Iterative Quick Sort in JavaScript

"use strict";
// Iterative Quick Sort in JavaScript
//
// PURPOSE
// Quick sort partitions around a pivot and sorts the two resulting regions. This iterative
// version stores pending intervals explicitly instead of using recursion.
//
// METHOD
// Choose a median-of-three pivot and partition into less-than, equal-to, and greater-than
// regions. Process the smaller region immediately and defer the larger one to keep the
// explicit stack bounded.
//
// COMPLEXITY
// O(n log n) average time, O(n squared) adversarial worst case. Equal-key input takes O(n).
// O(log n) pending intervals; 64 stack slots cover the supported bounded input lengths. Not
// stable.
//
// CONTRACT
// Sorts ascending in place and returns 0. Three-way partition handles repeated keys
// efficiently. Median-of-three reduces common fixed-endpoint pivot problems but does not
// provide introsort's worst-case guarantee.
// 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: [1, 1, 3, 5].
// 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 quick_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let lefts = new Int32Array(alg_size(64));
    let rights = new Int32Array(alg_size(64));
    let top = 0;
    let low = 0;
    let high = alg_sub(n, 1);
    let left = 0;
    let right = 0;
    let mid = 0;
    let pivot = 0;
    let temp = 0;
    while (((low < high) || (top > 0))) {
        if ((low >= high)) {
            top = alg_sub(top, 1);
            low = lefts[top];
            high = rights[top];
        }
        mid = alg_add(low, Math.floor(alg_sub(high, low) / 2));
        pivot = Math.max(Math.min(a[low], a[mid]), Math.min(Math.max(a[low], a[mid]), a[high]));
        left = low;
        mid = low;
        right = high;
        while ((mid <= right)) {
            if ((a[mid] < pivot)) {
                temp = a[left];
                a[left] = a[mid];
                a[mid] = temp;
                left = alg_add(left, 1);
                mid = alg_add(mid, 1);
            } else {
                if ((a[mid] > pivot)) {
                    temp = a[mid];
                    a[mid] = a[right];
                    a[right] = temp;
                    right = alg_sub(right, 1);
                } else {
                    mid = alg_add(mid, 1);
                }
            }
        }
        if ((alg_sub(left, low) < alg_sub(high, right))) {
            if ((alg_add(right, 1) < high)) {
                lefts[top] = alg_add(right, 1);
                rights[top] = high;
                top = alg_add(top, 1);
            }
            high = alg_sub(left, 1);
        } else {
            if ((low < alg_sub(left, 1))) {
                lefts[top] = low;
                rights[top] = alg_sub(left, 1);
                top = alg_add(top, 1);
            }
            low = alg_add(right, 1);
        }
    }
    return 0;
}

let a = new Int32Array([5, 1, 3, 1]);
let result = quick_sort(a);
console.log(result);
console.log(a);
// Expected a: [1, 1, 3, 5]