Segmented Sieve in JavaScript

"use strict";
// Segmented Sieve in JavaScript
//
// PURPOSE
// A segmented sieve marks composites only inside a requested interval, reducing memory
// compared with sieving all the way to its upper endpoint.
//
// METHOD
// Sieve base primes up to square root of high. For each prime, mark its multiples in
// [low,high], starting no earlier than p squared. Count unmarked values at least two.
//
// COMPLEXITY
// O(sqrt(high) log log high + (high-low+1) log log high) time, O(sqrt(high)+high-low+1)
// space.
//
// CONTRACT
// 0 <= low <= high <= 1000000. Returns number of primes in the inclusive interval.
// 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: 6.
// 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 segmented_sieve(low, high) {
    alg_require(Number.isInteger(low) && low >= -2147483648 && low <= 2147483647);
    alg_require(Number.isInteger(high) && high >= -2147483648 && high <= 2147483647);
    alg_require(((low >= 0) && (low <= high) && (high <= 1000000)));
    let limit = 1;
    while ((limit <= Math.floor(high / limit))) {
        limit = alg_add(limit, 1);
    }
    let base = new Int32Array(alg_size(alg_add(limit, 1)));
    let marked = new Int32Array(alg_size(alg_add(alg_sub(high, low), 1)));
    let p = 2;
    let multiple = 0;
    let count = 0;
    let i = 0;
    while ((p < limit)) {
        if ((base[p] == 0)) {
            multiple = alg_mul(p, p);
            while ((multiple < limit)) {
                base[multiple] = 1;
                multiple = alg_add(multiple, p);
            }
            multiple = Math.max(alg_mul(p, p), alg_mul(Math.floor(alg_sub(alg_add(low, p), 1) / p), p));
            while ((multiple <= high)) {
                marked[alg_sub(multiple, low)] = 1;
                multiple = alg_add(multiple, p);
            }
        }
        p = alg_add(p, 1);
    }
    i = Math.max(2, low);
    while ((i <= high)) {
        if ((marked[alg_sub(i, low)] == 0)) {
            count = alg_add(count, 1);
        }
        i = alg_add(i, 1);
    }
    return count;
}

let low = 10;
let high = 30;
let result = segmented_sieve(low, high);
console.log(result);