Fenwick Tree Linear Build in PHP

<?php
declare(strict_types=1);
// Fenwick Tree Linear Build in PHP
//
// PURPOSE
// A Fenwick tree stores partial sums so point additions and prefix queries take logarithmic
// time.
//
// METHOD
// Copy each value into its one-based tree position, then propagate the completed partial sum
// to its Fenwick parent. Each node is propagated only once.
//
// COMPLEXITY
// O(n) build time and O(1) auxiliary space beyond caller-owned tree.
//
// CONTRACT
// tree has n+1 entries. Overwrites tree; sums fit signed 32-bit. Build once, then reuse with
// Fenwick Point Add and Fenwick Prefix Sum.
// 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 tree after call: [0, 1, 3, 3, 10].
// 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_build(array $a, array &$tree): int {
    alg_require(array_is_list($a));
    alg_require(array_is_list($tree));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    alg_require((count($tree) == alg_add($n, 1)));
    $i = 0;
    $parent = 0;
    while (($i <= $n)) {
        $tree[$i] = 0;
        $i = alg_add($i, 1);
    }
    $i = 1;
    while (($i <= $n)) {
        $tree[$i] = alg_add($tree[$i], $a[alg_sub($i, 1)]);
        $parent = alg_add($i, ($i & alg_sub(0, $i)));
        if (($parent <= $n)) {
            $tree[$parent] = alg_add($tree[$parent], $tree[$i]);
        }
        $i = alg_add($i, 1);
    }
    return 0;
}

$a = [1, 2, 3, 4];
$tree = [0, 0, 0, 0, 0];
$result = fenwick_build($a, $tree);
echo $result, PHP_EOL;
// Expected tree: [0, 1, 3, 3, 10]
echo json_encode($tree), PHP_EOL;