Fenwick Tree Linear Build in JavaScript

"use strict";
// Fenwick Tree Linear Build in JavaScript
//
// PURPOSE
// A Fenwick tree stores partial sums so point additions and prefix queries take logarithmic
// time.
//
// METHOD
// Copy each value into its one-based tree position, then propagate the completed partial sum
// to its Fenwick parent. Each node is propagated only once.
//
// COMPLEXITY
// O(n) build time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// tree has n+1 entries. Overwrites tree; sums fit signed 32-bit. Build once, then reuse with
// Fenwick Point Add and Fenwick Prefix Sum.
// 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, 1, 3, 3, 10].
// 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 fenwick_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_add(n, 1)));
    let i = 0;
    let parent = 0;
    while ((i <= n)) {
        tree[i] = 0;
        i = alg_add(i, 1);
    }
    i = 1;
    while ((i <= n)) {
        tree[i] = alg_add(tree[i], a[alg_sub(i, 1)]);
        parent = alg_add(i, (i & alg_sub(0, i)));
        if ((parent <= n)) {
            tree[parent] = alg_add(tree[parent], tree[i]);
        }
        i = alg_add(i, 1);
    }
    return 0;
}

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