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 */
69 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
71 * Here follows specialised variants of bn_add_words() and bn_sub_words().
72 * They have the property performing operations on arrays of different sizes.
73 * The sizes of those arrays is expressed through cl, which is the common
74 * length ( basicall, min(len(a),len(b)) ), and dl, which is the delta
75 * between the two lengths, calculated as len(a)-len(b). All lengths are the
76 * number of BN_ULONGs... For the operations that require a result array as
77 * parameter, it must have the length cl+abs(dl). These functions should
78 * probably end up in bn_asm.c as soon as there are assembler counterparts
79 * for the systems that use assembler files.
82 BN_ULONG bn_sub_part_words(BN_ULONG *r,
83 const BN_ULONG *a, const BN_ULONG *b,
89 c = bn_sub_words(r, a, b, cl);
100 fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl,
105 r[0] = (0 - t - c) & BN_MASK2;
112 r[1] = (0 - t - c) & BN_MASK2;
119 r[2] = (0 - t - c) & BN_MASK2;
126 r[3] = (0 - t - c) & BN_MASK2;
138 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl,
143 r[0] = (t - c) & BN_MASK2;
150 r[1] = (t - c) & BN_MASK2;
157 r[2] = (t - c) & BN_MASK2;
164 r[3] = (t - c) & BN_MASK2;
176 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n",
180 switch (save_dl - dl) {
200 fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n",
226 BN_ULONG bn_add_part_words(BN_ULONG *r,
227 const BN_ULONG *a, const BN_ULONG *b,
233 c = bn_add_words(r, a, b, cl);
245 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl,
249 l = (c + b[0]) & BN_MASK2;
255 l = (c + b[1]) & BN_MASK2;
261 l = (c + b[2]) & BN_MASK2;
267 l = (c + b[3]) & BN_MASK2;
279 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n",
283 switch (dl - save_dl) {
303 fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n",
327 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
330 t = (a[0] + c) & BN_MASK2;
336 t = (a[1] + c) & BN_MASK2;
342 t = (a[2] + c) & BN_MASK2;
348 t = (a[3] + c) & BN_MASK2;
359 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl,
364 switch (save_dl - dl) {
384 fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n",
411 * Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of
412 * Computer Programming, Vol. 2)
416 * r is 2*n2 words in size,
417 * a and b are both n2 words in size.
418 * n2 must be a power of 2.
419 * We multiply and return the result.
420 * t must be 2*n2 words in size
423 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
426 /* dnX may not be positive, but n2/2+dnX has to be */
427 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
428 int dna, int dnb, BN_ULONG *t)
430 int n = n2 / 2, c1, c2;
431 int tna = n + dna, tnb = n + dnb;
432 unsigned int neg, zero;
436 fprintf(stderr, " bn_mul_recursive %d%+d * %d%+d\n", n2, dna, n2, dnb);
441 bn_mul_comba4(r, a, b);
446 * Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete
449 if (n2 == 8 && dna == 0 && dnb == 0) {
450 bn_mul_comba8(r, a, b);
453 # endif /* BN_MUL_COMBA */
454 /* Else do normal multiply */
455 if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
456 bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
458 memset(&r[2 * n2 + dna + dnb], 0,
459 sizeof(BN_ULONG) * -(dna + dnb));
462 /* r=(a[0]-a[1])*(b[1]-b[0]) */
463 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
464 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
466 switch (c1 * 3 + c2) {
468 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
469 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
475 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
476 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
485 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
486 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
493 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
494 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
499 if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take
500 * extra args to do this well */
502 bn_mul_comba4(&(t[n2]), t, &(t[n]));
504 memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
506 bn_mul_comba4(r, a, b);
507 bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
508 } else if (n == 8 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba8 could
509 * take extra args to do
512 bn_mul_comba8(&(t[n2]), t, &(t[n]));
514 memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
516 bn_mul_comba8(r, a, b);
517 bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
519 # endif /* BN_MUL_COMBA */
523 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
525 memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
526 bn_mul_recursive(r, a, b, n, 0, 0, p);
527 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
531 * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
532 * r[10] holds (a[0]*b[0])
533 * r[32] holds (b[1]*b[1])
536 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
538 if (neg) { /* if t[32] is negative */
539 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
541 /* Might have a carry */
542 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
546 * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
547 * r[10] holds (a[0]*b[0])
548 * r[32] holds (b[1]*b[1])
549 * c1 holds the carry bits
551 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
555 ln = (lo + c1) & BN_MASK2;
559 * The overflow will stop before we over write words we should not
562 if (ln < (BN_ULONG)c1) {
566 ln = (lo + 1) & BN_MASK2;
574 * n+tn is the word length t needs to be n*4 is size, as does r
576 /* tnX may not be negative but less than n */
577 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
578 int tna, int tnb, BN_ULONG *t)
580 int i, j, n2 = n * 2;
585 fprintf(stderr, " bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
589 bn_mul_normal(r, a, n + tna, b, n + tnb);
593 /* r=(a[0]-a[1])*(b[1]-b[0]) */
594 c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
595 c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
597 switch (c1 * 3 + c2) {
599 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
600 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
605 bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
606 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
614 bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
615 bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
621 bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
622 bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
626 * The zero case isn't yet implemented here. The speedup would probably
631 bn_mul_comba4(&(t[n2]), t, &(t[n]));
632 bn_mul_comba4(r, a, b);
633 bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
634 memset(&(r[n2 + tn * 2]), 0, sizeof(BN_ULONG) * (n2 - tn * 2));
638 bn_mul_comba8(&(t[n2]), t, &(t[n]));
639 bn_mul_comba8(r, a, b);
640 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
641 memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
644 bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
645 bn_mul_recursive(r, a, b, n, 0, 0, p);
648 * If there is only a bottom half to the number, just do it
655 bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
656 i, tna - i, tnb - i, p);
657 memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2));
658 } else if (j > 0) { /* eg, n == 16, i == 8 and tn == 11 */
659 bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
660 i, tna - i, tnb - i, p);
661 memset(&(r[n2 + tna + tnb]), 0,
662 sizeof(BN_ULONG) * (n2 - tna - tnb));
663 } else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
665 memset(&(r[n2]), 0, sizeof(BN_ULONG) * n2);
666 if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
667 && tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
668 bn_mul_normal(&(r[n2]), &(a[n]), tna, &(b[n]), tnb);
673 * these simplified conditions work exclusively because
674 * difference between tna and tnb is 1 or 0
676 if (i < tna || i < tnb) {
677 bn_mul_part_recursive(&(r[n2]),
679 i, tna - i, tnb - i, p);
681 } else if (i == tna || i == tnb) {
682 bn_mul_recursive(&(r[n2]),
684 i, tna - i, tnb - i, p);
693 * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
694 * r[10] holds (a[0]*b[0])
695 * r[32] holds (b[1]*b[1])
698 c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
700 if (neg) { /* if t[32] is negative */
701 c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
703 /* Might have a carry */
704 c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
708 * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
709 * r[10] holds (a[0]*b[0])
710 * r[32] holds (b[1]*b[1])
711 * c1 holds the carry bits
713 c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
717 ln = (lo + c1) & BN_MASK2;
721 * The overflow will stop before we over write words we should not
724 if (ln < (BN_ULONG)c1) {
728 ln = (lo + 1) & BN_MASK2;
736 * a and b must be the same size, which is n2.
737 * r needs to be n2 words and t needs to be n2*2
739 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
745 fprintf(stderr, " bn_mul_low_recursive %d * %d\n", n2, n2);
748 bn_mul_recursive(r, a, b, n, 0, 0, &(t[0]));
749 if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) {
750 bn_mul_low_recursive(&(t[0]), &(a[0]), &(b[n]), n, &(t[n2]));
751 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
752 bn_mul_low_recursive(&(t[0]), &(a[n]), &(b[0]), n, &(t[n2]));
753 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
755 bn_mul_low_normal(&(t[0]), &(a[0]), &(b[n]), n);
756 bn_mul_low_normal(&(t[n]), &(a[n]), &(b[0]), n);
757 bn_add_words(&(r[n]), &(r[n]), &(t[0]), n);
758 bn_add_words(&(r[n]), &(r[n]), &(t[n]), n);
763 * a and b must be the same size, which is n2.
764 * r needs to be n2 words and t needs to be n2*2
765 * l is the low words of the output.
768 void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
774 BN_ULONG ll, lc, *lp, *mp;
777 fprintf(stderr, " bn_mul_high %d * %d\n", n2, n2);
781 /* Calculate (al-ah)*(bh-bl) */
783 c1 = bn_cmp_words(&(a[0]), &(a[n]), n);
784 c2 = bn_cmp_words(&(b[n]), &(b[0]), n);
785 switch (c1 * 3 + c2) {
787 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
788 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
794 bn_sub_words(&(r[0]), &(a[n]), &(a[0]), n);
795 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
804 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
805 bn_sub_words(&(r[n]), &(b[0]), &(b[n]), n);
812 bn_sub_words(&(r[0]), &(a[0]), &(a[n]), n);
813 bn_sub_words(&(r[n]), &(b[n]), &(b[0]), n);
818 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
819 /* r[10] = (a[1]*b[1]) */
822 bn_mul_comba8(&(t[0]), &(r[0]), &(r[n]));
823 bn_mul_comba8(r, &(a[n]), &(b[n]));
827 bn_mul_recursive(&(t[0]), &(r[0]), &(r[n]), n, 0, 0, &(t[n2]));
828 bn_mul_recursive(r, &(a[n]), &(b[n]), n, 0, 0, &(t[n2]));
833 * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
834 * We know s0 and s1 so the only unknown is high(al*bl)
835 * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
836 * high(al*bl) == s1 - (r[0]+l[0]+t[0])
840 c1 = (int)(bn_add_words(lp, &(r[0]), &(l[0]), n));
847 neg = (int)(bn_sub_words(&(t[n2]), lp, &(t[0]), n));
849 bn_add_words(&(t[n2]), lp, &(t[0]), n);
854 bn_sub_words(&(t[n2 + n]), &(l[n]), &(t[n2]), n);
858 for (i = 0; i < n; i++)
859 lp[i] = ((~mp[i]) + 1) & BN_MASK2;
865 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
866 * r[10] = (a[1]*b[1])
870 * 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 */
903 ll = (r[i] + lc) & BN_MASK2;
911 r[i++] = (ll - lc) & BN_MASK2;
916 if (c2 != 0) { /* Add starting at r[1] */
921 ll = (r[i] + lc) & BN_MASK2;
929 r[i++] = (ll - lc) & BN_MASK2;
935 #endif /* BN_RECURSION */
937 int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
942 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
951 fprintf(stderr, "BN_mul %d * %d\n", a->top, b->top);
961 if ((al == 0) || (bl == 0)) {
968 if ((r == a) || (r == b)) {
969 if ((rr = BN_CTX_get(ctx)) == NULL)
973 rr->neg = a->neg ^ b->neg;
975 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
982 if (bn_wexpand(rr, 8) == NULL)
985 bn_mul_comba4(rr->d, a->d, b->d);
990 if (bn_wexpand(rr, 16) == NULL)
993 bn_mul_comba8(rr->d, a->d, b->d);
997 #endif /* BN_MUL_COMBA */
999 if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
1000 if (i >= -1 && i <= 1) {
1002 * Find out the power of two lower or equal to the longest of the
1006 j = BN_num_bits_word((BN_ULONG)al);
1009 j = BN_num_bits_word((BN_ULONG)bl);
1012 assert(j <= al || j <= bl);
1014 t = BN_CTX_get(ctx);
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);
1024 } else { /* al <= j || bl <= j */
1026 if (bn_wexpand(t, k * 2) == NULL)
1028 if (bn_wexpand(rr, k * 2) == NULL)
1030 bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
1036 if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
1037 BIGNUM *tmp_bn = (BIGNUM *)b;
1038 if (bn_wexpand(tmp_bn, al) == NULL)
1043 } else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
1044 BIGNUM *tmp_bn = (BIGNUM *)a;
1045 if (bn_wexpand(tmp_bn, bl) == NULL)
1052 /* symmetric and > 4 */
1054 j = BN_num_bits_word((BN_ULONG)al);
1057 t = BN_CTX_get(ctx);
1058 if (al == j) { /* exact multiple */
1059 if (bn_wexpand(t, k * 2) == NULL)
1061 if (bn_wexpand(rr, k * 2) == NULL)
1063 bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
1065 if (bn_wexpand(t, k * 4) == NULL)
1067 if (bn_wexpand(rr, k * 4) == NULL)
1069 bn_mul_part_recursive(rr->d, a->d, b->d, al - j, j, t->d);
1076 #endif /* BN_RECURSION */
1077 if (bn_wexpand(rr, top) == NULL)
1080 bn_mul_normal(rr->d, a->d, al, b->d, bl);
1082 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1086 if (r != rr && BN_copy(r, rr) == NULL)
1096 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
1101 fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
1118 (void)bn_mul_words(r, a, na, 0);
1121 rr[0] = bn_mul_words(r, a, na, b[0]);
1126 rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
1129 rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
1132 rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
1135 rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
1142 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
1145 fprintf(stderr, " bn_mul_low_normal %d * %d\n", n, n);
1147 bn_mul_words(r, a, n, b[0]);
1152 bn_mul_add_words(&(r[1]), a, n, b[1]);
1155 bn_mul_add_words(&(r[2]), a, n, b[2]);
1158 bn_mul_add_words(&(r[3]), a, n, b[3]);
1161 bn_mul_add_words(&(r[4]), a, n, b[4]);