#if 0
program checkFFT
use dfport
implicit none
double precision::x
integer,parameter::N=256
double precision,dimension(N*2)::p
double precision,dimension(N/2)::s
integer::ncount,j,idum
character(len=8)::tt
tt=clock()
idum=iachar(tt(8:8))-48
p=0.0
open(77,file='prime.dat',status='unknown')
loop1:do ncount=1,N
   x=ran(idum)
   p(2*ncount-1)=x
   write(77,'(f15.3)')x
enddo loop1
close(77)
call four1(p,N,1)
do j=1,N/2
  s(j)=p(2*j)*p(2*j)+p(2*j-1)*p(2*j-1)
enddo
x=0.0
do j=1,N/2
  x=x+s(j)
enddo
s=s/x
open(77,file='power.dat',status='unknown')
do j=1,N/2
  write(77,'(2(1x,f15.3))')dble(j-1)/dble(N),s(j)
enddo
close(77)
end program checkFFT
#endif

!-------------
! Optimized FFT using Intel oneMKL DFTI
! Mathematical equivalence: Standard DFT definition
!   Forward (isign=1):  X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N)
!   Backward (isign=-1): X[k] = sum_{n=0}^{N-1} x[n] * exp(+2*pi*i*k*n/N)
! Input/Output: dataa is interleaved complex array [Re(0),Im(0),Re(1),Im(1),...]
!-------------
SUBROUTINE four1(dataa,nn,isign)
use MKL_DFTI
implicit none
INTEGER, intent(in) :: isign, nn
DOUBLE PRECISION, dimension(2*nn), intent(inout) :: dataa

type(DFTI_DESCRIPTOR), pointer :: desc
integer :: status

! Create DFTI descriptor for 1D complex-to-complex transform
status = DftiCreateDescriptor(desc, DFTI_DOUBLE, DFTI_COMPLEX, 1, nn)
if (status /= 0) return

! Set input/output storage as interleaved complex (default)
status = DftiSetValue(desc, DFTI_PLACEMENT, DFTI_INPLACE)
if (status /= 0) then
   status = DftiFreeDescriptor(desc)
   return
endif

! Commit the descriptor
status = DftiCommitDescriptor(desc)
if (status /= 0) then
   status = DftiFreeDescriptor(desc)
   return
endif

! Execute FFT based on direction
if (isign == 1) then
   ! Forward FFT: exp(-2*pi*i*k*n/N)
   status = DftiComputeForward(desc, dataa)
else
   ! Backward FFT: exp(+2*pi*i*k*n/N)
   status = DftiComputeBackward(desc, dataa)
endif

! Free descriptor
status = DftiFreeDescriptor(desc)

return
END SUBROUTINE four1