public static void Invert(ulong[] x, ulong[] z)
{
if (Nat256.IsZero64(x))
{
throw new InvalidOperationException();
}
// Itoh-Tsujii inversion
ulong[] t0 = Nat256.Create64();
ulong[] t1 = Nat256.Create64();
Square(x, t0);
Multiply(t0, x, t0);
Square(t0, t0);
Multiply(t0, x, t0);
SquareN(t0, 3, t1);
Multiply(t1, t0, t1);
Square(t1, t1);
Multiply(t1, x, t1);
SquareN(t1, 7, t0);
Multiply(t0, t1, t0);
SquareN(t0, 14, t1);
Multiply(t1, t0, t1);
Square(t1, t1);
Multiply(t1, x, t1);
SquareN(t1, 29, t0);
Multiply(t0, t1, t0);
SquareN(t0, 58, t1);
Multiply(t1, t0, t1);
SquareN(t1, 116, t0);
Multiply(t0, t1, t0);
Square(t0, z);
}
public static void Invert(ulong[] x, ulong[] z)
{
if (Nat256.IsZero64(x))
{
throw new InvalidOperationException();
}
ulong[] array = Nat256.Create64();
ulong[] array2 = Nat256.Create64();
Square(x, array);
Multiply(array, x, array);
Square(array, array);
Multiply(array, x, array);
SquareN(array, 3, array2);
Multiply(array2, array, array2);
Square(array2, array2);
Multiply(array2, x, array2);
SquareN(array2, 7, array);
Multiply(array, array2, array);
SquareN(array, 14, array2);
Multiply(array2, array, array2);
Square(array2, array2);
Multiply(array2, x, array2);
SquareN(array2, 29, array);
Multiply(array, array2, array);
Square(array, array);
Multiply(array, x, array);
SquareN(array, 59, array2);
Multiply(array2, array, array2);
Square(array2, array2);
Multiply(array2, x, array2);
SquareN(array2, 119, array);
Multiply(array, array2, array);
Square(array, z);
}
public static void Invert(ulong[] x, ulong[] z)
{
if (Nat256.IsZero64(x))
{
throw new InvalidOperationException();
}
// Itoh-Tsujii inversion with bases { 2, 3 }
ulong[] t0 = Nat256.Create64();
ulong[] t1 = Nat256.Create64();
Square(x, t0);
// 3 | 192
SquareN(t0, 1, t1);
Multiply(t0, t1, t0);
SquareN(t1, 1, t1);
Multiply(t0, t1, t0);
// 2 | 64
SquareN(t0, 3, t1);
Multiply(t0, t1, t0);
// 2 | 32
SquareN(t0, 6, t1);
Multiply(t0, t1, t0);
// 2 | 16
SquareN(t0, 12, t1);
Multiply(t0, t1, t0);
// 2 | 8
SquareN(t0, 24, t1);
Multiply(t0, t1, t0);
// 2 | 4
SquareN(t0, 48, t1);
Multiply(t0, t1, t0);
// 2 | 2
SquareN(t0, 96, t1);
Multiply(t0, t1, z);
}
