Algorithms: Sorting

int cocktail_sort(std::vector<int>& a) {
    alg_require(a.size() <= 1000000);
    int n = (int)a.size();
    alg_require(((n >= 0) && (n <= 1000000)));
    alg_require(((int)a.size() == n));
    int low = 0;
    int high = alg_sub(n, 1);
    int i = 0;
    int changed = 1;
    int temp = 0;
    while (((low < high) && (changed != 0))) {
        changed = 0;

    static int cocktail_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int low = 0;
            int high = (n - 1);
            int i = 0;
            int changed = 1;
            int temp = 0;
            while (((low < high) && (changed != 0))) {
                changed = 0;

function cocktail_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $low = 0;
    $high = alg_sub($n, 1);
    $i = 0;
    $changed = 1;
    $temp = 0;
    while ((($low < $high) && ($changed != 0))) {
        $changed = 0;

    static int merge_sort(Span<int> a) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            int[] buf = new int[alg_size((n + 1))];
            int width = 1;
            int left = 0;
            int mid = 0;
            int right = 0;
            int i = 0;
            int j = 0;

function insertion_sort(array &$a): int {
    alg_require(array_is_list($a));
    $n = count($a);
    alg_require((($n >= 0) && ($n <= 1000000)));
    alg_require((count($a) == $n));
    $i = 1;
    $j = 0;
    $key = 0;
    while (($i < $n)) {
        $key = $a[$i];
        $j = alg_sub($i, 1);
        while ((($j >= 0) && ($a[$j] > $key))) {