LSD Radix Sort in PHP

<?php
declare(strict_types=1);
// LSD Radix Sort in PHP
//
// PURPOSE
// LSD radix sort orders bounded nonnegative integers one byte at a time using stable
// counting passes.
//
// METHOD
// For each of four base-256 digits, count occurrences, compute cumulative positions, then
// distribute from right to left to preserve stability.
//
// COMPLEXITY
// O(4(n+256)) time and O(n+256) auxiliary space for 32-bit keys. Stable.
//
// CONTRACT
// Keys are nonnegative signed 32-bit integers. Sorts ascending in place, returns 0.
// 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: [0, 1, 255, 256, 65536].
// 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 radix_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    for ($alg_i = 0; $alg_i < count($a); $alg_i++) {
        $alg_value = $a[$alg_i];
        alg_require(($alg_value >= 0));
    }
    $output = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $count = array_fill(0, alg_size(256), 0);
    $divisor = 1;
    $digit = 0;
    $pass_index = 0;
    $i = 0;
    while (($pass_index < 4)) {
        $i = 0;
        while (($i < 256)) {
            $count[$i] = 0;
            $i = alg_add($i, 1);
        }
        $i = 0;
        while (($i < $n)) {
            $digit = (intdiv($a[$i], $divisor) % 256);
            $count[$digit] = alg_add($count[$digit], 1);
            $i = alg_add($i, 1);
        }
        $i = 1;
        while (($i < 256)) {
            $count[$i] = alg_add($count[$i], $count[alg_sub($i, 1)]);
            $i = alg_add($i, 1);
        }
        $i = alg_sub($n, 1);
        while (($i >= 0)) {
            $digit = (intdiv($a[$i], $divisor) % 256);
            $count[$digit] = alg_sub($count[$digit], 1);
            $output[$count[$digit]] = $a[$i];
            $i = alg_sub($i, 1);
        }
        $i = 0;
        while (($i < $n)) {
            $a[$i] = $output[$i];
            $i = alg_add($i, 1);
        }
        $pass_index = alg_add($pass_index, 1);
        if (($pass_index < 4)) {
            $divisor = alg_mul($divisor, 256);
        }
    }
    return 0;
}

$a = [256, 1, 65536, 0, 255];
$result = radix_sort($a);
echo $result, PHP_EOL;
// Expected a: [0, 1, 255, 256, 65536]
echo json_encode($a), PHP_EOL;