Extended Euclid Modular Inverse in JavaScript

"use strict";
// Extended Euclid Modular Inverse in JavaScript
//
// PURPOSE
// Extended Euclid tracks a Bezout coefficient while computing the gcd. When gcd(a,m)=1, that
// coefficient is the modular inverse.
//
// METHOD
// Maintain consecutive remainders and coefficients. Update both with the Euclidean quotient;
// normalize the resulting coefficient into [0,m).
//
// COMPLEXITY
// O(log m) arithmetic steps and O(1) auxiliary space.
//
// CONTRACT
// 0 <= a < modulus, 2 <= modulus <= 10000. Returns -1 if no inverse exists. This bounded
// integer implementation is not constant time or suitable for cryptographic secrets.
// 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: 4.
// 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 modular_inverse(a, modulus) {
    alg_require(Number.isInteger(a) && a >= -2147483648 && a <= 2147483647);
    alg_require(Number.isInteger(modulus) && modulus >= -2147483648 && modulus <= 2147483647);
    alg_require(((modulus >= 2) && (modulus <= 10000) && (a >= 0) && (a < modulus)));
    let old_r = modulus;
    let r = a;
    let old_t = 0;
    let t = 1;
    let quotient = 0;
    let temp = 0;
    while ((r != 0)) {
        quotient = Math.floor(old_r / r);
        temp = alg_sub(old_r, alg_mul(quotient, r));
        old_r = r;
        r = temp;
        temp = alg_sub(old_t, alg_mul(quotient, t));
        old_t = t;
        t = temp;
    }
    if ((old_r != 1)) {
        return alg_sub(0, 1);
    }
    return (alg_add((old_t % modulus), modulus) % modulus);
}

let a = 3;
let modulus = 11;
let result = modular_inverse(a, modulus);
console.log(result);