1 /* $OpenBSD: bn_mul.c,v 1.20 2015/02/09 15:49:22 jsing Exp $ */
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 #include <openssl/opensslconf.h>
72 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
73 /* Here follows specialised variants of bn_add_words() and
74 bn_sub_words(). They have the property performing operations on
75 arrays of different sizes. The sizes of those arrays is expressed through
76 cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
77 which is the delta between the two lengths, calculated as len(a)-len(b).
78 All lengths are the number of BN_ULONGs... For the operations that require
79 a result array as parameter, it must have the length cl+abs(dl).
80 These functions should probably end up in bn_asm.c as soon as there are
81 assembler counterparts for the systems that use assembler files. */
84 bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
90 c = bn_sub_words(r, a, b, cl);
102 " bn_sub_part_words %d + %d (dl < 0, c = %d)\n",
107 r[0] = (0 - t - c) & BN_MASK2;
114 r[1] = (0 - t - c) & BN_MASK2;
121 r[2] = (0 - t - c) & BN_MASK2;
128 r[3] = (0 - t - c) & BN_MASK2;
141 " bn_sub_part_words %d + %d (dl > 0, c = %d)\n",
146 r[0] = (t - c) & BN_MASK2;
153 r[1] = (t - c) & BN_MASK2;
160 r[2] = (t - c) & BN_MASK2;
167 r[3] = (t - c) & BN_MASK2;
180 " bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
184 switch (save_dl - dl) {
205 " bn_sub_part_words %d + %d (dl > 0, copy)\n",
232 bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl,
238 c = bn_add_words(r, a, b, cl);
251 " bn_add_part_words %d + %d (dl < 0, c = %d)\n",
255 l = (c + b[0]) & BN_MASK2;
261 l = (c + b[1]) & BN_MASK2;
267 l = (c + b[2]) & BN_MASK2;
273 l = (c + b[3]) & BN_MASK2;
286 " bn_add_part_words %d + %d (dl < 0, c == 0)\n",
290 switch (dl - save_dl) {
311 " bn_add_part_words %d + %d (dl < 0, copy)\n",
336 " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
339 t = (a[0] + c) & BN_MASK2;
345 t = (a[1] + c) & BN_MASK2;
351 t = (a[2] + c) & BN_MASK2;
357 t = (a[3] + c) & BN_MASK2;
369 " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
373 switch (save_dl - dl) {
394 " bn_add_part_words %d + %d (dl > 0, copy)\n",
420 /* Karatsuba recursive multiplication algorithm
421 * (cf. Knuth, The Art of Computer Programming, Vol. 2) */
423 /* r is 2*n2 words in size,
424 * a and b are both n2 words in size.
425 * n2 must be a power of 2.
426 * We multiply and return the result.
427 * t must be 2*n2 words in size
430 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
433 /* dnX may not be positive, but n2/2+dnX has to be */
435 bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, int dna,
436 int dnb, BN_ULONG *t)
438 int n = n2 / 2, c1, c2;
439 int tna = n + dna, tnb = n + dnb;
440 unsigned int neg, zero;
444 fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
449 bn_mul_comba4(r, a, b);
453 /* Only call bn_mul_comba 8 if n2 == 8 and the
454 * two arrays are complete [steve]
456 if (n2 == 8 && dna == 0 && dnb == 0) {
457 bn_mul_comba8(r, a, b);
460 # endif /* BN_MUL_COMBA */
461 /* Else do normal multiply */
462 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
463 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
465 memset(&r[2*n2 + dna + dnb], 0,
466 sizeof(BN_ULONG) * -(dna + dnb));
469 /* r=(a[0]-a[1])*(b[1]-b[0]) */
470 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
471 c2 = bn_cmp_part_words(&(b[n]), b,tnb, tnb - n);
473 switch (c1 * 3 + c2) {
475 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
476 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
482 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
483 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
492 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
493 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
500 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
501 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
506 if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
507 extra args to do this well */
510 bn_mul_comba4(&(t[n2]), t, &(t[n]));
512 memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
514 bn_mul_comba4(r, a, b);
515 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
516 } else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
517 take extra args to do this
521 bn_mul_comba8(&(t[n2]), t, &(t[n]));
523 memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
525 bn_mul_comba8(r, a, b);
526 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
528 # endif /* BN_MUL_COMBA */
532 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
534 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
535 bn_mul_recursive(r, a, b, n, 0, 0, p);
536 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
539 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
540 * r[10] holds (a[0]*b[0])
541 * r[32] holds (b[1]*b[1])
544 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
546 if (neg) /* if t[32] is negative */
548 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
550 /* Might have a carry */
551 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
554 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
555 * r[10] holds (a[0]*b[0])
556 * r[32] holds (b[1]*b[1])
557 * c1 holds the carry bits
559 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
563 ln = (lo + c1) & BN_MASK2;
566 /* The overflow will stop before we over write
567 * words we should not overwrite */
568 if (ln < (BN_ULONG)c1) {
572 ln = (lo + 1) & BN_MASK2;
579 /* n+tn is the word length
580 * t needs to be n*4 is size, as does r */
581 /* tnX may not be negative but less than n */
583 bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n, int tna,
584 int tnb, BN_ULONG *t)
586 int i, j, n2 = n * 2;
591 fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
595 bn_mul_normal(r, a, n + tna, b, n + tnb);
599 /* r=(a[0]-a[1])*(b[1]-b[0]) */
600 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
601 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
603 switch (c1 * 3 + c2) {
605 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
606 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
611 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
612 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
620 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
621 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
627 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
628 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
631 /* The zero case isn't yet implemented here. The speedup
632 would probably be negligible. */
635 bn_mul_comba4(&(t[n2]), t, &(t[n]));
636 bn_mul_comba4(r, a, b);
637 bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
638 memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
642 bn_mul_comba8(&(t[n2]), t, &(t[n]));
643 bn_mul_comba8(r, a, b);
644 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
645 memset(&(r[n2 + tna + tnb]), 0,
646 sizeof(BN_ULONG) * (n2 - tna - tnb));
649 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
650 bn_mul_recursive(r, a, b, n, 0, 0, p);
652 /* If there is only a bottom half to the number,
659 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
660 i, tna - i, tnb - i, p);
661 memset(&(r[n2 + i * 2]), 0,
662 sizeof(BN_ULONG) * (n2 - i * 2));
664 else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
666 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
667 i, tna - i, tnb - i, p);
668 memset(&(r[n2 + tna + tnb]), 0,
669 sizeof(BN_ULONG) * (n2 - tna - tnb));
671 else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
673 memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
674 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
675 tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
676 bn_mul_normal(&(r[n2]), &(a[n]), tna,
681 /* these simplified conditions work
682 * exclusively because difference
683 * between tna and tnb is 1 or 0 */
684 if (i < tna || i < tnb) {
685 bn_mul_part_recursive(&(r[n2]),
687 tna - i, tnb - i, p);
689 } else if (i == tna || i == tnb) {
690 bn_mul_recursive(&(r[n2]),
692 tna - i, tnb - i, p);
700 /* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
701 * r[10] holds (a[0]*b[0])
702 * r[32] holds (b[1]*b[1])
705 c1 = (int)(bn_add_words(t, r,&(r[n2]), n2));
707 if (neg) /* if t[32] is negative */
709 c1 -= (int)(bn_sub_words(&(t[n2]), t,&(t[n2]), n2));
711 /* Might have a carry */
712 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
715 /* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
716 * r[10] holds (a[0]*b[0])
717 * r[32] holds (b[1]*b[1])
718 * c1 holds the carry bits
720 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
724 ln = (lo + c1)&BN_MASK2;
727 /* The overflow will stop before we over write
728 * words we should not overwrite */
729 if (ln < (BN_ULONG)c1) {
733 ln = (lo + 1) & BN_MASK2;
740 /* a and b must be the same size, which is n2.
741 * r needs to be n2 words and t needs to be n2*2
744 bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t)
749 fprintf(stderr, " bn_mul_low_recursive %d * %d\n",n2,n2);
752 bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
753 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
754 bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
755 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
756 bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
757 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
759 bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
760 bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
761 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
762 bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
766 /* a and b must be the same size, which is n2.
767 * r needs to be n2 words and t needs to be n2*2
768 * l is the low words of the output.
772 bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
778 BN_ULONG ll, lc, *lp, *mp;
781 fprintf(stderr, " bn_mul_high %d * %d\n",n2,n2);
785 /* Calculate (al-ah)*(bh-bl) */
787 c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
788 c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
789 switch (c1 * 3 + c2) {
791 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
792 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
798 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
799 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
808 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
809 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
816 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
817 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
822 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
823 /* r[10] = (a[1]*b[1]) */
826 bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
827 bn_mul_comba8(r, &(a[n]), &(b[n]));
831 bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
832 bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
836 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
837 * We know s0 and s1 so the only unknown is high(al*bl)
838 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
839 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
843 c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
850 neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
852 bn_add_words(&(t[n2]), lp, &(t[0]), n);
857 bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
861 for (i = 0; i < n; i++)
862 lp[i] = ((~mp[i]) + 1) & BN_MASK2;
867 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
868 * r[10] = (a[1]*b[1])
871 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
874 /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
875 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
876 * R[3]=r[1]+(carry/borrow)
880 c1 = (int)(bn_add_words(lp, &(t[n2 + n]), &(l[0]), n));
885 c1 += (int)(bn_add_words(&(t[n2]), lp, &(r[0]), n));
887 c1 -= (int)(bn_sub_words(&(t[n2]), &(t[n2]), &(t[0]), n));
889 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), &(t[0]), n));
891 c2 = (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n2 + n]), n));
892 c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(r[n]), n));
894 c2 -= (int)(bn_sub_words(&(r[0]), &(r[0]), &(t[n]), n));
896 c2 += (int)(bn_add_words(&(r[0]), &(r[0]), &(t[n]), n));
898 if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
904 ll = (r[i] + lc) & BN_MASK2;
912 r[i++] = (ll - lc) & BN_MASK2;
917 if (c2 != 0) /* Add starting at r[1] */
923 ll = (r[i] + lc) & BN_MASK2;
931 r[i++] = (ll - lc) & BN_MASK2;
937 #endif /* BN_RECURSION */
940 BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
945 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
954 fprintf(stderr, "BN_mul %d * %d\n",a->top,b->top);
964 if ((al == 0) || (bl == 0)) {
971 if ((r == a) || (r == b)) {
972 if ((rr = BN_CTX_get(ctx)) == NULL)
976 rr->neg = a->neg ^ b->neg;
978 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
985 if (bn_wexpand(rr, 8) == NULL)
988 bn_mul_comba4(rr->d, a->d, b->d);
993 if (bn_wexpand(rr, 16) == NULL)
996 bn_mul_comba8(rr->d, a->d, b->d);
1000 #endif /* BN_MUL_COMBA */
1002 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
1003 if (i >= -1 && i <= 1) {
1004 /* Find out the power of two lower or equal
1005 to the longest of the two numbers */
1007 j = BN_num_bits_word((BN_ULONG)al);
1010 j = BN_num_bits_word((BN_ULONG)bl);
1013 assert(j <= al || j <= bl);
1015 if ((t = BN_CTX_get(ctx)) == NULL)
1017 if (al > j || bl > j) {
1018 if (bn_wexpand(t, k * 4) == NULL)
1020 if (bn_wexpand(rr, k * 4) == NULL)
1022 bn_mul_part_recursive(rr->d, a->d, b->d,
1023 j, al - j, bl - j, t->d);
1025 else /* al <= j || bl <= j */
1027 if (bn_wexpand(t, k * 2) == NULL)
1029 if (bn_wexpand(rr, k * 2) == NULL)
1031 bn_mul_recursive(rr->d, a->d, b->d,
1032 j, al - j, bl - j, t->d);
1038 if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
1039 BIGNUM *tmp_bn = (BIGNUM *)b;
1040 if (bn_wexpand(tmp_bn, al) == NULL)
1045 } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
1046 BIGNUM *tmp_bn = (BIGNUM *)a;
1047 if (bn_wexpand(tmp_bn, bl) == NULL)
1054 /* symmetric and > 4 */
1056 j = BN_num_bits_word((BN_ULONG)al);
1059 if ((t = BN_CTX_get(ctx)) == NULL)
1061 if (al == j) /* exact multiple */
1063 if (bn_wexpand(t, k * 2) == NULL)
1065 if (bn_wexpand(rr, k * 2) == NULL)
1067 bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
1069 if (bn_wexpand(t, k * 4) == NULL)
1071 if (bn_wexpand(rr, k * 4) == NULL)
1073 bn_mul_part_recursive(rr->d, a->d, b->d,
1081 #endif /* BN_RECURSION */
1082 if (bn_wexpand(rr, top) == NULL)
1085 bn_mul_normal(rr->d, a->d, al, b->d, bl);
1087 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1101 bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1106 fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
1123 (void)bn_mul_words(r, a, na, 0);
1126 rr[0] = bn_mul_words(r, a, na, b[0]);
1131 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
1134 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
1137 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
1140 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
1148 bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1151 fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
1153 bn_mul_words(r, a, n, b[0]);
1158 bn_mul_add_words(&(r[1]), a, n, b[1]);
1161 bn_mul_add_words(&(r[2]), a, n, b[2]);
1164 bn_mul_add_words(&(r[3]), a, n, b[3]);
1167 bn_mul_add_words(&(r[4]), a, n, b[4]);