Modular Exponentiation in Python

from bisect import bisect_left

# Modular Exponentiation in Python
#
# PURPOSE
# Modular exponentiation computes a power while reducing every intermediate product modulo
# m. It is widely used in number theory, though this teaching version is not constant time.
#
# METHOD
# Reduce the base, then process exponent bits by squaring. Multiply the result on odd bits
# and reduce after each product.
#
# COMPLEXITY
# O(log exponent) modular multiplications, O(1) auxiliary space.
#
# CONTRACT
# base and exponent are nonnegative, modulus > 0. Products of two residues must fit the
# integer type; this is not a cryptographic implementation.
# 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: 24.
# 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 modular_power(base: int, exponent: int, modulus: int) -> int:
    alg_require(type(base) is int and -2147483648 <= base <= 2147483647)
    alg_require(type(exponent) is int and -2147483648 <= exponent <= 2147483647)
    alg_require(type(modulus) is int and -2147483648 <= modulus <= 2147483647)
    alg_require(base >= 0 and exponent >= 0 and (modulus > 0) and (modulus <= 46340))
    result: int = 1 % modulus
    base = base % modulus
    while exponent > 0:
        if exponent % 2 == 1:
            result = result * base % modulus
        base = base * base % modulus
        exponent = exponent // 2
    return result

base = 2
exponent = 10
modulus = 1000
result = modular_power(base, exponent, modulus)
print(result)