#!/usr/bin/python3
# -*- coding: utf-8 -*-
"""
Exponentiation
"""

print(2 ** 8)


# %% Loop
def exp_loop(b: int, n: int) -> int:
    result = 1
    for c in range(n):
        result *= b
        print("c=", c, "and result=", result)
    return result


for n in range(1, 17):
    val = exp_loop(2, n)
    print("2 to the ", n, "is ", val, "\n")


# %% What is the b^-n?
def exp_loop_neg_rec(b: int, n: int) -> float:
    result = 1
    if 0 <= n:
        for c in range(n):
            result *= b
            print("c=", c, "and result=", result)
        return result
    else:
        return 1 / exp_loop_neg_rec(b, -n)


for n in range(-1, -17, -1):
    val_float = exp_loop_neg_rec(2, n)
    print("2 to the ", n, "is ", val_float, "\n")


# %% Inefficient recursive exponentiation
def exp_rec(b: int, n: int) -> int:
    """
    Calculates b^n for positive n integers
    """
    print("Calling with b =", b, "and n=", n)
    if n == 0:
        return 1
    else:
        return b * exp_rec(b, n - 1)


for n in range(1, 17):
    val = exp_rec(2, n)
    print("2 to the ", n, "is ", val, "\n")


# %% Efficient recursive exponentiation
def exp_rec_eff(b: int, n: int) -> int:
    """
    Efficiently calculates b^n for positive n integers
    """
    print("Calling with b =", b, "and n=", n)
    if n == 1:
        return b
    elif (n & 1) == 0:
        return exp_rec_eff(b * b, n // 2)
    else:
        return exp_rec_eff(b * b, n // 2) * b


for n in range(1, 17):
    val = exp_rec_eff(2, n)
    print("2 to the ", n, "is ", val, "\n")