Euler Totient by Factorization in PHP

<?php
declare(strict_types=1);
// Euler Totient by Factorization in PHP
//
// PURPOSE
// Euler totient counts positive integers up to n that are coprime with n.
//
// METHOD
// For each distinct prime divisor p, remove all factors p from a working value and replace
// result with result-result/p. Handle any remaining prime factor.
//
// COMPLEXITY
// O(sqrt(n)) trial-division time and O(1) space.
//
// CONTRACT
// n >= 1. phi(1)=1.
// 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: 6.
// 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 totient(int $n): int {
    alg_require(($n >= 1));
    $result = $n;
    $p = 2;
    while (($p <= intdiv($n, $p))) {
        if ((($n % $p) == 0)) {
            while ((($n % $p) == 0)) {
                $n = intdiv($n, $p);
            }
            $result = alg_sub($result, intdiv($result, $p));
        }
        $p = alg_add($p, 1);
    }
    if (($n > 1)) {
        $result = alg_sub($result, intdiv($result, $n));
    }
    return $result;
}

$n = 9;
$result = totient($n);
echo $result, PHP_EOL;