/*-
* 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);
}
}
}
/* 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 tn,
int n, BN_ULONG *t)
{
int c1,c2,i,j,n2=n*2;
unsigned int neg;
BN_ULONG ln,lo,*p;
# ifdef BN_COUNT
printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
# endif
if (n < 8)
{
i=tn+n;
bn_mul_normal(r,a,i,b,i);
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1=bn_cmp_words(a,&(a[n]),n);
c2=bn_cmp_words(&(b[n]),b,n);
neg=0;
switch (c1*3+c2)
{
case -4:
bn_sub_words(t, &(a[n]),a, n); /* - */
bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
break;
case -3:
case -2:
bn_sub_words(t, &(a[n]),a, n); /* - */
bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
neg=1;
break;
case -1:
case 0:
case 1:
case 2:
bn_sub_words(t, a, &(a[n]),n); /* + */
bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
neg=1;
break;
case 3:
case 4:
bn_sub_words(t, a, &(a[n]),n);
bn_sub_words(&(t[n]),&(b[n]),b, 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]),tn,&(b[n]),tn);
memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
}
else
{
p= &(t[n2*2]);
bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
bn_mul_recursive(r,a,b,n,p);
i=n/2;
/* If there is only a bottom half to the number,
* just do it */
j=tn-i;
if (j == 0)
{
bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),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]),
j,i,p);
memset(&(r[n2+tn*2]),0,
sizeof(BN_ULONG)*(n2-tn*2));
}
else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
{
memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
{
bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
}
else
{
for (;;)
{
i/=2;
if (i < tn)
{
bn_mul_part_recursive(&(r[n2]),
&(a[n]),&(b[n]),
tn-i,i,p);
break;
}
else if (i == tn)
{
bn_mul_recursive(&(r[n2]),
&(a[n]),&(b[n]),
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);
}
}
}
/*-
* r is 2*n words in size,
* a and b are both n words in size. (There's not actually a 'b' here ...)
* n must be a power of 2.
* We multiply and return the result.
* t must be 2*n 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_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t)
{
int n = n2 / 2;
int zero, c1;
BN_ULONG ln, lo, *p;
if (n2 == 4) {
# ifndef BN_SQR_COMBA
bn_sqr_normal(r, a, 4, t);
# else
bn_sqr_comba4(r, a);
# endif
return;
} else if (n2 == 8) {
# ifndef BN_SQR_COMBA
bn_sqr_normal(r, a, 8, t);
# else
bn_sqr_comba8(r, a);
# endif
return;
}
if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
bn_sqr_normal(r, a, n2, t);
return;
}
/* r=(a[0]-a[1])*(a[1]-a[0]) */
c1 = bn_cmp_words(a, &(a[n]), n);
zero = 0;
if (c1 > 0)
bn_sub_words(t, a, &(a[n]), n);
else if (c1 < 0)
bn_sub_words(t, &(a[n]), a, n);
else
zero = 1;
/* The result will always be negative unless it is zero */
p = &(t[n2 * 2]);
if (!zero)
bn_sqr_recursive(&(t[n2]), t, n, p);
else
memset(&t[n2], 0, sizeof(*t) * n2);
bn_sqr_recursive(r, a, n, p);
bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
/*-
* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
/* t[32] is negative */
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
/*-
* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
* r[10] holds (a[0]*a[0])
* r[32] holds (a[1]*a[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);
}
}
}
