Fast Doubling Fibonacci in JavaScript

"use strict";
// Fast Doubling Fibonacci in JavaScript
//
// 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
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// EXAMPLE
// Expected return: 0.
// Run: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function fast_fibonacci(n) {
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((n >= 0) && (n <= 45)));
    let a = 0;
    let b = 1;
    let c = 0;
    let d = 0;
    let bit = 1;
    while ((bit <= Math.floor(n / 2))) {
        bit = alg_mul(bit, 2);
    }
    while ((bit > 0)) {
        c = alg_mul(a, alg_sub(alg_mul(2, b), a));
        d = alg_add(alg_mul(a, a), alg_mul(b, b));
        if (((Math.floor(n / bit) % 2) == 0)) {
            a = c;
            b = d;
        } else {
            a = d;
            b = alg_add(c, d);
        }
        bit = Math.floor(bit / 2);
    }
    return a;
}

let n = 0;
let result = fast_fibonacci(n);
console.log(result);