Modular Exponentiation in PHP

<?php
declare(strict_types=1);
// Modular Exponentiation in PHP
//
// PURPOSE
// Modular exponentiation computes a power while reducing every intermediate product modulo
// m. It is widely used in number theory, though this teaching version is not constant time.
//
// METHOD
// Reduce the base, then process exponent bits by squaring. Multiply the result on odd bits
// and reduce after each product.
//
// COMPLEXITY
// O(log exponent) modular multiplications, O(1) auxiliary space.
//
// CONTRACT
// base and exponent are nonnegative, modulus > 0. Products of two residues must fit the
// integer type; this is not a cryptographic implementation.
// 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: 24.
// 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 modular_power(int $base, int $exponent, int $modulus): int {
    alg_require((($base >= 0) && ($exponent >= 0) && ($modulus > 0) && ($modulus <= 46340)));
    $result = (1 % $modulus);
    $base = ($base % $modulus);
    while (($exponent > 0)) {
        if ((($exponent % 2) == 1)) {
            $result = (alg_mul($result, $base) % $modulus);
        }
        $base = (alg_mul($base, $base) % $modulus);
        $exponent = intdiv($exponent, 2);
    }
    return $result;
}

$base = 2;
$exponent = 10;
$modulus = 1000;
$result = modular_power($base, $exponent, $modulus);
echo $result, PHP_EOL;