d3409d5e |
1 | /* -*-c-*- |
2 | * |
1793c2bb |
3 | * $Id: mp-arith.c,v 1.16.2.2 2004/03/20 00:14:03 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 $ |
1793c2bb |
33 | * Revision 1.16.2.2 2004/03/20 00:14:03 mdw |
34 | * Bug fix. |
35 | * |
2b645fb7 |
36 | * Revision 1.16.2.1 2003/06/10 13:21:10 mdw |
37 | * Fix bug dividing small things by large ones. |
38 | * |
81578196 |
39 | * Revision 1.16 2003/05/16 09:09:24 mdw |
40 | * Fix @mp_lsl2c@. Turns out to be surprisingly tricky. |
41 | * |
75263f25 |
42 | * Revision 1.15 2002/10/19 17:56:50 mdw |
43 | * Fix bit operations. Test them (a bit) better. |
44 | * |
397041a9 |
45 | * Revision 1.14 2002/10/15 19:18:31 mdw |
46 | * New operation to negate numbers. |
47 | * |
09d00c6b |
48 | * Revision 1.13 2002/10/15 00:19:40 mdw |
49 | * Bit setting and clearing functions. |
50 | * |
dd22938e |
51 | * Revision 1.12 2002/10/09 00:36:03 mdw |
52 | * Fix bounds on workspace for Karatsuba operations. |
53 | * |
f09e814a |
54 | * Revision 1.11 2002/10/06 22:52:50 mdw |
55 | * Pile of changes for supporting two's complement properly. |
56 | * |
0f32e0f8 |
57 | * Revision 1.10 2001/04/03 19:36:05 mdw |
58 | * Add some simple bitwise operations so that Perl can use them. |
59 | * |
52cdaca9 |
60 | * Revision 1.9 2000/10/08 15:48:35 mdw |
61 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
62 | * |
4b536f42 |
63 | * Revision 1.8 2000/10/08 12:02:21 mdw |
64 | * Use @MP_EQ@ instead of @MP_CMP@. |
65 | * |
f1713c63 |
66 | * Revision 1.7 2000/06/22 19:02:53 mdw |
67 | * New function @mp_odd@ to extract powers of two from an integer. This is |
68 | * common code from the Rabin-Miller test, RSA key recovery and modular |
69 | * square-root extraction. |
70 | * |
d34decd2 |
71 | * Revision 1.6 2000/06/17 11:45:09 mdw |
72 | * Major memory management overhaul. Added arena support. Use the secure |
73 | * arena for secret integers. Replace and improve the MP management macros |
74 | * (e.g., replace MP_MODIFY by MP_DEST). |
75 | * |
bba03f55 |
76 | * Revision 1.5 1999/12/22 15:54:41 mdw |
77 | * Adjust Karatsuba parameters. Calculate destination size better. |
78 | * |
8017495b |
79 | * Revision 1.4 1999/12/13 15:35:16 mdw |
80 | * Slightly different rules on memory allocation. |
81 | * |
5bf74dea |
82 | * Revision 1.3 1999/12/11 10:57:43 mdw |
83 | * Karatsuba squaring algorithm. |
84 | * |
ef5f4810 |
85 | * Revision 1.2 1999/12/10 23:18:39 mdw |
86 | * Change interface for suggested destinations. |
87 | * |
d3409d5e |
88 | * Revision 1.1 1999/11/17 18:02:16 mdw |
89 | * New multiprecision integer arithmetic suite. |
90 | * |
91 | */ |
92 | |
93 | /*----- Header files ------------------------------------------------------*/ |
94 | |
95 | #include "mp.h" |
96 | |
ef5f4810 |
97 | /*----- Macros ------------------------------------------------------------*/ |
98 | |
99 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
100 | |
d3409d5e |
101 | /*----- Main code ---------------------------------------------------------*/ |
102 | |
81578196 |
103 | /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- * |
d3409d5e |
104 | * |
f09e814a |
105 | * Arguments: @mp *d@ = destination |
106 | * @mp *a@ = source |
107 | * @size_t n@ = number of bits to move |
d3409d5e |
108 | * |
f09e814a |
109 | * Returns: Result, @a@ shifted left or right by @n@. |
81578196 |
110 | * |
111 | * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced |
112 | * on the right with ones instead of zeroes: it's used |
113 | * internally by @mp_lsl2c@, though it may be useful on its |
114 | * own. |
d3409d5e |
115 | */ |
116 | |
f09e814a |
117 | mp *mp_lsl(mp *d, mp *a, size_t n) |
d3409d5e |
118 | { |
f09e814a |
119 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
120 | mpx_lsl(d->v, d->vl, a->v, a->vl, n); |
121 | d->f = a->f & (MP_NEG | MP_BURN); |
122 | MP_SHRINK(d); |
123 | return (d); |
124 | } |
d3409d5e |
125 | |
81578196 |
126 | mp *mp_lslc(mp *d, mp *a, size_t n) |
127 | { |
128 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
129 | mpx_lslc(d->v, d->vl, a->v, a->vl, n); |
130 | d->f = a->f & (MP_NEG | MP_BURN); |
131 | MP_SHRINK(d); |
132 | return (d); |
133 | } |
134 | |
f09e814a |
135 | mp *mp_lsr(mp *d, mp *a, size_t n) |
136 | { |
d34decd2 |
137 | MP_DEST(d, MP_LEN(a), a->f); |
f09e814a |
138 | mpx_lsr(d->v, d->vl, a->v, a->vl, n); |
139 | d->f = a->f & (MP_NEG | MP_BURN); |
d3409d5e |
140 | MP_SHRINK(d); |
141 | return (d); |
142 | } |
143 | |
f09e814a |
144 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
d3409d5e |
145 | * |
146 | * Arguments: @mp *d@ = destination |
147 | * @mp *a@ = source |
f09e814a |
148 | * @size_t n@ = number of bits to move |
d3409d5e |
149 | * |
f09e814a |
150 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
151 | * pretence of sign-extension for negative numbers. |
d3409d5e |
152 | */ |
153 | |
f09e814a |
154 | mp *mp_lsl2c(mp *d, mp *a, size_t n) |
d3409d5e |
155 | { |
f09e814a |
156 | if (!(a->f & MP_NEG)) |
157 | return (mp_lsl(d, a, n)); |
158 | d = mp_not2c(d, a); |
81578196 |
159 | d = mp_lslc(d, d, n); |
f09e814a |
160 | d = mp_not2c(d, d); |
161 | return (d); |
162 | } |
d3409d5e |
163 | |
f09e814a |
164 | mp *mp_lsr2c(mp *d, mp *a, size_t n) |
165 | { |
166 | if (!(a->f & MP_NEG)) |
167 | return (mp_lsr(d, a, n)); |
168 | d = mp_not2c(d, a); |
169 | d = mp_lsr(d, d, n); |
170 | d = mp_not2c(d, d); |
171 | return (d); |
d3409d5e |
172 | } |
173 | |
f09e814a |
174 | /* --- @mp_testbit@ --- * |
d3409d5e |
175 | * |
f09e814a |
176 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
177 | * @unsigned long n@ = which bit to test |
d3409d5e |
178 | * |
f09e814a |
179 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
180 | */ |
181 | |
09d00c6b |
182 | int mp_testbit(mp *x, unsigned long n) |
d3409d5e |
183 | { |
f09e814a |
184 | if (n > MPW_BITS * MP_LEN(x)) |
185 | return (0); |
09d00c6b |
186 | return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u); |
d3409d5e |
187 | } |
188 | |
f09e814a |
189 | /* --- @mp_testbit2c@ --- * |
d3409d5e |
190 | * |
f09e814a |
191 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
192 | * @unsigned long n@ = which bit to test |
d3409d5e |
193 | * |
f09e814a |
194 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
195 | * complement representation. |
d3409d5e |
196 | */ |
197 | |
09d00c6b |
198 | int mp_testbit2c(mp *x, unsigned long n) |
d3409d5e |
199 | { |
f09e814a |
200 | int r; |
09d00c6b |
201 | if (!(x->f & MP_NEG)) |
f09e814a |
202 | return (mp_testbit(x, n)); |
203 | x = mp_not2c(MP_NEW, x); |
204 | r = !mp_testbit(x, n); |
205 | MP_DROP(x); |
206 | return (r); |
d3409d5e |
207 | } |
208 | |
09d00c6b |
209 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
210 | * |
211 | * Arguments: @mp *d@ = a destination |
212 | * @mp *x@ = a large integer |
213 | * @unsigned long n@ = which bit to modify |
214 | * |
215 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
216 | */ |
217 | |
218 | mp *mp_setbit(mp *d, mp *x, unsigned long n) |
219 | { |
220 | size_t rq; |
221 | |
222 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
223 | if (d != x) { |
224 | if (d) MP_DROP(d); |
225 | d = MP_COPY(x); |
226 | } |
227 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
228 | d->v[n/MPW_BITS] |= 1 << n%MPW_BITS; |
229 | return (d); |
230 | } |
231 | |
232 | mp *mp_clearbit(mp *d, mp *x, unsigned long n) |
233 | { |
234 | size_t rq; |
235 | |
236 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
237 | if (d != x) { |
238 | if (d) MP_DROP(d); |
239 | d = MP_COPY(x); |
240 | } |
241 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
242 | d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS); |
243 | return (d); |
244 | } |
245 | |
246 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
247 | * |
248 | * Arguments: @mp *d@ = a destination |
249 | * @mp *x@ = a large integer |
250 | * @unsigned long n@ = which bit to modify |
251 | * |
252 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
253 | * Fakes up two's complement representation. |
254 | */ |
255 | |
256 | mp *mp_setbit2c(mp *d, mp *x, unsigned long n) |
257 | { |
258 | if (!(x->f & MP_NEG)) |
259 | return mp_setbit(d, x, n); |
260 | d = mp_not2c(d, x); |
261 | d = mp_clearbit(d, d, n); |
262 | d = mp_not2c(d, d); |
263 | return (d); |
264 | } |
265 | |
266 | mp *mp_clearbit2c(mp *d, mp *x, unsigned long n) |
267 | { |
268 | if (!(x->f & MP_NEG)) |
269 | return mp_clearbit(d, x, n); |
270 | d = mp_not2c(d, x); |
271 | d = mp_setbit(d, d, n); |
272 | d = mp_not2c(d, d); |
273 | return (d); |
274 | } |
275 | |
4b536f42 |
276 | /* --- @mp_eq@ --- * |
277 | * |
278 | * Arguments: @const mp *a, *b@ = two numbers |
279 | * |
280 | * Returns: Nonzero if the numbers are equal. |
281 | */ |
282 | |
283 | int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); } |
284 | |
d3409d5e |
285 | /* --- @mp_cmp@ --- * |
286 | * |
287 | * Arguments: @const mp *a, *b@ = two numbers |
288 | * |
289 | * Returns: Less than, equal to or greater than zero, according to |
290 | * whether @a@ is less than, equal to or greater than @b@. |
291 | */ |
292 | |
293 | int mp_cmp(const mp *a, const mp *b) |
294 | { |
295 | if (!((a->f ^ b->f) & MP_NEG)) |
296 | return (mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
297 | else if (a->f & MP_NEG) |
298 | return (-1); |
299 | else |
300 | return (+1); |
301 | } |
302 | |
397041a9 |
303 | /* --- @mp_neg@ --- * |
304 | * |
305 | * Arguments: @mp *d@ = destination |
306 | * @mp *a@ = argument |
307 | * |
308 | * Returns: The negation of the argument. |
309 | * |
310 | * Use: Negates its argument. |
311 | */ |
312 | |
313 | mp *mp_neg(mp *d, mp *a) |
314 | { |
315 | /* --- Surprising amounts of messing about required --- */ |
316 | |
317 | MP_SHRINK(a); |
318 | MP_COPY(a); |
81578196 |
319 | if (d) |
320 | MP_DROP(d); |
321 | if (a->v == a->vl) |
397041a9 |
322 | return (a); |
397041a9 |
323 | MP_DEST(a, MP_LEN(a), a->f); |
324 | a->f ^= MP_NEG; |
325 | return (a); |
326 | } |
327 | |
f09e814a |
328 | /* --- @mp_bitop@ --- * |
0f32e0f8 |
329 | * |
330 | * Arguments: @mp *d@ = destination |
331 | * @mp *a, *b@ = sources |
332 | * |
f09e814a |
333 | * Returns: The result of the given bitwise operation. These functions |
334 | * don't handle negative numbers at all sensibly. For that, use |
335 | * the @...2c@ variants. The functions are named after the |
336 | * truth tables they generate: |
337 | * |
338 | * a: 0011 |
339 | * b: 0101 |
340 | * @mpx_bitXXXX@ |
0f32e0f8 |
341 | */ |
342 | |
f09e814a |
343 | #define MP_BITBINOP(string) \ |
0f32e0f8 |
344 | \ |
f09e814a |
345 | mp *mp_bit##string(mp *d, mp *a, mp *b) \ |
0f32e0f8 |
346 | { \ |
75263f25 |
347 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \ |
f09e814a |
348 | mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \ |
0f32e0f8 |
349 | d->f = (a->f | b->f) & MP_BURN; \ |
350 | MP_SHRINK(d); \ |
351 | return (d); \ |
352 | } |
353 | |
f09e814a |
354 | MPX_DOBIN(MP_BITBINOP) |
355 | |
356 | /* --- @mp_not@ --- * |
357 | * |
358 | * Arguments: @mp *d@ = destination |
359 | * @mp *a@ = source |
360 | * |
361 | * Returns: The bitwise complement of the source. |
362 | */ |
0f32e0f8 |
363 | |
364 | mp *mp_not(mp *d, mp *a) |
365 | { |
366 | MP_DEST(d, MP_LEN(a), a->f); |
367 | mpx_not(d->v, d->vl, a->v, a->vl); |
368 | d->f = a->f & MP_BURN; |
369 | MP_SHRINK(d); |
370 | return (d); |
371 | } |
372 | |
f09e814a |
373 | /* --- @mp_bitop2c@ --- * |
374 | * |
375 | * Arguments: @mp *d@ = destination |
376 | * @mp *a, *b@ = sources |
377 | * |
378 | * Returns: The result of the given bitwise operation. Negative numbers |
379 | * are treated as two's complement, sign-extended infinitely to |
380 | * the left. The functions are named after the truth tables |
381 | * they generate: |
382 | * |
383 | * a: 0011 |
384 | * b: 0101 |
385 | * @mpx_bitXXXX@ |
386 | */ |
387 | |
388 | /* --- How this actually works --- * |
389 | * |
390 | * The two arguments are inverted (with a sign-swap) if they're currently |
391 | * negative. This means that we end up using a different function (one which |
392 | * reinverts as we go) for the main operation. Also, if the sign would be |
393 | * negative at the end, we preinvert the output and then invert again with a |
394 | * sign-swap. |
395 | * |
396 | * Start with: wxyz WXYZ |
397 | * If @a@ negative: yzwx or YZWX |
398 | * If @b@ negative: xwzy XWZY |
399 | * If both negative: zyxw ZYXW |
400 | */ |
401 | |
402 | #define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \ |
403 | \ |
404 | mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \ |
405 | { \ |
406 | if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \ |
407 | d = mp_bit##base(d, a, b); \ |
408 | p_base \ |
409 | } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \ |
410 | MP_COPY(b); \ |
411 | d = mp_not2c(d, a); \ |
412 | d = mp_bit##an(d, d, b); \ |
413 | MP_DROP(b); \ |
414 | p_an \ |
415 | } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \ |
416 | MP_COPY(a); \ |
417 | d = mp_not2c(d, b); \ |
418 | d = mp_bit##bn(d, a, d); \ |
419 | MP_DROP(a); \ |
420 | p_bn \ |
421 | } else { /* Both negative */ \ |
422 | mp *t = mp_not2c(MP_NEW, a); \ |
423 | mp *d = mp_not2c(d, b); \ |
424 | d = mp_bit##abn(d, t, d); \ |
425 | MP_DROP(t); \ |
426 | p_abn \ |
427 | } \ |
428 | return (d); \ |
429 | } \ |
430 | |
431 | #define NEG d = mp_not2c(d, d); |
432 | #define POS |
433 | MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS) |
434 | MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG) |
435 | MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS) |
436 | MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG) |
437 | MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS) |
438 | MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG) |
439 | MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS) |
440 | MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG) |
441 | MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS) |
442 | MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG) |
443 | MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS) |
444 | MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG) |
445 | MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS) |
446 | MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG) |
447 | MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS) |
448 | MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG) |
449 | #undef NEG |
450 | #undef POS |
451 | |
452 | /* --- @mp_not2c@ --- * |
453 | * |
454 | * Arguments: @mp *d@ = destination |
455 | * @mp *a@ = source |
456 | * |
457 | * Returns: The sign-extended complement of the argument. |
458 | */ |
459 | |
460 | mp *mp_not2c(mp *d, mp *a) |
461 | { |
462 | mpw one = 1; |
463 | |
464 | MP_DEST(d, MP_LEN(a) + 1, a->f); |
465 | if (d == a) { |
466 | if (a->f & MP_NEG) |
467 | MPX_USUBN(d->v, d->vl, 1); |
468 | else |
469 | MPX_UADDN(d->v, d->vl, 1); |
470 | } else { |
471 | if (a->f & MP_NEG) |
472 | mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
473 | else |
474 | mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
475 | } |
476 | d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG; |
477 | MP_SHRINK(d); |
478 | return (d); |
479 | } |
480 | |
d3409d5e |
481 | /* --- @mp_add@ --- * |
482 | * |
483 | * Arguments: @mp *d@ = destination |
ef5f4810 |
484 | * @mp *a, *b@ = sources |
d3409d5e |
485 | * |
486 | * Returns: Result, @a@ added to @b@. |
487 | */ |
488 | |
ef5f4810 |
489 | mp *mp_add(mp *d, mp *a, mp *b) |
d3409d5e |
490 | { |
d34decd2 |
491 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
492 | if (!((a->f ^ b->f) & MP_NEG)) |
493 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
494 | else { |
495 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
496 | mp *t = a; a = b; b = t; |
d3409d5e |
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 & MP_NEG); |
501 | MP_SHRINK(d); |
502 | return (d); |
503 | } |
504 | |
505 | /* --- @mp_sub@ --- * |
506 | * |
507 | * Arguments: @mp *d@ = destination |
ef5f4810 |
508 | * @mp *a, *b@ = sources |
d3409d5e |
509 | * |
510 | * Returns: Result, @b@ subtracted from @a@. |
511 | */ |
512 | |
ef5f4810 |
513 | mp *mp_sub(mp *d, mp *a, mp *b) |
d3409d5e |
514 | { |
515 | unsigned sgn = 0; |
d34decd2 |
516 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
517 | if ((a->f ^ b->f) & MP_NEG) |
518 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
519 | else { |
520 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
521 | mp *t = a; a = b; b = t; |
d3409d5e |
522 | sgn = MP_NEG; |
523 | } |
524 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
525 | } |
526 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG); |
527 | MP_SHRINK(d); |
528 | return (d); |
529 | } |
530 | |
531 | /* --- @mp_mul@ --- * |
532 | * |
533 | * Arguments: @mp *d@ = destination |
ef5f4810 |
534 | * @mp *a, *b@ = sources |
d3409d5e |
535 | * |
536 | * Returns: Result, @a@ multiplied by @b@. |
537 | */ |
538 | |
ef5f4810 |
539 | mp *mp_mul(mp *d, mp *a, mp *b) |
d3409d5e |
540 | { |
ef5f4810 |
541 | a = MP_COPY(a); |
542 | b = MP_COPY(b); |
543 | |
52cdaca9 |
544 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) { |
d34decd2 |
545 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); |
ef5f4810 |
546 | mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
8017495b |
547 | } else { |
dd22938e |
548 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); |
ef5f4810 |
549 | mpw *s; |
dd22938e |
550 | MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF); |
551 | s = mpalloc(d->a, 5 * m); |
552 | mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m); |
d34decd2 |
553 | mpfree(d->a, s); |
ef5f4810 |
554 | } |
555 | |
d3409d5e |
556 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
557 | MP_SHRINK(d); |
ef5f4810 |
558 | MP_DROP(a); |
559 | MP_DROP(b); |
d3409d5e |
560 | return (d); |
561 | } |
562 | |
563 | /* --- @mp_sqr@ --- * |
564 | * |
565 | * Arguments: @mp *d@ = destination |
ef5f4810 |
566 | * @mp *a@ = source |
d3409d5e |
567 | * |
568 | * Returns: Result, @a@ squared. |
569 | */ |
570 | |
ef5f4810 |
571 | mp *mp_sqr(mp *d, mp *a) |
d3409d5e |
572 | { |
ef5f4810 |
573 | size_t m = MP_LEN(a); |
574 | |
575 | a = MP_COPY(a); |
52cdaca9 |
576 | if (m > MPK_THRESH) { |
ef5f4810 |
577 | mpw *s; |
dd22938e |
578 | MP_DEST(d, 3 * m, a->f | MP_UNDEF); |
579 | s = mpalloc(d->a, 5 * m); |
580 | mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m); |
d34decd2 |
581 | mpfree(d->a, s); |
dd22938e |
582 | } else { |
583 | MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF); |
ef5f4810 |
584 | mpx_usqr(d->v, d->vl, a->v, a->vl); |
dd22938e |
585 | } |
d3409d5e |
586 | d->f = a->f & MP_BURN; |
587 | MP_SHRINK(d); |
ef5f4810 |
588 | MP_DROP(a); |
d3409d5e |
589 | return (d); |
590 | } |
591 | |
592 | /* --- @mp_div@ --- * |
593 | * |
594 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
ef5f4810 |
595 | * @mp *a, *b@ = sources |
d3409d5e |
596 | * |
597 | * Use: Calculates the quotient and remainder when @a@ is divided by |
598 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
599 | * Either of @qq@ or @rr@ may be null to indicate that the |
600 | * result is irrelevant. (Discarding both results is silly.) |
601 | * There is a performance advantage if @a == *rr@. |
602 | * |
603 | * The behaviour when @a@ and @b@ have the same sign is |
604 | * straightforward. When the signs differ, this implementation |
605 | * chooses @r@ to have the same sign as @b@, rather than the |
606 | * more normal choice that the remainder has the same sign as |
607 | * the dividend. This makes modular arithmetic a little more |
608 | * straightforward. |
609 | */ |
610 | |
ef5f4810 |
611 | void mp_div(mp **qq, mp **rr, mp *a, mp *b) |
d3409d5e |
612 | { |
613 | mp *r = rr ? *rr : MP_NEW; |
614 | mp *q = qq ? *qq : MP_NEW; |
615 | mpw *sv, *svl; |
616 | |
d3409d5e |
617 | /* --- Set the remainder up right --- * |
618 | * |
619 | * Just in case the divisor is larger, be able to cope with this. It's not |
620 | * important in @mpx_udiv@, but it is here because of the sign correction. |
621 | */ |
622 | |
d34decd2 |
623 | b = MP_COPY(b); |
624 | a = MP_COPY(a); |
625 | if (r) |
626 | MP_DROP(r); |
627 | r = a; |
1793c2bb |
628 | MP_DEST(r, MAX(MP_LEN(a), MP_LEN(b)) + 2, a->f | b->f); |
d3409d5e |
629 | |
630 | /* --- Fix up the quotient too --- */ |
631 | |
d34decd2 |
632 | r = MP_COPY(r); |
633 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); |
634 | MP_DROP(r); |
635 | |
636 | /* --- Set up some temporary workspace --- */ |
637 | |
638 | { |
639 | size_t rq = MP_LEN(b) + 1; |
640 | sv = mpalloc(r->a, rq); |
641 | svl = sv + rq; |
642 | } |
d3409d5e |
643 | |
644 | /* --- Perform the calculation --- */ |
645 | |
646 | mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl); |
647 | |
648 | /* --- Sort out the sign of the results --- * |
649 | * |
650 | * If the signs of the arguments differ, and the remainder is nonzero, I |
651 | * must add one to the absolute value of the quotient and subtract the |
652 | * remainder from @b@. |
653 | */ |
654 | |
d34decd2 |
655 | q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG); |
d3409d5e |
656 | if (q->f & MP_NEG) { |
ef5f4810 |
657 | mpw *v; |
658 | for (v = r->v; v < r->vl; v++) { |
d3409d5e |
659 | if (*v) { |
660 | MPX_UADDN(q->v, q->vl, 1); |
661 | mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl); |
662 | break; |
663 | } |
664 | } |
665 | } |
666 | |
d34decd2 |
667 | r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG); |
d3409d5e |
668 | |
669 | /* --- Store the return values --- */ |
670 | |
d34decd2 |
671 | mpfree(r->a, sv); |
672 | MP_DROP(b); |
673 | |
d3409d5e |
674 | if (!qq) |
675 | MP_DROP(q); |
676 | else { |
677 | MP_SHRINK(q); |
678 | *qq = q; |
679 | } |
680 | |
681 | if (!rr) |
682 | MP_DROP(r); |
683 | else { |
684 | MP_SHRINK(r); |
685 | *rr = r; |
686 | } |
d3409d5e |
687 | } |
688 | |
f1713c63 |
689 | /* --- @mp_odd@ --- * |
690 | * |
691 | * Arguments: @mp *d@ = pointer to destination integer |
692 | * @mp *m@ = pointer to source integer |
693 | * @size_t *s@ = where to store the power of 2 |
694 | * |
695 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
696 | * |
697 | * Use: Computes a power of two and an odd integer which, when |
698 | * multiplied, give a specified result. This sort of thing is |
699 | * useful in number theory quite often. |
700 | */ |
701 | |
702 | mp *mp_odd(mp *d, mp *m, size_t *s) |
703 | { |
704 | size_t ss = 0; |
705 | const mpw *v, *vl; |
706 | |
707 | v = m->v; |
708 | vl = m->vl; |
709 | for (; !*v && v < vl; v++) |
710 | ss += MPW_BITS; |
711 | if (v >= vl) |
712 | ss = 0; |
713 | else { |
714 | mpw x = *v; |
715 | mpw mask = MPW_MAX; |
716 | unsigned z = MPW_BITS / 2; |
717 | |
718 | while (z) { |
719 | mask >>= z; |
720 | if (!(x & mask)) { |
721 | x >>= z; |
722 | ss += z; |
723 | } |
724 | z >>= 1; |
725 | } |
726 | } |
727 | |
728 | *s = ss; |
729 | return (mp_lsr(d, m, ss)); |
730 | } |
731 | |
d3409d5e |
732 | /*----- Test rig ----------------------------------------------------------*/ |
733 | |
734 | #ifdef TEST_RIG |
735 | |
736 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
737 | { |
4b536f42 |
738 | if (!MP_EQ(expect, result)) { |
d3409d5e |
739 | fprintf(stderr, "\n*** %s failed", op); |
740 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
741 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10); |
742 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10); |
743 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10); |
744 | fputc('\n', stderr); |
745 | return (0); |
746 | } |
747 | return (1); |
748 | } |
749 | |
750 | #define RIG(name, op) \ |
ef5f4810 |
751 | static int t##name(dstr *v) \ |
d3409d5e |
752 | { \ |
753 | mp *a = *(mp **)v[0].buf; \ |
754 | mpw n = *(int *)v[1].buf; \ |
755 | mp b; \ |
756 | mp *r = *(mp **)v[2].buf; \ |
757 | mp *c = op(MP_NEW, a, n); \ |
758 | int ok; \ |
759 | mp_build(&b, &n, &n + 1); \ |
760 | ok = verify(#name, r, c, a, &b); \ |
761 | mp_drop(a); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
762 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
763 | return (ok); \ |
764 | } |
765 | |
766 | RIG(lsl, mp_lsl) |
767 | RIG(lsr, mp_lsr) |
f09e814a |
768 | RIG(lsl2c, mp_lsl2c) |
769 | RIG(lsr2c, mp_lsr2c) |
d3409d5e |
770 | |
771 | #undef RIG |
772 | |
773 | #define RIG(name, op) \ |
ef5f4810 |
774 | static int t##name(dstr *v) \ |
d3409d5e |
775 | { \ |
776 | mp *a = *(mp **)v[0].buf; \ |
777 | mp *b = *(mp **)v[1].buf; \ |
778 | mp *r = *(mp **)v[2].buf; \ |
779 | mp *c = op(MP_NEW, a, b); \ |
780 | int ok = verify(#name, r, c, a, b); \ |
781 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
782 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
783 | return (ok); \ |
784 | } |
785 | |
786 | RIG(add, mp_add) |
787 | RIG(sub, mp_sub) |
788 | RIG(mul, mp_mul) |
789 | |
790 | #undef RIG |
791 | |
792 | static int tdiv(dstr *v) |
793 | { |
794 | mp *a = *(mp **)v[0].buf; |
795 | mp *b = *(mp **)v[1].buf; |
796 | mp *q = *(mp **)v[2].buf; |
797 | mp *r = *(mp **)v[3].buf; |
798 | mp *c = MP_NEW, *d = MP_NEW; |
799 | int ok = 1; |
800 | mp_div(&c, &d, a, b); |
801 | ok &= verify("div(quotient)", q, c, a, b); |
802 | ok &= verify("div(remainder)", r, d, a, b); |
803 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
ef5f4810 |
804 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
805 | return (ok); |
806 | } |
807 | |
f09e814a |
808 | static int tbin(dstr *v) |
809 | { |
810 | static mp *(*fn[])(mp *, mp *, mp *) = { |
811 | #define DO(string) mp_bit##string##2c, |
812 | MPX_DOBIN(DO) |
813 | #undef DO |
814 | }; |
815 | int ok = 1; |
816 | unsigned op = 0; |
817 | mp *a = *(mp **)v[1].buf; |
818 | mp *b = *(mp **)v[2].buf; |
819 | mp *r = *(mp **)v[3].buf; |
820 | mp *c; |
821 | |
822 | if (strcmp(v[0].buf, "and") == 0) op = 1; |
823 | else if (strcmp(v[0].buf, "or") == 0) op = 7; |
824 | else if (strcmp(v[0].buf, "nand") == 0) op = 14; |
825 | else if (strcmp(v[0].buf, "nor") == 0) op = 8; |
826 | else if (strcmp(v[0].buf, "xor") == 0) op = 6; |
827 | else { |
828 | char *p = v[0].buf; |
829 | while (*p) { |
830 | op <<= 1; |
831 | if (*p++ == '1') |
832 | op |= 1; |
833 | } |
834 | } |
835 | |
836 | c = fn[op](MP_NEW, a, b); |
837 | ok = verify(v[0].buf, r, c, a, b); |
838 | mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c); |
839 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
840 | return (ok); |
841 | } |
842 | |
09d00c6b |
843 | static int tset(dstr *v) |
844 | { |
845 | mp *a = *(mp **)v[0].buf; |
846 | unsigned long n = *(unsigned long *)v[1].buf; |
847 | mp *r = *(mp **)v[2].buf; |
848 | mp *c; |
849 | int ok = 1; |
850 | |
851 | c = mp_setbit2c(MP_NEW, a, n); |
852 | if (!MP_EQ(c, r)) { |
853 | ok = 0; |
854 | fprintf(stderr, "\n***setbit (set) failed"); |
855 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
856 | fprintf(stderr, "\n*** n = %lu", n); |
857 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
858 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
859 | fputc('\n', stderr); |
860 | } |
861 | if (!mp_testbit2c(r, n)) { |
862 | ok = 0; |
863 | fprintf(stderr, "\n***setbit (test) failed"); |
864 | fprintf(stderr, "\n*** n = %lu", n); |
865 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
866 | fputc('\n', stderr); |
867 | } |
868 | mp_drop(a); |
869 | mp_drop(r); |
870 | mp_drop(c); |
871 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
872 | return (ok); |
873 | } |
874 | |
875 | static int tclr(dstr *v) |
876 | { |
877 | mp *a = *(mp **)v[0].buf; |
878 | unsigned long n = *(unsigned long *)v[1].buf; |
879 | mp *r = *(mp **)v[2].buf; |
880 | mp *c; |
881 | int ok = 1; |
882 | |
883 | c = mp_clearbit2c(MP_NEW, a, n); |
884 | if (!MP_EQ(c, r)) { |
885 | ok = 0; |
886 | fprintf(stderr, "\n***clrbit (set) failed"); |
887 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
888 | fprintf(stderr, "\n*** n = %lu", n); |
889 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
890 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
891 | fputc('\n', stderr); |
892 | } |
893 | if (mp_testbit2c(r, n)) { |
894 | ok = 0; |
895 | fprintf(stderr, "\n***clrbit (test) failed"); |
896 | fprintf(stderr, "\n*** n = %lu", n); |
897 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
898 | fputc('\n', stderr); |
899 | } |
900 | mp_drop(a); |
901 | mp_drop(c); |
902 | mp_drop(r); |
903 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
904 | return (ok); |
905 | } |
906 | |
397041a9 |
907 | static int tneg(dstr *v) |
908 | { |
909 | mp *a = *(mp **)v[0].buf; |
910 | mp *r = *(mp **)v[1].buf; |
911 | int ok = 1; |
912 | mp *n = mp_neg(MP_NEW, a); |
913 | if (!MP_EQ(r, n)) { |
914 | ok = 0; |
915 | fprintf(stderr, "\n*** neg failed\n"); |
916 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
917 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
918 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
919 | fputc('\n', stderr); |
920 | } |
921 | mp_drop(n); |
922 | n = mp_neg(a, a); |
923 | if (!MP_EQ(r, n)) { |
924 | ok = 0; |
925 | fprintf(stderr, "\n*** neg failed\n"); |
926 | fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10); |
927 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
928 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
929 | fputc('\n', stderr); |
930 | } |
931 | mp_drop(a); |
932 | mp_drop(r); |
933 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
934 | return (ok); |
935 | } |
936 | |
f1713c63 |
937 | static int todd(dstr *v) |
938 | { |
939 | mp *a = *(mp **)v[0].buf; |
940 | size_t rs = *(uint32 *)v[1].buf; |
941 | mp *rt = *(mp **)v[2].buf; |
942 | int ok = 1; |
943 | mp *t; |
944 | size_t s; |
945 | t = mp_odd(MP_NEW, a, &s); |
4b536f42 |
946 | if (s != rs || !MP_EQ(t, rt)) { |
f1713c63 |
947 | ok = 0; |
948 | fprintf(stderr, "\n*** odd failed"); |
949 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
950 | fprintf(stderr, "\n*** s = %lu", (unsigned long)s); |
951 | fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10); |
952 | fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs); |
953 | fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10); |
954 | fputc('\n', stderr); |
955 | } |
956 | mp_drop(a); |
957 | mp_drop(rt); |
958 | mp_drop(t); |
09d00c6b |
959 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
f1713c63 |
960 | return (ok); |
961 | } |
962 | |
d3409d5e |
963 | static test_chunk tests[] = { |
f09e814a |
964 | { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } }, |
965 | { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } }, |
966 | { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } }, |
967 | { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } }, |
09d00c6b |
968 | { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } }, |
969 | { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } }, |
d3409d5e |
970 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
971 | { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } }, |
972 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
973 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
f09e814a |
974 | { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } }, |
f1713c63 |
975 | { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } }, |
397041a9 |
976 | { "neg", tneg, { &type_mp, &type_mp, 0 } }, |
d3409d5e |
977 | { 0, 0, { 0 } }, |
978 | }; |
979 | |
980 | int main(int argc, char *argv[]) |
981 | { |
982 | sub_init(); |
983 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
984 | return (0); |
985 | } |
986 | |
987 | #endif |
988 | |
989 | /*----- That's all, folks -------------------------------------------------*/ |