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