Merge Based Inversion Count in JavaScript

"use strict";
// Merge Based Inversion Count in JavaScript
//
// PURPOSE
// An inversion is a pair i<j with a[i]>a[j]. Counting them during merging avoids testing
// every pair.
//
// METHOD
// Merge sorted runs bottom up. Whenever a right-run value precedes a larger left-run value,
// add the number of remaining left-run values.
//
// COMPLEXITY
// O(n log n) time, O(n) auxiliary space.
//
// CONTRACT
// Mutates input into sorted order. n <= 65536 so the inversion count fits signed 32-bit.
// 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: 2.
// Expected a after call: [1, 2, 3].
// 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 inversion_count(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    alg_require((n <= 65536));
    let buffer = new Int32Array(alg_size(alg_add(n, 1)));
    let width = 1;
    let left = 0;
    let mid = 0;
    let right = 0;
    let i = 0;
    let j = 0;
    let out = 0;
    let count = 0;
    while ((width < n)) {
        left = 0;
        while ((left < n)) {
            mid = Math.min(alg_add(left, width), n);
            right = Math.min(alg_add(left, alg_mul(2, width)), n);
            i = left;
            j = mid;
            out = left;
            while ((out < right)) {
                if (((i < mid) && ((j >= right) || (a[i] <= a[j])))) {
                    buffer[out] = a[i];
                    i = alg_add(i, 1);
                } else {
                    buffer[out] = a[j];
                    j = alg_add(j, 1);
                    count = alg_add(count, alg_sub(mid, i));
                }
                out = alg_add(out, 1);
            }
            left = alg_add(left, alg_mul(2, width));
        }
        i = 0;
        while ((i < n)) {
            a[i] = buffer[i];
            i = alg_add(i, 1);
        }
        width = alg_mul(width, 2);
    }
    return count;
}

let a = new Int32Array([3, 1, 2]);
let result = inversion_count(a);
console.log(result);
// Expected a: [1, 2, 3]
console.log(Array.from(a));