public static BigInteger GetElement(BigInteger idx)
{
if (idx == 0)
{
return(0);
}
var matrix = new Matrix2By2(1, 1, 1, 0);
return(CustomMatrixMultiply(CustomPow(matrix, idx), new Matrix2By2(1, 2, 2, -1))[0, 1]);
}
private static Matrix2By2 CustomPow(Matrix2By2 a, BigInteger power)
{
if (power == 1)
{
return(a);
}
var tmp = CustomPow(a, power / 2);
return(power % 2 == 0
? CustomMatrixMultiply(tmp, tmp)
: CustomMatrixMultiply(tmp, CustomMatrixMultiply(tmp, a)));
}
private static Matrix2By2 CustomMatrixMultiply(Matrix2By2 lop, Matrix2By2 rop)
{
var a1111 = lop[0, 0] * rop[0, 0];
var a1212 = lop[0, 1] * rop[0, 1];
var a1112 = lop[0, 0] * rop[0, 1];
var a1222 = lop[0, 1] * rop[1, 1];
var a2222 = lop[1, 1] * rop[1, 1];
a1112.Add(a1222);
a1111.Add(a1212);
a1212.Add(a2222);
return(new Matrix2By2(
a1111,
a1112,
a1112,
a1212));
}