raeq

import numpy as np
import matplotlib.pyplot as plt
from timeit import *

def collect_results():
    results = []
    for i in range(1000, 2000001, 100000):
        f = "fast_doubling_fibonacci_recursive"
        t1 = Timer(f"{f}({i})",
                   f"from __main__ import {f}")

raeq

def collect_results():
    results = []
    for i in range(1000, 2000001, 100000):
        f = "fast_doubling_fibonacci_recursive"
        t1 = Timer(f"{f}({i})",
                   f"from __main__ import {f}")
        st1 = t1.timeit(number=10)

        f = "matrix_fibonacci"
        t2 = Timer(f"{f}({i})",

raeq

from timeit import *

def collect_results():
    results = []
    for i in range(1000, 2000001, 100000):
        f = "fast_doubling_fibonacci_recursive"
        t1 = Timer(f"{f}({i})",
                   f"from __main__ import {f}")
        st1 = t1.timeit(number=10)

raeq

def fast_doubling_fibonacci_iterative(n):
    """

    Args:
        n ():

    Returns:
    >>> fast_doubling_fibonacci_iterative(80)
    23416728348467685
    >>> fast_doubling_fibonacci_iterative(800)

raeq

def fast_doubling_fibonacci_iterative(n):
    """

    Args:
        n ():

    Returns:
    >>> fast_doubling_fibonacci_iterative(80)
    23416728348467685
    >>> fast_doubling_fibonacci_iterative(800)

raeq

import functools
@functools.lru_cache()
def _fd_fib(n: int) -> tuple:
    """_fd_fib.

    Args:
        n (int): n

    Returns:
        tuple:

raeq

def karatsuba_fast_multiply(multiplier: int, multiplicand: int) -> int:
    """
    Karatsuba fast multiplication, published in 1962
    https://en.wikipedia.org/wiki/Karatsuba_algorithm

    Args:
        x ():
        y ():

    Returns: int

raeq

def karatsuba_fast_multiply(multiplier: int, multiplicand: int) -> int:
    """
    Karatsuba fast multiplication, published in 1962
    https://en.wikipedia.org/wiki/Karatsuba_algorithm

    Args:
        x ():
        y ():

    Returns: int

raeq

def karatsuba_fast_multiply(multiplier: int, multiplicand: int) -> int:
    """
    Karatsuba fast multiplication, published in 1962
    https://en.wikipedia.org/wiki/Karatsuba_algorithm

    Args:
        x ():
        y ():

    Returns: int

raeq

def lucas_power(n: float):
    """lucas_power.

    Args:
        n (float): n
    """

    if n == 1:
        return (1, 1)
    L, F = lucas_power(n // 2)