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 | |
67 | mp *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 | |
88 | mp *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 |
109 | mp *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 |
127 | mp *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 | |
144 | int 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 |
162 | mp *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 |
186 | mp *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 |
212 | mp *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 |
245 | mp *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 |
284 | void 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 | |
376 | static 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 | |
406 | RIG(lsl, mp_lsl) |
407 | RIG(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 | |
424 | RIG(add, mp_add) |
425 | RIG(sub, mp_sub) |
426 | RIG(mul, mp_mul) |
427 | |
428 | #undef RIG |
429 | |
430 | static 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 | |
446 | static 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 | |
456 | int 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 -------------------------------------------------*/ |