/* tnX may not be negative but less than n */
static 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;
BN_ULONG ln, lo, *p;
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);
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:
/* 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:
/* 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:
/* 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;
}
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);
}
}
}
/* 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;
#ifdef BN_COUNT
fprintf (stderr, " bn_sqr_recursive %d * %d\n", n2, n2);
#endif
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, n2 * sizeof (BN_ULONG));
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);
}
}
}
/* BN_div computes dv := num / divisor, rounding towards zero, and sets up
* rm such that dv*divisor + rm = num holds.
* Thus:
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
* rm->neg == num->neg (unless the remainder is zero)
* If 'dv' or 'rm' is NULL, the respective value is not returned.
*/
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift,i,loop;
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
bn_check_top(dv);
bn_check_top(rm);
bn_check_top(num);
bn_check_top(divisor);
if (BN_is_zero(divisor))
{
/*Begin: comment out , 17Aug2006, Chris */
#if 0
BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
#endif
/*End: comment out , 17Aug2006, Chris */
return(0);
}
if (BN_ucmp(num,divisor) < 0)
{
if (rm != NULL)
{ if (BN_copy(rm,num) == NULL) return(0); }
if (dv != NULL) BN_zero(dv);
return(1);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get(ctx);
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv == NULL || res == NULL) goto err;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/* only needed when BN_ucmp messes up the values between top and max */
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop;
resp= &(res->d[loop-1]);
/* space for temp */
if (!bn_wexpand(tmp,(div_n+1))) goto err;
if (BN_ucmp(&wnum,sdiv) >= 0)
{
/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
* bn_pollute) the const bignum arguments =>
* clean the values between top and max again */
bn_clear_top2max(&wnum);
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
*resp=1;
}
else
res->top--;
/* if res->top == 0 then clear the neg value otherwise decrease
* the resp pointer */
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i=0; i<loop-1; i++, wnump--, resp--)
{
BN_ULONG q,l0;
/* the first part of the loop uses the top two words of
* snum and sdiv to calculate a BN_ULONG q such that
* | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
q=bn_div_3_words(wnump,d1,d0);
#else
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem=(n1-q*d0)&BN_MASK2;
#endif
t2=(BN_ULLONG)d1*q;
for (;;)
{
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l,t2h,ql,qh;
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem=(n1-q*d0)&BN_MASK2;
#endif
#if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1,q);
#else
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
#endif
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
tmp->d[div_n]=l0;
wnum.d--;
/* ingore top values of the bignums just sub the two
* BN_ULONG arrays with bn_sub_words */
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
{
/* Note: As we have considered only the leading
* two BN_ULONGs in the calculation of q, sdiv * q
* might be greater than wnum (but then (q-1) * sdiv
* is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/* we can't have an overflow here (assuming
* that q != 0, but if q == 0 then tmp is
* zero anyway) */
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL)
{
/* Keep a copy of the neg flag in num because if rm==num
* BN_rshift() will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm,snum,norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
BN_CTX_end(ctx);
return(1);
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return(0);
}
/* dnX may not be positive, but n2/2+dnX has to be */
static 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;
/* 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;
}
/* 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;
}
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 {
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);
}
}
}
/*-
* 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;
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]);
bn_add_words(lp, &(r[0]), &(l[0]), n);
} else {
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);
}
}
}
/*-
* BN_div computes dv := num / divisor, rounding towards
* zero, and sets up rm such that dv*divisor + rm = num holds.
* Thus:
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
* rm->neg == num->neg (unless the remainder is zero)
* If 'dv' or 'rm' is NULL, the respective value is not returned.
*/
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift, i, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
int no_branch = 0;
/*
* Invalid zero-padding would have particularly bad consequences so don't
* just rely on bn_check_top() here (bn_check_top() works only for
* BN_DEBUG builds)
*/
if ((num->top > 0 && num->d[num->top - 1] == 0) ||
(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
bn_check_top(divisor);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
no_branch = 1;
}
bn_check_top(dv);
bn_check_top(rm);
/*- bn_check_top(num); *//*
* 'num' has been checked already
*/
/*- bn_check_top(divisor); *//*
* 'divisor' has been checked already
*/
if (BN_is_zero(divisor)) {
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
return (0);
}
if (!no_branch && BN_ucmp(num, divisor) < 0) {
if (rm != NULL) {
if (BN_copy(rm, num) == NULL)
return (0);
}
if (dv != NULL)
BN_zero(dv);
return (1);
}
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if (dv == NULL)
res = BN_CTX_get(ctx);
else
res = dv;
if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
goto err;
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
if (!(BN_lshift(sdiv, divisor, norm_shift)))
goto err;
sdiv->neg = 0;
norm_shift += BN_BITS2;
if (!(BN_lshift(snum, num, norm_shift)))
goto err;
snum->neg = 0;
if (no_branch) {
/*
* Since we don't know whether snum is larger than sdiv, we pad snum
* with enough zeroes without changing its value.
*/
if (snum->top <= sdiv->top + 1) {
if (bn_wexpand(snum, sdiv->top + 2) == NULL)
goto err;
for (i = snum->top; i < sdiv->top + 2; i++)
snum->d[i] = 0;
snum->top = sdiv->top + 2;
} else {
if (bn_wexpand(snum, snum->top + 1) == NULL)
goto err;
snum->d[snum->top] = 0;
snum->top++;
}
}
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/*
* Lets setup a 'window' into snum This is the part that corresponds to
* the current 'area' being divided
*/
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/*
* only needed when BN_ucmp messes up the values between top and max
*/
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
res->neg = (num->neg ^ divisor->neg);
if (!bn_wexpand(res, (loop + 1)))
goto err;
res->top = loop - no_branch;
resp = &(res->d[loop - 1]);
/* space for temp */
if (!bn_wexpand(tmp, (div_n + 1)))
goto err;
if (!no_branch) {
if (BN_ucmp(&wnum, sdiv) >= 0) {
/*
* If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
* the const bignum arguments => clean the values between top and
* max again
*/
bn_clear_top2max(&wnum);
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
*resp = 1;
} else
res->top--;
}
/*
* if res->top == 0 then clear the neg value otherwise decrease the resp
* pointer
*/
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i = 0; i < loop - 1; i++, wnump--, resp--) {
BN_ULONG q, l0;
/*
* the first part of the loop uses the top two words of snum and sdiv
* to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
*/
# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
q = bn_div_3_words(wnump, d1, d0);
# else
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if (n0 == d0)
q = BN_MASK2;
else { /* n0 < d0 */
# ifdef BN_LLONG
BN_ULLONG t2;
# if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
# else
q = bn_div_words(n0, n1, d0);
# endif
# ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem = (n1 - q * d0) & BN_MASK2;
# endif
t2 = (BN_ULLONG) d1 *q;
for (;;) {
if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
t2 -= d1;
}
# else /* !BN_LLONG */
BN_ULONG t2l, t2h;
q = bn_div_words(n0, n1, d0);
# ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0) & BN_MASK2;
# endif
# if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l, t2h, d1, q);
# elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
# else
{
BN_ULONG ql, qh;
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
}
# endif
for (;;) {
if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
if (t2l < d1)
t2h--;
t2l -= d1;
}
# endif /* !BN_LLONG */
}
# endif /* !BN_DIV3W */
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
tmp->d[div_n] = l0;
wnum.d--;
/*
* ingore top values of the bignums just sub the two BN_ULONG arrays
* with bn_sub_words
*/
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
/*
* Note: As we have considered only the leading two BN_ULONGs in
* the calculation of q, sdiv * q might be greater than wnum (but
* then (q-1) * sdiv is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/*
* we can't have an overflow here (assuming that q != 0, but
* if q == 0 then tmp is zero anyway)
*/
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL) {
/*
* Keep a copy of the neg flag in num because if rm==num BN_rshift()
* will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm, snum, norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
if (no_branch)
bn_correct_top(res);
BN_CTX_end(ctx);
return (1);
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return (0);
}
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;
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) {
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) {
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;
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;
}
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) {
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;
}
/* n+tn is the word length
* t needs to be n*4 is size, as does r */
EXPORT_C 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 && tna == tnb)
{
bn_mul_recursive(&(r[n2]),
&(a[n]),&(b[n]),
i,tna-i,tnb-i,p);
break;
}
else if (i < tna || i < tnb)
{
bn_mul_part_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);
}
}
}
EXPORT_C 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;
}
// bn_mul_part_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r|
// has length 4*|n|, |a| has length |n| + |tna|, |b| has length |n| + |tnb|, and
// |t| has length 8*|n|. |n| must be a power of two. Additionally, we must have
// 0 <= tna < n and 0 <= tnb < n, and |tna| and |tnb| must differ by at most
// one.
//
// TODO(davidben): Make this take |size_t| and perhaps the actual lengths of |a|
// and |b|.
static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a,
const BN_ULONG *b, int n, int tna, int tnb,
BN_ULONG *t) {
// |n| is a power of two.
assert(n != 0 && (n & (n - 1)) == 0);
// Check |tna| and |tnb| are in range.
assert(0 <= tna && tna < n);
assert(0 <= tnb && tnb < n);
assert(-1 <= tna - tnb && tna - tnb <= 1);
int n2 = n * 2;
if (n < 8) {
bn_mul_normal(r, a, n + tna, b, n + tnb);
OPENSSL_memset(r + n2 + tna + tnb, 0, n2 - tna - tnb);
return;
}
// Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|. |a1|
// and |b1| have size |tna| and |tnb|, respectively.
// Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
// for recursive calls.
// Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
// to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
//
// a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
// t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
// their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
// themselves store the absolute value.
BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
// Compute:
// t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
// r0,r1 = a0 * b0
// r2,r3 = a1 * b1
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);
// |bn_mul_normal| only writes |tna| + |tna| words. Zero the rest.
OPENSSL_memset(&r[n2 + tna + tnb], 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
} else {
BN_ULONG *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);
OPENSSL_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 {
int i = n;
for (;;) {
i /= 2;
if (i < tna || i < tnb) {
// E.g., n == 16, i == 8 and tna == 11. |tna| and |tnb| are within one
// of each other, so if |tna| is larger and tna > i, then we know
// tnb >= i, and this call is valid.
bn_mul_part_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
break;
}
if (i == tna || i == tnb) {
// If there is only a bottom half to the number, just do it. We know
// the larger of |tna - i| and |tnb - i| is zero. The other is zero or
// -1 by because of |tna| and |tnb| differ by at most one.
bn_mul_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
break;
}
// This loop will eventually terminate when |i| falls below
// |BN_MUL_RECURSIVE_SIZE_NORMAL| because we know one of |tna| and |tnb|
// exceeds that.
}
}
}
// t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
// t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
// The second term is stored as the absolute value, so we do this with a
// constant-time select.
BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
crypto_word_t_too_small);
c = constant_time_select_w(neg, c_neg, c_pos);
// We now have our three components. Add them together.
// r1,r2,c = r1,r2 + t2,t3,c
c += bn_add_words(&r[n], &r[n], &t[n2], n2);
// Propagate the carry bit to the end.
for (int i = n + n2; i < n2 + n2; i++) {
BN_ULONG old = r[i];
r[i] = old + c;
c = r[i] < old;
}
// The product should fit without carries.
assert(c == 0);
}
// bn_mul_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| has
// length 2*|n2|, |a| has length |n2| + |dna|, |b| has length |n2| + |dnb|, and
// |t| has length 4*|n2|. |n2| must be a power of two. Finally, we must have
// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dna| <= 0 and
// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dnb| <= 0.
//
// TODO(davidben): Simplify and |size_t| the calling convention around lengths
// here.
static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int n2, int dna, int dnb, BN_ULONG *t) {
// |n2| is a power of two.
assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
// Check |dna| and |dnb| are in range.
assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dna && dna <= 0);
assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dnb && dnb <= 0);
// 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;
}
// 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) {
OPENSSL_memset(&r[2 * n2 + dna + dnb], 0,
sizeof(BN_ULONG) * -(dna + dnb));
}
return;
}
// Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|.
// Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
// for recursive calls.
// Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
// to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
//
// a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
//
// Note that we know |n| >= |BN_MUL_RECURSIVE_SIZE_NORMAL|/2 above, so
// |tna| and |tnb| are non-negative.
int n = n2 / 2, tna = n + dna, tnb = n + dnb;
// t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
// their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
// themselves store the absolute value.
BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
// Compute:
// t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
// r0,r1 = a0 * b0
// r2,r3 = a1 * b1
if (n == 4 && dna == 0 && dnb == 0) {
bn_mul_comba4(&t[n2], t, &t[n]);
bn_mul_comba4(r, a, b);
bn_mul_comba4(&r[n2], &a[n], &b[n]);
} else if (n == 8 && dna == 0 && dnb == 0) {
bn_mul_comba8(&t[n2], t, &t[n]);
bn_mul_comba8(r, a, b);
bn_mul_comba8(&r[n2], &a[n], &b[n]);
} else {
BN_ULONG *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);
bn_mul_recursive(&r[n2], &a[n], &b[n], n, dna, dnb, p);
}
// t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
// t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
// The second term is stored as the absolute value, so we do this with a
// constant-time select.
BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
OPENSSL_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
crypto_word_t_too_small);
c = constant_time_select_w(neg, c_neg, c_pos);
// We now have our three components. Add them together.
// r1,r2,c = r1,r2 + t2,t3,c
c += bn_add_words(&r[n], &r[n], &t[n2], n2);
// Propagate the carry bit to the end.
for (int i = n + n2; i < n2 + n2; i++) {
BN_ULONG old = r[i];
r[i] = old + c;
c = r[i] < old;
}
// The product should fit without carries.
assert(c == 0);
}
