Counting Sort in PHP

<?php
declare(strict_types=1);
// Counting Sort in PHP
//
// PURPOSE
// Counting sort counts each possible key instead of comparing pairs. It is efficient when
// nonnegative integer keys occupy a small range.
//
// METHOD
// Count occurrences in a frequency array, then write each key the recorded number of times.
// The output prefix is sorted throughout reconstruction.
//
// COMPLEXITY
// O(n + k) time and O(k) auxiliary space, where k = maximum + 1. This key-only version does
// not demonstrate stable sorting of records.
//
// CONTRACT
// All n values must be between 0 and maximum inclusive. Sorts in place and returns 0. A huge
// maximum makes this approach unsuitable.
// 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
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 0.
// Expected a after call: [1, 1, 3, 5].
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function counting_sort(array &$a, int $maximum): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    alg_require((($maximum >= 0) && ($maximum <= 1000000)));
    for ($alg_i = 0; $alg_i < count($a); $alg_i++) {
        $alg_value = $a[$alg_i];
        alg_require((($alg_value >= 0) && ($alg_value <= $maximum)));
    }
    $counts = array_fill(0, alg_size(alg_add($maximum, 1)), 0);
    $i = 0;
    $value = 0;
    $out = 0;
    while (($i < $n)) {
        $counts[$a[$i]] = alg_add($counts[$a[$i]], 1);
        $i = alg_add($i, 1);
    }
    while (($value <= $maximum)) {
        while (($counts[$value] > 0)) {
            $a[$out] = $value;
            $out = alg_add($out, 1);
            $counts[$value] = alg_sub($counts[$value], 1);
        }
        $value = alg_add($value, 1);
    }
    return 0;
}

$a = [5, 1, 3, 1];
$maximum = 5;
$result = counting_sort($a, $maximum);
echo $result, PHP_EOL;
echo json_encode($a), PHP_EOL;
// Expected a: [1, 1, 3, 5]