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Fix bug dividing small things by large ones.
[u/mdw/catacomb] / mp-arith.c
1 /* -*-c-*-
2 *
3 * $Id: mp-arith.c,v 1.16.2.1 2003/06/10 13:21:10 mdw Exp $
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 $
33 * Revision 1.16.2.1 2003/06/10 13:21:10 mdw
34 * Fix bug dividing small things by large ones.
35 *
36 * Revision 1.16 2003/05/16 09:09:24 mdw
37 * Fix @mp_lsl2c@. Turns out to be surprisingly tricky.
38 *
39 * Revision 1.15 2002/10/19 17:56:50 mdw
40 * Fix bit operations. Test them (a bit) better.
41 *
42 * Revision 1.14 2002/10/15 19:18:31 mdw
43 * New operation to negate numbers.
44 *
45 * Revision 1.13 2002/10/15 00:19:40 mdw
46 * Bit setting and clearing functions.
47 *
48 * Revision 1.12 2002/10/09 00:36:03 mdw
49 * Fix bounds on workspace for Karatsuba operations.
50 *
51 * Revision 1.11 2002/10/06 22:52:50 mdw
52 * Pile of changes for supporting two's complement properly.
53 *
54 * Revision 1.10 2001/04/03 19:36:05 mdw
55 * Add some simple bitwise operations so that Perl can use them.
56 *
57 * Revision 1.9 2000/10/08 15:48:35 mdw
58 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
59 *
60 * Revision 1.8 2000/10/08 12:02:21 mdw
61 * Use @MP_EQ@ instead of @MP_CMP@.
62 *
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 *
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 *
73 * Revision 1.5 1999/12/22 15:54:41 mdw
74 * Adjust Karatsuba parameters. Calculate destination size better.
75 *
76 * Revision 1.4 1999/12/13 15:35:16 mdw
77 * Slightly different rules on memory allocation.
78 *
79 * Revision 1.3 1999/12/11 10:57:43 mdw
80 * Karatsuba squaring algorithm.
81 *
82 * Revision 1.2 1999/12/10 23:18:39 mdw
83 * Change interface for suggested destinations.
84 *
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
94 /*----- Macros ------------------------------------------------------------*/
95
96 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
97
98 /*----- Main code ---------------------------------------------------------*/
99
100 /* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
101 *
102 * Arguments: @mp *d@ = destination
103 * @mp *a@ = source
104 * @size_t n@ = number of bits to move
105 *
106 * Returns: Result, @a@ shifted left or right by @n@.
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.
112 */
113
114 mp *mp_lsl(mp *d, mp *a, size_t n)
115 {
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 }
122
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
132 mp *mp_lsr(mp *d, mp *a, size_t n)
133 {
134 MP_DEST(d, MP_LEN(a), a->f);
135 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
136 d->f = a->f & (MP_NEG | MP_BURN);
137 MP_SHRINK(d);
138 return (d);
139 }
140
141 /* --- @mp_lsl2c@, @mp_lsr2c@ --- *
142 *
143 * Arguments: @mp *d@ = destination
144 * @mp *a@ = source
145 * @size_t n@ = number of bits to move
146 *
147 * Returns: Result, @a@ shifted left or right by @n@. Handles the
148 * pretence of sign-extension for negative numbers.
149 */
150
151 mp *mp_lsl2c(mp *d, mp *a, size_t n)
152 {
153 if (!(a->f & MP_NEG))
154 return (mp_lsl(d, a, n));
155 d = mp_not2c(d, a);
156 d = mp_lslc(d, d, n);
157 d = mp_not2c(d, d);
158 return (d);
159 }
160
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);
169 }
170
171 /* --- @mp_testbit@ --- *
172 *
173 * Arguments: @mp *x@ = a large integer
174 * @unsigned long n@ = which bit to test
175 *
176 * Returns: Nonzero if the bit is set, zero if not.
177 */
178
179 int mp_testbit(mp *x, unsigned long n)
180 {
181 if (n > MPW_BITS * MP_LEN(x))
182 return (0);
183 return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u);
184 }
185
186 /* --- @mp_testbit2c@ --- *
187 *
188 * Arguments: @mp *x@ = a large integer
189 * @unsigned long n@ = which bit to test
190 *
191 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
192 * complement representation.
193 */
194
195 int mp_testbit2c(mp *x, unsigned long n)
196 {
197 int r;
198 if (!(x->f & MP_NEG))
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);
204 }
205
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
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
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
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);
316 if (d)
317 MP_DROP(d);
318 if (a->v == a->vl)
319 return (a);
320 MP_DEST(a, MP_LEN(a), a->f);
321 a->f ^= MP_NEG;
322 return (a);
323 }
324
325 /* --- @mp_bitop@ --- *
326 *
327 * Arguments: @mp *d@ = destination
328 * @mp *a, *b@ = sources
329 *
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@
338 */
339
340 #define MP_BITBINOP(string) \
341 \
342 mp *mp_bit##string(mp *d, mp *a, mp *b) \
343 { \
344 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \
345 mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \
346 d->f = (a->f | b->f) & MP_BURN; \
347 MP_SHRINK(d); \
348 return (d); \
349 }
350
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 */
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
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
478 /* --- @mp_add@ --- *
479 *
480 * Arguments: @mp *d@ = destination
481 * @mp *a, *b@ = sources
482 *
483 * Returns: Result, @a@ added to @b@.
484 */
485
486 mp *mp_add(mp *d, mp *a, mp *b)
487 {
488 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
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)) {
493 mp *t = a; a = b; b = t;
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
505 * @mp *a, *b@ = sources
506 *
507 * Returns: Result, @b@ subtracted from @a@.
508 */
509
510 mp *mp_sub(mp *d, mp *a, mp *b)
511 {
512 unsigned sgn = 0;
513 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
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)) {
518 mp *t = a; a = b; b = t;
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
531 * @mp *a, *b@ = sources
532 *
533 * Returns: Result, @a@ multiplied by @b@.
534 */
535
536 mp *mp_mul(mp *d, mp *a, mp *b)
537 {
538 a = MP_COPY(a);
539 b = MP_COPY(b);
540
541 if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) {
542 MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
543 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
544 } else {
545 size_t m = MAX(MP_LEN(a), MP_LEN(b));
546 mpw *s;
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);
550 mpfree(d->a, s);
551 }
552
553 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
554 MP_SHRINK(d);
555 MP_DROP(a);
556 MP_DROP(b);
557 return (d);
558 }
559
560 /* --- @mp_sqr@ --- *
561 *
562 * Arguments: @mp *d@ = destination
563 * @mp *a@ = source
564 *
565 * Returns: Result, @a@ squared.
566 */
567
568 mp *mp_sqr(mp *d, mp *a)
569 {
570 size_t m = MP_LEN(a);
571
572 a = MP_COPY(a);
573 if (m > MPK_THRESH) {
574 mpw *s;
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);
578 mpfree(d->a, s);
579 } else {
580 MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
581 mpx_usqr(d->v, d->vl, a->v, a->vl);
582 }
583 d->f = a->f & MP_BURN;
584 MP_SHRINK(d);
585 MP_DROP(a);
586 return (d);
587 }
588
589 /* --- @mp_div@ --- *
590 *
591 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
592 * @mp *a, *b@ = sources
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
608 void mp_div(mp **qq, mp **rr, mp *a, mp *b)
609 {
610 mp *r = rr ? *rr : MP_NEW;
611 mp *q = qq ? *qq : MP_NEW;
612 mpw *sv, *svl;
613
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
620 b = MP_COPY(b);
621 a = MP_COPY(a);
622 if (r)
623 MP_DROP(r);
624 r = a;
625 MP_DEST(r, MP_LEN(b) + 2, a->f | b->f);
626
627 /* --- Fix up the quotient too --- */
628
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 }
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
652 q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG);
653 if (q->f & MP_NEG) {
654 mpw *v;
655 for (v = r->v; v < r->vl; v++) {
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
664 r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG);
665
666 /* --- Store the return values --- */
667
668 mpfree(r->a, sv);
669 MP_DROP(b);
670
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 }
684 }
685
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
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 {
735 if (!MP_EQ(expect, result)) {
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) \
748 static int t##name(dstr *v) \
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); \
759 assert(mparena_count(MPARENA_GLOBAL) == 0); \
760 return (ok); \
761 }
762
763 RIG(lsl, mp_lsl)
764 RIG(lsr, mp_lsr)
765 RIG(lsl2c, mp_lsl2c)
766 RIG(lsr2c, mp_lsr2c)
767
768 #undef RIG
769
770 #define RIG(name, op) \
771 static int t##name(dstr *v) \
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); \
779 assert(mparena_count(MPARENA_GLOBAL) == 0); \
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);
801 assert(mparena_count(MPARENA_GLOBAL) == 0);
802 return (ok);
803 }
804
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
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
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
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);
943 if (s != rs || !MP_EQ(t, rt)) {
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);
956 assert(mparena_count(MPARENA_GLOBAL) == 0);
957 return (ok);
958 }
959
960 static test_chunk tests[] = {
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 } },
965 { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } },
966 { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } },
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 } },
971 { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } },
972 { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } },
973 { "neg", tneg, { &type_mp, &type_mp, 0 } },
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 -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)