Exponential Search in PHP

<?php
declare(strict_types=1);
// Exponential Search in PHP
//
// PURPOSE
// Exponential search locates a search interval by doubling its size, then uses binary
// search.
//
// METHOD
// Check index zero. Double a bound until it passes the target or the input end, then binary-
// search the bounded interval.
//
// COMPLEXITY
// O(log(p+1)) comparisons for a match near index p; O(log n) worst case, O(1) space.
//
// CONTRACT
// Ascending input; returns any matching index or -1.
// 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: 2.
// 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 exponential_search(array $a, int $target): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    if (($n == 0)) {
        return alg_sub(0, 1);
    }
    if (($a[0] == $target)) {
        return 0;
    }
    $bound = 1;
    while ((($bound < $n) && ($a[$bound] < $target))) {
        if (($bound > intdiv($n, 2))) {
            $bound = $n;
        } else {
            $bound = alg_mul($bound, 2);
        }
    }
    $low = intdiv($bound, 2);
    $high = min($bound, alg_sub($n, 1));
    $mid = 0;
    while (($low <= $high)) {
        $mid = alg_add($low, intdiv(alg_sub($high, $low), 2));
        if (($a[$mid] == $target)) {
            return $mid;
        }
        if (($a[$mid] < $target)) {
            $low = alg_add($mid, 1);
        } else {
            $high = alg_sub($mid, 1);
        }
    }
    return alg_sub(0, 1);
}

$a = [1, 3, 5, 7];
$target = 5;
$result = exponential_search($a, $target);
echo $result, PHP_EOL;