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 */
65 #include "internal/cryptlib.h"
68 #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
70 * Here follows specialised variants of bn_add_words() and bn_sub_words().
71 * They have the property performing operations on arrays of different sizes.
72 * The sizes of those arrays is expressed through cl, which is the common
73 * length ( basicall, min(len(a),len(b)) ), and dl, which is the delta
74 * between the two lengths, calculated as len(a)-len(b). All lengths are the
75 * number of BN_ULONGs... For the operations that require a result array as
76 * parameter, it must have the length cl+abs(dl). These functions should
77 * probably end up in bn_asm.c as soon as there are assembler counterparts
78 * for the systems that use assembler files.
81 BN_ULONG
bn_sub_part_words(BN_ULONG
*r
,
82 const BN_ULONG
*a
, const BN_ULONG
*b
,
88 c
= bn_sub_words(r
, a
, b
, cl
);
100 r
[0] = (0 - t
- c
) & BN_MASK2
;
107 r
[1] = (0 - t
- c
) & BN_MASK2
;
114 r
[2] = (0 - t
- c
) & BN_MASK2
;
121 r
[3] = (0 - t
- c
) & BN_MASK2
;
134 r
[0] = (t
- c
) & BN_MASK2
;
141 r
[1] = (t
- c
) & BN_MASK2
;
148 r
[2] = (t
- c
) & BN_MASK2
;
155 r
[3] = (t
- c
) & BN_MASK2
;
167 switch (save_dl
- dl
) {
209 BN_ULONG
bn_add_part_words(BN_ULONG
*r
,
210 const BN_ULONG
*a
, const BN_ULONG
*b
,
216 c
= bn_add_words(r
, a
, b
, cl
);
228 l
= (c
+ b
[0]) & BN_MASK2
;
234 l
= (c
+ b
[1]) & BN_MASK2
;
240 l
= (c
+ b
[2]) & BN_MASK2
;
246 l
= (c
+ b
[3]) & BN_MASK2
;
258 switch (dl
- save_dl
) {
298 t
= (a
[0] + c
) & BN_MASK2
;
304 t
= (a
[1] + c
) & BN_MASK2
;
310 t
= (a
[2] + c
) & BN_MASK2
;
316 t
= (a
[3] + c
) & BN_MASK2
;
328 switch (save_dl
- dl
) {
371 * Karatsuba recursive multiplication algorithm (cf. Knuth, The Art of
372 * Computer Programming, Vol. 2)
376 * r is 2*n2 words in size,
377 * a and b are both n2 words in size.
378 * n2 must be a power of 2.
379 * We multiply and return the result.
380 * t must be 2*n2 words in size
383 * a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
386 /* dnX may not be positive, but n2/2+dnX has to be */
387 void bn_mul_recursive(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n2
,
388 int dna
, int dnb
, BN_ULONG
*t
)
390 int n
= n2
/ 2, c1
, c2
;
391 int tna
= n
+ dna
, tnb
= n
+ dnb
;
392 unsigned int neg
, zero
;
398 bn_mul_comba4(r
, a
, b
);
403 * Only call bn_mul_comba 8 if n2 == 8 and the two arrays are complete
406 if (n2
== 8 && dna
== 0 && dnb
== 0) {
407 bn_mul_comba8(r
, a
, b
);
410 # endif /* BN_MUL_COMBA */
411 /* Else do normal multiply */
412 if (n2
< BN_MUL_RECURSIVE_SIZE_NORMAL
) {
413 bn_mul_normal(r
, a
, n2
+ dna
, b
, n2
+ dnb
);
415 memset(&r
[2 * n2
+ dna
+ dnb
], 0,
416 sizeof(BN_ULONG
) * -(dna
+ dnb
));
419 /* r=(a[0]-a[1])*(b[1]-b[0]) */
420 c1
= bn_cmp_part_words(a
, &(a
[n
]), tna
, n
- tna
);
421 c2
= bn_cmp_part_words(&(b
[n
]), b
, tnb
, tnb
- n
);
423 switch (c1
* 3 + c2
) {
425 bn_sub_part_words(t
, &(a
[n
]), a
, tna
, tna
- n
); /* - */
426 bn_sub_part_words(&(t
[n
]), b
, &(b
[n
]), tnb
, n
- tnb
); /* - */
432 bn_sub_part_words(t
, &(a
[n
]), a
, tna
, tna
- n
); /* - */
433 bn_sub_part_words(&(t
[n
]), &(b
[n
]), b
, tnb
, tnb
- n
); /* + */
442 bn_sub_part_words(t
, a
, &(a
[n
]), tna
, n
- tna
); /* + */
443 bn_sub_part_words(&(t
[n
]), b
, &(b
[n
]), tnb
, n
- tnb
); /* - */
450 bn_sub_part_words(t
, a
, &(a
[n
]), tna
, n
- tna
);
451 bn_sub_part_words(&(t
[n
]), &(b
[n
]), b
, tnb
, tnb
- n
);
456 if (n
== 4 && dna
== 0 && dnb
== 0) { /* XXX: bn_mul_comba4 could take
457 * extra args to do this well */
459 bn_mul_comba4(&(t
[n2
]), t
, &(t
[n
]));
461 memset(&t
[n2
], 0, sizeof(*t
) * 8);
463 bn_mul_comba4(r
, a
, b
);
464 bn_mul_comba4(&(r
[n2
]), &(a
[n
]), &(b
[n
]));
465 } else if (n
== 8 && dna
== 0 && dnb
== 0) { /* XXX: bn_mul_comba8 could
466 * take extra args to do
469 bn_mul_comba8(&(t
[n2
]), t
, &(t
[n
]));
471 memset(&t
[n2
], 0, sizeof(*t
) * 16);
473 bn_mul_comba8(r
, a
, b
);
474 bn_mul_comba8(&(r
[n2
]), &(a
[n
]), &(b
[n
]));
476 # endif /* BN_MUL_COMBA */
480 bn_mul_recursive(&(t
[n2
]), t
, &(t
[n
]), n
, 0, 0, p
);
482 memset(&t
[n2
], 0, sizeof(*t
) * n2
);
483 bn_mul_recursive(r
, a
, b
, n
, 0, 0, p
);
484 bn_mul_recursive(&(r
[n2
]), &(a
[n
]), &(b
[n
]), n
, dna
, dnb
, p
);
488 * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
489 * r[10] holds (a[0]*b[0])
490 * r[32] holds (b[1]*b[1])
493 c1
= (int)(bn_add_words(t
, r
, &(r
[n2
]), n2
));
495 if (neg
) { /* if t[32] is negative */
496 c1
-= (int)(bn_sub_words(&(t
[n2
]), t
, &(t
[n2
]), n2
));
498 /* Might have a carry */
499 c1
+= (int)(bn_add_words(&(t
[n2
]), &(t
[n2
]), t
, n2
));
503 * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
504 * r[10] holds (a[0]*b[0])
505 * r[32] holds (b[1]*b[1])
506 * c1 holds the carry bits
508 c1
+= (int)(bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[n2
]), n2
));
512 ln
= (lo
+ c1
) & BN_MASK2
;
516 * The overflow will stop before we over write words we should not
519 if (ln
< (BN_ULONG
)c1
) {
523 ln
= (lo
+ 1) & BN_MASK2
;
531 * n+tn is the word length t needs to be n*4 is size, as does r
533 /* tnX may not be negative but less than n */
534 void bn_mul_part_recursive(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n
,
535 int tna
, int tnb
, BN_ULONG
*t
)
537 int i
, j
, n2
= n
* 2;
542 bn_mul_normal(r
, a
, n
+ tna
, b
, n
+ tnb
);
546 /* r=(a[0]-a[1])*(b[1]-b[0]) */
547 c1
= bn_cmp_part_words(a
, &(a
[n
]), tna
, n
- tna
);
548 c2
= bn_cmp_part_words(&(b
[n
]), b
, tnb
, tnb
- n
);
550 switch (c1
* 3 + c2
) {
552 bn_sub_part_words(t
, &(a
[n
]), a
, tna
, tna
- n
); /* - */
553 bn_sub_part_words(&(t
[n
]), b
, &(b
[n
]), tnb
, n
- tnb
); /* - */
558 bn_sub_part_words(t
, &(a
[n
]), a
, tna
, tna
- n
); /* - */
559 bn_sub_part_words(&(t
[n
]), &(b
[n
]), b
, tnb
, tnb
- n
); /* + */
567 bn_sub_part_words(t
, a
, &(a
[n
]), tna
, n
- tna
); /* + */
568 bn_sub_part_words(&(t
[n
]), b
, &(b
[n
]), tnb
, n
- tnb
); /* - */
574 bn_sub_part_words(t
, a
, &(a
[n
]), tna
, n
- tna
);
575 bn_sub_part_words(&(t
[n
]), &(b
[n
]), b
, tnb
, tnb
- n
);
579 * The zero case isn't yet implemented here. The speedup would probably
584 bn_mul_comba4(&(t
[n2
]), t
, &(t
[n
]));
585 bn_mul_comba4(r
, a
, b
);
586 bn_mul_normal(&(r
[n2
]), &(a
[n
]), tn
, &(b
[n
]), tn
);
587 memset(&r
[n2
+ tn
* 2], 0, sizeof(*r
) * (n2
- tn
* 2));
591 bn_mul_comba8(&(t
[n2
]), t
, &(t
[n
]));
592 bn_mul_comba8(r
, a
, b
);
593 bn_mul_normal(&(r
[n2
]), &(a
[n
]), tna
, &(b
[n
]), tnb
);
594 memset(&r
[n2
+ tna
+ tnb
], 0, sizeof(*r
) * (n2
- tna
- tnb
));
597 bn_mul_recursive(&(t
[n2
]), t
, &(t
[n
]), n
, 0, 0, p
);
598 bn_mul_recursive(r
, a
, b
, n
, 0, 0, p
);
601 * If there is only a bottom half to the number, just do it
608 bn_mul_recursive(&(r
[n2
]), &(a
[n
]), &(b
[n
]),
609 i
, tna
- i
, tnb
- i
, p
);
610 memset(&r
[n2
+ i
* 2], 0, sizeof(*r
) * (n2
- i
* 2));
611 } else if (j
> 0) { /* eg, n == 16, i == 8 and tn == 11 */
612 bn_mul_part_recursive(&(r
[n2
]), &(a
[n
]), &(b
[n
]),
613 i
, tna
- i
, tnb
- i
, p
);
614 memset(&(r
[n2
+ tna
+ tnb
]), 0,
615 sizeof(BN_ULONG
) * (n2
- tna
- tnb
));
616 } else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
618 memset(&r
[n2
], 0, sizeof(*r
) * n2
);
619 if (tna
< BN_MUL_RECURSIVE_SIZE_NORMAL
620 && tnb
< BN_MUL_RECURSIVE_SIZE_NORMAL
) {
621 bn_mul_normal(&(r
[n2
]), &(a
[n
]), tna
, &(b
[n
]), tnb
);
626 * these simplified conditions work exclusively because
627 * difference between tna and tnb is 1 or 0
629 if (i
< tna
|| i
< tnb
) {
630 bn_mul_part_recursive(&(r
[n2
]),
632 i
, tna
- i
, tnb
- i
, p
);
634 } else if (i
== tna
|| i
== tnb
) {
635 bn_mul_recursive(&(r
[n2
]),
637 i
, tna
- i
, tnb
- i
, p
);
646 * t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
647 * r[10] holds (a[0]*b[0])
648 * r[32] holds (b[1]*b[1])
651 c1
= (int)(bn_add_words(t
, r
, &(r
[n2
]), n2
));
653 if (neg
) { /* if t[32] is negative */
654 c1
-= (int)(bn_sub_words(&(t
[n2
]), t
, &(t
[n2
]), n2
));
656 /* Might have a carry */
657 c1
+= (int)(bn_add_words(&(t
[n2
]), &(t
[n2
]), t
, n2
));
661 * t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
662 * r[10] holds (a[0]*b[0])
663 * r[32] holds (b[1]*b[1])
664 * c1 holds the carry bits
666 c1
+= (int)(bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[n2
]), n2
));
670 ln
= (lo
+ c1
) & BN_MASK2
;
674 * The overflow will stop before we over write words we should not
677 if (ln
< (BN_ULONG
)c1
) {
681 ln
= (lo
+ 1) & BN_MASK2
;
689 * a and b must be the same size, which is n2.
690 * r needs to be n2 words and t needs to be n2*2
692 void bn_mul_low_recursive(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n2
,
697 bn_mul_recursive(r
, a
, b
, n
, 0, 0, &(t
[0]));
698 if (n
>= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL
) {
699 bn_mul_low_recursive(&(t
[0]), &(a
[0]), &(b
[n
]), n
, &(t
[n2
]));
700 bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[0]), n
);
701 bn_mul_low_recursive(&(t
[0]), &(a
[n
]), &(b
[0]), n
, &(t
[n2
]));
702 bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[0]), n
);
704 bn_mul_low_normal(&(t
[0]), &(a
[0]), &(b
[n
]), n
);
705 bn_mul_low_normal(&(t
[n
]), &(a
[n
]), &(b
[0]), n
);
706 bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[0]), n
);
707 bn_add_words(&(r
[n
]), &(r
[n
]), &(t
[n
]), n
);
712 * a and b must be the same size, which is n2.
713 * r needs to be n2 words and t needs to be n2*2
714 * l is the low words of the output.
717 void bn_mul_high(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, BN_ULONG
*l
, int n2
,
723 BN_ULONG ll
, lc
, *lp
, *mp
;
727 /* Calculate (al-ah)*(bh-bl) */
729 c1
= bn_cmp_words(&(a
[0]), &(a
[n
]), n
);
730 c2
= bn_cmp_words(&(b
[n
]), &(b
[0]), n
);
731 switch (c1
* 3 + c2
) {
733 bn_sub_words(&(r
[0]), &(a
[n
]), &(a
[0]), n
);
734 bn_sub_words(&(r
[n
]), &(b
[0]), &(b
[n
]), n
);
740 bn_sub_words(&(r
[0]), &(a
[n
]), &(a
[0]), n
);
741 bn_sub_words(&(r
[n
]), &(b
[n
]), &(b
[0]), n
);
750 bn_sub_words(&(r
[0]), &(a
[0]), &(a
[n
]), n
);
751 bn_sub_words(&(r
[n
]), &(b
[0]), &(b
[n
]), n
);
758 bn_sub_words(&(r
[0]), &(a
[0]), &(a
[n
]), n
);
759 bn_sub_words(&(r
[n
]), &(b
[n
]), &(b
[0]), n
);
764 /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
765 /* 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
]));
773 bn_mul_recursive(&(t
[0]), &(r
[0]), &(r
[n
]), n
, 0, 0, &(t
[n2
]));
774 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])
786 c1
= (int)(bn_add_words(lp
, &(r
[0]), &(l
[0]), n
));
793 neg
= (int)(bn_sub_words(&(t
[n2
]), lp
, &(t
[0]), n
));
795 bn_add_words(&(t
[n2
]), lp
, &(t
[0]), n
);
800 bn_sub_words(&(t
[n2
+ n
]), &(l
[n
]), &(t
[n2
]), n
);
804 for (i
= 0; i
< n
; i
++)
805 lp
[i
] = ((~mp
[i
]) + 1) & BN_MASK2
;
811 * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
812 * r[10] = (a[1]*b[1])
816 * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
820 * R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
821 * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
822 * R[3]=r[1]+(carry/borrow)
826 c1
= (int)(bn_add_words(lp
, &(t
[n2
+ n
]), &(l
[0]), n
));
831 c1
+= (int)(bn_add_words(&(t
[n2
]), lp
, &(r
[0]), n
));
833 c1
-= (int)(bn_sub_words(&(t
[n2
]), &(t
[n2
]), &(t
[0]), n
));
835 c1
+= (int)(bn_add_words(&(t
[n2
]), &(t
[n2
]), &(t
[0]), n
));
837 c2
= (int)(bn_add_words(&(r
[0]), &(r
[0]), &(t
[n2
+ n
]), n
));
838 c2
+= (int)(bn_add_words(&(r
[0]), &(r
[0]), &(r
[n
]), n
));
840 c2
-= (int)(bn_sub_words(&(r
[0]), &(r
[0]), &(t
[n
]), n
));
842 c2
+= (int)(bn_add_words(&(r
[0]), &(r
[0]), &(t
[n
]), n
));
844 if (c1
!= 0) { /* Add starting at r[0], could be +ve or -ve */
849 ll
= (r
[i
] + lc
) & BN_MASK2
;
857 r
[i
++] = (ll
- lc
) & BN_MASK2
;
862 if (c2
!= 0) { /* Add starting at r[1] */
867 ll
= (r
[i
] + lc
) & BN_MASK2
;
875 r
[i
++] = (ll
- lc
) & BN_MASK2
;
881 #endif /* BN_RECURSION */
883 int BN_mul(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*b
, BN_CTX
*ctx
)
888 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
903 if ((al
== 0) || (bl
== 0)) {
910 if ((r
== a
) || (r
== b
)) {
911 if ((rr
= BN_CTX_get(ctx
)) == NULL
)
915 rr
->neg
= a
->neg
^ b
->neg
;
917 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
924 if (bn_wexpand(rr
, 8) == NULL
)
927 bn_mul_comba4(rr
->d
, a
->d
, b
->d
);
932 if (bn_wexpand(rr
, 16) == NULL
)
935 bn_mul_comba8(rr
->d
, a
->d
, b
->d
);
939 #endif /* BN_MUL_COMBA */
941 if ((al
>= BN_MULL_SIZE_NORMAL
) && (bl
>= BN_MULL_SIZE_NORMAL
)) {
942 if (i
>= -1 && i
<= 1) {
944 * Find out the power of two lower or equal to the longest of the
948 j
= BN_num_bits_word((BN_ULONG
)al
);
951 j
= BN_num_bits_word((BN_ULONG
)bl
);
954 assert(j
<= al
|| j
<= bl
);
959 if (al
> j
|| bl
> j
) {
960 if (bn_wexpand(t
, k
* 4) == NULL
)
962 if (bn_wexpand(rr
, k
* 4) == NULL
)
964 bn_mul_part_recursive(rr
->d
, a
->d
, b
->d
,
965 j
, al
- j
, bl
- j
, t
->d
);
966 } else { /* al <= j || bl <= j */
968 if (bn_wexpand(t
, k
* 2) == NULL
)
970 if (bn_wexpand(rr
, k
* 2) == NULL
)
972 bn_mul_recursive(rr
->d
, a
->d
, b
->d
, j
, al
- j
, bl
- j
, t
->d
);
978 if (i
== 1 && !BN_get_flags(b
, BN_FLG_STATIC_DATA
)) {
979 BIGNUM
*tmp_bn
= (BIGNUM
*)b
;
980 if (bn_wexpand(tmp_bn
, al
) == NULL
)
985 } else if (i
== -1 && !BN_get_flags(a
, BN_FLG_STATIC_DATA
)) {
986 BIGNUM
*tmp_bn
= (BIGNUM
*)a
;
987 if (bn_wexpand(tmp_bn
, bl
) == NULL
)
994 /* symmetric and > 4 */
996 j
= BN_num_bits_word((BN_ULONG
)al
);
1000 if (al
== j
) { /* exact multiple */
1001 if (bn_wexpand(t
, k
* 2) == NULL
)
1003 if (bn_wexpand(rr
, k
* 2) == NULL
)
1005 bn_mul_recursive(rr
->d
, a
->d
, b
->d
, al
, t
->d
);
1007 if (bn_wexpand(t
, k
* 4) == NULL
)
1009 if (bn_wexpand(rr
, k
* 4) == NULL
)
1011 bn_mul_part_recursive(rr
->d
, a
->d
, b
->d
, al
- j
, j
, t
->d
);
1018 #endif /* BN_RECURSION */
1019 if (bn_wexpand(rr
, top
) == NULL
)
1022 bn_mul_normal(rr
->d
, a
->d
, al
, b
->d
, bl
);
1024 #if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
1037 void bn_mul_normal(BN_ULONG
*r
, BN_ULONG
*a
, int na
, BN_ULONG
*b
, int nb
)
1055 (void)bn_mul_words(r
, a
, na
, 0);
1058 rr
[0] = bn_mul_words(r
, a
, na
, b
[0]);
1063 rr
[1] = bn_mul_add_words(&(r
[1]), a
, na
, b
[1]);
1066 rr
[2] = bn_mul_add_words(&(r
[2]), a
, na
, b
[2]);
1069 rr
[3] = bn_mul_add_words(&(r
[3]), a
, na
, b
[3]);
1072 rr
[4] = bn_mul_add_words(&(r
[4]), a
, na
, b
[4]);
1079 void bn_mul_low_normal(BN_ULONG
*r
, BN_ULONG
*a
, BN_ULONG
*b
, int n
)
1081 bn_mul_words(r
, a
, n
, b
[0]);
1086 bn_mul_add_words(&(r
[1]), a
, n
, b
[1]);
1089 bn_mul_add_words(&(r
[2]), a
, n
, b
[2]);
1092 bn_mul_add_words(&(r
[3]), a
, n
, b
[3]);
1095 bn_mul_add_words(&(r
[4]), a
, n
, b
[4]);