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openssl/crypto/bn/bn_mul.c
Geoff Thorpe d870740cd7 Put the first stage of my bignum debugging adventures into CVS. This code 
is itself experimental, and in addition may cause execution to break on
existing openssl "bugs" that previously were harmless or at least
invisible.
2003-11-04 22:54:49 +00:00

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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]
*/
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\n",n2,n2);
# 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 */
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",
tna, n, tnb, n);
# 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;
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))
{
if (!BN_zero(r)) goto err;
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
if (al == 8)
{
if (bn_wexpand(rr,16) == NULL) goto err;
rr->top=16;
bn_mul_comba8(rr->d,a->d,b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
{
if (i >= -1 && i <= 1)
{
int sav_j =0;
/* Find out the power of two lower or equal
to the longest of the two numbers */
if (i >= 0)
{
j = BN_num_bits_word((BN_ULONG)al);
}
if (i == -1)
{
j = BN_num_bits_word((BN_ULONG)bl);
}
sav_j = j;
j = 1<<(j-1);
assert(j <= al || j <= bl);
k = j+j;
t = BN_CTX_get(ctx);
if (al > j || bl > j)
{
bn_wexpand(t,k*4);
bn_wexpand(rr,k*4);
bn_mul_part_recursive(rr->d,a->d,b->d,
j,al-j,bl-j,t->d);
}
else /* al <= j || bl <= j */
{
bn_wexpand(t,k*2);
bn_wexpand(rr,k*2);
bn_mul_recursive(rr->d,a->d,b->d,
j,al-j,bl-j,t->d);
}
rr->top=top;
goto end;
}
#if 0
if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
{
BIGNUM *tmp_bn = (BIGNUM *)b;
if (bn_wexpand(tmp_bn,al) == NULL) goto err;
tmp_bn->d[bl]=0;
bl++;
i--;
}
else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
{
BIGNUM *tmp_bn = (BIGNUM *)a;
if (bn_wexpand(tmp_bn,bl) == NULL) goto err;
tmp_bn->d[al]=0;
al++;
i++;
}
if (i == 0)
{
/* symmetric and > 4 */
/* 16 or larger */
j=BN_num_bits_word((BN_ULONG)al);
j=1<<(j-1);
k=j+j;
t = BN_CTX_get(ctx);
if (al == j) /* exact multiple */
{
if (bn_wexpand(t,k*2) == NULL) goto err;
if (bn_wexpand(rr,k*2) == NULL) goto err;
bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
}
else
{
if (bn_wexpand(t,k*4) == NULL) goto err;
if (bn_wexpand(rr,k*4) == NULL) goto err;
bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
}
rr->top=top;
goto end;
}
#endif
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr,top) == NULL) goto err;
rr->top=top;
bn_mul_normal(rr->d,a->d,al,b->d,bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
bn_correct_top(rr);
if (r != rr) BN_copy(r,rr);
ret=1;
err:
BN_CTX_end(ctx);
bn_check_top(r);
return(ret);
}
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
{
BN_ULONG *rr;
#ifdef BN_COUNT
fprintf(stderr," bn_mul_normal %d * %d\n",na,nb);
#endif
if (na < nb)
{
int itmp;
BN_ULONG *ltmp;
itmp=na; na=nb; nb=itmp;
ltmp=a; a=b; b=ltmp;
}
rr= &(r[na]);
if (nb <= 0)
{
(void)bn_mul_words(r,a,na,0);
return;
}
else
rr[0]=bn_mul_words(r,a,na,b[0]);
for (;;)
{
if (--nb <= 0) return;
rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]);
if (--nb <= 0) return;
rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]);
if (--nb <= 0) return;
rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]);
if (--nb <= 0) return;
rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]);
rr+=4;
r+=4;
b+=4;
}
}
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
{
#ifdef BN_COUNT
fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
#endif
bn_mul_words(r,a,n,b[0]);
for (;;)
{
if (--n <= 0) return;
bn_mul_add_words(&(r[1]),a,n,b[1]);
if (--n <= 0) return;
bn_mul_add_words(&(r[2]),a,n,b[2]);
if (--n <= 0) return;
bn_mul_add_words(&(r[3]),a,n,b[3]);
if (--n <= 0) return;
bn_mul_add_words(&(r[4]),a,n,b[4]);
r+=4;
b+=4;
}
}
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