Jump Search in JavaScript

"use strict";
// Jump Search in JavaScript
//
// PURPOSE
// Jump search skips fixed-size blocks in a sorted sequence, then scans the candidate block.
//
// METHOD
// Choose a block width near square root of n. Jump until the block endpoint is at least the
// target, then scan the block.
//
// COMPLEXITY
// O(sqrt(n)) comparisons and O(1) auxiliary space. Binary search is usually faster on
// random-access arrays.
//
// CONTRACT
// Ascending input; returns first matching index or -1.
// 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: 1.
// 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 jump_search(a, target) {
    alg_require(a instanceof Int32Array);
    alg_require(Number.isInteger(target) && target >= -2147483648 && target <= 2147483647);
    let n = a.length;
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require((a.length == n));
    let step = 1;
    while ((step <= Math.floor(n / step))) {
        step = alg_add(step, 1);
    }
    let start = 0;
    let end = Math.min(step, n);
    while (((start < n) && (a[alg_sub(end, 1)] < target))) {
        start = end;
        end = Math.min(alg_add(end, step), n);
    }
    while ((start < end)) {
        if ((a[start] == target)) {
            return start;
        }
        start = alg_add(start, 1);
    }
    return alg_sub(0, 1);
}

let a = new Int32Array([1, 3, 3, 7]);
let target = 3;
let result = jump_search(a, target);
console.log(result);