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Fix bn_cmp_part_words() and move it to bn_lib.c.
[thirdparty/openssl.git] / crypto / bn / bn_mul.c
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 #include <stdio.h>
60 #include <assert.h>
61 #include "cryptlib.h"
62 #include "bn_lcl.h"
63
64 /* Here follows specialised variants of bn_add_words() and
65 bn_sub_words(). They have the property performing operations on
66 arrays of different sizes. The sizes of those arrays is expressed through
67 cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
68 which is the delta between the two lengths, calculated as len(a)-len(b).
69 All lengths are the number of BN_ULONGs... For the operations that require
70 a result array as parameter, it must have the length cl+abs(dl).
71 These functions should probably end up in bn_asm.c as soon as there are
72 assembler counterparts for the systems that use assembler files. */
73
74 BN_ULONG bn_sub_part_words(BN_ULONG *r,
75 const BN_ULONG *a, const BN_ULONG *b,
76 int cl, int dl)
77 {
78 BN_ULONG c, t;
79
80 assert(cl >= 0);
81 c = bn_sub_words(r, a, b, cl);
82
83 if (dl == 0)
84 return c;
85
86 r += cl;
87 a += cl;
88 b += cl;
89
90 if (dl < 0)
91 {
92 #ifdef BN_COUNT
93 fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
94 #endif
95 for (;;)
96 {
97 t = b[0];
98 r[0] = (0-t-c)&BN_MASK2;
99 if (t != 0) c=1;
100 if (++dl >= 0) break;
101
102 t = b[1];
103 r[1] = (0-t-c)&BN_MASK2;
104 if (t != 0) c=1;
105 if (++dl >= 0) break;
106
107 t = b[2];
108 r[2] = (0-t-c)&BN_MASK2;
109 if (t != 0) c=1;
110 if (++dl >= 0) break;
111
112 t = b[3];
113 r[3] = (0-t-c)&BN_MASK2;
114 if (t != 0) c=1;
115 if (++dl >= 0) break;
116
117 b += 4;
118 r += 4;
119 }
120 }
121 else
122 {
123 int save_dl = dl;
124 #ifdef BN_COUNT
125 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
126 #endif
127 while(c)
128 {
129 t = a[0];
130 r[0] = (t-c)&BN_MASK2;
131 if (t != 0) c=0;
132 if (--dl <= 0) break;
133
134 t = a[1];
135 r[1] = (t-c)&BN_MASK2;
136 if (t != 0) c=0;
137 if (--dl <= 0) break;
138
139 t = a[2];
140 r[2] = (t-c)&BN_MASK2;
141 if (t != 0) c=0;
142 if (--dl <= 0) break;
143
144 t = a[3];
145 r[3] = (t-c)&BN_MASK2;
146 if (t != 0) c=0;
147 if (--dl <= 0) break;
148
149 save_dl = dl;
150 a += 4;
151 r += 4;
152 }
153 if (dl > 0)
154 {
155 #ifdef BN_COUNT
156 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
157 #endif
158 if (save_dl > dl)
159 {
160 switch (save_dl - dl)
161 {
162 case 1:
163 r[1] = a[1];
164 if (--dl <= 0) break;
165 case 2:
166 r[2] = a[2];
167 if (--dl <= 0) break;
168 case 3:
169 r[3] = a[3];
170 if (--dl <= 0) break;
171 }
172 a += 4;
173 r += 4;
174 }
175 }
176 if (dl > 0)
177 {
178 #ifdef BN_COUNT
179 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
180 #endif
181 for(;;)
182 {
183 r[0] = a[0];
184 if (--dl <= 0) break;
185 r[1] = a[1];
186 if (--dl <= 0) break;
187 r[2] = a[2];
188 if (--dl <= 0) break;
189 r[3] = a[3];
190 if (--dl <= 0) break;
191
192 a += 4;
193 r += 4;
194 }
195 }
196 }
197 return c;
198 }
199
200 BN_ULONG bn_add_part_words(BN_ULONG *r,
201 const BN_ULONG *a, const BN_ULONG *b,
202 int cl, int dl)
203 {
204 BN_ULONG c, l, t;
205
206 assert(cl >= 0);
207 c = bn_add_words(r, a, b, cl);
208
209 if (dl == 0)
210 return c;
211
212 r += cl;
213 a += cl;
214 b += cl;
215
216 if (dl < 0)
217 {
218 int save_dl = dl;
219 #ifdef BN_COUNT
220 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
221 #endif
222 while (c)
223 {
224 l=(c+b[0])&BN_MASK2;
225 c=(l < c);
226 r[0]=l;
227 if (++dl >= 0) break;
228
229 l=(c+b[1])&BN_MASK2;
230 c=(l < c);
231 r[1]=l;
232 if (++dl >= 0) break;
233
234 l=(c+b[2])&BN_MASK2;
235 c=(l < c);
236 r[2]=l;
237 if (++dl >= 0) break;
238
239 l=(c+b[3])&BN_MASK2;
240 c=(l < c);
241 r[3]=l;
242 if (++dl >= 0) break;
243
244 save_dl = dl;
245 b+=4;
246 r+=4;
247 }
248 if (dl < 0)
249 {
250 #ifdef BN_COUNT
251 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
252 #endif
253 if (save_dl < dl)
254 {
255 switch (dl - save_dl)
256 {
257 case 1:
258 r[1] = b[1];
259 if (++dl >= 0) break;
260 case 2:
261 r[2] = b[2];
262 if (++dl >= 0) break;
263 case 3:
264 r[3] = b[3];
265 if (++dl >= 0) break;
266 }
267 b += 4;
268 r += 4;
269 }
270 }
271 if (dl < 0)
272 {
273 #ifdef BN_COUNT
274 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
275 #endif
276 for(;;)
277 {
278 r[0] = b[0];
279 if (++dl >= 0) break;
280 r[1] = b[1];
281 if (++dl >= 0) break;
282 r[2] = b[2];
283 if (++dl >= 0) break;
284 r[3] = b[3];
285 if (++dl >= 0) break;
286
287 b += 4;
288 r += 4;
289 }
290 }
291 }
292 else
293 {
294 int save_dl = dl;
295 #ifdef BN_COUNT
296 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
297 #endif
298 while (c)
299 {
300 t=(a[0]+c)&BN_MASK2;
301 c=(t < c);
302 r[0]=t;
303 if (--dl <= 0) break;
304
305 t=(a[1]+c)&BN_MASK2;
306 c=(t < c);
307 r[1]=t;
308 if (--dl <= 0) break;
309
310 t=(a[2]+c)&BN_MASK2;
311 c=(t < c);
312 r[2]=t;
313 if (--dl <= 0) break;
314
315 t=(a[3]+c)&BN_MASK2;
316 c=(t < c);
317 r[3]=t;
318 if (--dl <= 0) break;
319
320 save_dl = dl;
321 a+=4;
322 r+=4;
323 }
324 #ifdef BN_COUNT
325 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
326 #endif
327 if (dl > 0)
328 {
329 if (save_dl > dl)
330 {
331 switch (save_dl - dl)
332 {
333 case 1:
334 r[1] = a[1];
335 if (--dl <= 0) break;
336 case 2:
337 r[2] = a[2];
338 if (--dl <= 0) break;
339 case 3:
340 r[3] = a[3];
341 if (--dl <= 0) break;
342 }
343 a += 4;
344 r += 4;
345 }
346 }
347 if (dl > 0)
348 {
349 #ifdef BN_COUNT
350 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
351 #endif
352 for(;;)
353 {
354 r[0] = a[0];
355 if (--dl <= 0) break;
356 r[1] = a[1];
357 if (--dl <= 0) break;
358 r[2] = a[2];
359 if (--dl <= 0) break;
360 r[3] = a[3];
361 if (--dl <= 0) break;
362
363 a += 4;
364 r += 4;
365 }
366 }
367 }
368 return c;
369 }
370
371 #ifdef BN_RECURSION
372 /* Karatsuba recursive multiplication algorithm
373 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
374
375 /* r is 2*n2 words in size,
376 * a and b are both n2 words in size.
377 * n2 must be a power of 2.
378 * We multiply and return the result.
379 * t must be 2*n2 words in size
380 * We calculate
381 * a[0]*b[0]
382 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
383 * a[1]*b[1]
384 */
385 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
386 BN_ULONG *t)
387 {
388 int n=n2/2,c1,c2;
389 unsigned int neg,zero;
390 BN_ULONG ln,lo,*p;
391
392 # ifdef BN_COUNT
393 fprintf(stderr," bn_mul_recursive %d * %d\n",n2,n2);
394 # endif
395 # ifdef BN_MUL_COMBA
396 # if 0
397 if (n2 == 4)
398 {
399 bn_mul_comba4(r,a,b);
400 return;
401 }
402 # endif
403 if (n2 == 8)
404 {
405 bn_mul_comba8(r,a,b);
406 return;
407 }
408 # endif /* BN_MUL_COMBA */
409 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
410 {
411 /* This should not happen */
412 bn_mul_normal(r,a,n2,b,n2);
413 return;
414 }
415 /* r=(a[0]-a[1])*(b[1]-b[0]) */
416 c1=bn_cmp_words(a,&(a[n]),n);
417 c2=bn_cmp_words(&(b[n]),b,n);
418 zero=neg=0;
419 switch (c1*3+c2)
420 {
421 case -4:
422 bn_sub_words(t, &(a[n]),a, n); /* - */
423 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
424 break;
425 case -3:
426 zero=1;
427 break;
428 case -2:
429 bn_sub_words(t, &(a[n]),a, n); /* - */
430 bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
431 neg=1;
432 break;
433 case -1:
434 case 0:
435 case 1:
436 zero=1;
437 break;
438 case 2:
439 bn_sub_words(t, a, &(a[n]),n); /* + */
440 bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
441 neg=1;
442 break;
443 case 3:
444 zero=1;
445 break;
446 case 4:
447 bn_sub_words(t, a, &(a[n]),n);
448 bn_sub_words(&(t[n]),&(b[n]),b, n);
449 break;
450 }
451
452 # ifdef BN_MUL_COMBA
453 if (n == 4)
454 {
455 if (!zero)
456 bn_mul_comba4(&(t[n2]),t,&(t[n]));
457 else
458 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
459
460 bn_mul_comba4(r,a,b);
461 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
462 }
463 else if (n == 8)
464 {
465 if (!zero)
466 bn_mul_comba8(&(t[n2]),t,&(t[n]));
467 else
468 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
469
470 bn_mul_comba8(r,a,b);
471 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
472 }
473 else
474 # endif /* BN_MUL_COMBA */
475 {
476 p= &(t[n2*2]);
477 if (!zero)
478 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
479 else
480 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
481 bn_mul_recursive(r,a,b,n,p);
482 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
483 }
484
485 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
486 * r[10] holds (a[0]*b[0])
487 * r[32] holds (b[1]*b[1])
488 */
489
490 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
491
492 if (neg) /* if t[32] is negative */
493 {
494 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
495 }
496 else
497 {
498 /* Might have a carry */
499 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
500 }
501
502 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
503 * r[10] holds (a[0]*b[0])
504 * r[32] holds (b[1]*b[1])
505 * c1 holds the carry bits
506 */
507 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
508 if (c1)
509 {
510 p= &(r[n+n2]);
511 lo= *p;
512 ln=(lo+c1)&BN_MASK2;
513 *p=ln;
514
515 /* The overflow will stop before we over write
516 * words we should not overwrite */
517 if (ln < (BN_ULONG)c1)
518 {
519 do {
520 p++;
521 lo= *p;
522 ln=(lo+1)&BN_MASK2;
523 *p=ln;
524 } while (ln == 0);
525 }
526 }
527 }
528
529 /* n+tn is the word length
530 * t needs to be n*4 is size, as does r */
531 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
532 int n, BN_ULONG *t)
533 {
534 int i,j,n2=n*2;
535 unsigned int c1,c2,neg,zero;
536 BN_ULONG ln,lo,*p;
537
538 # ifdef BN_COUNT
539 fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
540 tn, n,tn, n);
541 # endif
542 if (n < 8)
543 {
544 i=tn+n;
545 bn_mul_normal(r,a,i,b,i);
546 return;
547 }
548
549 /* r=(a[0]-a[1])*(b[1]-b[0]) */
550 c1=bn_cmp_part_words(a,&(a[n]),tn,n-tn);
551 c2=bn_cmp_part_words(&(b[n]),b,tn,tn-n);
552 zero=neg=0;
553 switch (c1*3+c2)
554 {
555 case -4:
556 bn_sub_part_words(t, &(a[n]),a, tn,tn-n); /* - */
557 bn_sub_part_words(&(t[n]),b, &(b[n]),tn,n-tn); /* - */
558 break;
559 case -3:
560 zero=1;
561 /* break; */
562 case -2:
563 bn_sub_part_words(t, &(a[n]),a, tn,tn-n); /* - */
564 bn_sub_part_words(&(t[n]),&(b[n]),b, tn,tn-n); /* + */
565 neg=1;
566 break;
567 case -1:
568 case 0:
569 case 1:
570 zero=1;
571 /* break; */
572 case 2:
573 bn_sub_part_words(t, a, &(a[n]),tn,n-tn); /* + */
574 bn_sub_part_words(&(t[n]),b, &(b[n]),tn,n-tn); /* - */
575 neg=1;
576 break;
577 case 3:
578 zero=1;
579 /* break; */
580 case 4:
581 bn_sub_part_words(t, a, &(a[n]),tn,n-tn);
582 bn_sub_part_words(&(t[n]),&(b[n]),b, tn,tn-n);
583 break;
584 }
585 /* The zero case isn't yet implemented here. The speedup
586 would probably be negligible. */
587 # if 0
588 if (n == 4)
589 {
590 bn_mul_comba4(&(t[n2]),t,&(t[n]));
591 bn_mul_comba4(r,a,b);
592 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
593 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
594 }
595 else
596 # endif
597 if (n == 8)
598 {
599 bn_mul_comba8(&(t[n2]),t,&(t[n]));
600 bn_mul_comba8(r,a,b);
601 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
602 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
603 }
604 else
605 {
606 p= &(t[n2*2]);
607 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
608 bn_mul_recursive(r,a,b,n,p);
609 i=n/2;
610 /* If there is only a bottom half to the number,
611 * just do it */
612 j=tn-i;
613 if (j == 0)
614 {
615 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
616 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
617 }
618 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
619 {
620 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
621 j,i,p);
622 memset(&(r[n2+tn*2]),0,
623 sizeof(BN_ULONG)*(n2-tn*2));
624 }
625 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
626 {
627 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
628 if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
629 {
630 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
631 }
632 else
633 {
634 for (;;)
635 {
636 i/=2;
637 if (i < tn)
638 {
639 bn_mul_part_recursive(&(r[n2]),
640 &(a[n]),&(b[n]),
641 tn-i,i,p);
642 break;
643 }
644 else if (i == tn)
645 {
646 bn_mul_recursive(&(r[n2]),
647 &(a[n]),&(b[n]),
648 i,p);
649 break;
650 }
651 }
652 }
653 }
654 }
655
656 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
657 * r[10] holds (a[0]*b[0])
658 * r[32] holds (b[1]*b[1])
659 */
660
661 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
662
663 if (neg) /* if t[32] is negative */
664 {
665 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
666 }
667 else
668 {
669 /* Might have a carry */
670 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
671 }
672
673 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
674 * r[10] holds (a[0]*b[0])
675 * r[32] holds (b[1]*b[1])
676 * c1 holds the carry bits
677 */
678 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
679 if (c1)
680 {
681 p= &(r[n+n2]);
682 lo= *p;
683 ln=(lo+c1)&BN_MASK2;
684 *p=ln;
685
686 /* The overflow will stop before we over write
687 * words we should not overwrite */
688 if (ln < c1)
689 {
690 do {
691 p++;
692 lo= *p;
693 ln=(lo+1)&BN_MASK2;
694 *p=ln;
695 } while (ln == 0);
696 }
697 }
698 }
699
700 /* a and b must be the same size, which is n2.
701 * r needs to be n2 words and t needs to be n2*2
702 */
703 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
704 BN_ULONG *t)
705 {
706 int n=n2/2;
707
708 # ifdef BN_COUNT
709 fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
710 # endif
711
712 bn_mul_recursive(r,a,b,n,&(t[0]));
713 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
714 {
715 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
716 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
717 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
718 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
719 }
720 else
721 {
722 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
723 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
724 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
725 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
726 }
727 }
728
729 /* a and b must be the same size, which is n2.
730 * r needs to be n2 words and t needs to be n2*2
731 * l is the low words of the output.
732 * t needs to be n2*3
733 */
734 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
735 BN_ULONG *t)
736 {
737 int i,n;
738 int c1,c2;
739 int neg,oneg,zero;
740 BN_ULONG ll,lc,*lp,*mp;
741
742 # ifdef BN_COUNT
743 fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
744 # endif
745 n=n2/2;
746
747 /* Calculate (al-ah)*(bh-bl) */
748 neg=zero=0;
749 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
750 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
751 switch (c1*3+c2)
752 {
753 case -4:
754 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
755 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
756 break;
757 case -3:
758 zero=1;
759 break;
760 case -2:
761 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
762 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
763 neg=1;
764 break;
765 case -1:
766 case 0:
767 case 1:
768 zero=1;
769 break;
770 case 2:
771 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
772 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
773 neg=1;
774 break;
775 case 3:
776 zero=1;
777 break;
778 case 4:
779 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
780 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
781 break;
782 }
783
784 oneg=neg;
785 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
786 /* r[10] = (a[1]*b[1]) */
787 # ifdef BN_MUL_COMBA
788 if (n == 8)
789 {
790 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
791 bn_mul_comba8(r,&(a[n]),&(b[n]));
792 }
793 else
794 # endif
795 {
796 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
797 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
798 }
799
800 /* s0 == low(al*bl)
801 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
802 * We know s0 and s1 so the only unknown is high(al*bl)
803 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
804 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
805 */
806 if (l != NULL)
807 {
808 lp= &(t[n2+n]);
809 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
810 }
811 else
812 {
813 c1=0;
814 lp= &(r[0]);
815 }
816
817 if (neg)
818 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
819 else
820 {
821 bn_add_words(&(t[n2]),lp,&(t[0]),n);
822 neg=0;
823 }
824
825 if (l != NULL)
826 {
827 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
828 }
829 else
830 {
831 lp= &(t[n2+n]);
832 mp= &(t[n2]);
833 for (i=0; i<n; i++)
834 lp[i]=((~mp[i])+1)&BN_MASK2;
835 }
836
837 /* s[0] = low(al*bl)
838 * t[3] = high(al*bl)
839 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
840 * r[10] = (a[1]*b[1])
841 */
842 /* R[10] = al*bl
843 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
844 * R[32] = ah*bh
845 */
846 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
847 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
848 * R[3]=r[1]+(carry/borrow)
849 */
850 if (l != NULL)
851 {
852 lp= &(t[n2]);
853 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
854 }
855 else
856 {
857 lp= &(t[n2+n]);
858 c1=0;
859 }
860 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
861 if (oneg)
862 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
863 else
864 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
865
866 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
867 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
868 if (oneg)
869 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
870 else
871 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
872
873 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
874 {
875 i=0;
876 if (c1 > 0)
877 {
878 lc=c1;
879 do {
880 ll=(r[i]+lc)&BN_MASK2;
881 r[i++]=ll;
882 lc=(lc > ll);
883 } while (lc);
884 }
885 else
886 {
887 lc= -c1;
888 do {
889 ll=r[i];
890 r[i++]=(ll-lc)&BN_MASK2;
891 lc=(lc > ll);
892 } while (lc);
893 }
894 }
895 if (c2 != 0) /* Add starting at r[1] */
896 {
897 i=n;
898 if (c2 > 0)
899 {
900 lc=c2;
901 do {
902 ll=(r[i]+lc)&BN_MASK2;
903 r[i++]=ll;
904 lc=(lc > ll);
905 } while (lc);
906 }
907 else
908 {
909 lc= -c2;
910 do {
911 ll=r[i];
912 r[i++]=(ll-lc)&BN_MASK2;
913 lc=(lc > ll);
914 } while (lc);
915 }
916 }
917 }
918 #endif /* BN_RECURSION */
919
920 int BN_mul(BIGNUM *r, /* almost const */ const BIGNUM *a, /* almost const */ const BIGNUM *b, BN_CTX *ctx)
921 {
922 int top,al,bl;
923 BIGNUM *rr;
924 int ret = 0;
925 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
926 int i;
927 #endif
928 #ifdef BN_RECURSION
929 BIGNUM *t;
930 int j,k;
931 #endif
932 BIGNUM *free_a = NULL, *free_b = NULL;
933
934 #ifdef BN_COUNT
935 fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
936 #endif
937
938 bn_check_top(a);
939 bn_check_top(b);
940 bn_check_top(r);
941
942 al=a->top;
943 bl=b->top;
944
945 if ((al == 0) || (bl == 0))
946 {
947 BN_zero(r);
948 return(1);
949 }
950 top=al+bl;
951
952 BN_CTX_start(ctx);
953 if ((r == a) || (r == b))
954 {
955 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
956 }
957 else
958 rr = r;
959 rr->neg=a->neg^b->neg;
960
961 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
962 i = al-bl;
963 #endif
964 #ifdef BN_MUL_COMBA
965 if (i == 0)
966 {
967 # if 0
968 if (al == 4)
969 {
970 if (bn_wexpand(rr,8) == NULL) goto err;
971 rr->top=8;
972 bn_mul_comba4(rr->d,a->d,b->d);
973 goto end;
974 }
975 # endif
976 if (al == 8)
977 {
978 if (bn_wexpand(rr,16) == NULL) goto err;
979 rr->top=16;
980 bn_mul_comba8(rr->d,a->d,b->d);
981 goto end;
982 }
983 }
984 #endif /* BN_MUL_COMBA */
985 #ifdef BN_RECURSION
986 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
987 {
988 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
989 {
990 BIGNUM *tmp_bn = (BIGNUM *)b;
991 bn_wexpand(tmp_bn,al);
992 tmp_bn->d[bl]=0;
993 bl++;
994 i--;
995 }
996 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
997 {
998 BIGNUM *tmp_bn = (BIGNUM *)a;
999 bn_wexpand(tmp_bn,bl);
1000 tmp_bn->d[al]=0;
1001 al++;
1002 i++;
1003 }
1004 if (i == 0)
1005 {
1006 /* symmetric and > 4 */
1007 /* 16 or larger */
1008 j=BN_num_bits_word((BN_ULONG)al);
1009 j=1<<(j-1);
1010 k=j+j;
1011 t = BN_CTX_get(ctx);
1012 if (al == j) /* exact multiple */
1013 {
1014 bn_wexpand(t,k*2);
1015 bn_wexpand(rr,k*2);
1016 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1017 }
1018 else
1019 {
1020 bn_wexpand(t,k*4);
1021 bn_wexpand(rr,k*4);
1022 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1023 }
1024 rr->top=top;
1025 goto end;
1026 }
1027 }
1028 #endif /* BN_RECURSION */
1029 if (bn_wexpand(rr,top) == NULL) goto err;
1030 rr->top=top;
1031 bn_mul_normal(rr->d,a->d,al,b->d,bl);
1032
1033 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1034 end:
1035 #endif
1036 bn_fix_top(rr);
1037 if (r != rr) BN_copy(r,rr);
1038 ret=1;
1039 err:
1040 if (free_a) BN_free(free_a);
1041 if (free_b) BN_free(free_b);
1042 BN_CTX_end(ctx);
1043 return(ret);
1044 }
1045
1046 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1047 {
1048 BN_ULONG *rr;
1049
1050 #ifdef BN_COUNT
1051 fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1052 #endif
1053
1054 if (na < nb)
1055 {
1056 int itmp;
1057 BN_ULONG *ltmp;
1058
1059 itmp=na; na=nb; nb=itmp;
1060 ltmp=a; a=b; b=ltmp;
1061
1062 }
1063 rr= &(r[na]);
1064 rr[0]=bn_mul_words(r,a,na,b[0]);
1065
1066 for (;;)
1067 {
1068 if (--nb <= 0) return;
1069 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1070 if (--nb <= 0) return;
1071 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1072 if (--nb <= 0) return;
1073 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1074 if (--nb <= 0) return;
1075 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1076 rr+=4;
1077 r+=4;
1078 b+=4;
1079 }
1080 }
1081
1082 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1083 {
1084 #ifdef BN_COUNT
1085 fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1086 #endif
1087 bn_mul_words(r,a,n,b[0]);
1088
1089 for (;;)
1090 {
1091 if (--n <= 0) return;
1092 bn_mul_add_words(&(r[1]),a,n,b[1]);
1093 if (--n <= 0) return;
1094 bn_mul_add_words(&(r[2]),a,n,b[2]);
1095 if (--n <= 0) return;
1096 bn_mul_add_words(&(r[3]),a,n,b[3]);
1097 if (--n <= 0) return;
1098 bn_mul_add_words(&(r[4]),a,n,b[4]);
1099 r+=4;
1100 b+=4;
1101 }
1102 }
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