codon/stdlib/algorithms/timsort.codon

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BLOCK_SIZE = 64
CACHELINE_SIZE = 64
MIN_GALLOP = 7

from algorithms.insertionsort import _insertion_sort


def _count_run(
    arr: Array[T], begin: int, end: int, keyf: Callable[[T], S], T: type, S: type
) -> Tuple[int, int]:
    """
    Returns the # of elements in the next run and if the run is "inorder" or "reversed"
    """
    inorder = 1

    if end - begin == 1:
        return 1, inorder

    n = 2
    i = begin + 1
    if keyf(arr[i - 1]) >= keyf(arr[i]):
        inorder = 0
        i += 1
        while i < end:
            if keyf(arr[i - 1]) < keyf(arr[i]):
                break
            i += 1
            n += 1

    else:
        i += 1
        while i < end:
            if keyf(arr[i - 1]) >= keyf(arr[i]):
                break
            i += 1
            n += 1

    return n, inorder


def _merge_compute_minrun(n: int) -> int:
    """
    Computes the minrun for Timsort
    """
    r = 0
    while n >= 64:
        r |= n & 1
        n >>= 1
    return n + r


def _reverse_sortslice(arr: Array[T], begin: int, end: int, T: type) -> void:
    if end - begin < 2:
        return
    arr[begin], arr[end - 1] = arr[end - 1], arr[begin]
    _reverse_sortslice(arr, begin + 1, end - 1)


def _modified_comp(
    a: T, b: T, keyf: Callable[[T], S], left: bool, T: type, S: type
) -> bool:
    """
    Abstracts the left or right compare in gallop
    """
    if left:
        return keyf(b) >= keyf(a)
    else:
        return keyf(a) < keyf(b)


def _gallop(
    arr: Array[T],
    a: Tuple[int, int],
    b: Tuple[int, int],
    keyf: Callable[[T], S],
    hint: int,
    left: bool,
    T: type,
    S: type,
) -> int:
    """
    Gallop for Timsort
    """

    key = arr[0]  # just to initialize k
    if left:
        key = arr[b[0] + b[1] - 1]
    else:
        key = arr[b[0]]

    curr = a[0] + hint
    ofs, lastofs = 1, 0

    if _modified_comp(key, arr[curr], keyf, left):
        # Gallop left
        maxofs = hint + 1

        while ofs < maxofs:
            if _modified_comp(key, arr[curr - ofs], keyf, left):
                lastofs = ofs
                ofs = (ofs << 1) + 1
            else:
                break

        if ofs > maxofs:
            ofs = maxofs

        ofs, lastofs = hint - lastofs, hint - ofs

    else:
        # Gallop right
        maxofs = a[1] - hint

        while ofs < maxofs:
            if _modified_comp(key, arr[curr + ofs], keyf, left):
                break
            lastofs = ofs
            ofs = (ofs << 1) + 1

        if ofs > maxofs:
            ofs = maxofs

        lastofs += hint
        ofs += hint

    lastofs += 1
    while lastofs < ofs:
        m = lastofs + ((ofs - lastofs) >> 1)
        if _modified_comp(key, arr[a[0] + m], keyf, left):
            ofs = m
        else:
            lastofs = m + 1

    return ofs


def _merge_with_gallop(
    arr: Array[T],
    a: Tuple[int, int],
    b: Tuple[int, int],
    keyf: Callable[[T], S],
    T: type,
    S: type,
) -> void:
    min_gallop = MIN_GALLOP

    combined = Array[T](a[1] + b[1])
    a_copy = combined.slice(0, a[1])
    b_copy = combined.slice(a[1], len(combined))

    j = 0
    for i in range(a[0], a[0] + a[1]):
        combined[j] = arr[i]
        j += 1
    for i in range(b[0], b[0] + b[1]):
        combined[j] = arr[i]
        j += 1

    i, j, k = 0, 0, a[0]

    while i < len(a_copy) and j < len(b_copy):
        acount, bcount = 0, 0

        while i < len(a_copy) and j < len(b_copy):
            if keyf(b_copy[j]) < keyf(a_copy[i]):
                arr[k] = b_copy[j]
                acount = 0
                bcount += 1
                j += 1
                k += 1
                if bcount >= min_gallop:
                    break
            else:
                arr[k] = a_copy[i]
                acount += 1
                bcount = 0
                i += 1
                k += 1
                if acount >= min_gallop:
                    break

        if i == len(a_copy) or j == len(b_copy):
            break

        min_gallop += 1

        while i < len(a_copy) and j < len(b_copy):
            if min_gallop > 1:
                min_gallop -= 1

            acount = _gallop(
                combined, (0, len(a_copy)), (len(a_copy), len(b_copy)), keyf, i, False
            )
            if acount:
                while i < acount:
                    arr[k] = a_copy[i]
                    i += 1
                    k += 1
                arr[k] = b_copy[j]
                j += 1
                k += 1

            if i == len(a_copy) or j == len(b_copy):
                break

            b_end = _gallop(
                combined, (len(a_copy), len(b_copy)), (0, len(a_copy)), keyf, j, True
            )
            bcount = len(b_copy) - b_end
            if bcount:
                while j < b_end:
                    arr[k] = b_copy[j]
                    j += 1
                    k += 1
                arr[k] = a_copy[i]
                i += 1
                k += 1

            if acount < MIN_GALLOP and bcount < MIN_GALLOP:
                break

        min_gallop += 1

    while i < len(a_copy):
        arr[k] = a_copy[i]
        i += 1
        k += 1

    while j < len(b_copy):
        arr[k] = b_copy[j]
        j += 1
        k += 1


def _merge_at(
    arr: Array[T],
    a: Tuple[int, int],
    b: Tuple[int, int],
    keyf: Callable[[T], S],
    T: type,
    S: type,
) -> void:
    start_a, len_a = a
    start_b, len_b = b

    # Where does b start in a?
    k = _gallop(arr, a, b, keyf, 0, False)
    start_a, len_a = start_a + k, len_a - k
    if len_a == 0:
        return

    # Where does a end in b?
    len_b = _gallop(arr, b, a, keyf, len_b - 1, True)
    if len_b == 0:
        return

    _merge_with_gallop(arr, (start_a, len_a), (start_b, len_b), keyf)


def _merge_collapse(
    arr: Array[T],
    stack: List[Tuple[int, int]],
    keyf: Callable[[T], S],
    T: type,
    S: type,
) -> void:
    if len(stack) <= 1:
        return

    while len(stack) > 2:
        X = stack[-3]
        Y = stack[-2]
        Z = stack[-1]

        if X[1] > Y[1] + Z[1] and Y[1] > Z[1]:
            break

        C = stack.pop()
        B = stack.pop()
        A = stack.pop()

        if A[1] <= B[1] + C[1]:
            if A[1] < C[1]:
                _merge_at(arr, A, B, keyf)
                stack.append((A[0], A[1] + B[1]))
                stack.append(C)
            else:
                _merge_at(arr, B, C, keyf)
                stack.append(A)
                stack.append((B[0], B[1] + C[1]))

        else:
            _merge_at(arr, B, C, keyf)
            stack.append(A)
            stack.append((B[0], B[1] + C[1]))

    if len(stack) == 2:
        X = stack[-2]
        Y = stack[-1]

        if X[1] <= Y[1]:
            C = stack.pop()
            B = stack.pop()
            _merge_at(arr, B, C, keyf)
            stack.append((B[0], B[1] + C[1]))
            return


def _final_merge(
    arr: Array[T],
    stack: List[Tuple[int, int]],
    keyf: Callable[[T], S],
    T: type,
    S: type,
) -> void:
    while len(stack) > 1:
        C = stack.pop()
        B = stack.pop()
        _merge_at(arr, B, C, keyf)
        stack.append((B[0], B[1] + C[1]))


def _tim_sort(
    arr: Array[T], begin: int, end: int, keyf: Callable[[T], S], T: type, S: type
) -> void:
    if end - begin < 2:
        return

    merge_pending = List[Tuple[int, int]]()
    minrun = _merge_compute_minrun(end - begin)
    i = begin
    while i < end:
        n, inorder = _count_run(arr, i, end, keyf)
        if not inorder:
            _reverse_sortslice(arr, i, i + n)

        if n < minrun:
            force = min(minrun, end)
            _insertion_sort(arr, i, i + force, keyf)
            n = force

        merge_pending.append((i, n))
        _merge_collapse(arr, merge_pending, keyf)
        i += n

    _final_merge(arr, merge_pending, keyf)


def tim_sort_array(
    collection: Array[T], size: int, keyf: Callable[[T], S], T: type, S: type
) -> void:
    """
    Timsort
    By Tim Peters, published at https://github.com/python/cpython/blob/master/Objects/listobject.c#L2187

    Sorts the array inplace.
    """
    _tim_sort(collection, 0, size, keyf)


def tim_sort_inplace(
    collection: List[T], keyf: Callable[[T], S], T: type, S: type
) -> void:
    """
    Timsort
    By Tim Peters, published at https://github.com/python/cpython/blob/master/Objects/listobject.c#L2187

    Sorts the list inplace.
    """
    tim_sort_array(collection.arr, collection.len, keyf)


def tim_sort(collection: List[T], keyf: Callable[[T], S], T: type, S: type) -> List[T]:
    """
    Timsort
    By Tim Peters, published at https://github.com/python/cpython/blob/master/Objects/listobject.c#L2187

    Returns a sorted list.
    """
    newlst = list(collection)
    tim_sort_inplace(newlst, keyf)
    return newlst