Fibonacci number in O( log N ) operations.

matrix_fib.py

import time
import random


class MatrixFibonacci:
    A = [[1, 1],
         [1, 0]]

    def __init__(self):
        self.__memo = {}

    def __multiply_matrices(self, M1, M2):
        """2x2 matrices multiplication"""

        a11 = M1[0][0]*M2[0][0] + M1[0][1]*M2[1][0]
        a12 = M1[0][0]*M2[0][1] + M1[0][1]*M2[1][1]
        a21 = M1[1][0]*M2[0][0] + M1[1][1]*M2[1][0]
        a22 = M1[1][0]*M2[0][1] + M1[1][1]*M2[1][1]
        r = [[a11, a12], [a21, a22]]
        return r

    def __get_matrix_power(self, M, p):
        """Calculate matrix power (p is a power of 2)"""

        if p == 1:
            return M
        if p in self.__memo:
            return self.__memo[p]
        K = self.__get_matrix_power(M, int(p/2))
        R = self.__multiply_matrices(K, K)
        self.__memo[p] = R
        return R

    def get_number(self, n):
        """Get nth Fibonacci number (n is int, non-negative)."""

        if n == 0:
            return 0
        if n == 1:
            return 1
        # Decompose to powers of 2,
        # i.e. 62 = 2^5 + 2^4 + 2^3 + 2^2 + 2^0 = 32 + 16 + 8 + 4 + 1.
        powers = [int(pow(2, b))
                  for (b, d) in enumerate(reversed(bin(n-1)[2:])) if d == '1']
        # Less pythonic: http://pastebin.com/h8cKDkHX

        matrices = [self.__get_matrix_power(MatrixFibonacci.A, p)
                    for p in powers]
        while len(matrices) > 1:
            M1 = matrices.pop()
            M2 = matrices.pop()
            R = self.__multiply_matrices(M1, M2)
            matrices.append(R)
        return matrices[0][0][0]


class IterationFibonacci:
    def __init__(self):
        pass

    def get_number(self, n):
        """Get nth Fibonacci number (n is int, non-negative)."""

        if n == 0:
            return 0
        a = 0
        b = 1
        c = 1
        for i in range(n-1):
            c = a + b
            a = b
            b = c
        return c


def benchmark():
    random.seed()

    for around in range(10, 1010, 10):
        ifib = IterationFibonacci()
        mfib = MatrixFibonacci()
        ti = 0
        tm = 0
        count = 10000
        for _ in range(count):
            n = random.randint(around-5, around+5)
            t = time.time()
            ifib.get_number(n)
            t1 = time.time() - t
            ti += t1

            t = time.time()
            mfib.get_number(n)
            t2 = time.time() - t
            tm += t2

        print("{0}\t{1}\t{2}".format(around, ti, tm))


if __name__ == "__main__":
    benchmark()