d3409d5e |
1 | /* -*-c-*- |
2 | * |
397041a9 |
3 | * $Id: mp-arith.c,v 1.14 2002/10/15 19:18:31 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 $ |
397041a9 |
33 | * Revision 1.14 2002/10/15 19:18:31 mdw |
34 | * New operation to negate numbers. |
35 | * |
09d00c6b |
36 | * Revision 1.13 2002/10/15 00:19:40 mdw |
37 | * Bit setting and clearing functions. |
38 | * |
dd22938e |
39 | * Revision 1.12 2002/10/09 00:36:03 mdw |
40 | * Fix bounds on workspace for Karatsuba operations. |
41 | * |
f09e814a |
42 | * Revision 1.11 2002/10/06 22:52:50 mdw |
43 | * Pile of changes for supporting two's complement properly. |
44 | * |
0f32e0f8 |
45 | * Revision 1.10 2001/04/03 19:36:05 mdw |
46 | * Add some simple bitwise operations so that Perl can use them. |
47 | * |
52cdaca9 |
48 | * Revision 1.9 2000/10/08 15:48:35 mdw |
49 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
50 | * |
4b536f42 |
51 | * Revision 1.8 2000/10/08 12:02:21 mdw |
52 | * Use @MP_EQ@ instead of @MP_CMP@. |
53 | * |
f1713c63 |
54 | * Revision 1.7 2000/06/22 19:02:53 mdw |
55 | * New function @mp_odd@ to extract powers of two from an integer. This is |
56 | * common code from the Rabin-Miller test, RSA key recovery and modular |
57 | * square-root extraction. |
58 | * |
d34decd2 |
59 | * Revision 1.6 2000/06/17 11:45:09 mdw |
60 | * Major memory management overhaul. Added arena support. Use the secure |
61 | * arena for secret integers. Replace and improve the MP management macros |
62 | * (e.g., replace MP_MODIFY by MP_DEST). |
63 | * |
bba03f55 |
64 | * Revision 1.5 1999/12/22 15:54:41 mdw |
65 | * Adjust Karatsuba parameters. Calculate destination size better. |
66 | * |
8017495b |
67 | * Revision 1.4 1999/12/13 15:35:16 mdw |
68 | * Slightly different rules on memory allocation. |
69 | * |
5bf74dea |
70 | * Revision 1.3 1999/12/11 10:57:43 mdw |
71 | * Karatsuba squaring algorithm. |
72 | * |
ef5f4810 |
73 | * Revision 1.2 1999/12/10 23:18:39 mdw |
74 | * Change interface for suggested destinations. |
75 | * |
d3409d5e |
76 | * Revision 1.1 1999/11/17 18:02:16 mdw |
77 | * New multiprecision integer arithmetic suite. |
78 | * |
79 | */ |
80 | |
81 | /*----- Header files ------------------------------------------------------*/ |
82 | |
83 | #include "mp.h" |
84 | |
ef5f4810 |
85 | /*----- Macros ------------------------------------------------------------*/ |
86 | |
87 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
88 | |
d3409d5e |
89 | /*----- Main code ---------------------------------------------------------*/ |
90 | |
f09e814a |
91 | /* --- @mp_lsl@, @mp_lsr@ --- * |
d3409d5e |
92 | * |
f09e814a |
93 | * Arguments: @mp *d@ = destination |
94 | * @mp *a@ = source |
95 | * @size_t n@ = number of bits to move |
d3409d5e |
96 | * |
f09e814a |
97 | * Returns: Result, @a@ shifted left or right by @n@. |
d3409d5e |
98 | */ |
99 | |
f09e814a |
100 | mp *mp_lsl(mp *d, mp *a, size_t n) |
d3409d5e |
101 | { |
f09e814a |
102 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
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 | } |
d3409d5e |
108 | |
f09e814a |
109 | mp *mp_lsr(mp *d, mp *a, size_t n) |
110 | { |
d34decd2 |
111 | MP_DEST(d, MP_LEN(a), a->f); |
f09e814a |
112 | mpx_lsr(d->v, d->vl, a->v, a->vl, n); |
113 | d->f = a->f & (MP_NEG | MP_BURN); |
d3409d5e |
114 | MP_SHRINK(d); |
115 | return (d); |
116 | } |
117 | |
f09e814a |
118 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
d3409d5e |
119 | * |
120 | * Arguments: @mp *d@ = destination |
121 | * @mp *a@ = source |
f09e814a |
122 | * @size_t n@ = number of bits to move |
d3409d5e |
123 | * |
f09e814a |
124 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
125 | * pretence of sign-extension for negative numbers. |
d3409d5e |
126 | */ |
127 | |
f09e814a |
128 | mp *mp_lsl2c(mp *d, mp *a, size_t n) |
d3409d5e |
129 | { |
f09e814a |
130 | if (!(a->f & MP_NEG)) |
131 | return (mp_lsl(d, a, n)); |
132 | d = mp_not2c(d, a); |
133 | d = mp_lsl(d, d, n); |
134 | d = mp_not2c(d, d); |
135 | return (d); |
136 | } |
d3409d5e |
137 | |
f09e814a |
138 | mp *mp_lsr2c(mp *d, mp *a, size_t n) |
139 | { |
140 | if (!(a->f & MP_NEG)) |
141 | return (mp_lsr(d, a, n)); |
142 | d = mp_not2c(d, a); |
143 | d = mp_lsr(d, d, n); |
144 | d = mp_not2c(d, d); |
145 | return (d); |
d3409d5e |
146 | } |
147 | |
f09e814a |
148 | /* --- @mp_testbit@ --- * |
d3409d5e |
149 | * |
f09e814a |
150 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
151 | * @unsigned long n@ = which bit to test |
d3409d5e |
152 | * |
f09e814a |
153 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
154 | */ |
155 | |
09d00c6b |
156 | int mp_testbit(mp *x, unsigned long n) |
d3409d5e |
157 | { |
f09e814a |
158 | if (n > MPW_BITS * MP_LEN(x)) |
159 | return (0); |
09d00c6b |
160 | return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u); |
d3409d5e |
161 | } |
162 | |
f09e814a |
163 | /* --- @mp_testbit2c@ --- * |
d3409d5e |
164 | * |
f09e814a |
165 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
166 | * @unsigned long n@ = which bit to test |
d3409d5e |
167 | * |
f09e814a |
168 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
169 | * complement representation. |
d3409d5e |
170 | */ |
171 | |
09d00c6b |
172 | int mp_testbit2c(mp *x, unsigned long n) |
d3409d5e |
173 | { |
f09e814a |
174 | int r; |
09d00c6b |
175 | if (!(x->f & MP_NEG)) |
f09e814a |
176 | return (mp_testbit(x, n)); |
177 | x = mp_not2c(MP_NEW, x); |
178 | r = !mp_testbit(x, n); |
179 | MP_DROP(x); |
180 | return (r); |
d3409d5e |
181 | } |
182 | |
09d00c6b |
183 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
184 | * |
185 | * Arguments: @mp *d@ = a destination |
186 | * @mp *x@ = a large integer |
187 | * @unsigned long n@ = which bit to modify |
188 | * |
189 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
190 | */ |
191 | |
192 | mp *mp_setbit(mp *d, mp *x, unsigned long n) |
193 | { |
194 | size_t rq; |
195 | |
196 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
197 | if (d != x) { |
198 | if (d) MP_DROP(d); |
199 | d = MP_COPY(x); |
200 | } |
201 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
202 | d->v[n/MPW_BITS] |= 1 << n%MPW_BITS; |
203 | return (d); |
204 | } |
205 | |
206 | mp *mp_clearbit(mp *d, mp *x, unsigned long n) |
207 | { |
208 | size_t rq; |
209 | |
210 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
211 | if (d != x) { |
212 | if (d) MP_DROP(d); |
213 | d = MP_COPY(x); |
214 | } |
215 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
216 | d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS); |
217 | return (d); |
218 | } |
219 | |
220 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
221 | * |
222 | * Arguments: @mp *d@ = a destination |
223 | * @mp *x@ = a large integer |
224 | * @unsigned long n@ = which bit to modify |
225 | * |
226 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
227 | * Fakes up two's complement representation. |
228 | */ |
229 | |
230 | mp *mp_setbit2c(mp *d, mp *x, unsigned long n) |
231 | { |
232 | if (!(x->f & MP_NEG)) |
233 | return mp_setbit(d, x, n); |
234 | d = mp_not2c(d, x); |
235 | d = mp_clearbit(d, d, n); |
236 | d = mp_not2c(d, d); |
237 | return (d); |
238 | } |
239 | |
240 | mp *mp_clearbit2c(mp *d, mp *x, unsigned long n) |
241 | { |
242 | if (!(x->f & MP_NEG)) |
243 | return mp_clearbit(d, x, n); |
244 | d = mp_not2c(d, x); |
245 | d = mp_setbit(d, d, n); |
246 | d = mp_not2c(d, d); |
247 | return (d); |
248 | } |
249 | |
4b536f42 |
250 | /* --- @mp_eq@ --- * |
251 | * |
252 | * Arguments: @const mp *a, *b@ = two numbers |
253 | * |
254 | * Returns: Nonzero if the numbers are equal. |
255 | */ |
256 | |
257 | int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); } |
258 | |
d3409d5e |
259 | /* --- @mp_cmp@ --- * |
260 | * |
261 | * Arguments: @const mp *a, *b@ = two numbers |
262 | * |
263 | * Returns: Less than, equal to or greater than zero, according to |
264 | * whether @a@ is less than, equal to or greater than @b@. |
265 | */ |
266 | |
267 | int mp_cmp(const mp *a, const mp *b) |
268 | { |
269 | if (!((a->f ^ b->f) & MP_NEG)) |
270 | return (mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
271 | else if (a->f & MP_NEG) |
272 | return (-1); |
273 | else |
274 | return (+1); |
275 | } |
276 | |
397041a9 |
277 | /* --- @mp_neg@ --- * |
278 | * |
279 | * Arguments: @mp *d@ = destination |
280 | * @mp *a@ = argument |
281 | * |
282 | * Returns: The negation of the argument. |
283 | * |
284 | * Use: Negates its argument. |
285 | */ |
286 | |
287 | mp *mp_neg(mp *d, mp *a) |
288 | { |
289 | /* --- Surprising amounts of messing about required --- */ |
290 | |
291 | MP_SHRINK(a); |
292 | MP_COPY(a); |
293 | if (d) MP_DROP(d); |
294 | if (a->v == a->vl) { |
295 | return (a); |
296 | } |
297 | MP_DEST(a, MP_LEN(a), a->f); |
298 | a->f ^= MP_NEG; |
299 | return (a); |
300 | } |
301 | |
f09e814a |
302 | /* --- @mp_bitop@ --- * |
0f32e0f8 |
303 | * |
304 | * Arguments: @mp *d@ = destination |
305 | * @mp *a, *b@ = sources |
306 | * |
f09e814a |
307 | * Returns: The result of the given bitwise operation. These functions |
308 | * don't handle negative numbers at all sensibly. For that, use |
309 | * the @...2c@ variants. The functions are named after the |
310 | * truth tables they generate: |
311 | * |
312 | * a: 0011 |
313 | * b: 0101 |
314 | * @mpx_bitXXXX@ |
0f32e0f8 |
315 | */ |
316 | |
f09e814a |
317 | #define MP_BITBINOP(string) \ |
0f32e0f8 |
318 | \ |
f09e814a |
319 | mp *mp_bit##string(mp *d, mp *a, mp *b) \ |
0f32e0f8 |
320 | { \ |
321 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), a->f | b->f); \ |
f09e814a |
322 | mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \ |
0f32e0f8 |
323 | d->f = (a->f | b->f) & MP_BURN; \ |
324 | MP_SHRINK(d); \ |
325 | return (d); \ |
326 | } |
327 | |
f09e814a |
328 | MPX_DOBIN(MP_BITBINOP) |
329 | |
330 | /* --- @mp_not@ --- * |
331 | * |
332 | * Arguments: @mp *d@ = destination |
333 | * @mp *a@ = source |
334 | * |
335 | * Returns: The bitwise complement of the source. |
336 | */ |
0f32e0f8 |
337 | |
338 | mp *mp_not(mp *d, mp *a) |
339 | { |
340 | MP_DEST(d, MP_LEN(a), a->f); |
341 | mpx_not(d->v, d->vl, a->v, a->vl); |
342 | d->f = a->f & MP_BURN; |
343 | MP_SHRINK(d); |
344 | return (d); |
345 | } |
346 | |
f09e814a |
347 | /* --- @mp_bitop2c@ --- * |
348 | * |
349 | * Arguments: @mp *d@ = destination |
350 | * @mp *a, *b@ = sources |
351 | * |
352 | * Returns: The result of the given bitwise operation. Negative numbers |
353 | * are treated as two's complement, sign-extended infinitely to |
354 | * the left. The functions are named after the truth tables |
355 | * they generate: |
356 | * |
357 | * a: 0011 |
358 | * b: 0101 |
359 | * @mpx_bitXXXX@ |
360 | */ |
361 | |
362 | /* --- How this actually works --- * |
363 | * |
364 | * The two arguments are inverted (with a sign-swap) if they're currently |
365 | * negative. This means that we end up using a different function (one which |
366 | * reinverts as we go) for the main operation. Also, if the sign would be |
367 | * negative at the end, we preinvert the output and then invert again with a |
368 | * sign-swap. |
369 | * |
370 | * Start with: wxyz WXYZ |
371 | * If @a@ negative: yzwx or YZWX |
372 | * If @b@ negative: xwzy XWZY |
373 | * If both negative: zyxw ZYXW |
374 | */ |
375 | |
376 | #define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \ |
377 | \ |
378 | mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \ |
379 | { \ |
380 | if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \ |
381 | d = mp_bit##base(d, a, b); \ |
382 | p_base \ |
383 | } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \ |
384 | MP_COPY(b); \ |
385 | d = mp_not2c(d, a); \ |
386 | d = mp_bit##an(d, d, b); \ |
387 | MP_DROP(b); \ |
388 | p_an \ |
389 | } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \ |
390 | MP_COPY(a); \ |
391 | d = mp_not2c(d, b); \ |
392 | d = mp_bit##bn(d, a, d); \ |
393 | MP_DROP(a); \ |
394 | p_bn \ |
395 | } else { /* Both negative */ \ |
396 | mp *t = mp_not2c(MP_NEW, a); \ |
397 | mp *d = mp_not2c(d, b); \ |
398 | d = mp_bit##abn(d, t, d); \ |
399 | MP_DROP(t); \ |
400 | p_abn \ |
401 | } \ |
402 | return (d); \ |
403 | } \ |
404 | |
405 | #define NEG d = mp_not2c(d, d); |
406 | #define POS |
407 | MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS) |
408 | MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG) |
409 | MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS) |
410 | MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG) |
411 | MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS) |
412 | MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG) |
413 | MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS) |
414 | MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG) |
415 | MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS) |
416 | MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG) |
417 | MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS) |
418 | MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG) |
419 | MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS) |
420 | MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG) |
421 | MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS) |
422 | MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG) |
423 | #undef NEG |
424 | #undef POS |
425 | |
426 | /* --- @mp_not2c@ --- * |
427 | * |
428 | * Arguments: @mp *d@ = destination |
429 | * @mp *a@ = source |
430 | * |
431 | * Returns: The sign-extended complement of the argument. |
432 | */ |
433 | |
434 | mp *mp_not2c(mp *d, mp *a) |
435 | { |
436 | mpw one = 1; |
437 | |
438 | MP_DEST(d, MP_LEN(a) + 1, a->f); |
439 | if (d == a) { |
440 | if (a->f & MP_NEG) |
441 | MPX_USUBN(d->v, d->vl, 1); |
442 | else |
443 | MPX_UADDN(d->v, d->vl, 1); |
444 | } else { |
445 | if (a->f & MP_NEG) |
446 | mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
447 | else |
448 | mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
449 | } |
450 | d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG; |
451 | MP_SHRINK(d); |
452 | return (d); |
453 | } |
454 | |
d3409d5e |
455 | /* --- @mp_add@ --- * |
456 | * |
457 | * Arguments: @mp *d@ = destination |
ef5f4810 |
458 | * @mp *a, *b@ = sources |
d3409d5e |
459 | * |
460 | * Returns: Result, @a@ added to @b@. |
461 | */ |
462 | |
ef5f4810 |
463 | mp *mp_add(mp *d, mp *a, mp *b) |
d3409d5e |
464 | { |
d34decd2 |
465 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
466 | if (!((a->f ^ b->f) & MP_NEG)) |
467 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
468 | else { |
469 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
470 | mp *t = a; a = b; b = t; |
d3409d5e |
471 | } |
472 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
473 | } |
474 | d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG); |
475 | MP_SHRINK(d); |
476 | return (d); |
477 | } |
478 | |
479 | /* --- @mp_sub@ --- * |
480 | * |
481 | * Arguments: @mp *d@ = destination |
ef5f4810 |
482 | * @mp *a, *b@ = sources |
d3409d5e |
483 | * |
484 | * Returns: Result, @b@ subtracted from @a@. |
485 | */ |
486 | |
ef5f4810 |
487 | mp *mp_sub(mp *d, mp *a, mp *b) |
d3409d5e |
488 | { |
489 | unsigned sgn = 0; |
d34decd2 |
490 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
491 | if ((a->f ^ b->f) & MP_NEG) |
492 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
493 | else { |
494 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
495 | mp *t = a; a = b; b = t; |
d3409d5e |
496 | sgn = MP_NEG; |
497 | } |
498 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
499 | } |
500 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG); |
501 | MP_SHRINK(d); |
502 | return (d); |
503 | } |
504 | |
505 | /* --- @mp_mul@ --- * |
506 | * |
507 | * Arguments: @mp *d@ = destination |
ef5f4810 |
508 | * @mp *a, *b@ = sources |
d3409d5e |
509 | * |
510 | * Returns: Result, @a@ multiplied by @b@. |
511 | */ |
512 | |
ef5f4810 |
513 | mp *mp_mul(mp *d, mp *a, mp *b) |
d3409d5e |
514 | { |
ef5f4810 |
515 | a = MP_COPY(a); |
516 | b = MP_COPY(b); |
517 | |
52cdaca9 |
518 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) { |
d34decd2 |
519 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); |
ef5f4810 |
520 | mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
8017495b |
521 | } else { |
dd22938e |
522 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); |
ef5f4810 |
523 | mpw *s; |
dd22938e |
524 | MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF); |
525 | s = mpalloc(d->a, 5 * m); |
526 | mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m); |
d34decd2 |
527 | mpfree(d->a, s); |
ef5f4810 |
528 | } |
529 | |
d3409d5e |
530 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
531 | MP_SHRINK(d); |
ef5f4810 |
532 | MP_DROP(a); |
533 | MP_DROP(b); |
d3409d5e |
534 | return (d); |
535 | } |
536 | |
537 | /* --- @mp_sqr@ --- * |
538 | * |
539 | * Arguments: @mp *d@ = destination |
ef5f4810 |
540 | * @mp *a@ = source |
d3409d5e |
541 | * |
542 | * Returns: Result, @a@ squared. |
543 | */ |
544 | |
ef5f4810 |
545 | mp *mp_sqr(mp *d, mp *a) |
d3409d5e |
546 | { |
ef5f4810 |
547 | size_t m = MP_LEN(a); |
548 | |
549 | a = MP_COPY(a); |
52cdaca9 |
550 | if (m > MPK_THRESH) { |
ef5f4810 |
551 | mpw *s; |
dd22938e |
552 | MP_DEST(d, 3 * m, a->f | MP_UNDEF); |
553 | s = mpalloc(d->a, 5 * m); |
554 | mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m); |
d34decd2 |
555 | mpfree(d->a, s); |
dd22938e |
556 | } else { |
557 | MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF); |
ef5f4810 |
558 | mpx_usqr(d->v, d->vl, a->v, a->vl); |
dd22938e |
559 | } |
d3409d5e |
560 | d->f = a->f & MP_BURN; |
561 | MP_SHRINK(d); |
ef5f4810 |
562 | MP_DROP(a); |
d3409d5e |
563 | return (d); |
564 | } |
565 | |
566 | /* --- @mp_div@ --- * |
567 | * |
568 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
ef5f4810 |
569 | * @mp *a, *b@ = sources |
d3409d5e |
570 | * |
571 | * Use: Calculates the quotient and remainder when @a@ is divided by |
572 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
573 | * Either of @qq@ or @rr@ may be null to indicate that the |
574 | * result is irrelevant. (Discarding both results is silly.) |
575 | * There is a performance advantage if @a == *rr@. |
576 | * |
577 | * The behaviour when @a@ and @b@ have the same sign is |
578 | * straightforward. When the signs differ, this implementation |
579 | * chooses @r@ to have the same sign as @b@, rather than the |
580 | * more normal choice that the remainder has the same sign as |
581 | * the dividend. This makes modular arithmetic a little more |
582 | * straightforward. |
583 | */ |
584 | |
ef5f4810 |
585 | void mp_div(mp **qq, mp **rr, mp *a, mp *b) |
d3409d5e |
586 | { |
587 | mp *r = rr ? *rr : MP_NEW; |
588 | mp *q = qq ? *qq : MP_NEW; |
589 | mpw *sv, *svl; |
590 | |
d3409d5e |
591 | /* --- Set the remainder up right --- * |
592 | * |
593 | * Just in case the divisor is larger, be able to cope with this. It's not |
594 | * important in @mpx_udiv@, but it is here because of the sign correction. |
595 | */ |
596 | |
d34decd2 |
597 | b = MP_COPY(b); |
598 | a = MP_COPY(a); |
599 | if (r) |
600 | MP_DROP(r); |
601 | r = a; |
602 | MP_DEST(r, MP_LEN(a) + 2, a->f | b->f); |
d3409d5e |
603 | |
604 | /* --- Fix up the quotient too --- */ |
605 | |
d34decd2 |
606 | r = MP_COPY(r); |
607 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); |
608 | MP_DROP(r); |
609 | |
610 | /* --- Set up some temporary workspace --- */ |
611 | |
612 | { |
613 | size_t rq = MP_LEN(b) + 1; |
614 | sv = mpalloc(r->a, rq); |
615 | svl = sv + rq; |
616 | } |
d3409d5e |
617 | |
618 | /* --- Perform the calculation --- */ |
619 | |
620 | mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl); |
621 | |
622 | /* --- Sort out the sign of the results --- * |
623 | * |
624 | * If the signs of the arguments differ, and the remainder is nonzero, I |
625 | * must add one to the absolute value of the quotient and subtract the |
626 | * remainder from @b@. |
627 | */ |
628 | |
d34decd2 |
629 | q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG); |
d3409d5e |
630 | if (q->f & MP_NEG) { |
ef5f4810 |
631 | mpw *v; |
632 | for (v = r->v; v < r->vl; v++) { |
d3409d5e |
633 | if (*v) { |
634 | MPX_UADDN(q->v, q->vl, 1); |
635 | mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl); |
636 | break; |
637 | } |
638 | } |
639 | } |
640 | |
d34decd2 |
641 | r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG); |
d3409d5e |
642 | |
643 | /* --- Store the return values --- */ |
644 | |
d34decd2 |
645 | mpfree(r->a, sv); |
646 | MP_DROP(b); |
647 | |
d3409d5e |
648 | if (!qq) |
649 | MP_DROP(q); |
650 | else { |
651 | MP_SHRINK(q); |
652 | *qq = q; |
653 | } |
654 | |
655 | if (!rr) |
656 | MP_DROP(r); |
657 | else { |
658 | MP_SHRINK(r); |
659 | *rr = r; |
660 | } |
d3409d5e |
661 | } |
662 | |
f1713c63 |
663 | /* --- @mp_odd@ --- * |
664 | * |
665 | * Arguments: @mp *d@ = pointer to destination integer |
666 | * @mp *m@ = pointer to source integer |
667 | * @size_t *s@ = where to store the power of 2 |
668 | * |
669 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
670 | * |
671 | * Use: Computes a power of two and an odd integer which, when |
672 | * multiplied, give a specified result. This sort of thing is |
673 | * useful in number theory quite often. |
674 | */ |
675 | |
676 | mp *mp_odd(mp *d, mp *m, size_t *s) |
677 | { |
678 | size_t ss = 0; |
679 | const mpw *v, *vl; |
680 | |
681 | v = m->v; |
682 | vl = m->vl; |
683 | for (; !*v && v < vl; v++) |
684 | ss += MPW_BITS; |
685 | if (v >= vl) |
686 | ss = 0; |
687 | else { |
688 | mpw x = *v; |
689 | mpw mask = MPW_MAX; |
690 | unsigned z = MPW_BITS / 2; |
691 | |
692 | while (z) { |
693 | mask >>= z; |
694 | if (!(x & mask)) { |
695 | x >>= z; |
696 | ss += z; |
697 | } |
698 | z >>= 1; |
699 | } |
700 | } |
701 | |
702 | *s = ss; |
703 | return (mp_lsr(d, m, ss)); |
704 | } |
705 | |
d3409d5e |
706 | /*----- Test rig ----------------------------------------------------------*/ |
707 | |
708 | #ifdef TEST_RIG |
709 | |
710 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
711 | { |
4b536f42 |
712 | if (!MP_EQ(expect, result)) { |
d3409d5e |
713 | fprintf(stderr, "\n*** %s failed", op); |
714 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
715 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10); |
716 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10); |
717 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10); |
718 | fputc('\n', stderr); |
719 | return (0); |
720 | } |
721 | return (1); |
722 | } |
723 | |
724 | #define RIG(name, op) \ |
ef5f4810 |
725 | static int t##name(dstr *v) \ |
d3409d5e |
726 | { \ |
727 | mp *a = *(mp **)v[0].buf; \ |
728 | mpw n = *(int *)v[1].buf; \ |
729 | mp b; \ |
730 | mp *r = *(mp **)v[2].buf; \ |
731 | mp *c = op(MP_NEW, a, n); \ |
732 | int ok; \ |
733 | mp_build(&b, &n, &n + 1); \ |
734 | ok = verify(#name, r, c, a, &b); \ |
735 | mp_drop(a); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
736 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
737 | return (ok); \ |
738 | } |
739 | |
740 | RIG(lsl, mp_lsl) |
741 | RIG(lsr, mp_lsr) |
f09e814a |
742 | RIG(lsl2c, mp_lsl2c) |
743 | RIG(lsr2c, mp_lsr2c) |
d3409d5e |
744 | |
745 | #undef RIG |
746 | |
747 | #define RIG(name, op) \ |
ef5f4810 |
748 | static int t##name(dstr *v) \ |
d3409d5e |
749 | { \ |
750 | mp *a = *(mp **)v[0].buf; \ |
751 | mp *b = *(mp **)v[1].buf; \ |
752 | mp *r = *(mp **)v[2].buf; \ |
753 | mp *c = op(MP_NEW, a, b); \ |
754 | int ok = verify(#name, r, c, a, b); \ |
755 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
756 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
757 | return (ok); \ |
758 | } |
759 | |
760 | RIG(add, mp_add) |
761 | RIG(sub, mp_sub) |
762 | RIG(mul, mp_mul) |
763 | |
764 | #undef RIG |
765 | |
766 | static int tdiv(dstr *v) |
767 | { |
768 | mp *a = *(mp **)v[0].buf; |
769 | mp *b = *(mp **)v[1].buf; |
770 | mp *q = *(mp **)v[2].buf; |
771 | mp *r = *(mp **)v[3].buf; |
772 | mp *c = MP_NEW, *d = MP_NEW; |
773 | int ok = 1; |
774 | mp_div(&c, &d, a, b); |
775 | ok &= verify("div(quotient)", q, c, a, b); |
776 | ok &= verify("div(remainder)", r, d, a, b); |
777 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
ef5f4810 |
778 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
779 | return (ok); |
780 | } |
781 | |
f09e814a |
782 | static int tbin(dstr *v) |
783 | { |
784 | static mp *(*fn[])(mp *, mp *, mp *) = { |
785 | #define DO(string) mp_bit##string##2c, |
786 | MPX_DOBIN(DO) |
787 | #undef DO |
788 | }; |
789 | int ok = 1; |
790 | unsigned op = 0; |
791 | mp *a = *(mp **)v[1].buf; |
792 | mp *b = *(mp **)v[2].buf; |
793 | mp *r = *(mp **)v[3].buf; |
794 | mp *c; |
795 | |
796 | if (strcmp(v[0].buf, "and") == 0) op = 1; |
797 | else if (strcmp(v[0].buf, "or") == 0) op = 7; |
798 | else if (strcmp(v[0].buf, "nand") == 0) op = 14; |
799 | else if (strcmp(v[0].buf, "nor") == 0) op = 8; |
800 | else if (strcmp(v[0].buf, "xor") == 0) op = 6; |
801 | else { |
802 | char *p = v[0].buf; |
803 | while (*p) { |
804 | op <<= 1; |
805 | if (*p++ == '1') |
806 | op |= 1; |
807 | } |
808 | } |
809 | |
810 | c = fn[op](MP_NEW, a, b); |
811 | ok = verify(v[0].buf, r, c, a, b); |
812 | mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c); |
813 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
814 | return (ok); |
815 | } |
816 | |
09d00c6b |
817 | static int tset(dstr *v) |
818 | { |
819 | mp *a = *(mp **)v[0].buf; |
820 | unsigned long n = *(unsigned long *)v[1].buf; |
821 | mp *r = *(mp **)v[2].buf; |
822 | mp *c; |
823 | int ok = 1; |
824 | |
825 | c = mp_setbit2c(MP_NEW, a, n); |
826 | if (!MP_EQ(c, r)) { |
827 | ok = 0; |
828 | fprintf(stderr, "\n***setbit (set) failed"); |
829 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
830 | fprintf(stderr, "\n*** n = %lu", n); |
831 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
832 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
833 | fputc('\n', stderr); |
834 | } |
835 | if (!mp_testbit2c(r, n)) { |
836 | ok = 0; |
837 | fprintf(stderr, "\n***setbit (test) failed"); |
838 | fprintf(stderr, "\n*** n = %lu", n); |
839 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
840 | fputc('\n', stderr); |
841 | } |
842 | mp_drop(a); |
843 | mp_drop(r); |
844 | mp_drop(c); |
845 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
846 | return (ok); |
847 | } |
848 | |
849 | static int tclr(dstr *v) |
850 | { |
851 | mp *a = *(mp **)v[0].buf; |
852 | unsigned long n = *(unsigned long *)v[1].buf; |
853 | mp *r = *(mp **)v[2].buf; |
854 | mp *c; |
855 | int ok = 1; |
856 | |
857 | c = mp_clearbit2c(MP_NEW, a, n); |
858 | if (!MP_EQ(c, r)) { |
859 | ok = 0; |
860 | fprintf(stderr, "\n***clrbit (set) failed"); |
861 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
862 | fprintf(stderr, "\n*** n = %lu", n); |
863 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
864 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
865 | fputc('\n', stderr); |
866 | } |
867 | if (mp_testbit2c(r, n)) { |
868 | ok = 0; |
869 | fprintf(stderr, "\n***clrbit (test) failed"); |
870 | fprintf(stderr, "\n*** n = %lu", n); |
871 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
872 | fputc('\n', stderr); |
873 | } |
874 | mp_drop(a); |
875 | mp_drop(c); |
876 | mp_drop(r); |
877 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
878 | return (ok); |
879 | } |
880 | |
397041a9 |
881 | static int tneg(dstr *v) |
882 | { |
883 | mp *a = *(mp **)v[0].buf; |
884 | mp *r = *(mp **)v[1].buf; |
885 | int ok = 1; |
886 | mp *n = mp_neg(MP_NEW, a); |
887 | if (!MP_EQ(r, n)) { |
888 | ok = 0; |
889 | fprintf(stderr, "\n*** neg failed\n"); |
890 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
891 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
892 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
893 | fputc('\n', stderr); |
894 | } |
895 | mp_drop(n); |
896 | n = mp_neg(a, a); |
897 | if (!MP_EQ(r, n)) { |
898 | ok = 0; |
899 | fprintf(stderr, "\n*** neg failed\n"); |
900 | fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10); |
901 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
902 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
903 | fputc('\n', stderr); |
904 | } |
905 | mp_drop(a); |
906 | mp_drop(r); |
907 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
908 | return (ok); |
909 | } |
910 | |
f1713c63 |
911 | static int todd(dstr *v) |
912 | { |
913 | mp *a = *(mp **)v[0].buf; |
914 | size_t rs = *(uint32 *)v[1].buf; |
915 | mp *rt = *(mp **)v[2].buf; |
916 | int ok = 1; |
917 | mp *t; |
918 | size_t s; |
919 | t = mp_odd(MP_NEW, a, &s); |
4b536f42 |
920 | if (s != rs || !MP_EQ(t, rt)) { |
f1713c63 |
921 | ok = 0; |
922 | fprintf(stderr, "\n*** odd failed"); |
923 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
924 | fprintf(stderr, "\n*** s = %lu", (unsigned long)s); |
925 | fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10); |
926 | fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs); |
927 | fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10); |
928 | fputc('\n', stderr); |
929 | } |
930 | mp_drop(a); |
931 | mp_drop(rt); |
932 | mp_drop(t); |
09d00c6b |
933 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
f1713c63 |
934 | return (ok); |
935 | } |
936 | |
d3409d5e |
937 | static test_chunk tests[] = { |
f09e814a |
938 | { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } }, |
939 | { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } }, |
940 | { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } }, |
941 | { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } }, |
09d00c6b |
942 | { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } }, |
943 | { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } }, |
d3409d5e |
944 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
945 | { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } }, |
946 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
947 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
f09e814a |
948 | { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } }, |
f1713c63 |
949 | { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } }, |
397041a9 |
950 | { "neg", tneg, { &type_mp, &type_mp, 0 } }, |
d3409d5e |
951 | { 0, 0, { 0 } }, |
952 | }; |
953 | |
954 | int main(int argc, char *argv[]) |
955 | { |
956 | sub_init(); |
957 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
958 | return (0); |
959 | } |
960 | |
961 | #endif |
962 | |
963 | /*----- That's all, folks -------------------------------------------------*/ |