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Ship `rc2-tab.h' and `skipjack-tab.h'.
[u/mdw/catacomb] / mp-arith.c
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d3409d5e 1/* -*-c-*-
2 *
75263f25 3 * $Id: mp-arith.c,v 1.15 2002/10/19 17:56:50 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 $
75263f25 33 * Revision 1.15 2002/10/19 17:56:50 mdw
34 * Fix bit operations. Test them (a bit) better.
35 *
397041a9 36 * Revision 1.14 2002/10/15 19:18:31 mdw
37 * New operation to negate numbers.
38 *
09d00c6b 39 * Revision 1.13 2002/10/15 00:19:40 mdw
40 * Bit setting and clearing functions.
41 *
dd22938e 42 * Revision 1.12 2002/10/09 00:36:03 mdw
43 * Fix bounds on workspace for Karatsuba operations.
44 *
f09e814a 45 * Revision 1.11 2002/10/06 22:52:50 mdw
46 * Pile of changes for supporting two's complement properly.
47 *
0f32e0f8 48 * Revision 1.10 2001/04/03 19:36:05 mdw
49 * Add some simple bitwise operations so that Perl can use them.
50 *
52cdaca9 51 * Revision 1.9 2000/10/08 15:48:35 mdw
52 * Rename Karatsuba constants now that we have @gfx_kmul@ too.
53 *
4b536f42 54 * Revision 1.8 2000/10/08 12:02:21 mdw
55 * Use @MP_EQ@ instead of @MP_CMP@.
56 *
f1713c63 57 * Revision 1.7 2000/06/22 19:02:53 mdw
58 * New function @mp_odd@ to extract powers of two from an integer. This is
59 * common code from the Rabin-Miller test, RSA key recovery and modular
60 * square-root extraction.
61 *
d34decd2 62 * Revision 1.6 2000/06/17 11:45:09 mdw
63 * Major memory management overhaul. Added arena support. Use the secure
64 * arena for secret integers. Replace and improve the MP management macros
65 * (e.g., replace MP_MODIFY by MP_DEST).
66 *
bba03f55 67 * Revision 1.5 1999/12/22 15:54:41 mdw
68 * Adjust Karatsuba parameters. Calculate destination size better.
69 *
8017495b 70 * Revision 1.4 1999/12/13 15:35:16 mdw
71 * Slightly different rules on memory allocation.
72 *
5bf74dea 73 * Revision 1.3 1999/12/11 10:57:43 mdw
74 * Karatsuba squaring algorithm.
75 *
ef5f4810 76 * Revision 1.2 1999/12/10 23:18:39 mdw
77 * Change interface for suggested destinations.
78 *
d3409d5e 79 * Revision 1.1 1999/11/17 18:02:16 mdw
80 * New multiprecision integer arithmetic suite.
81 *
82 */
83
84/*----- Header files ------------------------------------------------------*/
85
86#include "mp.h"
87
ef5f4810 88/*----- Macros ------------------------------------------------------------*/
89
90#define MAX(x, y) ((x) >= (y) ? (x) : (y))
91
d3409d5e 92/*----- Main code ---------------------------------------------------------*/
93
f09e814a 94/* --- @mp_lsl@, @mp_lsr@ --- *
d3409d5e 95 *
f09e814a 96 * Arguments: @mp *d@ = destination
97 * @mp *a@ = source
98 * @size_t n@ = number of bits to move
d3409d5e 99 *
f09e814a 100 * Returns: Result, @a@ shifted left or right by @n@.
d3409d5e 101 */
102
f09e814a 103mp *mp_lsl(mp *d, mp *a, size_t n)
d3409d5e 104{
f09e814a 105 MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
106 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
107 d->f = a->f & (MP_NEG | MP_BURN);
108 MP_SHRINK(d);
109 return (d);
110}
d3409d5e 111
f09e814a 112mp *mp_lsr(mp *d, mp *a, size_t n)
113{
d34decd2 114 MP_DEST(d, MP_LEN(a), a->f);
f09e814a 115 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
116 d->f = a->f & (MP_NEG | MP_BURN);
d3409d5e 117 MP_SHRINK(d);
118 return (d);
119}
120
f09e814a 121/* --- @mp_lsl2c@, @mp_lsr2c@ --- *
d3409d5e 122 *
123 * Arguments: @mp *d@ = destination
124 * @mp *a@ = source
f09e814a 125 * @size_t n@ = number of bits to move
d3409d5e 126 *
f09e814a 127 * Returns: Result, @a@ shifted left or right by @n@. Handles the
128 * pretence of sign-extension for negative numbers.
d3409d5e 129 */
130
f09e814a 131mp *mp_lsl2c(mp *d, mp *a, size_t n)
d3409d5e 132{
f09e814a 133 if (!(a->f & MP_NEG))
134 return (mp_lsl(d, a, n));
135 d = mp_not2c(d, a);
136 d = mp_lsl(d, d, n);
137 d = mp_not2c(d, d);
138 return (d);
139}
d3409d5e 140
f09e814a 141mp *mp_lsr2c(mp *d, mp *a, size_t n)
142{
143 if (!(a->f & MP_NEG))
144 return (mp_lsr(d, a, n));
145 d = mp_not2c(d, a);
146 d = mp_lsr(d, d, n);
147 d = mp_not2c(d, d);
148 return (d);
d3409d5e 149}
150
f09e814a 151/* --- @mp_testbit@ --- *
d3409d5e 152 *
f09e814a 153 * Arguments: @mp *x@ = a large integer
09d00c6b 154 * @unsigned long n@ = which bit to test
d3409d5e 155 *
f09e814a 156 * Returns: Nonzero if the bit is set, zero if not.
d3409d5e 157 */
158
09d00c6b 159int mp_testbit(mp *x, unsigned long n)
d3409d5e 160{
f09e814a 161 if (n > MPW_BITS * MP_LEN(x))
162 return (0);
09d00c6b 163 return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u);
d3409d5e 164}
165
f09e814a 166/* --- @mp_testbit2c@ --- *
d3409d5e 167 *
f09e814a 168 * Arguments: @mp *x@ = a large integer
09d00c6b 169 * @unsigned long n@ = which bit to test
d3409d5e 170 *
f09e814a 171 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
172 * complement representation.
d3409d5e 173 */
174
09d00c6b 175int mp_testbit2c(mp *x, unsigned long n)
d3409d5e 176{
f09e814a 177 int r;
09d00c6b 178 if (!(x->f & MP_NEG))
f09e814a 179 return (mp_testbit(x, n));
180 x = mp_not2c(MP_NEW, x);
181 r = !mp_testbit(x, n);
182 MP_DROP(x);
183 return (r);
d3409d5e 184}
185
09d00c6b 186/* --- @mp_setbit@, @mp_clearbit@ --- *
187 *
188 * Arguments: @mp *d@ = a destination
189 * @mp *x@ = a large integer
190 * @unsigned long n@ = which bit to modify
191 *
192 * Returns: The argument @x@, with the appropriate bit set or cleared.
193 */
194
195mp *mp_setbit(mp *d, mp *x, unsigned long n)
196{
197 size_t rq;
198
199 rq = n + MPW_BITS; rq -= rq % MPW_BITS;
200 if (d != x) {
201 if (d) MP_DROP(d);
202 d = MP_COPY(x);
203 }
204 MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
205 d->v[n/MPW_BITS] |= 1 << n%MPW_BITS;
206 return (d);
207}
208
209mp *mp_clearbit(mp *d, mp *x, unsigned long n)
210{
211 size_t rq;
212
213 rq = n + MPW_BITS; rq -= rq % MPW_BITS;
214 if (d != x) {
215 if (d) MP_DROP(d);
216 d = MP_COPY(x);
217 }
218 MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
219 d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS);
220 return (d);
221}
222
223/* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
224 *
225 * Arguments: @mp *d@ = a destination
226 * @mp *x@ = a large integer
227 * @unsigned long n@ = which bit to modify
228 *
229 * Returns: The argument @x@, with the appropriate bit set or cleared.
230 * Fakes up two's complement representation.
231 */
232
233mp *mp_setbit2c(mp *d, mp *x, unsigned long n)
234{
235 if (!(x->f & MP_NEG))
236 return mp_setbit(d, x, n);
237 d = mp_not2c(d, x);
238 d = mp_clearbit(d, d, n);
239 d = mp_not2c(d, d);
240 return (d);
241}
242
243mp *mp_clearbit2c(mp *d, mp *x, unsigned long n)
244{
245 if (!(x->f & MP_NEG))
246 return mp_clearbit(d, x, n);
247 d = mp_not2c(d, x);
248 d = mp_setbit(d, d, n);
249 d = mp_not2c(d, d);
250 return (d);
251}
252
4b536f42 253/* --- @mp_eq@ --- *
254 *
255 * Arguments: @const mp *a, *b@ = two numbers
256 *
257 * Returns: Nonzero if the numbers are equal.
258 */
259
260int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); }
261
d3409d5e 262/* --- @mp_cmp@ --- *
263 *
264 * Arguments: @const mp *a, *b@ = two numbers
265 *
266 * Returns: Less than, equal to or greater than zero, according to
267 * whether @a@ is less than, equal to or greater than @b@.
268 */
269
270int mp_cmp(const mp *a, const mp *b)
271{
272 if (!((a->f ^ b->f) & MP_NEG))
273 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
274 else if (a->f & MP_NEG)
275 return (-1);
276 else
277 return (+1);
278}
279
397041a9 280/* --- @mp_neg@ --- *
281 *
282 * Arguments: @mp *d@ = destination
283 * @mp *a@ = argument
284 *
285 * Returns: The negation of the argument.
286 *
287 * Use: Negates its argument.
288 */
289
290mp *mp_neg(mp *d, mp *a)
291{
292 /* --- Surprising amounts of messing about required --- */
293
294 MP_SHRINK(a);
295 MP_COPY(a);
296 if (d) MP_DROP(d);
297 if (a->v == a->vl) {
298 return (a);
299 }
300 MP_DEST(a, MP_LEN(a), a->f);
301 a->f ^= MP_NEG;
302 return (a);
303}
304
f09e814a 305/* --- @mp_bitop@ --- *
0f32e0f8 306 *
307 * Arguments: @mp *d@ = destination
308 * @mp *a, *b@ = sources
309 *
f09e814a 310 * Returns: The result of the given bitwise operation. These functions
311 * don't handle negative numbers at all sensibly. For that, use
312 * the @...2c@ variants. The functions are named after the
313 * truth tables they generate:
314 *
315 * a: 0011
316 * b: 0101
317 * @mpx_bitXXXX@
0f32e0f8 318 */
319
f09e814a 320#define MP_BITBINOP(string) \
0f32e0f8 321 \
f09e814a 322mp *mp_bit##string(mp *d, mp *a, mp *b) \
0f32e0f8 323{ \
75263f25 324 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \
f09e814a 325 mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \
0f32e0f8 326 d->f = (a->f | b->f) & MP_BURN; \
327 MP_SHRINK(d); \
328 return (d); \
329}
330
f09e814a 331MPX_DOBIN(MP_BITBINOP)
332
333/* --- @mp_not@ --- *
334 *
335 * Arguments: @mp *d@ = destination
336 * @mp *a@ = source
337 *
338 * Returns: The bitwise complement of the source.
339 */
0f32e0f8 340
341mp *mp_not(mp *d, mp *a)
342{
343 MP_DEST(d, MP_LEN(a), a->f);
344 mpx_not(d->v, d->vl, a->v, a->vl);
345 d->f = a->f & MP_BURN;
346 MP_SHRINK(d);
347 return (d);
348}
349
f09e814a 350/* --- @mp_bitop2c@ --- *
351 *
352 * Arguments: @mp *d@ = destination
353 * @mp *a, *b@ = sources
354 *
355 * Returns: The result of the given bitwise operation. Negative numbers
356 * are treated as two's complement, sign-extended infinitely to
357 * the left. The functions are named after the truth tables
358 * they generate:
359 *
360 * a: 0011
361 * b: 0101
362 * @mpx_bitXXXX@
363 */
364
365/* --- How this actually works --- *
366 *
367 * The two arguments are inverted (with a sign-swap) if they're currently
368 * negative. This means that we end up using a different function (one which
369 * reinverts as we go) for the main operation. Also, if the sign would be
370 * negative at the end, we preinvert the output and then invert again with a
371 * sign-swap.
372 *
373 * Start with: wxyz WXYZ
374 * If @a@ negative: yzwx or YZWX
375 * If @b@ negative: xwzy XWZY
376 * If both negative: zyxw ZYXW
377 */
378
379#define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \
380 \
381mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \
382{ \
383 if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \
384 d = mp_bit##base(d, a, b); \
385 p_base \
386 } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \
387 MP_COPY(b); \
388 d = mp_not2c(d, a); \
389 d = mp_bit##an(d, d, b); \
390 MP_DROP(b); \
391 p_an \
392 } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \
393 MP_COPY(a); \
394 d = mp_not2c(d, b); \
395 d = mp_bit##bn(d, a, d); \
396 MP_DROP(a); \
397 p_bn \
398 } else { /* Both negative */ \
399 mp *t = mp_not2c(MP_NEW, a); \
400 mp *d = mp_not2c(d, b); \
401 d = mp_bit##abn(d, t, d); \
402 MP_DROP(t); \
403 p_abn \
404 } \
405 return (d); \
406} \
407
408#define NEG d = mp_not2c(d, d);
409#define POS
410MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS)
411MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG)
412MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS)
413MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG)
414MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS)
415MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG)
416MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS)
417MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG)
418MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS)
419MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG)
420MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS)
421MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG)
422MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS)
423MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG)
424MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS)
425MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG)
426#undef NEG
427#undef POS
428
429/* --- @mp_not2c@ --- *
430 *
431 * Arguments: @mp *d@ = destination
432 * @mp *a@ = source
433 *
434 * Returns: The sign-extended complement of the argument.
435 */
436
437mp *mp_not2c(mp *d, mp *a)
438{
439 mpw one = 1;
440
441 MP_DEST(d, MP_LEN(a) + 1, a->f);
442 if (d == a) {
443 if (a->f & MP_NEG)
444 MPX_USUBN(d->v, d->vl, 1);
445 else
446 MPX_UADDN(d->v, d->vl, 1);
447 } else {
448 if (a->f & MP_NEG)
449 mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1);
450 else
451 mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1);
452 }
453 d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG;
454 MP_SHRINK(d);
455 return (d);
456}
457
d3409d5e 458/* --- @mp_add@ --- *
459 *
460 * Arguments: @mp *d@ = destination
ef5f4810 461 * @mp *a, *b@ = sources
d3409d5e 462 *
463 * Returns: Result, @a@ added to @b@.
464 */
465
ef5f4810 466mp *mp_add(mp *d, mp *a, mp *b)
d3409d5e 467{
d34decd2 468 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
d3409d5e 469 if (!((a->f ^ b->f) & MP_NEG))
470 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
471 else {
472 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 473 mp *t = a; a = b; b = t;
d3409d5e 474 }
475 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
476 }
477 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
478 MP_SHRINK(d);
479 return (d);
480}
481
482/* --- @mp_sub@ --- *
483 *
484 * Arguments: @mp *d@ = destination
ef5f4810 485 * @mp *a, *b@ = sources
d3409d5e 486 *
487 * Returns: Result, @b@ subtracted from @a@.
488 */
489
ef5f4810 490mp *mp_sub(mp *d, mp *a, mp *b)
d3409d5e 491{
492 unsigned sgn = 0;
d34decd2 493 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
d3409d5e 494 if ((a->f ^ b->f) & MP_NEG)
495 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
496 else {
497 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 498 mp *t = a; a = b; b = t;
d3409d5e 499 sgn = MP_NEG;
500 }
501 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
502 }
503 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
504 MP_SHRINK(d);
505 return (d);
506}
507
508/* --- @mp_mul@ --- *
509 *
510 * Arguments: @mp *d@ = destination
ef5f4810 511 * @mp *a, *b@ = sources
d3409d5e 512 *
513 * Returns: Result, @a@ multiplied by @b@.
514 */
515
ef5f4810 516mp *mp_mul(mp *d, mp *a, mp *b)
d3409d5e 517{
ef5f4810 518 a = MP_COPY(a);
519 b = MP_COPY(b);
520
52cdaca9 521 if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) {
d34decd2 522 MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
ef5f4810 523 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
8017495b 524 } else {
dd22938e 525 size_t m = MAX(MP_LEN(a), MP_LEN(b));
ef5f4810 526 mpw *s;
dd22938e 527 MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF);
528 s = mpalloc(d->a, 5 * m);
529 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m);
d34decd2 530 mpfree(d->a, s);
ef5f4810 531 }
532
d3409d5e 533 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
534 MP_SHRINK(d);
ef5f4810 535 MP_DROP(a);
536 MP_DROP(b);
d3409d5e 537 return (d);
538}
539
540/* --- @mp_sqr@ --- *
541 *
542 * Arguments: @mp *d@ = destination
ef5f4810 543 * @mp *a@ = source
d3409d5e 544 *
545 * Returns: Result, @a@ squared.
546 */
547
ef5f4810 548mp *mp_sqr(mp *d, mp *a)
d3409d5e 549{
ef5f4810 550 size_t m = MP_LEN(a);
551
552 a = MP_COPY(a);
52cdaca9 553 if (m > MPK_THRESH) {
ef5f4810 554 mpw *s;
dd22938e 555 MP_DEST(d, 3 * m, a->f | MP_UNDEF);
556 s = mpalloc(d->a, 5 * m);
557 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m);
d34decd2 558 mpfree(d->a, s);
dd22938e 559 } else {
560 MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
ef5f4810 561 mpx_usqr(d->v, d->vl, a->v, a->vl);
dd22938e 562 }
d3409d5e 563 d->f = a->f & MP_BURN;
564 MP_SHRINK(d);
ef5f4810 565 MP_DROP(a);
d3409d5e 566 return (d);
567}
568
569/* --- @mp_div@ --- *
570 *
571 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
ef5f4810 572 * @mp *a, *b@ = sources
d3409d5e 573 *
574 * Use: Calculates the quotient and remainder when @a@ is divided by
575 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
576 * Either of @qq@ or @rr@ may be null to indicate that the
577 * result is irrelevant. (Discarding both results is silly.)
578 * There is a performance advantage if @a == *rr@.
579 *
580 * The behaviour when @a@ and @b@ have the same sign is
581 * straightforward. When the signs differ, this implementation
582 * chooses @r@ to have the same sign as @b@, rather than the
583 * more normal choice that the remainder has the same sign as
584 * the dividend. This makes modular arithmetic a little more
585 * straightforward.
586 */
587
ef5f4810 588void mp_div(mp **qq, mp **rr, mp *a, mp *b)
d3409d5e 589 {
590 mp *r = rr ? *rr : MP_NEW;
591 mp *q = qq ? *qq : MP_NEW;
592 mpw *sv, *svl;
593
d3409d5e 594 /* --- Set the remainder up right --- *
595 *
596 * Just in case the divisor is larger, be able to cope with this. It's not
597 * important in @mpx_udiv@, but it is here because of the sign correction.
598 */
599
d34decd2 600 b = MP_COPY(b);
601 a = MP_COPY(a);
602 if (r)
603 MP_DROP(r);
604 r = a;
605 MP_DEST(r, MP_LEN(a) + 2, a->f | b->f);
d3409d5e 606
607 /* --- Fix up the quotient too --- */
608
d34decd2 609 r = MP_COPY(r);
610 MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
611 MP_DROP(r);
612
613 /* --- Set up some temporary workspace --- */
614
615 {
616 size_t rq = MP_LEN(b) + 1;
617 sv = mpalloc(r->a, rq);
618 svl = sv + rq;
619 }
d3409d5e 620
621 /* --- Perform the calculation --- */
622
623 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
624
625 /* --- Sort out the sign of the results --- *
626 *
627 * If the signs of the arguments differ, and the remainder is nonzero, I
628 * must add one to the absolute value of the quotient and subtract the
629 * remainder from @b@.
630 */
631
d34decd2 632 q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG);
d3409d5e 633 if (q->f & MP_NEG) {
ef5f4810 634 mpw *v;
635 for (v = r->v; v < r->vl; v++) {
d3409d5e 636 if (*v) {
637 MPX_UADDN(q->v, q->vl, 1);
638 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
639 break;
640 }
641 }
642 }
643
d34decd2 644 r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG);
d3409d5e 645
646 /* --- Store the return values --- */
647
d34decd2 648 mpfree(r->a, sv);
649 MP_DROP(b);
650
d3409d5e 651 if (!qq)
652 MP_DROP(q);
653 else {
654 MP_SHRINK(q);
655 *qq = q;
656 }
657
658 if (!rr)
659 MP_DROP(r);
660 else {
661 MP_SHRINK(r);
662 *rr = r;
663 }
d3409d5e 664}
665
f1713c63 666/* --- @mp_odd@ --- *
667 *
668 * Arguments: @mp *d@ = pointer to destination integer
669 * @mp *m@ = pointer to source integer
670 * @size_t *s@ = where to store the power of 2
671 *
672 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
673 *
674 * Use: Computes a power of two and an odd integer which, when
675 * multiplied, give a specified result. This sort of thing is
676 * useful in number theory quite often.
677 */
678
679mp *mp_odd(mp *d, mp *m, size_t *s)
680{
681 size_t ss = 0;
682 const mpw *v, *vl;
683
684 v = m->v;
685 vl = m->vl;
686 for (; !*v && v < vl; v++)
687 ss += MPW_BITS;
688 if (v >= vl)
689 ss = 0;
690 else {
691 mpw x = *v;
692 mpw mask = MPW_MAX;
693 unsigned z = MPW_BITS / 2;
694
695 while (z) {
696 mask >>= z;
697 if (!(x & mask)) {
698 x >>= z;
699 ss += z;
700 }
701 z >>= 1;
702 }
703 }
704
705 *s = ss;
706 return (mp_lsr(d, m, ss));
707}
708
d3409d5e 709/*----- Test rig ----------------------------------------------------------*/
710
711#ifdef TEST_RIG
712
713static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
714{
4b536f42 715 if (!MP_EQ(expect, result)) {
d3409d5e 716 fprintf(stderr, "\n*** %s failed", op);
717 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
718 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
719 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
720 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
721 fputc('\n', stderr);
722 return (0);
723 }
724 return (1);
725}
726
727#define RIG(name, op) \
ef5f4810 728 static int t##name(dstr *v) \
d3409d5e 729 { \
730 mp *a = *(mp **)v[0].buf; \
731 mpw n = *(int *)v[1].buf; \
732 mp b; \
733 mp *r = *(mp **)v[2].buf; \
734 mp *c = op(MP_NEW, a, n); \
735 int ok; \
736 mp_build(&b, &n, &n + 1); \
737 ok = verify(#name, r, c, a, &b); \
738 mp_drop(a); mp_drop(c); mp_drop(r); \
ef5f4810 739 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 740 return (ok); \
741 }
742
743RIG(lsl, mp_lsl)
744RIG(lsr, mp_lsr)
f09e814a 745RIG(lsl2c, mp_lsl2c)
746RIG(lsr2c, mp_lsr2c)
d3409d5e 747
748#undef RIG
749
750#define RIG(name, op) \
ef5f4810 751 static int t##name(dstr *v) \
d3409d5e 752 { \
753 mp *a = *(mp **)v[0].buf; \
754 mp *b = *(mp **)v[1].buf; \
755 mp *r = *(mp **)v[2].buf; \
756 mp *c = op(MP_NEW, a, b); \
757 int ok = verify(#name, r, c, a, b); \
758 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
ef5f4810 759 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 760 return (ok); \
761 }
762
763RIG(add, mp_add)
764RIG(sub, mp_sub)
765RIG(mul, mp_mul)
766
767#undef RIG
768
769static int tdiv(dstr *v)
770{
771 mp *a = *(mp **)v[0].buf;
772 mp *b = *(mp **)v[1].buf;
773 mp *q = *(mp **)v[2].buf;
774 mp *r = *(mp **)v[3].buf;
775 mp *c = MP_NEW, *d = MP_NEW;
776 int ok = 1;
777 mp_div(&c, &d, a, b);
778 ok &= verify("div(quotient)", q, c, a, b);
779 ok &= verify("div(remainder)", r, d, a, b);
780 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
ef5f4810 781 assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e 782 return (ok);
783}
784
f09e814a 785static int tbin(dstr *v)
786{
787 static mp *(*fn[])(mp *, mp *, mp *) = {
788#define DO(string) mp_bit##string##2c,
789MPX_DOBIN(DO)
790#undef DO
791 };
792 int ok = 1;
793 unsigned op = 0;
794 mp *a = *(mp **)v[1].buf;
795 mp *b = *(mp **)v[2].buf;
796 mp *r = *(mp **)v[3].buf;
797 mp *c;
798
799 if (strcmp(v[0].buf, "and") == 0) op = 1;
800 else if (strcmp(v[0].buf, "or") == 0) op = 7;
801 else if (strcmp(v[0].buf, "nand") == 0) op = 14;
802 else if (strcmp(v[0].buf, "nor") == 0) op = 8;
803 else if (strcmp(v[0].buf, "xor") == 0) op = 6;
804 else {
805 char *p = v[0].buf;
806 while (*p) {
807 op <<= 1;
808 if (*p++ == '1')
809 op |= 1;
810 }
811 }
812
813 c = fn[op](MP_NEW, a, b);
814 ok = verify(v[0].buf, r, c, a, b);
815 mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c);
816 assert(mparena_count(MPARENA_GLOBAL) == 0);
817 return (ok);
818}
819
09d00c6b 820static int tset(dstr *v)
821{
822 mp *a = *(mp **)v[0].buf;
823 unsigned long n = *(unsigned long *)v[1].buf;
824 mp *r = *(mp **)v[2].buf;
825 mp *c;
826 int ok = 1;
827
828 c = mp_setbit2c(MP_NEW, a, n);
829 if (!MP_EQ(c, r)) {
830 ok = 0;
831 fprintf(stderr, "\n***setbit (set) failed");
832 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
833 fprintf(stderr, "\n*** n = %lu", n);
834 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
835 fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
836 fputc('\n', stderr);
837 }
838 if (!mp_testbit2c(r, n)) {
839 ok = 0;
840 fprintf(stderr, "\n***setbit (test) failed");
841 fprintf(stderr, "\n*** n = %lu", n);
842 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
843 fputc('\n', stderr);
844 }
845 mp_drop(a);
846 mp_drop(r);
847 mp_drop(c);
848 assert(mparena_count(MPARENA_GLOBAL) == 0);
849 return (ok);
850}
851
852static int tclr(dstr *v)
853{
854 mp *a = *(mp **)v[0].buf;
855 unsigned long n = *(unsigned long *)v[1].buf;
856 mp *r = *(mp **)v[2].buf;
857 mp *c;
858 int ok = 1;
859
860 c = mp_clearbit2c(MP_NEW, a, n);
861 if (!MP_EQ(c, r)) {
862 ok = 0;
863 fprintf(stderr, "\n***clrbit (set) failed");
864 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
865 fprintf(stderr, "\n*** n = %lu", n);
866 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
867 fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
868 fputc('\n', stderr);
869 }
870 if (mp_testbit2c(r, n)) {
871 ok = 0;
872 fprintf(stderr, "\n***clrbit (test) failed");
873 fprintf(stderr, "\n*** n = %lu", n);
874 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
875 fputc('\n', stderr);
876 }
877 mp_drop(a);
878 mp_drop(c);
879 mp_drop(r);
880 assert(mparena_count(MPARENA_GLOBAL) == 0);
881 return (ok);
882}
883
397041a9 884static int tneg(dstr *v)
885{
886 mp *a = *(mp **)v[0].buf;
887 mp *r = *(mp **)v[1].buf;
888 int ok = 1;
889 mp *n = mp_neg(MP_NEW, a);
890 if (!MP_EQ(r, n)) {
891 ok = 0;
892 fprintf(stderr, "\n*** neg failed\n");
893 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
894 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
895 fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
896 fputc('\n', stderr);
897 }
898 mp_drop(n);
899 n = mp_neg(a, a);
900 if (!MP_EQ(r, n)) {
901 ok = 0;
902 fprintf(stderr, "\n*** neg failed\n");
903 fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10);
904 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
905 fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
906 fputc('\n', stderr);
907 }
908 mp_drop(a);
909 mp_drop(r);
910 assert(mparena_count(MPARENA_GLOBAL) == 0);
911 return (ok);
912}
913
f1713c63 914static int todd(dstr *v)
915{
916 mp *a = *(mp **)v[0].buf;
917 size_t rs = *(uint32 *)v[1].buf;
918 mp *rt = *(mp **)v[2].buf;
919 int ok = 1;
920 mp *t;
921 size_t s;
922 t = mp_odd(MP_NEW, a, &s);
4b536f42 923 if (s != rs || !MP_EQ(t, rt)) {
f1713c63 924 ok = 0;
925 fprintf(stderr, "\n*** odd failed");
926 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
927 fprintf(stderr, "\n*** s = %lu", (unsigned long)s);
928 fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10);
929 fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs);
930 fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10);
931 fputc('\n', stderr);
932 }
933 mp_drop(a);
934 mp_drop(rt);
935 mp_drop(t);
09d00c6b 936 assert(mparena_count(MPARENA_GLOBAL) == 0);
f1713c63 937 return (ok);
938}
939
d3409d5e 940static test_chunk tests[] = {
f09e814a 941 { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } },
942 { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } },
943 { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } },
944 { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } },
09d00c6b 945 { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } },
946 { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } },
d3409d5e 947 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
948 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
949 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
950 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
f09e814a 951 { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } },
f1713c63 952 { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } },
397041a9 953 { "neg", tneg, { &type_mp, &type_mp, 0 } },
d3409d5e 954 { 0, 0, { 0 } },
955};
956
957int main(int argc, char *argv[])
958{
959 sub_init();
960 test_run(argc, argv, tests, SRCDIR "/tests/mp");
961 return (0);
962}
963
964#endif
965
966/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)