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