Iterative Segment Tree Build in JavaScript

"use strict";
// Iterative Segment Tree Build in JavaScript
//
// PURPOSE
// An iterative sum segment tree stores leaves in the second half of a flat array and parents
// in the first half.
//
// METHOD
// Copy values into tree[n+i], then compute every internal node from its two children in
// descending index order.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// n>=1, tree length is 2*n. Build once and reuse for point assignments and half-open range
// queries. Sums must fit.
// 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 tree after call: [0, 10, 3, 7, 1, 2, 3, 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 segment_build(a, tree) {
    alg_require(a instanceof Int32Array);
    alg_require(tree instanceof Int32Array);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    alg_require((tree.length == alg_mul(2, n)));
    alg_require((n >= 1));
    let i = 0;
    tree[0] = 0;
    while ((i < n)) {
        tree[alg_add(n, i)] = a[i];
        i = alg_add(i, 1);
    }
    i = alg_sub(n, 1);
    while ((i > 0)) {
        tree[i] = alg_add(tree[alg_mul(2, i)], tree[alg_add(alg_mul(2, i), 1)]);
        i = alg_sub(i, 1);
    }
    return 0;
}

let a = new Int32Array([1, 2, 3, 4]);
let tree = new Int32Array([0, 0, 0, 0, 0, 0, 0, 0]);
let result = segment_build(a, tree);
console.log(result);
// Expected tree: [0, 10, 3, 7, 1, 2, 3, 4]
console.log(Array.from(tree));