public virtual Number Pow (Number x, Number y)
{
if (y.IsZero ())
return ToElement (Number.One);
if (y.IsOne ())
return x;
Number a = x;
Number b = ToElement (Number.One);
if (y.GetBit (0) == 1)
b = a;
for (int i = 1; i < y.BitCount (); i ++) {
a = Multiply (a, a);
if (y.GetBit (i) == 1)
b = Multiply (a, b);
}
return b;
}
public override unsafe Number Multiply (Number x, Number y)
{
if (x.IsZero () || y.IsZero ())
return Number.Zero;
if (x.length < y.length) {
Number swap = x;
x = y;
y = swap;
}
uint[] z = new uint[mod.length + 1];
fixed (uint* px = x.data, py = y.data, pz = z, pp = mod.data) {
uint y0 = py[0];
int i = 0;
for (; i < x.length; i++) {
uint u = (uint)((pz[0] + px[i] * y0) * invMod);
uint xi = px[i];
ulong carry1 = ((ulong)xi) * ((ulong)py[0]);
ulong carry2 = ((ulong)u) * ((ulong)pp[0]);
ulong carry = (((ulong)(uint)carry1) + ((ulong)(uint)carry2) + ((ulong)pz[0])) >> 32;
carry1 >>= 32; carry2 >>= 32;
int k = 1;
for (; k < y.length; k++) {
carry1 += ((ulong)xi) * ((ulong)py[k]);
carry2 += ((ulong)u) * ((ulong)pp[k]);
carry += ((ulong)(uint)carry1) + ((ulong)(uint)carry2) + ((ulong)pz[k]);
pz[k - 1] = (uint)carry;
carry >>= 32; carry1 >>= 32; carry2 >>= 32;
}
for (; carry1 != 0 && k < mod.length; k++) {
carry2 += ((ulong)u) * ((ulong)pp[k]);
carry += ((ulong)(uint)carry1) + ((ulong)(uint)carry2) + ((ulong)pz[k]);
pz[k - 1] = (uint)carry;
carry >>= 32; carry1 >>= 32; carry2 >>= 32;
}
for (; k < mod.length; k++) {
carry2 += ((ulong)u) * ((ulong)pp[k]);
carry += ((ulong)(uint)carry2) + ((ulong)pz[k]);
pz[k - 1] = (uint)carry;
carry >>= 32; carry2 >>= 32;
}
carry += carry1 + carry2 + ((ulong)pz[k]);
pz[k - 1] = (uint)carry;
pz[k] = (uint)(carry >> 32);
}
for (; i < mod.length; i++) {
uint u = (uint)(pz[0] * invMod);
ulong carry = (((ulong)u) * ((ulong)pp[0]) + ((ulong)pz[0])) >> 32;
int k = 1;
for (; k < mod.length; k++) {
carry += ((ulong)u) * ((ulong)pp[k]) + ((ulong)pz[k]);
pz[k - 1] = (uint)carry;
carry >>= 32;
}
carry += ((ulong)pz[k]);
pz[k - 1] = (uint)carry;
pz[k] = (uint)(carry >> 32);
}
if (pz[mod.length] != 0 || Number.Compare (z, mod.length, mod.data, mod.length) >= 0)
return new Number (z, Number.Subtract (pz, z.Length, pp, mod.length, pz));
return new Number (z);
}
}