' qsort

Public Sub QSort(ByRef A() As Variant, ByVal Lb As Long, ByVal Ub As Long)
    Dim lbStack(32) As Long
    Dim ubStack(32) As Long
    Dim sp As Long              ' stack pointer
    Dim lbx As Long             ' current lower-bound
    Dim ubx As Long             ' current upper-bound
    Dim m As Long
    Dim p As Long               ' index to pivot
    Dim i As Long
    Dim j As Long
    Dim t As Variant            ' temp used for exchanges

    lbStack(0) = Lb
    ubStack(0) = Ub
    sp = 0
    Do While sp >= 0
        lbx = lbStack(sp)
        ubx = ubStack(sp)

        Do While (lbx < ubx)

            ' select pivot and exchange with 1st element
            p = lbx + (ubx - lbx) \ 2

            ' exchange lbx, p
            t = A(lbx)
            A(lbx) = A(p)
            A(p) = t

            ' partition into two segments
            i = lbx + 1
            j = ubx
            Do
                Do While i < j
                    If A(lbx) <= A(i) Then Exit Do
                    i = i + 1
                Loop

                Do While j >= i
                    If A(j) <= A(lbx) Then Exit Do
                    j = j - 1
                Loop

                If i >= j Then Exit Do

                ' exchange i, j
                t = A(i)
                A(i) = A(j)
                A(j) = t

                j = j - 1
                i = i + 1
            Loop

            ' pivot belongs in A[j]
            ' exchange lbx, j
            t = A(lbx)
            A(lbx) = A(j)
            A(j) = t

            m = j

            ' keep processing smallest segment, and stack largest
            If m - lbx <= ubx - m Then
                If m + 1 < ubx Then
                    lbStack(sp) = m + 1
                    ubStack(sp) = ubx
                    sp = sp + 1
                End If
                ubx = m - 1
            Else
                If m - 1 > lbx Then
                    lbStack(sp) = lbx
                    ubStack(sp) = m - 1
                    sp = sp + 1
                End If
                lbx = m + 1
            End If
        Loop
        sp = sp - 1
    Loop
End Sub