Fix from stable branch.
[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 #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
80 BN_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
207 BN_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 void 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 */
548 void 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         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 && tna == tnb)
659                                                 {
660                                                 bn_mul_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_part_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 < (BN_ULONG)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  */
724 void 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  */
755 void 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
941 int 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                 BN_zero(r);
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)
1091 end:
1092 #endif
1093         bn_correct_top(rr);
1094         if (r != rr) BN_copy(r,rr);
1095         ret=1;
1096 err:
1097         bn_check_top(r);
1098         BN_CTX_end(ctx);
1099         return(ret);
1100         }
1101
1102 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1103         {
1104         BN_ULONG *rr;
1105
1106 #ifdef BN_COUNT
1107         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1108 #endif
1109
1110         if (na < nb)
1111                 {
1112                 int itmp;
1113                 BN_ULONG *ltmp;
1114
1115                 itmp=na; na=nb; nb=itmp;
1116                 ltmp=a;   a=b;   b=ltmp;
1117
1118                 }
1119         rr= &(r[na]);
1120         if (nb <= 0)
1121                 {
1122                 (void)bn_mul_words(r,a,na,0);
1123                 return;
1124                 }
1125         else
1126                 rr[0]=bn_mul_words(r,a,na,b[0]);
1127
1128         for (;;)
1129                 {
1130                 if (--nb <= 0) return;
1131                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1132                 if (--nb <= 0) return;
1133                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1134                 if (--nb <= 0) return;
1135                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1136                 if (--nb <= 0) return;
1137                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1138                 rr+=4;
1139                 r+=4;
1140                 b+=4;
1141                 }
1142         }
1143
1144 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1145         {
1146 #ifdef BN_COUNT
1147         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1148 #endif
1149         bn_mul_words(r,a,n,b[0]);
1150
1151         for (;;)
1152                 {
1153                 if (--n <= 0) return;
1154                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1155                 if (--n <= 0) return;
1156                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1157                 if (--n <= 0) return;
1158                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1159                 if (--n <= 0) return;
1160                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1161                 r+=4;
1162                 b+=4;
1163                 }
1164         }