module fft_mod
  implicit none
  integer,       parameter :: dp=selected_real_kind(15,300)
  real(kind=dp), parameter :: pi=3.141592653589793238460_dp
contains

  ! In place Cooley-Tukey FFT
  recursive subroutine fft(x)
    complex(kind=dp), dimension(:), intent(inout)  :: x
    complex(kind=dp)                               :: t
    integer                                        :: N
    integer                                        :: i
    complex(kind=dp), dimension(:), allocatable    :: even, odd

    N=size(x)

    if(N .le. 1) return

    allocate(odd((N+1)/2))
    allocate(even(N/2))

    ! divide
    odd =x(1:N:2)
    even=x(2:N:2)

    ! conquer
    call fft(odd)
    call fft(even)

    ! combine
    do i=1,N/2
       t=exp(cmplx(0.0_dp,-2.0_dp*pi*real(i-1,dp)/real(N,dp),kind=dp))*even(i)
       x(i)     = odd(i) + t
       x(i+N/2) = odd(i) - t
    end do

    deallocate(odd)
    deallocate(even)

  end subroutine fft

end module fft_mod

program test
  use fft_mod
  implicit none
  complex(kind=dp), dimension(8) :: data = (/1.0, 1.0, 1.0, 1.0, 0.0,

0.0, 0.0, 0.0/)
  integer :: i

  call fft(data)

  do i=1,8
     write(*,'("(", F20.15, ",", F20.15, "i )")') data(i)
  end do

end program test