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