Iterative Segment Tree Point Assignment in PHP

<?php
declare(strict_types=1);
// Iterative Segment Tree Point Assignment in PHP
//
// PURPOSE
// A point assignment changes a leaf and recomputes only its ancestors.
//
// METHOD
// Write the new leaf value, move upward by dividing the index by two, and recompute each
// parent from its children.
//
// COMPLEXITY
// O(log n) time, O(1) auxiliary space.
//
// CONTRACT
// tree is an existing iterative sum tree of length 2*n; n>=1, 0<=index<n. Mutates tree;
// returns 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.
// Expected tree after call: [0, 17, 10, 7, 1, 9, 3, 4].
// 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 segment_set(array &$tree, int $index, int $value): int {
    alg_require(array_is_list($tree));
    $n = intdiv(count($tree), 2);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($tree) == alg_mul(2, $n)));
    alg_require((($n >= 1) && ($index >= 0) && ($index < $n)));
    $index = alg_add($index, $n);
    $tree[$index] = $value;
    $index = intdiv($index, 2);
    while (($index > 0)) {
        $tree[$index] = alg_add($tree[alg_mul(2, $index)], $tree[alg_add(alg_mul(2, $index), 1)]);
        $index = intdiv($index, 2);
    }
    return 0;
}

$tree = [0, 10, 3, 7, 1, 2, 3, 4];
$index = 1;
$value = 9;
$result = segment_set($tree, $index, $value);
echo $result, PHP_EOL;
// Expected tree: [0, 17, 10, 7, 1, 9, 3, 4]
echo json_encode($tree), PHP_EOL;