private void karmul_lower(int vp, FF x, int xp, FF y, int yp, FF t, int tp, int n)
{ // Calculates Least Significant bottom half of x*y
int nd2;
if (n == 1)
{ // only calculate bottom half of product
v[vp].copy(BIG.smul(x.v[xp], y.v[yp]));
return;
}
nd2 = n / 2;
karmul(vp, x, xp, y, yp, t, tp + n, nd2);
t.karmul_lower(tp, x, xp + nd2, y, yp, t, tp + n, nd2);
rinc(vp + nd2, t, tp, nd2);
t.karmul_lower(tp, x, xp, y, yp + nd2, t, tp + n, nd2);
rinc(vp + nd2, t, tp, nd2);
rnorm(vp + nd2, -nd2); // truncate it
}
/* return This mod modulus, N is modulus, ND is Montgomery Constant */
public FF reduce(FF N, FF ND)
{ // fast karatsuba Montgomery reduction
int n = N.length;
FF t = new FF(2 * n);
FF r = new FF(n);
FF m = new FF(n);
r.sducopy(this);
m.karmul_lower(0, this, 0, ND, 0, t, 0, n);
karmul_upper(N, m, t, n);
m.sducopy(this);
r.add(N);
r.sub(m);
r.norm();
return(r);
}