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bn_mul.c
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bn_mul.c
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/* crypto/bn/bn_mul.c */
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.]
*/
#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif
#include <stdio.h>
#include <assert.h>
#include "cryptlib.h"
#include "bn_lcl.h"
#if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS)
/* Here follows specialised variants of bn_add_words() and
bn_sub_words(). They have the property performing operations on
arrays of different sizes. The sizes of those arrays is expressed through
cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl,
which is the delta between the two lengths, calculated as len(a)-len(b).
All lengths are the number of BN_ULONGs... For the operations that require
a result array as parameter, it must have the length cl+abs(dl).
These functions should probably end up in bn_asm.c as soon as there are
assembler counterparts for the systems that use assembler files. */
BN_ULONG bn_sub_part_words(BN_ULONG *r,
const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl)
{
BN_ULONG c, t;
assert(cl >= 0);
c = bn_sub_words(r, a, b, cl);
if (dl == 0)
return c;
r += cl;
a += cl;
b += cl;
if (dl < 0)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
#endif
for (;;)
{
t = b[0];
r[0] = (0-t-c)&BN_MASK2;
if (t != 0) c=1;
if (++dl >= 0) break;
t = b[1];
r[1] = (0-t-c)&BN_MASK2;
if (t != 0) c=1;
if (++dl >= 0) break;
t = b[2];
r[2] = (0-t-c)&BN_MASK2;
if (t != 0) c=1;
if (++dl >= 0) break;
t = b[3];
r[3] = (0-t-c)&BN_MASK2;
if (t != 0) c=1;
if (++dl >= 0) break;
b += 4;
r += 4;
}
}
else
{
int save_dl = dl;
#ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c);
#endif
while(c)
{
t = a[0];
r[0] = (t-c)&BN_MASK2;
if (t != 0) c=0;
if (--dl <= 0) break;
t = a[1];
r[1] = (t-c)&BN_MASK2;
if (t != 0) c=0;
if (--dl <= 0) break;
t = a[2];
r[2] = (t-c)&BN_MASK2;
if (t != 0) c=0;
if (--dl <= 0) break;
t = a[3];
r[3] = (t-c)&BN_MASK2;
if (t != 0) c=0;
if (--dl <= 0) break;
save_dl = dl;
a += 4;
r += 4;
}
if (dl > 0)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
#endif
if (save_dl > dl)
{
switch (save_dl - dl)
{
case 1:
r[1] = a[1];
if (--dl <= 0) break;
case 2:
r[2] = a[2];
if (--dl <= 0) break;
case 3:
r[3] = a[3];
if (--dl <= 0) break;
}
a += 4;
r += 4;
}
}
if (dl > 0)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl);
#endif
for(;;)
{
r[0] = a[0];
if (--dl <= 0) break;
r[1] = a[1];
if (--dl <= 0) break;
r[2] = a[2];
if (--dl <= 0) break;
r[3] = a[3];
if (--dl <= 0) break;
a += 4;
r += 4;
}
}
}
return c;
}
#endif
BN_ULONG bn_add_part_words(BN_ULONG *r,
const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl)
{
BN_ULONG c, l, t;
assert(cl >= 0);
c = bn_add_words(r, a, b, cl);
if (dl == 0)
return c;
r += cl;
a += cl;
b += cl;
if (dl < 0)
{
int save_dl = dl;
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c);
#endif
while (c)
{
l=(c+b[0])&BN_MASK2;
c=(l < c);
r[0]=l;
if (++dl >= 0) break;
l=(c+b[1])&BN_MASK2;
c=(l < c);
r[1]=l;
if (++dl >= 0) break;
l=(c+b[2])&BN_MASK2;
c=(l < c);
r[2]=l;
if (++dl >= 0) break;
l=(c+b[3])&BN_MASK2;
c=(l < c);
r[3]=l;
if (++dl >= 0) break;
save_dl = dl;
b+=4;
r+=4;
}
if (dl < 0)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl);
#endif
if (save_dl < dl)
{
switch (dl - save_dl)
{
case 1:
r[1] = b[1];
if (++dl >= 0) break;
case 2:
r[2] = b[2];
if (++dl >= 0) break;
case 3:
r[3] = b[3];
if (++dl >= 0) break;
}
b += 4;
r += 4;
}
}
if (dl < 0)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl);
#endif
for(;;)
{
r[0] = b[0];
if (++dl >= 0) break;
r[1] = b[1];
if (++dl >= 0) break;
r[2] = b[2];
if (++dl >= 0) break;
r[3] = b[3];
if (++dl >= 0) break;
b += 4;
r += 4;
}
}
}
else
{
int save_dl = dl;
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl);
#endif
while (c)
{
t=(a[0]+c)&BN_MASK2;
c=(t < c);
r[0]=t;
if (--dl <= 0) break;
t=(a[1]+c)&BN_MASK2;
c=(t < c);
r[1]=t;
if (--dl <= 0) break;
t=(a[2]+c)&BN_MASK2;
c=(t < c);
r[2]=t;
if (--dl <= 0) break;
t=(a[3]+c)&BN_MASK2;
c=(t < c);
r[3]=t;
if (--dl <= 0) break;
save_dl = dl;
a+=4;
r+=4;
}
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl);
#endif
if (dl > 0)
{
if (save_dl > dl)
{
switch (save_dl - dl)
{
case 1:
r[1] = a[1];
if (--dl <= 0) break;
case 2:
r[2] = a[2];
if (--dl <= 0) break;
case 3:
r[3] = a[3];
if (--dl <= 0) break;
}
a += 4;
r += 4;
}
}
if (dl > 0)
{
#ifdef BN_COUNT
fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl);
#endif
for(;;)
{
r[0] = a[0];
if (--dl <= 0) break;
r[1] = a[1];
if (--dl <= 0) break;
r[2] = a[2];
if (--dl <= 0) break;
r[3] = a[3];
if (--dl <= 0) break;
a += 4;
r += 4;
}
}
}
return c;
}
#ifdef BN_RECURSION
/* Karatsuba recursive multiplication algorithm
* (cf. Knuth, The Art of Computer Programming, Vol. 2) */
/* r is 2*n2 words in size,
* a and b are both n2 words in size.
* n2 must be a power of 2.
* We multiply and return the result.
* t must be 2*n2 words in size
* We calculate
* a[0]*b[0]
* a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
* a[1]*b[1]
*/
/* dnX may not be positive, but n2/2+dnX has to be */
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
int dna, int dnb, BN_ULONG *t)
{
int n=n2/2,c1,c2;
int tna=n+dna, tnb=n+dnb;
unsigned int neg,zero;
BN_ULONG ln,lo,*p;
# ifdef BN_COUNT
fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb);
# endif
# ifdef BN_MUL_COMBA
# if 0
if (n2 == 4)
{
bn_mul_comba4(r,a,b);
return;
}
# endif
/* Only call bn_mul_comba 8 if n2 == 8 and the
* two arrays are complete [steve]
*/
if (n2 == 8 && dna == 0 && dnb == 0)
{
bn_mul_comba8(r,a,b);
return;
}
# endif /* BN_MUL_COMBA */
/* Else do normal multiply */
if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
{
bn_mul_normal(r,a,n2+dna,b,n2+dnb);
if ((dna + dnb) < 0)
memset(&r[2*n2 + dna + dnb], 0,
sizeof(BN_ULONG) * -(dna + dnb));
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
zero=neg=0;
switch (c1*3+c2)
{
case -4:
bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
break;
case -3:
zero=1;
break;
case -2:
bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
neg=1;
break;
case -1:
case 0:
case 1:
zero=1;
break;
case 2:
bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
neg=1;
break;
case 3:
zero=1;
break;
case 4:
bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
break;
}
# ifdef BN_MUL_COMBA
if (n == 4 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba4 could take
extra args to do this well */
{
if (!zero)
bn_mul_comba4(&(t[n2]),t,&(t[n]));
else
memset(&(t[n2]),0,8*sizeof(BN_ULONG));
bn_mul_comba4(r,a,b);
bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
}
else if (n == 8 && dna == 0 && dnb == 0) /* XXX: bn_mul_comba8 could
take extra args to do this
well */
{
if (!zero)
bn_mul_comba8(&(t[n2]),t,&(t[n]));
else
memset(&(t[n2]),0,16*sizeof(BN_ULONG));
bn_mul_comba8(r,a,b);
bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
}
else
# endif /* BN_MUL_COMBA */
{
p= &(t[n2*2]);
if (!zero)
bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
else
memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
bn_mul_recursive(r,a,b,n,0,0,p);
bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,dna,dnb,p);
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
if (neg) /* if t[32] is negative */
{
c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
}
else
{
/* Might have a carry */
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
if (c1)
{
p= &(r[n+n2]);
lo= *p;
ln=(lo+c1)&BN_MASK2;
*p=ln;
/* The overflow will stop before we over write
* words we should not overwrite */
if (ln < (BN_ULONG)c1)
{
do {
p++;
lo= *p;
ln=(lo+1)&BN_MASK2;
*p=ln;
} while (ln == 0);
}
}
}
/* n+tn is the word length
* t needs to be n*4 is size, as does r */
/* tnX may not be negative but less than n */
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
int tna, int tnb, BN_ULONG *t)
{
int i,j,n2=n*2;
int c1,c2,neg,zero;
BN_ULONG ln,lo,*p;
# ifdef BN_COUNT
fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n",
n, tna, n, tnb);
# endif
if (n < 8)
{
bn_mul_normal(r,a,n+tna,b,n+tnb);
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1=bn_cmp_part_words(a,&(a[n]),tna,n-tna);
c2=bn_cmp_part_words(&(b[n]),b,tnb,tnb-n);
zero=neg=0;
switch (c1*3+c2)
{
case -4:
bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
break;
case -3:
zero=1;
/* break; */
case -2:
bn_sub_part_words(t, &(a[n]),a, tna,tna-n); /* - */
bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n); /* + */
neg=1;
break;
case -1:
case 0:
case 1:
zero=1;
/* break; */
case 2:
bn_sub_part_words(t, a, &(a[n]),tna,n-tna); /* + */
bn_sub_part_words(&(t[n]),b, &(b[n]),tnb,n-tnb); /* - */
neg=1;
break;
case 3:
zero=1;
/* break; */
case 4:
bn_sub_part_words(t, a, &(a[n]),tna,n-tna);
bn_sub_part_words(&(t[n]),&(b[n]),b, tnb,tnb-n);
break;
}
/* The zero case isn't yet implemented here. The speedup
would probably be negligible. */
# if 0
if (n == 4)
{
bn_mul_comba4(&(t[n2]),t,&(t[n]));
bn_mul_comba4(r,a,b);
bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
}
else
# endif
if (n == 8)
{
bn_mul_comba8(&(t[n2]),t,&(t[n]));
bn_mul_comba8(r,a,b);
bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
memset(&(r[n2+tna+tnb]),0,sizeof(BN_ULONG)*(n2-tna-tnb));
}
else
{
p= &(t[n2*2]);
bn_mul_recursive(&(t[n2]),t,&(t[n]),n,0,0,p);
bn_mul_recursive(r,a,b,n,0,0,p);
i=n/2;
/* If there is only a bottom half to the number,
* just do it */
if (tna > tnb)
j = tna - i;
else
j = tnb - i;
if (j == 0)
{
bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),
i,tna-i,tnb-i,p);
memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
}
else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
{
bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
i,tna-i,tnb-i,p);
memset(&(r[n2+tna+tnb]),0,
sizeof(BN_ULONG)*(n2-tna-tnb));
}
else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
{
memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL
&& tnb < BN_MUL_RECURSIVE_SIZE_NORMAL)
{
bn_mul_normal(&(r[n2]),&(a[n]),tna,&(b[n]),tnb);
}
else
{
for (;;)
{
i/=2;
/* these simplified conditions work
* exclusively because difference
* between tna and tnb is 1 or 0 */
if (i < tna || i < tnb)
{
bn_mul_part_recursive(&(r[n2]),
&(a[n]),&(b[n]),
i,tna-i,tnb-i,p);
break;
}
else if (i == tna || i == tnb)
{
bn_mul_recursive(&(r[n2]),
&(a[n]),&(b[n]),
i,tna-i,tnb-i,p);
break;
}
}
}
}
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
if (neg) /* if t[32] is negative */
{
c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
}
else
{
/* Might have a carry */
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
if (c1)
{
p= &(r[n+n2]);
lo= *p;
ln=(lo+c1)&BN_MASK2;
*p=ln;
/* The overflow will stop before we over write
* words we should not overwrite */
if (ln < (BN_ULONG)c1)
{
do {
p++;
lo= *p;
ln=(lo+1)&BN_MASK2;
*p=ln;
} while (ln == 0);
}
}
}
/* a and b must be the same size, which is n2.
* r needs to be n2 words and t needs to be n2*2
*/
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
BN_ULONG *t)
{
int n=n2/2;
# ifdef BN_COUNT
fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2);
# endif
bn_mul_recursive(r,a,b,n,0,0,&(t[0]));
if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL)
{
bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2]));
bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2]));
bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
}
else
{
bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n);
bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n);
bn_add_words(&(r[n]),&(r[n]),&(t[0]),n);
bn_add_words(&(r[n]),&(r[n]),&(t[n]),n);
}
}
/* a and b must be the same size, which is n2.
* r needs to be n2 words and t needs to be n2*2
* l is the low words of the output.
* t needs to be n2*3
*/
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
BN_ULONG *t)
{
int i,n;
int c1,c2;
int neg,oneg,zero;
BN_ULONG ll,lc,*lp,*mp;
# ifdef BN_COUNT
fprintf(stderr," bn_mul_high %d * %d\n",n2,n2);
# endif
n=n2/2;
/* Calculate (al-ah)*(bh-bl) */
neg=zero=0;
c1=bn_cmp_words(&(a[0]),&(a[n]),n);
c2=bn_cmp_words(&(b[n]),&(b[0]),n);
switch (c1*3+c2)
{
case -4:
bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
break;
case -3:
zero=1;
break;
case -2:
bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n);
bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
neg=1;
break;
case -1:
case 0:
case 1:
zero=1;
break;
case 2:
bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n);
neg=1;
break;
case 3:
zero=1;
break;
case 4:
bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n);
bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n);
break;
}
oneg=neg;
/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */
/* r[10] = (a[1]*b[1]) */
# ifdef BN_MUL_COMBA
if (n == 8)
{
bn_mul_comba8(&(t[0]),&(r[0]),&(r[n]));
bn_mul_comba8(r,&(a[n]),&(b[n]));
}
else
# endif
{
bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2]));
bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2]));
}
/* s0 == low(al*bl)
* s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl)
* We know s0 and s1 so the only unknown is high(al*bl)
* high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl))
* high(al*bl) == s1 - (r[0]+l[0]+t[0])
*/
if (l != NULL)
{
lp= &(t[n2+n]);
c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n));
}
else
{
c1=0;
lp= &(r[0]);
}
if (neg)
neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n));
else
{
bn_add_words(&(t[n2]),lp,&(t[0]),n);
neg=0;
}
if (l != NULL)
{
bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n);
}
else
{
lp= &(t[n2+n]);
mp= &(t[n2]);
for (i=0; i<n; i++)
lp[i]=((~mp[i])+1)&BN_MASK2;
}
/* s[0] = low(al*bl)
* t[3] = high(al*bl)
* t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign
* r[10] = (a[1]*b[1])
*/
/* R[10] = al*bl
* R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0])
* R[32] = ah*bh
*/
/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow)
* R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow)
* R[3]=r[1]+(carry/borrow)
*/
if (l != NULL)
{
lp= &(t[n2]);
c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n));
}
else
{
lp= &(t[n2+n]);
c1=0;
}
c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n));
if (oneg)
c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n));
else
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n));
c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n));
c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n));
if (oneg)
c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n));
else
c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n));
if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */
{
i=0;
if (c1 > 0)
{
lc=c1;
do {
ll=(r[i]+lc)&BN_MASK2;
r[i++]=ll;
lc=(lc > ll);
} while (lc);
}
else
{
lc= -c1;
do {
ll=r[i];
r[i++]=(ll-lc)&BN_MASK2;
lc=(lc > ll);
} while (lc);
}
}
if (c2 != 0) /* Add starting at r[1] */
{
i=n;
if (c2 > 0)
{
lc=c2;
do {
ll=(r[i]+lc)&BN_MASK2;
r[i++]=ll;
lc=(lc > ll);
} while (lc);
}
else
{
lc= -c2;
do {
ll=r[i];
r[i++]=(ll-lc)&BN_MASK2;
lc=(lc > ll);
} while (lc);
}
}
}
#endif /* BN_RECURSION */
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret=0;
int top,al,bl;
BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_RECURSION
BIGNUM *t=NULL;
int j=0,k;
#endif
#ifdef BN_COUNT
fprintf(stderr,"BN_mul %d * %d\n",a->top,b->top);
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al=a->top;
bl=b->top;
if ((al == 0) || (bl == 0))
{
BN_zero(r);
return(1);
}
top=al+bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b))
{
if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
}
else
rr = r;
rr->neg=a->neg^b->neg;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al-bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0)
{
# if 0
if (al == 4)
{
if (bn_wexpand(rr,8) == NULL) goto err;
rr->top=8;
bn_mul_comba4(rr->d,a->d,b->d);
goto end;
}
# endif