3e8baaad9a05b0530f427b49ea444854a75f8bcb
[openssl.git] / crypto / bn / bn_mul.c
1 /* crypto/bn/bn_mul.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3  * All rights reserved.
4  *
5  * This package is an SSL implementation written
6  * by Eric Young (eay@cryptsoft.com).
7  * The implementation was written so as to conform with Netscapes SSL.
8  * 
9  * This library is free for commercial and non-commercial use as long as
10  * the following conditions are aheared to.  The following conditions
11  * apply to all code found in this distribution, be it the RC4, RSA,
12  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
13  * included with this distribution is covered by the same copyright terms
14  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15  * 
16  * Copyright remains Eric Young's, and as such any Copyright notices in
17  * the code are not to be removed.
18  * If this package is used in a product, Eric Young should be given attribution
19  * as the author of the parts of the library used.
20  * This can be in the form of a textual message at program startup or
21  * in documentation (online or textual) provided with the package.
22  * 
23  * Redistribution and use in source and binary forms, with or without
24  * modification, are permitted provided that the following conditions
25  * are met:
26  * 1. Redistributions of source code must retain the copyright
27  *    notice, this list of conditions and the following disclaimer.
28  * 2. Redistributions in binary form must reproduce the above copyright
29  *    notice, this list of conditions and the following disclaimer in the
30  *    documentation and/or other materials provided with the distribution.
31  * 3. All advertising materials mentioning features or use of this software
32  *    must display the following acknowledgement:
33  *    "This product includes cryptographic software written by
34  *     Eric Young (eay@cryptsoft.com)"
35  *    The word 'cryptographic' can be left out if the rouines from the library
36  *    being used are not cryptographic related :-).
37  * 4. If you include any Windows specific code (or a derivative thereof) from 
38  *    the apps directory (application code) you must include an acknowledgement:
39  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40  * 
41  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51  * SUCH DAMAGE.
52  * 
53  * The licence and distribution terms for any publically available version or
54  * derivative of this code cannot be changed.  i.e. this code cannot simply be
55  * copied and put under another distribution licence
56  * [including the GNU Public Licence.]
57  */
58
59 #include <stdio.h>
60 #include "cryptlib.h"
61 #include "bn_lcl.h"
62
63 #ifdef BN_RECURSION
64 /* Karatsuba recursive multiplication algorithm
65  * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
66
67 /* r is 2*n2 words in size,
68  * a and b are both n2 words in size.
69  * n2 must be a power of 2.
70  * We multiply and return the result.
71  * t must be 2*n2 words in size
72  * We calculate
73  * a[0]*b[0]
74  * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
75  * a[1]*b[1]
76  */
77 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
78              BN_ULONG *t)
79         {
80         int n=n2/2,c1,c2;
81         unsigned int neg,zero;
82         BN_ULONG ln,lo,*p;
83
84 # ifdef BN_COUNT
85         printf(" bn_mul_recursive %d * %d\n",n2,n2);
86 # endif
87 # ifdef BN_MUL_COMBA
88 #  if 0
89         if (n2 == 4)
90                 {
91                 bn_mul_comba4(r,a,b);
92                 return;
93                 }
94 #  endif
95         if (n2 == 8)
96                 {
97                 bn_mul_comba8(r,a,b);
98                 return; 
99                 }
100 # endif /* BN_MUL_COMBA */
101         if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
102                 {
103                 /* This should not happen */
104                 bn_mul_normal(r,a,n2,b,n2);
105                 return;
106                 }
107         /* r=(a[0]-a[1])*(b[1]-b[0]) */
108         c1=bn_cmp_words(a,&(a[n]),n);
109         c2=bn_cmp_words(&(b[n]),b,n);
110         zero=neg=0;
111         switch (c1*3+c2)
112                 {
113         case -4:
114                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
115                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
116                 break;
117         case -3:
118                 zero=1;
119                 break;
120         case -2:
121                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
122                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
123                 neg=1;
124                 break;
125         case -1:
126         case 0:
127         case 1:
128                 zero=1;
129                 break;
130         case 2:
131                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
132                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
133                 neg=1;
134                 break;
135         case 3:
136                 zero=1;
137                 break;
138         case 4:
139                 bn_sub_words(t,      a,      &(a[n]),n);
140                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
141                 break;
142                 }
143
144 # ifdef BN_MUL_COMBA
145         if (n == 4)
146                 {
147                 if (!zero)
148                         bn_mul_comba4(&(t[n2]),t,&(t[n]));
149                 else
150                         memset(&(t[n2]),0,8*sizeof(BN_ULONG));
151                 
152                 bn_mul_comba4(r,a,b);
153                 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
154                 }
155         else if (n == 8)
156                 {
157                 if (!zero)
158                         bn_mul_comba8(&(t[n2]),t,&(t[n]));
159                 else
160                         memset(&(t[n2]),0,16*sizeof(BN_ULONG));
161                 
162                 bn_mul_comba8(r,a,b);
163                 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
164                 }
165         else
166 # endif /* BN_MUL_COMBA */
167                 {
168                 p= &(t[n2*2]);
169                 if (!zero)
170                         bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
171                 else
172                         memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
173                 bn_mul_recursive(r,a,b,n,p);
174                 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
175                 }
176
177         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
178          * r[10] holds (a[0]*b[0])
179          * r[32] holds (b[1]*b[1])
180          */
181
182         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
183
184         if (neg) /* if t[32] is negative */
185                 {
186                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
187                 }
188         else
189                 {
190                 /* Might have a carry */
191                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
192                 }
193
194         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
195          * r[10] holds (a[0]*b[0])
196          * r[32] holds (b[1]*b[1])
197          * c1 holds the carry bits
198          */
199         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
200         if (c1)
201                 {
202                 p= &(r[n+n2]);
203                 lo= *p;
204                 ln=(lo+c1)&BN_MASK2;
205                 *p=ln;
206
207                 /* The overflow will stop before we over write
208                  * words we should not overwrite */
209                 if (ln < (BN_ULONG)c1)
210                         {
211                         do      {
212                                 p++;
213                                 lo= *p;
214                                 ln=(lo+1)&BN_MASK2;
215                                 *p=ln;
216                                 } while (ln == 0);
217                         }
218                 }
219         }
220
221 /* n+tn is the word length
222  * t needs to be n*4 is size, as does r */
223 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
224              int n, BN_ULONG *t)
225         {
226         int i,j,n2=n*2;
227         unsigned int c1,c2,neg,zero;
228         BN_ULONG ln,lo,*p;
229
230 # ifdef BN_COUNT
231         printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
232 # endif
233         if (n < 8)
234                 {
235                 i=tn+n;
236                 bn_mul_normal(r,a,i,b,i);
237                 return;
238                 }
239
240         /* r=(a[0]-a[1])*(b[1]-b[0]) */
241         c1=bn_cmp_words(a,&(a[n]),n);
242         c2=bn_cmp_words(&(b[n]),b,n);
243         zero=neg=0;
244         switch (c1*3+c2)
245                 {
246         case -4:
247                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
248                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
249                 break;
250         case -3:
251                 zero=1;
252                 /* break; */
253         case -2:
254                 bn_sub_words(t,      &(a[n]),a,      n); /* - */
255                 bn_sub_words(&(t[n]),&(b[n]),b,      n); /* + */
256                 neg=1;
257                 break;
258         case -1:
259         case 0:
260         case 1:
261                 zero=1;
262                 /* break; */
263         case 2:
264                 bn_sub_words(t,      a,      &(a[n]),n); /* + */
265                 bn_sub_words(&(t[n]),b,      &(b[n]),n); /* - */
266                 neg=1;
267                 break;
268         case 3:
269                 zero=1;
270                 /* break; */
271         case 4:
272                 bn_sub_words(t,      a,      &(a[n]),n);
273                 bn_sub_words(&(t[n]),&(b[n]),b,      n);
274                 break;
275                 }
276                 /* The zero case isn't yet implemented here. The speedup
277                    would probably be negligible. */
278 # if 0
279         if (n == 4)
280                 {
281                 bn_mul_comba4(&(t[n2]),t,&(t[n]));
282                 bn_mul_comba4(r,a,b);
283                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
284                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
285                 }
286         else
287 # endif
288         if (n == 8)
289                 {
290                 bn_mul_comba8(&(t[n2]),t,&(t[n]));
291                 bn_mul_comba8(r,a,b);
292                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
293                 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
294                 }
295         else
296                 {
297                 p= &(t[n2*2]);
298                 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
299                 bn_mul_recursive(r,a,b,n,p);
300                 i=n/2;
301                 /* If there is only a bottom half to the number,
302                  * just do it */
303                 j=tn-i;
304                 if (j == 0)
305                         {
306                         bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
307                         memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
308                         }
309                 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
310                                 {
311                                 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
312                                         j,i,p);
313                                 memset(&(r[n2+tn*2]),0,
314                                         sizeof(BN_ULONG)*(n2-tn*2));
315                                 }
316                 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
317                         {
318                         memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
319                         if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
320                                 {
321                                 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
322                                 }
323                         else
324                                 {
325                                 for (;;)
326                                         {
327                                         i/=2;
328                                         if (i < tn)
329                                                 {
330                                                 bn_mul_part_recursive(&(r[n2]),
331                                                         &(a[n]),&(b[n]),
332                                                         tn-i,i,p);
333                                                 break;
334                                                 }
335                                         else if (i == tn)
336                                                 {
337                                                 bn_mul_recursive(&(r[n2]),
338                                                         &(a[n]),&(b[n]),
339                                                         i,p);
340                                                 break;
341                                                 }
342                                         }
343                                 }
344                         }
345                 }
346
347         /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
348          * r[10] holds (a[0]*b[0])
349          * r[32] holds (b[1]*b[1])
350          */
351
352         c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
353
354         if (neg) /* if t[32] is negative */
355                 {
356                 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
357                 }
358         else
359                 {
360                 /* Might have a carry */
361                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
362                 }
363
364         /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
365          * r[10] holds (a[0]*b[0])
366          * r[32] holds (b[1]*b[1])
367          * c1 holds the carry bits
368          */
369         c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
370         if (c1)
371                 {
372                 p= &(r[n+n2]);
373                 lo= *p;
374                 ln=(lo+c1)&BN_MASK2;
375                 *p=ln;
376
377                 /* The overflow will stop before we over write
378                  * words we should not overwrite */
379                 if (ln < c1)
380                         {
381                         do      {
382                                 p++;
383                                 lo= *p;
384                                 ln=(lo+1)&BN_MASK2;
385                                 *p=ln;
386                                 } while (ln == 0);
387                         }
388                 }
389         }
390
391 /* a and b must be the same size, which is n2.
392  * r needs to be n2 words and t needs to be n2*2
393  */
394 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
395              BN_ULONG *t)
396         {
397         int n=n2/2;
398
399 # ifdef BN_COUNT
400         printf(" bn_mul_low_recursive %d * %d\n",n2,n2);
401 # endif
402
403         bn_mul_recursive(r,a,b,n,&(t[0]));
404         if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
405                 {
406                 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
407                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
408                 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
409                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
410                 }
411         else
412                 {
413                 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
414                 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
415                 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
416                 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
417                 }
418         }
419
420 /* a and b must be the same size, which is n2.
421  * r needs to be n2 words and t needs to be n2*2
422  * l is the low words of the output.
423  * t needs to be n2*3
424  */
425 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
426              BN_ULONG *t)
427         {
428         int i,n;
429         int c1,c2;
430         int neg,oneg,zero;
431         BN_ULONG ll,lc,*lp,*mp;
432
433 # ifdef BN_COUNT
434         printf(" bn_mul_high %d * %d\n",n2,n2);
435 # endif
436         n=n2/2;
437
438         /* Calculate (al-ah)*(bh-bl) */
439         neg=zero=0;
440         c1=bn_cmp_words(&(a[0]),&(a[n]),n);
441         c2=bn_cmp_words(&(b[n]),&(b[0]),n);
442         switch (c1*3+c2)
443                 {
444         case -4:
445                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
446                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
447                 break;
448         case -3:
449                 zero=1;
450                 break;
451         case -2:
452                 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
453                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
454                 neg=1;
455                 break;
456         case -1:
457         case 0:
458         case 1:
459                 zero=1;
460                 break;
461         case 2:
462                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
463                 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
464                 neg=1;
465                 break;
466         case 3:
467                 zero=1;
468                 break;
469         case 4:
470                 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
471                 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
472                 break;
473                 }
474                 
475         oneg=neg;
476         /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
477         /* r[10] = (a[1]*b[1]) */
478 # ifdef BN_MUL_COMBA
479         if (n == 8)
480                 {
481                 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
482                 bn_mul_comba8(r,&(a[n]),&(b[n]));
483                 }
484         else
485 # endif
486                 {
487                 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2]));
488                 bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2]));
489                 }
490
491         /* s0 == low(al*bl)
492          * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
493          * We know s0 and s1 so the only unknown is high(al*bl)
494          * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
495          * high(al*bl) == s1 - (r[0]+l[0]+t[0])
496          */
497         if (l != NULL)
498                 {
499                 lp= &(t[n2+n]);
500                 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
501                 }
502         else
503                 {
504                 c1=0;
505                 lp= &(r[0]);
506                 }
507
508         if (neg)
509                 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
510         else
511                 {
512                 bn_add_words(&(t[n2]),lp,&(t[0]),n);
513                 neg=0;
514                 }
515
516         if (l != NULL)
517                 {
518                 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
519                 }
520         else
521                 {
522                 lp= &(t[n2+n]);
523                 mp= &(t[n2]);
524                 for (i=0; i<n; i++)
525                         lp[i]=((~mp[i])+1)&BN_MASK2;
526                 }
527
528         /* s[0] = low(al*bl)
529          * t[3] = high(al*bl)
530          * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
531          * r[10] = (a[1]*b[1])
532          */
533         /* R[10] = al*bl
534          * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
535          * R[32] = ah*bh
536          */
537         /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
538          * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
539          * R[3]=r[1]+(carry/borrow)
540          */
541         if (l != NULL)
542                 {
543                 lp= &(t[n2]);
544                 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
545                 }
546         else
547                 {
548                 lp= &(t[n2+n]);
549                 c1=0;
550                 }
551         c1+=(int)(bn_add_words(&(t[n2]),lp,  &(r[0]),n));
552         if (oneg)
553                 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
554         else
555                 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
556
557         c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
558         c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
559         if (oneg)
560                 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
561         else
562                 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
563         
564         if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
565                 {
566                 i=0;
567                 if (c1 > 0)
568                         {
569                         lc=c1;
570                         do      {
571                                 ll=(r[i]+lc)&BN_MASK2;
572                                 r[i++]=ll;
573                                 lc=(lc > ll);
574                                 } while (lc);
575                         }
576                 else
577                         {
578                         lc= -c1;
579                         do      {
580                                 ll=r[i];
581                                 r[i++]=(ll-lc)&BN_MASK2;
582                                 lc=(lc > ll);
583                                 } while (lc);
584                         }
585                 }
586         if (c2 != 0) /* Add starting at r[1] */
587                 {
588                 i=n;
589                 if (c2 > 0)
590                         {
591                         lc=c2;
592                         do      {
593                                 ll=(r[i]+lc)&BN_MASK2;
594                                 r[i++]=ll;
595                                 lc=(lc > ll);
596                                 } while (lc);
597                         }
598                 else
599                         {
600                         lc= -c2;
601                         do      {
602                                 ll=r[i];
603                                 r[i++]=(ll-lc)&BN_MASK2;
604                                 lc=(lc > ll);
605                                 } while (lc);
606                         }
607                 }
608         }
609 #endif /* BN_RECURSION */
610
611 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
612         {
613         int top,al,bl;
614         BIGNUM *rr;
615         int ret = 0;
616 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
617         int i;
618 #endif
619 #ifdef BN_RECURSION
620         BIGNUM *t;
621         int j,k;
622 #endif
623
624 #ifdef BN_COUNT
625         printf("BN_mul %d * %d\n",a->top,b->top);
626 #endif
627
628         bn_check_top(a);
629         bn_check_top(b);
630         bn_check_top(r);
631
632         al=a->top;
633         bl=b->top;
634         r->neg=a->neg^b->neg;
635
636         if ((al == 0) || (bl == 0))
637                 {
638                 BN_zero(r);
639                 return(1);
640                 }
641         top=al+bl;
642
643         BN_CTX_start(ctx);
644         if ((r == a) || (r == b))
645                 {
646                 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
647                 }
648         else
649                 rr = r;
650
651 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
652         i = al-bl;
653 #endif
654 #ifdef BN_MUL_COMBA
655         if (i == 0)
656                 {
657 # if 0
658                 if (al == 4)
659                         {
660                         if (bn_wexpand(rr,8) == NULL) goto err;
661                         rr->top=8;
662                         bn_mul_comba4(rr->d,a->d,b->d);
663                         goto end;
664                         }
665 # endif
666                 if (al == 8)
667                         {
668                         if (bn_wexpand(rr,16) == NULL) goto err;
669                         rr->top=16;
670                         bn_mul_comba8(rr->d,a->d,b->d);
671                         goto end;
672                         }
673                 }
674 #endif /* BN_MUL_COMBA */
675 #ifdef BN_RECURSION
676         if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
677                 {
678                 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
679                         {
680                         bn_wexpand(b,al);
681                         b->d[bl]=0;
682                         bl++;
683                         i--;
684                         }
685                 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
686                         {
687                         bn_wexpand(a,bl);
688                         a->d[al]=0;
689                         al++;
690                         i++;
691                         }
692                 if (i == 0)
693                         {
694                         /* symmetric and > 4 */
695                         /* 16 or larger */
696                         j=BN_num_bits_word((BN_ULONG)al);
697                         j=1<<(j-1);
698                         k=j+j;
699                         t = BN_CTX_get(ctx);
700                         if (al == j) /* exact multiple */
701                                 {
702                                 bn_wexpand(t,k*2);
703                                 bn_wexpand(rr,k*2);
704                                 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
705                                 }
706                         else
707                                 {
708                                 bn_wexpand(a,k);
709                                 bn_wexpand(b,k);
710                                 bn_wexpand(t,k*4);
711                                 bn_wexpand(rr,k*4);
712                                 for (i=a->top; i<k; i++)
713                                         a->d[i]=0;
714                                 for (i=b->top; i<k; i++)
715                                         b->d[i]=0;
716                                 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
717                                 }
718                         rr->top=top;
719                         goto end;
720                         }
721                 }
722 #endif /* BN_RECURSION */
723         if (bn_wexpand(rr,top) == NULL) goto err;
724         rr->top=top;
725         bn_mul_normal(rr->d,a->d,al,b->d,bl);
726
727 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
728 end:
729 #endif
730         bn_fix_top(rr);
731         if (r != rr) BN_copy(r,rr);
732         ret=1;
733 err:
734         BN_CTX_end(ctx);
735         return(ret);
736         }
737
738 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
739         {
740         BN_ULONG *rr;
741
742 #ifdef BN_COUNT
743         printf(" bn_mul_normal %d * %d\n",na,nb);
744 #endif
745
746         if (na < nb)
747                 {
748                 int itmp;
749                 BN_ULONG *ltmp;
750
751                 itmp=na; na=nb; nb=itmp;
752                 ltmp=a;   a=b;   b=ltmp;
753
754                 }
755         rr= &(r[na]);
756         rr[0]=bn_mul_words(r,a,na,b[0]);
757
758         for (;;)
759                 {
760                 if (--nb <= 0) return;
761                 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
762                 if (--nb <= 0) return;
763                 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
764                 if (--nb <= 0) return;
765                 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
766                 if (--nb <= 0) return;
767                 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
768                 rr+=4;
769                 r+=4;
770                 b+=4;
771                 }
772         }
773
774 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
775         {
776 #ifdef BN_COUNT
777         printf(" bn_mul_low_normal %d * %d\n",n,n);
778 #endif
779         bn_mul_words(r,a,n,b[0]);
780
781         for (;;)
782                 {
783                 if (--n <= 0) return;
784                 bn_mul_add_words(&(r[1]),a,n,b[1]);
785                 if (--n <= 0) return;
786                 bn_mul_add_words(&(r[2]),a,n,b[2]);
787                 if (--n <= 0) return;
788                 bn_mul_add_words(&(r[3]),a,n,b[3]);
789                 if (--n <= 0) return;
790                 bn_mul_add_words(&(r[4]),a,n,b[4]);
791                 r+=4;
792                 b+=4;
793                 }
794         }