!!#################################################################################

!! Compute the factorial of an Integer
!integer Function factorial (anInteger)
!  integer, intent (in) :: anInteger
!  integer :: i, x
!
!  x = 1
!  do i = 1, anInteger
!    x = x * i
!  enddo
!  
!  factorial = x
!End Function factorial

!! Returns the natural logarithm of the gamma function, ln[gamma(xx)] for xx > 0
real Function gammaLn (xx)
  real :: xx
  real :: x, y, tmp, ser
  real :: cof (0:5) = (/76.18009172947146, -86.50532032941677,     24.01409824083091,&
                        -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5/)
  integer :: j

  y = xx ; x = xx
  tmp = x + 5.5
  tmp = tmp - ((x + 0.5) * log(tmp))
  ser = 1.000000000190015
  do j = 0, 5
    y = y + 1
    ser = ser + cof(j) / y
  enddo

  gammaLn = - tmp + log (2.5066282746310005*ser / x)

End Function gammaLn

!! Sorts a given data series from the lowest to the highest value
Subroutine upward (series, n)
  integer :: n
  real :: series (0:Ntime-1)  !series (0:n-1)
  integer :: i, j
  real :: temp

  do i = 0, n - 2
    do j = 0, n - 2 - i
      if ( series (j + 1) .lt. series (j) ) then
        temp = series (j)
        series (j) = series (j + 1)
        series (j + 1) = temp
      endif
    enddo
  enddo

!  do i = 0, n-1
!    print*, series (i)
!  enddo
End Subroutine upward

!!