Upper Bound in JavaScript

"use strict";
// Upper Bound in JavaScript
//
// PURPOSE
// A boundary search finds an insertion position in a sorted array, including arrays with
// repeated values. This is useful for maintaining sorted collections and counting
// occurrences.
//
// METHOD
// Use a half-open interval [lo, hi). Move lo beyond elements that belong before the
// requested boundary; otherwise move hi to mid. The interval shrinks until both bounds
// coincide.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// Input is sorted ascending. Returns the first index whose value is greater than target, or
// n if none exists. Does not change the input.
// 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: 3.
// 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 upper_bound(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 lo = 0;
    let hi = n;
    let mid = 0;
    while ((lo < hi)) {
        mid = alg_add(lo, Math.floor(alg_sub(hi, lo) / 2));
        if ((a[mid] <= target)) {
            lo = alg_add(mid, 1);
        } else {
            hi = mid;
        }
    }
    return lo;
}

let a = new Int32Array([1, 2, 2, 4]);
let target = 2;
let result = upper_bound(a, target);
console.log(result);