Heap Sort in PHP

<?php
declare(strict_types=1);
// Heap Sort in PHP
//
// PURPOSE
// Heap sort uses a max heap so the largest remaining value can be moved to the end. It gives
// a worst-case time guarantee without a second array.
//
// METHOD
// Build a max heap from the bottom up. Swap its root with the last active element, shrink
// the heap, and sift the new root downward. The suffix is sorted after every extraction.
//
// COMPLEXITY
// O(n log n) time, O(1) auxiliary space; heap construction is O(n). Not stable.
//
// CONTRACT
// Sorts n elements 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: [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 heap_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $start = alg_sub(intdiv($n, 2), 1);
    $end = alg_sub($n, 1);
    $root = 0;
    $child = 0;
    $temp = 0;
    while (($start >= 0)) {
        $root = $start;
        while ((alg_add(alg_mul(2, $root), 1) < $n)) {
            $child = alg_add(alg_mul(2, $root), 1);
            if (((alg_add($child, 1) < $n) && ($a[$child] < $a[alg_add($child, 1)]))) {
                $child = alg_add($child, 1);
            }
            if (($a[$root] >= $a[$child])) {
                break;
            }
            $temp = $a[$root];
            $a[$root] = $a[$child];
            $a[$child] = $temp;
            $root = $child;
        }
        $start = alg_sub($start, 1);
    }
    while (($end > 0)) {
        $temp = $a[0];
        $a[0] = $a[$end];
        $a[$end] = $temp;
        $root = 0;
        while ((alg_add(alg_mul(2, $root), 1) < $end)) {
            $child = alg_add(alg_mul(2, $root), 1);
            if (((alg_add($child, 1) < $end) && ($a[$child] < $a[alg_add($child, 1)]))) {
                $child = alg_add($child, 1);
            }
            if (($a[$root] >= $a[$child])) {
                break;
            }
            $temp = $a[$root];
            $a[$root] = $a[$child];
            $a[$child] = $temp;
            $root = $child;
        }
        $end = alg_sub($end, 1);
    }
    return 0;
}

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