Exponentiation by Squaring in Python

from bisect import bisect_left

# Exponentiation by Squaring in Python
#
# PURPOSE
# Binary exponentiation evaluates an integer power using the bits of the exponent. Squaring
# skips the repeated multiplication used by the direct method.
#
# METHOD
# When the exponent is odd, multiply the accumulator by the current base. Halve the exponent
# and square the base for the next bit. The accumulator times the remaining power stays
# equal to the answer.
#
# COMPLEXITY
# O(log exponent) multiplications and O(1) auxiliary space; arithmetic bit costs are
# excluded.
#
# CONTRACT
# Exponent is nonnegative. Returns 1 for exponent 0, including 0 to power 0 by this
# programming convention. All intermediate products must fit.
# Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
# counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
# Sorted order, correct tree topology, and caller-owned data-structure invariants are
# preconditions; checking them on every query would change query complexity.
# Scalar and shape checks are included. Value-range checks are included where needed to
# prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
# workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
# uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
# partly updated after arithmetic failure. These are single-threaded, in-memory
# implementations.
#
# LANGUAGE DETAILS
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 1024.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def power(base: int, exponent: int) -> int:
    alg_require(type(base) is int and -2147483648 <= base <= 2147483647)
    alg_require(type(exponent) is int and -2147483648 <= exponent <= 2147483647)
    alg_require(exponent >= 0)
    result: int = 1
    while exponent > 0:
        if exponent % 2 == 1:
            result *= base
        exponent = exponent // 2
        if exponent > 0:
            base *= base
    return result

base = 2
exponent = 10
result = power(base, exponent)
print(result)