d3409d5e |
1 | /* -*-c-*- |
2 | * |
2b645fb7 |
3 | * $Id: mp-arith.c,v 1.16.2.1 2003/06/10 13:21:10 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 $ |
2b645fb7 |
33 | * Revision 1.16.2.1 2003/06/10 13:21:10 mdw |
34 | * Fix bug dividing small things by large ones. |
35 | * |
81578196 |
36 | * Revision 1.16 2003/05/16 09:09:24 mdw |
37 | * Fix @mp_lsl2c@. Turns out to be surprisingly tricky. |
38 | * |
75263f25 |
39 | * Revision 1.15 2002/10/19 17:56:50 mdw |
40 | * Fix bit operations. Test them (a bit) better. |
41 | * |
397041a9 |
42 | * Revision 1.14 2002/10/15 19:18:31 mdw |
43 | * New operation to negate numbers. |
44 | * |
09d00c6b |
45 | * Revision 1.13 2002/10/15 00:19:40 mdw |
46 | * Bit setting and clearing functions. |
47 | * |
dd22938e |
48 | * Revision 1.12 2002/10/09 00:36:03 mdw |
49 | * Fix bounds on workspace for Karatsuba operations. |
50 | * |
f09e814a |
51 | * Revision 1.11 2002/10/06 22:52:50 mdw |
52 | * Pile of changes for supporting two's complement properly. |
53 | * |
0f32e0f8 |
54 | * Revision 1.10 2001/04/03 19:36:05 mdw |
55 | * Add some simple bitwise operations so that Perl can use them. |
56 | * |
52cdaca9 |
57 | * Revision 1.9 2000/10/08 15:48:35 mdw |
58 | * Rename Karatsuba constants now that we have @gfx_kmul@ too. |
59 | * |
4b536f42 |
60 | * Revision 1.8 2000/10/08 12:02:21 mdw |
61 | * Use @MP_EQ@ instead of @MP_CMP@. |
62 | * |
f1713c63 |
63 | * Revision 1.7 2000/06/22 19:02:53 mdw |
64 | * New function @mp_odd@ to extract powers of two from an integer. This is |
65 | * common code from the Rabin-Miller test, RSA key recovery and modular |
66 | * square-root extraction. |
67 | * |
d34decd2 |
68 | * Revision 1.6 2000/06/17 11:45:09 mdw |
69 | * Major memory management overhaul. Added arena support. Use the secure |
70 | * arena for secret integers. Replace and improve the MP management macros |
71 | * (e.g., replace MP_MODIFY by MP_DEST). |
72 | * |
bba03f55 |
73 | * Revision 1.5 1999/12/22 15:54:41 mdw |
74 | * Adjust Karatsuba parameters. Calculate destination size better. |
75 | * |
8017495b |
76 | * Revision 1.4 1999/12/13 15:35:16 mdw |
77 | * Slightly different rules on memory allocation. |
78 | * |
5bf74dea |
79 | * Revision 1.3 1999/12/11 10:57:43 mdw |
80 | * Karatsuba squaring algorithm. |
81 | * |
ef5f4810 |
82 | * Revision 1.2 1999/12/10 23:18:39 mdw |
83 | * Change interface for suggested destinations. |
84 | * |
d3409d5e |
85 | * Revision 1.1 1999/11/17 18:02:16 mdw |
86 | * New multiprecision integer arithmetic suite. |
87 | * |
88 | */ |
89 | |
90 | /*----- Header files ------------------------------------------------------*/ |
91 | |
92 | #include "mp.h" |
93 | |
ef5f4810 |
94 | /*----- Macros ------------------------------------------------------------*/ |
95 | |
96 | #define MAX(x, y) ((x) >= (y) ? (x) : (y)) |
97 | |
d3409d5e |
98 | /*----- Main code ---------------------------------------------------------*/ |
99 | |
81578196 |
100 | /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- * |
d3409d5e |
101 | * |
f09e814a |
102 | * Arguments: @mp *d@ = destination |
103 | * @mp *a@ = source |
104 | * @size_t n@ = number of bits to move |
d3409d5e |
105 | * |
f09e814a |
106 | * Returns: Result, @a@ shifted left or right by @n@. |
81578196 |
107 | * |
108 | * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced |
109 | * on the right with ones instead of zeroes: it's used |
110 | * internally by @mp_lsl2c@, though it may be useful on its |
111 | * own. |
d3409d5e |
112 | */ |
113 | |
f09e814a |
114 | mp *mp_lsl(mp *d, mp *a, size_t n) |
d3409d5e |
115 | { |
f09e814a |
116 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
117 | mpx_lsl(d->v, d->vl, a->v, a->vl, n); |
118 | d->f = a->f & (MP_NEG | MP_BURN); |
119 | MP_SHRINK(d); |
120 | return (d); |
121 | } |
d3409d5e |
122 | |
81578196 |
123 | mp *mp_lslc(mp *d, mp *a, size_t n) |
124 | { |
125 | MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f); |
126 | mpx_lslc(d->v, d->vl, a->v, a->vl, n); |
127 | d->f = a->f & (MP_NEG | MP_BURN); |
128 | MP_SHRINK(d); |
129 | return (d); |
130 | } |
131 | |
f09e814a |
132 | mp *mp_lsr(mp *d, mp *a, size_t n) |
133 | { |
d34decd2 |
134 | MP_DEST(d, MP_LEN(a), a->f); |
f09e814a |
135 | mpx_lsr(d->v, d->vl, a->v, a->vl, n); |
136 | d->f = a->f & (MP_NEG | MP_BURN); |
d3409d5e |
137 | MP_SHRINK(d); |
138 | return (d); |
139 | } |
140 | |
f09e814a |
141 | /* --- @mp_lsl2c@, @mp_lsr2c@ --- * |
d3409d5e |
142 | * |
143 | * Arguments: @mp *d@ = destination |
144 | * @mp *a@ = source |
f09e814a |
145 | * @size_t n@ = number of bits to move |
d3409d5e |
146 | * |
f09e814a |
147 | * Returns: Result, @a@ shifted left or right by @n@. Handles the |
148 | * pretence of sign-extension for negative numbers. |
d3409d5e |
149 | */ |
150 | |
f09e814a |
151 | mp *mp_lsl2c(mp *d, mp *a, size_t n) |
d3409d5e |
152 | { |
f09e814a |
153 | if (!(a->f & MP_NEG)) |
154 | return (mp_lsl(d, a, n)); |
155 | d = mp_not2c(d, a); |
81578196 |
156 | d = mp_lslc(d, d, n); |
f09e814a |
157 | d = mp_not2c(d, d); |
158 | return (d); |
159 | } |
d3409d5e |
160 | |
f09e814a |
161 | mp *mp_lsr2c(mp *d, mp *a, size_t n) |
162 | { |
163 | if (!(a->f & MP_NEG)) |
164 | return (mp_lsr(d, a, n)); |
165 | d = mp_not2c(d, a); |
166 | d = mp_lsr(d, d, n); |
167 | d = mp_not2c(d, d); |
168 | return (d); |
d3409d5e |
169 | } |
170 | |
f09e814a |
171 | /* --- @mp_testbit@ --- * |
d3409d5e |
172 | * |
f09e814a |
173 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
174 | * @unsigned long n@ = which bit to test |
d3409d5e |
175 | * |
f09e814a |
176 | * Returns: Nonzero if the bit is set, zero if not. |
d3409d5e |
177 | */ |
178 | |
09d00c6b |
179 | int mp_testbit(mp *x, unsigned long n) |
d3409d5e |
180 | { |
f09e814a |
181 | if (n > MPW_BITS * MP_LEN(x)) |
182 | return (0); |
09d00c6b |
183 | return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u); |
d3409d5e |
184 | } |
185 | |
f09e814a |
186 | /* --- @mp_testbit2c@ --- * |
d3409d5e |
187 | * |
f09e814a |
188 | * Arguments: @mp *x@ = a large integer |
09d00c6b |
189 | * @unsigned long n@ = which bit to test |
d3409d5e |
190 | * |
f09e814a |
191 | * Returns: Nonzero if the bit is set, zero if not. Fakes up two's |
192 | * complement representation. |
d3409d5e |
193 | */ |
194 | |
09d00c6b |
195 | int mp_testbit2c(mp *x, unsigned long n) |
d3409d5e |
196 | { |
f09e814a |
197 | int r; |
09d00c6b |
198 | if (!(x->f & MP_NEG)) |
f09e814a |
199 | return (mp_testbit(x, n)); |
200 | x = mp_not2c(MP_NEW, x); |
201 | r = !mp_testbit(x, n); |
202 | MP_DROP(x); |
203 | return (r); |
d3409d5e |
204 | } |
205 | |
09d00c6b |
206 | /* --- @mp_setbit@, @mp_clearbit@ --- * |
207 | * |
208 | * Arguments: @mp *d@ = a destination |
209 | * @mp *x@ = a large integer |
210 | * @unsigned long n@ = which bit to modify |
211 | * |
212 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
213 | */ |
214 | |
215 | mp *mp_setbit(mp *d, mp *x, unsigned long n) |
216 | { |
217 | size_t rq; |
218 | |
219 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
220 | if (d != x) { |
221 | if (d) MP_DROP(d); |
222 | d = MP_COPY(x); |
223 | } |
224 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
225 | d->v[n/MPW_BITS] |= 1 << n%MPW_BITS; |
226 | return (d); |
227 | } |
228 | |
229 | mp *mp_clearbit(mp *d, mp *x, unsigned long n) |
230 | { |
231 | size_t rq; |
232 | |
233 | rq = n + MPW_BITS; rq -= rq % MPW_BITS; |
234 | if (d != x) { |
235 | if (d) MP_DROP(d); |
236 | d = MP_COPY(x); |
237 | } |
238 | MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN)); |
239 | d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS); |
240 | return (d); |
241 | } |
242 | |
243 | /* --- @mp_setbit2c@, @mp_clearbit2c@ --- * |
244 | * |
245 | * Arguments: @mp *d@ = a destination |
246 | * @mp *x@ = a large integer |
247 | * @unsigned long n@ = which bit to modify |
248 | * |
249 | * Returns: The argument @x@, with the appropriate bit set or cleared. |
250 | * Fakes up two's complement representation. |
251 | */ |
252 | |
253 | mp *mp_setbit2c(mp *d, mp *x, unsigned long n) |
254 | { |
255 | if (!(x->f & MP_NEG)) |
256 | return mp_setbit(d, x, n); |
257 | d = mp_not2c(d, x); |
258 | d = mp_clearbit(d, d, n); |
259 | d = mp_not2c(d, d); |
260 | return (d); |
261 | } |
262 | |
263 | mp *mp_clearbit2c(mp *d, mp *x, unsigned long n) |
264 | { |
265 | if (!(x->f & MP_NEG)) |
266 | return mp_clearbit(d, x, n); |
267 | d = mp_not2c(d, x); |
268 | d = mp_setbit(d, d, n); |
269 | d = mp_not2c(d, d); |
270 | return (d); |
271 | } |
272 | |
4b536f42 |
273 | /* --- @mp_eq@ --- * |
274 | * |
275 | * Arguments: @const mp *a, *b@ = two numbers |
276 | * |
277 | * Returns: Nonzero if the numbers are equal. |
278 | */ |
279 | |
280 | int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); } |
281 | |
d3409d5e |
282 | /* --- @mp_cmp@ --- * |
283 | * |
284 | * Arguments: @const mp *a, *b@ = two numbers |
285 | * |
286 | * Returns: Less than, equal to or greater than zero, according to |
287 | * whether @a@ is less than, equal to or greater than @b@. |
288 | */ |
289 | |
290 | int mp_cmp(const mp *a, const mp *b) |
291 | { |
292 | if (!((a->f ^ b->f) & MP_NEG)) |
293 | return (mpx_ucmp(a->v, a->vl, b->v, b->vl)); |
294 | else if (a->f & MP_NEG) |
295 | return (-1); |
296 | else |
297 | return (+1); |
298 | } |
299 | |
397041a9 |
300 | /* --- @mp_neg@ --- * |
301 | * |
302 | * Arguments: @mp *d@ = destination |
303 | * @mp *a@ = argument |
304 | * |
305 | * Returns: The negation of the argument. |
306 | * |
307 | * Use: Negates its argument. |
308 | */ |
309 | |
310 | mp *mp_neg(mp *d, mp *a) |
311 | { |
312 | /* --- Surprising amounts of messing about required --- */ |
313 | |
314 | MP_SHRINK(a); |
315 | MP_COPY(a); |
81578196 |
316 | if (d) |
317 | MP_DROP(d); |
318 | if (a->v == a->vl) |
397041a9 |
319 | return (a); |
397041a9 |
320 | MP_DEST(a, MP_LEN(a), a->f); |
321 | a->f ^= MP_NEG; |
322 | return (a); |
323 | } |
324 | |
f09e814a |
325 | /* --- @mp_bitop@ --- * |
0f32e0f8 |
326 | * |
327 | * Arguments: @mp *d@ = destination |
328 | * @mp *a, *b@ = sources |
329 | * |
f09e814a |
330 | * Returns: The result of the given bitwise operation. These functions |
331 | * don't handle negative numbers at all sensibly. For that, use |
332 | * the @...2c@ variants. The functions are named after the |
333 | * truth tables they generate: |
334 | * |
335 | * a: 0011 |
336 | * b: 0101 |
337 | * @mpx_bitXXXX@ |
0f32e0f8 |
338 | */ |
339 | |
f09e814a |
340 | #define MP_BITBINOP(string) \ |
0f32e0f8 |
341 | \ |
f09e814a |
342 | mp *mp_bit##string(mp *d, mp *a, mp *b) \ |
0f32e0f8 |
343 | { \ |
75263f25 |
344 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \ |
f09e814a |
345 | mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \ |
0f32e0f8 |
346 | d->f = (a->f | b->f) & MP_BURN; \ |
347 | MP_SHRINK(d); \ |
348 | return (d); \ |
349 | } |
350 | |
f09e814a |
351 | MPX_DOBIN(MP_BITBINOP) |
352 | |
353 | /* --- @mp_not@ --- * |
354 | * |
355 | * Arguments: @mp *d@ = destination |
356 | * @mp *a@ = source |
357 | * |
358 | * Returns: The bitwise complement of the source. |
359 | */ |
0f32e0f8 |
360 | |
361 | mp *mp_not(mp *d, mp *a) |
362 | { |
363 | MP_DEST(d, MP_LEN(a), a->f); |
364 | mpx_not(d->v, d->vl, a->v, a->vl); |
365 | d->f = a->f & MP_BURN; |
366 | MP_SHRINK(d); |
367 | return (d); |
368 | } |
369 | |
f09e814a |
370 | /* --- @mp_bitop2c@ --- * |
371 | * |
372 | * Arguments: @mp *d@ = destination |
373 | * @mp *a, *b@ = sources |
374 | * |
375 | * Returns: The result of the given bitwise operation. Negative numbers |
376 | * are treated as two's complement, sign-extended infinitely to |
377 | * the left. The functions are named after the truth tables |
378 | * they generate: |
379 | * |
380 | * a: 0011 |
381 | * b: 0101 |
382 | * @mpx_bitXXXX@ |
383 | */ |
384 | |
385 | /* --- How this actually works --- * |
386 | * |
387 | * The two arguments are inverted (with a sign-swap) if they're currently |
388 | * negative. This means that we end up using a different function (one which |
389 | * reinverts as we go) for the main operation. Also, if the sign would be |
390 | * negative at the end, we preinvert the output and then invert again with a |
391 | * sign-swap. |
392 | * |
393 | * Start with: wxyz WXYZ |
394 | * If @a@ negative: yzwx or YZWX |
395 | * If @b@ negative: xwzy XWZY |
396 | * If both negative: zyxw ZYXW |
397 | */ |
398 | |
399 | #define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \ |
400 | \ |
401 | mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \ |
402 | { \ |
403 | if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \ |
404 | d = mp_bit##base(d, a, b); \ |
405 | p_base \ |
406 | } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \ |
407 | MP_COPY(b); \ |
408 | d = mp_not2c(d, a); \ |
409 | d = mp_bit##an(d, d, b); \ |
410 | MP_DROP(b); \ |
411 | p_an \ |
412 | } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \ |
413 | MP_COPY(a); \ |
414 | d = mp_not2c(d, b); \ |
415 | d = mp_bit##bn(d, a, d); \ |
416 | MP_DROP(a); \ |
417 | p_bn \ |
418 | } else { /* Both negative */ \ |
419 | mp *t = mp_not2c(MP_NEW, a); \ |
420 | mp *d = mp_not2c(d, b); \ |
421 | d = mp_bit##abn(d, t, d); \ |
422 | MP_DROP(t); \ |
423 | p_abn \ |
424 | } \ |
425 | return (d); \ |
426 | } \ |
427 | |
428 | #define NEG d = mp_not2c(d, d); |
429 | #define POS |
430 | MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS) |
431 | MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG) |
432 | MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS) |
433 | MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG) |
434 | MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS) |
435 | MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG) |
436 | MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS) |
437 | MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG) |
438 | MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS) |
439 | MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG) |
440 | MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS) |
441 | MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG) |
442 | MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS) |
443 | MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG) |
444 | MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS) |
445 | MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG) |
446 | #undef NEG |
447 | #undef POS |
448 | |
449 | /* --- @mp_not2c@ --- * |
450 | * |
451 | * Arguments: @mp *d@ = destination |
452 | * @mp *a@ = source |
453 | * |
454 | * Returns: The sign-extended complement of the argument. |
455 | */ |
456 | |
457 | mp *mp_not2c(mp *d, mp *a) |
458 | { |
459 | mpw one = 1; |
460 | |
461 | MP_DEST(d, MP_LEN(a) + 1, a->f); |
462 | if (d == a) { |
463 | if (a->f & MP_NEG) |
464 | MPX_USUBN(d->v, d->vl, 1); |
465 | else |
466 | MPX_UADDN(d->v, d->vl, 1); |
467 | } else { |
468 | if (a->f & MP_NEG) |
469 | mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
470 | else |
471 | mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1); |
472 | } |
473 | d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG; |
474 | MP_SHRINK(d); |
475 | return (d); |
476 | } |
477 | |
d3409d5e |
478 | /* --- @mp_add@ --- * |
479 | * |
480 | * Arguments: @mp *d@ = destination |
ef5f4810 |
481 | * @mp *a, *b@ = sources |
d3409d5e |
482 | * |
483 | * Returns: Result, @a@ added to @b@. |
484 | */ |
485 | |
ef5f4810 |
486 | mp *mp_add(mp *d, mp *a, mp *b) |
d3409d5e |
487 | { |
d34decd2 |
488 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
489 | if (!((a->f ^ b->f) & MP_NEG)) |
490 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
491 | else { |
492 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
493 | mp *t = a; a = b; b = t; |
d3409d5e |
494 | } |
495 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
496 | } |
497 | d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG); |
498 | MP_SHRINK(d); |
499 | return (d); |
500 | } |
501 | |
502 | /* --- @mp_sub@ --- * |
503 | * |
504 | * Arguments: @mp *d@ = destination |
ef5f4810 |
505 | * @mp *a, *b@ = sources |
d3409d5e |
506 | * |
507 | * Returns: Result, @b@ subtracted from @a@. |
508 | */ |
509 | |
ef5f4810 |
510 | mp *mp_sub(mp *d, mp *a, mp *b) |
d3409d5e |
511 | { |
512 | unsigned sgn = 0; |
d34decd2 |
513 | MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f); |
d3409d5e |
514 | if ((a->f ^ b->f) & MP_NEG) |
515 | mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
516 | else { |
517 | if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) { |
ef5f4810 |
518 | mp *t = a; a = b; b = t; |
d3409d5e |
519 | sgn = MP_NEG; |
520 | } |
521 | mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
522 | } |
523 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG); |
524 | MP_SHRINK(d); |
525 | return (d); |
526 | } |
527 | |
528 | /* --- @mp_mul@ --- * |
529 | * |
530 | * Arguments: @mp *d@ = destination |
ef5f4810 |
531 | * @mp *a, *b@ = sources |
d3409d5e |
532 | * |
533 | * Returns: Result, @a@ multiplied by @b@. |
534 | */ |
535 | |
ef5f4810 |
536 | mp *mp_mul(mp *d, mp *a, mp *b) |
d3409d5e |
537 | { |
ef5f4810 |
538 | a = MP_COPY(a); |
539 | b = MP_COPY(b); |
540 | |
52cdaca9 |
541 | if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) { |
d34decd2 |
542 | MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF); |
ef5f4810 |
543 | mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl); |
8017495b |
544 | } else { |
dd22938e |
545 | size_t m = MAX(MP_LEN(a), MP_LEN(b)); |
ef5f4810 |
546 | mpw *s; |
dd22938e |
547 | MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF); |
548 | s = mpalloc(d->a, 5 * m); |
549 | mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m); |
d34decd2 |
550 | mpfree(d->a, s); |
ef5f4810 |
551 | } |
552 | |
d3409d5e |
553 | d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG); |
554 | MP_SHRINK(d); |
ef5f4810 |
555 | MP_DROP(a); |
556 | MP_DROP(b); |
d3409d5e |
557 | return (d); |
558 | } |
559 | |
560 | /* --- @mp_sqr@ --- * |
561 | * |
562 | * Arguments: @mp *d@ = destination |
ef5f4810 |
563 | * @mp *a@ = source |
d3409d5e |
564 | * |
565 | * Returns: Result, @a@ squared. |
566 | */ |
567 | |
ef5f4810 |
568 | mp *mp_sqr(mp *d, mp *a) |
d3409d5e |
569 | { |
ef5f4810 |
570 | size_t m = MP_LEN(a); |
571 | |
572 | a = MP_COPY(a); |
52cdaca9 |
573 | if (m > MPK_THRESH) { |
ef5f4810 |
574 | mpw *s; |
dd22938e |
575 | MP_DEST(d, 3 * m, a->f | MP_UNDEF); |
576 | s = mpalloc(d->a, 5 * m); |
577 | mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m); |
d34decd2 |
578 | mpfree(d->a, s); |
dd22938e |
579 | } else { |
580 | MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF); |
ef5f4810 |
581 | mpx_usqr(d->v, d->vl, a->v, a->vl); |
dd22938e |
582 | } |
d3409d5e |
583 | d->f = a->f & MP_BURN; |
584 | MP_SHRINK(d); |
ef5f4810 |
585 | MP_DROP(a); |
d3409d5e |
586 | return (d); |
587 | } |
588 | |
589 | /* --- @mp_div@ --- * |
590 | * |
591 | * Arguments: @mp **qq, **rr@ = destination, quotient and remainder |
ef5f4810 |
592 | * @mp *a, *b@ = sources |
d3409d5e |
593 | * |
594 | * Use: Calculates the quotient and remainder when @a@ is divided by |
595 | * @b@. The destinations @*qq@ and @*rr@ must be distinct. |
596 | * Either of @qq@ or @rr@ may be null to indicate that the |
597 | * result is irrelevant. (Discarding both results is silly.) |
598 | * There is a performance advantage if @a == *rr@. |
599 | * |
600 | * The behaviour when @a@ and @b@ have the same sign is |
601 | * straightforward. When the signs differ, this implementation |
602 | * chooses @r@ to have the same sign as @b@, rather than the |
603 | * more normal choice that the remainder has the same sign as |
604 | * the dividend. This makes modular arithmetic a little more |
605 | * straightforward. |
606 | */ |
607 | |
ef5f4810 |
608 | void mp_div(mp **qq, mp **rr, mp *a, mp *b) |
d3409d5e |
609 | { |
610 | mp *r = rr ? *rr : MP_NEW; |
611 | mp *q = qq ? *qq : MP_NEW; |
612 | mpw *sv, *svl; |
613 | |
d3409d5e |
614 | /* --- Set the remainder up right --- * |
615 | * |
616 | * Just in case the divisor is larger, be able to cope with this. It's not |
617 | * important in @mpx_udiv@, but it is here because of the sign correction. |
618 | */ |
619 | |
d34decd2 |
620 | b = MP_COPY(b); |
621 | a = MP_COPY(a); |
622 | if (r) |
623 | MP_DROP(r); |
624 | r = a; |
2b645fb7 |
625 | MP_DEST(r, MP_LEN(b) + 2, a->f | b->f); |
d3409d5e |
626 | |
627 | /* --- Fix up the quotient too --- */ |
628 | |
d34decd2 |
629 | r = MP_COPY(r); |
630 | MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF); |
631 | MP_DROP(r); |
632 | |
633 | /* --- Set up some temporary workspace --- */ |
634 | |
635 | { |
636 | size_t rq = MP_LEN(b) + 1; |
637 | sv = mpalloc(r->a, rq); |
638 | svl = sv + rq; |
639 | } |
d3409d5e |
640 | |
641 | /* --- Perform the calculation --- */ |
642 | |
643 | mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl); |
644 | |
645 | /* --- Sort out the sign of the results --- * |
646 | * |
647 | * If the signs of the arguments differ, and the remainder is nonzero, I |
648 | * must add one to the absolute value of the quotient and subtract the |
649 | * remainder from @b@. |
650 | */ |
651 | |
d34decd2 |
652 | q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG); |
d3409d5e |
653 | if (q->f & MP_NEG) { |
ef5f4810 |
654 | mpw *v; |
655 | for (v = r->v; v < r->vl; v++) { |
d3409d5e |
656 | if (*v) { |
657 | MPX_UADDN(q->v, q->vl, 1); |
658 | mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl); |
659 | break; |
660 | } |
661 | } |
662 | } |
663 | |
d34decd2 |
664 | r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG); |
d3409d5e |
665 | |
666 | /* --- Store the return values --- */ |
667 | |
d34decd2 |
668 | mpfree(r->a, sv); |
669 | MP_DROP(b); |
670 | |
d3409d5e |
671 | if (!qq) |
672 | MP_DROP(q); |
673 | else { |
674 | MP_SHRINK(q); |
675 | *qq = q; |
676 | } |
677 | |
678 | if (!rr) |
679 | MP_DROP(r); |
680 | else { |
681 | MP_SHRINK(r); |
682 | *rr = r; |
683 | } |
d3409d5e |
684 | } |
685 | |
f1713c63 |
686 | /* --- @mp_odd@ --- * |
687 | * |
688 | * Arguments: @mp *d@ = pointer to destination integer |
689 | * @mp *m@ = pointer to source integer |
690 | * @size_t *s@ = where to store the power of 2 |
691 | * |
692 | * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%. |
693 | * |
694 | * Use: Computes a power of two and an odd integer which, when |
695 | * multiplied, give a specified result. This sort of thing is |
696 | * useful in number theory quite often. |
697 | */ |
698 | |
699 | mp *mp_odd(mp *d, mp *m, size_t *s) |
700 | { |
701 | size_t ss = 0; |
702 | const mpw *v, *vl; |
703 | |
704 | v = m->v; |
705 | vl = m->vl; |
706 | for (; !*v && v < vl; v++) |
707 | ss += MPW_BITS; |
708 | if (v >= vl) |
709 | ss = 0; |
710 | else { |
711 | mpw x = *v; |
712 | mpw mask = MPW_MAX; |
713 | unsigned z = MPW_BITS / 2; |
714 | |
715 | while (z) { |
716 | mask >>= z; |
717 | if (!(x & mask)) { |
718 | x >>= z; |
719 | ss += z; |
720 | } |
721 | z >>= 1; |
722 | } |
723 | } |
724 | |
725 | *s = ss; |
726 | return (mp_lsr(d, m, ss)); |
727 | } |
728 | |
d3409d5e |
729 | /*----- Test rig ----------------------------------------------------------*/ |
730 | |
731 | #ifdef TEST_RIG |
732 | |
733 | static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b) |
734 | { |
4b536f42 |
735 | if (!MP_EQ(expect, result)) { |
d3409d5e |
736 | fprintf(stderr, "\n*** %s failed", op); |
737 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
738 | fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10); |
739 | fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10); |
740 | fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10); |
741 | fputc('\n', stderr); |
742 | return (0); |
743 | } |
744 | return (1); |
745 | } |
746 | |
747 | #define RIG(name, op) \ |
ef5f4810 |
748 | static int t##name(dstr *v) \ |
d3409d5e |
749 | { \ |
750 | mp *a = *(mp **)v[0].buf; \ |
751 | mpw n = *(int *)v[1].buf; \ |
752 | mp b; \ |
753 | mp *r = *(mp **)v[2].buf; \ |
754 | mp *c = op(MP_NEW, a, n); \ |
755 | int ok; \ |
756 | mp_build(&b, &n, &n + 1); \ |
757 | ok = verify(#name, r, c, a, &b); \ |
758 | mp_drop(a); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
759 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
760 | return (ok); \ |
761 | } |
762 | |
763 | RIG(lsl, mp_lsl) |
764 | RIG(lsr, mp_lsr) |
f09e814a |
765 | RIG(lsl2c, mp_lsl2c) |
766 | RIG(lsr2c, mp_lsr2c) |
d3409d5e |
767 | |
768 | #undef RIG |
769 | |
770 | #define RIG(name, op) \ |
ef5f4810 |
771 | static int t##name(dstr *v) \ |
d3409d5e |
772 | { \ |
773 | mp *a = *(mp **)v[0].buf; \ |
774 | mp *b = *(mp **)v[1].buf; \ |
775 | mp *r = *(mp **)v[2].buf; \ |
776 | mp *c = op(MP_NEW, a, b); \ |
777 | int ok = verify(#name, r, c, a, b); \ |
778 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \ |
ef5f4810 |
779 | assert(mparena_count(MPARENA_GLOBAL) == 0); \ |
d3409d5e |
780 | return (ok); \ |
781 | } |
782 | |
783 | RIG(add, mp_add) |
784 | RIG(sub, mp_sub) |
785 | RIG(mul, mp_mul) |
786 | |
787 | #undef RIG |
788 | |
789 | static int tdiv(dstr *v) |
790 | { |
791 | mp *a = *(mp **)v[0].buf; |
792 | mp *b = *(mp **)v[1].buf; |
793 | mp *q = *(mp **)v[2].buf; |
794 | mp *r = *(mp **)v[3].buf; |
795 | mp *c = MP_NEW, *d = MP_NEW; |
796 | int ok = 1; |
797 | mp_div(&c, &d, a, b); |
798 | ok &= verify("div(quotient)", q, c, a, b); |
799 | ok &= verify("div(remainder)", r, d, a, b); |
800 | mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q); |
ef5f4810 |
801 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
d3409d5e |
802 | return (ok); |
803 | } |
804 | |
f09e814a |
805 | static int tbin(dstr *v) |
806 | { |
807 | static mp *(*fn[])(mp *, mp *, mp *) = { |
808 | #define DO(string) mp_bit##string##2c, |
809 | MPX_DOBIN(DO) |
810 | #undef DO |
811 | }; |
812 | int ok = 1; |
813 | unsigned op = 0; |
814 | mp *a = *(mp **)v[1].buf; |
815 | mp *b = *(mp **)v[2].buf; |
816 | mp *r = *(mp **)v[3].buf; |
817 | mp *c; |
818 | |
819 | if (strcmp(v[0].buf, "and") == 0) op = 1; |
820 | else if (strcmp(v[0].buf, "or") == 0) op = 7; |
821 | else if (strcmp(v[0].buf, "nand") == 0) op = 14; |
822 | else if (strcmp(v[0].buf, "nor") == 0) op = 8; |
823 | else if (strcmp(v[0].buf, "xor") == 0) op = 6; |
824 | else { |
825 | char *p = v[0].buf; |
826 | while (*p) { |
827 | op <<= 1; |
828 | if (*p++ == '1') |
829 | op |= 1; |
830 | } |
831 | } |
832 | |
833 | c = fn[op](MP_NEW, a, b); |
834 | ok = verify(v[0].buf, r, c, a, b); |
835 | mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c); |
836 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
837 | return (ok); |
838 | } |
839 | |
09d00c6b |
840 | static int tset(dstr *v) |
841 | { |
842 | mp *a = *(mp **)v[0].buf; |
843 | unsigned long n = *(unsigned long *)v[1].buf; |
844 | mp *r = *(mp **)v[2].buf; |
845 | mp *c; |
846 | int ok = 1; |
847 | |
848 | c = mp_setbit2c(MP_NEW, a, n); |
849 | if (!MP_EQ(c, r)) { |
850 | ok = 0; |
851 | fprintf(stderr, "\n***setbit (set) failed"); |
852 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
853 | fprintf(stderr, "\n*** n = %lu", n); |
854 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
855 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
856 | fputc('\n', stderr); |
857 | } |
858 | if (!mp_testbit2c(r, n)) { |
859 | ok = 0; |
860 | fprintf(stderr, "\n***setbit (test) failed"); |
861 | fprintf(stderr, "\n*** n = %lu", n); |
862 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
863 | fputc('\n', stderr); |
864 | } |
865 | mp_drop(a); |
866 | mp_drop(r); |
867 | mp_drop(c); |
868 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
869 | return (ok); |
870 | } |
871 | |
872 | static int tclr(dstr *v) |
873 | { |
874 | mp *a = *(mp **)v[0].buf; |
875 | unsigned long n = *(unsigned long *)v[1].buf; |
876 | mp *r = *(mp **)v[2].buf; |
877 | mp *c; |
878 | int ok = 1; |
879 | |
880 | c = mp_clearbit2c(MP_NEW, a, n); |
881 | if (!MP_EQ(c, r)) { |
882 | ok = 0; |
883 | fprintf(stderr, "\n***clrbit (set) failed"); |
884 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16); |
885 | fprintf(stderr, "\n*** n = %lu", n); |
886 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
887 | fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16); |
888 | fputc('\n', stderr); |
889 | } |
890 | if (mp_testbit2c(r, n)) { |
891 | ok = 0; |
892 | fprintf(stderr, "\n***clrbit (test) failed"); |
893 | fprintf(stderr, "\n*** n = %lu", n); |
894 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16); |
895 | fputc('\n', stderr); |
896 | } |
897 | mp_drop(a); |
898 | mp_drop(c); |
899 | mp_drop(r); |
900 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
901 | return (ok); |
902 | } |
903 | |
397041a9 |
904 | static int tneg(dstr *v) |
905 | { |
906 | mp *a = *(mp **)v[0].buf; |
907 | mp *r = *(mp **)v[1].buf; |
908 | int ok = 1; |
909 | mp *n = mp_neg(MP_NEW, a); |
910 | if (!MP_EQ(r, n)) { |
911 | ok = 0; |
912 | fprintf(stderr, "\n*** neg failed\n"); |
913 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
914 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
915 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
916 | fputc('\n', stderr); |
917 | } |
918 | mp_drop(n); |
919 | n = mp_neg(a, a); |
920 | if (!MP_EQ(r, n)) { |
921 | ok = 0; |
922 | fprintf(stderr, "\n*** neg failed\n"); |
923 | fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10); |
924 | fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10); |
925 | fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10); |
926 | fputc('\n', stderr); |
927 | } |
928 | mp_drop(a); |
929 | mp_drop(r); |
930 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
931 | return (ok); |
932 | } |
933 | |
f1713c63 |
934 | static int todd(dstr *v) |
935 | { |
936 | mp *a = *(mp **)v[0].buf; |
937 | size_t rs = *(uint32 *)v[1].buf; |
938 | mp *rt = *(mp **)v[2].buf; |
939 | int ok = 1; |
940 | mp *t; |
941 | size_t s; |
942 | t = mp_odd(MP_NEW, a, &s); |
4b536f42 |
943 | if (s != rs || !MP_EQ(t, rt)) { |
f1713c63 |
944 | ok = 0; |
945 | fprintf(stderr, "\n*** odd failed"); |
946 | fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10); |
947 | fprintf(stderr, "\n*** s = %lu", (unsigned long)s); |
948 | fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10); |
949 | fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs); |
950 | fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10); |
951 | fputc('\n', stderr); |
952 | } |
953 | mp_drop(a); |
954 | mp_drop(rt); |
955 | mp_drop(t); |
09d00c6b |
956 | assert(mparena_count(MPARENA_GLOBAL) == 0); |
f1713c63 |
957 | return (ok); |
958 | } |
959 | |
d3409d5e |
960 | static test_chunk tests[] = { |
f09e814a |
961 | { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } }, |
962 | { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } }, |
963 | { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } }, |
964 | { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } }, |
09d00c6b |
965 | { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } }, |
966 | { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } }, |
d3409d5e |
967 | { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } }, |
968 | { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } }, |
969 | { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } }, |
970 | { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } }, |
f09e814a |
971 | { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } }, |
f1713c63 |
972 | { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } }, |
397041a9 |
973 | { "neg", tneg, { &type_mp, &type_mp, 0 } }, |
d3409d5e |
974 | { 0, 0, { 0 } }, |
975 | }; |
976 | |
977 | int main(int argc, char *argv[]) |
978 | { |
979 | sub_init(); |
980 | test_run(argc, argv, tests, SRCDIR "/tests/mp"); |
981 | return (0); |
982 | } |
983 | |
984 | #endif |
985 | |
986 | /*----- That's all, folks -------------------------------------------------*/ |