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