projects / u / mdw / catacomb / blame
? search:
summary | shortlog | log | commit | commitdiff | tree
blob | blame (incremental) | history | HEAD
.gitignore: Ignore `auto-version' script.
[u/mdw/catacomb] / mp-arith.c
CommitLineData
d3409d5e 1/* -*-c-*-
2 *
a69a3efd 3 * $Id$
d3409d5e 4 *
5 * Basic arithmetic on multiprecision integers
6 *
7 * (c) 1999 Straylight/Edgeware
8 */
9
45c0fd36 10/*----- Licensing notice --------------------------------------------------*
d3409d5e 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.
45c0fd36 18 *
d3409d5e 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.
45c0fd36 23 *
d3409d5e 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
d3409d5e 30/*----- Header files ------------------------------------------------------*/
31
32#include "mp.h"
33
ef5f4810 34/*----- Macros ------------------------------------------------------------*/
35
36#define MAX(x, y) ((x) >= (y) ? (x) : (y))
37
d3409d5e 38/*----- Main code ---------------------------------------------------------*/
39
81578196 40/* --- @mp_lsl@, @mp_lslc@, @mp_lsr@ --- *
d3409d5e 41 *
f09e814a 42 * Arguments: @mp *d@ = destination
43 * @mp *a@ = source
44 * @size_t n@ = number of bits to move
d3409d5e 45 *
f09e814a 46 * Returns: Result, @a@ shifted left or right by @n@.
81578196 47 *
48 * Use: Bitwise shift operators. @mp_lslc@ fills the bits introduced
49 * on the right with ones instead of zeroes: it's used
50 * internally by @mp_lsl2c@, though it may be useful on its
51 * own.
d3409d5e 52 */
53
f09e814a 54mp *mp_lsl(mp *d, mp *a, size_t n)
d3409d5e 55{
f09e814a 56 MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
57 mpx_lsl(d->v, d->vl, a->v, a->vl, n);
58 d->f = a->f & (MP_NEG | MP_BURN);
59 MP_SHRINK(d);
60 return (d);
61}
d3409d5e 62
81578196 63mp *mp_lslc(mp *d, mp *a, size_t n)
64{
65 MP_DEST(d, MP_LEN(a) + (n + MPW_BITS - 1) / MPW_BITS, a->f);
66 mpx_lslc(d->v, d->vl, a->v, a->vl, n);
67 d->f = a->f & (MP_NEG | MP_BURN);
68 MP_SHRINK(d);
69 return (d);
70}
71
f09e814a 72mp *mp_lsr(mp *d, mp *a, size_t n)
73{
d34decd2 74 MP_DEST(d, MP_LEN(a), a->f);
f09e814a 75 mpx_lsr(d->v, d->vl, a->v, a->vl, n);
76 d->f = a->f & (MP_NEG | MP_BURN);
d3409d5e 77 MP_SHRINK(d);
78 return (d);
79}
80
f09e814a 81/* --- @mp_lsl2c@, @mp_lsr2c@ --- *
d3409d5e 82 *
83 * Arguments: @mp *d@ = destination
84 * @mp *a@ = source
f09e814a 85 * @size_t n@ = number of bits to move
d3409d5e 86 *
f09e814a 87 * Returns: Result, @a@ shifted left or right by @n@. Handles the
88 * pretence of sign-extension for negative numbers.
d3409d5e 89 */
90
f09e814a 91mp *mp_lsl2c(mp *d, mp *a, size_t n)
d3409d5e 92{
a69a3efd 93 if (!MP_NEGP(a))
f09e814a 94 return (mp_lsl(d, a, n));
95 d = mp_not2c(d, a);
81578196 96 d = mp_lslc(d, d, n);
f09e814a 97 d = mp_not2c(d, d);
98 return (d);
99}
d3409d5e 100
f09e814a 101mp *mp_lsr2c(mp *d, mp *a, size_t n)
102{
a69a3efd 103 if (!MP_NEGP(a))
f09e814a 104 return (mp_lsr(d, a, n));
105 d = mp_not2c(d, a);
106 d = mp_lsr(d, d, n);
107 d = mp_not2c(d, d);
108 return (d);
d3409d5e 109}
110
f09e814a 111/* --- @mp_testbit@ --- *
d3409d5e 112 *
f09e814a 113 * Arguments: @mp *x@ = a large integer
09d00c6b 114 * @unsigned long n@ = which bit to test
d3409d5e 115 *
f09e814a 116 * Returns: Nonzero if the bit is set, zero if not.
d3409d5e 117 */
118
09d00c6b 119int mp_testbit(mp *x, unsigned long n)
d3409d5e 120{
f09e814a 121 if (n > MPW_BITS * MP_LEN(x))
122 return (0);
09d00c6b 123 return ((x->v[n/MPW_BITS] >> n%MPW_BITS) & 1u);
d3409d5e 124}
125
f09e814a 126/* --- @mp_testbit2c@ --- *
d3409d5e 127 *
f09e814a 128 * Arguments: @mp *x@ = a large integer
09d00c6b 129 * @unsigned long n@ = which bit to test
d3409d5e 130 *
f09e814a 131 * Returns: Nonzero if the bit is set, zero if not. Fakes up two's
132 * complement representation.
d3409d5e 133 */
134
09d00c6b 135int mp_testbit2c(mp *x, unsigned long n)
d3409d5e 136{
f09e814a 137 int r;
a69a3efd 138 if (!MP_NEGP(x))
f09e814a 139 return (mp_testbit(x, n));
140 x = mp_not2c(MP_NEW, x);
141 r = !mp_testbit(x, n);
142 MP_DROP(x);
143 return (r);
d3409d5e 144}
145
09d00c6b 146/* --- @mp_setbit@, @mp_clearbit@ --- *
147 *
148 * Arguments: @mp *d@ = a destination
149 * @mp *x@ = a large integer
150 * @unsigned long n@ = which bit to modify
151 *
152 * Returns: The argument @x@, with the appropriate bit set or cleared.
153 */
154
155mp *mp_setbit(mp *d, mp *x, unsigned long n)
156{
157 size_t rq;
158
159 rq = n + MPW_BITS; rq -= rq % MPW_BITS;
160 if (d != x) {
161 if (d) MP_DROP(d);
162 d = MP_COPY(x);
163 }
164 MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
165 d->v[n/MPW_BITS] |= 1 << n%MPW_BITS;
166 return (d);
167}
168
169mp *mp_clearbit(mp *d, mp *x, unsigned long n)
170{
171 size_t rq;
172
173 rq = n + MPW_BITS; rq -= rq % MPW_BITS;
174 if (d != x) {
175 if (d) MP_DROP(d);
176 d = MP_COPY(x);
177 }
178 MP_DEST(d, rq, x->f & (MP_NEG | MP_BURN));
179 d->v[n/MPW_BITS] &= ~(1 << n%MPW_BITS);
180 return (d);
181}
182
183/* --- @mp_setbit2c@, @mp_clearbit2c@ --- *
184 *
185 * Arguments: @mp *d@ = a destination
186 * @mp *x@ = a large integer
187 * @unsigned long n@ = which bit to modify
188 *
189 * Returns: The argument @x@, with the appropriate bit set or cleared.
190 * Fakes up two's complement representation.
191 */
192
193mp *mp_setbit2c(mp *d, mp *x, unsigned long n)
194{
a69a3efd 195 if (!MP_NEGP(x))
09d00c6b 196 return mp_setbit(d, x, n);
197 d = mp_not2c(d, x);
198 d = mp_clearbit(d, d, n);
199 d = mp_not2c(d, d);
200 return (d);
201}
202
203mp *mp_clearbit2c(mp *d, mp *x, unsigned long n)
204{
a69a3efd 205 if (!MP_NEGP(x))
09d00c6b 206 return mp_clearbit(d, x, n);
207 d = mp_not2c(d, x);
208 d = mp_setbit(d, d, n);
209 d = mp_not2c(d, d);
210 return (d);
211}
212
4b536f42 213/* --- @mp_eq@ --- *
214 *
215 * Arguments: @const mp *a, *b@ = two numbers
216 *
217 * Returns: Nonzero if the numbers are equal.
218 */
219
220int mp_eq(const mp *a, const mp *b) { return (MP_EQ(a, b)); }
221
d3409d5e 222/* --- @mp_cmp@ --- *
223 *
224 * Arguments: @const mp *a, *b@ = two numbers
225 *
226 * Returns: Less than, equal to or greater than zero, according to
227 * whether @a@ is less than, equal to or greater than @b@.
228 */
229
230int mp_cmp(const mp *a, const mp *b)
231{
4108c8d2 232 if (!((a->f ^ b->f) & MP_NEG)) {
233 if (a->f & MP_NEG)
234 return (-mpx_ucmp(a->v, a->vl, b->v, b->vl));
235 else
236 return (mpx_ucmp(a->v, a->vl, b->v, b->vl));
237 } else if (a->f & MP_NEG)
d3409d5e 238 return (-1);
239 else
240 return (+1);
241}
242
397041a9 243/* --- @mp_neg@ --- *
244 *
245 * Arguments: @mp *d@ = destination
246 * @mp *a@ = argument
247 *
248 * Returns: The negation of the argument.
249 *
250 * Use: Negates its argument.
251 */
252
253mp *mp_neg(mp *d, mp *a)
254{
255 /* --- Surprising amounts of messing about required --- */
256
257 MP_SHRINK(a);
258 MP_COPY(a);
81578196 259 if (d)
260 MP_DROP(d);
261 if (a->v == a->vl)
397041a9 262 return (a);
397041a9 263 MP_DEST(a, MP_LEN(a), a->f);
264 a->f ^= MP_NEG;
265 return (a);
266}
267
f09e814a 268/* --- @mp_bitop@ --- *
0f32e0f8 269 *
270 * Arguments: @mp *d@ = destination
271 * @mp *a, *b@ = sources
272 *
f09e814a 273 * Returns: The result of the given bitwise operation. These functions
274 * don't handle negative numbers at all sensibly. For that, use
275 * the @...2c@ variants. The functions are named after the
276 * truth tables they generate:
277 *
278 * a: 0011
279 * b: 0101
280 * @mpx_bitXXXX@
0f32e0f8 281 */
282
f09e814a 283#define MP_BITBINOP(string) \
0f32e0f8 284 \
f09e814a 285mp *mp_bit##string(mp *d, mp *a, mp *b) \
0f32e0f8 286{ \
75263f25 287 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)), (a->f | b->f) & ~MP_NEG); \
f09e814a 288 mpx_bit##string(d->v, d->vl, a->v, a->vl, b->v, b->vl); \
0f32e0f8 289 d->f = (a->f | b->f) & MP_BURN; \
290 MP_SHRINK(d); \
291 return (d); \
292}
293
f09e814a 294MPX_DOBIN(MP_BITBINOP)
295
296/* --- @mp_not@ --- *
297 *
298 * Arguments: @mp *d@ = destination
299 * @mp *a@ = source
300 *
301 * Returns: The bitwise complement of the source.
45c0fd36 302 */
0f32e0f8 303
304mp *mp_not(mp *d, mp *a)
305{
306 MP_DEST(d, MP_LEN(a), a->f);
307 mpx_not(d->v, d->vl, a->v, a->vl);
308 d->f = a->f & MP_BURN;
309 MP_SHRINK(d);
310 return (d);
311}
312
f09e814a 313/* --- @mp_bitop2c@ --- *
314 *
315 * Arguments: @mp *d@ = destination
316 * @mp *a, *b@ = sources
317 *
318 * Returns: The result of the given bitwise operation. Negative numbers
319 * are treated as two's complement, sign-extended infinitely to
320 * the left. The functions are named after the truth tables
321 * they generate:
322 *
323 * a: 0011
324 * b: 0101
325 * @mpx_bitXXXX@
326 */
327
328/* --- How this actually works --- *
329 *
330 * The two arguments are inverted (with a sign-swap) if they're currently
331 * negative. This means that we end up using a different function (one which
332 * reinverts as we go) for the main operation. Also, if the sign would be
333 * negative at the end, we preinvert the output and then invert again with a
334 * sign-swap.
335 *
45c0fd36 336 * Start with: wxyz WXYZ
f09e814a 337 * If @a@ negative: yzwx or YZWX
45c0fd36
MW		 338 * If @b@ negative: xwzy XWZY
339 * If both negative: zyxw ZYXW
f09e814a 340 */
341
342#define MP_BIT2CBINOP(n, base, an, bn, abn, p_base, p_an, p_bn, p_abn) \
343 \
344mp *mp_bit##n##2c(mp *d, mp *a, mp *b) \
345{ \
346 if (!((a->f | b->f) & MP_NEG)) { /* Both positive */ \
347 d = mp_bit##base(d, a, b); \
348 p_base \
349 } else if (!(b->f & MP_NEG)) { /* Only @b@ positive */ \
350 MP_COPY(b); \
351 d = mp_not2c(d, a); \
352 d = mp_bit##an(d, d, b); \
353 MP_DROP(b); \
354 p_an \
355 } else if (!(a->f & MP_NEG)) { /* Only @a@ positive */ \
356 MP_COPY(a); \
357 d = mp_not2c(d, b); \
358 d = mp_bit##bn(d, a, d); \
359 MP_DROP(a); \
360 p_bn \
361 } else { /* Both negative */ \
362 mp *t = mp_not2c(MP_NEW, a); \
15f21155 363 d = mp_not2c(d, b); \
f09e814a 364 d = mp_bit##abn(d, t, d); \
365 MP_DROP(t); \
366 p_abn \
367 } \
368 return (d); \
369} \
370
371#define NEG d = mp_not2c(d, d);
372#define POS
373MP_BIT2CBINOP(0000, 0000, 0000, 0000, 0000, POS, POS, POS, POS)
374MP_BIT2CBINOP(0001, 0001, 0100, 0010, 0111, POS, POS, POS, NEG)
375MP_BIT2CBINOP(0010, 0010, 0111, 0001, 0100, POS, NEG, POS, POS)
376MP_BIT2CBINOP(0011, 0011, 0011, 0011, 0011, POS, NEG, POS, NEG)
377MP_BIT2CBINOP(0100, 0100, 0001, 0111, 0010, POS, POS, NEG, POS)
378MP_BIT2CBINOP(0101, 0101, 0101, 0101, 0101, POS, POS, NEG, NEG)
379MP_BIT2CBINOP(0110, 0110, 0110, 0110, 0110, POS, NEG, NEG, POS)
380MP_BIT2CBINOP(0111, 0111, 0010, 0100, 0001, POS, NEG, NEG, NEG)
381MP_BIT2CBINOP(1000, 0111, 0010, 0100, 0001, NEG, POS, POS, POS)
382MP_BIT2CBINOP(1001, 0110, 0110, 0110, 0110, NEG, POS, POS, NEG)
383MP_BIT2CBINOP(1010, 0101, 0101, 0101, 0101, NEG, NEG, POS, POS)
384MP_BIT2CBINOP(1011, 0100, 0001, 0111, 0010, NEG, NEG, POS, NEG)
385MP_BIT2CBINOP(1100, 0011, 0011, 0011, 0011, NEG, POS, NEG, POS)
386MP_BIT2CBINOP(1101, 0010, 0111, 0001, 0100, NEG, POS, NEG, NEG)
387MP_BIT2CBINOP(1110, 0001, 0100, 0010, 0111, NEG, NEG, NEG, POS)
388MP_BIT2CBINOP(1111, 0000, 0000, 0000, 0000, NEG, NEG, NEG, NEG)
389#undef NEG
390#undef POS
391
392/* --- @mp_not2c@ --- *
393 *
394 * Arguments: @mp *d@ = destination
395 * @mp *a@ = source
396 *
397 * Returns: The sign-extended complement of the argument.
398 */
399
400mp *mp_not2c(mp *d, mp *a)
401{
402 mpw one = 1;
403
404 MP_DEST(d, MP_LEN(a) + 1, a->f);
405 if (d == a) {
a69a3efd 406 if (MP_NEGP(a))
f09e814a 407 MPX_USUBN(d->v, d->vl, 1);
408 else
409 MPX_UADDN(d->v, d->vl, 1);
410 } else {
a69a3efd 411 if (MP_NEGP(a))
f09e814a 412 mpx_usub(d->v, d->vl, a->v, a->vl, &one, &one + 1);
413 else
414 mpx_uadd(d->v, d->vl, a->v, a->vl, &one, &one + 1);
415 }
416 d->f = (a->f & (MP_NEG | MP_BURN)) ^ MP_NEG;
417 MP_SHRINK(d);
418 return (d);
419}
420
d3409d5e 421/* --- @mp_add@ --- *
422 *
423 * Arguments: @mp *d@ = destination
ef5f4810 424 * @mp *a, *b@ = sources
d3409d5e 425 *
426 * Returns: Result, @a@ added to @b@.
427 */
428
ef5f4810 429mp *mp_add(mp *d, mp *a, mp *b)
d3409d5e 430{
d34decd2 431 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
d3409d5e 432 if (!((a->f ^ b->f) & MP_NEG))
433 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
434 else {
435 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 436 mp *t = a; a = b; b = t;
d3409d5e 437 }
438 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
439 }
440 d->f = ((a->f | b->f) & MP_BURN) | (a->f & MP_NEG);
441 MP_SHRINK(d);
442 return (d);
443}
444
445/* --- @mp_sub@ --- *
446 *
447 * Arguments: @mp *d@ = destination
ef5f4810 448 * @mp *a, *b@ = sources
d3409d5e 449 *
450 * Returns: Result, @b@ subtracted from @a@.
451 */
452
ef5f4810 453mp *mp_sub(mp *d, mp *a, mp *b)
d3409d5e 454{
455 unsigned sgn = 0;
d34decd2 456 MP_DEST(d, MAX(MP_LEN(a), MP_LEN(b)) + 1, a->f | b->f);
d3409d5e 457 if ((a->f ^ b->f) & MP_NEG)
458 mpx_uadd(d->v, d->vl, a->v, a->vl, b->v, b->vl);
459 else {
460 if (MPX_UCMP(a->v, a->vl, <, b->v, b->vl)) {
ef5f4810 461 mp *t = a; a = b; b = t;
d3409d5e 462 sgn = MP_NEG;
463 }
464 mpx_usub(d->v, d->vl, a->v, a->vl, b->v, b->vl);
465 }
466 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ sgn) & MP_NEG);
467 MP_SHRINK(d);
468 return (d);
469}
470
471/* --- @mp_mul@ --- *
472 *
473 * Arguments: @mp *d@ = destination
ef5f4810 474 * @mp *a, *b@ = sources
d3409d5e 475 *
476 * Returns: Result, @a@ multiplied by @b@.
477 */
478
ef5f4810 479mp *mp_mul(mp *d, mp *a, mp *b)
d3409d5e 480{
ef5f4810 481 a = MP_COPY(a);
482 b = MP_COPY(b);
483
52cdaca9 484 if (MP_LEN(a) <= MPK_THRESH || MP_LEN(b) <= MPK_THRESH) {
d34decd2 485 MP_DEST(d, MP_LEN(a) + MP_LEN(b), a->f | b->f | MP_UNDEF);
ef5f4810 486 mpx_umul(d->v, d->vl, a->v, a->vl, b->v, b->vl);
8017495b 487 } else {
dd22938e 488 size_t m = MAX(MP_LEN(a), MP_LEN(b));
ef5f4810 489 mpw *s;
dd22938e 490 MP_DEST(d, 3 * m, a->f | b->f | MP_UNDEF);
491 s = mpalloc(d->a, 5 * m);
492 mpx_kmul(d->v, d->vl, a->v, a->vl, b->v, b->vl, s, s + 5 * m);
d34decd2 493 mpfree(d->a, s);
ef5f4810 494 }
495
d3409d5e 496 d->f = ((a->f | b->f) & MP_BURN) | ((a->f ^ b->f) & MP_NEG);
497 MP_SHRINK(d);
ef5f4810 498 MP_DROP(a);
499 MP_DROP(b);
d3409d5e 500 return (d);
501}
502
503/* --- @mp_sqr@ --- *
504 *
505 * Arguments: @mp *d@ = destination
ef5f4810 506 * @mp *a@ = source
d3409d5e 507 *
508 * Returns: Result, @a@ squared.
509 */
510
ef5f4810 511mp *mp_sqr(mp *d, mp *a)
d3409d5e 512{
ef5f4810 513 size_t m = MP_LEN(a);
514
515 a = MP_COPY(a);
52cdaca9 516 if (m > MPK_THRESH) {
ef5f4810 517 mpw *s;
dd22938e 518 MP_DEST(d, 3 * m, a->f | MP_UNDEF);
519 s = mpalloc(d->a, 5 * m);
520 mpx_ksqr(d->v, d->vl, a->v, a->vl, s, s + 5 * m);
d34decd2 521 mpfree(d->a, s);
dd22938e 522 } else {
523 MP_DEST(d, 2 * m + 2, a->f | MP_UNDEF);
ef5f4810 524 mpx_usqr(d->v, d->vl, a->v, a->vl);
dd22938e 525 }
d3409d5e 526 d->f = a->f & MP_BURN;
527 MP_SHRINK(d);
ef5f4810 528 MP_DROP(a);
d3409d5e 529 return (d);
530}
531
532/* --- @mp_div@ --- *
533 *
534 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
ef5f4810 535 * @mp *a, *b@ = sources
d3409d5e 536 *
537 * Use: Calculates the quotient and remainder when @a@ is divided by
538 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
539 * Either of @qq@ or @rr@ may be null to indicate that the
540 * result is irrelevant. (Discarding both results is silly.)
541 * There is a performance advantage if @a == *rr@.
542 *
543 * The behaviour when @a@ and @b@ have the same sign is
544 * straightforward. When the signs differ, this implementation
545 * chooses @r@ to have the same sign as @b@, rather than the
546 * more normal choice that the remainder has the same sign as
547 * the dividend. This makes modular arithmetic a little more
548 * straightforward.
549 */
550
ef5f4810 551void mp_div(mp **qq, mp **rr, mp *a, mp *b)
d3409d5e 552 {
553 mp *r = rr ? *rr : MP_NEW;
554 mp *q = qq ? *qq : MP_NEW;
555 mpw *sv, *svl;
556
d3409d5e 557 /* --- Set the remainder up right --- *
558 *
559 * Just in case the divisor is larger, be able to cope with this. It's not
560 * important in @mpx_udiv@, but it is here because of the sign correction.
561 */
562
d34decd2 563 b = MP_COPY(b);
564 a = MP_COPY(a);
565 if (r)
566 MP_DROP(r);
567 r = a;
a9c8f3d6 568 MP_DEST(r, MAX(MP_LEN(a), MP_LEN(b)) + 2, a->f | b->f);
d3409d5e 569
570 /* --- Fix up the quotient too --- */
571
d34decd2 572 r = MP_COPY(r);
573 MP_DEST(q, MP_LEN(r), r->f | MP_UNDEF);
574 MP_DROP(r);
575
576 /* --- Set up some temporary workspace --- */
577
578 {
579 size_t rq = MP_LEN(b) + 1;
580 sv = mpalloc(r->a, rq);
581 svl = sv + rq;
582 }
d3409d5e 583
584 /* --- Perform the calculation --- */
585
586 mpx_udiv(q->v, q->vl, r->v, r->vl, b->v, b->vl, sv, svl);
587
588 /* --- Sort out the sign of the results --- *
589 *
590 * If the signs of the arguments differ, and the remainder is nonzero, I
591 * must add one to the absolute value of the quotient and subtract the
592 * remainder from @b@.
593 */
594
d34decd2 595 q->f = ((r->f | b->f) & MP_BURN) | ((r->f ^ b->f) & MP_NEG);
a69a3efd 596 if (MP_NEGP(q)) {
ef5f4810 597 mpw *v;
598 for (v = r->v; v < r->vl; v++) {
d3409d5e 599 if (*v) {
600 MPX_UADDN(q->v, q->vl, 1);
601 mpx_usub(r->v, r->vl, b->v, b->vl, r->v, r->vl);
602 break;
603 }
604 }
605 }
606
d34decd2 607 r->f = ((r->f | b->f) & MP_BURN) | (b->f & MP_NEG);
d3409d5e 608
609 /* --- Store the return values --- */
610
d34decd2 611 mpfree(r->a, sv);
612 MP_DROP(b);
613
d3409d5e 614 if (!qq)
615 MP_DROP(q);
616 else {
617 MP_SHRINK(q);
618 *qq = q;
619 }
620
621 if (!rr)
622 MP_DROP(r);
623 else {
624 MP_SHRINK(r);
625 *rr = r;
626 }
d3409d5e 627}
628
f1713c63 629/* --- @mp_odd@ --- *
630 *
631 * Arguments: @mp *d@ = pointer to destination integer
632 * @mp *m@ = pointer to source integer
633 * @size_t *s@ = where to store the power of 2
634 *
635 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
636 *
637 * Use: Computes a power of two and an odd integer which, when
638 * multiplied, give a specified result. This sort of thing is
639 * useful in number theory quite often.
640 */
641
642mp *mp_odd(mp *d, mp *m, size_t *s)
643{
644 size_t ss = 0;
645 const mpw *v, *vl;
646
647 v = m->v;
648 vl = m->vl;
649 for (; !*v && v < vl; v++)
650 ss += MPW_BITS;
651 if (v >= vl)
652 ss = 0;
653 else {
654 mpw x = *v;
c29970a7
MW		 655 unsigned z = MPW_P2;
656 mpw mask = ((mpw)1 << z) - 1;
f1713c63 657
658 while (z) {
f1713c63 659 if (!(x & mask)) {
660 x >>= z;
661 ss += z;
662 }
663 z >>= 1;
c29970a7 664 mask >>= z;
f1713c63 665 }
666 }
667
668 *s = ss;
669 return (mp_lsr(d, m, ss));
670}
671
d3409d5e 672/*----- Test rig ----------------------------------------------------------*/
673
674#ifdef TEST_RIG
675
676static int verify(const char *op, mp *expect, mp *result, mp *a, mp *b)
677{
4b536f42 678 if (!MP_EQ(expect, result)) {
d3409d5e 679 fprintf(stderr, "\n*** %s failed", op);
45c0fd36
MW		 680 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
681 fputs("\n*** b = ", stderr); mp_writefile(b, stderr, 10);
d3409d5e 682 fputs("\n*** result = ", stderr); mp_writefile(result, stderr, 10);
683 fputs("\n*** expect = ", stderr); mp_writefile(expect, stderr, 10);
684 fputc('\n', stderr);
685 return (0);
686 }
687 return (1);
688}
689
690#define RIG(name, op) \
ef5f4810 691 static int t##name(dstr *v) \
d3409d5e 692 { \
693 mp *a = *(mp **)v[0].buf; \
694 mpw n = *(int *)v[1].buf; \
695 mp b; \
696 mp *r = *(mp **)v[2].buf; \
697 mp *c = op(MP_NEW, a, n); \
698 int ok; \
699 mp_build(&b, &n, &n + 1); \
700 ok = verify(#name, r, c, a, &b); \
701 mp_drop(a); mp_drop(c); mp_drop(r); \
ef5f4810 702 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 703 return (ok); \
704 }
705
706RIG(lsl, mp_lsl)
707RIG(lsr, mp_lsr)
f09e814a 708RIG(lsl2c, mp_lsl2c)
709RIG(lsr2c, mp_lsr2c)
d3409d5e 710
711#undef RIG
712
713#define RIG(name, op) \
ef5f4810 714 static int t##name(dstr *v) \
d3409d5e 715 { \
716 mp *a = *(mp **)v[0].buf; \
717 mp *b = *(mp **)v[1].buf; \
718 mp *r = *(mp **)v[2].buf; \
719 mp *c = op(MP_NEW, a, b); \
720 int ok = verify(#name, r, c, a, b); \
721 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
ef5f4810 722 assert(mparena_count(MPARENA_GLOBAL) == 0); \
d3409d5e 723 return (ok); \
724 }
725
726RIG(add, mp_add)
727RIG(sub, mp_sub)
728RIG(mul, mp_mul)
f4535c64 729RIG(exp, mp_exp)
d3409d5e 730
731#undef RIG
732
733static int tdiv(dstr *v)
734{
735 mp *a = *(mp **)v[0].buf;
736 mp *b = *(mp **)v[1].buf;
737 mp *q = *(mp **)v[2].buf;
738 mp *r = *(mp **)v[3].buf;
739 mp *c = MP_NEW, *d = MP_NEW;
740 int ok = 1;
741 mp_div(&c, &d, a, b);
742 ok &= verify("div(quotient)", q, c, a, b);
743 ok &= verify("div(remainder)", r, d, a, b);
744 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(d); mp_drop(r); mp_drop(q);
ef5f4810 745 assert(mparena_count(MPARENA_GLOBAL) == 0);
d3409d5e 746 return (ok);
747}
748
f09e814a 749static int tbin(dstr *v)
750{
751 static mp *(*fn[])(mp *, mp *, mp *) = {
45c0fd36 752#define DO(string) mp_bit##string##2c,
f09e814a 753MPX_DOBIN(DO)
754#undef DO
755 };
756 int ok = 1;
757 unsigned op = 0;
758 mp *a = *(mp **)v[1].buf;
759 mp *b = *(mp **)v[2].buf;
760 mp *r = *(mp **)v[3].buf;
761 mp *c;
45c0fd36 762
f09e814a 763 if (strcmp(v[0].buf, "and") == 0) op = 1;
764 else if (strcmp(v[0].buf, "or") == 0) op = 7;
765 else if (strcmp(v[0].buf, "nand") == 0) op = 14;
766 else if (strcmp(v[0].buf, "nor") == 0) op = 8;
767 else if (strcmp(v[0].buf, "xor") == 0) op = 6;
768 else {
769 char *p = v[0].buf;
770 while (*p) {
771 op <<= 1;
772 if (*p++ == '1')
773 op |= 1;
774 }
775 }
776
777 c = fn[op](MP_NEW, a, b);
778 ok = verify(v[0].buf, r, c, a, b);
779 mp_drop(a); mp_drop(b); mp_drop(r); mp_drop(c);
780 assert(mparena_count(MPARENA_GLOBAL) == 0);
781 return (ok);
782}
783
09d00c6b 784static int tset(dstr *v)
785{
786 mp *a = *(mp **)v[0].buf;
787 unsigned long n = *(unsigned long *)v[1].buf;
788 mp *r = *(mp **)v[2].buf;
789 mp *c;
790 int ok = 1;
791
792 c = mp_setbit2c(MP_NEW, a, n);
793 if (!MP_EQ(c, r)) {
794 ok = 0;
795 fprintf(stderr, "\n***setbit (set) failed");
796 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
797 fprintf(stderr, "\n*** n = %lu", n);
798 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
799 fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
800 fputc('\n', stderr);
801 }
802 if (!mp_testbit2c(r, n)) {
803 ok = 0;
804 fprintf(stderr, "\n***setbit (test) failed");
805 fprintf(stderr, "\n*** n = %lu", n);
806 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
807 fputc('\n', stderr);
808 }
809 mp_drop(a);
810 mp_drop(r);
811 mp_drop(c);
812 assert(mparena_count(MPARENA_GLOBAL) == 0);
813 return (ok);
814}
815
816static int tclr(dstr *v)
817{
818 mp *a = *(mp **)v[0].buf;
819 unsigned long n = *(unsigned long *)v[1].buf;
820 mp *r = *(mp **)v[2].buf;
821 mp *c;
822 int ok = 1;
823
824 c = mp_clearbit2c(MP_NEW, a, n);
825 if (!MP_EQ(c, r)) {
826 ok = 0;
827 fprintf(stderr, "\n***clrbit (set) failed");
828 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 16);
829 fprintf(stderr, "\n*** n = %lu", n);
830 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
831 fputs("\n*** c = ", stderr); mp_writefile(c, stderr, 16);
832 fputc('\n', stderr);
833 }
834 if (mp_testbit2c(r, n)) {
835 ok = 0;
836 fprintf(stderr, "\n***clrbit (test) failed");
837 fprintf(stderr, "\n*** n = %lu", n);
838 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 16);
839 fputc('\n', stderr);
840 }
841 mp_drop(a);
842 mp_drop(c);
843 mp_drop(r);
844 assert(mparena_count(MPARENA_GLOBAL) == 0);
845 return (ok);
846}
847
397041a9 848static int tneg(dstr *v)
849{
850 mp *a = *(mp **)v[0].buf;
851 mp *r = *(mp **)v[1].buf;
852 int ok = 1;
853 mp *n = mp_neg(MP_NEW, a);
854 if (!MP_EQ(r, n)) {
855 ok = 0;
856 fprintf(stderr, "\n*** neg failed\n");
857 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
858 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
859 fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
860 fputc('\n', stderr);
861 }
862 mp_drop(n);
863 n = mp_neg(a, a);
864 if (!MP_EQ(r, n)) {
865 ok = 0;
866 fprintf(stderr, "\n*** neg failed\n");
867 fputs("\n*** a* = ", stderr); mp_writefile(a, stderr, 10);
868 fputs("\n*** r = ", stderr); mp_writefile(r, stderr, 10);
869 fputs("\n*** n = ", stderr); mp_writefile(n, stderr, 10);
870 fputc('\n', stderr);
871 }
872 mp_drop(a);
873 mp_drop(r);
874 assert(mparena_count(MPARENA_GLOBAL) == 0);
45c0fd36 875 return (ok);
397041a9 876}
877
f1713c63 878static int todd(dstr *v)
879{
880 mp *a = *(mp **)v[0].buf;
881 size_t rs = *(uint32 *)v[1].buf;
882 mp *rt = *(mp **)v[2].buf;
883 int ok = 1;
884 mp *t;
885 size_t s;
886 t = mp_odd(MP_NEW, a, &s);
4b536f42 887 if (s != rs || !MP_EQ(t, rt)) {
f1713c63 888 ok = 0;
889 fprintf(stderr, "\n*** odd failed");
890 fputs("\n*** a = ", stderr); mp_writefile(a, stderr, 10);
891 fprintf(stderr, "\n*** s = %lu", (unsigned long)s);
892 fputs("\n*** t = ", stderr); mp_writefile(t, stderr, 10);
893 fprintf(stderr, "\n*** rs = %lu", (unsigned long)rs);
894 fputs("\n*** rt = ", stderr); mp_writefile(rt, stderr, 10);
895 fputc('\n', stderr);
896 }
897 mp_drop(a);
898 mp_drop(rt);
899 mp_drop(t);
09d00c6b 900 assert(mparena_count(MPARENA_GLOBAL) == 0);
f1713c63 901 return (ok);
902}
903
d3409d5e 904static test_chunk tests[] = {
f09e814a 905 { "lsl", tlsl, { &type_mp, &type_int, &type_mp, 0 } },
906 { "lsr", tlsr, { &type_mp, &type_int, &type_mp, 0 } },
907 { "lsl2c", tlsl2c, { &type_mp, &type_int, &type_mp, 0 } },
908 { "lsr2c", tlsr2c, { &type_mp, &type_int, &type_mp, 0 } },
09d00c6b 909 { "setbit", tset, { &type_mp, &type_ulong, &type_mp, 0 } },
910 { "clrbit", tclr, { &type_mp, &type_ulong, &type_mp, 0 } },
d3409d5e 911 { "add", tadd, { &type_mp, &type_mp, &type_mp, 0 } },
912 { "sub", tsub, { &type_mp, &type_mp, &type_mp, 0 } },
913 { "mul", tmul, { &type_mp, &type_mp, &type_mp, 0 } },
914 { "div", tdiv, { &type_mp, &type_mp, &type_mp, &type_mp, 0 } },
f4535c64 915 { "exp", texp, { &type_mp, &type_mp, &type_mp, 0 } },
f09e814a 916 { "bin2c", tbin, { &type_string, &type_mp, &type_mp, &type_mp, 0 } },
f1713c63 917 { "odd", todd, { &type_mp, &type_uint32, &type_mp, 0 } },
397041a9 918 { "neg", tneg, { &type_mp, &type_mp, 0 } },
d3409d5e 919 { 0, 0, { 0 } },
920};
921
922int main(int argc, char *argv[])
923{
924 sub_init();
925 test_run(argc, argv, tests, SRCDIR "/tests/mp");
926 return (0);
927}
928
929#endif
930
931/*----- That's all, folks -------------------------------------------------*/
Catacomb cryptographic library (downstream of http://git.distorted.org.uk/~mdw/catacomb/)