fibonacci_matrix_exponentiation.cc

const int MOD = 1e9 + 7;
int add(int a, int b)
{
	int res = a + b;
	if(res >= MOD)
		return res - MOD;
	return res;
}

int mult(int a, int b)
{
	long long res = a;
	res *= b;
	if(res >= MOD)
		return res % MOD;
	return res;
}

const int SZ = 2;
struct matrix
{
	int arr[SZ][SZ];

	void reset()
	{
		memset(arr, 0, sizeof(arr));
	}

	void makeiden()
	{
		reset();
		for(int i=0;i<SZ;i++)
		{
			arr[i][i] = 1;
		}
	}

	matrix operator + (const matrix &o) const 
	{
		matrix res;
		for(int i=0;i<SZ;i++)
		{
			for(int j=0;j<SZ;j++)
			{
				res.arr[i][j] = add(arr[i][j], o.arr[i][j]);
			}
		}
		return res;
	}

	matrix operator * (const matrix &o) const 
	{
		matrix res;
		for(int i=0;i<SZ;i++)
		{
			for(int j=0;j<SZ;j++)
			{
				res.arr[i][j] = 0;
				for(int k=0;k<SZ;k++)
				{
					res.arr[i][j] = add(res.arr[i][j] , mult(arr[i][k] , o.arr[k][j]));
				}
			}
		}
		return res;
	}
};

matrix power(matrix a, int b)
{
	matrix res;
	res.makeiden();
	while(b)
	{
		if(b & 1)
		{
			res = res * a;
		}
		a = a * a;
		b >>= 1;
	}
	return res;
}

// fib(1) = fib(2) = 1
int fib(int n) {
	if (n == 1) return 1;
	if (n == 2) return 1;
	matrix X;
	X.arr[0][0] = X.arr[0][1] = X.arr[1][0] = 1;
	X.arr[1][1] = 0;
	X = power(X, n-2);
	return add(X.arr[0][0], X.arr[1][0]);
}