PHP の組み込みソート関数は、等しい値を持つ連想配列をソートするときにキーの順序を保持できますか?

<code class="php">function mergesort(&$array, $cmp_function = 'strcmp') {
    // Handle small arrays
    if (count($array) < 2) return;

    // Split the array into two parts
    $halfway = count($array) / 2;
    $array1 = array_slice($array, 0, $halfway);
    $array2 = array_slice($array, $halfway);

    // Recursively sort the two halves
    mergesort($array1, $cmp_function);
    mergesort($array2, $cmp_function);

    // Merge the sorted halves into the original array
    $array = array();
    $ptr1 = $ptr2 = 0;
    while ($ptr1 < count($array1) && $ptr2 < count($array2)) {
        if (call_user_func($cmp_function, $array1[$ptr1], $array2[$ptr2]) < 1) {
            $array[] = $array1[$ptr1++];
        } else {
            $array[] = $array2[$ptr2++];
        }
    }

    // Merge the remainder
    while ($ptr1 < count($array1)) $array[] = $array1[$ptr1++];
    while ($ptr2 < count($array2)) $array[] = $array2[$ptr2++];
}</code>