Euclidean GCD in Python

from bisect import bisect_left

# Euclidean GCD in Python
#
# PURPOSE
# The Euclidean algorithm finds the greatest common divisor by replacing a pair with the
# smaller number and the remainder. Common divisors are preserved by this replacement.
#
# METHOD
# Repeatedly compute a modulo b, move b into a, and put the remainder into b. Stop when b is
# zero; the last nonzero value divides both original inputs.
#
# COMPLEXITY
# O(log(min(a,b))) arithmetic steps for positive inputs, O(1) auxiliary space.
#
# CONTRACT
# a and b are nonnegative integers. Defines gcd(0,0) as 0. Avoid negative values because
# remainder conventions vary by language.
# 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: 6.
# 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 gcd(a: int, b: int) -> int:
    alg_require(type(a) is int and -2147483648 <= a <= 2147483647)
    alg_require(type(b) is int and -2147483648 <= b <= 2147483647)
    alg_require(a >= 0 and b >= 0)
    remainder: int = 0
    while b != 0:
        remainder = a % b
        a = b
        b = remainder
    return a

a = 48
b = 18
result = gcd(a, b)
print(result)