Pascal Triangle Binomial Coefficient in JavaScript

"use strict";
// Pascal Triangle Binomial Coefficient in JavaScript
//
// PURPOSE
// Pascal identity computes n choose k from neighboring coefficients in the previous row. A
// single row is enough when updated right to left.
//
// METHOD
// Initialize row[0] to one. For each new row, update row[j] from row[j] plus row[j-1] in
// descending j order, preserving the old row values needed later.
//
// COMPLEXITY
// O(nk) time and O(k) auxiliary space.
//
// CONTRACT
// n >= 0 and 0 <= k <= n. All coefficients computed must fit the integer type.
// 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: 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 binomial(n, k) {
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(Number.isInteger(k) && k >= -2147483648 && k <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((n >= 0) && (n <= 30) && (k >= 0) && (k <= n)));
    let row = new Int32Array(alg_size(alg_add(k, 1)));
    row[0] = 1;
    let i = 1;
    let j = 0;
    while ((i <= n)) {
        j = Math.min(i, k);
        while ((j > 0)) {
            row[j] = alg_add(row[j], row[alg_sub(j, 1)]);
            j = alg_sub(j, 1);
        }
        i = alg_add(i, 1);
    }
    return row[k];
}

let n = 5;
let k = 2;
let result = binomial(n, k);
console.log(result);