Merge Sort in PHP

<?php
declare(strict_types=1);
// Merge Sort in PHP
//
// PURPOSE
// Merge sort combines sorted runs into larger runs. The bottom-up form avoids recursion and
// guarantees predictable worst-case performance.
//
// METHOD
// Merge adjacent runs of width one into a temporary buffer, copy back, then double the
// width. Each pass leaves runs of twice the previous width sorted.
//
// COMPLEXITY
// O(n log n) time and O(n) auxiliary space. Stable because ties are taken from the left run.
//
// CONTRACT
// Sorts n elements ascending in place; returns 0. Empty input is valid. Uses a temporary
// buffer.
// 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 merge_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $buf = array_fill(0, alg_size(alg_add($n, 1)), 0);
    $width = 1;
    $left = 0;
    $mid = 0;
    $right = 0;
    $i = 0;
    $j = 0;
    $k = 0;
    while (($width < $n)) {
        $left = 0;
        while (($left < $n)) {
            $mid = min(alg_add($left, $width), $n);
            $right = min(alg_add($left, alg_mul(2, $width)), $n);
            $i = $left;
            $j = $mid;
            $k = $left;
            while (($k < $right)) {
                if ((($i < $mid) && (($j >= $right) || ($a[$i] <= $a[$j])))) {
                    $buf[$k] = $a[$i];
                    $i = alg_add($i, 1);
                } else {
                    $buf[$k] = $a[$j];
                    $j = alg_add($j, 1);
                }
                $k = alg_add($k, 1);
            }
            $left = alg_add($left, alg_mul(2, $width));
        }
        $i = 0;
        while (($i < $n)) {
            $a[$i] = $buf[$i];
            $i = alg_add($i, 1);
        }
        $width = alg_mul($width, 2);
    }
    return 0;
}

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