Fast Doubling Fibonacci in Python

from bisect import bisect_left

# Fast Doubling Fibonacci in Python
#
# PURPOSE
# Fast doubling computes Fibonacci numbers using identities for doubling an index, reducing
# the number of recurrence steps logarithmically.
#
# METHOD
# Read n bits from most significant to least. Derive F(2k) and F(2k+1) from F(k),F(k+1),
# then advance one extra position for a set bit.
#
# COMPLEXITY
# O(log n) arithmetic operations, O(1) auxiliary space under bounded integer arithmetic.
#
# CONTRACT
# 0 <= n <= 45 so all intermediates fit signed 32-bit. Returns F(n), with F(0)=0.
# 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: 0.
# 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 fast_fibonacci(n: int) -> int:
    alg_require(type(n) is int and -2147483648 <= n <= 2147483647)
    alg_require(n >= 0 and n <= 1000000)
    alg_require(n >= 0 and n <= 45)
    a: int = 0
    b: int = 1
    c: int = 0
    d: int = 0
    bit: int = 1
    while bit <= n // 2:
        bit *= 2
    while bit > 0:
        c = a * (2 * b - a)
        d = a * a + b * b
        if n // bit % 2 == 0:
            a = c
            b = d
        else:
            a = d
            b = c + d
        bit = bit // 2
    return a

n = 0
result = fast_fibonacci(n)
print(result)