LSD Radix Sort in JavaScript

"use strict";
// LSD Radix Sort in JavaScript
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 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.
// Expected a after call: [0, 1, 255, 256, 65536].
// 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 radix_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    for (let alg_i = 0; alg_i < a.length; alg_i++) {
        let alg_value = a[alg_i];
        alg_require((alg_value >= 0));
    }
    let output = new Int32Array(alg_size(alg_add(n, 1)));
    let count = new Int32Array(alg_size(256));
    let divisor = 1;
    let digit = 0;
    let pass_index = 0;
    let i = 0;
    while ((pass_index < 4)) {
        i = 0;
        while ((i < 256)) {
            count[i] = 0;
            i = alg_add(i, 1);
        }
        i = 0;
        while ((i < n)) {
            digit = (Math.floor(a[i] / divisor) % 256);
            count[digit] = alg_add(count[digit], 1);
            i = alg_add(i, 1);
        }
        i = 1;
        while ((i < 256)) {
            count[i] = alg_add(count[i], count[alg_sub(i, 1)]);
            i = alg_add(i, 1);
        }
        i = alg_sub(n, 1);
        while ((i >= 0)) {
            digit = (Math.floor(a[i] / divisor) % 256);
            count[digit] = alg_sub(count[digit], 1);
            output[count[digit]] = a[i];
            i = alg_sub(i, 1);
        }
        i = 0;
        while ((i < n)) {
            a[i] = output[i];
            i = alg_add(i, 1);
        }
        pass_index = alg_add(pass_index, 1);
        if ((pass_index < 4)) {
            divisor = alg_mul(divisor, 256);
        }
    }
    return 0;
}

let a = new Int32Array([256, 1, 65536, 0, 255]);
let result = radix_sort(a);
console.log(result);
// Expected a: [0, 1, 255, 256, 65536]
console.log(Array.from(a));