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