1 /* $NetBSD: mpi.c,v 1.1.1.3 2014/04/24 12:45:39 pettai Exp $ */
2
3 /*
4 mpi.c
5
6 by Michael J. Fromberger <sting@linguist.dartmouth.edu>
7 Copyright (C) 1998 Michael J. Fromberger, All Rights Reserved
8
9 Arbitrary precision integer arithmetic library
10
11 Id: mpi.c,v 1.2 2005/05/05 14:38:47 tom Exp
12 */
13
14 #include "mpi.h"
15 #include <stdlib.h>
16 #include <string.h>
17 #include <ctype.h>
18
19 #if MP_DEBUG
20 #include <stdio.h>
21
22 #define DIAG(T,V) {fprintf(stderr,T);mp_print(V,stderr);fputc('\n',stderr);}
23 #else
24 #define DIAG(T,V)
25 #endif
26
27 /*
28 If MP_LOGTAB is not defined, use the math library to compute the
29 logarithms on the fly. Otherwise, use the static table below.
30 Pick which works best for your system.
31 */
32 #if MP_LOGTAB
33
34 /* {{{ s_logv_2[] - log table for 2 in various bases */
35
36 /*
37 A table of the logs of 2 for various bases (the 0 and 1 entries of
38 this table are meaningless and should not be referenced).
39
40 This table is used to compute output lengths for the mp_toradix()
41 function. Since a number n in radix r takes up about log_r(n)
42 digits, we estimate the output size by taking the least integer
43 greater than log_r(n), where:
44
45 log_r(n) = log_2(n) * log_r(2)
46
47 This table, therefore, is a table of log_r(2) for 2 <= r <= 36,
48 which are the output bases supported.
49 */
50
51 #include "logtab.h"
52
53 /* }}} */
54 #define LOG_V_2(R) s_logv_2[(R)]
55
56 #else
57
58 #include <math.h>
59 #define LOG_V_2(R) (log(2.0)/log(R))
60
61 #endif
62
63 /* Default precision for newly created mp_int's */
64 static unsigned int s_mp_defprec = MP_DEFPREC;
65
66 /* {{{ Digit arithmetic macros */
67
68 /*
69 When adding and multiplying digits, the results can be larger than
70 can be contained in an mp_digit. Thus, an mp_word is used. These
71 macros mask off the upper and lower digits of the mp_word (the
72 mp_word may be more than 2 mp_digits wide, but we only concern
73 ourselves with the low-order 2 mp_digits)
74
75 If your mp_word DOES have more than 2 mp_digits, you need to
76 uncomment the first line, and comment out the second.
77 */
78
79 /* #define CARRYOUT(W) (((W)>>DIGIT_BIT)&MP_DIGIT_MAX) */
80 #define CARRYOUT(W) ((W)>>DIGIT_BIT)
81 #define ACCUM(W) ((W)&MP_DIGIT_MAX)
82
83 /* }}} */
84
85 /* {{{ Comparison constants */
86
87 #define MP_LT -1
88 #define MP_EQ 0
89 #define MP_GT 1
90
91 /* }}} */
92
93 /* {{{ Constant strings */
94
95 /* Constant strings returned by mp_strerror() */
96 static const char *mp_err_string[] = {
97 "unknown result code", /* say what? */
98 "boolean true", /* MP_OKAY, MP_YES */
99 "boolean false", /* MP_NO */
100 "out of memory", /* MP_MEM */
101 "argument out of range", /* MP_RANGE */
102 "invalid input parameter", /* MP_BADARG */
103 "result is undefined" /* MP_UNDEF */
104 };
105
106 /* Value to digit maps for radix conversion */
107
108 /* s_dmap_1 - standard digits and letters */
109 static const char *s_dmap_1 =
110 "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
111
112 #if 0
113 /* s_dmap_2 - base64 ordering for digits */
114 static const char *s_dmap_2 =
115 "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
116 #endif
117
118 /* }}} */
119
120 /* {{{ Static function declarations */
121
122 /*
123 If MP_MACRO is false, these will be defined as actual functions;
124 otherwise, suitable macro definitions will be used. This works
125 around the fact that ANSI C89 doesn't support an 'inline' keyword
126 (although I hear C9x will ... about bloody time). At present, the
127 macro definitions are identical to the function bodies, but they'll
128 expand in place, instead of generating a function call.
129
130 I chose these particular functions to be made into macros because
131 some profiling showed they are called a lot on a typical workload,
132 and yet they are primarily housekeeping.
133 */
134 #if MP_MACRO == 0
135 void s_mp_setz(mp_digit *dp, mp_size count); /* zero digits */
136 void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count); /* copy */
137 void *s_mp_alloc(size_t nb, size_t ni); /* general allocator */
138 void s_mp_free(void *ptr); /* general free function */
139 #else
140
141 /* Even if these are defined as macros, we need to respect the settings
142 of the MP_MEMSET and MP_MEMCPY configuration options...
143 */
144 #if MP_MEMSET == 0
145 #define s_mp_setz(dp, count) \
146 {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=0;}
147 #else
148 #define s_mp_setz(dp, count) memset(dp, 0, (count) * sizeof(mp_digit))
149 #endif /* MP_MEMSET */
150
151 #if MP_MEMCPY == 0
152 #define s_mp_copy(sp, dp, count) \
153 {int ix;for(ix=0;ix<(count);ix++)(dp)[ix]=(sp)[ix];}
154 #else
155 #define s_mp_copy(sp, dp, count) memcpy(dp, sp, (count) * sizeof(mp_digit))
156 #endif /* MP_MEMCPY */
157
158 #define s_mp_alloc(nb, ni) calloc(nb, ni)
159 #define s_mp_free(ptr) {if(ptr) free(ptr);}
160 #endif /* MP_MACRO */
161
162 mp_err s_mp_grow(mp_int *mp, mp_size min); /* increase allocated size */
163 mp_err s_mp_pad(mp_int *mp, mp_size min); /* left pad with zeroes */
164
165 void s_mp_clamp(mp_int *mp); /* clip leading zeroes */
166
167 void s_mp_exch(mp_int *a, mp_int *b); /* swap a and b in place */
168
169 mp_err s_mp_lshd(mp_int *mp, mp_size p); /* left-shift by p digits */
170 void s_mp_rshd(mp_int *mp, mp_size p); /* right-shift by p digits */
171 void s_mp_div_2d(mp_int *mp, mp_digit d); /* divide by 2^d in place */
172 void s_mp_mod_2d(mp_int *mp, mp_digit d); /* modulo 2^d in place */
173 mp_err s_mp_mul_2d(mp_int *mp, mp_digit d); /* multiply by 2^d in place*/
174 void s_mp_div_2(mp_int *mp); /* divide by 2 in place */
175 mp_err s_mp_mul_2(mp_int *mp); /* multiply by 2 in place */
176 mp_digit s_mp_norm(mp_int *a, mp_int *b); /* normalize for division */
177 mp_err s_mp_add_d(mp_int *mp, mp_digit d); /* unsigned digit addition */
178 mp_err s_mp_sub_d(mp_int *mp, mp_digit d); /* unsigned digit subtract */
179 mp_err s_mp_mul_d(mp_int *mp, mp_digit d); /* unsigned digit multiply */
180 mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r);
181 /* unsigned digit divide */
182 mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu);
183 /* Barrett reduction */
184 mp_err s_mp_add(mp_int *a, mp_int *b); /* magnitude addition */
185 mp_err s_mp_sub(mp_int *a, mp_int *b); /* magnitude subtract */
186 mp_err s_mp_mul(mp_int *a, mp_int *b); /* magnitude multiply */
187 #if 0
188 void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len);
189 /* multiply buffers in place */
190 #endif
191 #if MP_SQUARE
192 mp_err s_mp_sqr(mp_int *a); /* magnitude square */
193 #else
194 #define s_mp_sqr(a) s_mp_mul(a, a)
195 #endif
196 mp_err s_mp_div(mp_int *a, mp_int *b); /* magnitude divide */
197 mp_err s_mp_2expt(mp_int *a, mp_digit k); /* a = 2^k */
198 int s_mp_cmp(mp_int *a, mp_int *b); /* magnitude comparison */
199 int s_mp_cmp_d(mp_int *a, mp_digit d); /* magnitude digit compare */
200 int s_mp_ispow2(mp_int *v); /* is v a power of 2? */
201 int s_mp_ispow2d(mp_digit d); /* is d a power of 2? */
202
203 int s_mp_tovalue(char ch, int r); /* convert ch to value */
204 char s_mp_todigit(int val, int r, int low); /* convert val to digit */
205 int s_mp_outlen(int bits, int r); /* output length in bytes */
206
207 /* }}} */
208
209 /* {{{ Default precision manipulation */
210
mp_get_prec(void)211 unsigned int mp_get_prec(void)
212 {
213 return s_mp_defprec;
214
215 } /* end mp_get_prec() */
216
mp_set_prec(unsigned int prec)217 void mp_set_prec(unsigned int prec)
218 {
219 if(prec == 0)
220 s_mp_defprec = MP_DEFPREC;
221 else
222 s_mp_defprec = prec;
223
224 } /* end mp_set_prec() */
225
226 /* }}} */
227
228 /*------------------------------------------------------------------------*/
229 /* {{{ mp_init(mp) */
230
231 /*
232 mp_init(mp)
233
234 Initialize a new zero-valued mp_int. Returns MP_OKAY if successful,
235 MP_MEM if memory could not be allocated for the structure.
236 */
237
mp_init(mp_int * mp)238 mp_err mp_init(mp_int *mp)
239 {
240 return mp_init_size(mp, s_mp_defprec);
241
242 } /* end mp_init() */
243
244 /* }}} */
245
246 /* {{{ mp_init_array(mp[], count) */
247
mp_init_array(mp_int mp[],int count)248 mp_err mp_init_array(mp_int mp[], int count)
249 {
250 mp_err res;
251 int pos;
252
253 ARGCHK(mp !=NULL && count > 0, MP_BADARG);
254
255 for(pos = 0; pos < count; ++pos) {
256 if((res = mp_init(&mp[pos])) != MP_OKAY)
257 goto CLEANUP;
258 }
259
260 return MP_OKAY;
261
262 CLEANUP:
263 while(--pos >= 0)
264 mp_clear(&mp[pos]);
265
266 return res;
267
268 } /* end mp_init_array() */
269
270 /* }}} */
271
272 /* {{{ mp_init_size(mp, prec) */
273
274 /*
275 mp_init_size(mp, prec)
276
277 Initialize a new zero-valued mp_int with at least the given
278 precision; returns MP_OKAY if successful, or MP_MEM if memory could
279 not be allocated for the structure.
280 */
281
mp_init_size(mp_int * mp,mp_size prec)282 mp_err mp_init_size(mp_int *mp, mp_size prec)
283 {
284 ARGCHK(mp != NULL && prec > 0, MP_BADARG);
285
286 if((DIGITS(mp) = s_mp_alloc(prec, sizeof(mp_digit))) == NULL)
287 return MP_MEM;
288
289 SIGN(mp) = MP_ZPOS;
290 USED(mp) = 1;
291 ALLOC(mp) = prec;
292
293 return MP_OKAY;
294
295 } /* end mp_init_size() */
296
297 /* }}} */
298
299 /* {{{ mp_init_copy(mp, from) */
300
301 /*
302 mp_init_copy(mp, from)
303
304 Initialize mp as an exact copy of from. Returns MP_OKAY if
305 successful, MP_MEM if memory could not be allocated for the new
306 structure.
307 */
308
mp_init_copy(mp_int * mp,mp_int * from)309 mp_err mp_init_copy(mp_int *mp, mp_int *from)
310 {
311 ARGCHK(mp != NULL && from != NULL, MP_BADARG);
312
313 if(mp == from)
314 return MP_OKAY;
315
316 if((DIGITS(mp) = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
317 return MP_MEM;
318
319 s_mp_copy(DIGITS(from), DIGITS(mp), USED(from));
320 USED(mp) = USED(from);
321 ALLOC(mp) = USED(from);
322 SIGN(mp) = SIGN(from);
323
324 return MP_OKAY;
325
326 } /* end mp_init_copy() */
327
328 /* }}} */
329
330 /* {{{ mp_copy(from, to) */
331
332 /*
333 mp_copy(from, to)
334
335 Copies the mp_int 'from' to the mp_int 'to'. It is presumed that
336 'to' has already been initialized (if not, use mp_init_copy()
337 instead). If 'from' and 'to' are identical, nothing happens.
338 */
339
mp_copy(mp_int * from,mp_int * to)340 mp_err mp_copy(mp_int *from, mp_int *to)
341 {
342 ARGCHK(from != NULL && to != NULL, MP_BADARG);
343
344 if(from == to)
345 return MP_OKAY;
346
347 { /* copy */
348 mp_digit *tmp;
349
350 /*
351 If the allocated buffer in 'to' already has enough space to hold
352 all the used digits of 'from', we'll re-use it to avoid hitting
353 the memory allocater more than necessary; otherwise, we'd have
354 to grow anyway, so we just allocate a hunk and make the copy as
355 usual
356 */
357 if(ALLOC(to) >= USED(from)) {
358 s_mp_setz(DIGITS(to) + USED(from), ALLOC(to) - USED(from));
359 s_mp_copy(DIGITS(from), DIGITS(to), USED(from));
360
361 } else {
362 if((tmp = s_mp_alloc(USED(from), sizeof(mp_digit))) == NULL)
363 return MP_MEM;
364
365 s_mp_copy(DIGITS(from), tmp, USED(from));
366
367 if(DIGITS(to) != NULL) {
368 #if MP_CRYPTO
369 s_mp_setz(DIGITS(to), ALLOC(to));
370 #endif
371 s_mp_free(DIGITS(to));
372 }
373
374 DIGITS(to) = tmp;
375 ALLOC(to) = USED(from);
376 }
377
378 /* Copy the precision and sign from the original */
379 USED(to) = USED(from);
380 SIGN(to) = SIGN(from);
381 } /* end copy */
382
383 return MP_OKAY;
384
385 } /* end mp_copy() */
386
387 /* }}} */
388
389 /* {{{ mp_exch(mp1, mp2) */
390
391 /*
392 mp_exch(mp1, mp2)
393
394 Exchange mp1 and mp2 without allocating any intermediate memory
395 (well, unless you count the stack space needed for this call and the
396 locals it creates...). This cannot fail.
397 */
398
mp_exch(mp_int * mp1,mp_int * mp2)399 void mp_exch(mp_int *mp1, mp_int *mp2)
400 {
401 #if MP_ARGCHK == 2
402 assert(mp1 != NULL && mp2 != NULL);
403 #else
404 if(mp1 == NULL || mp2 == NULL)
405 return;
406 #endif
407
408 s_mp_exch(mp1, mp2);
409
410 } /* end mp_exch() */
411
412 /* }}} */
413
414 /* {{{ mp_clear(mp) */
415
416 /*
417 mp_clear(mp)
418
419 Release the storage used by an mp_int, and void its fields so that
420 if someone calls mp_clear() again for the same int later, we won't
421 get tollchocked.
422 */
423
mp_clear(mp_int * mp)424 void mp_clear(mp_int *mp)
425 {
426 if(mp == NULL)
427 return;
428
429 if(DIGITS(mp) != NULL) {
430 #if MP_CRYPTO
431 s_mp_setz(DIGITS(mp), ALLOC(mp));
432 #endif
433 s_mp_free(DIGITS(mp));
434 DIGITS(mp) = NULL;
435 }
436
437 USED(mp) = 0;
438 ALLOC(mp) = 0;
439
440 } /* end mp_clear() */
441
442 /* }}} */
443
444 /* {{{ mp_clear_array(mp[], count) */
445
mp_clear_array(mp_int mp[],int count)446 void mp_clear_array(mp_int mp[], int count)
447 {
448 ARGCHK(mp != NULL && count > 0, MP_BADARG);
449
450 while(--count >= 0)
451 mp_clear(&mp[count]);
452
453 } /* end mp_clear_array() */
454
455 /* }}} */
456
457 /* {{{ mp_zero(mp) */
458
459 /*
460 mp_zero(mp)
461
462 Set mp to zero. Does not change the allocated size of the structure,
463 and therefore cannot fail (except on a bad argument, which we ignore)
464 */
mp_zero(mp_int * mp)465 void mp_zero(mp_int *mp)
466 {
467 if(mp == NULL)
468 return;
469
470 s_mp_setz(DIGITS(mp), ALLOC(mp));
471 USED(mp) = 1;
472 SIGN(mp) = MP_ZPOS;
473
474 } /* end mp_zero() */
475
476 /* }}} */
477
478 /* {{{ mp_set(mp, d) */
479
mp_set(mp_int * mp,mp_digit d)480 void mp_set(mp_int *mp, mp_digit d)
481 {
482 if(mp == NULL)
483 return;
484
485 mp_zero(mp);
486 DIGIT(mp, 0) = d;
487
488 } /* end mp_set() */
489
490 /* }}} */
491
492 /* {{{ mp_set_int(mp, z) */
493
mp_set_int(mp_int * mp,long z)494 mp_err mp_set_int(mp_int *mp, long z)
495 {
496 int ix;
497 unsigned long v = abs(z);
498 mp_err res;
499
500 ARGCHK(mp != NULL, MP_BADARG);
501
502 mp_zero(mp);
503 if(z == 0)
504 return MP_OKAY; /* shortcut for zero */
505
506 for(ix = sizeof(long) - 1; ix >= 0; ix--) {
507
508 if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
509 return res;
510
511 res = s_mp_add_d(mp,
512 (mp_digit)((v >> (ix * CHAR_BIT)) & UCHAR_MAX));
513 if(res != MP_OKAY)
514 return res;
515
516 }
517
518 if(z < 0)
519 SIGN(mp) = MP_NEG;
520
521 return MP_OKAY;
522
523 } /* end mp_set_int() */
524
525 /* }}} */
526
527 /*------------------------------------------------------------------------*/
528 /* {{{ Digit arithmetic */
529
530 /* {{{ mp_add_d(a, d, b) */
531
532 /*
533 mp_add_d(a, d, b)
534
535 Compute the sum b = a + d, for a single digit d. Respects the sign of
536 its primary addend (single digits are unsigned anyway).
537 */
538
mp_add_d(mp_int * a,mp_digit d,mp_int * b)539 mp_err mp_add_d(mp_int *a, mp_digit d, mp_int *b)
540 {
541 mp_err res = MP_OKAY;
542
543 ARGCHK(a != NULL && b != NULL, MP_BADARG);
544
545 if((res = mp_copy(a, b)) != MP_OKAY)
546 return res;
547
548 if(SIGN(b) == MP_ZPOS) {
549 res = s_mp_add_d(b, d);
550 } else if(s_mp_cmp_d(b, d) >= 0) {
551 res = s_mp_sub_d(b, d);
552 } else {
553 SIGN(b) = MP_ZPOS;
554
555 DIGIT(b, 0) = d - DIGIT(b, 0);
556 }
557
558 return res;
559
560 } /* end mp_add_d() */
561
562 /* }}} */
563
564 /* {{{ mp_sub_d(a, d, b) */
565
566 /*
567 mp_sub_d(a, d, b)
568
569 Compute the difference b = a - d, for a single digit d. Respects the
570 sign of its subtrahend (single digits are unsigned anyway).
571 */
572
mp_sub_d(mp_int * a,mp_digit d,mp_int * b)573 mp_err mp_sub_d(mp_int *a, mp_digit d, mp_int *b)
574 {
575 mp_err res;
576
577 ARGCHK(a != NULL && b != NULL, MP_BADARG);
578
579 if((res = mp_copy(a, b)) != MP_OKAY)
580 return res;
581
582 if(SIGN(b) == MP_NEG) {
583 if((res = s_mp_add_d(b, d)) != MP_OKAY)
584 return res;
585
586 } else if(s_mp_cmp_d(b, d) >= 0) {
587 if((res = s_mp_sub_d(b, d)) != MP_OKAY)
588 return res;
589
590 } else {
591 mp_neg(b, b);
592
593 DIGIT(b, 0) = d - DIGIT(b, 0);
594 SIGN(b) = MP_NEG;
595 }
596
597 if(s_mp_cmp_d(b, 0) == 0)
598 SIGN(b) = MP_ZPOS;
599
600 return MP_OKAY;
601
602 } /* end mp_sub_d() */
603
604 /* }}} */
605
606 /* {{{ mp_mul_d(a, d, b) */
607
608 /*
609 mp_mul_d(a, d, b)
610
611 Compute the product b = a * d, for a single digit d. Respects the sign
612 of its multiplicand (single digits are unsigned anyway)
613 */
614
mp_mul_d(mp_int * a,mp_digit d,mp_int * b)615 mp_err mp_mul_d(mp_int *a, mp_digit d, mp_int *b)
616 {
617 mp_err res;
618
619 ARGCHK(a != NULL && b != NULL, MP_BADARG);
620
621 if(d == 0) {
622 mp_zero(b);
623 return MP_OKAY;
624 }
625
626 if((res = mp_copy(a, b)) != MP_OKAY)
627 return res;
628
629 res = s_mp_mul_d(b, d);
630
631 return res;
632
633 } /* end mp_mul_d() */
634
635 /* }}} */
636
637 /* {{{ mp_mul_2(a, c) */
638
mp_mul_2(mp_int * a,mp_int * c)639 mp_err mp_mul_2(mp_int *a, mp_int *c)
640 {
641 mp_err res;
642
643 ARGCHK(a != NULL && c != NULL, MP_BADARG);
644
645 if((res = mp_copy(a, c)) != MP_OKAY)
646 return res;
647
648 return s_mp_mul_2(c);
649
650 } /* end mp_mul_2() */
651
652 /* }}} */
653
654 /* {{{ mp_div_d(a, d, q, r) */
655
656 /*
657 mp_div_d(a, d, q, r)
658
659 Compute the quotient q = a / d and remainder r = a mod d, for a
660 single digit d. Respects the sign of its divisor (single digits are
661 unsigned anyway).
662 */
663
mp_div_d(mp_int * a,mp_digit d,mp_int * q,mp_digit * r)664 mp_err mp_div_d(mp_int *a, mp_digit d, mp_int *q, mp_digit *r)
665 {
666 mp_err res;
667 mp_digit rem;
668 int pow;
669
670 ARGCHK(a != NULL, MP_BADARG);
671
672 if(d == 0)
673 return MP_RANGE;
674
675 /* Shortcut for powers of two ... */
676 if((pow = s_mp_ispow2d(d)) >= 0) {
677 mp_digit mask;
678
679 mask = (1 << pow) - 1;
680 rem = DIGIT(a, 0) & mask;
681
682 if(q) {
683 mp_copy(a, q);
684 s_mp_div_2d(q, pow);
685 }
686
687 if(r)
688 *r = rem;
689
690 return MP_OKAY;
691 }
692
693 /*
694 If the quotient is actually going to be returned, we'll try to
695 avoid hitting the memory allocator by copying the dividend into it
696 and doing the division there. This can't be any _worse_ than
697 always copying, and will sometimes be better (since it won't make
698 another copy)
699
700 If it's not going to be returned, we need to allocate a temporary
701 to hold the quotient, which will just be discarded.
702 */
703 if(q) {
704 if((res = mp_copy(a, q)) != MP_OKAY)
705 return res;
706
707 res = s_mp_div_d(q, d, &rem);
708 if(s_mp_cmp_d(q, 0) == MP_EQ)
709 SIGN(q) = MP_ZPOS;
710
711 } else {
712 mp_int qp;
713
714 if((res = mp_init_copy(&qp, a)) != MP_OKAY)
715 return res;
716
717 res = s_mp_div_d(&qp, d, &rem);
718 if(s_mp_cmp_d(&qp, 0) == 0)
719 SIGN(&qp) = MP_ZPOS;
720
721 mp_clear(&qp);
722 }
723
724 if(r)
725 *r = rem;
726
727 return res;
728
729 } /* end mp_div_d() */
730
731 /* }}} */
732
733 /* {{{ mp_div_2(a, c) */
734
735 /*
736 mp_div_2(a, c)
737
738 Compute c = a / 2, disregarding the remainder.
739 */
740
mp_div_2(mp_int * a,mp_int * c)741 mp_err mp_div_2(mp_int *a, mp_int *c)
742 {
743 mp_err res;
744
745 ARGCHK(a != NULL && c != NULL, MP_BADARG);
746
747 if((res = mp_copy(a, c)) != MP_OKAY)
748 return res;
749
750 s_mp_div_2(c);
751
752 return MP_OKAY;
753
754 } /* end mp_div_2() */
755
756 /* }}} */
757
758 /* {{{ mp_expt_d(a, d, b) */
759
mp_expt_d(mp_int * a,mp_digit d,mp_int * c)760 mp_err mp_expt_d(mp_int *a, mp_digit d, mp_int *c)
761 {
762 mp_int s, x;
763 mp_err res;
764
765 ARGCHK(a != NULL && c != NULL, MP_BADARG);
766
767 if((res = mp_init(&s)) != MP_OKAY)
768 return res;
769 if((res = mp_init_copy(&x, a)) != MP_OKAY)
770 goto X;
771
772 DIGIT(&s, 0) = 1;
773
774 while(d != 0) {
775 if(d & 1) {
776 if((res = s_mp_mul(&s, &x)) != MP_OKAY)
777 goto CLEANUP;
778 }
779
780 d >>= 1;
781
782 if((res = s_mp_sqr(&x)) != MP_OKAY)
783 goto CLEANUP;
784 }
785
786 s_mp_exch(&s, c);
787
788 CLEANUP:
789 mp_clear(&x);
790 X:
791 mp_clear(&s);
792
793 return res;
794
795 } /* end mp_expt_d() */
796
797 /* }}} */
798
799 /* }}} */
800
801 /*------------------------------------------------------------------------*/
802 /* {{{ Full arithmetic */
803
804 /* {{{ mp_abs(a, b) */
805
806 /*
807 mp_abs(a, b)
808
809 Compute b = |a|. 'a' and 'b' may be identical.
810 */
811
mp_abs(mp_int * a,mp_int * b)812 mp_err mp_abs(mp_int *a, mp_int *b)
813 {
814 mp_err res;
815
816 ARGCHK(a != NULL && b != NULL, MP_BADARG);
817
818 if((res = mp_copy(a, b)) != MP_OKAY)
819 return res;
820
821 SIGN(b) = MP_ZPOS;
822
823 return MP_OKAY;
824
825 } /* end mp_abs() */
826
827 /* }}} */
828
829 /* {{{ mp_neg(a, b) */
830
831 /*
832 mp_neg(a, b)
833
834 Compute b = -a. 'a' and 'b' may be identical.
835 */
836
mp_neg(mp_int * a,mp_int * b)837 mp_err mp_neg(mp_int *a, mp_int *b)
838 {
839 mp_err res;
840
841 ARGCHK(a != NULL && b != NULL, MP_BADARG);
842
843 if((res = mp_copy(a, b)) != MP_OKAY)
844 return res;
845
846 if(s_mp_cmp_d(b, 0) == MP_EQ)
847 SIGN(b) = MP_ZPOS;
848 else
849 SIGN(b) = (SIGN(b) == MP_NEG) ? MP_ZPOS : MP_NEG;
850
851 return MP_OKAY;
852
853 } /* end mp_neg() */
854
855 /* }}} */
856
857 /* {{{ mp_add(a, b, c) */
858
859 /*
860 mp_add(a, b, c)
861
862 Compute c = a + b. All parameters may be identical.
863 */
864
mp_add(mp_int * a,mp_int * b,mp_int * c)865 mp_err mp_add(mp_int *a, mp_int *b, mp_int *c)
866 {
867 mp_err res;
868 int cmp;
869
870 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
871
872 if(SIGN(a) == SIGN(b)) { /* same sign: add values, keep sign */
873
874 /* Commutativity of addition lets us do this in either order,
875 so we avoid having to use a temporary even if the result
876 is supposed to replace the output
877 */
878 if(c == b) {
879 if((res = s_mp_add(c, a)) != MP_OKAY)
880 return res;
881 } else {
882 if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
883 return res;
884
885 if((res = s_mp_add(c, b)) != MP_OKAY)
886 return res;
887 }
888
889 } else if((cmp = s_mp_cmp(a, b)) > 0) { /* different sign: a > b */
890
891 /* If the output is going to be clobbered, we will use a temporary
892 variable; otherwise, we'll do it without touching the memory
893 allocator at all, if possible
894 */
895 if(c == b) {
896 mp_int tmp;
897
898 if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
899 return res;
900 if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
901 mp_clear(&tmp);
902 return res;
903 }
904
905 s_mp_exch(&tmp, c);
906 mp_clear(&tmp);
907
908 } else {
909
910 if(c != a && (res = mp_copy(a, c)) != MP_OKAY)
911 return res;
912 if((res = s_mp_sub(c, b)) != MP_OKAY)
913 return res;
914
915 }
916
917 } else if(cmp == 0) { /* different sign, a == b */
918
919 mp_zero(c);
920 return MP_OKAY;
921
922 } else { /* different sign: a < b */
923
924 /* See above... */
925 if(c == a) {
926 mp_int tmp;
927
928 if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
929 return res;
930 if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
931 mp_clear(&tmp);
932 return res;
933 }
934
935 s_mp_exch(&tmp, c);
936 mp_clear(&tmp);
937
938 } else {
939
940 if(c != b && (res = mp_copy(b, c)) != MP_OKAY)
941 return res;
942 if((res = s_mp_sub(c, a)) != MP_OKAY)
943 return res;
944
945 }
946 }
947
948 if(USED(c) == 1 && DIGIT(c, 0) == 0)
949 SIGN(c) = MP_ZPOS;
950
951 return MP_OKAY;
952
953 } /* end mp_add() */
954
955 /* }}} */
956
957 /* {{{ mp_sub(a, b, c) */
958
959 /*
960 mp_sub(a, b, c)
961
962 Compute c = a - b. All parameters may be identical.
963 */
964
mp_sub(mp_int * a,mp_int * b,mp_int * c)965 mp_err mp_sub(mp_int *a, mp_int *b, mp_int *c)
966 {
967 mp_err res;
968 int cmp;
969
970 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
971
972 if(SIGN(a) != SIGN(b)) {
973 if(c == a) {
974 if((res = s_mp_add(c, b)) != MP_OKAY)
975 return res;
976 } else {
977 if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
978 return res;
979 if((res = s_mp_add(c, a)) != MP_OKAY)
980 return res;
981 SIGN(c) = SIGN(a);
982 }
983
984 } else if((cmp = s_mp_cmp(a, b)) > 0) { /* Same sign, a > b */
985 if(c == b) {
986 mp_int tmp;
987
988 if((res = mp_init_copy(&tmp, a)) != MP_OKAY)
989 return res;
990 if((res = s_mp_sub(&tmp, b)) != MP_OKAY) {
991 mp_clear(&tmp);
992 return res;
993 }
994 s_mp_exch(&tmp, c);
995 mp_clear(&tmp);
996
997 } else {
998 if(c != a && ((res = mp_copy(a, c)) != MP_OKAY))
999 return res;
1000
1001 if((res = s_mp_sub(c, b)) != MP_OKAY)
1002 return res;
1003 }
1004
1005 } else if(cmp == 0) { /* Same sign, equal magnitude */
1006 mp_zero(c);
1007 return MP_OKAY;
1008
1009 } else { /* Same sign, b > a */
1010 if(c == a) {
1011 mp_int tmp;
1012
1013 if((res = mp_init_copy(&tmp, b)) != MP_OKAY)
1014 return res;
1015
1016 if((res = s_mp_sub(&tmp, a)) != MP_OKAY) {
1017 mp_clear(&tmp);
1018 return res;
1019 }
1020 s_mp_exch(&tmp, c);
1021 mp_clear(&tmp);
1022
1023 } else {
1024 if(c != b && ((res = mp_copy(b, c)) != MP_OKAY))
1025 return res;
1026
1027 if((res = s_mp_sub(c, a)) != MP_OKAY)
1028 return res;
1029 }
1030
1031 SIGN(c) = !SIGN(b);
1032 }
1033
1034 if(USED(c) == 1 && DIGIT(c, 0) == 0)
1035 SIGN(c) = MP_ZPOS;
1036
1037 return MP_OKAY;
1038
1039 } /* end mp_sub() */
1040
1041 /* }}} */
1042
1043 /* {{{ mp_mul(a, b, c) */
1044
1045 /*
1046 mp_mul(a, b, c)
1047
1048 Compute c = a * b. All parameters may be identical.
1049 */
1050
mp_mul(mp_int * a,mp_int * b,mp_int * c)1051 mp_err mp_mul(mp_int *a, mp_int *b, mp_int *c)
1052 {
1053 mp_err res;
1054 mp_sign sgn;
1055
1056 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
1057
1058 sgn = (SIGN(a) == SIGN(b)) ? MP_ZPOS : MP_NEG;
1059
1060 if(c == b) {
1061 if((res = s_mp_mul(c, a)) != MP_OKAY)
1062 return res;
1063
1064 } else {
1065 if((res = mp_copy(a, c)) != MP_OKAY)
1066 return res;
1067
1068 if((res = s_mp_mul(c, b)) != MP_OKAY)
1069 return res;
1070 }
1071
1072 if(sgn == MP_ZPOS || s_mp_cmp_d(c, 0) == MP_EQ)
1073 SIGN(c) = MP_ZPOS;
1074 else
1075 SIGN(c) = sgn;
1076
1077 return MP_OKAY;
1078
1079 } /* end mp_mul() */
1080
1081 /* }}} */
1082
1083 /* {{{ mp_mul_2d(a, d, c) */
1084
1085 /*
1086 mp_mul_2d(a, d, c)
1087
1088 Compute c = a * 2^d. a may be the same as c.
1089 */
1090
mp_mul_2d(mp_int * a,mp_digit d,mp_int * c)1091 mp_err mp_mul_2d(mp_int *a, mp_digit d, mp_int *c)
1092 {
1093 mp_err res;
1094
1095 ARGCHK(a != NULL && c != NULL, MP_BADARG);
1096
1097 if((res = mp_copy(a, c)) != MP_OKAY)
1098 return res;
1099
1100 if(d == 0)
1101 return MP_OKAY;
1102
1103 return s_mp_mul_2d(c, d);
1104
1105 } /* end mp_mul() */
1106
1107 /* }}} */
1108
1109 /* {{{ mp_sqr(a, b) */
1110
1111 #if MP_SQUARE
mp_sqr(mp_int * a,mp_int * b)1112 mp_err mp_sqr(mp_int *a, mp_int *b)
1113 {
1114 mp_err res;
1115
1116 ARGCHK(a != NULL && b != NULL, MP_BADARG);
1117
1118 if((res = mp_copy(a, b)) != MP_OKAY)
1119 return res;
1120
1121 if((res = s_mp_sqr(b)) != MP_OKAY)
1122 return res;
1123
1124 SIGN(b) = MP_ZPOS;
1125
1126 return MP_OKAY;
1127
1128 } /* end mp_sqr() */
1129 #endif
1130
1131 /* }}} */
1132
1133 /* {{{ mp_div(a, b, q, r) */
1134
1135 /*
1136 mp_div(a, b, q, r)
1137
1138 Compute q = a / b and r = a mod b. Input parameters may be re-used
1139 as output parameters. If q or r is NULL, that portion of the
1140 computation will be discarded (although it will still be computed)
1141
1142 Pay no attention to the hacker behind the curtain.
1143 */
1144
mp_div(mp_int * a,mp_int * b,mp_int * q,mp_int * r)1145 mp_err mp_div(mp_int *a, mp_int *b, mp_int *q, mp_int *r)
1146 {
1147 mp_err res;
1148 mp_int qtmp, rtmp;
1149 int cmp;
1150
1151 ARGCHK(a != NULL && b != NULL, MP_BADARG);
1152
1153 if(mp_cmp_z(b) == MP_EQ)
1154 return MP_RANGE;
1155
1156 /* If a <= b, we can compute the solution without division, and
1157 avoid any memory allocation
1158 */
1159 if((cmp = s_mp_cmp(a, b)) < 0) {
1160 if(r) {
1161 if((res = mp_copy(a, r)) != MP_OKAY)
1162 return res;
1163 }
1164
1165 if(q)
1166 mp_zero(q);
1167
1168 return MP_OKAY;
1169
1170 } else if(cmp == 0) {
1171
1172 /* Set quotient to 1, with appropriate sign */
1173 if(q) {
1174 int qneg = (SIGN(a) != SIGN(b));
1175
1176 mp_set(q, 1);
1177 if(qneg)
1178 SIGN(q) = MP_NEG;
1179 }
1180
1181 if(r)
1182 mp_zero(r);
1183
1184 return MP_OKAY;
1185 }
1186
1187 /* If we get here, it means we actually have to do some division */
1188
1189 /* Set up some temporaries... */
1190 if((res = mp_init_copy(&qtmp, a)) != MP_OKAY)
1191 return res;
1192 if((res = mp_init_copy(&rtmp, b)) != MP_OKAY)
1193 goto CLEANUP;
1194
1195 if((res = s_mp_div(&qtmp, &rtmp)) != MP_OKAY)
1196 goto CLEANUP;
1197
1198 /* Compute the signs for the output */
1199 SIGN(&rtmp) = SIGN(a); /* Sr = Sa */
1200 if(SIGN(a) == SIGN(b))
1201 SIGN(&qtmp) = MP_ZPOS; /* Sq = MP_ZPOS if Sa = Sb */
1202 else
1203 SIGN(&qtmp) = MP_NEG; /* Sq = MP_NEG if Sa != Sb */
1204
1205 if(s_mp_cmp_d(&qtmp, 0) == MP_EQ)
1206 SIGN(&qtmp) = MP_ZPOS;
1207 if(s_mp_cmp_d(&rtmp, 0) == MP_EQ)
1208 SIGN(&rtmp) = MP_ZPOS;
1209
1210 /* Copy output, if it is needed */
1211 if(q)
1212 s_mp_exch(&qtmp, q);
1213
1214 if(r)
1215 s_mp_exch(&rtmp, r);
1216
1217 CLEANUP:
1218 mp_clear(&rtmp);
1219 mp_clear(&qtmp);
1220
1221 return res;
1222
1223 } /* end mp_div() */
1224
1225 /* }}} */
1226
1227 /* {{{ mp_div_2d(a, d, q, r) */
1228
mp_div_2d(mp_int * a,mp_digit d,mp_int * q,mp_int * r)1229 mp_err mp_div_2d(mp_int *a, mp_digit d, mp_int *q, mp_int *r)
1230 {
1231 mp_err res;
1232
1233 ARGCHK(a != NULL, MP_BADARG);
1234
1235 if(q) {
1236 if((res = mp_copy(a, q)) != MP_OKAY)
1237 return res;
1238
1239 s_mp_div_2d(q, d);
1240 }
1241
1242 if(r) {
1243 if((res = mp_copy(a, r)) != MP_OKAY)
1244 return res;
1245
1246 s_mp_mod_2d(r, d);
1247 }
1248
1249 return MP_OKAY;
1250
1251 } /* end mp_div_2d() */
1252
1253 /* }}} */
1254
1255 /* {{{ mp_expt(a, b, c) */
1256
1257 /*
1258 mp_expt(a, b, c)
1259
1260 Compute c = a ** b, that is, raise a to the b power. Uses a
1261 standard iterative square-and-multiply technique.
1262 */
1263
mp_expt(mp_int * a,mp_int * b,mp_int * c)1264 mp_err mp_expt(mp_int *a, mp_int *b, mp_int *c)
1265 {
1266 mp_int s, x;
1267 mp_err res;
1268 mp_digit d;
1269 int dig, bit;
1270
1271 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
1272
1273 if(mp_cmp_z(b) < 0)
1274 return MP_RANGE;
1275
1276 if((res = mp_init(&s)) != MP_OKAY)
1277 return res;
1278
1279 mp_set(&s, 1);
1280
1281 if((res = mp_init_copy(&x, a)) != MP_OKAY)
1282 goto X;
1283
1284 /* Loop over low-order digits in ascending order */
1285 for(dig = 0; dig < (USED(b) - 1); dig++) {
1286 d = DIGIT(b, dig);
1287
1288 /* Loop over bits of each non-maximal digit */
1289 for(bit = 0; bit < DIGIT_BIT; bit++) {
1290 if(d & 1) {
1291 if((res = s_mp_mul(&s, &x)) != MP_OKAY)
1292 goto CLEANUP;
1293 }
1294
1295 d >>= 1;
1296
1297 if((res = s_mp_sqr(&x)) != MP_OKAY)
1298 goto CLEANUP;
1299 }
1300 }
1301
1302 /* Consider now the last digit... */
1303 d = DIGIT(b, dig);
1304
1305 while(d) {
1306 if(d & 1) {
1307 if((res = s_mp_mul(&s, &x)) != MP_OKAY)
1308 goto CLEANUP;
1309 }
1310
1311 d >>= 1;
1312
1313 if((res = s_mp_sqr(&x)) != MP_OKAY)
1314 goto CLEANUP;
1315 }
1316
1317 if(mp_iseven(b))
1318 SIGN(&s) = SIGN(a);
1319
1320 res = mp_copy(&s, c);
1321
1322 CLEANUP:
1323 mp_clear(&x);
1324 X:
1325 mp_clear(&s);
1326
1327 return res;
1328
1329 } /* end mp_expt() */
1330
1331 /* }}} */
1332
1333 /* {{{ mp_2expt(a, k) */
1334
1335 /* Compute a = 2^k */
1336
mp_2expt(mp_int * a,mp_digit k)1337 mp_err mp_2expt(mp_int *a, mp_digit k)
1338 {
1339 ARGCHK(a != NULL, MP_BADARG);
1340
1341 return s_mp_2expt(a, k);
1342
1343 } /* end mp_2expt() */
1344
1345 /* }}} */
1346
1347 /* {{{ mp_mod(a, m, c) */
1348
1349 /*
1350 mp_mod(a, m, c)
1351
1352 Compute c = a (mod m). Result will always be 0 <= c < m.
1353 */
1354
mp_mod(mp_int * a,mp_int * m,mp_int * c)1355 mp_err mp_mod(mp_int *a, mp_int *m, mp_int *c)
1356 {
1357 mp_err res;
1358 int mag;
1359
1360 ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
1361
1362 if(SIGN(m) == MP_NEG)
1363 return MP_RANGE;
1364
1365 /*
1366 If |a| > m, we need to divide to get the remainder and take the
1367 absolute value.
1368
1369 If |a| < m, we don't need to do any division, just copy and adjust
1370 the sign (if a is negative).
1371
1372 If |a| == m, we can simply set the result to zero.
1373
1374 This order is intended to minimize the average path length of the
1375 comparison chain on common workloads -- the most frequent cases are
1376 that |a| != m, so we do those first.
1377 */
1378 if((mag = s_mp_cmp(a, m)) > 0) {
1379 if((res = mp_div(a, m, NULL, c)) != MP_OKAY)
1380 return res;
1381
1382 if(SIGN(c) == MP_NEG) {
1383 if((res = mp_add(c, m, c)) != MP_OKAY)
1384 return res;
1385 }
1386
1387 } else if(mag < 0) {
1388 if((res = mp_copy(a, c)) != MP_OKAY)
1389 return res;
1390
1391 if(mp_cmp_z(a) < 0) {
1392 if((res = mp_add(c, m, c)) != MP_OKAY)
1393 return res;
1394
1395 }
1396
1397 } else {
1398 mp_zero(c);
1399
1400 }
1401
1402 return MP_OKAY;
1403
1404 } /* end mp_mod() */
1405
1406 /* }}} */
1407
1408 /* {{{ mp_mod_d(a, d, c) */
1409
1410 /*
1411 mp_mod_d(a, d, c)
1412
1413 Compute c = a (mod d). Result will always be 0 <= c < d
1414 */
mp_mod_d(mp_int * a,mp_digit d,mp_digit * c)1415 mp_err mp_mod_d(mp_int *a, mp_digit d, mp_digit *c)
1416 {
1417 mp_err res;
1418 mp_digit rem;
1419
1420 ARGCHK(a != NULL && c != NULL, MP_BADARG);
1421
1422 if(s_mp_cmp_d(a, d) > 0) {
1423 if((res = mp_div_d(a, d, NULL, &rem)) != MP_OKAY)
1424 return res;
1425
1426 } else {
1427 if(SIGN(a) == MP_NEG)
1428 rem = d - DIGIT(a, 0);
1429 else
1430 rem = DIGIT(a, 0);
1431 }
1432
1433 if(c)
1434 *c = rem;
1435
1436 return MP_OKAY;
1437
1438 } /* end mp_mod_d() */
1439
1440 /* }}} */
1441
1442 /* {{{ mp_sqrt(a, b) */
1443
1444 /*
1445 mp_sqrt(a, b)
1446
1447 Compute the integer square root of a, and store the result in b.
1448 Uses an integer-arithmetic version of Newton's iterative linear
1449 approximation technique to determine this value; the result has the
1450 following two properties:
1451
1452 b^2 <= a
1453 (b+1)^2 >= a
1454
1455 It is a range error to pass a negative value.
1456 */
mp_sqrt(mp_int * a,mp_int * b)1457 mp_err mp_sqrt(mp_int *a, mp_int *b)
1458 {
1459 mp_int x, t;
1460 mp_err res;
1461
1462 ARGCHK(a != NULL && b != NULL, MP_BADARG);
1463
1464 /* Cannot take square root of a negative value */
1465 if(SIGN(a) == MP_NEG)
1466 return MP_RANGE;
1467
1468 /* Special cases for zero and one, trivial */
1469 if(mp_cmp_d(a, 0) == MP_EQ || mp_cmp_d(a, 1) == MP_EQ)
1470 return mp_copy(a, b);
1471
1472 /* Initialize the temporaries we'll use below */
1473 if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
1474 return res;
1475
1476 /* Compute an initial guess for the iteration as a itself */
1477 if((res = mp_init_copy(&x, a)) != MP_OKAY)
1478 goto X;
1479
1480 s_mp_rshd(&x, (USED(&x)/2)+1);
1481 mp_add_d(&x, 1, &x);
1482
1483 for(;;) {
1484 /* t = (x * x) - a */
1485 mp_copy(&x, &t); /* can't fail, t is big enough for original x */
1486 if((res = mp_sqr(&t, &t)) != MP_OKAY ||
1487 (res = mp_sub(&t, a, &t)) != MP_OKAY)
1488 goto CLEANUP;
1489
1490 /* t = t / 2x */
1491 s_mp_mul_2(&x);
1492 if((res = mp_div(&t, &x, &t, NULL)) != MP_OKAY)
1493 goto CLEANUP;
1494 s_mp_div_2(&x);
1495
1496 /* Terminate the loop, if the quotient is zero */
1497 if(mp_cmp_z(&t) == MP_EQ)
1498 break;
1499
1500 /* x = x - t */
1501 if((res = mp_sub(&x, &t, &x)) != MP_OKAY)
1502 goto CLEANUP;
1503
1504 }
1505
1506 /* Copy result to output parameter */
1507 mp_sub_d(&x, 1, &x);
1508 s_mp_exch(&x, b);
1509
1510 CLEANUP:
1511 mp_clear(&x);
1512 X:
1513 mp_clear(&t);
1514
1515 return res;
1516
1517 } /* end mp_sqrt() */
1518
1519 /* }}} */
1520
1521 /* }}} */
1522
1523 /*------------------------------------------------------------------------*/
1524 /* {{{ Modular arithmetic */
1525
1526 #if MP_MODARITH
1527 /* {{{ mp_addmod(a, b, m, c) */
1528
1529 /*
1530 mp_addmod(a, b, m, c)
1531
1532 Compute c = (a + b) mod m
1533 */
1534
mp_addmod(mp_int * a,mp_int * b,mp_int * m,mp_int * c)1535 mp_err mp_addmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
1536 {
1537 mp_err res;
1538
1539 ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
1540
1541 if((res = mp_add(a, b, c)) != MP_OKAY)
1542 return res;
1543 if((res = mp_mod(c, m, c)) != MP_OKAY)
1544 return res;
1545
1546 return MP_OKAY;
1547
1548 }
1549
1550 /* }}} */
1551
1552 /* {{{ mp_submod(a, b, m, c) */
1553
1554 /*
1555 mp_submod(a, b, m, c)
1556
1557 Compute c = (a - b) mod m
1558 */
1559
mp_submod(mp_int * a,mp_int * b,mp_int * m,mp_int * c)1560 mp_err mp_submod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
1561 {
1562 mp_err res;
1563
1564 ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
1565
1566 if((res = mp_sub(a, b, c)) != MP_OKAY)
1567 return res;
1568 if((res = mp_mod(c, m, c)) != MP_OKAY)
1569 return res;
1570
1571 return MP_OKAY;
1572
1573 }
1574
1575 /* }}} */
1576
1577 /* {{{ mp_mulmod(a, b, m, c) */
1578
1579 /*
1580 mp_mulmod(a, b, m, c)
1581
1582 Compute c = (a * b) mod m
1583 */
1584
mp_mulmod(mp_int * a,mp_int * b,mp_int * m,mp_int * c)1585 mp_err mp_mulmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
1586 {
1587 mp_err res;
1588
1589 ARGCHK(a != NULL && b != NULL && m != NULL && c != NULL, MP_BADARG);
1590
1591 if((res = mp_mul(a, b, c)) != MP_OKAY)
1592 return res;
1593 if((res = mp_mod(c, m, c)) != MP_OKAY)
1594 return res;
1595
1596 return MP_OKAY;
1597
1598 }
1599
1600 /* }}} */
1601
1602 /* {{{ mp_sqrmod(a, m, c) */
1603
1604 #if MP_SQUARE
mp_sqrmod(mp_int * a,mp_int * m,mp_int * c)1605 mp_err mp_sqrmod(mp_int *a, mp_int *m, mp_int *c)
1606 {
1607 mp_err res;
1608
1609 ARGCHK(a != NULL && m != NULL && c != NULL, MP_BADARG);
1610
1611 if((res = mp_sqr(a, c)) != MP_OKAY)
1612 return res;
1613 if((res = mp_mod(c, m, c)) != MP_OKAY)
1614 return res;
1615
1616 return MP_OKAY;
1617
1618 } /* end mp_sqrmod() */
1619 #endif
1620
1621 /* }}} */
1622
1623 /* {{{ mp_exptmod(a, b, m, c) */
1624
1625 /*
1626 mp_exptmod(a, b, m, c)
1627
1628 Compute c = (a ** b) mod m. Uses a standard square-and-multiply
1629 method with modular reductions at each step. (This is basically the
1630 same code as mp_expt(), except for the addition of the reductions)
1631
1632 The modular reductions are done using Barrett's algorithm (see
1633 s_mp_reduce() below for details)
1634 */
1635
mp_exptmod(mp_int * a,mp_int * b,mp_int * m,mp_int * c)1636 mp_err mp_exptmod(mp_int *a, mp_int *b, mp_int *m, mp_int *c)
1637 {
1638 mp_int s, x, mu;
1639 mp_err res;
1640 mp_digit d, *db = DIGITS(b);
1641 mp_size ub = USED(b);
1642 int dig, bit;
1643
1644 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
1645
1646 if(mp_cmp_z(b) < 0 || mp_cmp_z(m) <= 0)
1647 return MP_RANGE;
1648
1649 if((res = mp_init(&s)) != MP_OKAY)
1650 return res;
1651 if((res = mp_init_copy(&x, a)) != MP_OKAY)
1652 goto X;
1653 if((res = mp_mod(&x, m, &x)) != MP_OKAY ||
1654 (res = mp_init(&mu)) != MP_OKAY)
1655 goto MU;
1656
1657 mp_set(&s, 1);
1658
1659 /* mu = b^2k / m */
1660 s_mp_add_d(&mu, 1);
1661 s_mp_lshd(&mu, 2 * USED(m));
1662 if((res = mp_div(&mu, m, &mu, NULL)) != MP_OKAY)
1663 goto CLEANUP;
1664
1665 /* Loop over digits of b in ascending order, except highest order */
1666 for(dig = 0; dig < (ub - 1); dig++) {
1667 d = *db++;
1668
1669 /* Loop over the bits of the lower-order digits */
1670 for(bit = 0; bit < DIGIT_BIT; bit++) {
1671 if(d & 1) {
1672 if((res = s_mp_mul(&s, &x)) != MP_OKAY)
1673 goto CLEANUP;
1674 if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
1675 goto CLEANUP;
1676 }
1677
1678 d >>= 1;
1679
1680 if((res = s_mp_sqr(&x)) != MP_OKAY)
1681 goto CLEANUP;
1682 if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
1683 goto CLEANUP;
1684 }
1685 }
1686
1687 /* Now do the last digit... */
1688 d = *db;
1689
1690 while(d) {
1691 if(d & 1) {
1692 if((res = s_mp_mul(&s, &x)) != MP_OKAY)
1693 goto CLEANUP;
1694 if((res = s_mp_reduce(&s, m, &mu)) != MP_OKAY)
1695 goto CLEANUP;
1696 }
1697
1698 d >>= 1;
1699
1700 if((res = s_mp_sqr(&x)) != MP_OKAY)
1701 goto CLEANUP;
1702 if((res = s_mp_reduce(&x, m, &mu)) != MP_OKAY)
1703 goto CLEANUP;
1704 }
1705
1706 s_mp_exch(&s, c);
1707
1708 CLEANUP:
1709 mp_clear(&mu);
1710 MU:
1711 mp_clear(&x);
1712 X:
1713 mp_clear(&s);
1714
1715 return res;
1716
1717 } /* end mp_exptmod() */
1718
1719 /* }}} */
1720
1721 /* {{{ mp_exptmod_d(a, d, m, c) */
1722
mp_exptmod_d(mp_int * a,mp_digit d,mp_int * m,mp_int * c)1723 mp_err mp_exptmod_d(mp_int *a, mp_digit d, mp_int *m, mp_int *c)
1724 {
1725 mp_int s, x;
1726 mp_err res;
1727
1728 ARGCHK(a != NULL && c != NULL, MP_BADARG);
1729
1730 if((res = mp_init(&s)) != MP_OKAY)
1731 return res;
1732 if((res = mp_init_copy(&x, a)) != MP_OKAY)
1733 goto X;
1734
1735 mp_set(&s, 1);
1736
1737 while(d != 0) {
1738 if(d & 1) {
1739 if((res = s_mp_mul(&s, &x)) != MP_OKAY ||
1740 (res = mp_mod(&s, m, &s)) != MP_OKAY)
1741 goto CLEANUP;
1742 }
1743
1744 d /= 2;
1745
1746 if((res = s_mp_sqr(&x)) != MP_OKAY ||
1747 (res = mp_mod(&x, m, &x)) != MP_OKAY)
1748 goto CLEANUP;
1749 }
1750
1751 s_mp_exch(&s, c);
1752
1753 CLEANUP:
1754 mp_clear(&x);
1755 X:
1756 mp_clear(&s);
1757
1758 return res;
1759
1760 } /* end mp_exptmod_d() */
1761
1762 /* }}} */
1763 #endif /* if MP_MODARITH */
1764
1765 /* }}} */
1766
1767 /*------------------------------------------------------------------------*/
1768 /* {{{ Comparison functions */
1769
1770 /* {{{ mp_cmp_z(a) */
1771
1772 /*
1773 mp_cmp_z(a)
1774
1775 Compare a <=> 0. Returns <0 if a<0, 0 if a=0, >0 if a>0.
1776 */
1777
mp_cmp_z(mp_int * a)1778 int mp_cmp_z(mp_int *a)
1779 {
1780 if(SIGN(a) == MP_NEG)
1781 return MP_LT;
1782 else if(USED(a) == 1 && DIGIT(a, 0) == 0)
1783 return MP_EQ;
1784 else
1785 return MP_GT;
1786
1787 } /* end mp_cmp_z() */
1788
1789 /* }}} */
1790
1791 /* {{{ mp_cmp_d(a, d) */
1792
1793 /*
1794 mp_cmp_d(a, d)
1795
1796 Compare a <=> d. Returns <0 if a<d, 0 if a=d, >0 if a>d
1797 */
1798
mp_cmp_d(mp_int * a,mp_digit d)1799 int mp_cmp_d(mp_int *a, mp_digit d)
1800 {
1801 ARGCHK(a != NULL, MP_EQ);
1802
1803 if(SIGN(a) == MP_NEG)
1804 return MP_LT;
1805
1806 return s_mp_cmp_d(a, d);
1807
1808 } /* end mp_cmp_d() */
1809
1810 /* }}} */
1811
1812 /* {{{ mp_cmp(a, b) */
1813
mp_cmp(mp_int * a,mp_int * b)1814 int mp_cmp(mp_int *a, mp_int *b)
1815 {
1816 ARGCHK(a != NULL && b != NULL, MP_EQ);
1817
1818 if(SIGN(a) == SIGN(b)) {
1819 int mag;
1820
1821 if((mag = s_mp_cmp(a, b)) == MP_EQ)
1822 return MP_EQ;
1823
1824 if(SIGN(a) == MP_ZPOS)
1825 return mag;
1826 else
1827 return -mag;
1828
1829 } else if(SIGN(a) == MP_ZPOS) {
1830 return MP_GT;
1831 } else {
1832 return MP_LT;
1833 }
1834
1835 } /* end mp_cmp() */
1836
1837 /* }}} */
1838
1839 /* {{{ mp_cmp_mag(a, b) */
1840
1841 /*
1842 mp_cmp_mag(a, b)
1843
1844 Compares |a| <=> |b|, and returns an appropriate comparison result
1845 */
1846
mp_cmp_mag(mp_int * a,mp_int * b)1847 int mp_cmp_mag(mp_int *a, mp_int *b)
1848 {
1849 ARGCHK(a != NULL && b != NULL, MP_EQ);
1850
1851 return s_mp_cmp(a, b);
1852
1853 } /* end mp_cmp_mag() */
1854
1855 /* }}} */
1856
1857 /* {{{ mp_cmp_int(a, z) */
1858
1859 /*
1860 This just converts z to an mp_int, and uses the existing comparison
1861 routines. This is sort of inefficient, but it's not clear to me how
1862 frequently this wil get used anyway. For small positive constants,
1863 you can always use mp_cmp_d(), and for zero, there is mp_cmp_z().
1864 */
mp_cmp_int(mp_int * a,long z)1865 int mp_cmp_int(mp_int *a, long z)
1866 {
1867 mp_int tmp;
1868 int out;
1869
1870 ARGCHK(a != NULL, MP_EQ);
1871
1872 mp_init(&tmp); mp_set_int(&tmp, z);
1873 out = mp_cmp(a, &tmp);
1874 mp_clear(&tmp);
1875
1876 return out;
1877
1878 } /* end mp_cmp_int() */
1879
1880 /* }}} */
1881
1882 /* {{{ mp_isodd(a) */
1883
1884 /*
1885 mp_isodd(a)
1886
1887 Returns a true (non-zero) value if a is odd, false (zero) otherwise.
1888 */
mp_isodd(mp_int * a)1889 int mp_isodd(mp_int *a)
1890 {
1891 ARGCHK(a != NULL, 0);
1892
1893 return (DIGIT(a, 0) & 1);
1894
1895 } /* end mp_isodd() */
1896
1897 /* }}} */
1898
1899 /* {{{ mp_iseven(a) */
1900
mp_iseven(mp_int * a)1901 int mp_iseven(mp_int *a)
1902 {
1903 return !mp_isodd(a);
1904
1905 } /* end mp_iseven() */
1906
1907 /* }}} */
1908
1909 /* }}} */
1910
1911 /*------------------------------------------------------------------------*/
1912 /* {{{ Number theoretic functions */
1913
1914 #if MP_NUMTH
1915 /* {{{ mp_gcd(a, b, c) */
1916
1917 /*
1918 Like the old mp_gcd() function, except computes the GCD using the
1919 binary algorithm due to Josef Stein in 1961 (via Knuth).
1920 */
mp_gcd(mp_int * a,mp_int * b,mp_int * c)1921 mp_err mp_gcd(mp_int *a, mp_int *b, mp_int *c)
1922 {
1923 mp_err res;
1924 mp_int u, v, t;
1925 mp_size k = 0;
1926
1927 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
1928
1929 if(mp_cmp_z(a) == MP_EQ && mp_cmp_z(b) == MP_EQ)
1930 return MP_RANGE;
1931 if(mp_cmp_z(a) == MP_EQ) {
1932 return mp_copy(b, c);
1933 } else if(mp_cmp_z(b) == MP_EQ) {
1934 return mp_copy(a, c);
1935 }
1936
1937 if((res = mp_init(&t)) != MP_OKAY)
1938 return res;
1939 if((res = mp_init_copy(&u, a)) != MP_OKAY)
1940 goto U;
1941 if((res = mp_init_copy(&v, b)) != MP_OKAY)
1942 goto V;
1943
1944 SIGN(&u) = MP_ZPOS;
1945 SIGN(&v) = MP_ZPOS;
1946
1947 /* Divide out common factors of 2 until at least 1 of a, b is even */
1948 while(mp_iseven(&u) && mp_iseven(&v)) {
1949 s_mp_div_2(&u);
1950 s_mp_div_2(&v);
1951 ++k;
1952 }
1953
1954 /* Initialize t */
1955 if(mp_isodd(&u)) {
1956 if((res = mp_copy(&v, &t)) != MP_OKAY)
1957 goto CLEANUP;
1958
1959 /* t = -v */
1960 if(SIGN(&v) == MP_ZPOS)
1961 SIGN(&t) = MP_NEG;
1962 else
1963 SIGN(&t) = MP_ZPOS;
1964
1965 } else {
1966 if((res = mp_copy(&u, &t)) != MP_OKAY)
1967 goto CLEANUP;
1968
1969 }
1970
1971 for(;;) {
1972 while(mp_iseven(&t)) {
1973 s_mp_div_2(&t);
1974 }
1975
1976 if(mp_cmp_z(&t) == MP_GT) {
1977 if((res = mp_copy(&t, &u)) != MP_OKAY)
1978 goto CLEANUP;
1979
1980 } else {
1981 if((res = mp_copy(&t, &v)) != MP_OKAY)
1982 goto CLEANUP;
1983
1984 /* v = -t */
1985 if(SIGN(&t) == MP_ZPOS)
1986 SIGN(&v) = MP_NEG;
1987 else
1988 SIGN(&v) = MP_ZPOS;
1989 }
1990
1991 if((res = mp_sub(&u, &v, &t)) != MP_OKAY)
1992 goto CLEANUP;
1993
1994 if(s_mp_cmp_d(&t, 0) == MP_EQ)
1995 break;
1996 }
1997
1998 s_mp_2expt(&v, k); /* v = 2^k */
1999 res = mp_mul(&u, &v, c); /* c = u * v */
2000
2001 CLEANUP:
2002 mp_clear(&v);
2003 V:
2004 mp_clear(&u);
2005 U:
2006 mp_clear(&t);
2007
2008 return res;
2009
2010 } /* end mp_bgcd() */
2011
2012 /* }}} */
2013
2014 /* {{{ mp_lcm(a, b, c) */
2015
2016 /* We compute the least common multiple using the rule:
2017
2018 ab = [a, b](a, b)
2019
2020 ... by computing the product, and dividing out the gcd.
2021 */
2022
mp_lcm(mp_int * a,mp_int * b,mp_int * c)2023 mp_err mp_lcm(mp_int *a, mp_int *b, mp_int *c)
2024 {
2025 mp_int gcd, prod;
2026 mp_err res;
2027
2028 ARGCHK(a != NULL && b != NULL && c != NULL, MP_BADARG);
2029
2030 /* Set up temporaries */
2031 if((res = mp_init(&gcd)) != MP_OKAY)
2032 return res;
2033 if((res = mp_init(&prod)) != MP_OKAY)
2034 goto GCD;
2035
2036 if((res = mp_mul(a, b, &prod)) != MP_OKAY)
2037 goto CLEANUP;
2038 if((res = mp_gcd(a, b, &gcd)) != MP_OKAY)
2039 goto CLEANUP;
2040
2041 res = mp_div(&prod, &gcd, c, NULL);
2042
2043 CLEANUP:
2044 mp_clear(&prod);
2045 GCD:
2046 mp_clear(&gcd);
2047
2048 return res;
2049
2050 } /* end mp_lcm() */
2051
2052 /* }}} */
2053
2054 /* {{{ mp_xgcd(a, b, g, x, y) */
2055
2056 /*
2057 mp_xgcd(a, b, g, x, y)
2058
2059 Compute g = (a, b) and values x and y satisfying Bezout's identity
2060 (that is, ax + by = g). This uses the extended binary GCD algorithm
2061 based on the Stein algorithm used for mp_gcd()
2062 */
2063
mp_xgcd(mp_int * a,mp_int * b,mp_int * g,mp_int * x,mp_int * y)2064 mp_err mp_xgcd(mp_int *a, mp_int *b, mp_int *g, mp_int *x, mp_int *y)
2065 {
2066 mp_int gx, xc, yc, u, v, A, B, C, D;
2067 mp_int *clean[9];
2068 mp_err res;
2069 int last = -1;
2070
2071 if(mp_cmp_z(b) == 0)
2072 return MP_RANGE;
2073
2074 /* Initialize all these variables we need */
2075 if((res = mp_init(&u)) != MP_OKAY) goto CLEANUP;
2076 clean[++last] = &u;
2077 if((res = mp_init(&v)) != MP_OKAY) goto CLEANUP;
2078 clean[++last] = &v;
2079 if((res = mp_init(&gx)) != MP_OKAY) goto CLEANUP;
2080 clean[++last] = &gx;
2081 if((res = mp_init(&A)) != MP_OKAY) goto CLEANUP;
2082 clean[++last] = &A;
2083 if((res = mp_init(&B)) != MP_OKAY) goto CLEANUP;
2084 clean[++last] = &B;
2085 if((res = mp_init(&C)) != MP_OKAY) goto CLEANUP;
2086 clean[++last] = &C;
2087 if((res = mp_init(&D)) != MP_OKAY) goto CLEANUP;
2088 clean[++last] = &D;
2089 if((res = mp_init_copy(&xc, a)) != MP_OKAY) goto CLEANUP;
2090 clean[++last] = &xc;
2091 mp_abs(&xc, &xc);
2092 if((res = mp_init_copy(&yc, b)) != MP_OKAY) goto CLEANUP;
2093 clean[++last] = &yc;
2094 mp_abs(&yc, &yc);
2095
2096 mp_set(&gx, 1);
2097
2098 /* Divide by two until at least one of them is even */
2099 while(mp_iseven(&xc) && mp_iseven(&yc)) {
2100 s_mp_div_2(&xc);
2101 s_mp_div_2(&yc);
2102 if((res = s_mp_mul_2(&gx)) != MP_OKAY)
2103 goto CLEANUP;
2104 }
2105
2106 mp_copy(&xc, &u);
2107 mp_copy(&yc, &v);
2108 mp_set(&A, 1); mp_set(&D, 1);
2109
2110 /* Loop through binary GCD algorithm */
2111 for(;;) {
2112 while(mp_iseven(&u)) {
2113 s_mp_div_2(&u);
2114
2115 if(mp_iseven(&A) && mp_iseven(&B)) {
2116 s_mp_div_2(&A); s_mp_div_2(&B);
2117 } else {
2118 if((res = mp_add(&A, &yc, &A)) != MP_OKAY) goto CLEANUP;
2119 s_mp_div_2(&A);
2120 if((res = mp_sub(&B, &xc, &B)) != MP_OKAY) goto CLEANUP;
2121 s_mp_div_2(&B);
2122 }
2123 }
2124
2125 while(mp_iseven(&v)) {
2126 s_mp_div_2(&v);
2127
2128 if(mp_iseven(&C) && mp_iseven(&D)) {
2129 s_mp_div_2(&C); s_mp_div_2(&D);
2130 } else {
2131 if((res = mp_add(&C, &yc, &C)) != MP_OKAY) goto CLEANUP;
2132 s_mp_div_2(&C);
2133 if((res = mp_sub(&D, &xc, &D)) != MP_OKAY) goto CLEANUP;
2134 s_mp_div_2(&D);
2135 }
2136 }
2137
2138 if(mp_cmp(&u, &v) >= 0) {
2139 if((res = mp_sub(&u, &v, &u)) != MP_OKAY) goto CLEANUP;
2140 if((res = mp_sub(&A, &C, &A)) != MP_OKAY) goto CLEANUP;
2141 if((res = mp_sub(&B, &D, &B)) != MP_OKAY) goto CLEANUP;
2142
2143 } else {
2144 if((res = mp_sub(&v, &u, &v)) != MP_OKAY) goto CLEANUP;
2145 if((res = mp_sub(&C, &A, &C)) != MP_OKAY) goto CLEANUP;
2146 if((res = mp_sub(&D, &B, &D)) != MP_OKAY) goto CLEANUP;
2147
2148 }
2149
2150 /* If we're done, copy results to output */
2151 if(mp_cmp_z(&u) == 0) {
2152 if(x)
2153 if((res = mp_copy(&C, x)) != MP_OKAY) goto CLEANUP;
2154
2155 if(y)
2156 if((res = mp_copy(&D, y)) != MP_OKAY) goto CLEANUP;
2157
2158 if(g)
2159 if((res = mp_mul(&gx, &v, g)) != MP_OKAY) goto CLEANUP;
2160
2161 break;
2162 }
2163 }
2164
2165 CLEANUP:
2166 while(last >= 0)
2167 mp_clear(clean[last--]);
2168
2169 return res;
2170
2171 } /* end mp_xgcd() */
2172
2173 /* }}} */
2174
2175 /* {{{ mp_invmod(a, m, c) */
2176
2177 /*
2178 mp_invmod(a, m, c)
2179
2180 Compute c = a^-1 (mod m), if there is an inverse for a (mod m).
2181 This is equivalent to the question of whether (a, m) = 1. If not,
2182 MP_UNDEF is returned, and there is no inverse.
2183 */
2184
mp_invmod(mp_int * a,mp_int * m,mp_int * c)2185 mp_err mp_invmod(mp_int *a, mp_int *m, mp_int *c)
2186 {
2187 mp_int g, x;
2188 mp_err res;
2189
2190 ARGCHK(a && m && c, MP_BADARG);
2191
2192 if(mp_cmp_z(a) == 0 || mp_cmp_z(m) == 0)
2193 return MP_RANGE;
2194
2195 if((res = mp_init(&g)) != MP_OKAY)
2196 return res;
2197 if((res = mp_init(&x)) != MP_OKAY)
2198 goto X;
2199
2200 if((res = mp_xgcd(a, m, &g, &x, NULL)) != MP_OKAY)
2201 goto CLEANUP;
2202
2203 if(mp_cmp_d(&g, 1) != MP_EQ) {
2204 res = MP_UNDEF;
2205 goto CLEANUP;
2206 }
2207
2208 res = mp_mod(&x, m, c);
2209 SIGN(c) = SIGN(a);
2210
2211 CLEANUP:
2212 mp_clear(&x);
2213 X:
2214 mp_clear(&g);
2215
2216 return res;
2217
2218 } /* end mp_invmod() */
2219
2220 /* }}} */
2221 #endif /* if MP_NUMTH */
2222
2223 /* }}} */
2224
2225 /*------------------------------------------------------------------------*/
2226 /* {{{ mp_print(mp, ofp) */
2227
2228 #if MP_IOFUNC
2229 /*
2230 mp_print(mp, ofp)
2231
2232 Print a textual representation of the given mp_int on the output
2233 stream 'ofp'. Output is generated using the internal radix.
2234 */
2235
mp_print(mp_int * mp,FILE * ofp)2236 void mp_print(mp_int *mp, FILE *ofp)
2237 {
2238 int ix;
2239
2240 if(mp == NULL || ofp == NULL)
2241 return;
2242
2243 fputc((SIGN(mp) == MP_NEG) ? '-' : '+', ofp);
2244
2245 for(ix = USED(mp) - 1; ix >= 0; ix--) {
2246 fprintf(ofp, DIGIT_FMT, DIGIT(mp, ix));
2247 }
2248
2249 } /* end mp_print() */
2250
2251 #endif /* if MP_IOFUNC */
2252
2253 /* }}} */
2254
2255 /*------------------------------------------------------------------------*/
2256 /* {{{ More I/O Functions */
2257
2258 /* {{{ mp_read_signed_bin(mp, str, len) */
2259
2260 /*
2261 mp_read_signed_bin(mp, str, len)
2262
2263 Read in a raw value (base 256) into the given mp_int
2264 */
2265
mp_read_signed_bin(mp_int * mp,unsigned char * str,int len)2266 mp_err mp_read_signed_bin(mp_int *mp, unsigned char *str, int len)
2267 {
2268 mp_err res;
2269
2270 ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
2271
2272 if((res = mp_read_unsigned_bin(mp, str + 1, len - 1)) == MP_OKAY) {
2273 /* Get sign from first byte */
2274 if(str[0])
2275 SIGN(mp) = MP_NEG;
2276 else
2277 SIGN(mp) = MP_ZPOS;
2278 }
2279
2280 return res;
2281
2282 } /* end mp_read_signed_bin() */
2283
2284 /* }}} */
2285
2286 /* {{{ mp_signed_bin_size(mp) */
2287
mp_signed_bin_size(mp_int * mp)2288 int mp_signed_bin_size(mp_int *mp)
2289 {
2290 ARGCHK(mp != NULL, 0);
2291
2292 return mp_unsigned_bin_size(mp) + 1;
2293
2294 } /* end mp_signed_bin_size() */
2295
2296 /* }}} */
2297
2298 /* {{{ mp_to_signed_bin(mp, str) */
2299
mp_to_signed_bin(mp_int * mp,unsigned char * str)2300 mp_err mp_to_signed_bin(mp_int *mp, unsigned char *str)
2301 {
2302 ARGCHK(mp != NULL && str != NULL, MP_BADARG);
2303
2304 /* Caller responsible for allocating enough memory (use mp_raw_size(mp)) */
2305 str[0] = (char)SIGN(mp);
2306
2307 return mp_to_unsigned_bin(mp, str + 1);
2308
2309 } /* end mp_to_signed_bin() */
2310
2311 /* }}} */
2312
2313 /* {{{ mp_read_unsigned_bin(mp, str, len) */
2314
2315 /*
2316 mp_read_unsigned_bin(mp, str, len)
2317
2318 Read in an unsigned value (base 256) into the given mp_int
2319 */
2320
mp_read_unsigned_bin(mp_int * mp,unsigned char * str,int len)2321 mp_err mp_read_unsigned_bin(mp_int *mp, unsigned char *str, int len)
2322 {
2323 int ix;
2324 mp_err res;
2325
2326 ARGCHK(mp != NULL && str != NULL && len > 0, MP_BADARG);
2327
2328 mp_zero(mp);
2329
2330 for(ix = 0; ix < len; ix++) {
2331 if((res = s_mp_mul_2d(mp, CHAR_BIT)) != MP_OKAY)
2332 return res;
2333
2334 if((res = mp_add_d(mp, str[ix], mp)) != MP_OKAY)
2335 return res;
2336 }
2337
2338 return MP_OKAY;
2339
2340 } /* end mp_read_unsigned_bin() */
2341
2342 /* }}} */
2343
2344 /* {{{ mp_unsigned_bin_size(mp) */
2345
mp_unsigned_bin_size(mp_int * mp)2346 int mp_unsigned_bin_size(mp_int *mp)
2347 {
2348 mp_digit topdig;
2349 int count;
2350
2351 ARGCHK(mp != NULL, 0);
2352
2353 /* Special case for the value zero */
2354 if(USED(mp) == 1 && DIGIT(mp, 0) == 0)
2355 return 1;
2356
2357 count = (USED(mp) - 1) * sizeof(mp_digit);
2358 topdig = DIGIT(mp, USED(mp) - 1);
2359
2360 while(topdig != 0) {
2361 ++count;
2362 topdig >>= CHAR_BIT;
2363 }
2364
2365 return count;
2366
2367 } /* end mp_unsigned_bin_size() */
2368
2369 /* }}} */
2370
2371 /* {{{ mp_to_unsigned_bin(mp, str) */
2372
mp_to_unsigned_bin(mp_int * mp,unsigned char * str)2373 mp_err mp_to_unsigned_bin(mp_int *mp, unsigned char *str)
2374 {
2375 mp_digit *dp, *end, d;
2376 unsigned char *spos;
2377
2378 ARGCHK(mp != NULL && str != NULL, MP_BADARG);
2379
2380 dp = DIGITS(mp);
2381 end = dp + USED(mp) - 1;
2382 spos = str;
2383
2384 /* Special case for zero, quick test */
2385 if(dp == end && *dp == 0) {
2386 *str = '\0';
2387 return MP_OKAY;
2388 }
2389
2390 /* Generate digits in reverse order */
2391 while(dp < end) {
2392 int ix;
2393
2394 d = *dp;
2395 for(ix = 0; ix < sizeof(mp_digit); ++ix) {
2396 *spos = d & UCHAR_MAX;
2397 d >>= CHAR_BIT;
2398 ++spos;
2399 }
2400
2401 ++dp;
2402 }
2403
2404 /* Now handle last digit specially, high order zeroes are not written */
2405 d = *end;
2406 while(d != 0) {
2407 *spos = d & UCHAR_MAX;
2408 d >>= CHAR_BIT;
2409 ++spos;
2410 }
2411
2412 /* Reverse everything to get digits in the correct order */
2413 while(--spos > str) {
2414 unsigned char t = *str;
2415 *str = *spos;
2416 *spos = t;
2417
2418 ++str;
2419 }
2420
2421 return MP_OKAY;
2422
2423 } /* end mp_to_unsigned_bin() */
2424
2425 /* }}} */
2426
2427 /* {{{ mp_count_bits(mp) */
2428
mp_count_bits(mp_int * mp)2429 int mp_count_bits(mp_int *mp)
2430 {
2431 int len;
2432 mp_digit d;
2433
2434 ARGCHK(mp != NULL, MP_BADARG);
2435
2436 len = DIGIT_BIT * (USED(mp) - 1);
2437 d = DIGIT(mp, USED(mp) - 1);
2438
2439 while(d != 0) {
2440 ++len;
2441 d >>= 1;
2442 }
2443
2444 return len;
2445
2446 } /* end mp_count_bits() */
2447
2448 /* }}} */
2449
2450 /* {{{ mp_read_radix(mp, str, radix) */
2451
2452 /*
2453 mp_read_radix(mp, str, radix)
2454
2455 Read an integer from the given string, and set mp to the resulting
2456 value. The input is presumed to be in base 10. Leading non-digit
2457 characters are ignored, and the function reads until a non-digit
2458 character or the end of the string.
2459 */
2460
mp_read_radix(mp_int * mp,unsigned char * str,int radix)2461 mp_err mp_read_radix(mp_int *mp, unsigned char *str, int radix)
2462 {
2463 int ix = 0, val = 0;
2464 mp_err res;
2465 mp_sign sig = MP_ZPOS;
2466
2467 ARGCHK(mp != NULL && str != NULL && radix >= 2 && radix <= MAX_RADIX,
2468 MP_BADARG);
2469
2470 mp_zero(mp);
2471
2472 /* Skip leading non-digit characters until a digit or '-' or '+' */
2473 while(str[ix] &&
2474 (s_mp_tovalue(str[ix], radix) < 0) &&
2475 str[ix] != '-' &&
2476 str[ix] != '+') {
2477 ++ix;
2478 }
2479
2480 if(str[ix] == '-') {
2481 sig = MP_NEG;
2482 ++ix;
2483 } else if(str[ix] == '+') {
2484 sig = MP_ZPOS; /* this is the default anyway... */
2485 ++ix;
2486 }
2487
2488 while((val = s_mp_tovalue(str[ix], radix)) >= 0) {
2489 if((res = s_mp_mul_d(mp, radix)) != MP_OKAY)
2490 return res;
2491 if((res = s_mp_add_d(mp, val)) != MP_OKAY)
2492 return res;
2493 ++ix;
2494 }
2495
2496 if(s_mp_cmp_d(mp, 0) == MP_EQ)
2497 SIGN(mp) = MP_ZPOS;
2498 else
2499 SIGN(mp) = sig;
2500
2501 return MP_OKAY;
2502
2503 } /* end mp_read_radix() */
2504
2505 /* }}} */
2506
2507 /* {{{ mp_radix_size(mp, radix) */
2508
mp_radix_size(mp_int * mp,int radix)2509 int mp_radix_size(mp_int *mp, int radix)
2510 {
2511 int len;
2512 ARGCHK(mp != NULL, 0);
2513
2514 len = s_mp_outlen(mp_count_bits(mp), radix) + 1; /* for NUL terminator */
2515
2516 if(mp_cmp_z(mp) < 0)
2517 ++len; /* for sign */
2518
2519 return len;
2520
2521 } /* end mp_radix_size() */
2522
2523 /* }}} */
2524
2525 /* {{{ mp_value_radix_size(num, qty, radix) */
2526
2527 /* num = number of digits
2528 qty = number of bits per digit
2529 radix = target base
2530
2531 Return the number of digits in the specified radix that would be
2532 needed to express 'num' digits of 'qty' bits each.
2533 */
mp_value_radix_size(int num,int qty,int radix)2534 int mp_value_radix_size(int num, int qty, int radix)
2535 {
2536 ARGCHK(num >= 0 && qty > 0 && radix >= 2 && radix <= MAX_RADIX, 0);
2537
2538 return s_mp_outlen(num * qty, radix);
2539
2540 } /* end mp_value_radix_size() */
2541
2542 /* }}} */
2543
2544 /* {{{ mp_toradix(mp, str, radix) */
2545
mp_toradix(mp_int * mp,unsigned char * str,int radix)2546 mp_err mp_toradix(mp_int *mp, unsigned char *str, int radix)
2547 {
2548 int ix, pos = 0;
2549
2550 ARGCHK(mp != NULL && str != NULL, MP_BADARG);
2551 ARGCHK(radix > 1 && radix <= MAX_RADIX, MP_RANGE);
2552
2553 if(mp_cmp_z(mp) == MP_EQ) {
2554 str[0] = '0';
2555 str[1] = '\0';
2556 } else {
2557 mp_err res;
2558 mp_int tmp;
2559 mp_sign sgn;
2560 mp_digit rem, rdx = (mp_digit)radix;
2561 char ch;
2562
2563 if((res = mp_init_copy(&tmp, mp)) != MP_OKAY)
2564 return res;
2565
2566 /* Save sign for later, and take absolute value */
2567 sgn = SIGN(&tmp); SIGN(&tmp) = MP_ZPOS;
2568
2569 /* Generate output digits in reverse order */
2570 while(mp_cmp_z(&tmp) != 0) {
2571 if((res = s_mp_div_d(&tmp, rdx, &rem)) != MP_OKAY) {
2572 mp_clear(&tmp);
2573 return res;
2574 }
2575
2576 /* Generate digits, use capital letters */
2577 ch = s_mp_todigit(rem, radix, 0);
2578
2579 str[pos++] = ch;
2580 }
2581
2582 /* Add - sign if original value was negative */
2583 if(sgn == MP_NEG)
2584 str[pos++] = '-';
2585
2586 /* Add trailing NUL to end the string */
2587 str[pos--] = '\0';
2588
2589 /* Reverse the digits and sign indicator */
2590 ix = 0;
2591 while(ix < pos) {
2592 char tmp = str[ix];
2593
2594 str[ix] = str[pos];
2595 str[pos] = tmp;
2596 ++ix;
2597 --pos;
2598 }
2599
2600 mp_clear(&tmp);
2601 }
2602
2603 return MP_OKAY;
2604
2605 } /* end mp_toradix() */
2606
2607 /* }}} */
2608
2609 /* {{{ mp_char2value(ch, r) */
2610
mp_char2value(char ch,int r)2611 int mp_char2value(char ch, int r)
2612 {
2613 return s_mp_tovalue(ch, r);
2614
2615 } /* end mp_tovalue() */
2616
2617 /* }}} */
2618
2619 /* }}} */
2620
2621 /* {{{ mp_strerror(ec) */
2622
2623 /*
2624 mp_strerror(ec)
2625
2626 Return a string describing the meaning of error code 'ec'. The
2627 string returned is allocated in static memory, so the caller should
2628 not attempt to modify or free the memory associated with this
2629 string.
2630 */
mp_strerror(mp_err ec)2631 const char *mp_strerror(mp_err ec)
2632 {
2633 int aec = (ec < 0) ? -ec : ec;
2634
2635 /* Code values are negative, so the senses of these comparisons
2636 are accurate */
2637 if(ec < MP_LAST_CODE || ec > MP_OKAY) {
2638 return mp_err_string[0]; /* unknown error code */
2639 } else {
2640 return mp_err_string[aec + 1];
2641 }
2642
2643 } /* end mp_strerror() */
2644
2645 /* }}} */
2646
2647 /*========================================================================*/
2648 /*------------------------------------------------------------------------*/
2649 /* Static function definitions (internal use only) */
2650
2651 /* {{{ Memory management */
2652
2653 /* {{{ s_mp_grow(mp, min) */
2654
2655 /* Make sure there are at least 'min' digits allocated to mp */
s_mp_grow(mp_int * mp,mp_size min)2656 mp_err s_mp_grow(mp_int *mp, mp_size min)
2657 {
2658 if(min > ALLOC(mp)) {
2659 mp_digit *tmp;
2660
2661 /* Set min to next nearest default precision block size */
2662 min = ((min + (s_mp_defprec - 1)) / s_mp_defprec) * s_mp_defprec;
2663
2664 if((tmp = s_mp_alloc(min, sizeof(mp_digit))) == NULL)
2665 return MP_MEM;
2666
2667 s_mp_copy(DIGITS(mp), tmp, USED(mp));
2668
2669 #if MP_CRYPTO
2670 s_mp_setz(DIGITS(mp), ALLOC(mp));
2671 #endif
2672 s_mp_free(DIGITS(mp));
2673 DIGITS(mp) = tmp;
2674 ALLOC(mp) = min;
2675 }
2676
2677 return MP_OKAY;
2678
2679 } /* end s_mp_grow() */
2680
2681 /* }}} */
2682
2683 /* {{{ s_mp_pad(mp, min) */
2684
2685 /* Make sure the used size of mp is at least 'min', growing if needed */
s_mp_pad(mp_int * mp,mp_size min)2686 mp_err s_mp_pad(mp_int *mp, mp_size min)
2687 {
2688 if(min > USED(mp)) {
2689 mp_err res;
2690
2691 /* Make sure there is room to increase precision */
2692 if(min > ALLOC(mp) && (res = s_mp_grow(mp, min)) != MP_OKAY)
2693 return res;
2694
2695 /* Increase precision; should already be 0-filled */
2696 USED(mp) = min;
2697 }
2698
2699 return MP_OKAY;
2700
2701 } /* end s_mp_pad() */
2702
2703 /* }}} */
2704
2705 /* {{{ s_mp_setz(dp, count) */
2706
2707 #if MP_MACRO == 0
2708 /* Set 'count' digits pointed to by dp to be zeroes */
s_mp_setz(mp_digit * dp,mp_size count)2709 void s_mp_setz(mp_digit *dp, mp_size count)
2710 {
2711 #if MP_MEMSET == 0
2712 int ix;
2713
2714 for(ix = 0; ix < count; ix++)
2715 dp[ix] = 0;
2716 #else
2717 memset(dp, 0, count * sizeof(mp_digit));
2718 #endif
2719
2720 } /* end s_mp_setz() */
2721 #endif
2722
2723 /* }}} */
2724
2725 /* {{{ s_mp_copy(sp, dp, count) */
2726
2727 #if MP_MACRO == 0
2728 /* Copy 'count' digits from sp to dp */
s_mp_copy(mp_digit * sp,mp_digit * dp,mp_size count)2729 void s_mp_copy(mp_digit *sp, mp_digit *dp, mp_size count)
2730 {
2731 #if MP_MEMCPY == 0
2732 int ix;
2733
2734 for(ix = 0; ix < count; ix++)
2735 dp[ix] = sp[ix];
2736 #else
2737 memcpy(dp, sp, count * sizeof(mp_digit));
2738 #endif
2739
2740 } /* end s_mp_copy() */
2741 #endif
2742
2743 /* }}} */
2744
2745 /* {{{ s_mp_alloc(nb, ni) */
2746
2747 #if MP_MACRO == 0
2748 /* Allocate ni records of nb bytes each, and return a pointer to that */
s_mp_alloc(size_t nb,size_t ni)2749 void *s_mp_alloc(size_t nb, size_t ni)
2750 {
2751 return calloc(nb, ni);
2752
2753 } /* end s_mp_alloc() */
2754 #endif
2755
2756 /* }}} */
2757
2758 /* {{{ s_mp_free(ptr) */
2759
2760 #if MP_MACRO == 0
2761 /* Free the memory pointed to by ptr */
s_mp_free(void * ptr)2762 void s_mp_free(void *ptr)
2763 {
2764 if(ptr)
2765 free(ptr);
2766
2767 } /* end s_mp_free() */
2768 #endif
2769
2770 /* }}} */
2771
2772 /* {{{ s_mp_clamp(mp) */
2773
2774 /* Remove leading zeroes from the given value */
s_mp_clamp(mp_int * mp)2775 void s_mp_clamp(mp_int *mp)
2776 {
2777 mp_size du = USED(mp);
2778 mp_digit *zp = DIGITS(mp) + du - 1;
2779
2780 while(du > 1 && !*zp--)
2781 --du;
2782
2783 USED(mp) = du;
2784
2785 } /* end s_mp_clamp() */
2786
2787
2788 /* }}} */
2789
2790 /* {{{ s_mp_exch(a, b) */
2791
2792 /* Exchange the data for a and b; (b, a) = (a, b) */
s_mp_exch(mp_int * a,mp_int * b)2793 void s_mp_exch(mp_int *a, mp_int *b)
2794 {
2795 mp_int tmp;
2796
2797 tmp = *a;
2798 *a = *b;
2799 *b = tmp;
2800
2801 } /* end s_mp_exch() */
2802
2803 /* }}} */
2804
2805 /* }}} */
2806
2807 /* {{{ Arithmetic helpers */
2808
2809 /* {{{ s_mp_lshd(mp, p) */
2810
2811 /*
2812 Shift mp leftward by p digits, growing if needed, and zero-filling
2813 the in-shifted digits at the right end. This is a convenient
2814 alternative to multiplication by powers of the radix
2815 */
2816
s_mp_lshd(mp_int * mp,mp_size p)2817 mp_err s_mp_lshd(mp_int *mp, mp_size p)
2818 {
2819 mp_err res;
2820 mp_size pos;
2821 mp_digit *dp;
2822 int ix;
2823
2824 if(p == 0)
2825 return MP_OKAY;
2826
2827 if((res = s_mp_pad(mp, USED(mp) + p)) != MP_OKAY)
2828 return res;
2829
2830 pos = USED(mp) - 1;
2831 dp = DIGITS(mp);
2832
2833 /* Shift all the significant figures over as needed */
2834 for(ix = pos - p; ix >= 0; ix--)
2835 dp[ix + p] = dp[ix];
2836
2837 /* Fill the bottom digits with zeroes */
2838 for(ix = 0; ix < p; ix++)
2839 dp[ix] = 0;
2840
2841 return MP_OKAY;
2842
2843 } /* end s_mp_lshd() */
2844
2845 /* }}} */
2846
2847 /* {{{ s_mp_rshd(mp, p) */
2848
2849 /*
2850 Shift mp rightward by p digits. Maintains the invariant that
2851 digits above the precision are all zero. Digits shifted off the
2852 end are lost. Cannot fail.
2853 */
2854
s_mp_rshd(mp_int * mp,mp_size p)2855 void s_mp_rshd(mp_int *mp, mp_size p)
2856 {
2857 mp_size ix;
2858 mp_digit *dp;
2859
2860 if(p == 0)
2861 return;
2862
2863 /* Shortcut when all digits are to be shifted off */
2864 if(p >= USED(mp)) {
2865 s_mp_setz(DIGITS(mp), ALLOC(mp));
2866 USED(mp) = 1;
2867 SIGN(mp) = MP_ZPOS;
2868 return;
2869 }
2870
2871 /* Shift all the significant figures over as needed */
2872 dp = DIGITS(mp);
2873 for(ix = p; ix < USED(mp); ix++)
2874 dp[ix - p] = dp[ix];
2875
2876 /* Fill the top digits with zeroes */
2877 ix -= p;
2878 while(ix < USED(mp))
2879 dp[ix++] = 0;
2880
2881 /* Strip off any leading zeroes */
2882 s_mp_clamp(mp);
2883
2884 } /* end s_mp_rshd() */
2885
2886 /* }}} */
2887
2888 /* {{{ s_mp_div_2(mp) */
2889
2890 /* Divide by two -- take advantage of radix properties to do it fast */
s_mp_div_2(mp_int * mp)2891 void s_mp_div_2(mp_int *mp)
2892 {
2893 s_mp_div_2d(mp, 1);
2894
2895 } /* end s_mp_div_2() */
2896
2897 /* }}} */
2898
2899 /* {{{ s_mp_mul_2(mp) */
2900
s_mp_mul_2(mp_int * mp)2901 mp_err s_mp_mul_2(mp_int *mp)
2902 {
2903 int ix;
2904 mp_digit kin = 0, kout, *dp = DIGITS(mp);
2905 mp_err res;
2906
2907 /* Shift digits leftward by 1 bit */
2908 for(ix = 0; ix < USED(mp); ix++) {
2909 kout = (dp[ix] >> (DIGIT_BIT - 1)) & 1;
2910 dp[ix] = (dp[ix] << 1) | kin;
2911
2912 kin = kout;
2913 }
2914
2915 /* Deal with rollover from last digit */
2916 if(kin) {
2917 if(ix >= ALLOC(mp)) {
2918 if((res = s_mp_grow(mp, ALLOC(mp) + 1)) != MP_OKAY)
2919 return res;
2920 dp = DIGITS(mp);
2921 }
2922
2923 dp[ix] = kin;
2924 USED(mp) += 1;
2925 }
2926
2927 return MP_OKAY;
2928
2929 } /* end s_mp_mul_2() */
2930
2931 /* }}} */
2932
2933 /* {{{ s_mp_mod_2d(mp, d) */
2934
2935 /*
2936 Remainder the integer by 2^d, where d is a number of bits. This
2937 amounts to a bitwise AND of the value, and does not require the full
2938 division code
2939 */
s_mp_mod_2d(mp_int * mp,mp_digit d)2940 void s_mp_mod_2d(mp_int *mp, mp_digit d)
2941 {
2942 unsigned int ndig = (d / DIGIT_BIT), nbit = (d % DIGIT_BIT);
2943 unsigned int ix;
2944 mp_digit dmask, *dp = DIGITS(mp);
2945
2946 if(ndig >= USED(mp))
2947 return;
2948
2949 /* Flush all the bits above 2^d in its digit */
2950 dmask = (1 << nbit) - 1;
2951 dp[ndig] &= dmask;
2952
2953 /* Flush all digits above the one with 2^d in it */
2954 for(ix = ndig + 1; ix < USED(mp); ix++)
2955 dp[ix] = 0;
2956
2957 s_mp_clamp(mp);
2958
2959 } /* end s_mp_mod_2d() */
2960
2961 /* }}} */
2962
2963 /* {{{ s_mp_mul_2d(mp, d) */
2964
2965 /*
2966 Multiply by the integer 2^d, where d is a number of bits. This
2967 amounts to a bitwise shift of the value, and does not require the
2968 full multiplication code.
2969 */
s_mp_mul_2d(mp_int * mp,mp_digit d)2970 mp_err s_mp_mul_2d(mp_int *mp, mp_digit d)
2971 {
2972 mp_err res;
2973 mp_digit save, next, mask, *dp;
2974 mp_size used;
2975 int ix;
2976
2977 if((res = s_mp_lshd(mp, d / DIGIT_BIT)) != MP_OKAY)
2978 return res;
2979
2980 dp = DIGITS(mp); used = USED(mp);
2981 d %= DIGIT_BIT;
2982
2983 mask = (1 << d) - 1;
2984
2985 /* If the shift requires another digit, make sure we've got one to
2986 work with */
2987 if((dp[used - 1] >> (DIGIT_BIT - d)) & mask) {
2988 if((res = s_mp_grow(mp, used + 1)) != MP_OKAY)
2989 return res;
2990 dp = DIGITS(mp);
2991 }
2992
2993 /* Do the shifting... */
2994 save = 0;
2995 for(ix = 0; ix < used; ix++) {
2996 next = (dp[ix] >> (DIGIT_BIT - d)) & mask;
2997 dp[ix] = (dp[ix] << d) | save;
2998 save = next;
2999 }
3000
3001 /* If, at this point, we have a nonzero carryout into the next
3002 digit, we'll increase the size by one digit, and store it...
3003 */
3004 if(save) {
3005 dp[used] = save;
3006 USED(mp) += 1;
3007 }
3008
3009 s_mp_clamp(mp);
3010 return MP_OKAY;
3011
3012 } /* end s_mp_mul_2d() */
3013
3014 /* }}} */
3015
3016 /* {{{ s_mp_div_2d(mp, d) */
3017
3018 /*
3019 Divide the integer by 2^d, where d is a number of bits. This
3020 amounts to a bitwise shift of the value, and does not require the
3021 full division code (used in Barrett reduction, see below)
3022 */
s_mp_div_2d(mp_int * mp,mp_digit d)3023 void s_mp_div_2d(mp_int *mp, mp_digit d)
3024 {
3025 int ix;
3026 mp_digit save, next, mask, *dp = DIGITS(mp);
3027
3028 s_mp_rshd(mp, d / DIGIT_BIT);
3029 d %= DIGIT_BIT;
3030
3031 mask = (1 << d) - 1;
3032
3033 save = 0;
3034 for(ix = USED(mp) - 1; ix >= 0; ix--) {
3035 next = dp[ix] & mask;
3036 dp[ix] = (dp[ix] >> d) | (save << (DIGIT_BIT - d));
3037 save = next;
3038 }
3039
3040 s_mp_clamp(mp);
3041
3042 } /* end s_mp_div_2d() */
3043
3044 /* }}} */
3045
3046 /* {{{ s_mp_norm(a, b) */
3047
3048 /*
3049 s_mp_norm(a, b)
3050
3051 Normalize a and b for division, where b is the divisor. In order
3052 that we might make good guesses for quotient digits, we want the
3053 leading digit of b to be at least half the radix, which we
3054 accomplish by multiplying a and b by a constant. This constant is
3055 returned (so that it can be divided back out of the remainder at the
3056 end of the division process).
3057
3058 We multiply by the smallest power of 2 that gives us a leading digit
3059 at least half the radix. By choosing a power of 2, we simplify the
3060 multiplication and division steps to simple shifts.
3061 */
s_mp_norm(mp_int * a,mp_int * b)3062 mp_digit s_mp_norm(mp_int *a, mp_int *b)
3063 {
3064 mp_digit t, d = 0;
3065
3066 t = DIGIT(b, USED(b) - 1);
3067 while(t < (RADIX / 2)) {
3068 t <<= 1;
3069 ++d;
3070 }
3071
3072 if(d != 0) {
3073 s_mp_mul_2d(a, d);
3074 s_mp_mul_2d(b, d);
3075 }
3076
3077 return d;
3078
3079 } /* end s_mp_norm() */
3080
3081 /* }}} */
3082
3083 /* }}} */
3084
3085 /* {{{ Primitive digit arithmetic */
3086
3087 /* {{{ s_mp_add_d(mp, d) */
3088
3089 /* Add d to |mp| in place */
s_mp_add_d(mp_int * mp,mp_digit d)3090 mp_err s_mp_add_d(mp_int *mp, mp_digit d) /* unsigned digit addition */
3091 {
3092 mp_word w, k = 0;
3093 mp_size ix = 1, used = USED(mp);
3094 mp_digit *dp = DIGITS(mp);
3095
3096 w = dp[0] + d;
3097 dp[0] = ACCUM(w);
3098 k = CARRYOUT(w);
3099
3100 while(ix < used && k) {
3101 w = dp[ix] + k;
3102 dp[ix] = ACCUM(w);
3103 k = CARRYOUT(w);
3104 ++ix;
3105 }
3106
3107 if(k != 0) {
3108 mp_err res;
3109
3110 if((res = s_mp_pad(mp, USED(mp) + 1)) != MP_OKAY)
3111 return res;
3112
3113 DIGIT(mp, ix) = k;
3114 }
3115
3116 return MP_OKAY;
3117
3118 } /* end s_mp_add_d() */
3119
3120 /* }}} */
3121
3122 /* {{{ s_mp_sub_d(mp, d) */
3123
3124 /* Subtract d from |mp| in place, assumes |mp| > d */
s_mp_sub_d(mp_int * mp,mp_digit d)3125 mp_err s_mp_sub_d(mp_int *mp, mp_digit d) /* unsigned digit subtract */
3126 {
3127 mp_word w, b = 0;
3128 mp_size ix = 1, used = USED(mp);
3129 mp_digit *dp = DIGITS(mp);
3130
3131 /* Compute initial subtraction */
3132 w = (RADIX + dp[0]) - d;
3133 b = CARRYOUT(w) ? 0 : 1;
3134 dp[0] = ACCUM(w);
3135
3136 /* Propagate borrows leftward */
3137 while(b && ix < used) {
3138 w = (RADIX + dp[ix]) - b;
3139 b = CARRYOUT(w) ? 0 : 1;
3140 dp[ix] = ACCUM(w);
3141 ++ix;
3142 }
3143
3144 /* Remove leading zeroes */
3145 s_mp_clamp(mp);
3146
3147 /* If we have a borrow out, it's a violation of the input invariant */
3148 if(b)
3149 return MP_RANGE;
3150 else
3151 return MP_OKAY;
3152
3153 } /* end s_mp_sub_d() */
3154
3155 /* }}} */
3156
3157 /* {{{ s_mp_mul_d(a, d) */
3158
3159 /* Compute a = a * d, single digit multiplication */
s_mp_mul_d(mp_int * a,mp_digit d)3160 mp_err s_mp_mul_d(mp_int *a, mp_digit d)
3161 {
3162 mp_word w, k = 0;
3163 mp_size ix, max;
3164 mp_err res;
3165 mp_digit *dp = DIGITS(a);
3166
3167 /*
3168 Single-digit multiplication will increase the precision of the
3169 output by at most one digit. However, we can detect when this
3170 will happen -- if the high-order digit of a, times d, gives a
3171 two-digit result, then the precision of the result will increase;
3172 otherwise it won't. We use this fact to avoid calling s_mp_pad()
3173 unless absolutely necessary.
3174 */
3175 max = USED(a);
3176 w = dp[max - 1] * d;
3177 if(CARRYOUT(w) != 0) {
3178 if((res = s_mp_pad(a, max + 1)) != MP_OKAY)
3179 return res;
3180 dp = DIGITS(a);
3181 }
3182
3183 for(ix = 0; ix < max; ix++) {
3184 w = (dp[ix] * d) + k;
3185 dp[ix] = ACCUM(w);
3186 k = CARRYOUT(w);
3187 }
3188
3189 /* If there is a precision increase, take care of it here; the above
3190 test guarantees we have enough storage to do this safely.
3191 */
3192 if(k) {
3193 dp[max] = k;
3194 USED(a) = max + 1;
3195 }
3196
3197 s_mp_clamp(a);
3198
3199 return MP_OKAY;
3200
3201 } /* end s_mp_mul_d() */
3202
3203 /* }}} */
3204
3205 /* {{{ s_mp_div_d(mp, d, r) */
3206
3207 /*
3208 s_mp_div_d(mp, d, r)
3209
3210 Compute the quotient mp = mp / d and remainder r = mp mod d, for a
3211 single digit d. If r is null, the remainder will be discarded.
3212 */
3213
s_mp_div_d(mp_int * mp,mp_digit d,mp_digit * r)3214 mp_err s_mp_div_d(mp_int *mp, mp_digit d, mp_digit *r)
3215 {
3216 mp_word w = 0, t;
3217 mp_int quot;
3218 mp_err res;
3219 mp_digit *dp = DIGITS(mp), *qp;
3220 int ix;
3221
3222 if(d == 0)
3223 return MP_RANGE;
3224
3225 /* Make room for the quotient */
3226 if((res = mp_init_size(", USED(mp))) != MP_OKAY)
3227 return res;
3228
3229 USED(") = USED(mp); /* so clamping will work below */
3230 qp = DIGITS(");
3231
3232 /* Divide without subtraction */
3233 for(ix = USED(mp) - 1; ix >= 0; ix--) {
3234 w = (w << DIGIT_BIT) | dp[ix];
3235
3236 if(w >= d) {
3237 t = w / d;
3238 w = w % d;
3239 } else {
3240 t = 0;
3241 }
3242
3243 qp[ix] = t;
3244 }
3245
3246 /* Deliver the remainder, if desired */
3247 if(r)
3248 *r = w;
3249
3250 s_mp_clamp(");
3251 mp_exch(", mp);
3252 mp_clear(");
3253
3254 return MP_OKAY;
3255
3256 } /* end s_mp_div_d() */
3257
3258 /* }}} */
3259
3260 /* }}} */
3261
3262 /* {{{ Primitive full arithmetic */
3263
3264 /* {{{ s_mp_add(a, b) */
3265
3266 /* Compute a = |a| + |b| */
s_mp_add(mp_int * a,mp_int * b)3267 mp_err s_mp_add(mp_int *a, mp_int *b) /* magnitude addition */
3268 {
3269 mp_word w = 0;
3270 mp_digit *pa, *pb;
3271 mp_size ix, used = USED(b);
3272 mp_err res;
3273
3274 /* Make sure a has enough precision for the output value */
3275 if((used > USED(a)) && (res = s_mp_pad(a, used)) != MP_OKAY)
3276 return res;
3277
3278 /*
3279 Add up all digits up to the precision of b. If b had initially
3280 the same precision as a, or greater, we took care of it by the
3281 padding step above, so there is no problem. If b had initially
3282 less precision, we'll have to make sure the carry out is duly
3283 propagated upward among the higher-order digits of the sum.
3284 */
3285 pa = DIGITS(a);
3286 pb = DIGITS(b);
3287 for(ix = 0; ix < used; ++ix) {
3288 w += *pa + *pb++;
3289 *pa++ = ACCUM(w);
3290 w = CARRYOUT(w);
3291 }
3292
3293 /* If we run out of 'b' digits before we're actually done, make
3294 sure the carries get propagated upward...
3295 */
3296 used = USED(a);
3297 while(w && ix < used) {
3298 w += *pa;
3299 *pa++ = ACCUM(w);
3300 w = CARRYOUT(w);
3301 ++ix;
3302 }
3303
3304 /* If there's an overall carry out, increase precision and include
3305 it. We could have done this initially, but why touch the memory
3306 allocator unless we're sure we have to?
3307 */
3308 if(w) {
3309 if((res = s_mp_pad(a, used + 1)) != MP_OKAY)
3310 return res;
3311
3312 DIGIT(a, ix) = w; /* pa may not be valid after s_mp_pad() call */
3313 }
3314
3315 return MP_OKAY;
3316
3317 } /* end s_mp_add() */
3318
3319 /* }}} */
3320
3321 /* {{{ s_mp_sub(a, b) */
3322
3323 /* Compute a = |a| - |b|, assumes |a| >= |b| */
s_mp_sub(mp_int * a,mp_int * b)3324 mp_err s_mp_sub(mp_int *a, mp_int *b) /* magnitude subtract */
3325 {
3326 mp_word w = 0;
3327 mp_digit *pa, *pb;
3328 mp_size ix, used = USED(b);
3329
3330 /*
3331 Subtract and propagate borrow. Up to the precision of b, this
3332 accounts for the digits of b; after that, we just make sure the
3333 carries get to the right place. This saves having to pad b out to
3334 the precision of a just to make the loops work right...
3335 */
3336 pa = DIGITS(a);
3337 pb = DIGITS(b);
3338
3339 for(ix = 0; ix < used; ++ix) {
3340 w = (RADIX + *pa) - w - *pb++;
3341 *pa++ = ACCUM(w);
3342 w = CARRYOUT(w) ? 0 : 1;
3343 }
3344
3345 used = USED(a);
3346 while(ix < used) {
3347 w = RADIX + *pa - w;
3348 *pa++ = ACCUM(w);
3349 w = CARRYOUT(w) ? 0 : 1;
3350 ++ix;
3351 }
3352
3353 /* Clobber any leading zeroes we created */
3354 s_mp_clamp(a);
3355
3356 /*
3357 If there was a borrow out, then |b| > |a| in violation
3358 of our input invariant. We've already done the work,
3359 but we'll at least complain about it...
3360 */
3361 if(w)
3362 return MP_RANGE;
3363 else
3364 return MP_OKAY;
3365
3366 } /* end s_mp_sub() */
3367
3368 /* }}} */
3369
s_mp_reduce(mp_int * x,mp_int * m,mp_int * mu)3370 mp_err s_mp_reduce(mp_int *x, mp_int *m, mp_int *mu)
3371 {
3372 mp_int q;
3373 mp_err res;
3374 mp_size um = USED(m);
3375
3376 if((res = mp_init_copy(&q, x)) != MP_OKAY)
3377 return res;
3378
3379 s_mp_rshd(&q, um - 1); /* q1 = x / b^(k-1) */
3380 s_mp_mul(&q, mu); /* q2 = q1 * mu */
3381 s_mp_rshd(&q, um + 1); /* q3 = q2 / b^(k+1) */
3382
3383 /* x = x mod b^(k+1), quick (no division) */
3384 s_mp_mod_2d(x, (mp_digit)(DIGIT_BIT * (um + 1)));
3385
3386 /* q = q * m mod b^(k+1), quick (no division), uses the short multiplier */
3387 #ifndef SHRT_MUL
3388 s_mp_mul(&q, m);
3389 s_mp_mod_2d(&q, (mp_digit)(DIGIT_BIT * (um + 1)));
3390 #else
3391 s_mp_mul_dig(&q, m, um + 1);
3392 #endif
3393
3394 /* x = x - q */
3395 if((res = mp_sub(x, &q, x)) != MP_OKAY)
3396 goto CLEANUP;
3397
3398 /* If x < 0, add b^(k+1) to it */
3399 if(mp_cmp_z(x) < 0) {
3400 mp_set(&q, 1);
3401 if((res = s_mp_lshd(&q, um + 1)) != MP_OKAY)
3402 goto CLEANUP;
3403 if((res = mp_add(x, &q, x)) != MP_OKAY)
3404 goto CLEANUP;
3405 }
3406
3407 /* Back off if it's too big */
3408 while(mp_cmp(x, m) >= 0) {
3409 if((res = s_mp_sub(x, m)) != MP_OKAY)
3410 break;
3411 }
3412
3413 CLEANUP:
3414 mp_clear(&q);
3415
3416 return res;
3417
3418 } /* end s_mp_reduce() */
3419
3420
3421
3422 /* {{{ s_mp_mul(a, b) */
3423
3424 /* Compute a = |a| * |b| */
s_mp_mul(mp_int * a,mp_int * b)3425 mp_err s_mp_mul(mp_int *a, mp_int *b)
3426 {
3427 mp_word w, k = 0;
3428 mp_int tmp;
3429 mp_err res;
3430 mp_size ix, jx, ua = USED(a), ub = USED(b);
3431 mp_digit *pa, *pb, *pt, *pbt;
3432
3433 if((res = mp_init_size(&tmp, ua + ub)) != MP_OKAY)
3434 return res;
3435
3436 /* This has the effect of left-padding with zeroes... */
3437 USED(&tmp) = ua + ub;
3438
3439 /* We're going to need the base value each iteration */
3440 pbt = DIGITS(&tmp);
3441
3442 /* Outer loop: Digits of b */
3443
3444 pb = DIGITS(b);
3445 for(ix = 0; ix < ub; ++ix, ++pb) {
3446 if(*pb == 0)
3447 continue;
3448
3449 /* Inner product: Digits of a */
3450 pa = DIGITS(a);
3451 for(jx = 0; jx < ua; ++jx, ++pa) {
3452 pt = pbt + ix + jx;
3453 w = *pb * *pa + k + *pt;
3454 *pt = ACCUM(w);
3455 k = CARRYOUT(w);
3456 }
3457
3458 pbt[ix + jx] = k;
3459 k = 0;
3460 }
3461
3462 s_mp_clamp(&tmp);
3463 s_mp_exch(&tmp, a);
3464
3465 mp_clear(&tmp);
3466
3467 return MP_OKAY;
3468
3469 } /* end s_mp_mul() */
3470
3471 /* }}} */
3472
3473 /* {{{ s_mp_kmul(a, b, out, len) */
3474
3475 #if 0
3476 void s_mp_kmul(mp_digit *a, mp_digit *b, mp_digit *out, mp_size len)
3477 {
3478 mp_word w, k = 0;
3479 mp_size ix, jx;
3480 mp_digit *pa, *pt;
3481
3482 for(ix = 0; ix < len; ++ix, ++b) {
3483 if(*b == 0)
3484 continue;
3485
3486 pa = a;
3487 for(jx = 0; jx < len; ++jx, ++pa) {
3488 pt = out + ix + jx;
3489 w = *b * *pa + k + *pt;
3490 *pt = ACCUM(w);
3491 k = CARRYOUT(w);
3492 }
3493
3494 out[ix + jx] = k;
3495 k = 0;
3496 }
3497
3498 } /* end s_mp_kmul() */
3499 #endif
3500
3501 /* }}} */
3502
3503 /* {{{ s_mp_sqr(a) */
3504
3505 /*
3506 Computes the square of a, in place. This can be done more
3507 efficiently than a general multiplication, because many of the
3508 computation steps are redundant when squaring. The inner product
3509 step is a bit more complicated, but we save a fair number of
3510 iterations of the multiplication loop.
3511 */
3512 #if MP_SQUARE
s_mp_sqr(mp_int * a)3513 mp_err s_mp_sqr(mp_int *a)
3514 {
3515 mp_word w, k = 0;
3516 mp_int tmp;
3517 mp_err res;
3518 mp_size ix, jx, kx, used = USED(a);
3519 mp_digit *pa1, *pa2, *pt, *pbt;
3520
3521 if((res = mp_init_size(&tmp, 2 * used)) != MP_OKAY)
3522 return res;
3523
3524 /* Left-pad with zeroes */
3525 USED(&tmp) = 2 * used;
3526
3527 /* We need the base value each time through the loop */
3528 pbt = DIGITS(&tmp);
3529
3530 pa1 = DIGITS(a);
3531 for(ix = 0; ix < used; ++ix, ++pa1) {
3532 if(*pa1 == 0)
3533 continue;
3534
3535 w = DIGIT(&tmp, ix + ix) + (*pa1 * *pa1);
3536
3537 pbt[ix + ix] = ACCUM(w);
3538 k = CARRYOUT(w);
3539
3540 /*
3541 The inner product is computed as:
3542
3543 (C, S) = t[i,j] + 2 a[i] a[j] + C
3544
3545 This can overflow what can be represented in an mp_word, and
3546 since C arithmetic does not provide any way to check for
3547 overflow, we have to check explicitly for overflow conditions
3548 before they happen.
3549 */
3550 for(jx = ix + 1, pa2 = DIGITS(a) + jx; jx < used; ++jx, ++pa2) {
3551 mp_word u = 0, v;
3552
3553 /* Store this in a temporary to avoid indirections later */
3554 pt = pbt + ix + jx;
3555
3556 /* Compute the multiplicative step */
3557 w = *pa1 * *pa2;
3558
3559 /* If w is more than half MP_WORD_MAX, the doubling will
3560 overflow, and we need to record a carry out into the next
3561 word */
3562 u = (w >> (MP_WORD_BIT - 1)) & 1;
3563
3564 /* Double what we've got, overflow will be ignored as defined
3565 for C arithmetic (we've already noted if it is to occur)
3566 */
3567 w *= 2;
3568
3569 /* Compute the additive step */
3570 v = *pt + k;
3571
3572 /* If we do not already have an overflow carry, check to see
3573 if the addition will cause one, and set the carry out if so
3574 */
3575 u |= ((MP_WORD_MAX - v) < w);
3576
3577 /* Add in the rest, again ignoring overflow */
3578 w += v;
3579
3580 /* Set the i,j digit of the output */
3581 *pt = ACCUM(w);
3582
3583 /* Save carry information for the next iteration of the loop.
3584 This is why k must be an mp_word, instead of an mp_digit */
3585 k = CARRYOUT(w) | (u << DIGIT_BIT);
3586
3587 } /* for(jx ...) */
3588
3589 /* Set the last digit in the cycle and reset the carry */
3590 k = DIGIT(&tmp, ix + jx) + k;
3591 pbt[ix + jx] = ACCUM(k);
3592 k = CARRYOUT(k);
3593
3594 /* If we are carrying out, propagate the carry to the next digit
3595 in the output. This may cascade, so we have to be somewhat
3596 circumspect -- but we will have enough precision in the output
3597 that we won't overflow
3598 */
3599 kx = 1;
3600 while(k) {
3601 k = pbt[ix + jx + kx] + 1;
3602 pbt[ix + jx + kx] = ACCUM(k);
3603 k = CARRYOUT(k);
3604 ++kx;
3605 }
3606 } /* for(ix ...) */
3607
3608 s_mp_clamp(&tmp);
3609 s_mp_exch(&tmp, a);
3610
3611 mp_clear(&tmp);
3612
3613 return MP_OKAY;
3614
3615 } /* end s_mp_sqr() */
3616 #endif
3617
3618 /* }}} */
3619
3620 /* {{{ s_mp_div(a, b) */
3621
3622 /*
3623 s_mp_div(a, b)
3624
3625 Compute a = a / b and b = a mod b. Assumes b > a.
3626 */
3627
s_mp_div(mp_int * a,mp_int * b)3628 mp_err s_mp_div(mp_int *a, mp_int *b)
3629 {
3630 mp_int quot, rem, t;
3631 mp_word q;
3632 mp_err res;
3633 mp_digit d;
3634 int ix;
3635
3636 if(mp_cmp_z(b) == 0)
3637 return MP_RANGE;
3638
3639 /* Shortcut if b is power of two */
3640 if((ix = s_mp_ispow2(b)) >= 0) {
3641 mp_copy(a, b); /* need this for remainder */
3642 s_mp_div_2d(a, (mp_digit)ix);
3643 s_mp_mod_2d(b, (mp_digit)ix);
3644
3645 return MP_OKAY;
3646 }
3647
3648 /* Allocate space to store the quotient */
3649 if((res = mp_init_size(", USED(a))) != MP_OKAY)
3650 return res;
3651
3652 /* A working temporary for division */
3653 if((res = mp_init_size(&t, USED(a))) != MP_OKAY)
3654 goto T;
3655
3656 /* Allocate space for the remainder */
3657 if((res = mp_init_size(&rem, USED(a))) != MP_OKAY)
3658 goto REM;
3659
3660 /* Normalize to optimize guessing */
3661 d = s_mp_norm(a, b);
3662
3663 /* Perform the division itself...woo! */
3664 ix = USED(a) - 1;
3665
3666 while(ix >= 0) {
3667 /* Find a partial substring of a which is at least b */
3668 while(s_mp_cmp(&rem, b) < 0 && ix >= 0) {
3669 if((res = s_mp_lshd(&rem, 1)) != MP_OKAY)
3670 goto CLEANUP;
3671
3672 if((res = s_mp_lshd(", 1)) != MP_OKAY)
3673 goto CLEANUP;
3674
3675 DIGIT(&rem, 0) = DIGIT(a, ix);
3676 s_mp_clamp(&rem);
3677 --ix;
3678 }
3679
3680 /* If we didn't find one, we're finished dividing */
3681 if(s_mp_cmp(&rem, b) < 0)
3682 break;
3683
3684 /* Compute a guess for the next quotient digit */
3685 q = DIGIT(&rem, USED(&rem) - 1);
3686 if(q <= DIGIT(b, USED(b) - 1) && USED(&rem) > 1)
3687 q = (q << DIGIT_BIT) | DIGIT(&rem, USED(&rem) - 2);
3688
3689 q /= DIGIT(b, USED(b) - 1);
3690
3691 /* The guess can be as much as RADIX + 1 */
3692 if(q >= RADIX)
3693 q = RADIX - 1;
3694
3695 /* See what that multiplies out to */
3696 mp_copy(b, &t);
3697 if((res = s_mp_mul_d(&t, q)) != MP_OKAY)
3698 goto CLEANUP;
3699
3700 /*
3701 If it's too big, back it off. We should not have to do this
3702 more than once, or, in rare cases, twice. Knuth describes a
3703 method by which this could be reduced to a maximum of once, but
3704 I didn't implement that here.
3705 */
3706 while(s_mp_cmp(&t, &rem) > 0) {
3707 --q;
3708 s_mp_sub(&t, b);
3709 }
3710
3711 /* At this point, q should be the right next digit */
3712 if((res = s_mp_sub(&rem, &t)) != MP_OKAY)
3713 goto CLEANUP;
3714
3715 /*
3716 Include the digit in the quotient. We allocated enough memory
3717 for any quotient we could ever possibly get, so we should not
3718 have to check for failures here
3719 */
3720 DIGIT(", 0) = q;
3721 }
3722
3723 /* Denormalize remainder */
3724 if(d != 0)
3725 s_mp_div_2d(&rem, d);
3726
3727 s_mp_clamp(");
3728 s_mp_clamp(&rem);
3729
3730 /* Copy quotient back to output */
3731 s_mp_exch(", a);
3732
3733 /* Copy remainder back to output */
3734 s_mp_exch(&rem, b);
3735
3736 CLEANUP:
3737 mp_clear(&rem);
3738 REM:
3739 mp_clear(&t);
3740 T:
3741 mp_clear(");
3742
3743 return res;
3744
3745 } /* end s_mp_div() */
3746
3747 /* }}} */
3748
3749 /* {{{ s_mp_2expt(a, k) */
3750
s_mp_2expt(mp_int * a,mp_digit k)3751 mp_err s_mp_2expt(mp_int *a, mp_digit k)
3752 {
3753 mp_err res;
3754 mp_size dig, bit;
3755
3756 dig = k / DIGIT_BIT;
3757 bit = k % DIGIT_BIT;
3758
3759 mp_zero(a);
3760 if((res = s_mp_pad(a, dig + 1)) != MP_OKAY)
3761 return res;
3762
3763 DIGIT(a, dig) |= (1 << bit);
3764
3765 return MP_OKAY;
3766
3767 } /* end s_mp_2expt() */
3768
3769 /* }}} */
3770
3771
3772 /* }}} */
3773
3774 /* }}} */
3775
3776 /* {{{ Primitive comparisons */
3777
3778 /* {{{ s_mp_cmp(a, b) */
3779
3780 /* Compare |a| <=> |b|, return 0 if equal, <0 if a<b, >0 if a>b */
s_mp_cmp(mp_int * a,mp_int * b)3781 int s_mp_cmp(mp_int *a, mp_int *b)
3782 {
3783 mp_size ua = USED(a), ub = USED(b);
3784
3785 if(ua > ub)
3786 return MP_GT;
3787 else if(ua < ub)
3788 return MP_LT;
3789 else {
3790 int ix = ua - 1;
3791 mp_digit *ap = DIGITS(a) + ix, *bp = DIGITS(b) + ix;
3792
3793 while(ix >= 0) {
3794 if(*ap > *bp)
3795 return MP_GT;
3796 else if(*ap < *bp)
3797 return MP_LT;
3798
3799 --ap; --bp; --ix;
3800 }
3801
3802 return MP_EQ;
3803 }
3804
3805 } /* end s_mp_cmp() */
3806
3807 /* }}} */
3808
3809 /* {{{ s_mp_cmp_d(a, d) */
3810
3811 /* Compare |a| <=> d, return 0 if equal, <0 if a<d, >0 if a>d */
s_mp_cmp_d(mp_int * a,mp_digit d)3812 int s_mp_cmp_d(mp_int *a, mp_digit d)
3813 {
3814 mp_size ua = USED(a);
3815 mp_digit *ap = DIGITS(a);
3816
3817 if(ua > 1)
3818 return MP_GT;
3819
3820 if(*ap < d)
3821 return MP_LT;
3822 else if(*ap > d)
3823 return MP_GT;
3824 else
3825 return MP_EQ;
3826
3827 } /* end s_mp_cmp_d() */
3828
3829 /* }}} */
3830
3831 /* {{{ s_mp_ispow2(v) */
3832
3833 /*
3834 Returns -1 if the value is not a power of two; otherwise, it returns
3835 k such that v = 2^k, i.e. lg(v).
3836 */
s_mp_ispow2(mp_int * v)3837 int s_mp_ispow2(mp_int *v)
3838 {
3839 mp_digit d, *dp;
3840 mp_size uv = USED(v);
3841 int extra = 0, ix;
3842
3843 d = DIGIT(v, uv - 1); /* most significant digit of v */
3844
3845 while(d && ((d & 1) == 0)) {
3846 d >>= 1;
3847 ++extra;
3848 }
3849
3850 if(d == 1) {
3851 ix = uv - 2;
3852 dp = DIGITS(v) + ix;
3853
3854 while(ix >= 0) {
3855 if(*dp)
3856 return -1; /* not a power of two */
3857
3858 --dp; --ix;
3859 }
3860
3861 return ((uv - 1) * DIGIT_BIT) + extra;
3862 }
3863
3864 return -1;
3865
3866 } /* end s_mp_ispow2() */
3867
3868 /* }}} */
3869
3870 /* {{{ s_mp_ispow2d(d) */
3871
s_mp_ispow2d(mp_digit d)3872 int s_mp_ispow2d(mp_digit d)
3873 {
3874 int pow = 0;
3875
3876 while((d & 1) == 0) {
3877 ++pow; d >>= 1;
3878 }
3879
3880 if(d == 1)
3881 return pow;
3882
3883 return -1;
3884
3885 } /* end s_mp_ispow2d() */
3886
3887 /* }}} */
3888
3889 /* }}} */
3890
3891 /* {{{ Primitive I/O helpers */
3892
3893 /* {{{ s_mp_tovalue(ch, r) */
3894
3895 /*
3896 Convert the given character to its digit value, in the given radix.
3897 If the given character is not understood in the given radix, -1 is
3898 returned. Otherwise the digit's numeric value is returned.
3899
3900 The results will be odd if you use a radix < 2 or > 62, you are
3901 expected to know what you're up to.
3902 */
s_mp_tovalue(char ch,int r)3903 int s_mp_tovalue(char ch, int r)
3904 {
3905 int val, xch;
3906
3907 if(r > 36)
3908 xch = ch;
3909 else
3910 xch = toupper(ch);
3911
3912 if(isdigit(xch))
3913 val = xch - '0';
3914 else if(isupper(xch))
3915 val = xch - 'A' + 10;
3916 else if(islower(xch))
3917 val = xch - 'a' + 36;
3918 else if(xch == '+')
3919 val = 62;
3920 else if(xch == '/')
3921 val = 63;
3922 else
3923 return -1;
3924
3925 if(val < 0 || val >= r)
3926 return -1;
3927
3928 return val;
3929
3930 } /* end s_mp_tovalue() */
3931
3932 /* }}} */
3933
3934 /* {{{ s_mp_todigit(val, r, low) */
3935
3936 /*
3937 Convert val to a radix-r digit, if possible. If val is out of range
3938 for r, returns zero. Otherwise, returns an ASCII character denoting
3939 the value in the given radix.
3940
3941 The results may be odd if you use a radix < 2 or > 64, you are
3942 expected to know what you're doing.
3943 */
3944
s_mp_todigit(int val,int r,int low)3945 char s_mp_todigit(int val, int r, int low)
3946 {
3947 char ch;
3948
3949 if(val < 0 || val >= r)
3950 return 0;
3951
3952 ch = s_dmap_1[val];
3953
3954 if(r <= 36 && low)
3955 ch = tolower(ch);
3956
3957 return ch;
3958
3959 } /* end s_mp_todigit() */
3960
3961 /* }}} */
3962
3963 /* {{{ s_mp_outlen(bits, radix) */
3964
3965 /*
3966 Return an estimate for how long a string is needed to hold a radix
3967 r representation of a number with 'bits' significant bits.
3968
3969 Does not include space for a sign or a NUL terminator.
3970 */
s_mp_outlen(int bits,int r)3971 int s_mp_outlen(int bits, int r)
3972 {
3973 return (int)((double)bits * LOG_V_2(r));
3974
3975 } /* end s_mp_outlen() */
3976
3977 /* }}} */
3978
3979 /* }}} */
3980
3981 /*------------------------------------------------------------------------*/
3982 /* HERE THERE BE DRAGONS */
3983 /* crc==4242132123, version==2, Sat Feb 02 06:43:52 2002 */
3984
3985 /* Source: /cvs/libtom/libtommath/mtest/mpi.c,v */
3986 /* Revision: 1.2 */
3987 /* Date: 2005/05/05 14:38:47 */
3988