Sieve of Eratosthenes in JavaScript

"use strict";
// Sieve of Eratosthenes in JavaScript
//
// PURPOSE
// The sieve identifies all primes up to a limit by marking multiples of smaller primes. This
// example returns their count.
//
// METHOD
// Keep a composite marker array. For each unmarked p up to the square root, mark multiples
// starting at p squared; smaller multiples were already handled. Count the remaining
// unmarked values from two onward.
//
// COMPLEXITY
// O(n log log n) time and O(n) auxiliary space.
//
// CONTRACT
// n >= 0. Returns the number of primes <= n. The marker array requires memory proportional
// to n.
// 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: 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 sieve_count(n) {
    alg_require(Number.isInteger(n) && n >= -2147483648 && n <= 2147483647);
    alg_require(((n >= 0) && (n <= 1000000)));
    let composite = new Int32Array(alg_size(alg_add(n, 1)));
    let p = 2;
    let multiple = 0;
    let count = 0;
    while ((p <= Math.floor(n / p))) {
        if ((composite[p] == 0)) {
            multiple = alg_mul(p, p);
            while ((multiple <= n)) {
                composite[multiple] = 1;
                multiple = alg_add(multiple, p);
            }
        }
        p = alg_add(p, 1);
    }
    p = 2;
    while ((p <= n)) {
        if ((composite[p] == 0)) {
            count = alg_add(count, 1);
        }
        p = alg_add(p, 1);
    }
    return count;
}

let n = 10;
let result = sieve_count(n);
console.log(result);