Fast Doubling Fibonacci in PHP

<?php
declare(strict_types=1);
// Fast Doubling Fibonacci in PHP
//
// PURPOSE
// Fast doubling computes Fibonacci numbers using identities for doubling an index, reducing
// the number of recurrence steps logarithmically.
//
// METHOD
// Read n bits from most significant to least. Derive F(2k) and F(2k+1) from F(k),F(k+1),
// then advance one extra position for a set bit.
//
// COMPLEXITY
// O(log n) arithmetic operations, O(1) auxiliary space under bounded integer arithmetic.
//
// CONTRACT
// 0 <= n <= 45 so all intermediates fit signed 32-bit. Returns F(n), with F(0)=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.
// 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 fast_fibonacci(int $n): int {
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((($n >= 0) && ($n <= 45)));
    $a = 0;
    $b = 1;
    $c = 0;
    $d = 0;
    $bit = 1;
    while (($bit <= intdiv($n, 2))) {
        $bit = alg_mul($bit, 2);
    }
    while (($bit > 0)) {
        $c = alg_mul($a, alg_sub(alg_mul(2, $b), $a));
        $d = alg_add(alg_mul($a, $a), alg_mul($b, $b));
        if (((intdiv($n, $bit) % 2) == 0)) {
            $a = $c;
            $b = $d;
        } else {
            $a = $d;
            $b = alg_add($c, $d);
        }
        $bit = intdiv($bit, 2);
    }
    return $a;
}

$n = 0;
$result = fast_fibonacci($n);
echo $result, PHP_EOL;