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