Avoid gcc warning: BN_DEC_CONV when SIXTY_FOUR_BIT is defined is unsigned.
[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(__i386) || defined(__i386__))/* Assembler implementation exists only for x86 */
70 /* Here follows specialised variants of bn_add_words() and
71    bn_sub_words().  They have the property performing operations on
72    arrays of different sizes.  The sizes of those arrays is expressed through
73    cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
74    which is the delta between the two lengths, calculated as len(a)-len(b).
75    All lengths are the number of BN_ULONGs...  For the operations that require
76    a result array as parameter, it must have the length cl+abs(dl).
77    These functions should probably end up in bn_asm.c as soon as there are
78    assembler counterparts for the systems that use assembler files.  */
79
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         if (n2 == 8)
412                 {
413                 bn_mul_comba8(r,a,b);
414                 return; 
415                 }
416 # endif /* BN_MUL_COMBA */
417         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
418                 {
419                 /* This should not happen */
420                 bn_mul_normal(r,a,n2,b,n2);
421                 return;
422                 }
423         /* r=(a[0]-a[1])*(b[1]-b[0]) */
424         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
425         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
426         zero=neg=0;
427         switch (c1*3+c2)
428                 {
429         case -4:
430                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
431                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
432                 break;
433         case -3:
434                 zero=1;
435                 break;
436         case -2:
437                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
438                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
439                 neg=1;
440                 break;
441         case -1:
442         case 0:
443         case 1:
444                 zero=1;
445                 break;
446         case 2:
447                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
448                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
449                 neg=1;
450                 break;
451         case 3:
452                 zero=1;
453                 break;
454         case 4:
455                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
456                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
457                 break;
458                 }
459
460 # ifdef BN_MUL_COMBA
461         if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
462                                                extra args to do this well */
463                 {
464                 if (!zero)
465                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
466                 else
467                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
468                 
469                 bn_mul_comba4(r,a,b);
470                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
471                 }
472         else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
473                                                     take extra args to do this
474                                                     well */
475                 {
476                 if (!zero)
477                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
478                 else
479                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
480                 
481                 bn_mul_comba8(r,a,b);
482                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
483                 }
484         else
485 # endif /* BN_MUL_COMBA */
486                 {
487                 p= &(t[n2*2]);
488                 if (!zero)
489                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
490                 else
491                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
492                 bn_mul_recursive(r,a,b,n,0,0,p);
493                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
494                 }
495
496         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
497          * r[10] holds (a[0]*b[0])
498          * r[32] holds (b[1]*b[1])
499          */
500
501         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
502
503         if (neg) /* if t[32] is negative */
504                 {
505                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
506                 }
507         else
508                 {
509                 /* Might have a carry */
510                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
511                 }
512
513         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
514          * r[10] holds (a[0]*b[0])
515          * r[32] holds (b[1]*b[1])
516          * c1 holds the carry bits
517          */
518         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
519         if (c1)
520                 {
521                 p= &(r[n+n2]);
522                 lo= *p;
523                 ln=(lo+c1)&BN_MASK2;
524                 *p=ln;
525
526                 /* The overflow will stop before we over write
527                  * words we should not overwrite */
528                 if (ln < (BN_ULONG)c1)
529                         {
530                         do      {
531                                 p++;
532                                 lo= *p;
533                                 ln=(lo+1)&BN_MASK2;
534                                 *p=ln;
535                                 } while (ln == 0);
536                         }
537                 }
538         }
539
540 /* n+tn is the word length
541  * t needs to be n*4 is size, as does r */
542 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
543              int tna, int tnb, BN_ULONG *t)
544         {
545         int i,j,n2=n*2;
546         unsigned int c1,c2,neg,zero;
547         BN_ULONG ln,lo,*p;
548
549 # ifdef BN_COUNT
550         fprintf(stderr," bn_mul_part_recursive (%d+%d) * (%d+%d)\n",
551                 tna, n, tnb, n);
552 # endif
553         if (n < 8)
554                 {
555                 bn_mul_normal(r,a,n+tna,b,n+tnb);
556                 return;
557                 }
558
559         /* r=(a[0]-a[1])*(b[1]-b[0]) */
560         c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
561         c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
562         zero=neg=0;
563         switch (c1*3+c2)
564                 {
565         case -4:
566                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
567                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
568                 break;
569         case -3:
570                 zero=1;
571                 /* break; */
572         case -2:
573                 bn_sub_part_words(t,      &(a[n]),a,      tna,tna-n); /* - */
574                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n); /* + */
575                 neg=1;
576                 break;
577         case -1:
578         case 0:
579         case 1:
580                 zero=1;
581                 /* break; */
582         case 2:
583                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna); /* + */
584                 bn_sub_part_words(&(t[n]),b,      &(b[n]),tnb,n-tnb); /* - */
585                 neg=1;
586                 break;
587         case 3:
588                 zero=1;
589                 /* break; */
590         case 4:
591                 bn_sub_part_words(t,      a,      &(a[n]),tna,n-tna);
592                 bn_sub_part_words(&(t[n]),&(b[n]),b,      tnb,tnb-n);
593                 break;
594                 }
595                 /* The zero case isn't yet implemented here. The speedup
596                    would probably be negligible. */
597 # if 0
598         if (n == 4)
599                 {
600                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
601                 bn_mul_comba4(r,a,b);
602                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
603                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
604                 }
605         else
606 # endif
607         if (n == 8)
608                 {
609                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
610                 bn_mul_comba8(r,a,b);
611                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
612                 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
613                 }
614         else
615                 {
616                 p= &(t[n2*2]);
617                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
618                 bn_mul_recursive(r,a,b,n,0,0,p);
619                 i=n/2;
620                 /* If there is only a bottom half to the number,
621                  * just do it */
622                 if (tna > tnb)
623                         j = tna - i;
624                 else
625                         j = tnb - i;
626                 if (j == 0)
627                         {
628                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
629                                 i,tna-i,tnb-i,p);
630                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
631                         }
632                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
633                                 {
634                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
635                                         i,tna-i,tnb-i,p);
636                                 memset(&(r[n2+tna+tnb]),0,
637                                         sizeof(BN_ULONG)*(n2-tna-tnb));
638                                 }
639                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
640                         {
641                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
642                         if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
643                                 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
644                                 {
645                                 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
646                                 }
647                         else
648                                 {
649                                 for (;;)
650                                         {
651                                         i/=2;
652                                         if (i < tna && i < tnb)
653                                                 {
654                                                 bn_mul_part_recursive(&(r[n2]),
655                                                         &(a[n]),&(b[n]),
656                                                         i,tna-i,tnb-i,p);
657                                                 break;
658                                                 }
659                                         else if (i <= tna && i <= tnb)
660                                                 {
661                                                 bn_mul_recursive(&(r[n2]),
662                                                         &(a[n]),&(b[n]),
663                                                         i,tna-i,tnb-i,p);
664                                                 break;
665                                                 }
666                                         }
667                                 }
668                         }
669                 }
670
671         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
672          * r[10] holds (a[0]*b[0])
673          * r[32] holds (b[1]*b[1])
674          */
675
676         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
677
678         if (neg) /* if t[32] is negative */
679                 {
680                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
681                 }
682         else
683                 {
684                 /* Might have a carry */
685                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
686                 }
687
688         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
689          * r[10] holds (a[0]*b[0])
690          * r[32] holds (b[1]*b[1])
691          * c1 holds the carry bits
692          */
693         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
694         if (c1)
695                 {
696                 p= &(r[n+n2]);
697                 lo= *p;
698                 ln=(lo+c1)&BN_MASK2;
699                 *p=ln;
700
701                 /* The overflow will stop before we over write
702                  * words we should not overwrite */
703                 if (ln < c1)
704                         {
705                         do      {
706                                 p++;
707                                 lo= *p;
708                                 ln=(lo+1)&BN_MASK2;
709                                 *p=ln;
710                                 } while (ln == 0);
711                         }
712                 }
713         }
714
715 /* a and b must be the same size, which is n2.
716  * r needs to be n2 words and t needs to be n2*2
717  */
718 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
719              BN_ULONG *t)
720         {
721         int n=n2/2;
722
723 # ifdef BN_COUNT
724         fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
725 # endif
726
727         bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
728         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
729                 {
730                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
731                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
732                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
733                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
734                 }
735         else
736                 {
737                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
738                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
739                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
740                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
741                 }
742         }
743
744 /* a and b must be the same size, which is n2.
745  * r needs to be n2 words and t needs to be n2*2
746  * l is the low words of the output.
747  * t needs to be n2*3
748  */
749 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
750              BN_ULONG *t)
751         {
752         int i,n;
753         int c1,c2;
754         int neg,oneg,zero;
755         BN_ULONG ll,lc,*lp,*mp;
756
757 # ifdef BN_COUNT
758         fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
759 # endif
760         n=n2/2;
761
762         /* Calculate (al-ah)*(bh-bl) */
763         neg=zero=0;
764         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
765         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
766         switch (c1*3+c2)
767                 {
768         case -4:
769                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
770                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
771                 break;
772         case -3:
773                 zero=1;
774                 break;
775         case -2:
776                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
777                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
778                 neg=1;
779                 break;
780         case -1:
781         case 0:
782         case 1:
783                 zero=1;
784                 break;
785         case 2:
786                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
787                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
788                 neg=1;
789                 break;
790         case 3:
791                 zero=1;
792                 break;
793         case 4:
794                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
795                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
796                 break;
797                 }
798                 
799         oneg=neg;
800         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
801         /* r[10] = (a[1]*b[1]) */
802 # ifdef BN_MUL_COMBA
803         if (n == 8)
804                 {
805                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
806                 bn_mul_comba8(r,&(a[n]),&(b[n]));
807                 }
808         else
809 # endif
810                 {
811                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
812                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
813                 }
814
815         /* s0 == low(al*bl)
816          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
817          * We know s0 and s1 so the only unknown is high(al*bl)
818          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
819          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
820          */
821         if (l != NULL)
822                 {
823                 lp= &(t[n2+n]);
824                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
825                 }
826         else
827                 {
828                 c1=0;
829                 lp= &(r[0]);
830                 }
831
832         if (neg)
833                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
834         else
835                 {
836                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
837                 neg=0;
838                 }
839
840         if (l != NULL)
841                 {
842                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
843                 }
844         else
845                 {
846                 lp= &(t[n2+n]);
847                 mp= &(t[n2]);
848                 for (i=0; i<n; i++)
849                         lp[i]=((~mp[i])+1)&BN_MASK2;
850                 }
851
852         /* s[0] = low(al*bl)
853          * t[3] = high(al*bl)
854          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
855          * r[10] = (a[1]*b[1])
856          */
857         /* R[10] = al*bl
858          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
859          * R[32] = ah*bh
860          */
861         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
862          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
863          * R[3]=r[1]+(carry/borrow)
864          */
865         if (l != NULL)
866                 {
867                 lp= &(t[n2]);
868                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
869                 }
870         else
871                 {
872                 lp= &(t[n2+n]);
873                 c1=0;
874                 }
875         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
876         if (oneg)
877                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
878         else
879                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
880
881         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
882         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
883         if (oneg)
884                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
885         else
886                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
887         
888         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
889                 {
890                 i=0;
891                 if (c1 > 0)
892                         {
893                         lc=c1;
894                         do      {
895                                 ll=(r[i]+lc)&BN_MASK2;
896                                 r[i++]=ll;
897                                 lc=(lc > ll);
898                                 } while (lc);
899                         }
900                 else
901                         {
902                         lc= -c1;
903                         do      {
904                                 ll=r[i];
905                                 r[i++]=(ll-lc)&BN_MASK2;
906                                 lc=(lc > ll);
907                                 } while (lc);
908                         }
909                 }
910         if (c2 != 0) /* Add starting at r[1] */
911                 {
912                 i=n;
913                 if (c2 > 0)
914                         {
915                         lc=c2;
916                         do      {
917                                 ll=(r[i]+lc)&BN_MASK2;
918                                 r[i++]=ll;
919                                 lc=(lc > ll);
920                                 } while (lc);
921                         }
922                 else
923                         {
924                         lc= -c2;
925                         do      {
926                                 ll=r[i];
927                                 r[i++]=(ll-lc)&BN_MASK2;
928                                 lc=(lc > ll);
929                                 } while (lc);
930                         }
931                 }
932         }
933 #endif /* BN_RECURSION */
934
935 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
936         {
937         int ret=0;
938         int top,al,bl;
939         BIGNUM *rr;
940 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
941         int i;
942 #endif
943 #ifdef BN_RECURSION
944         BIGNUM *t=NULL;
945         int j=0,k;
946 #endif
947
948 #ifdef BN_COUNT
949         fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
950 #endif
951
952         bn_check_top(a);
953         bn_check_top(b);
954         bn_check_top(r);
955
956         al=a->top;
957         bl=b->top;
958
959         if ((al == 0) || (bl == 0))
960                 {
961                 BN_zero(r);
962                 return(1);
963                 }
964         top=al+bl;
965
966         BN_CTX_start(ctx);
967         if ((r == a) || (r == b))
968                 {
969                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
970                 }
971         else
972                 rr = r;
973         rr->neg=a->neg^b->neg;
974
975 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
976         i = al-bl;
977 #endif
978 #ifdef BN_MUL_COMBA
979         if (i == 0)
980                 {
981 # if 0
982                 if (al == 4)
983                         {
984                         if (bn_wexpand(rr,8) == NULL) goto err;
985                         rr->top=8;
986                         bn_mul_comba4(rr->d,a->d,b->d);
987                         goto end;
988                         }
989 # endif
990                 if (al == 8)
991                         {
992                         if (bn_wexpand(rr,16) == NULL) goto err;
993                         rr->top=16;
994                         bn_mul_comba8(rr->d,a->d,b->d);
995                         goto end;
996                         }
997                 }
998 #endif /* BN_MUL_COMBA */
999 #ifdef BN_RECURSION
1000         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
1001                 {
1002                 if (i >= -1 && i <= 1)
1003                         {
1004                         int sav_j =0;
1005                         /* Find out the power of two lower or equal
1006                            to the longest of the two numbers */
1007                         if (i >= 0)
1008                                 {
1009                                 j = BN_num_bits_word((BN_ULONG)al);
1010                                 }
1011                         if (i == -1)
1012                                 {
1013                                 j = BN_num_bits_word((BN_ULONG)bl);
1014                                 }
1015                         sav_j = j;
1016                         j = 1<<(j-1);
1017                         assert(j <= al || j <= bl);
1018                         k = j+j;
1019                         t = BN_CTX_get(ctx);
1020                         if (al > j || bl > j)
1021                                 {
1022                                 bn_wexpand(t,k*4);
1023                                 bn_wexpand(rr,k*4);
1024                                 bn_mul_part_recursive(rr->d,a->d,b->d,
1025                                         j,al-j,bl-j,t->d);
1026                                 }
1027                         else    /* al <= j || bl <= j */
1028                                 {
1029                                 bn_wexpand(t,k*2);
1030                                 bn_wexpand(rr,k*2);
1031                                 bn_mul_recursive(rr->d,a->d,b->d,
1032                                         j,al-j,bl-j,t->d);
1033                                 }
1034                         rr->top=top;
1035                         goto end;
1036                         }
1037 #if 0
1038                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
1039                         {
1040                         BIGNUM *tmp_bn = (BIGNUM *)b;
1041                         bn_wexpand(tmp_bn,al);
1042                         tmp_bn->d[bl]=0;
1043                         bl++;
1044                         i--;
1045                         }
1046                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1047                         {
1048                         BIGNUM *tmp_bn = (BIGNUM *)a;
1049                         bn_wexpand(tmp_bn,bl);
1050                         tmp_bn->d[al]=0;
1051                         al++;
1052                         i++;
1053                         }
1054                 if (i == 0)
1055                         {
1056                         /* symmetric and > 4 */
1057                         /* 16 or larger */
1058                         j=BN_num_bits_word((BN_ULONG)al);
1059                         j=1<<(j-1);
1060                         k=j+j;
1061                         t = BN_CTX_get(ctx);
1062                         if (al == j) /* exact multiple */
1063                                 {
1064                                 bn_wexpand(t,k*2);
1065                                 bn_wexpand(rr,k*2);
1066                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1067                                 }
1068                         else
1069                                 {
1070                                 bn_wexpand(t,k*4);
1071                                 bn_wexpand(rr,k*4);
1072                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1073                                 }
1074                         rr->top=top;
1075                         goto end;
1076                         }
1077 #endif
1078                 }
1079 #endif /* BN_RECURSION */
1080         if (bn_wexpand(rr,top) == NULL) goto err;
1081         rr->top=top;
1082         bn_mul_normal(rr->d,a->d,al,b->d,bl);
1083
1084 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1085 end:
1086 #endif
1087         bn_fix_top(rr);
1088         if (r != rr) BN_copy(r,rr);
1089         ret=1;
1090 err:
1091         BN_CTX_end(ctx);
1092         return(ret);
1093         }
1094
1095 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1096         {
1097         BN_ULONG *rr;
1098
1099 #ifdef BN_COUNT
1100         fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
1101 #endif
1102
1103         if (na < nb)
1104                 {
1105                 int itmp;
1106                 BN_ULONG *ltmp;
1107
1108                 itmp=na; na=nb; nb=itmp;
1109                 ltmp=a;   a=b;   b=ltmp;
1110
1111                 }
1112         rr= &(r[na]);
1113         if (nb <= 0)
1114                 {
1115                 (void)bn_mul_words(r,a,na,0);
1116                 return;
1117                 }
1118         else
1119                 rr[0]=bn_mul_words(r,a,na,b[0]);
1120
1121         for (;;)
1122                 {
1123                 if (--nb <= 0) return;
1124                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1125                 if (--nb <= 0) return;
1126                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1127                 if (--nb <= 0) return;
1128                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1129                 if (--nb <= 0) return;
1130                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1131                 rr+=4;
1132                 r+=4;
1133                 b+=4;
1134                 }
1135         }
1136
1137 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1138         {
1139 #ifdef BN_COUNT
1140         fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
1141 #endif
1142         bn_mul_words(r,a,n,b[0]);
1143
1144         for (;;)
1145                 {
1146                 if (--n <= 0) return;
1147                 bn_mul_add_words(&(r[1]),a,n,b[1]);
1148                 if (--n <= 0) return;
1149                 bn_mul_add_words(&(r[2]),a,n,b[2]);
1150                 if (--n <= 0) return;
1151                 bn_mul_add_words(&(r[3]),a,n,b[3]);
1152                 if (--n <= 0) return;
1153                 bn_mul_add_words(&(r[4]),a,n,b[4]);
1154                 r+=4;
1155                 b+=4;
1156                 }
1157         }