Shell Sort in JavaScript

"use strict";
// Shell Sort in JavaScript
//
// PURPOSE
// Shell sort applies insertion sort to elements separated by a gap. Early passes move values
// over long distances before a final gap-one pass.
//
// METHOD
// Start at n/2 and halve the gap. For each gap, insert each value into its gap-separated
// sorted subsequence. Gap one finishes the full ordering.
//
// COMPLEXITY
// O(n squared) worst-case time for this halving gap sequence; O(1) auxiliary space. Not
// stable.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0. Complexity depends on the chosen gap
// sequence.
// 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 shell_sort(a) {
    alg_require(a instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let gap = Math.floor(n / 2);
    let i = 0;
    let j = 0;
    let key = 0;
    while ((gap > 0)) {
        i = gap;
        while ((i < n)) {
            key = a[i];
            j = i;
            while (((j >= gap) && (a[alg_sub(j, gap)] > key))) {
                a[j] = a[alg_sub(j, gap)];
                j = alg_sub(j, gap);
            }
            a[j] = key;
            i = alg_add(i, 1);
        }
        gap = Math.floor(gap / 2);
    }
    return 0;
}

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