Fenwick Prefix Sum in PHP

<?php
declare(strict_types=1);
// Fenwick Prefix Sum in PHP
//
// PURPOSE
// A Fenwick prefix query combines disjoint stored partial sums covering the requested
// prefix.
//
// METHOD
// Starting from the exclusive prefix endpoint, add the current partial sum and clear its
// lowest set bit to move to the preceding block.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree length is n+1, 0<=end<=n. Returns sum of original values in [0,end). Empty prefix
// returns zero.
// 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 fenwick_sum(array $tree, int $end): int {
    alg_require(array_is_list($tree));
    $n = alg_sub(count($tree), 1);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($tree) == alg_add($n, 1)));
    alg_require((($end >= 0) && ($end <= $n)));
    $total = 0;
    while (($end > 0)) {
        $total = alg_add($total, $tree[$end]);
        $end = alg_sub($end, ($end & alg_sub(0, $end)));
    }
    return $total;
}

$tree = [0, 1, 3, 3, 10];
$end = 3;
$result = fenwick_sum($tree, $end);
echo $result, PHP_EOL;