Quickselect in PHP

<?php
declare(strict_types=1);
// Quickselect in PHP
//
// PURPOSE
// Quickselect finds a zero-based order statistic without fully sorting the input.
//
// METHOD
// Partition around the middle-position pivot using a three-way partition. Retain only the
// side containing rank k, or return the pivot when k lies in the equal region.
//
// COMPLEXITY
// O(n) expected time for random input; O(n squared) worst case for this deterministic pivot.
// O(1) auxiliary space.
//
// CONTRACT
// 0 <= k < n. Mutates input. Returns the kth smallest value, counting duplicates.
// 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: 5.
// Expected a after call: [2, 2, 5, 7, 9].
// 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 quickselect(array &$a, int $k): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    alg_require((($k >= 0) && ($k < $n)));
    $low = 0;
    $high = alg_sub($n, 1);
    $left = 0;
    $mid = 0;
    $right = 0;
    $pivot = 0;
    $temp = 0;
    while (($low <= $high)) {
        $pivot = $a[alg_add($low, intdiv(alg_sub($high, $low), 2))];
        $left = $low;
        $mid = $low;
        $right = $high;
        while (($mid <= $right)) {
            if (($a[$mid] < $pivot)) {
                $temp = $a[$left];
                $a[$left] = $a[$mid];
                $a[$mid] = $temp;
                $left = alg_add($left, 1);
                $mid = alg_add($mid, 1);
            } else {
                if (($a[$mid] > $pivot)) {
                    $temp = $a[$mid];
                    $a[$mid] = $a[$right];
                    $a[$right] = $temp;
                    $right = alg_sub($right, 1);
                } else {
                    $mid = alg_add($mid, 1);
                }
            }
        }
        if (($k < $left)) {
            $high = alg_sub($left, 1);
        } else {
            if (($k > $right)) {
                $low = alg_add($right, 1);
            } else {
                return $pivot;
            }
        }
    }
    return alg_sub(0, 1);
}

$a = [7, 2, 9, 2, 5];
$k = 2;
$result = quickselect($a, $k);
echo $result, PHP_EOL;
// Expected a: [2, 2, 5, 7, 9]
echo json_encode($a), PHP_EOL;