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