Z Algorithm in PHP

<?php
declare(strict_types=1);
// Z Algorithm in PHP
//
// PURPOSE
// The Z array records how many tokens match the prefix at every position.
//
// METHOD
// Maintain the rightmost matching interval. Reuse a previously computed Z value when inside
// it, then extend only beyond its boundary.
//
// COMPLEXITY
// O(n) time and O(1) auxiliary space beyond caller-owned output.
//
// CONTRACT
// Integer token input; output has n entries. Defines Z[0]=0; 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 output after call: [0, 2, 1, 0, 1].
// 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 z_array(array $a, array &$output): int {
    alg_require(array_is_list($a));
    alg_require(array_is_list($output));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    alg_require((count($output) == $n));
    $left = 0;
    $right = 0;
    $i = 0;
    while (($i < $n)) {
        $output[$i] = 0;
        $i = alg_add($i, 1);
    }
    $i = 1;
    while (($i < $n)) {
        if (($i <= $right)) {
            $output[$i] = min(alg_add(alg_sub($right, $i), 1), $output[alg_sub($i, $left)]);
        }
        while (((alg_add($i, $output[$i]) < $n) && ($a[$output[$i]] == $a[alg_add($i, $output[$i])]))) {
            $output[$i] = alg_add($output[$i], 1);
        }
        if ((alg_sub(alg_add($i, $output[$i]), 1) > $right)) {
            $left = $i;
            $right = alg_sub(alg_add($i, $output[$i]), 1);
        }
        $i = alg_add($i, 1);
    }
    return 0;
}

$a = [1, 1, 1, 2, 1];
$output = [0, 0, 0, 0, 0];
$result = z_array($a, $output);
echo $result, PHP_EOL;
// Expected output: [0, 2, 1, 0, 1]
echo json_encode($output), PHP_EOL;