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } }, |
519 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
520 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
f1713c63 |
521 | { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } }, |
d3409d5e |
522 | { 0, 0, { 0 } }, |
523 | }; |
524 | |
525 | int main(int argc, char *argv[]) |
526 | { |
527 | sub_init(); |
528 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
529 | return (0); |
530 | } |
531 | |
532 | #endif |
533 | |
534 | /*----- That's all, folks -------------------------------------------------*/ |