d3409d5e |
1 | /* -*-c-*- |
2 | * |
8017495b |
3 | * $Id: mp-arith.c,v 1.4 1999/12/13 15:35:16 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 $ |
8017495b |
33 | * Revision 1.4 1999/12/13 15:35:16 mdw |
34 | * Slightly different rules on memory allocation. |
35 | * |
5bf74dea |
36 | * Revision 1.3 1999/12/11 10:57:43 mdw |
37 | * Karatsuba squaring algorithm. |
38 | * |
ef5f4810 |
39 | * Revision 1.2 1999/12/10 23:18:39 mdw |
40 | * Change interface for suggested destinations. |
41 | * |
d3409d5e |
42 | * Revision 1.1 1999/11/17 18:02:16 mdw |
43 | * New multiprecision integer arithmetic suite. |
44 | * |
45 | */ |
46 | |
47 | /*----- Header files ------------------------------------------------------*/ |
48 | |
49 | #include "mp.h" |
50 | |
ef5f4810 |
51 | /*----- Macros ------------------------------------------------------------*/ |
52 | |
53 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
54 | |
d3409d5e |
55 | /*----- Main code ---------------------------------------------------------*/ |
56 | |
57 | /* --- @mp_2c@ --- * |
58 | * |
59 | * Arguments: @mp *a@ = source |
60 | * |
61 | * Returns: Result, @a@ converted to two's complement notation. |
62 | */ |
63 | |
64 | mp *mp_2c(mp *d, mp *a) |
65 | { |
66 | if (!(a->f & MP_NEG)) |
67 | return (MP_COPY(a)); |
68 | |
69 | MP_MODIFY(d, MP_LEN(a)); |
70 | mpx_2c(d->v, d->vl, a->v, a->vl); |
71 | d->f = a->f & MP_BURN; |
72 | MP_SHRINK(d); |
73 | return (d); |
74 | } |
75 | |
76 | /* --- @mp_sm@ --- * |
77 | * |
78 | * Arguments: @mp *d@ = destination |
79 | * @mp *a@ = source |
80 | * |
81 | * Returns: Result, @a@ converted to the native signed-magnitude |
82 | * notation. |
83 | */ |
84 | |
85 | mp *mp_sm(mp *d, mp *a) |
86 | { |
87 | if (!MP_LEN(a) || a->vl[-1] < MPW_MAX / 2) |
88 | return (MP_COPY(a)); |
89 | |
90 | MP_MODIFY(d, MP_LEN(a)); |
91 | mpx_2c(d->v, d->vl, a->v, a->vl); |
92 | d->f = (a->f & (MP_BURN | MP_NEG)) ^ MP_NEG; |
93 | MP_SHRINK(d); |
94 | return (d); |
95 | } |
96 | |
97 | /* --- @mp_lsl@ --- * |
98 | * |
99 | * Arguments: @mp *d@ = destination |
ef5f4810 |
100 | * @mp *a@ = source |
d3409d5e |
101 | * @size_t n@ = number of bits to move |
102 | * |
103 | * Returns: Result, @a@ shifted left by @n@. |
104 | */ |
105 | |
ef5f4810 |
106 | mp *mp_lsl(mp *d, mp *a, size_t n) |
d3409d5e |
107 | { |
108 | MP_MODIFY(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS); |
109 | mpx_lsl(d->v, d->vl, a->v, a->vl, n); |
110 | d->f = a->f & (MP_NEG | MP_BURN); |
111 | MP_SHRINK(d); |
112 | return (d); |
113 | } |
114 | |
115 | /* --- @mp_lsr@ --- * |
116 | * |
117 | * Arguments: @mp *d@ = destination |
ef5f4810 |
118 | * @mp *a@ = source |
d3409d5e |
119 | * @size_t n@ = number of bits to move |
120 | * |
121 | * Returns: Result, @a@ shifted left by @n@. |
122 | */ |
123 | |
ef5f4810 |
124 | mp *mp_lsr(mp *d, mp *a, size_t n) |
d3409d5e |
125 | { |
126 | MP_MODIFY(d, MP_LEN(a)); |
127 | mpx_lsr(d->v, d->vl, a->v, a->vl, n); |
128 | d->f = a->f & (MP_NEG | MP_BURN); |
129 | MP_SHRINK(d); |
130 | return (d); |
131 | } |
132 | |
133 | /* --- @mp_cmp@ --- * |
134 | * |
135 | * Arguments: @const mp *a, *b@ = two numbers |
136 | * |
137 | * Returns: Less than, equal to or greater than zero, according to |
138 | * whether @a@ is less than, equal to or greater than @b@. |
139 | */ |
140 | |
141 | int mp_cmp(const mp *a, const mp *b) |
142 | { |
143 | if (!((a->f ^ b->f) & MP_NEG)) |
144 | return (mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
145 | else if (a->f & MP_NEG) |
146 | return (-1); |
147 | else |
148 | return (+1); |
149 | } |
150 | |
151 | /* --- @mp_add@ --- * |
152 | * |
153 | * Arguments: @mp *d@ = destination |
ef5f4810 |
154 | * @mp *a, *b@ = sources |
d3409d5e |
155 | * |
156 | * Returns: Result, @a@ added to @b@. |
157 | */ |
158 | |
ef5f4810 |
159 | mp *mp_add(mp *d, mp *a, mp *b) |
d3409d5e |
160 | { |
ef5f4810 |
161 | MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1); |
d3409d5e |
162 | if (!((a->f ^ b->f) & MP_NEG)) |
163 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
164 | else { |
165 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
166 | mp *t = a; a = b; b = t; |
d3409d5e |
167 | } |
168 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
169 | } |
170 | d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG); |
171 | MP_SHRINK(d); |
172 | return (d); |
173 | } |
174 | |
175 | /* --- @mp_sub@ --- * |
176 | * |
177 | * Arguments: @mp *d@ = destination |
ef5f4810 |
178 | * @mp *a, *b@ = sources |
d3409d5e |
179 | * |
180 | * Returns: Result, @b@ subtracted from @a@. |
181 | */ |
182 | |
ef5f4810 |
183 | mp *mp_sub(mp *d, mp *a, mp *b) |
d3409d5e |
184 | { |
185 | unsigned sgn = 0; |
ef5f4810 |
186 | MP_MODIFY(d, MAX(MP_LEN(a), MP_LEN(b)) + 1); |
d3409d5e |
187 | if ((a->f ^ b->f) & MP_NEG) |
188 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
189 | else { |
190 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
191 | mp *t = a; a = b; b = t; |
d3409d5e |
192 | sgn = MP_NEG; |
193 | } |
194 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
195 | } |
196 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG); |
197 | MP_SHRINK(d); |
198 | return (d); |
199 | } |
200 | |
201 | /* --- @mp_mul@ --- * |
202 | * |
203 | * Arguments: @mp *d@ = destination |
ef5f4810 |
204 | * @mp *a, *b@ = sources |
d3409d5e |
205 | * |
206 | * Returns: Result, @a@ multiplied by @b@. |
207 | */ |
208 | |
ef5f4810 |
209 | mp *mp_mul(mp *d, mp *a, mp *b) |
d3409d5e |
210 | { |
8017495b |
211 | size_t m = MAX(MP_LEN(a), MP_LEN(b)) * 2 + KARATSUBA_SLOP; |
212 | |
ef5f4810 |
213 | a = MP_COPY(a); |
214 | b = MP_COPY(b); |
215 | |
8017495b |
216 | if (MP_LEN(a) <= KARATSUBA_CUTOFF || MP_LEN(b) <= KARATSUBA_CUTOFF) { |
217 | MP_MODIFY(d, MP_LEN(a) + MP_LEN(b)); |
ef5f4810 |
218 | mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
8017495b |
219 | } else { |
ef5f4810 |
220 | mpw *s; |
221 | m += 32; |
222 | s = MP_ALLOC(m); |
8017495b |
223 | MP_MODIFY(d, 2 * m + 2); |
ef5f4810 |
224 | mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + m); |
225 | MP_FREE(s); |
226 | } |
227 | |
d3409d5e |
228 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
229 | MP_SHRINK(d); |
ef5f4810 |
230 | MP_DROP(a); |
231 | MP_DROP(b); |
d3409d5e |
232 | return (d); |
233 | } |
234 | |
235 | /* --- @mp_sqr@ --- * |
236 | * |
237 | * Arguments: @mp *d@ = destination |
ef5f4810 |
238 | * @mp *a@ = source |
d3409d5e |
239 | * |
240 | * Returns: Result, @a@ squared. |
241 | */ |
242 | |
ef5f4810 |
243 | mp *mp_sqr(mp *d, mp *a) |
d3409d5e |
244 | { |
ef5f4810 |
245 | size_t m = MP_LEN(a); |
246 | |
247 | a = MP_COPY(a); |
8017495b |
248 | MP_MODIFY(d, 2 * m + 2); |
ef5f4810 |
249 | if (m > KARATSUBA_CUTOFF) { |
250 | mpw *s; |
251 | m = 2 * (m + 1) + 32; |
252 | s = MP_ALLOC(m); |
5bf74dea |
253 | mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + m); |
ef5f4810 |
254 | MP_FREE(s); |
255 | } else |
256 | mpx_usqr(d->v, d->vl, a->v, a->vl); |
d3409d5e |
257 | d->f = a->f & MP_BURN; |
258 | MP_SHRINK(d); |
ef5f4810 |
259 | MP_DROP(a); |
d3409d5e |
260 | return (d); |
261 | } |
262 | |
263 | /* --- @mp_div@ --- * |
264 | * |
265 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
ef5f4810 |
266 | * @mp *a, *b@ = sources |
d3409d5e |
267 | * |
268 | * Use: Calculates the quotient and remainder when @a@ is divided by |
269 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
270 | * Either of @qq@ or @rr@ may be null to indicate that the |
271 | * result is irrelevant. (Discarding both results is silly.) |
272 | * There is a performance advantage if @a == *rr@. |
273 | * |
274 | * The behaviour when @a@ and @b@ have the same sign is |
275 | * straightforward. When the signs differ, this implementation |
276 | * chooses @r@ to have the same sign as @b@, rather than the |
277 | * more normal choice that the remainder has the same sign as |
278 | * the dividend. This makes modular arithmetic a little more |
279 | * straightforward. |
280 | */ |
281 | |
ef5f4810 |
282 | void mp_div(mp **qq, mp **rr, mp *a, mp *b) |
d3409d5e |
283 | { |
284 | mp *r = rr ? *rr : MP_NEW; |
285 | mp *q = qq ? *qq : MP_NEW; |
286 | mpw *sv, *svl; |
287 | |
288 | /* --- Set up some temporary workspace --- */ |
289 | |
290 | { |
291 | size_t rq = MP_LEN(b) + 1; |
292 | sv = MP_ALLOC(rq); |
293 | svl = sv + rq; |
294 | } |
295 | |
296 | /* --- Set the remainder up right --- * |
297 | * |
298 | * Just in case the divisor is larger, be able to cope with this. It's not |
299 | * important in @mpx_udiv@, but it is here because of the sign correction. |
300 | */ |
301 | |
302 | { |
303 | size_t rq = MP_LEN(a) + 2; |
304 | if (MP_LEN(b) > rq) |
305 | rq = MP_LEN(b); |
306 | |
ef5f4810 |
307 | b = MP_COPY(b); |
d3409d5e |
308 | if (r == a) { |
ef5f4810 |
309 | MP_SPLIT(a); |
310 | a = r = MP_COPY(a); |
d3409d5e |
311 | MP_ENSURE(r, MP_LEN(r) + 2); |
312 | } else { |
ef5f4810 |
313 | a = MP_COPY(a); |
d3409d5e |
314 | MP_MODIFY(r, MP_LEN(a) + 2); |
315 | memcpy(r->v, a->v, MPWS(MP_LEN(a))); |
316 | memset(r->v + MP_LEN(a), 0, MPWS(2)); |
317 | } |
318 | } |
319 | |
320 | /* --- Fix up the quotient too --- */ |
321 | |
d3409d5e |
322 | MP_MODIFY(q, MP_LEN(a)); |
323 | |
324 | /* --- Perform the calculation --- */ |
325 | |
326 | mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl); |
327 | |
328 | /* --- Sort out the sign of the results --- * |
329 | * |
330 | * If the signs of the arguments differ, and the remainder is nonzero, I |
331 | * must add one to the absolute value of the quotient and subtract the |
332 | * remainder from @b@. |
333 | */ |
334 | |
335 | q->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
336 | if (q->f & MP_NEG) { |
ef5f4810 |
337 | mpw *v; |
338 | for (v = r->v; v < r->vl; v++) { |
d3409d5e |
339 | if (*v) { |
340 | MPX_UADDN(q->v, q->vl, 1); |
341 | mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl); |
342 | break; |
343 | } |
344 | } |
345 | } |
346 | |
347 | r->f = ((a->f | b->f) & MP_BURN) | (b->f & MP_NEG); |
348 | |
349 | /* --- Store the return values --- */ |
350 | |
351 | if (!qq) |
352 | MP_DROP(q); |
353 | else { |
354 | MP_SHRINK(q); |
355 | *qq = q; |
356 | } |
357 | |
358 | if (!rr) |
359 | MP_DROP(r); |
360 | else { |
361 | MP_SHRINK(r); |
362 | *rr = r; |
363 | } |
364 | |
ef5f4810 |
365 | MP_DROP(a); |
366 | MP_DROP(b); |
d3409d5e |
367 | MP_FREE(sv); |
368 | } |
369 | |
370 | /*----- Test rig ----------------------------------------------------------*/ |
371 | |
372 | #ifdef TEST_RIG |
373 | |
374 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
375 | { |
376 | if (MP_CMP(expect, !=, result)) { |
377 | fprintf(stderr, "\n*** %s failed", op); |
378 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
379 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10); |
380 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10); |
381 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10); |
382 | fputc('\n', stderr); |
383 | return (0); |
384 | } |
385 | return (1); |
386 | } |
387 | |
388 | #define RIG(name, op) \ |
ef5f4810 |
389 | static int t##name(dstr *v) \ |
d3409d5e |
390 | { \ |
391 | mp *a = *(mp **)v[0].buf; \ |
392 | mpw n = *(int *)v[1].buf; \ |
393 | mp b; \ |
394 | mp *r = *(mp **)v[2].buf; \ |
395 | mp *c = op(MP_NEW, a, n); \ |
396 | int ok; \ |
397 | mp_build(&b, &n, &n + 1); \ |
398 | ok = verify(#name, r, c, a, &b); \ |
399 | mp_drop(a); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
400 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
401 | return (ok); \ |
402 | } |
403 | |
404 | RIG(lsl, mp_lsl) |
405 | RIG(lsr, mp_lsr) |
406 | |
407 | #undef RIG |
408 | |
409 | #define RIG(name, op) \ |
ef5f4810 |
410 | static int t##name(dstr *v) \ |
d3409d5e |
411 | { \ |
412 | mp *a = *(mp **)v[0].buf; \ |
413 | mp *b = *(mp **)v[1].buf; \ |
414 | mp *r = *(mp **)v[2].buf; \ |
415 | mp *c = op(MP_NEW, a, b); \ |
416 | int ok = verify(#name, r, c, a, b); \ |
417 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
418 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
419 | return (ok); \ |
420 | } |
421 | |
422 | RIG(add, mp_add) |
423 | RIG(sub, mp_sub) |
424 | RIG(mul, mp_mul) |
425 | |
426 | #undef RIG |
427 | |
428 | static int tdiv(dstr *v) |
429 | { |
430 | mp *a = *(mp **)v[0].buf; |
431 | mp *b = *(mp **)v[1].buf; |
432 | mp *q = *(mp **)v[2].buf; |
433 | mp *r = *(mp **)v[3].buf; |
434 | mp *c = MP_NEW, *d = MP_NEW; |
435 | int ok = 1; |
436 | mp_div(&c, &d, a, b); |
437 | ok &= verify("div(quotient)", q, c, a, b); |
438 | ok &= verify("div(remainder)", r, d, a, b); |
439 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
ef5f4810 |
440 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
441 | return (ok); |
442 | } |
443 | |
444 | static test_chunk tests[] = { |
445 | { "lsl", tlsl, { &type_mp, &type_mp, &type_mp, 0 } }, |
446 | { "lsr", tlsr, { &type_mp, &type_mp, &type_mp, 0 } }, |
447 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
448 | { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } }, |
449 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
450 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
451 | { 0, 0, { 0 } }, |
452 | }; |
453 | |
454 | int main(int argc, char *argv[]) |
455 | { |
456 | sub_init(); |
457 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
458 | return (0); |
459 | } |
460 | |
461 | #endif |
462 | |
463 | /*----- That's all, folks -------------------------------------------------*/ |