1 /* crypto/bn/bn_mul.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
60 # undef NDEBUG /* avoid conflicting definitions */
68 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
69 /* Here follows specialised variants of bn_add_words() and
70 bn_sub_words(). They have the property performing operations on
71 arrays of different sizes. The sizes of those arrays is expressed through
72 cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
73 which is the delta between the two lengths, calculated as len(a)-len(b).
74 All lengths are the number of BN_ULONGs... For the operations that require
75 a result array as parameter, it must have the length cl+abs(dl).
76 These functions should probably end up in bn_asm.c as soon as there are
77 assembler counterparts for the systems that use assembler files. */
79 BN_ULONG bn_sub_part_words(BN_ULONG *r,
80 const BN_ULONG *a, const BN_ULONG *b,
86 c = bn_sub_words(r, a, b, cl);
100 r[0] = (0-t-c)&BN_MASK2;
102 if (++dl >= 0) break;
105 r[1] = (0-t-c)&BN_MASK2;
107 if (++dl >= 0) break;
110 r[2] = (0-t-c)&BN_MASK2;
112 if (++dl >= 0) break;
115 r[3] = (0-t-c)&BN_MASK2;
117 if (++dl >= 0) break;
129 r[0] = (t-c)&BN_MASK2;
131 if (--dl <= 0) break;
134 r[1] = (t-c)&BN_MASK2;
136 if (--dl <= 0) break;
139 r[2] = (t-c)&BN_MASK2;
141 if (--dl <= 0) break;
144 r[3] = (t-c)&BN_MASK2;
146 if (--dl <= 0) break;
156 switch (save_dl - dl)
160 if (--dl <= 0) break;
163 if (--dl <= 0) break;
166 if (--dl <= 0) break;
177 if (--dl <= 0) break;
179 if (--dl <= 0) break;
181 if (--dl <= 0) break;
183 if (--dl <= 0) break;
194 BN_ULONG bn_add_part_words(BN_ULONG *r,
195 const BN_ULONG *a, const BN_ULONG *b,
201 c = bn_add_words(r, a, b, cl);
218 if (++dl >= 0) break;
223 if (++dl >= 0) break;
228 if (++dl >= 0) break;
233 if (++dl >= 0) break;
243 switch (dl - save_dl)
247 if (++dl >= 0) break;
250 if (++dl >= 0) break;
253 if (++dl >= 0) break;
264 if (++dl >= 0) break;
266 if (++dl >= 0) break;
268 if (++dl >= 0) break;
270 if (++dl >= 0) break;
285 if (--dl <= 0) break;
290 if (--dl <= 0) break;
295 if (--dl <= 0) break;
300 if (--dl <= 0) break;
310 switch (save_dl - dl)
314 if (--dl <= 0) break;
317 if (--dl <= 0) break;
320 if (--dl <= 0) break;
331 if (--dl <= 0) break;
333 if (--dl <= 0) break;
335 if (--dl <= 0) break;
337 if (--dl <= 0) break;
348 /* Karatsuba recursive multiplication algorithm
349 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
351 /* r is 2*n2 words in size,
352 * a and b are both n2 words in size.
353 * n2 must be a power of 2.
354 * We multiply and return the result.
355 * t must be 2*n2 words in size
358 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
361 /* dnX may not be positive, but n2/2+dnX has to be */
362 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
363 int dna, int dnb, BN_ULONG *t)
366 int tna=n+dna, tnb=n+dnb;
367 unsigned int neg,zero;
374 bn_mul_comba4(r,a,b);
378 /* Only call bn_mul_comba 8 if n2 == 8 and the
379 * two arrays are complete [steve]
381 if (n2 == 8 && dna == 0 && dnb == 0)
383 bn_mul_comba8(r,a,b);
386 # endif /* BN_MUL_COMBA */
387 /* Else do normal multiply */
388 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
390 bn_mul_normal(r,a,n2+dna,b,n2+dnb);
392 memset(&r[2*n2 + dna + dnb], 0,
393 sizeof(BN_ULONG) * -(dna + dnb));
396 /* r=(a[0]-a[1])*(b[1]-b[0]) */
397 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
398 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
403 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
404 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
410 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
411 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
420 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
421 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
428 bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
429 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
434 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
435 extra args to do this well */
438 bn_mul_comba4(&(t[n2]),t,&(t[n]));
440 memset(&(t[n2]),0,8*sizeof(BN_ULONG));
442 bn_mul_comba4(r,a,b);
443 bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
445 else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
446 take extra args to do this
450 bn_mul_comba8(&(t[n2]),t,&(t[n]));
452 memset(&(t[n2]),0,16*sizeof(BN_ULONG));
454 bn_mul_comba8(r,a,b);
455 bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
458 # endif /* BN_MUL_COMBA */
462 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
464 memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
465 bn_mul_recursive(r,a,b,n,0,0,p);
466 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
469 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
470 * r[10] holds (a[0]*b[0])
471 * r[32] holds (b[1]*b[1])
474 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
476 if (neg) /* if t[32] is negative */
478 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
482 /* Might have a carry */
483 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
486 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
487 * r[10] holds (a[0]*b[0])
488 * r[32] holds (b[1]*b[1])
489 * c1 holds the carry bits
491 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
499 /* The overflow will stop before we over write
500 * words we should not overwrite */
501 if (ln < (BN_ULONG)c1)
513 /* n+tn is the word length
514 * t needs to be n*4 is size, as does r */
515 /* tnX may not be negative but less than n */
516 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
517 int tna, int tnb, BN_ULONG *t)
525 bn_mul_normal(r,a,n+tna,b,n+tnb);
529 /* r=(a[0]-a[1])*(b[1]-b[0]) */
530 c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
531 c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
536 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
537 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
542 bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
543 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
551 bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
552 bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
558 bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
559 bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
562 /* The zero case isn't yet implemented here. The speedup
563 would probably be negligible. */
567 bn_mul_comba4(&(t[n2]),t,&(t[n]));
568 bn_mul_comba4(r,a,b);
569 bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
570 memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
576 bn_mul_comba8(&(t[n2]),t,&(t[n]));
577 bn_mul_comba8(r,a,b);
578 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
579 memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
584 bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
585 bn_mul_recursive(r,a,b,n,0,0,p);
587 /* If there is only a bottom half to the number,
595 bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
597 memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
599 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
601 bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
603 memset(&(r[n2+tna+tnb]),0,
604 sizeof(BN_ULONG)*(n2-tna-tnb));
606 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
608 memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
609 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
610 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
612 bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
619 /* these simplified conditions work
620 * exclusively because difference
621 * between tna and tnb is 1 or 0 */
622 if (i < tna || i < tnb)
624 bn_mul_part_recursive(&(r[n2]),
629 else if (i == tna || i == tnb)
631 bn_mul_recursive(&(r[n2]),
641 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
642 * r[10] holds (a[0]*b[0])
643 * r[32] holds (b[1]*b[1])
646 c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
648 if (neg) /* if t[32] is negative */
650 c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
654 /* Might have a carry */
655 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
658 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
659 * r[10] holds (a[0]*b[0])
660 * r[32] holds (b[1]*b[1])
661 * c1 holds the carry bits
663 c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
671 /* The overflow will stop before we over write
672 * words we should not overwrite */
673 if (ln < (BN_ULONG)c1)
685 /* a and b must be the same size, which is n2.
686 * r needs to be n2 words and t needs to be n2*2
688 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
693 bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
694 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
696 bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
697 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
698 bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
699 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
703 bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
704 bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
705 bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
706 bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
710 /* a and b must be the same size, which is n2.
711 * r needs to be n2 words and t needs to be n2*2
712 * l is the low words of the output.
715 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
721 BN_ULONG ll,lc,*lp,*mp;
725 /* Calculate (al-ah)*(bh-bl) */
727 c1=bn_cmp_words(&(a[0]),&(a[n]),n);
728 c2=bn_cmp_words(&(b[n]),&(b[0]),n);
732 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
733 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
739 bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
740 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
749 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
750 bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
757 bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
758 bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
763 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
764 /* r[10] = (a[1]*b[1]) */
768 bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
769 bn_mul_comba8(r,&(a[n]),&(b[n]));
774 bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
775 bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
779 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
780 * We know s0 and s1 so the only unknown is high(al*bl)
781 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
782 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
787 c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
796 neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
799 bn_add_words(&(t[n2]),lp,&(t[0]),n);
805 bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
812 lp[i]=((~mp[i])+1)&BN_MASK2;
817 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
818 * r[10] = (a[1]*b[1])
821 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
824 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
825 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
826 * R[3]=r[1]+(carry/borrow)
831 c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
838 c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
840 c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
842 c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
844 c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
845 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
847 c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
849 c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
851 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
858 ll=(r[i]+lc)&BN_MASK2;
868 r[i++]=(ll-lc)&BN_MASK2;
873 if (c2 != 0) /* Add starting at r[1] */
880 ll=(r[i]+lc)&BN_MASK2;
890 r[i++]=(ll-lc)&BN_MASK2;
896 #endif /* BN_RECURSION */
898 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
903 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
918 if ((al == 0) || (bl == 0))
926 if ((r == a) || (r == b))
928 if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
932 rr->neg=a->neg^b->neg;
934 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
943 if (bn_wexpand(rr,8) == NULL) goto err;
945 bn_mul_comba4(rr->d,a->d,b->d);
951 if (bn_wexpand(rr,16) == NULL) goto err;
953 bn_mul_comba8(rr->d,a->d,b->d);
957 #endif /* BN_MUL_COMBA */
959 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
961 if (i >= -1 && i <= 1)
963 /* Find out the power of two lower or equal
964 to the longest of the two numbers */
967 j = BN_num_bits_word((BN_ULONG)al);
971 j = BN_num_bits_word((BN_ULONG)bl);
974 assert(j <= al || j <= bl);
979 if (al > j || bl > j)
981 if (bn_wexpand(t,k*4) == NULL) goto err;
982 if (bn_wexpand(rr,k*4) == NULL) goto err;
983 bn_mul_part_recursive(rr->d,a->d,b->d,
986 else /* al <= j || bl <= j */
988 if (bn_wexpand(t,k*2) == NULL) goto err;
989 if (bn_wexpand(rr,k*2) == NULL) goto err;
990 bn_mul_recursive(rr->d,a->d,b->d,
997 if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
999 BIGNUM *tmp_bn = (BIGNUM *)b;
1000 if (bn_wexpand(tmp_bn,al) == NULL) goto err;
1005 else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
1007 BIGNUM *tmp_bn = (BIGNUM *)a;
1008 if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
1015 /* symmetric and > 4 */
1017 j=BN_num_bits_word((BN_ULONG)al);
1020 t = BN_CTX_get(ctx);
1021 if (al == j) /* exact multiple */
1023 if (bn_wexpand(t,k*2) == NULL) goto err;
1024 if (bn_wexpand(rr,k*2) == NULL) goto err;
1025 bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
1029 if (bn_wexpand(t,k*4) == NULL) goto err;
1030 if (bn_wexpand(rr,k*4) == NULL) goto err;
1031 bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
1038 #endif /* BN_RECURSION */
1039 if (bn_wexpand(rr,top) == NULL) goto err;
1041 bn_mul_normal(rr->d,a->d,al,b->d,bl);
1043 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1047 if (r != rr) BN_copy(r,rr);
1055 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1064 itmp=na; na=nb; nb=itmp;
1065 ltmp=a; a=b; b=ltmp;
1071 (void)bn_mul_words(r,a,na,0);
1075 rr[0]=bn_mul_words(r,a,na,b[0]);
1079 if (--nb <= 0) return;
1080 rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
1081 if (--nb <= 0) return;
1082 rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
1083 if (--nb <= 0) return;
1084 rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
1085 if (--nb <= 0) return;
1086 rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
1093 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1095 bn_mul_words(r,a,n,b[0]);
1099 if (--n <= 0) return;
1100 bn_mul_add_words(&(r[1]),a,n,b[1]);
1101 if (--n <= 0) return;
1102 bn_mul_add_words(&(r[2]),a,n,b[2]);
1103 if (--n <= 0) return;
1104 bn_mul_add_words(&(r[3]),a,n,b[3]);
1105 if (--n <= 0) return;
1106 bn_mul_add_words(&(r[4]),a,n,b[4]);