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1/* crypto/bn/bn_mul.c */
2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58
59#ifndef BN_DEBUG
60# undef NDEBUG /* avoid conflicting definitions */
61# define NDEBUG
62#endif
63
64#include <stdio.h>
65#include <assert.h>
66#include "cryptlib.h"
67#include "bn_lcl.h"
68
69#if defined(OPENSSL_NO_ASM) || !(defined(__i386) || defined(__i386__)) || defined(__DJGPP__) /* Assembler implementation exists only for x86 */
70/* Here follows specialised variants of bn_add_words() and
71 bn_sub_words(). They have the property performing operations on
72 arrays of different sizes. The sizes of those arrays is expressed through
73 cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
74 which is the delta between the two lengths, calculated as len(a)-len(b).
75 All lengths are the number of BN_ULONGs... For the operations that require
76 a result array as parameter, it must have the length cl+abs(dl).
77 These functions should probably end up in bn_asm.c as soon as there are
78 assembler counterparts for the systems that use assembler files. */
79
80BN_ULONG bn_sub_part_words(BN_ULONG *r,
81 const BN_ULONG *a, const BN_ULONG *b,
82 int cl, int dl)
83 {
84 BN_ULONG c, t;
85
86 assert(cl >= 0);
87 c = bn_sub_words(r, a, b, cl);
88
89 if (dl == 0)
90 return c;
91
92 r += cl;
93 a += cl;
94 b += cl;
95
96 if (dl < 0)
97 {
98#ifdef BN_COUNT
99 fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
100#endif
101 for (;;)
102 {
103 t = b[0];
104 r[0] = (0-t-c)&BN_MASK2;
105 if (t != 0) c=1;
106 if (++dl >= 0) break;
107
108 t = b[1];
109 r[1] = (0-t-c)&BN_MASK2;
110 if (t != 0) c=1;
111 if (++dl >= 0) break;
112
113 t = b[2];
114 r[2] = (0-t-c)&BN_MASK2;
115 if (t != 0) c=1;
116 if (++dl >= 0) break;
117
118 t = b[3];
119 r[3] = (0-t-c)&BN_MASK2;
120 if (t != 0) c=1;
121 if (++dl >= 0) break;
122
123 b += 4;
124 r += 4;
125 }
126 }
127 else
128 {
129 int save_dl = dl;
130#ifdef BN_COUNT
131 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
132#endif
133 while(c)
134 {
135 t = a[0];
136 r[0] = (t-c)&BN_MASK2;
137 if (t != 0) c=0;
138 if (--dl <= 0) break;
139
140 t = a[1];
141 r[1] = (t-c)&BN_MASK2;
142 if (t != 0) c=0;
143 if (--dl <= 0) break;
144
145 t = a[2];
146 r[2] = (t-c)&BN_MASK2;
147 if (t != 0) c=0;
148 if (--dl <= 0) break;
149
150 t = a[3];
151 r[3] = (t-c)&BN_MASK2;
152 if (t != 0) c=0;
153 if (--dl <= 0) break;
154
155 save_dl = dl;
156 a += 4;
157 r += 4;
158 }
159 if (dl > 0)
160 {
161#ifdef BN_COUNT
162 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
163#endif
164 if (save_dl > dl)
165 {
166 switch (save_dl - dl)
167 {
168 case 1:
169 r[1] = a[1];
170 if (--dl <= 0) break;
171 case 2:
172 r[2] = a[2];
173 if (--dl <= 0) break;
174 case 3:
175 r[3] = a[3];
176 if (--dl <= 0) break;
177 }
178 a += 4;
179 r += 4;
180 }
181 }
182 if (dl > 0)
183 {
184#ifdef BN_COUNT
185 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
186#endif
187 for(;;)
188 {
189 r[0] = a[0];
190 if (--dl <= 0) break;
191 r[1] = a[1];
192 if (--dl <= 0) break;
193 r[2] = a[2];
194 if (--dl <= 0) break;
195 r[3] = a[3];
196 if (--dl <= 0) break;
197
198 a += 4;
199 r += 4;
200 }
201 }
202 }
203 return c;
204 }
205#endif
206
207BN_ULONG bn_add_part_words(BN_ULONG *r,
208 const BN_ULONG *a, const BN_ULONG *b,
209 int cl, int dl)
210 {
211 BN_ULONG c, l, t;
212
213 assert(cl >= 0);
214 c = bn_add_words(r, a, b, cl);
215
216 if (dl == 0)
217 return c;
218
219 r += cl;
220 a += cl;
221 b += cl;
222
223 if (dl < 0)
224 {
225 int save_dl = dl;
226#ifdef BN_COUNT
227 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
228#endif
229 while (c)
230 {
231 l=(c+b[0])&BN_MASK2;
232 c=(l < c);
233 r[0]=l;
234 if (++dl >= 0) break;
235
236 l=(c+b[1])&BN_MASK2;
237 c=(l < c);
238 r[1]=l;
239 if (++dl >= 0) break;
240
241 l=(c+b[2])&BN_MASK2;
242 c=(l < c);
243 r[2]=l;
244 if (++dl >= 0) break;
245
246 l=(c+b[3])&BN_MASK2;
247 c=(l < c);
248 r[3]=l;
249 if (++dl >= 0) break;
250
251 save_dl = dl;
252 b+=4;
253 r+=4;
254 }
255 if (dl < 0)
256 {
257#ifdef BN_COUNT
258 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
259#endif
260 if (save_dl < dl)
261 {
262 switch (dl - save_dl)
263 {
264 case 1:
265 r[1] = b[1];
266 if (++dl >= 0) break;
267 case 2:
268 r[2] = b[2];
269 if (++dl >= 0) break;
270 case 3:
271 r[3] = b[3];
272 if (++dl >= 0) break;
273 }
274 b += 4;
275 r += 4;
276 }
277 }
278 if (dl < 0)
279 {
280#ifdef BN_COUNT
281 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
282#endif
283 for(;;)
284 {
285 r[0] = b[0];
286 if (++dl >= 0) break;
287 r[1] = b[1];
288 if (++dl >= 0) break;
289 r[2] = b[2];
290 if (++dl >= 0) break;
291 r[3] = b[3];
292 if (++dl >= 0) break;
293
294 b += 4;
295 r += 4;
296 }
297 }
298 }
299 else
300 {
301 int save_dl = dl;
302#ifdef BN_COUNT
303 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
304#endif
305 while (c)
306 {
307 t=(a[0]+c)&BN_MASK2;
308 c=(t < c);
309 r[0]=t;
310 if (--dl <= 0) break;
311
312 t=(a[1]+c)&BN_MASK2;
313 c=(t < c);
314 r[1]=t;
315 if (--dl <= 0) break;
316
317 t=(a[2]+c)&BN_MASK2;
318 c=(t < c);
319 r[2]=t;
320 if (--dl <= 0) break;
321
322 t=(a[3]+c)&BN_MASK2;
323 c=(t < c);
324 r[3]=t;
325 if (--dl <= 0) break;
326
327 save_dl = dl;
328 a+=4;
329 r+=4;
330 }
331#ifdef BN_COUNT
332 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
333#endif
334 if (dl > 0)
335 {
336 if (save_dl > dl)
337 {
338 switch (save_dl - dl)
339 {
340 case 1:
341 r[1] = a[1];
342 if (--dl <= 0) break;
343 case 2:
344 r[2] = a[2];
345 if (--dl <= 0) break;
346 case 3:
347 r[3] = a[3];
348 if (--dl <= 0) break;
349 }
350 a += 4;
351 r += 4;
352 }
353 }
354 if (dl > 0)
355 {
356#ifdef BN_COUNT
357 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
358#endif
359 for(;;)
360 {
361 r[0] = a[0];
362 if (--dl <= 0) break;
363 r[1] = a[1];
364 if (--dl <= 0) break;
365 r[2] = a[2];
366 if (--dl <= 0) break;
367 r[3] = a[3];
368 if (--dl <= 0) break;
369
370 a += 4;
371 r += 4;
372 }
373 }
374 }
375 return c;
376 }
377
378#ifdef BN_RECURSION
379/* Karatsuba recursive multiplication algorithm
380 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
381
382/* r is 2*n2 words in size,
383 * a and b are both n2 words in size.
384 * n2 must be a power of 2.
385 * We multiply and return the result.
386 * t must be 2*n2 words in size
387 * We calculate
388 * a[0]*b[0]
389 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
390 * a[1]*b[1]
391 */
392void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
393 int dna, int dnb, BN_ULONG *t)
394 {
395 int n=n2/2,c1,c2;
396 int tna=n+dna, tnb=n+dnb;
397 unsigned int neg,zero;
398 BN_ULONG ln,lo,*p;
399
400# ifdef BN_COUNT
401 fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
402# endif
403# ifdef BN_MUL_COMBA
404# if 0
405 if (n2 == 4)
406 {
407 bn_mul_comba4(r,a,b);
408 return;
409 }
410# endif
411 /* Only call bn_mul_comba 8 if n2 == 8 and the
412 * two arrays are complete [steve]
413 */
414 if (n2 == 8 && dna == 0 && dnb == 0)
415 {
416 bn_mul_comba8(r,a,b);
417 return;
418 }
419# endif /* BN_MUL_COMBA */
420 /* Else do normal multiply */
421 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
422 {
423 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
424 if ((dna + dnb) < 0)
425 memset(&r[2*n2 + dna + dnb], 0,
426 sizeof(BN_ULONG) * -(dna + dnb));
427 return;
428 }
429 /* r=(a[0]-a[1])*(b[1]-b[0]) */
430 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
431 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
432 zero=neg=0;
433 switch (c1*3+c2)
434 {
435 case -4:
436 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
437 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
438 break;
439 case -3:
440 zero=1;
441 break;
442 case -2:
443 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
444 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
445 neg=1;
446 break;
447 case -1:
448 case 0:
449 case 1:
450 zero=1;
451 break;
452 case 2:
453 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
454 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
455 neg=1;
456 break;
457 case 3:
458 zero=1;
459 break;
460 case 4:
461 bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
462 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
463 break;
464 }
465
466# ifdef BN_MUL_COMBA
467 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
468 extra args to do this well */
469 {
470 if (!zero)
471 bn_mul_comba4(&(t[n2]),t,&(t[n]));
472 else
473 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
474
475 bn_mul_comba4(r,a,b);
476 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
477 }
478 else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
479 take extra args to do this
480 well */
481 {
482 if (!zero)
483 bn_mul_comba8(&(t[n2]),t,&(t[n]));
484 else
485 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
486
487 bn_mul_comba8(r,a,b);
488 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
489 }
490 else
491# endif /* BN_MUL_COMBA */
492 {
493 p= &(t[n2*2]);
494 if (!zero)
495 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
496 else
497 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
498 bn_mul_recursive(r,a,b,n,0,0,p);
499 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
500 }
501
502 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
503 * r[10] holds (a[0]*b[0])
504 * r[32] holds (b[1]*b[1])
505 */
506
507 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
508
509 if (neg) /* if t[32] is negative */
510 {
511 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
512 }
513 else
514 {
515 /* Might have a carry */
516 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
517 }
518
519 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
520 * r[10] holds (a[0]*b[0])
521 * r[32] holds (b[1]*b[1])
522 * c1 holds the carry bits
523 */
524 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
525 if (c1)
526 {
527 p= &(r[n+n2]);
528 lo= *p;
529 ln=(lo+c1)&BN_MASK2;
530 *p=ln;
531
532 /* The overflow will stop before we over write
533 * words we should not overwrite */
534 if (ln < (BN_ULONG)c1)
535 {
536 do {
537 p++;
538 lo= *p;
539 ln=(lo+1)&BN_MASK2;
540 *p=ln;
541 } while (ln == 0);
542 }
543 }
544 }
545
546/* n+tn is the word length
547 * t needs to be n*4 is size, as does r */
548void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
549 int tna, int tnb, BN_ULONG *t)
550 {
551 int i,j,n2=n*2;
552 unsigned int c1,c2,neg,zero;
553 BN_ULONG ln,lo,*p;
554
555# ifdef BN_COUNT
556 fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
557 tna, n, tnb, n);
558# endif
559 if (n < 8)
560 {
561 bn_mul_normal(r,a,n+tna,b,n+tnb);
562 return;
563 }
564
565 /* r=(a[0]-a[1])*(b[1]-b[0]) */
566 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
567 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
568 zero=neg=0;
569 switch (c1*3+c2)
570 {
571 case -4:
572 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
573 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
574 break;
575 case -3:
576 zero=1;
577 /* break; */
578 case -2:
579 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
580 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
581 neg=1;
582 break;
583 case -1:
584 case 0:
585 case 1:
586 zero=1;
587 /* break; */
588 case 2:
589 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
590 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
591 neg=1;
592 break;
593 case 3:
594 zero=1;
595 /* break; */
596 case 4:
597 bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
598 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
599 break;
600 }
601 /* The zero case isn't yet implemented here. The speedup
602 would probably be negligible. */
603# if 0
604 if (n == 4)
605 {
606 bn_mul_comba4(&(t[n2]),t,&(t[n]));
607 bn_mul_comba4(r,a,b);
608 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
609 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
610 }
611 else
612# endif
613 if (n == 8)
614 {
615 bn_mul_comba8(&(t[n2]),t,&(t[n]));
616 bn_mul_comba8(r,a,b);
617 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
618 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
619 }
620 else
621 {
622 p= &(t[n2*2]);
623 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
624 bn_mul_recursive(r,a,b,n,0,0,p);
625 i=n/2;
626 /* If there is only a bottom half to the number,
627 * just do it */
628 if (tna > tnb)
629 j = tna - i;
630 else
631 j = tnb - i;
632 if (j == 0)
633 {
634 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
635 i,tna-i,tnb-i,p);
636 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
637 }
638 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
639 {
640 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
641 i,tna-i,tnb-i,p);
642 memset(&(r[n2+tna+tnb]),0,
643 sizeof(BN_ULONG)*(n2-tna-tnb));
644 }
645 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
646 {
647 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
648 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
649 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
650 {
651 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
652 }
653 else
654 {
655 for (;;)
656 {
657 i/=2;
658 if (i < tna && i < tnb)
659 {
660 bn_mul_part_recursive(&(r[n2]),
661 &(a[n]),&(b[n]),
662 i,tna-i,tnb-i,p);
663 break;
664 }
665 else if (i <= tna && i <= tnb)
666 {
667 bn_mul_recursive(&(r[n2]),
668 &(a[n]),&(b[n]),
669 i,tna-i,tnb-i,p);
670 break;
671 }
672 }
673 }
674 }
675 }
676
677 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
678 * r[10] holds (a[0]*b[0])
679 * r[32] holds (b[1]*b[1])
680 */
681
682 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
683
684 if (neg) /* if t[32] is negative */
685 {
686 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
687 }
688 else
689 {
690 /* Might have a carry */
691 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
692 }
693
694 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
695 * r[10] holds (a[0]*b[0])
696 * r[32] holds (b[1]*b[1])
697 * c1 holds the carry bits
698 */
699 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
700 if (c1)
701 {
702 p= &(r[n+n2]);
703 lo= *p;
704 ln=(lo+c1)&BN_MASK2;
705 *p=ln;
706
707 /* The overflow will stop before we over write
708 * words we should not overwrite */
709 if (ln < c1)
710 {
711 do {
712 p++;
713 lo= *p;
714 ln=(lo+1)&BN_MASK2;
715 *p=ln;
716 } while (ln == 0);
717 }
718 }
719 }
720
721/* a and b must be the same size, which is n2.
722 * r needs to be n2 words and t needs to be n2*2
723 */
724void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
725 BN_ULONG *t)
726 {
727 int n=n2/2;
728
729# ifdef BN_COUNT
730 fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
731# endif
732
733 bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
734 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
735 {
736 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
737 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
738 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
739 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
740 }
741 else
742 {
743 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
744 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
745 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
746 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
747 }
748 }
749
750/* a and b must be the same size, which is n2.
751 * r needs to be n2 words and t needs to be n2*2
752 * l is the low words of the output.
753 * t needs to be n2*3
754 */
755void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
756 BN_ULONG *t)
757 {
758 int i,n;
759 int c1,c2;
760 int neg,oneg,zero;
761 BN_ULONG ll,lc,*lp,*mp;
762
763# ifdef BN_COUNT
764 fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
765# endif
766 n=n2/2;
767
768 /* Calculate (al-ah)*(bh-bl) */
769 neg=zero=0;
770 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
771 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
772 switch (c1*3+c2)
773 {
774 case -4:
775 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
776 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
777 break;
778 case -3:
779 zero=1;
780 break;
781 case -2:
782 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
783 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
784 neg=1;
785 break;
786 case -1:
787 case 0:
788 case 1:
789 zero=1;
790 break;
791 case 2:
792 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
793 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
794 neg=1;
795 break;
796 case 3:
797 zero=1;
798 break;
799 case 4:
800 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
801 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
802 break;
803 }
804
805 oneg=neg;
806 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
807 /* r[10] = (a[1]*b[1]) */
808# ifdef BN_MUL_COMBA
809 if (n == 8)
810 {
811 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
812 bn_mul_comba8(r,&(a[n]),&(b[n]));
813 }
814 else
815# endif
816 {
817 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
818 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
819 }
820
821 /* s0 == low(al*bl)
822 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
823 * We know s0 and s1 so the only unknown is high(al*bl)
824 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
825 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
826 */
827 if (l != NULL)
828 {
829 lp= &(t[n2+n]);
830 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
831 }
832 else
833 {
834 c1=0;
835 lp= &(r[0]);
836 }
837
838 if (neg)
839 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
840 else
841 {
842 bn_add_words(&(t[n2]),lp,&(t[0]),n);
843 neg=0;
844 }
845
846 if (l != NULL)
847 {
848 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
849 }
850 else
851 {
852 lp= &(t[n2+n]);
853 mp= &(t[n2]);
854 for (i=0; i<n; i++)
855 lp[i]=((~mp[i])+1)&BN_MASK2;
856 }
857
858 /* s[0] = low(al*bl)
859 * t[3] = high(al*bl)
860 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
861 * r[10] = (a[1]*b[1])
862 */
863 /* R[10] = al*bl
864 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
865 * R[32] = ah*bh
866 */
867 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
868 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
869 * R[3]=r[1]+(carry/borrow)
870 */
871 if (l != NULL)
872 {
873 lp= &(t[n2]);
874 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
875 }
876 else
877 {
878 lp= &(t[n2+n]);
879 c1=0;
880 }
881 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
882 if (oneg)
883 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
884 else
885 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
886
887 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
888 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
889 if (oneg)
890 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
891 else
892 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
893
894 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
895 {
896 i=0;
897 if (c1 > 0)
898 {
899 lc=c1;
900 do {
901 ll=(r[i]+lc)&BN_MASK2;
902 r[i++]=ll;
903 lc=(lc > ll);
904 } while (lc);
905 }
906 else
907 {
908 lc= -c1;
909 do {
910 ll=r[i];
911 r[i++]=(ll-lc)&BN_MASK2;
912 lc=(lc > ll);
913 } while (lc);
914 }
915 }
916 if (c2 != 0) /* Add starting at r[1] */
917 {
918 i=n;
919 if (c2 > 0)
920 {
921 lc=c2;
922 do {
923 ll=(r[i]+lc)&BN_MASK2;
924 r[i++]=ll;
925 lc=(lc > ll);
926 } while (lc);
927 }
928 else
929 {
930 lc= -c2;
931 do {
932 ll=r[i];
933 r[i++]=(ll-lc)&BN_MASK2;
934 lc=(lc > ll);
935 } while (lc);
936 }
937 }
938 }
939#endif /* BN_RECURSION */
940
941int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
942 {
943 int ret=0;
944 int top,al,bl;
945 BIGNUM *rr;
946#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
947 int i;
948#endif
949#ifdef BN_RECURSION
950 BIGNUM *t=NULL;
951 int j=0,k;
952#endif
953
954#ifdef BN_COUNT
955 fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
956#endif
957
958 bn_check_top(a);
959 bn_check_top(b);
960 bn_check_top(r);
961
962 al=a->top;
963 bl=b->top;
964
965 if ((al == 0) || (bl == 0))
966 {
967 if (!BN_zero(r)) goto err;
968 return(1);
969 }
970 top=al+bl;
971
972 BN_CTX_start(ctx);
973 if ((r == a) || (r == b))
974 {
975 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
976 }
977 else
978 rr = r;
979 rr->neg=a->neg^b->neg;
980
981#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
982 i = al-bl;
983#endif
984#ifdef BN_MUL_COMBA
985 if (i == 0)
986 {
987# if 0
988 if (al == 4)
989 {
990 if (bn_wexpand(rr,8) == NULL) goto err;
991 rr->top=8;
992 bn_mul_comba4(rr->d,a->d,b->d);
993 goto end;
994 }
995# endif
996 if (al == 8)
997 {
998 if (bn_wexpand(rr,16) == NULL) goto err;
999 rr->top=16;
1000 bn_mul_comba8(rr->d,a->d,b->d);
1001 goto end;
1002 }
1003 }
1004#endif /* BN_MUL_COMBA */
1005#ifdef BN_RECURSION
1006 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1007 {
1008 if (i >= -1 && i <= 1)
1009 {
1010 int sav_j =0;
1011 /* Find out the power of two lower or equal
1012 to the longest of the two numbers */
1013 if (i >= 0)
1014 {
1015 j = BN_num_bits_word((BN_ULONG)al);
1016 }
1017 if (i == -1)
1018 {
1019 j = BN_num_bits_word((BN_ULONG)bl);
1020 }
1021 sav_j = j;
1022 j = 1<<(j-1);
1023 assert(j <= al || j <= bl);
1024 k = j+j;
1025 t = BN_CTX_get(ctx);
1026 if (al > j || bl > j)
1027 {
1028 bn_wexpand(t,k*4);
1029 bn_wexpand(rr,k*4);
1030 bn_mul_part_recursive(rr->d,a->d,b->d,
1031 j,al-j,bl-j,t->d);
1032 }
1033 else /* al <= j || bl <= j */
1034 {
1035 bn_wexpand(t,k*2);
1036 bn_wexpand(rr,k*2);
1037 bn_mul_recursive(rr->d,a->d,b->d,
1038 j,al-j,bl-j,t->d);
1039 }
1040 rr->top=top;
1041 goto end;
1042 }
1043#if 0
1044 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1045 {
1046 BIGNUM *tmp_bn = (BIGNUM *)b;
1047 if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1048 tmp_bn->d[bl]=0;
1049 bl++;
1050 i--;
1051 }
1052 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1053 {
1054 BIGNUM *tmp_bn = (BIGNUM *)a;
1055 if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1056 tmp_bn->d[al]=0;
1057 al++;
1058 i++;
1059 }
1060 if (i == 0)
1061 {
1062 /* symmetric and > 4 */
1063 /* 16 or larger */
1064 j=BN_num_bits_word((BN_ULONG)al);
1065 j=1<<(j-1);
1066 k=j+j;
1067 t = BN_CTX_get(ctx);
1068 if (al == j) /* exact multiple */
1069 {
1070 if (bn_wexpand(t,k*2) == NULL) goto err;
1071 if (bn_wexpand(rr,k*2) == NULL) goto err;
1072 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1073 }
1074 else
1075 {
1076 if (bn_wexpand(t,k*4) == NULL) goto err;
1077 if (bn_wexpand(rr,k*4) == NULL) goto err;
1078 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1079 }
1080 rr->top=top;
1081 goto end;
1082 }
1083#endif
1084 }
1085#endif /* BN_RECURSION */
1086 if (bn_wexpand(rr,top) == NULL) goto err;
1087 rr->top=top;
1088 bn_mul_normal(rr->d,a->d,al,b->d,bl);
1089
1090#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1091end:
1092#endif
1093 bn_fix_top(rr);
1094 if (r != rr) BN_copy(r,rr);
1095 ret=1;
1096err:
1097 BN_CTX_end(ctx);
1098 return(ret);
1099 }
1100
1101void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1102 {
1103 BN_ULONG *rr;
1104
1105#ifdef BN_COUNT
1106 fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1107#endif
1108
1109 if (na < nb)
1110 {
1111 int itmp;
1112 BN_ULONG *ltmp;
1113
1114 itmp=na; na=nb; nb=itmp;
1115 ltmp=a; a=b; b=ltmp;
1116
1117 }
1118 rr= &(r[na]);
1119 if (nb <= 0)
1120 {
1121 (void)bn_mul_words(r,a,na,0);
1122 return;
1123 }
1124 else
1125 rr[0]=bn_mul_words(r,a,na,b[0]);
1126
1127 for (;;)
1128 {
1129 if (--nb <= 0) return;
1130 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1131 if (--nb <= 0) return;
1132 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1133 if (--nb <= 0) return;
1134 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1135 if (--nb <= 0) return;
1136 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1137 rr+=4;
1138 r+=4;
1139 b+=4;
1140 }
1141 }
1142
1143void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1144 {
1145#ifdef BN_COUNT
1146 fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1147#endif
1148 bn_mul_words(r,a,n,b[0]);
1149
1150 for (;;)
1151 {
1152 if (--n <= 0) return;
1153 bn_mul_add_words(&(r[1]),a,n,b[1]);
1154 if (--n <= 0) return;
1155 bn_mul_add_words(&(r[2]),a,n,b[2]);
1156 if (--n <= 0) return;
1157 bn_mul_add_words(&(r[3]),a,n,b[3]);
1158 if (--n <= 0) return;
1159 bn_mul_add_words(&(r[4]),a,n,b[4]);
1160 r+=4;
1161 b+=4;
1162 }
1163 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-08-18 21:39:28 +0000