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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(OPENSSL_BN_ASM_PART_WORDS)
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 */
392/* dnX may not be positive, but n2/2+dnX has to be */
393void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
394 int dna, int dnb, BN_ULONG *t)
395 {
396 int n=n2/2,c1,c2;
397 int tna=n+dna, tnb=n+dnb;
398 unsigned int neg,zero;
399 BN_ULONG ln,lo,*p;
400
401# ifdef BN_COUNT
402 fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
403# endif
404# ifdef BN_MUL_COMBA
405# if 0
406 if (n2 == 4)
407 {
408 bn_mul_comba4(r,a,b);
409 return;
410 }
411# endif
412 /* Only call bn_mul_comba 8 if n2 == 8 and the
413 * two arrays are complete [steve]
414 */
415 if (n2 == 8 && dna == 0 && dnb == 0)
416 {
417 bn_mul_comba8(r,a,b);
418 return;
419 }
420# endif /* BN_MUL_COMBA */
421 /* Else do normal multiply */
422 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
423 {
424 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
425 if ((dna + dnb) < 0)
426 memset(&r[2*n2 + dna + dnb], 0,
427 sizeof(BN_ULONG) * -(dna + dnb));
428 return;
429 }
430 /* r=(a[0]-a[1])*(b[1]-b[0]) */
431 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
432 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
433 zero=neg=0;
434 switch (c1*3+c2)
435 {
436 case -4:
437 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
438 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
439 break;
440 case -3:
441 zero=1;
442 break;
443 case -2:
444 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
445 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
446 neg=1;
447 break;
448 case -1:
449 case 0:
450 case 1:
451 zero=1;
452 break;
453 case 2:
454 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
455 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
456 neg=1;
457 break;
458 case 3:
459 zero=1;
460 break;
461 case 4:
462 bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
463 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
464 break;
465 }
466
467# ifdef BN_MUL_COMBA
468 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
469 extra args to do this well */
470 {
471 if (!zero)
472 bn_mul_comba4(&(t[n2]),t,&(t[n]));
473 else
474 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
475
476 bn_mul_comba4(r,a,b);
477 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
478 }
479 else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
480 take extra args to do this
481 well */
482 {
483 if (!zero)
484 bn_mul_comba8(&(t[n2]),t,&(t[n]));
485 else
486 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
487
488 bn_mul_comba8(r,a,b);
489 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
490 }
491 else
492# endif /* BN_MUL_COMBA */
493 {
494 p= &(t[n2*2]);
495 if (!zero)
496 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
497 else
498 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
499 bn_mul_recursive(r,a,b,n,0,0,p);
500 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
501 }
502
503 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
504 * r[10] holds (a[0]*b[0])
505 * r[32] holds (b[1]*b[1])
506 */
507
508 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
509
510 if (neg) /* if t[32] is negative */
511 {
512 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
513 }
514 else
515 {
516 /* Might have a carry */
517 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
518 }
519
520 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
521 * r[10] holds (a[0]*b[0])
522 * r[32] holds (b[1]*b[1])
523 * c1 holds the carry bits
524 */
525 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
526 if (c1)
527 {
528 p= &(r[n+n2]);
529 lo= *p;
530 ln=(lo+c1)&BN_MASK2;
531 *p=ln;
532
533 /* The overflow will stop before we over write
534 * words we should not overwrite */
535 if (ln < (BN_ULONG)c1)
536 {
537 do {
538 p++;
539 lo= *p;
540 ln=(lo+1)&BN_MASK2;
541 *p=ln;
542 } while (ln == 0);
543 }
544 }
545 }
546
547/* n+tn is the word length
548 * t needs to be n*4 is size, as does r */
549/* tnX may not be negative but less than n */
550void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
551 int tna, int tnb, BN_ULONG *t)
552 {
553 int i,j,n2=n*2;
554 int c1,c2,neg,zero;
555 BN_ULONG ln,lo,*p;
556
557# ifdef BN_COUNT
558 fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
559 n, tna, n, tnb);
560# endif
561 if (n < 8)
562 {
563 bn_mul_normal(r,a,n+tna,b,n+tnb);
564 return;
565 }
566
567 /* r=(a[0]-a[1])*(b[1]-b[0]) */
568 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
569 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
570 zero=neg=0;
571 switch (c1*3+c2)
572 {
573 case -4:
574 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
575 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
576 break;
577 case -3:
578 zero=1;
579 /* break; */
580 case -2:
581 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
582 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
583 neg=1;
584 break;
585 case -1:
586 case 0:
587 case 1:
588 zero=1;
589 /* break; */
590 case 2:
591 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
592 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
593 neg=1;
594 break;
595 case 3:
596 zero=1;
597 /* break; */
598 case 4:
599 bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
600 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
601 break;
602 }
603 /* The zero case isn't yet implemented here. The speedup
604 would probably be negligible. */
605# if 0
606 if (n == 4)
607 {
608 bn_mul_comba4(&(t[n2]),t,&(t[n]));
609 bn_mul_comba4(r,a,b);
610 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
611 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
612 }
613 else
614# endif
615 if (n == 8)
616 {
617 bn_mul_comba8(&(t[n2]),t,&(t[n]));
618 bn_mul_comba8(r,a,b);
619 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
620 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
621 }
622 else
623 {
624 p= &(t[n2*2]);
625 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
626 bn_mul_recursive(r,a,b,n,0,0,p);
627 i=n/2;
628 /* If there is only a bottom half to the number,
629 * just do it */
630 if (tna > tnb)
631 j = tna - i;
632 else
633 j = tnb - i;
634 if (j == 0)
635 {
636 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
637 i,tna-i,tnb-i,p);
638 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
639 }
640 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
641 {
642 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
643 i,tna-i,tnb-i,p);
644 memset(&(r[n2+tna+tnb]),0,
645 sizeof(BN_ULONG)*(n2-tna-tnb));
646 }
647 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
648 {
649 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
650 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
651 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
652 {
653 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
654 }
655 else
656 {
657 for (;;)
658 {
659 i/=2;
660 /* these simplified conditions work
661 * exclusively because difference
662 * between tna and tnb is 1 or 0 */
663 if (i < tna || i < tnb)
664 {
665 bn_mul_part_recursive(&(r[n2]),
666 &(a[n]),&(b[n]),
667 i,tna-i,tnb-i,p);
668 break;
669 }
670 else if (i == tna || i == tnb)
671 {
672 bn_mul_recursive(&(r[n2]),
673 &(a[n]),&(b[n]),
674 i,tna-i,tnb-i,p);
675 break;
676 }
677 }
678 }
679 }
680 }
681
682 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
683 * r[10] holds (a[0]*b[0])
684 * r[32] holds (b[1]*b[1])
685 */
686
687 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
688
689 if (neg) /* if t[32] is negative */
690 {
691 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
692 }
693 else
694 {
695 /* Might have a carry */
696 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
697 }
698
699 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
700 * r[10] holds (a[0]*b[0])
701 * r[32] holds (b[1]*b[1])
702 * c1 holds the carry bits
703 */
704 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
705 if (c1)
706 {
707 p= &(r[n+n2]);
708 lo= *p;
709 ln=(lo+c1)&BN_MASK2;
710 *p=ln;
711
712 /* The overflow will stop before we over write
713 * words we should not overwrite */
714 if (ln < (BN_ULONG)c1)
715 {
716 do {
717 p++;
718 lo= *p;
719 ln=(lo+1)&BN_MASK2;
720 *p=ln;
721 } while (ln == 0);
722 }
723 }
724 }
725
726/* a and b must be the same size, which is n2.
727 * r needs to be n2 words and t needs to be n2*2
728 */
729void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
730 BN_ULONG *t)
731 {
732 int n=n2/2;
733
734# ifdef BN_COUNT
735 fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
736# endif
737
738 bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
739 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
740 {
741 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
742 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
743 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
744 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
745 }
746 else
747 {
748 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
749 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
750 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
751 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
752 }
753 }
754
755/* a and b must be the same size, which is n2.
756 * r needs to be n2 words and t needs to be n2*2
757 * l is the low words of the output.
758 * t needs to be n2*3
759 */
760void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
761 BN_ULONG *t)
762 {
763 int i,n;
764 int c1,c2;
765 int neg,oneg,zero;
766 BN_ULONG ll,lc,*lp,*mp;
767
768# ifdef BN_COUNT
769 fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
770# endif
771 n=n2/2;
772
773 /* Calculate (al-ah)*(bh-bl) */
774 neg=zero=0;
775 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
776 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
777 switch (c1*3+c2)
778 {
779 case -4:
780 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
781 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
782 break;
783 case -3:
784 zero=1;
785 break;
786 case -2:
787 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
788 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
789 neg=1;
790 break;
791 case -1:
792 case 0:
793 case 1:
794 zero=1;
795 break;
796 case 2:
797 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
798 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
799 neg=1;
800 break;
801 case 3:
802 zero=1;
803 break;
804 case 4:
805 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
806 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
807 break;
808 }
809
810 oneg=neg;
811 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
812 /* r[10] = (a[1]*b[1]) */
813# ifdef BN_MUL_COMBA
814 if (n == 8)
815 {
816 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
817 bn_mul_comba8(r,&(a[n]),&(b[n]));
818 }
819 else
820# endif
821 {
822 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
823 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
824 }
825
826 /* s0 == low(al*bl)
827 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
828 * We know s0 and s1 so the only unknown is high(al*bl)
829 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
830 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
831 */
832 if (l != NULL)
833 {
834 lp= &(t[n2+n]);
835 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
836 }
837 else
838 {
839 c1=0;
840 lp= &(r[0]);
841 }
842
843 if (neg)
844 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
845 else
846 {
847 bn_add_words(&(t[n2]),lp,&(t[0]),n);
848 neg=0;
849 }
850
851 if (l != NULL)
852 {
853 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
854 }
855 else
856 {
857 lp= &(t[n2+n]);
858 mp= &(t[n2]);
859 for (i=0; i<n; i++)
860 lp[i]=((~mp[i])+1)&BN_MASK2;
861 }
862
863 /* s[0] = low(al*bl)
864 * t[3] = high(al*bl)
865 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
866 * r[10] = (a[1]*b[1])
867 */
868 /* R[10] = al*bl
869 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
870 * R[32] = ah*bh
871 */
872 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
873 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
874 * R[3]=r[1]+(carry/borrow)
875 */
876 if (l != NULL)
877 {
878 lp= &(t[n2]);
879 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
880 }
881 else
882 {
883 lp= &(t[n2+n]);
884 c1=0;
885 }
886 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
887 if (oneg)
888 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
889 else
890 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
891
892 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
893 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
894 if (oneg)
895 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
896 else
897 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
898
899 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
900 {
901 i=0;
902 if (c1 > 0)
903 {
904 lc=c1;
905 do {
906 ll=(r[i]+lc)&BN_MASK2;
907 r[i++]=ll;
908 lc=(lc > ll);
909 } while (lc);
910 }
911 else
912 {
913 lc= -c1;
914 do {
915 ll=r[i];
916 r[i++]=(ll-lc)&BN_MASK2;
917 lc=(lc > ll);
918 } while (lc);
919 }
920 }
921 if (c2 != 0) /* Add starting at r[1] */
922 {
923 i=n;
924 if (c2 > 0)
925 {
926 lc=c2;
927 do {
928 ll=(r[i]+lc)&BN_MASK2;
929 r[i++]=ll;
930 lc=(lc > ll);
931 } while (lc);
932 }
933 else
934 {
935 lc= -c2;
936 do {
937 ll=r[i];
938 r[i++]=(ll-lc)&BN_MASK2;
939 lc=(lc > ll);
940 } while (lc);
941 }
942 }
943 }
944#endif /* BN_RECURSION */
945
946int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
947 {
948 int ret=0;
949 int top,al,bl;
950 BIGNUM *rr;
951#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
952 int i;
953#endif
954#ifdef BN_RECURSION
955 BIGNUM *t=NULL;
956 int j=0,k;
957#endif
958
959#ifdef BN_COUNT
960 fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
961#endif
962
963 bn_check_top(a);
964 bn_check_top(b);
965 bn_check_top(r);
966
967 al=a->top;
968 bl=b->top;
969
970 if ((al == 0) || (bl == 0))
971 {
972 BN_zero(r);
973 return(1);
974 }
975 top=al+bl;
976
977 BN_CTX_start(ctx);
978 if ((r == a) || (r == b))
979 {
980 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
981 }
982 else
983 rr = r;
984 rr->neg=a->neg^b->neg;
985
986#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
987 i = al-bl;
988#endif
989#ifdef BN_MUL_COMBA
990 if (i == 0)
991 {
992# if 0
993 if (al == 4)
994 {
995 if (bn_wexpand(rr,8) == NULL) goto err;
996 rr->top=8;
997 bn_mul_comba4(rr->d,a->d,b->d);
998 goto end;
999 }
1000# endif
1001 if (al == 8)
1002 {
1003 if (bn_wexpand(rr,16) == NULL) goto err;
1004 rr->top=16;
1005 bn_mul_comba8(rr->d,a->d,b->d);
1006 goto end;
1007 }
1008 }
1009#endif /* BN_MUL_COMBA */
1010#ifdef BN_RECURSION
1011 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1012 {
1013 if (i >= -1 && i <= 1)
1014 {
1015 int sav_j =0;
1016 /* Find out the power of two lower or equal
1017 to the longest of the two numbers */
1018 if (i >= 0)
1019 {
1020 j = BN_num_bits_word((BN_ULONG)al);
1021 }
1022 if (i == -1)
1023 {
1024 j = BN_num_bits_word((BN_ULONG)bl);
1025 }
1026 sav_j = j;
1027 j = 1<<(j-1);
1028 assert(j <= al || j <= bl);
1029 k = j+j;
1030 t = BN_CTX_get(ctx);
1031 if (al > j || bl > j)
1032 {
1033 bn_wexpand(t,k*4);
1034 bn_wexpand(rr,k*4);
1035 bn_mul_part_recursive(rr->d,a->d,b->d,
1036 j,al-j,bl-j,t->d);
1037 }
1038 else /* al <= j || bl <= j */
1039 {
1040 bn_wexpand(t,k*2);
1041 bn_wexpand(rr,k*2);
1042 bn_mul_recursive(rr->d,a->d,b->d,
1043 j,al-j,bl-j,t->d);
1044 }
1045 rr->top=top;
1046 goto end;
1047 }
1048#if 0
1049 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1050 {
1051 BIGNUM *tmp_bn = (BIGNUM *)b;
1052 if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1053 tmp_bn->d[bl]=0;
1054 bl++;
1055 i--;
1056 }
1057 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1058 {
1059 BIGNUM *tmp_bn = (BIGNUM *)a;
1060 if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1061 tmp_bn->d[al]=0;
1062 al++;
1063 i++;
1064 }
1065 if (i == 0)
1066 {
1067 /* symmetric and > 4 */
1068 /* 16 or larger */
1069 j=BN_num_bits_word((BN_ULONG)al);
1070 j=1<<(j-1);
1071 k=j+j;
1072 t = BN_CTX_get(ctx);
1073 if (al == j) /* exact multiple */
1074 {
1075 if (bn_wexpand(t,k*2) == NULL) goto err;
1076 if (bn_wexpand(rr,k*2) == NULL) goto err;
1077 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1078 }
1079 else
1080 {
1081 if (bn_wexpand(t,k*4) == NULL) goto err;
1082 if (bn_wexpand(rr,k*4) == NULL) goto err;
1083 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1084 }
1085 rr->top=top;
1086 goto end;
1087 }
1088#endif
1089 }
1090#endif /* BN_RECURSION */
1091 if (bn_wexpand(rr,top) == NULL) goto err;
1092 rr->top=top;
1093 bn_mul_normal(rr->d,a->d,al,b->d,bl);
1094
1095#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1096end:
1097#endif
1098 bn_correct_top(rr);
1099 if (r != rr) BN_copy(r,rr);
1100 ret=1;
1101err:
1102 bn_check_top(r);
1103 BN_CTX_end(ctx);
1104 return(ret);
1105 }
1106
1107void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1108 {
1109 BN_ULONG *rr;
1110
1111#ifdef BN_COUNT
1112 fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1113#endif
1114
1115 if (na < nb)
1116 {
1117 int itmp;
1118 BN_ULONG *ltmp;
1119
1120 itmp=na; na=nb; nb=itmp;
1121 ltmp=a; a=b; b=ltmp;
1122
1123 }
1124 rr= &(r[na]);
1125 if (nb <= 0)
1126 {
1127 (void)bn_mul_words(r,a,na,0);
1128 return;
1129 }
1130 else
1131 rr[0]=bn_mul_words(r,a,na,b[0]);
1132
1133 for (;;)
1134 {
1135 if (--nb <= 0) return;
1136 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1137 if (--nb <= 0) return;
1138 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1139 if (--nb <= 0) return;
1140 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1141 if (--nb <= 0) return;
1142 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1143 rr+=4;
1144 r+=4;
1145 b+=4;
1146 }
1147 }
1148
1149void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1150 {
1151#ifdef BN_COUNT
1152 fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1153#endif
1154 bn_mul_words(r,a,n,b[0]);
1155
1156 for (;;)
1157 {
1158 if (--n <= 0) return;
1159 bn_mul_add_words(&(r[1]),a,n,b[1]);
1160 if (--n <= 0) return;
1161 bn_mul_add_words(&(r[2]),a,n,b[2]);
1162 if (--n <= 0) return;
1163 bn_mul_add_words(&(r[3]),a,n,b[3]);
1164 if (--n <= 0) return;
1165 bn_mul_add_words(&(r[4]),a,n,b[4]);
1166 r+=4;
1167 b+=4;
1168 }
1169 }
generated by cgit v1.2.3-55-g6feb (git 2.39.1) at 2025-04-04 08:48:40 +0000