!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2017  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \par History
!>      JGH (30-Nov-2000): ESSL FFT Library added
!>      JGH (05-Jan-2001): Added SGI library FFT
!>      JGH (14-Jan-2001): Added parallel 3d FFT
!>      JGH (10-Feb-2006): New interface type
!>      JGH (31-Mar-2008): Remove local allocates and reshapes (performance)
!>                         Possible problems can be related with setting arrays
!>                         not to zero
!>                         Some interfaces could be further simplified by avoiding
!>                         an initial copy. However, this assumes contiguous arrays
!>      IAB (15-Oct-2008): Moved mp_cart_sub calls out of cube_tranpose_* and into
!>                         fft_scratch type, reducing number of calls dramatically
!>      IAB (05-Dec-2008): Moved all other non-essential MPI calls into scratch type
!>      IAB (09-Jan-2009): Added fft_plan_type to store FFT data, including cached FFTW plans
!>      IAB (13-Feb-2009): Extended plan caching to serial 3D FFT (fft3d_s)
!>      IAB (09-Oct-2009): Added OpenMP directives to parallel 3D FFT
!>                         (c) The Numerical Algorithms Group (NAG) Ltd, 2008-2009 on behalf of the HECToR project
!> \author JGH
! **************************************************************************************************
MODULE fft_tools
   USE ISO_C_BINDING,                   ONLY: C_F_POINTER,&
                                              C_INT,&
                                              C_LOC,&
                                              C_PTR,&
                                              C_SIZE_T
   USE cp_log_handling,                 ONLY: cp_logger_get_default_io_unit
   USE cp_para_types,                   ONLY: cp_para_env_type
   USE fast,                            ONLY: zero_c
   USE fft_lib,                         ONLY: &
        fft_1dm, fft_3d, fft_create_plan_1dm, fft_create_plan_3d, fft_destroy_plan, &
        fft_do_cleanup, fft_do_init, fft_get_lengths, fft_library
   USE fft_plan,                        ONLY: fft_plan_type
   USE kinds,                           ONLY: dp,&
                                              dp_size,&
                                              int_size,&
                                              sp
   USE message_passing,                 ONLY: &
        mp_alltoall, mp_cart_coords, mp_cart_rank, mp_cart_sub, mp_comm_compare, mp_comm_free, &
        mp_comm_null, mp_environ, mp_irecv, mp_isend, mp_rank_compare, mp_sum, mp_sync, mp_waitall
   USE termination,                     ONLY: stop_memory

!$ USE OMP_LIB, ONLY: omp_get_max_threads, omp_get_thread_num, omp_get_num_threads

#include "../base/base_uses.f90"

   IMPLICIT NONE

   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'fft_tools'

   ! Types for the pool of scratch data needed in FFT routines
   ! keep the subroutine "is_equal" up-to-date
   ! needs a default initialization
   TYPE fft_scratch_sizes
      INTEGER                              :: nx = 0, ny = 0, nz = 0
      INTEGER                              :: lmax = 0, mmax = 0, nmax = 0
      INTEGER                              :: mx1 = 0, mx2 = 0, mx3 = 0
      INTEGER                              :: my1 = 0, my2 = 0, my3 = 0
      INTEGER                              :: mz1 = 0, mz2 = 0, mz3 = 0
      INTEGER                              :: mcz1 = 0, mcz2 = 0, mcy3 = 0, mcx2 = 0
      INTEGER                              :: lg = 0, mg = 0
      INTEGER                              :: nbx = 0, nbz = 0
      INTEGER                              :: nmray = 0, nyzray = 0
      INTEGER                              :: gs_group = 0, rs_group = 0
      INTEGER, DIMENSION(2)                :: g_pos = 0, r_pos = 0, r_dim = 0
      INTEGER                              :: numtask = 0
   END TYPE fft_scratch_sizes

   TYPE fft_scratch_type
      INTEGER                              :: fft_scratch_id
      INTEGER                              :: tf_type
      LOGICAL                              :: in_use
      INTEGER                              :: group
      INTEGER, DIMENSION(3)                :: nfft
      ! to be used in cube_transpose_* routines
      INTEGER, DIMENSION(2)                :: cart_sub_comm = mp_comm_null, dim, pos
      ! to be used in fft3d_s
      COMPLEX(KIND=dp), DIMENSION(:, :, :), POINTER &
         :: ziptr, zoptr
      ! to be used in fft3d_ps : block distribution
      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER &
         :: p1buf, p2buf, p3buf, p4buf, p5buf, p6buf, p7buf
      ! to be used in fft3d_ps : plane distribution
      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER &
         :: r1buf, r2buf
      COMPLEX(KIND=dp), DIMENSION(:, :, :), POINTER &
         :: tbuf
      ! to be used in fft3d_pb
      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER &
         :: a1buf, a2buf, a3buf, a4buf, a5buf, a6buf
      ! to be used in communication routines
      INTEGER, DIMENSION(:), POINTER       :: scount, rcount, sdispl, rdispl
      INTEGER, DIMENSION(:, :), POINTER     :: pgcube
      INTEGER, DIMENSION(:), POINTER       :: xzcount, yzcount, xzdispl, yzdispl
      INTEGER                              :: in, mip
      REAL(KIND=dp)                        :: rsratio
      COMPLEX(KIND=dp), DIMENSION(:), POINTER &
         :: xzbuf, yzbuf
      COMPLEX(KIND=sp), DIMENSION(:), POINTER &
         :: xzbuf_sgl, yzbuf_sgl
      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER &
         :: rbuf1, rbuf2, rbuf3, rbuf4, rbuf5, rbuf6, rr
      COMPLEX(KIND=sp), DIMENSION(:, :), POINTER &
         :: ss, tt
      INTEGER, DIMENSION(:, :), POINTER     :: pgrid
      INTEGER, DIMENSION(:), POINTER       :: xcor, zcor, pzcoord
      TYPE(fft_scratch_sizes)              :: sizes
      TYPE(fft_plan_type), DIMENSION(6)   :: fft_plan
      INTEGER                              :: last_tick
   END TYPE fft_scratch_type

   TYPE fft_scratch_pool_type
      TYPE(fft_scratch_type), POINTER       :: fft_scratch
      TYPE(fft_scratch_pool_type), POINTER  :: fft_scratch_next
   END TYPE fft_scratch_pool_type

   INTEGER, SAVE                           :: init_fft_pool = 0
   ! the clock for fft pool. Allows to identify the least recently used scratch
   INTEGER, SAVE                           :: tick_fft_pool = 0
   ! limit the number of scratch pools to fft_pool_scratch_limit.
   INTEGER, SAVE                           :: fft_pool_scratch_limit = 15
   TYPE(fft_scratch_pool_type), POINTER, SAVE:: fft_scratch_first
   ! END of types for the pool of scratch data needed in FFT routines

   PRIVATE
   PUBLIC :: init_fft, fft3d, finalize_fft
   PUBLIC :: fft_radix_operations
   PUBLIC :: FWFFT, BWFFT
   PUBLIC :: FFT_RADIX_CLOSEST, FFT_RADIX_NEXT
   PUBLIC :: FFT_RADIX_NEXT_ODD

   INTEGER, PARAMETER :: FWFFT = +1, BWFFT = -1
   INTEGER, PARAMETER :: FFT_RADIX_CLOSEST = 493, FFT_RADIX_NEXT = 494
   INTEGER, PARAMETER :: FFT_RADIX_ALLOWED = 495, FFT_RADIX_DISALLOWED = 496
   INTEGER, PARAMETER :: FFT_RADIX_NEXT_ODD = 497

   REAL(KIND=dp), PARAMETER :: ratio_sparse_alltoall = 0.5_dp

   ! these saved variables are FFT globals
   INTEGER, SAVE :: fft_type = 0
   LOGICAL, SAVE :: alltoall_sgl = .FALSE.
   LOGICAL, SAVE :: use_fftsg_sizes = .TRUE.
   INTEGER, SAVE :: fft_plan_style = 1

   ! these are only needed for pw_methods_cuda (-D__PW_CUDA)
   PUBLIC :: get_fft_scratch, release_fft_scratch
   PUBLIC :: cube_transpose_1, cube_transpose_2
   PUBLIC :: yz_to_x, x_to_yz, xz_to_yz, yz_to_xz
   PUBLIC :: fft_scratch_sizes, fft_scratch_type

   INTERFACE fft3d
      MODULE PROCEDURE fft3d_s, fft3d_ps, fft3d_pb
   END INTERFACE

#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
   INTERFACE
      INTEGER(KIND=C_INT) FUNCTION cudaFreeHost(buffer) BIND(C, name="cudaFreeHost")
         IMPORT
         IMPLICIT NONE
         TYPE(C_PTR), VALUE :: buffer
      END FUNCTION cudaFreeHost
   END INTERFACE

   INTERFACE
      INTEGER(KIND=C_INT) FUNCTION cudaHostAlloc(buffer, length, flag) BIND(C, name="cudaHostAlloc")
         IMPORT
         IMPLICIT NONE
         TYPE(C_PTR)                   :: buffer
         INTEGER(KIND=C_SIZE_T), VALUE :: length
         INTEGER(KIND=C_INT), VALUE    :: flag
      END FUNCTION cudaHostAlloc
   END INTERFACE
#endif

! **************************************************************************************************

CONTAINS

! **************************************************************************************************
!> \brief ...
!> \param fftlib ...
!> \param alltoall ...
!> \param fftsg_sizes ...
!> \param pool_limit ...
!> \param wisdom_file ...
!> \param plan_style ...
!> \author JGH
! **************************************************************************************************
   SUBROUTINE init_fft(fftlib, alltoall, fftsg_sizes, pool_limit, wisdom_file, &
                       plan_style)

      CHARACTER(LEN=*), INTENT(IN)                       :: fftlib
      LOGICAL, INTENT(IN)                                :: alltoall, fftsg_sizes
      INTEGER, INTENT(IN)                                :: pool_limit
      CHARACTER(LEN=*), INTENT(IN)                       :: wisdom_file
      INTEGER, INTENT(IN)                                :: plan_style

      CHARACTER(len=*), PARAMETER :: routineN = 'init_fft', routineP = moduleN//':'//routineN

      use_fftsg_sizes = fftsg_sizes
      alltoall_sgl = alltoall
      fft_pool_scratch_limit = pool_limit
      fft_type = fft_library(fftlib)
      fft_plan_style = plan_style

      IF (fft_type <= 0) CPABORT("Unknown FFT library: "//TRIM(fftlib))

      CALL fft_do_init(fft_type, wisdom_file)

      ! setup the FFT scratch pool, if one is associated, clear first
      CALL release_fft_scratch_pool()
      CALL init_fft_scratch_pool()

   END SUBROUTINE init_fft

! **************************************************************************************************
!> \brief does whatever is needed to finalize the current fft setup
!> \param para_env ...
!> \param wisdom_file ...
!> \par History
!>      10.2007 created [Joost VandeVondele]
! **************************************************************************************************
   SUBROUTINE finalize_fft(para_env, wisdom_file)
      TYPE(cp_para_env_type), POINTER                    :: para_env
      CHARACTER(LEN=*), INTENT(IN)                       :: wisdom_file

      CHARACTER(len=*), PARAMETER :: routineN = 'finalize_fft', routineP = moduleN//':'//routineN

! release the FFT scratch pool

      CALL release_fft_scratch_pool()

      ! finalize fft libs

      CALL fft_do_cleanup(fft_type, wisdom_file, para_env%ionode)

   END SUBROUTINE finalize_fft

! **************************************************************************************************
!> \brief Determine the allowed lengths of FFT's   '''
!> \param radix_in ...
!> \param radix_out ...
!> \param operation ...
!> \par History
!>      new library structure (JGH)
!> \author Ari Seitsonen
! **************************************************************************************************
   SUBROUTINE fft_radix_operations(radix_in, radix_out, operation)

      INTEGER, INTENT(IN)                                :: radix_in
      INTEGER, INTENT(OUT)                               :: radix_out
      INTEGER, INTENT(IN)                                :: operation

      CHARACTER(len=*), PARAMETER :: routineN = 'fft_radix_operations', &
         routineP = moduleN//':'//routineN
      INTEGER, PARAMETER                                 :: fft_type_sg = 1

      INTEGER                                            :: i, iloc, ldata
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: DATA

      ldata = 1024
      ALLOCATE (DATA(ldata))
      DATA = -1

      ! if the user wants to use fftsg sizes go for it
      IF (use_fftsg_sizes) THEN
         CALL fft_get_lengths(fft_type_sg, DATA, ldata)
      ELSE
         CALL fft_get_lengths(fft_type, DATA, ldata)
      ENDIF

      iloc = 0
      DO i = 1, ldata
         IF (DATA(i) == radix_in) THEN
            iloc = i
            EXIT
         ELSE
            IF (OPERATION == FFT_RADIX_ALLOWED) THEN
               CYCLE
            ELSE IF (DATA(i) > radix_in) THEN
               iloc = i
               EXIT
            END IF
         END IF
      END DO

      IF (iloc == 0) THEN
         CPABORT("Index to radix array not found.")
      END IF

      IF (OPERATION == FFT_RADIX_ALLOWED) THEN
         IF (DATA(iloc) == radix_in) THEN
            radix_out = FFT_RADIX_ALLOWED
         ELSE
            radix_out = FFT_RADIX_DISALLOWED
         END IF

      ELSE IF (OPERATION == FFT_RADIX_CLOSEST) THEN
         IF (DATA(iloc) == radix_in) THEN
            radix_out = DATA(iloc)
         ELSE
            IF (ABS(DATA(iloc-1)-radix_in) <= &
                ABS(DATA(iloc)-radix_in)) THEN
               radix_out = DATA(iloc-1)
            ELSE
               radix_out = DATA(iloc)
            END IF
         END IF

      ELSE IF (OPERATION == FFT_RADIX_NEXT) THEN
         radix_out = DATA(iloc)

      ELSE IF (OPERATION == FFT_RADIX_NEXT_ODD) THEN
         DO i = iloc, ldata
            IF (MOD(DATA(i), 2) == 1) THEN
               radix_out = DATA(i)
               EXIT
            END IF
         END DO
         IF (MOD(radix_out, 2) == 0) THEN
            CPABORT("No odd radix found.")
         END IF

      ELSE
         CPABORT("Disallowed radix operation.")
      END IF

      DEALLOCATE (DATA)

   END SUBROUTINE fft_radix_operations

! **************************************************************************************************
!> \brief Calls the 3D-FFT function from the initialized library
!> \param fsign ...
!> \param n ...
!> \param zin ...
!> \param zout ...
!> \param scale ...
!> \param status ...
!> \param debug ...
!> \par History
!>      none
!> \author JGH
! **************************************************************************************************
   SUBROUTINE fft3d_s(fsign, n, zin, zout, scale, status, debug)

      INTEGER, INTENT(IN)                                :: fsign
      INTEGER, DIMENSION(:), INTENT(INOUT)               :: n
      COMPLEX(KIND=dp), DIMENSION(:, :, :), &
         INTENT(INOUT)                                   :: zin
      COMPLEX(KIND=dp), DIMENSION(:, :, :), &
         INTENT(INOUT), OPTIONAL, TARGET                 :: zout
      REAL(KIND=dp), INTENT(IN), OPTIONAL                :: scale
      INTEGER, INTENT(OUT), OPTIONAL                     :: status
      LOGICAL, INTENT(IN), OPTIONAL                      :: debug

      CHARACTER(len=*), PARAMETER :: routineN = 'fft3d_s', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(1, 1, 1), TARGET       :: zdum
      COMPLEX(KIND=dp), DIMENSION(:, :, :), POINTER      :: zoptr
      INTEGER                                            :: handle, ld(3), lo(3), output_unit, sign, &
                                                            stat
      LOGICAL                                            :: fft_in_place, test
      REAL(KIND=dp)                                      :: in_sum, norm, out_sum
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CALL timeset(routineN, handle)
      output_unit = cp_logger_get_default_io_unit()

      IF (PRESENT(scale)) THEN
         norm = scale
      ELSE
         norm = 1.0_dp
      END IF

      IF (PRESENT(debug)) THEN
         test = debug
      ELSE
         test = .FALSE.
      END IF

      IF (PRESENT(zout)) THEN
         fft_in_place = .FALSE.
      ELSE
         fft_in_place = .TRUE.
      END IF

      IF (test) THEN
         in_sum = SUM(ABS(zin))
      ENDIF

      ld(1) = SIZE(zin, 1)
      ld(2) = SIZE(zin, 2)
      ld(3) = SIZE(zin, 3)

      IF (n(1) /= ld(1) .OR. n(2) /= ld(2) .OR. n(3) /= ld(3)) THEN
         CPABORT("Size and dimension (zin) have to be the same.")
      END IF

      sign = fsign
      CALL get_fft_scratch(fft_scratch, tf_type=400, n=n)

      IF (fft_in_place) THEN
         zoptr => zdum
         IF (fsign == FWFFT) THEN
            CALL fft_3d(fft_scratch%fft_plan(1), norm, zin, zoptr, stat)
         ELSE
            CALL fft_3d(fft_scratch%fft_plan(2), norm, zin, zoptr, stat)
         ENDIF
      ELSE
         IF (fsign == FWFFT) THEN
            CALL fft_3d(fft_scratch%fft_plan(3), norm, zin, zout, stat)
         ELSE
            CALL fft_3d(fft_scratch%fft_plan(4), norm, zin, zout, stat)
         ENDIF
      END IF

      CALL release_fft_scratch(fft_scratch)

      IF (PRESENT(zout)) THEN
         lo(1) = SIZE(zout, 1)
         lo(2) = SIZE(zout, 2)
         lo(3) = SIZE(zout, 3)
         IF (n(1) /= lo(1) .OR. n(2) /= lo(2) .OR. n(3) /= lo(3)) THEN
            CPABORT("Size and dimension (zout) have to be the same.")
         END IF
      END IF

      IF (PRESENT(status)) THEN
         status = stat
      END IF

      IF (test .AND. output_unit > 0) THEN
         IF (PRESENT(zout)) THEN
            out_sum = SUM(ABS(zout))
            WRITE (output_unit, '(A)') "  Out of place 3D FFT (local)  : fft3d_s"
            WRITE (output_unit, '(A,T60,3I7)') "     Transform lengths ", n
            WRITE (output_unit, '(A,T60,3I7)') "     Input array dimensions ", ld
            WRITE (output_unit, '(A,T60,3I7)') "     Output array dimensions ", lo
            WRITE (output_unit, '(A,T61,E20.14)') "     Sum of input data ", in_sum
            WRITE (output_unit, '(A,T61,E20.14)') "     Sum of output data ", out_sum
         ELSE
            out_sum = SUM(ABS(zin))
            WRITE (output_unit, '(A)') "  In place 3D FFT (local)  : fft3d_s"
            WRITE (output_unit, '(A,T60,3I7)') "     Transform lengths ", n
            WRITE (output_unit, '(A,T60,3I7)') "     Input/output array dimensions ", ld
            WRITE (output_unit, '(A,T61,E20.14)') "     Sum of input data ", in_sum
            WRITE (output_unit, '(A,T61,E20.14)') "     Sum of output data ", out_sum
         END IF
      END IF

      CALL timestop(handle)

   END SUBROUTINE fft3d_s

! **************************************************************************************************
!> \brief ...
!> \param fsign ...
!> \param n ...
!> \param cin ...
!> \param gin ...
!> \param gs_group ...
!> \param rs_group ...
!> \param yzp ...
!> \param nyzray ...
!> \param bo ...
!> \param scale ...
!> \param status ...
!> \param debug ...
! **************************************************************************************************
   SUBROUTINE fft3d_ps(fsign, n, cin, gin, gs_group, rs_group, yzp, nyzray, &
                       bo, scale, status, debug)

      INTEGER, INTENT(IN)                                :: fsign
      INTEGER, DIMENSION(:), INTENT(IN)                  :: n
      COMPLEX(KIND=dp), DIMENSION(:, :, :), &
         INTENT(INOUT)                                   :: cin
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(INOUT)   :: gin
      INTEGER, INTENT(IN)                                :: gs_group, rs_group
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: yzp
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: nyzray
      INTEGER, DIMENSION(:, :, 0:, :), INTENT(IN)        :: bo
      REAL(KIND=dp), INTENT(IN), OPTIONAL                :: scale
      INTEGER, INTENT(OUT), OPTIONAL                     :: status
      LOGICAL, INTENT(IN), OPTIONAL                      :: debug

      CHARACTER(len=*), PARAMETER :: routineN = 'fft3d_ps', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: pbuf, qbuf, rbuf, sbuf
      COMPLEX(KIND=dp), DIMENSION(:, :, :), POINTER      :: tbuf
      INTEGER :: g_pos, handle, ierr, iout, lg, lmax, mcx2, mcz1, mcz2, mg, mmax, mx1, mx2, my1, &
         mz2, n1, n2, nmax, numtask, numtask_g, numtask_r, nx, ny, nz, output_unit, r_dim(2), &
         r_pos(2), rp, sign, stat
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: p2p
      LOGICAL                                            :: test
      REAL(KIND=dp)                                      :: norm, sum_data
      TYPE(fft_scratch_sizes)                            :: fft_scratch_size
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CALL timeset(routineN, handle)
      output_unit = cp_logger_get_default_io_unit()

      IF (PRESENT(debug)) THEN
         test = debug
      ELSE
         test = .FALSE.
      END IF

      CALL mp_environ(numtask_g, g_pos, gs_group)
      CALL mp_environ(numtask_r, r_dim, r_pos, rs_group)
      IF (numtask_g /= numtask_r) THEN
         CPABORT("Real space and G space groups are different.")
      END IF
      numtask = numtask_r
      CALL mp_comm_compare(rs_group, gs_group, iout)
      IF (iout > 3) THEN
         CPABORT("Real space and G space groups are different.")
      END IF

      IF (PRESENT(scale)) THEN
         norm = scale
      ELSE
         norm = 1.0_dp
      END IF

      sign = fsign

      lg = SIZE(gin, 1)
      mg = SIZE(gin, 2)

      nx = SIZE(cin, 1)
      ny = SIZE(cin, 2)
      nz = SIZE(cin, 3)

      IF (mg == 0) THEN
         mmax = 1
      ELSE
         mmax = mg
      END IF
      lmax = MAX(lg, (nx*ny*nz)/mmax+1)

      ALLOCATE (p2p(0:numtask-1), STAT=ierr)
      IF (ierr /= 0) CALL stop_memory(routineN, moduleN, __LINE__, &
                                      "p2p", int_size*numtask)

      CALL mp_rank_compare(gs_group, rs_group, p2p)

      rp = p2p(g_pos)
      mx1 = bo(2, 1, rp, 1)-bo(1, 1, rp, 1)+1
      my1 = bo(2, 2, rp, 1)-bo(1, 2, rp, 1)+1
      mx2 = bo(2, 1, rp, 2)-bo(1, 1, rp, 2)+1
      mz2 = bo(2, 3, rp, 2)-bo(1, 3, rp, 2)+1

      n1 = MAXVAL(bo(2, 1, :, 1)-bo(1, 1, :, 1)+1)
      n2 = MAXVAL(bo(2, 2, :, 1)-bo(1, 2, :, 1)+1)
      nmax = MAX((2*n2)/numtask, 2)*mx2*mz2
      nmax = MAX(nmax, n1*MAXVAL(nyzray))
      n1 = MAXVAL(bo(2, 1, :, 2))
      n2 = MAXVAL(bo(2, 3, :, 2))

      fft_scratch_size%nx = nx
      fft_scratch_size%ny = ny
      fft_scratch_size%nz = nz
      fft_scratch_size%lmax = lmax
      fft_scratch_size%mmax = mmax
      fft_scratch_size%mx1 = mx1
      fft_scratch_size%mx2 = mx2
      fft_scratch_size%my1 = my1
      fft_scratch_size%mz2 = mz2
      fft_scratch_size%lg = lg
      fft_scratch_size%mg = mg
      fft_scratch_size%nbx = n1
      fft_scratch_size%nbz = n2
      mcz1 = MAXVAL(bo(2, 3, :, 1)-bo(1, 3, :, 1)+1)
      mcx2 = MAXVAL(bo(2, 1, :, 2)-bo(1, 1, :, 2)+1)
      mcz2 = MAXVAL(bo(2, 3, :, 2)-bo(1, 3, :, 2)+1)
      fft_scratch_size%mcz1 = mcz1
      fft_scratch_size%mcx2 = mcx2
      fft_scratch_size%mcz2 = mcz2
      fft_scratch_size%nmax = nmax
      fft_scratch_size%nmray = MAXVAL(nyzray)
      fft_scratch_size%nyzray = nyzray(g_pos)
      fft_scratch_size%gs_group = gs_group
      fft_scratch_size%rs_group = rs_group
      fft_scratch_size%g_pos = g_pos
      fft_scratch_size%r_pos = r_pos
      fft_scratch_size%r_dim = r_dim
      fft_scratch_size%numtask = numtask

      IF (test) THEN
         IF (g_pos == 0 .AND. output_unit > 0) THEN
            WRITE (output_unit, '(A)') "  Parallel 3D FFT : fft3d_ps"
            WRITE (output_unit, '(A,T60,3I7)') "     Transform lengths ", n
            WRITE (output_unit, '(A,T67,2I7)') "     Array dimensions (gin) ", lg, mg
            WRITE (output_unit, '(A,T60,3I7)') "     Array dimensions (cin) ", nx, ny, nz
         END IF
      END IF

      IF (r_dim(2) > 1) THEN

         !
         ! real space is distributed over x and y coordinate
         ! we have two stages of communication
         !

         IF (r_dim(1) == 1) THEN
            CPABORT("This processor distribution is not supported.")
         END IF
         CALL get_fft_scratch(fft_scratch, tf_type=300, n=n, fft_sizes=fft_scratch_size)

         IF (sign == FWFFT) THEN
            ! cin -> gin

            IF (test) THEN
               sum_data = ABS(SUM(cin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  Two step communication algorithm "
                  WRITE (output_unit, '(A,T60,3I7)') "     Transform Z ", n(3), mx1*my1
                  WRITE (output_unit, '(A,T60,3I7)') "     Transform Y ", n(2), mx2*mz2
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), nyzray(g_pos)
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            pbuf => fft_scratch%p1buf
            qbuf => fft_scratch%p2buf

            ! FFT along z
            CALL fft_1dm(fft_scratch%fft_plan(1), cin, qbuf, norm, stat)

            rbuf => fft_scratch%p3buf

            IF (test) THEN
               sum_data = ABS(SUM(qbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) T", sum_data
               END IF
            END IF

            ! Exchange data ( transpose of matrix )
            CALL cube_transpose_2(qbuf, bo(:, :, :, 1), bo(:, :, :, 2), rbuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(rbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) T", sum_data
               END IF
            END IF

            pbuf => fft_scratch%p4buf

            ! FFT along y
            CALL fft_1dm(fft_scratch%fft_plan(2), rbuf, pbuf, 1.0_dp, stat)

            qbuf => fft_scratch%p5buf

            IF (test) THEN
               sum_data = ABS(SUM(pbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) TS", sum_data
               END IF
            END IF

            ! Exchange data ( transpose of matrix ) and sort
            CALL xz_to_yz(pbuf, rs_group, r_dim, g_pos, p2p, yzp, nyzray, &
                          bo(:, :, :, 2), qbuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(qbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(5) TS", sum_data
               END IF
            END IF

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(3), qbuf, gin, 1.0_dp, stat)

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(6) ", sum_data
               END IF
            END IF

         ELSE IF (sign == BWFFT) THEN
            ! gin -> cin

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  Two step communication algorithm "
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), nyzray(g_pos)
                  WRITE (output_unit, '(A,T60,3I7)') "     Transform Y ", n(2), mx2*mz2
                  WRITE (output_unit, '(A,T60,3I7)') "     Transform Z ", n(3), mx1*my1
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            pbuf => fft_scratch%p7buf

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(4), gin, pbuf, norm, stat)

            qbuf => fft_scratch%p4buf

            IF (test) THEN
               sum_data = ABS(SUM(pbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) TS", sum_data
               END IF
            END IF

            ! Exchange data ( transpose of matrix ) and sort
            CALL yz_to_xz(pbuf, rs_group, r_dim, g_pos, p2p, yzp, nyzray, &
                          bo(:, :, :, 2), qbuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(qbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) TS", sum_data
               END IF
            END IF

            rbuf => fft_scratch%p3buf

            ! FFT along y
            CALL fft_1dm(fft_scratch%fft_plan(5), qbuf, rbuf, 1.0_dp, stat)

            pbuf => fft_scratch%p2buf

            IF (test) THEN
               sum_data = ABS(SUM(rbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) T", sum_data
               END IF
            END IF

            ! Exchange data ( transpose of matrix )
            CALL cube_transpose_1(rbuf, bo(:, :, :, 2), bo(:, :, :, 1), pbuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(pbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(5) T", sum_data
               END IF
            END IF

            qbuf => fft_scratch%p1buf

            ! FFT along z
            CALL fft_1dm(fft_scratch%fft_plan(6), pbuf, cin, 1.0_dp, stat)

            IF (test) THEN
               sum_data = ABS(SUM(cin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(6) ", sum_data
               END IF
            END IF

         ELSE

            CPABORT("Illegal fsign parameter.")

         ENDIF

         CALL release_fft_scratch(fft_scratch)

      ELSE

         !
         ! real space is only distributed over x coordinate
         ! we have one stage of communication, after the transform of
         ! direction x
         !

         CALL get_fft_scratch(fft_scratch, tf_type=200, n=n, fft_sizes=fft_scratch_size)

         sbuf => fft_scratch%r1buf
         tbuf => fft_scratch%tbuf

         CALL zero_c(sbuf)
         CALL zero_c(tbuf)

         IF (sign == FWFFT) THEN
            ! cin -> gin

            IF (test) THEN
               sum_data = ABS(SUM(cin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "     One step communication algorithm "
                  WRITE (output_unit, '(A,T60,3I7)') "     Transform YZ ", n(2), n(3), nx
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), nyzray(g_pos)
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            ! FFT along y and z
            CALL fft_1dm(fft_scratch%fft_plan(1), cin, sbuf, 1._dp, stat)
            CALL fft_1dm(fft_scratch%fft_plan(2), sbuf, tbuf, 1._dp, stat)

            IF (test) THEN
               sum_data = ABS(SUM(tbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) TS", sum_data
               END IF
            END IF

            ! Exchange data ( transpose of matrix ) and sort
            CALL yz_to_x(tbuf, gs_group, g_pos, p2p, yzp, nyzray, &
                         bo(:, :, :, 2), sbuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(sbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) TS", sum_data
               END IF
            END IF
            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(3), sbuf, gin, norm, stat)

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) ", sum_data
               END IF
            END IF

         ELSE IF (sign == BWFFT) THEN
            ! gin -> cin

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  One step communication algorithm "
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), nyzray(g_pos)
                  WRITE (output_unit, '(A,T60,3I7)') "     Transform YZ ", n(2), n(3), nx
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(4), gin, sbuf, norm, stat)

            IF (test) THEN
               sum_data = ABS(SUM(sbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) TS", sum_data
               END IF
            END IF

            ! Exchange data ( transpose of matrix ) and sort
            CALL x_to_yz(sbuf, gs_group, g_pos, p2p, yzp, nyzray, &
                         bo(:, :, :, 2), tbuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(tbuf))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) TS", sum_data
               END IF
            END IF

            ! FFT along y and z
            CALL fft_1dm(fft_scratch%fft_plan(5), tbuf, sbuf, 1._dp, stat)
            CALL fft_1dm(fft_scratch%fft_plan(6), sbuf, cin, 1._dp, stat)

            IF (test) THEN
               sum_data = ABS(SUM(cin))
               CALL mp_sum(sum_data, gs_group)
               IF (g_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) ", sum_data
               END IF
            END IF
         ELSE
            CPABORT("Illegal fsign parameter.")
         ENDIF

         CALL release_fft_scratch(fft_scratch)

      ENDIF

      DEALLOCATE (p2p)

      IF (PRESENT(status)) THEN
         status = stat
      END IF
      CALL timestop(handle)

   END SUBROUTINE fft3d_ps

! **************************************************************************************************
!> \brief ...
!> \param fsign ...
!> \param n ...
!> \param zin ...
!> \param gin ...
!> \param group ...
!> \param bo ...
!> \param scale ...
!> \param status ...
!> \param debug ...
! **************************************************************************************************
   SUBROUTINE fft3d_pb(fsign, n, zin, gin, group, bo, scale, status, debug)

      INTEGER, INTENT(IN)                                :: fsign
      INTEGER, DIMENSION(3), INTENT(IN)                  :: n
      COMPLEX(KIND=dp), DIMENSION(:, :, :), &
         INTENT(INOUT)                                   :: zin
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(INOUT)   :: gin
      INTEGER, INTENT(IN)                                :: group
      INTEGER, DIMENSION(:, :, 0:, :), INTENT(IN)        :: bo
      REAL(KIND=dp), INTENT(IN), OPTIONAL                :: scale
      INTEGER, INTENT(OUT), OPTIONAL                     :: status
      LOGICAL, INTENT(IN), OPTIONAL                      :: debug

      CHARACTER(len=*), PARAMETER :: routineN = 'fft3d_pb', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: abuf, bbuf
      INTEGER                                            :: handle, lg(2), lz(3), mcx2, mcy3, mcz1, &
                                                            mcz2, mx1, mx2, mx3, my1, my2, my3, &
                                                            my_pos, mz1, mz2, mz3, np, &
                                                            output_unit, sign, stat
      INTEGER, DIMENSION(2)                              :: dim, pos
      LOGICAL                                            :: test
      REAL(KIND=dp)                                      :: norm, sum_data
      TYPE(fft_scratch_sizes)                            :: fft_scratch_size
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

!------------------------------------------------------------------------------
! "Real Space"  1) xyZ      or      1) xYZ
!               2) xYz      or         not used
! "G Space"     3) Xyz      or      3) XYz
!
! There is one communicator (2-dimensional) for all distributions
! np = n1 * n2, where np is the total number of processors
! If n2 = 1, we have the second case and only one transpose step is needed
!
! Assignment of dimensions to axis for different steps
! First case: 1) n1=x; n2=y
!             2) n1=x; n2=z
!             3) n1=y; n2=z
! Second case 1) n1=x
!             3) n1=z
!
! The more general case with two communicators for the initial and final
! distribution is not covered.
!------------------------------------------------------------------------------

      CALL timeset(routineN, handle)
      output_unit = cp_logger_get_default_io_unit()

      CALL mp_environ(np, dim, pos, group)
      CALL mp_cart_rank(group, pos, my_pos)

      IF (PRESENT(debug)) THEN
         test = debug
      ELSE
         test = .FALSE.
      END IF

      IF (PRESENT(scale)) THEN
         norm = scale
      ELSE
         norm = 1.0_dp
      END IF

      sign = fsign

      IF (test) THEN
         lg(1) = SIZE(gin, 1)
         lg(2) = SIZE(gin, 2)
         lz(1) = SIZE(zin, 1)
         lz(2) = SIZE(zin, 2)
         lz(3) = SIZE(zin, 3)
         IF (my_pos == 0 .AND. output_unit > 0) THEN
            WRITE (output_unit, '(A)') "  Parallel 3D FFT : fft3d_pb"
            WRITE (output_unit, '(A,T60,3I7)') "     Transform lengths ", n
            WRITE (output_unit, '(A,T67,2I7)') "     Array dimensions (gin) ", lg
            WRITE (output_unit, '(A,T60,3I7)') "     Array dimensions (cin) ", lz
         END IF
      END IF

      mx1 = bo(2, 1, my_pos, 1)-bo(1, 1, my_pos, 1)+1
      my1 = bo(2, 2, my_pos, 1)-bo(1, 2, my_pos, 1)+1
      mz1 = bo(2, 3, my_pos, 1)-bo(1, 3, my_pos, 1)+1
      mx2 = bo(2, 1, my_pos, 2)-bo(1, 1, my_pos, 2)+1
      my2 = bo(2, 2, my_pos, 2)-bo(1, 2, my_pos, 2)+1
      mz2 = bo(2, 3, my_pos, 2)-bo(1, 3, my_pos, 2)+1
      mx3 = bo(2, 1, my_pos, 3)-bo(1, 1, my_pos, 3)+1
      my3 = bo(2, 2, my_pos, 3)-bo(1, 2, my_pos, 3)+1
      mz3 = bo(2, 3, my_pos, 3)-bo(1, 3, my_pos, 3)+1
      fft_scratch_size%mx1 = mx1
      fft_scratch_size%mx2 = mx2
      fft_scratch_size%mx3 = mx3
      fft_scratch_size%my1 = my1
      fft_scratch_size%my2 = my2
      fft_scratch_size%my3 = my3
      fft_scratch_size%mz1 = mz1
      fft_scratch_size%mz2 = mz2
      fft_scratch_size%mz3 = mz3
      mcz1 = MAXVAL(bo(2, 3, :, 1)-bo(1, 3, :, 1)+1)
      mcx2 = MAXVAL(bo(2, 1, :, 2)-bo(1, 1, :, 2)+1)
      mcz2 = MAXVAL(bo(2, 3, :, 2)-bo(1, 3, :, 2)+1)
      mcy3 = MAXVAL(bo(2, 2, :, 3)-bo(1, 2, :, 3)+1)
      fft_scratch_size%mcz1 = mcz1
      fft_scratch_size%mcx2 = mcx2
      fft_scratch_size%mcz2 = mcz2
      fft_scratch_size%mcy3 = mcy3
      fft_scratch_size%gs_group = group
      fft_scratch_size%rs_group = group
      fft_scratch_size%g_pos = my_pos
      fft_scratch_size%numtask = DIM(1)*DIM(2)

      IF (DIM(1) > 1 .AND. DIM(2) > 1) THEN

         !
         ! First case; two stages of communication
         !

         CALL get_fft_scratch(fft_scratch, tf_type=100, n=n, fft_sizes=fft_scratch_size)

         IF (sign == FWFFT) THEN
            ! Stage 1 -> 3

            bbuf => fft_scratch%a2buf

            IF (test) THEN
               sum_data = ABS(SUM(zin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  Two step communication algorithm "
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Z ", n(3), mx1*my1
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            ! FFT along z
            CALL fft_1dm(fft_scratch%fft_plan(1), zin, bbuf, norm, stat)

            abuf => fft_scratch%a3buf

            IF (test) THEN
               sum_data = ABS(SUM(bbuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) T", sum_data
               END IF
            END IF

            CALL cube_transpose_2(bbuf, bo(:, :, :, 1), bo(:, :, :, 2), abuf, fft_scratch)

            bbuf => fft_scratch%a4buf

            IF (test) THEN
               sum_data = ABS(SUM(abuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Y ", n(2), mx2*mz2
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) ", sum_data
               END IF
            END IF

            ! FFT along y
            CALL fft_1dm(fft_scratch%fft_plan(2), abuf, bbuf, 1.0_dp, stat)

            abuf => fft_scratch%a5buf

            IF (test) THEN
               sum_data = ABS(SUM(bbuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) T", sum_data
               END IF
            END IF

            CALL cube_transpose_4(bbuf, bo(:, :, :, 2), bo(:, :, :, 3), abuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(abuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), my3*mz3
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(5) ", sum_data
               END IF
            END IF

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(3), abuf, gin, 1.0_dp, stat)

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(6) ", sum_data
               END IF
            END IF

         ELSEIF (sign == BWFFT) THEN
            ! Stage 3 -> 1

            bbuf => fft_scratch%a5buf

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  Two step communication algorithm "
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), my3*mz3
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(4), gin, bbuf, 1.0_dp, stat)

            abuf => fft_scratch%a4buf

            IF (test) THEN
               sum_data = ABS(SUM(bbuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) T", sum_data
               END IF
            END IF

            CALL cube_transpose_3(bbuf, bo(:, :, :, 3), bo(:, :, :, 2), abuf, fft_scratch)

            bbuf => fft_scratch%a3buf

            IF (test) THEN
               sum_data = ABS(SUM(abuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Y ", n(2), mx2*mz2
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) ", sum_data
               END IF
            END IF

            ! FFT along y
            CALL fft_1dm(fft_scratch%fft_plan(5), abuf, bbuf, 1.0_dp, stat)

            abuf => fft_scratch%a2buf

            IF (test) THEN
               sum_data = ABS(SUM(bbuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) T", sum_data
               END IF
            END IF

            CALL cube_transpose_1(bbuf, bo(:, :, :, 2), bo(:, :, :, 1), abuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(abuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Z ", n(3), mx1*my1
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(5) ", sum_data
               END IF
            END IF

            ! FFT along z
            CALL fft_1dm(fft_scratch%fft_plan(6), abuf, zin, norm, stat)

            IF (test) THEN
               sum_data = ABS(SUM(zin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(6) ", sum_data
               END IF
            END IF

         ELSE
            CPABORT("Illegal fsign parameter.")
         END IF

         CALL release_fft_scratch(fft_scratch)

      ELSEIF (DIM(2) == 1) THEN

         !
         ! Second case; one stage of communication
         !

         CALL get_fft_scratch(fft_scratch, tf_type=101, n=n, fft_sizes=fft_scratch_size)

         IF (sign == FWFFT) THEN
            ! Stage 1 -> 3

            IF (test) THEN
               sum_data = ABS(SUM(zin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  one step communication algorithm "
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Z ", n(3), mx1*my1
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Y ", n(2), mx1*mz1
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            abuf => fft_scratch%a3buf
            bbuf => fft_scratch%a4buf
            ! FFT along z and y
            CALL fft_1dm(fft_scratch%fft_plan(1), zin, abuf, norm, stat)
            CALL fft_1dm(fft_scratch%fft_plan(2), abuf, bbuf, 1.0_dp, stat)

            abuf => fft_scratch%a5buf

            IF (test) THEN
               sum_data = ABS(SUM(bbuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) T", sum_data
               END IF
            END IF

            CALL cube_transpose_6(bbuf, group, bo(:, :, :, 1), bo(:, :, :, 3), abuf, fft_scratch)

            IF (test) THEN
               sum_data = ABS(SUM(abuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), my3*mz3
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) ", sum_data
               END IF
            END IF

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(3), abuf, gin, 1.0_dp, stat)

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) ", sum_data
               END IF
            END IF

         ELSEIF (sign == BWFFT) THEN
            ! Stage 3 -> 1

            IF (test) THEN
               sum_data = ABS(SUM(gin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A)') "  one step communication algorithm "
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform X ", n(1), my3*mz3
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(1) ", sum_data
               END IF
            END IF

            bbuf => fft_scratch%a5buf

            ! FFT along x
            CALL fft_1dm(fft_scratch%fft_plan(4), gin, bbuf, 1.0_dp, stat)

            abuf => fft_scratch%a4buf

            IF (test) THEN
               sum_data = ABS(SUM(bbuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(2) T", sum_data
               END IF
            END IF

            CALL cube_transpose_5(bbuf, group, bo(:, :, :, 3), bo(:, :, :, 1), abuf, fft_scratch)

            bbuf => fft_scratch%a3buf

            IF (test) THEN
               sum_data = ABS(SUM(abuf))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Y ", n(2), mx1*mz1
                  WRITE (output_unit, '(A,T67,2I7)') "     Transform Z ", n(3), mx1*my1
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(3) ", sum_data
               END IF
            END IF

            ! FFT along y
            CALL fft_1dm(fft_scratch%fft_plan(5), abuf, bbuf, 1.0_dp, stat)

            ! FFT along z
            CALL fft_1dm(fft_scratch%fft_plan(6), bbuf, zin, norm, stat)

            IF (test) THEN
               sum_data = ABS(SUM(zin))
               CALL mp_sum(sum_data, group)
               IF (my_pos == 0 .AND. output_unit > 0) THEN
                  WRITE (output_unit, '(A,T61,E20.14)') "     Sum of data(4) ", sum_data
               END IF
            END IF

         ELSE
            CPABORT("Illegal fsign parameter.")
         ENDIF

         CALL release_fft_scratch(fft_scratch)

      ELSE

         CPABORT("This partition not implemented.")

      END IF

      IF (PRESENT(status)) THEN
         status = stat
      END IF

      CALL timestop(handle)

   END SUBROUTINE fft3d_pb

! **************************************************************************************************
!> \brief ...
!> \param sb ...
!> \param group ...
!> \param my_pos ...
!> \param p2p ...
!> \param yzp ...
!> \param nray ...
!> \param bo ...
!> \param tb ...
!> \param fft_scratch ...
!> \par History
!>      15. Feb. 2006 : single precision all_to_all
!> \author JGH (14-Jan-2001)
! **************************************************************************************************
   SUBROUTINE x_to_yz(sb, group, my_pos, p2p, yzp, nray, bo, tb, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: sb
      INTEGER, INTENT(IN)                                :: group, my_pos
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: p2p
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: yzp
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: nray
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: bo
      COMPLEX(KIND=dp), DIMENSION(:, :, :), &
         INTENT(INOUT)                                   :: tb
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'x_to_yz', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rr
      COMPLEX(KIND=sp), DIMENSION(:, :), POINTER         :: ss, tt
      INTEGER                                            :: handle, ip, ir, ix, ixx, iy, iz, mpr, &
                                                            nm, np, nr, nx
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl

      CALL timeset(routineN, handle)

      np = SIZE(p2p)
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl

      IF (alltoall_sgl) THEN
         ss => fft_scratch%ss
         tt => fft_scratch%tt
         ss(:, :) = CMPLX(sb(:, :), KIND=sp)
         tt(:, :) = 0._sp
      ELSE
         rr => fft_scratch%rr
      END IF

      mpr = p2p(my_pos)
      nm = MAXVAL(nray(0:np-1))
      nr = nray(my_pos)
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ix,nx), &
!$OMP             SHARED(np,p2p,bo,nr,scount,sdispl)
      DO ip = 0, np-1
         ix = p2p(ip)
         nx = bo(2, 1, ix)-bo(1, 1, ix)+1
         scount(ip) = nr*nx
         sdispl(ip) = nr*(bo(1, 1, ix)-1)
      END DO
!$OMP END PARALLEL DO
      nx = bo(2, 1, mpr)-bo(1, 1, mpr)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(nr), &
!$OMP             SHARED(np,nray,nx,rcount,rdispl,nm)
      DO ip = 0, np-1
         nr = nray(ip)
         rcount(ip) = nr*nx
         rdispl(ip) = nm*nx*ip
      END DO
!$OMP END PARALLEL DO
      IF (alltoall_sgl) THEN
         CALL mp_alltoall(ss, scount, sdispl, tt, rcount, rdispl, group)
      ELSE
         CALL mp_alltoall(sb, scount, sdispl, rr, rcount, rdispl, group)
      END IF

      nx = bo(2, 1, mpr)-bo(1, 1, mpr)+1
!$OMP PARALLEL DO DEFAULT(NONE) COLLAPSE(2) &
!$OMP             PRIVATE(ixx,ir,iy,iz,ix) &
!$OMP             SHARED(np,nray,nx,alltoall_sgl,yzp,tt,rr,tb)
      DO ip = 0, np-1
         DO ix = 1, nx
            ixx = nray(ip)*(ix-1)
            IF (alltoall_sgl) THEN
               DO ir = 1, nray(ip)
                  iy = yzp(1, ir, ip)
                  iz = yzp(2, ir, ip)
                  tb(iy, iz, ix) = tt(ir+ixx, ip)
               END DO
            ELSE
               DO ir = 1, nray(ip)
                  iy = yzp(1, ir, ip)
                  iz = yzp(2, ir, ip)
                  tb(iy, iz, ix) = rr(ir+ixx, ip)
               END DO
            END IF
         END DO
      END DO
!$OMP END PARALLEL DO

      CALL timestop(handle)

   END SUBROUTINE x_to_yz

! **************************************************************************************************
!> \brief ...
!> \param tb ...
!> \param group ...
!> \param my_pos ...
!> \param p2p ...
!> \param yzp ...
!> \param nray ...
!> \param bo ...
!> \param sb ...
!> \param fft_scratch ...
!> \par History
!>      15. Feb. 2006 : single precision all_to_all
!> \author JGH (14-Jan-2001)
! **************************************************************************************************
   SUBROUTINE yz_to_x(tb, group, my_pos, p2p, yzp, nray, bo, sb, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :, :), INTENT(IN)   :: tb
      INTEGER, INTENT(IN)                                :: group, my_pos
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: p2p
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: yzp
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: nray
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: bo
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(INOUT)   :: sb
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'yz_to_x', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rr
      COMPLEX(KIND=sp), DIMENSION(:, :), POINTER         :: ss, tt
      INTEGER                                            :: handle, ip, ir, ix, ixx, iy, iz, mpr, &
                                                            nm, np, nr, nx
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl

      CALL timeset(routineN, handle)

      np = SIZE(p2p)
      mpr = p2p(my_pos)
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl

      IF (alltoall_sgl) THEN
         ss => fft_scratch%ss
         tt => fft_scratch%tt
         ss = 0._sp
         tt = 0._sp
      ELSE
         rr => fft_scratch%rr
      END IF

      nx = bo(2, 1, mpr)-bo(1, 1, mpr)+1
!$OMP PARALLEL DO DEFAULT(NONE) COLLAPSE(2) &
!$OMP             PRIVATE(ip, ixx, ir, iy, iz, ix) &
!$OMP             SHARED(np,nray,nx,alltoall_sgl,yzp,tb,tt,rr)
      DO ip = 0, np-1
         DO ix = 1, nx
            ixx = nray(ip)*(ix-1)
            IF (alltoall_sgl) THEN
               DO ir = 1, nray(ip)
                  iy = yzp(1, ir, ip)
                  iz = yzp(2, ir, ip)
                  tt(ir+ixx, ip) = CMPLX(tb(iy, iz, ix), KIND=sp)
               END DO
            ELSE
               DO ir = 1, nray(ip)
                  iy = yzp(1, ir, ip)
                  iz = yzp(2, ir, ip)
                  rr(ir+ixx, ip) = tb(iy, iz, ix)
               END DO
            END IF
         END DO
      END DO
!$OMP END PARALLEL DO
      nm = MAXVAL(nray(0:np-1))
      nr = nray(my_pos)
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ix,nx), &
!$OMP             SHARED(np,p2p,bo,rcount,rdispl,nr)
      DO ip = 0, np-1
         ix = p2p(ip)
         nx = bo(2, 1, ix)-bo(1, 1, ix)+1
         rcount(ip) = nr*nx
         rdispl(ip) = nr*(bo(1, 1, ix)-1)
      END DO
!$OMP END PARALLEL DO
      nx = bo(2, 1, mpr)-bo(1, 1, mpr)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(nr), &
!$OMP             SHARED(np,nray,scount,sdispl,nx,nm)
      DO ip = 0, np-1
         nr = nray(ip)
         scount(ip) = nr*nx
         sdispl(ip) = nm*nx*ip
      END DO
!$OMP END PARALLEL DO

      IF (alltoall_sgl) THEN
         CALL mp_alltoall(tt, scount, sdispl, ss, rcount, rdispl, group)
         sb = ss
      ELSE
         CALL mp_alltoall(rr, scount, sdispl, sb, rcount, rdispl, group)
      END IF

      CALL timestop(handle)

   END SUBROUTINE yz_to_x

! **************************************************************************************************
!> \brief ...
!> \param sb ...
!> \param group ...
!> \param dims ...
!> \param my_pos ...
!> \param p2p ...
!> \param yzp ...
!> \param nray ...
!> \param bo ...
!> \param tb ...
!> \param fft_scratch ...
!> \par History
!>      15. Feb. 2006 : single precision all_to_all
!> \author JGH (18-Jan-2001)
! **************************************************************************************************
   SUBROUTINE yz_to_xz(sb, group, dims, my_pos, p2p, yzp, nray, bo, tb, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: sb
      INTEGER, INTENT(IN)                                :: group
      INTEGER, DIMENSION(2), INTENT(IN)                  :: dims
      INTEGER, INTENT(IN)                                :: my_pos
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: p2p
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: yzp
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: nray
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: bo
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(INOUT)   :: tb
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'yz_to_xz', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:), POINTER            :: xzbuf, yzbuf
      COMPLEX(KIND=sp), DIMENSION(:), POINTER            :: xzbuf_sgl, yzbuf_sgl
      INTEGER                                            :: handle, icrs, ip, ipl, ipr, ir, ix, iz, &
                                                            jj, jx, jy, jz, myx, myz, np, npx, &
                                                            npz, nx, nz, rs_pos
      INTEGER, DIMENSION(:), POINTER                     :: pzcoord, rcount, rdispl, scount, sdispl, &
                                                            xcor, zcor
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid

      CALL timeset(routineN, handle)

      np = SIZE(p2p)

      rs_pos = p2p(my_pos)

      IF (alltoall_sgl) THEN
         yzbuf_sgl => fft_scratch%yzbuf_sgl
         xzbuf_sgl => fft_scratch%xzbuf_sgl
      ELSE
         yzbuf => fft_scratch%yzbuf
         xzbuf => fft_scratch%xzbuf
      END IF
      npx = dims(1)
      npz = dims(2)
      pgrid => fft_scratch%pgrid
      xcor => fft_scratch%xcor
      zcor => fft_scratch%zcor
      pzcoord => fft_scratch%pzcoord
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl

      nx = SIZE(sb, 2)

! If the send and recv counts are not already cached, then
! calculate and store them
      IF (fft_scratch%in == 0) THEN

         scount = 0

         DO ix = 0, npx-1
            ip = pgrid(ix, 0)
            xcor(bo(1, 1, ip):bo(2, 1, ip)) = ix
         END DO
         DO iz = 0, npz-1
            ip = pgrid(0, iz)
            zcor(bo(1, 3, ip):bo(2, 3, ip)) = iz
         END DO
         DO jx = 1, nx
            IF (alltoall_sgl) THEN
               DO ir = 1, nray(my_pos)
                  jy = yzp(1, ir, my_pos)
                  jz = yzp(2, ir, my_pos)
                  ip = pgrid(xcor(jx), zcor(jz))
                  scount(ip) = scount(ip)+1
               END DO
            ELSE
               DO ir = 1, nray(my_pos)
                  jy = yzp(1, ir, my_pos)
                  jz = yzp(2, ir, my_pos)
                  ip = pgrid(xcor(jx), zcor(jz))
                  scount(ip) = scount(ip)+1
               END DO
            END IF
         END DO

         CALL mp_alltoall(scount, rcount, 1, group)
         fft_scratch%yzcount = scount
         fft_scratch%xzcount = rcount

         ! Work out the correct displacements in the buffers
         sdispl(0) = 0
         rdispl(0) = 0
         DO ip = 1, np-1
            sdispl(ip) = sdispl(ip-1)+scount(ip-1)
            rdispl(ip) = rdispl(ip-1)+rcount(ip-1)
         END DO

         fft_scratch%yzdispl = sdispl
         fft_scratch%xzdispl = rdispl

         icrs = 0
         DO ip = 0, np-1
            IF (scount(ip) /= 0) icrs = icrs+1
            IF (rcount(ip) /= 0) icrs = icrs+1
         END DO
         CALL mp_sum(icrs, group)
         fft_scratch%rsratio = REAL(icrs, KIND=dp)/(REAL(2*np, KIND=dp)*REAL(np, KIND=dp))

         fft_scratch%in = 1
      ELSE
         scount = fft_scratch%yzcount
         rcount = fft_scratch%xzcount
         sdispl = fft_scratch%yzdispl
         rdispl = fft_scratch%xzdispl
      END IF

! Do the actual packing
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl,jj,nx,ir,jx,jy,jz),&
!$OMP             SHARED(np,p2p,pzcoord,bo,nray,yzp,zcor),&
!$OMP             SHARED(yzbuf,sb,scount,sdispl,my_pos),&
!$OMP             SHARED(yzbuf_sgl,alltoall_sgl)
      DO ip = 0, np-1
         IF (scount(ip) == 0) CYCLE
         ipl = p2p(ip)
         jj = 0
         nx = bo(2, 1, ipl)-bo(1, 1, ipl)+1
         DO ir = 1, nray(my_pos)
            jz = yzp(2, ir, my_pos)
            IF (zcor(jz) == pzcoord(ipl)) THEN
               jj = jj+1
               jy = yzp(1, ir, my_pos)
               IF (alltoall_sgl) THEN
                  DO jx = 0, nx-1
                     yzbuf_sgl(sdispl(ip)+jj+jx*scount(ip)/nx) = CMPLX(sb(ir, jx+bo(1, 1, ipl)), KIND=sp)
                  END DO
               ELSE
                  DO jx = 0, nx-1
                     yzbuf(sdispl(ip)+jj+jx*scount(ip)/nx) = sb(ir, jx+bo(1, 1, ipl))
                  END DO
               END IF
            END IF
         END DO
      END DO
!$OMP END PARALLEL DO

      IF (alltoall_sgl) THEN
         CALL mp_alltoall(yzbuf_sgl, scount, sdispl, xzbuf_sgl, rcount, rdispl, group)
      ELSE
         IF (fft_scratch%rsratio < ratio_sparse_alltoall) THEN
            CALL sparse_alltoall(yzbuf, scount, sdispl, xzbuf, rcount, rdispl, group)
         ELSE
            CALL mp_alltoall(yzbuf, scount, sdispl, xzbuf, rcount, rdispl, group)
         END IF
      END IF

      myx = fft_scratch%sizes%r_pos(1)
      myz = fft_scratch%sizes%r_pos(2)
      nz = bo(2, 3, rs_pos)-bo(1, 3, rs_pos)+1

!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipr,jj,ir,jx,jy,jz),&
!$OMP             SHARED(tb,np,p2p,bo,rs_pos,nray),&
!$OMP             SHARED(yzp,alltoall_sgl,zcor,myz),&
!$OMP             SHARED(xzbuf,xzbuf_sgl,nz,rdispl)
      DO ip = 0, np-1
         ipr = p2p(ip)
         jj = 0
         DO jx = 0, bo(2, 1, rs_pos)-bo(1, 1, rs_pos)
            DO ir = 1, nray(ip)
               jz = yzp(2, ir, ip)
               IF (alltoall_sgl) THEN
                  IF (zcor(jz) == myz) THEN
                     jj = jj+1
                     jy = yzp(1, ir, ip)
                     jz = jz-bo(1, 3, rs_pos)+1
                     tb(jy, jz+jx*nz) = xzbuf_sgl(jj+rdispl(ipr))
                  END IF
               ELSE
                  IF (zcor(jz) == myz) THEN
                     jj = jj+1
                     jy = yzp(1, ir, ip)
                     jz = jz-bo(1, 3, rs_pos)+1
                     tb(jy, jz+jx*nz) = xzbuf(jj+rdispl(ipr))
                  END IF
               END IF
            END DO
         END DO
      END DO
!$OMP END PARALLEL DO

      CALL timestop(handle)

   END SUBROUTINE yz_to_xz

! **************************************************************************************************
!> \brief ...
!> \param sb ...
!> \param group ...
!> \param dims ...
!> \param my_pos ...
!> \param p2p ...
!> \param yzp ...
!> \param nray ...
!> \param bo ...
!> \param tb ...
!> \param fft_scratch ...
!> \par History
!>      15. Feb. 2006 : single precision all_to_all
!> \author JGH (19-Jan-2001)
! **************************************************************************************************
   SUBROUTINE xz_to_yz(sb, group, dims, my_pos, p2p, yzp, nray, bo, tb, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: sb
      INTEGER, INTENT(IN)                                :: group
      INTEGER, DIMENSION(2), INTENT(IN)                  :: dims
      INTEGER, INTENT(IN)                                :: my_pos
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: p2p
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: yzp
      INTEGER, DIMENSION(0:), INTENT(IN)                 :: nray
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: bo
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(INOUT)   :: tb
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'xz_to_yz', routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:), POINTER            :: xzbuf, yzbuf
      COMPLEX(KIND=sp), DIMENSION(:), POINTER            :: xzbuf_sgl, yzbuf_sgl
      INTEGER                                            :: handle, icrs, ip, ipl, ir, ix, ixx, iz, &
                                                            jj, jx, jy, jz, mp, myx, myz, np, npx, &
                                                            npz, nx, nz
      INTEGER, DIMENSION(:), POINTER                     :: pzcoord, rcount, rdispl, scount, sdispl, &
                                                            xcor, zcor
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid

      CALL timeset(routineN, handle)

      np = SIZE(p2p)

      IF (alltoall_sgl) THEN
         yzbuf_sgl => fft_scratch%yzbuf_sgl
         xzbuf_sgl => fft_scratch%xzbuf_sgl
      ELSE
         yzbuf => fft_scratch%yzbuf
         xzbuf => fft_scratch%xzbuf
      END IF
      npx = dims(1)
      npz = dims(2)
      pgrid => fft_scratch%pgrid
      xcor => fft_scratch%xcor
      zcor => fft_scratch%zcor
      pzcoord => fft_scratch%pzcoord
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl

! If the send and recv counts are not already cached, then
! calculate and store them
      IF (fft_scratch%in == 0) THEN

         rcount = 0
         nx = MAXVAL(bo(2, 1, :))

         DO ix = 0, npx-1
            ip = pgrid(ix, 0)
            xcor(bo(1, 1, ip):bo(2, 1, ip)) = ix
         END DO
         DO iz = 0, npz-1
            ip = pgrid(0, iz)
            zcor(bo(1, 3, ip):bo(2, 3, ip)) = iz
         END DO
         DO jx = 1, nx
            DO ir = 1, nray(my_pos)
               jy = yzp(1, ir, my_pos)
               jz = yzp(2, ir, my_pos)
               ip = pgrid(xcor(jx), zcor(jz))
               rcount(ip) = rcount(ip)+1
            END DO
         END DO

         CALL mp_alltoall(rcount, scount, 1, group)
         fft_scratch%xzcount = scount
         fft_scratch%yzcount = rcount

         ! Work out the correct displacements in the buffers
         sdispl(0) = 0
         rdispl(0) = 0
         DO ip = 1, np-1
            sdispl(ip) = sdispl(ip-1)+scount(ip-1)
            rdispl(ip) = rdispl(ip-1)+rcount(ip-1)
         END DO

         fft_scratch%xzdispl = sdispl
         fft_scratch%yzdispl = rdispl

         icrs = 0
         DO ip = 0, np-1
            IF (scount(ip) /= 0) icrs = icrs+1
            IF (rcount(ip) /= 0) icrs = icrs+1
         END DO
         CALL mp_sum(icrs, group)
         fft_scratch%rsratio = REAL(icrs, KIND=dp)/(REAL(2*np, KIND=dp)*REAL(np, KIND=dp))

         fft_scratch%in = 1
      ELSE
         scount = fft_scratch%xzcount
         rcount = fft_scratch%yzcount
         sdispl = fft_scratch%xzdispl
         rdispl = fft_scratch%yzdispl
      END IF

! Now do the actual packing
      myx = fft_scratch%sizes%r_pos(1)
      myz = fft_scratch%sizes%r_pos(2)
      mp = p2p(my_pos)
      nz = bo(2, 3, mp)-bo(1, 3, mp)+1
      nx = bo(2, 1, mp)-bo(1, 1, mp)+1

!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(jj,ipl,ir,jx,jy,jz,ixx),&
!$OMP             SHARED(np,p2p,nray,yzp,zcor,myz,bo,mp),&
!$OMP             SHARED(alltoall_sgl,nx,scount,sdispl),&
!$OMP             SHARED(xzbuf,xzbuf_sgl,sb,nz)
      DO ip = 0, np-1
         jj = 0
         ipl = p2p(ip)
         DO ir = 1, nray(ip)
            jz = yzp(2, ir, ip)
            IF (zcor(jz) == myz) THEN
               jj = jj+1
               jy = yzp(1, ir, ip)
               jz = yzp(2, ir, ip)-bo(1, 3, mp)+1
               IF (alltoall_sgl) THEN
                  DO jx = 0, nx-1
                     ixx = jj+jx*scount(ipl)/nx
                     xzbuf_sgl(ixx+sdispl(ipl)) = CMPLX(sb(jy, jz+jx*nz), KIND=sp)
                  END DO
               ELSE
                  DO jx = 0, nx-1
                     ixx = jj+jx*scount(ipl)/nx
                     xzbuf(ixx+sdispl(ipl)) = sb(jy, jz+jx*nz)
                  END DO
               END IF
            END IF
         END DO
      END DO
!$OMP END PARALLEL DO

      IF (alltoall_sgl) THEN
         CALL mp_alltoall(xzbuf_sgl, scount, sdispl, yzbuf_sgl, rcount, rdispl, group)
      ELSE
         IF (fft_scratch%rsratio < ratio_sparse_alltoall) THEN
            CALL sparse_alltoall(xzbuf, scount, sdispl, yzbuf, rcount, rdispl, group)
         ELSE
            CALL mp_alltoall(xzbuf, scount, sdispl, yzbuf, rcount, rdispl, group)
         END IF
      END IF

!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl,jj,nx,ir,jx,jy,jz),&
!$OMP             SHARED(p2p,pzcoord,bo,nray,my_pos,yzp),&
!$OMP             SHARED(rcount,rdispl,tb,yzbuf,zcor),&
!$OMP             SHARED(yzbuf_sgl,alltoall_sgl,np)
      DO ip = 0, np-1
         IF (rcount(ip) == 0) CYCLE
         ipl = p2p(ip)
         jj = 0
         nx = bo(2, 1, ipl)-bo(1, 1, ipl)+1
         DO ir = 1, nray(my_pos)
            jz = yzp(2, ir, my_pos)
            IF (zcor(jz) == pzcoord(ipl)) THEN
               jj = jj+1
               jy = yzp(1, ir, my_pos)
               IF (alltoall_sgl) THEN
                  DO jx = 0, nx-1
                     tb(ir, jx+bo(1, 1, ipl)) = yzbuf_sgl(rdispl(ip)+jj+jx*rcount(ip)/nx)
                  END DO
               ELSE
                  DO jx = 0, nx-1
                     tb(ir, jx+bo(1, 1, ipl)) = yzbuf(rdispl(ip)+jj+jx*rcount(ip)/nx)
                  END DO
               END IF
            END IF
         END DO
      END DO
!$OMP END PARALLEL DO

      CALL timestop(handle)

   END SUBROUTINE xz_to_yz

! **************************************************************************************************
!> \brief ...
!> \param cin ...
!> \param boin ...
!> \param boout ...
!> \param sout ...
!> \param fft_scratch ...
!> \par History
!>      none
!> \author JGH (20-Jan-2001)
! **************************************************************************************************
   SUBROUTINE cube_transpose_1(cin, boin, boout, sout, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: cin
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: boin, boout
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(OUT)     :: sout
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'cube_transpose_1', &
         routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rbuf
      INTEGER                                            :: handle, ip, ipl, ir, is, ixy, iz, mip, &
                                                            mz, np, nx, ny, nz, sub_group
      INTEGER, DIMENSION(2)                              :: dim, pos
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid

      CALL timeset(routineN, handle)

      sub_group = fft_scratch%cart_sub_comm(2)
      mip = fft_scratch%mip
      dim = fft_scratch%dim
      pos = fft_scratch%pos
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl
      pgrid => fft_scratch%pgcube
      np = DIM(2)

      nx = boin(2, 1, mip)-boin(1, 1, mip)+1
      nz = boin(2, 3, mip)-boin(1, 3, mip)+1

!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl,ny), &
!$OMP             SHARED(np,pgrid,boout,scount,sdispl,nx,nz)
      DO ip = 0, np-1
         ipl = pgrid(ip, 2)
         ny = boout(2, 2, ipl)-boout(1, 2, ipl)+1
         scount(ip) = nx*nz*ny
         sdispl(ip) = nx*nz*(boout(1, 2, ipl)-1)
      END DO
!$OMP END PARALLEL DO
      ny = boout(2, 2, mip)-boout(1, 2, mip)+1
      mz = MAXVAL(boin(2, 3, :)-boin(1, 3, :)+1)
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl,nz), &
!$OMP             SHARED(np,pgrid,boin,nx,ny,rcount,rdispl,mz)
      DO ip = 0, np-1
         ipl = pgrid(ip, 2)
         nz = boin(2, 3, ipl)-boin(1, 3, ipl)+1
         rcount(ip) = nx*nz*ny
         rdispl(ip) = nx*ny*mz*ip
      END DO
!$OMP END PARALLEL DO

      rbuf => fft_scratch%rbuf1

      CALL mp_alltoall(cin, scount, sdispl, rbuf, rcount, rdispl, sub_group)

!$OMP PARALLEL DO DEFAULT(NONE) COLLAPSE(2) &
!$OMP             PRIVATE(ip,ipl,nz,iz,is,ir) &
!$OMP             SHARED(nx,ny,np,pgrid,boin,sout,rbuf)
      DO ixy = 1, nx*ny
         DO ip = 0, np-1
            ipl = pgrid(ip, 2)
            nz = boin(2, 3, ipl)-boin(1, 3, ipl)+1
            DO iz = 1, nz
               is = boin(1, 3, ipl)+iz-1
               ir = iz+nz*(ixy-1)
               sout(is, ixy) = rbuf(ir, ip)
            END DO
         END DO
      END DO
!$OMP END PARALLEL DO

      CALL timestop(handle)

   END SUBROUTINE cube_transpose_1

! **************************************************************************************************
!> \brief ...
!> \param cin ...
!> \param boin ...
!> \param boout ...
!> \param sout ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE cube_transpose_2(cin, boin, boout, sout, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: cin
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: boin, boout
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(OUT)     :: sout
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'cube_transpose_2', &
         routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rbuf
      INTEGER                                            :: handle, ip, ipl, ir, ixy, iz, mip, mz, &
                                                            np, nx, ny, nz, sub_group
      INTEGER, DIMENSION(2)                              :: dim, pos
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid

      CALL timeset(routineN, handle)

      sub_group = fft_scratch%cart_sub_comm(2)
      mip = fft_scratch%mip
      dim = fft_scratch%dim
      pos = fft_scratch%pos
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl
      pgrid => fft_scratch%pgcube
      np = DIM(2)

      nx = boin(2, 1, mip)-boin(1, 1, mip)+1
      ny = boin(2, 2, mip)-boin(1, 2, mip)+1
      mz = MAXVAL(boout(2, 3, :)-boout(1, 3, :)+1)

      rbuf => fft_scratch%rbuf2

!$OMP PARALLEL DEFAULT(NONE), &
!$OMP          PRIVATE(ip,ipl,nz,iz,ir), &
!$OMP          SHARED(nx,ny,np,pgrid,boout,rbuf,cin,scount,sdispl,mz)
!$OMP DO COLLAPSE(2)
      DO ixy = 1, nx*ny
         DO ip = 0, np-1
            ipl = pgrid(ip, 2)
            nz = boout(2, 3, ipl)-boout(1, 3, ipl)+1
            DO iz = boout(1, 3, ipl), boout(2, 3, ipl)
               ir = iz-boout(1, 3, ipl)+1+(ixy-1)*nz
               rbuf(ir, ip) = cin(iz, ixy)
            END DO
         END DO
      END DO
!$OMP END DO
!$OMP DO
      DO ip = 0, np-1
         ipl = pgrid(ip, 2)
         nz = boout(2, 3, ipl)-boout(1, 3, ipl)+1
         scount(ip) = nx*ny*nz
         sdispl(ip) = nx*ny*mz*ip
      END DO
!$OMP END DO
!$OMP END PARALLEL
      nz = boout(2, 3, mip)-boout(1, 3, mip)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl,ny), &
!$OMP             SHARED(np,pgrid,boin,nx,nz,rcount,rdispl)
      DO ip = 0, np-1
         ipl = pgrid(ip, 2)
         ny = boin(2, 2, ipl)-boin(1, 2, ipl)+1
         rcount(ip) = nx*ny*nz
         rdispl(ip) = nx*nz*(boin(1, 2, ipl)-1)
      END DO
!$OMP END PARALLEL DO

      CALL mp_alltoall(rbuf, scount, sdispl, sout, rcount, rdispl, sub_group)

      CALL timestop(handle)

   END SUBROUTINE cube_transpose_2

! **************************************************************************************************
!> \brief ...
!> \param cin ...
!> \param boin ...
!> \param boout ...
!> \param sout ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE cube_transpose_3(cin, boin, boout, sout, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: cin
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: boin, boout
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(OUT)     :: sout
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'cube_transpose_3', &
         routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rbuf
      INTEGER                                            :: handle, ip, ipl, ir, is, ixz, iy, lb, &
                                                            mip, my, my_id, np, num_threads, nx, &
                                                            ny, nz, sub_group, ub
      INTEGER, DIMENSION(2)                              :: dim, pos
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid

      CALL timeset(routineN, handle)

      sub_group = fft_scratch%cart_sub_comm(1)
      mip = fft_scratch%mip
      dim = fft_scratch%dim
      pos = fft_scratch%pos
      np = DIM(1)
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl
      pgrid => fft_scratch%pgcube

      ny = boin(2, 2, mip)-boin(1, 2, mip)+1
      nz = boin(2, 3, mip)-boin(1, 3, mip)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl, nx), &
!$OMP             SHARED(np,pgrid,boout,ny,nz,scount,sdispl)
      DO ip = 0, np-1
         ipl = pgrid(ip, 1)
         nx = boout(2, 1, ipl)-boout(1, 1, ipl)+1
         scount(ip) = nx*nz*ny
         sdispl(ip) = ny*nz*(boout(1, 1, ipl)-1)
      END DO
!$OMP END PARALLEL DO
      nx = boout(2, 1, mip)-boout(1, 1, mip)+1
      my = MAXVAL(boin(2, 2, :)-boin(1, 2, :)+1)
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl, ny), &
!$OMP             SHARED(np,pgrid,boin,nx,nz,my,rcount,rdispl)
      DO ip = 0, np-1
         ipl = pgrid(ip, 1)
         ny = boin(2, 2, ipl)-boin(1, 2, ipl)+1
         rcount(ip) = nx*nz*ny
         rdispl(ip) = nx*my*nz*ip
      END DO
!$OMP END PARALLEL DO

      rbuf => fft_scratch%rbuf3
      num_threads = 1
      my_id = 0
!$OMP PARALLEL DEFAULT(NONE), &
!$OMP          PRIVATE(NUM_THREADS, my_id, lb, ub), &
!$OMP          SHARED(rbuf)
!$    num_threads = MIN(omp_get_max_threads(), SIZE(rbuf, 2))
!$    my_id = omp_get_thread_num()
      IF (my_id < num_threads) THEN
         lb = (SIZE(rbuf, 2)*my_id)/num_threads
         ub = (SIZE(rbuf, 2)*(my_id+1))/num_threads-1
         rbuf(:, lb:ub) = 0.0_dp
      END IF
!$OMP END PARALLEL

      CALL mp_alltoall(cin, scount, sdispl, rbuf, rcount, rdispl, sub_group)

!$OMP PARALLEL DO DEFAULT(NONE) COLLAPSE(2) &
!$OMP             PRIVATE(ip,ipl,ny,iy,is,ir) &
!$OMP             SHARED(nx,nz,np,pgrid,boin,rbuf,sout)
      DO ixz = 1, nx*nz
         DO ip = 0, np-1
            ipl = pgrid(ip, 1)
            ny = boin(2, 2, ipl)-boin(1, 2, ipl)+1
            DO iy = 1, ny
               is = boin(1, 2, ipl)+iy-1
               ir = iy+ny*(ixz-1)
               sout(is, ixz) = rbuf(ir, ip)
            END DO
         END DO
      END DO
!$OMP END PARALLEL DO

      CALL timestop(handle)

   END SUBROUTINE cube_transpose_3

! **************************************************************************************************
!> \brief ...
!> \param cin ...
!> \param boin ...
!> \param boout ...
!> \param sout ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE cube_transpose_4(cin, boin, boout, sout, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: cin
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: boin, boout
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(OUT)     :: sout
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'cube_transpose_4', &
         routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rbuf
      INTEGER                                            :: handle, ip, ipl, ir, iy, izx, lb, mip, &
                                                            my, my_id, np, num_threads, nx, ny, &
                                                            nz, sub_group, ub
      INTEGER, DIMENSION(2)                              :: dim, pos
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid

      CALL timeset(routineN, handle)

      sub_group = fft_scratch%cart_sub_comm(1)
      mip = fft_scratch%mip
      dim = fft_scratch%dim
      pos = fft_scratch%pos
      np = DIM(1)
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl
      pgrid => fft_scratch%pgcube

      nx = boin(2, 1, mip)-boin(1, 1, mip)+1
      nz = boin(2, 3, mip)-boin(1, 3, mip)+1
      my = MAXVAL(boout(2, 2, :)-boout(1, 2, :)+1)

      rbuf => fft_scratch%rbuf4
      num_threads = 1
      my_id = 0
!$OMP PARALLEL DEFAULT(NONE), &
!$OMP          PRIVATE(NUM_THREADS,my_id,lb,ub,ip,ipl,ny,iy,ir), &
!$OMP          SHARED(rbuf,nz,nx,np,pgrid,boout,cin,my,scount,sdispl)
!$    num_threads = MIN(omp_get_max_threads(), SIZE(rbuf, 2))
!$    my_id = omp_get_thread_num()
      IF (my_id < num_threads) THEN
         lb = (SIZE(rbuf, 2)*my_id)/num_threads
         ub = (SIZE(rbuf, 2)*(my_id+1))/num_threads-1
         rbuf(:, lb:ub) = 0.0_dp
      END IF
!$OMP BARRIER

!$OMP DO COLLAPSE(2)
      DO izx = 1, nz*nx
         DO ip = 0, np-1
            ipl = pgrid(ip, 1)
            ny = boout(2, 2, ipl)-boout(1, 2, ipl)+1
            DO iy = boout(1, 2, ipl), boout(2, 2, ipl)
               ir = iy-boout(1, 2, ipl)+1+(izx-1)*ny
               rbuf(ir, ip) = cin(iy, izx)
            END DO
         END DO
      END DO
!$OMP END DO
!$OMP DO
      DO ip = 0, np-1
         ipl = pgrid(ip, 1)
         ny = boout(2, 2, ipl)-boout(1, 2, ipl)+1
         scount(ip) = nx*ny*nz
         sdispl(ip) = nx*nz*my*ip
      END DO
!$OMP END DO
!$OMP END PARALLEL
      ny = boout(2, 2, mip)-boout(1, 2, mip)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ipl,nx), &
!$OMP             SHARED(np,pgrid,boin,rcount,rdispl,ny,nz)
      DO ip = 0, np-1
         ipl = pgrid(ip, 1)
         nx = boin(2, 1, ipl)-boin(1, 1, ipl)+1
         rcount(ip) = nx*ny*nz
         rdispl(ip) = ny*nz*(boin(1, 1, ipl)-1)
      END DO
!$OMP END PARALLEL DO

      CALL mp_alltoall(rbuf, scount, sdispl, sout, rcount, rdispl, sub_group)

      CALL timestop(handle)

   END SUBROUTINE cube_transpose_4

! **************************************************************************************************
!> \brief ...
!> \param cin ...
!> \param group ...
!> \param boin ...
!> \param boout ...
!> \param sout ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE cube_transpose_5(cin, group, boin, boout, sout, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: cin
      INTEGER, INTENT(IN)                                :: group
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: boin, boout
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(OUT)     :: sout
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'cube_transpose_5', &
         routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rbuf
      INTEGER                                            :: handle, ip, ir, is, ixz, iy, lb, mip, &
                                                            my, my_id, np, num_threads, nx, ny, &
                                                            nz, ub
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl

      CALL timeset(routineN, handle)

      np = fft_scratch%sizes%numtask
      mip = fft_scratch%mip
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl

      ny = boin(2, 2, mip)-boin(1, 2, mip)+1
      nz = boin(2, 3, mip)-boin(1, 3, mip)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(nx), &
!$OMP             SHARED(np,boout,ny,nz,scount,sdispl)
      DO ip = 0, np-1
         nx = boout(2, 1, ip)-boout(1, 1, ip)+1
         scount(ip) = nx*nz*ny
         sdispl(ip) = ny*nz*(boout(1, 1, ip)-1)
      END DO
!$OMP END PARALLEL DO
      nx = boout(2, 1, mip)-boout(1, 1, mip)+1
      my = MAXVAL(boin(2, 2, :)-boin(1, 2, :)+1)
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(ny), &
!$OMP             SHARED(np,boin,nx,nz,rcount,rdispl,my)
      DO ip = 0, np-1
         ny = boin(2, 2, ip)-boin(1, 2, ip)+1
         rcount(ip) = nx*nz*ny
         rdispl(ip) = nx*my*nz*ip
      END DO
!$OMP END PARALLEL DO

      rbuf => fft_scratch%rbuf5
      num_threads = 1
      my_id = 0
!$OMP PARALLEL DEFAULT(NONE), &
!$OMP          PRIVATE(NUM_THREADS, my_id, lb, ub), &
!$OMP          SHARED(rbuf)
!$    num_threads = MIN(omp_get_max_threads(), SIZE(rbuf, 2))
!$    my_id = omp_get_thread_num()
      IF (my_id < num_threads) THEN
         lb = (SIZE(rbuf, 2)*my_id)/num_threads
         ub = (SIZE(rbuf, 2)*(my_id+1))/num_threads-1
         rbuf(:, lb:ub) = 0.0_dp
      END IF
!$OMP END PARALLEL

      CALL mp_alltoall(cin, scount, sdispl, rbuf, rcount, rdispl, group)

!$OMP PARALLEL DO DEFAULT(NONE) COLLAPSE(2) &
!$OMP             PRIVATE(ip,ny,iy,is,ir) &
!$OMP             SHARED(nx,nz,np,boin,sout,rbuf)
      DO ixz = 1, nx*nz
         DO ip = 0, np-1
            ny = boin(2, 2, ip)-boin(1, 2, ip)+1
            DO iy = 1, ny
               is = boin(1, 2, ip)+iy-1
               ir = iy+ny*(ixz-1)
               sout(is, ixz) = rbuf(ir, ip)
            END DO
         END DO
      END DO
!$OMP END PARALLEL DO

      CALL timestop(handle)

   END SUBROUTINE cube_transpose_5

! **************************************************************************************************
!> \brief ...
!> \param cin ...
!> \param group ...
!> \param boin ...
!> \param boout ...
!> \param sout ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE cube_transpose_6(cin, group, boin, boout, sout, fft_scratch)

      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(IN)      :: cin
      INTEGER, INTENT(IN)                                :: group
      INTEGER, DIMENSION(:, :, 0:), INTENT(IN)           :: boin, boout
      COMPLEX(KIND=dp), DIMENSION(:, :), INTENT(OUT)     :: sout
      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'cube_transpose_6', &
         routineP = moduleN//':'//routineN

      COMPLEX(KIND=dp), DIMENSION(:, :), POINTER         :: rbuf
      INTEGER                                            :: handle, ip, ir, iy, izx, lb, mip, my, &
                                                            my_id, np, num_threads, nx, ny, nz, ub
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl, scount, sdispl

      CALL timeset(routineN, handle)

      np = fft_scratch%sizes%numtask
      mip = fft_scratch%mip
      scount => fft_scratch%scount
      rcount => fft_scratch%rcount
      sdispl => fft_scratch%sdispl
      rdispl => fft_scratch%rdispl

      nx = boin(2, 1, mip)-boin(1, 1, mip)+1
      nz = boin(2, 3, mip)-boin(1, 3, mip)+1
      my = MAXVAL(boout(2, 2, :)-boout(1, 2, :)+1)

      rbuf => fft_scratch%rbuf5
      num_threads = 1
      my_id = 0
!$OMP PARALLEL DEFAULT(NONE), &
!$OMP          PRIVATE(NUM_THREADS,my_id,lb,ub,ip,ny,iy,ir), &
!$OMP          SHARED(rbuf,nx,nz,np,boout,cin,my,scount,sdispl)
!$    num_threads = MIN(omp_get_max_threads(), SIZE(rbuf, 2))
!$    my_id = omp_get_thread_num()
      IF (my_id < num_threads) THEN
         lb = (SIZE(rbuf, 2)*my_id)/num_threads
         ub = (SIZE(rbuf, 2)*(my_id+1))/num_threads-1
         rbuf(:, lb:ub) = 0.0_dp
      END IF
!$OMP BARRIER

!$OMP DO COLLAPSE(2)
      DO izx = 1, nz*nx
         DO ip = 0, np-1
            ny = boout(2, 2, ip)-boout(1, 2, ip)+1
            DO iy = boout(1, 2, ip), boout(2, 2, ip)
               ir = iy-boout(1, 2, ip)+1+(izx-1)*ny
               rbuf(ir, ip) = cin(iy, izx)
            END DO
         END DO
      END DO
!$OMP END DO
!$OMP DO
      DO ip = 0, np-1
         ny = boout(2, 2, ip)-boout(1, 2, ip)+1
         scount(ip) = nx*ny*nz
         sdispl(ip) = nx*nz*my*ip
      END DO
!$OMP END DO
!$OMP END PARALLEL
      ny = boout(2, 2, mip)-boout(1, 2, mip)+1
!$OMP PARALLEL DO DEFAULT(NONE), &
!$OMP             PRIVATE(nx), &
!$OMP             SHARED(np,boin,rcount,rdispl,nz,ny)
      DO ip = 0, np-1
         nx = boin(2, 1, ip)-boin(1, 1, ip)+1
         rcount(ip) = nx*ny*nz
         rdispl(ip) = ny*nz*(boin(1, 1, ip)-1)
      END DO
!$OMP END PARALLEL DO

      CALL mp_alltoall(rbuf, scount, sdispl, sout, rcount, rdispl, group)

      CALL timestop(handle)

   END SUBROUTINE cube_transpose_6

! **************************************************************************************************
!> \brief ...
! **************************************************************************************************
   SUBROUTINE init_fft_scratch_pool()

      CHARACTER(len=*), PARAMETER :: routineN = 'init_fft_scratch_pool', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: i

      CALL release_fft_scratch_pool()

      ! Allocate first scratch and mark it as used
      ALLOCATE (fft_scratch_first)
      ALLOCATE (fft_scratch_first%fft_scratch)
      NULLIFY (fft_scratch_first%fft_scratch_next)
      fft_scratch_first%fft_scratch%fft_scratch_id = 0
      fft_scratch_first%fft_scratch%in_use = .TRUE.
      fft_scratch_first%fft_scratch%group = 0
      NULLIFY (fft_scratch_first%fft_scratch%ziptr)
      NULLIFY (fft_scratch_first%fft_scratch%zoptr)
      NULLIFY (fft_scratch_first%fft_scratch%p1buf)
      NULLIFY (fft_scratch_first%fft_scratch%p2buf)
      NULLIFY (fft_scratch_first%fft_scratch%p3buf)
      NULLIFY (fft_scratch_first%fft_scratch%p4buf)
      NULLIFY (fft_scratch_first%fft_scratch%p5buf)
      NULLIFY (fft_scratch_first%fft_scratch%p6buf)
      NULLIFY (fft_scratch_first%fft_scratch%p7buf)
      NULLIFY (fft_scratch_first%fft_scratch%r1buf)
      NULLIFY (fft_scratch_first%fft_scratch%r2buf)
      NULLIFY (fft_scratch_first%fft_scratch%tbuf)
      NULLIFY (fft_scratch_first%fft_scratch%a1buf)
      NULLIFY (fft_scratch_first%fft_scratch%a2buf)
      NULLIFY (fft_scratch_first%fft_scratch%a3buf)
      NULLIFY (fft_scratch_first%fft_scratch%a4buf)
      NULLIFY (fft_scratch_first%fft_scratch%a5buf)
      NULLIFY (fft_scratch_first%fft_scratch%a6buf)
      NULLIFY (fft_scratch_first%fft_scratch%scount, fft_scratch_first%fft_scratch%rcount, &
               fft_scratch_first%fft_scratch%sdispl, fft_scratch_first%fft_scratch%rdispl)
      NULLIFY (fft_scratch_first%fft_scratch%rr, &
               fft_scratch_first%fft_scratch%ss, fft_scratch_first%fft_scratch%tt)
      NULLIFY (fft_scratch_first%fft_scratch%xzbuf, fft_scratch_first%fft_scratch%yzbuf, &
               fft_scratch_first%fft_scratch%xzbuf_sgl, fft_scratch_first%fft_scratch%yzbuf_sgl)
      NULLIFY (fft_scratch_first%fft_scratch%pgrid)
      NULLIFY (fft_scratch_first%fft_scratch%pgcube)
      NULLIFY (fft_scratch_first%fft_scratch%xcor, fft_scratch_first%fft_scratch%zcor)
      NULLIFY (fft_scratch_first%fft_scratch%pzcoord)
      NULLIFY (fft_scratch_first%fft_scratch%xzcount, fft_scratch_first%fft_scratch%yzcount, &
               fft_scratch_first%fft_scratch%xzdispl, fft_scratch_first%fft_scratch%yzdispl)
      NULLIFY (fft_scratch_first%fft_scratch%rbuf1, fft_scratch_first%fft_scratch%rbuf2, &
               fft_scratch_first%fft_scratch%rbuf3, fft_scratch_first%fft_scratch%rbuf4)
      NULLIFY (fft_scratch_first%fft_scratch%rbuf5, fft_scratch_first%fft_scratch%rbuf6)
      fft_scratch_first%fft_scratch%in = 0
      fft_scratch_first%fft_scratch%rsratio = 1._dp
      DO i = 1, 6
         fft_scratch_first%fft_scratch%fft_plan(i)%valid = .FALSE.
      END DO
      ! this is a very special scratch, it seems, we always keep it 'most - recent' so we will never delete it
      fft_scratch_first%fft_scratch%last_tick = HUGE(fft_scratch_first%fft_scratch%last_tick)

      init_fft_pool = init_fft_pool+1

   END SUBROUTINE init_fft_scratch_pool

! **************************************************************************************************
!> \brief ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE deallocate_fft_scratch_type(fft_scratch)
      TYPE(fft_scratch_type), INTENT(INOUT)    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'deallocate_fft_scratch_type', &
                                     routineP = moduleN//':'//routineN

#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
      INTEGER                   :: ierr
      COMPLEX(KIND=dp), POINTER :: dummy_ptr_z
#endif

      ! deallocate structures
      IF (ASSOCIATED(fft_scratch%ziptr)) THEN
         DEALLOCATE (fft_scratch%ziptr)
      END IF
      IF (ASSOCIATED(fft_scratch%zoptr)) THEN
         DEALLOCATE (fft_scratch%zoptr)
      END IF
      IF (ASSOCIATED(fft_scratch%p1buf)) THEN
         DEALLOCATE (fft_scratch%p1buf)
      END IF
      IF (ASSOCIATED(fft_scratch%p2buf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%p2buf(1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%p2buf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%p3buf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%p3buf(1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%p3buf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%p4buf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%p4buf(1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%p4buf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%p5buf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%p5buf(1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%p5buf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%p6buf)) THEN
         DEALLOCATE (fft_scratch%p6buf)
      END IF
      IF (ASSOCIATED(fft_scratch%p7buf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%p7buf(1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%p7buf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%r1buf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%r1buf(1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%r1buf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%r2buf)) THEN
         DEALLOCATE (fft_scratch%r2buf)
      END IF
      IF (ASSOCIATED(fft_scratch%tbuf)) THEN
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
         dummy_ptr_z => fft_scratch%tbuf(1, 1, 1)
         ierr = cudaFreeHost(c_loc(dummy_ptr_z))
#else
         DEALLOCATE (fft_scratch%tbuf)
#endif
      END IF
      IF (ASSOCIATED(fft_scratch%a1buf)) THEN
         DEALLOCATE (fft_scratch%a1buf)
      END IF
      IF (ASSOCIATED(fft_scratch%a2buf)) THEN
         DEALLOCATE (fft_scratch%a2buf)
      END IF
      IF (ASSOCIATED(fft_scratch%a3buf)) THEN
         DEALLOCATE (fft_scratch%a3buf)
      END IF
      IF (ASSOCIATED(fft_scratch%a4buf)) THEN
         DEALLOCATE (fft_scratch%a4buf)
      END IF
      IF (ASSOCIATED(fft_scratch%a5buf)) THEN
         DEALLOCATE (fft_scratch%a5buf)
      END IF
      IF (ASSOCIATED(fft_scratch%a6buf)) THEN
         DEALLOCATE (fft_scratch%a6buf)
      END IF
      IF (ASSOCIATED(fft_scratch%scount)) THEN
         DEALLOCATE (fft_scratch%scount, fft_scratch%rcount, &
                     fft_scratch%sdispl, fft_scratch%rdispl)
      END IF
      IF (ASSOCIATED(fft_scratch%rr)) THEN
         DEALLOCATE (fft_scratch%rr)
      END IF
      IF (ASSOCIATED(fft_scratch%xzbuf)) THEN
         DEALLOCATE (fft_scratch%xzbuf)
      END IF
      IF (ASSOCIATED(fft_scratch%yzbuf)) THEN
         DEALLOCATE (fft_scratch%yzbuf)
      END IF
      IF (ASSOCIATED(fft_scratch%xzbuf_sgl)) THEN
         DEALLOCATE (fft_scratch%xzbuf_sgl)
      END IF
      IF (ASSOCIATED(fft_scratch%yzbuf_sgl)) THEN
         DEALLOCATE (fft_scratch%yzbuf_sgl)
      END IF
      IF (ASSOCIATED(fft_scratch%ss)) THEN
         DEALLOCATE (fft_scratch%ss)
      END IF
      IF (ASSOCIATED(fft_scratch%tt)) THEN
         DEALLOCATE (fft_scratch%tt)
      END IF
      IF (ASSOCIATED(fft_scratch%pgrid)) THEN
         DEALLOCATE (fft_scratch%pgrid)
      END IF
      IF (ASSOCIATED(fft_scratch%pgcube)) THEN
         DEALLOCATE (fft_scratch%pgcube)
      END IF
      IF (ASSOCIATED(fft_scratch%xcor)) THEN
         DEALLOCATE (fft_scratch%xcor, fft_scratch%zcor)
      END IF
      IF (ASSOCIATED(fft_scratch%pzcoord)) THEN
         DEALLOCATE (fft_scratch%pzcoord)
      END IF
      IF (ASSOCIATED(fft_scratch%xzcount)) THEN
         DEALLOCATE (fft_scratch%xzcount, fft_scratch%yzcount)
         DEALLOCATE (fft_scratch%xzdispl, fft_scratch%yzdispl)
         fft_scratch%in = 0
         fft_scratch%rsratio = 1._dp
      END IF
      IF (ASSOCIATED(fft_scratch%rbuf1)) THEN
         DEALLOCATE (fft_scratch%rbuf1)
      END IF
      IF (ASSOCIATED(fft_scratch%rbuf2)) THEN
         DEALLOCATE (fft_scratch%rbuf2)
      END IF
      IF (ASSOCIATED(fft_scratch%rbuf3)) THEN
         DEALLOCATE (fft_scratch%rbuf3)
      END IF
      IF (ASSOCIATED(fft_scratch%rbuf4)) THEN
         DEALLOCATE (fft_scratch%rbuf4)
      END IF
      IF (ASSOCIATED(fft_scratch%rbuf5)) THEN
         DEALLOCATE (fft_scratch%rbuf5)
      END IF
      IF (ASSOCIATED(fft_scratch%rbuf6)) THEN
         DEALLOCATE (fft_scratch%rbuf6)
      END IF

      IF (fft_scratch%cart_sub_comm(1) .NE. mp_comm_null) THEN
         CALL mp_comm_free(fft_scratch%cart_sub_comm(1))
      END IF
      IF (fft_scratch%cart_sub_comm(2) .NE. mp_comm_null) THEN
         CALL mp_comm_free(fft_scratch%cart_sub_comm(2))
      END IF
      fft_scratch%cart_sub_comm = mp_comm_null

      CALL fft_destroy_plan(fft_scratch%fft_plan(1))
      CALL fft_destroy_plan(fft_scratch%fft_plan(2))
      CALL fft_destroy_plan(fft_scratch%fft_plan(3))
      CALL fft_destroy_plan(fft_scratch%fft_plan(4))
      CALL fft_destroy_plan(fft_scratch%fft_plan(5))
      CALL fft_destroy_plan(fft_scratch%fft_plan(6))

   END SUBROUTINE deallocate_fft_scratch_type

! **************************************************************************************************
!> \brief ...
! **************************************************************************************************
   SUBROUTINE release_fft_scratch_pool()

      CHARACTER(len=*), PARAMETER :: routineN = 'release_fft_scratch_pool', &
         routineP = moduleN//':'//routineN

      TYPE(fft_scratch_pool_type), POINTER               :: fft_scratch, fft_scratch_current

      IF (init_fft_pool == 0) NULLIFY (fft_scratch_first)

      fft_scratch => fft_scratch_first
      DO
         IF (ASSOCIATED(fft_scratch)) THEN
            fft_scratch_current => fft_scratch
            fft_scratch => fft_scratch_current%fft_scratch_next
            NULLIFY (fft_scratch_current%fft_scratch_next)

            CALL deallocate_fft_scratch_type(fft_scratch_current%fft_scratch)

            DEALLOCATE (fft_scratch_current%fft_scratch)
            DEALLOCATE (fft_scratch_current)
         ELSE
            EXIT
         END IF
      END DO

      init_fft_pool = 0

   END SUBROUTINE release_fft_scratch_pool

! **************************************************************************************************
!> \brief ...
! **************************************************************************************************
   SUBROUTINE resize_fft_scratch_pool()

      CHARACTER(len=*), PARAMETER :: routineN = 'resize_fft_scratch_pool', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: last_tick, nscratch
      TYPE(fft_scratch_pool_type), POINTER               :: fft_scratch_current, fft_scratch_old

      nscratch = 0

      last_tick = HUGE(last_tick)
      NULLIFY (fft_scratch_old)

      ! start at the global pool, count, and find a deletion candidate
      fft_scratch_current => fft_scratch_first
      DO
         IF (ASSOCIATED(fft_scratch_current)) THEN
            nscratch = nscratch+1
            ! is this a candidate for deletion (i.e. least recently used, and not in use)
            IF (.NOT. fft_scratch_current%fft_scratch%in_use) THEN
               IF (fft_scratch_current%fft_scratch%last_tick < last_tick) THEN
                  last_tick = fft_scratch_current%fft_scratch%last_tick
                  fft_scratch_old => fft_scratch_current
               ENDIF
            ENDIF
            fft_scratch_current => fft_scratch_current%fft_scratch_next
         ELSE
            EXIT
         ENDIF
      ENDDO

      ! we should delete a scratch
      IF (nscratch > fft_pool_scratch_limit) THEN
         ! note that we never deallocate the first (special) element of the list
         IF (ASSOCIATED(fft_scratch_old)) THEN
            fft_scratch_current => fft_scratch_first
            DO
               IF (ASSOCIATED(fft_scratch_current)) THEN
                  ! should we delete the next in the list?
                  IF (ASSOCIATED(fft_scratch_current%fft_scratch_next, fft_scratch_old)) THEN
                     ! fix the linked list
                     fft_scratch_current%fft_scratch_next => fft_scratch_old%fft_scratch_next

                     ! deallocate the element
                     CALL deallocate_fft_scratch_type(fft_scratch_old%fft_scratch)
                     DEALLOCATE (fft_scratch_old%fft_scratch)
                     DEALLOCATE (fft_scratch_old)

                  ELSE
                     fft_scratch_current => fft_scratch_current%fft_scratch_next
                  ENDIF
               ELSE
                  EXIT
               ENDIF
            ENDDO

         ELSE
            CPWARN("The number of the scratches exceeded the limit, but none could be deallocated")
         ENDIF
      ENDIF

   END SUBROUTINE resize_fft_scratch_pool

! **************************************************************************************************
!> \brief ...
!> \param fft_scratch ...
!> \param tf_type ...
!> \param n ...
!> \param fft_sizes ...
! **************************************************************************************************
   SUBROUTINE get_fft_scratch(fft_scratch, tf_type, n, fft_sizes)
      TYPE(fft_scratch_type), POINTER          :: fft_scratch
      INTEGER, INTENT(IN)                      :: tf_type
      INTEGER, DIMENSION(:), INTENT(IN)        :: n
      TYPE(fft_scratch_sizes), INTENT(IN), &
         OPTIONAL                               :: fft_sizes

      CHARACTER(len=*), PARAMETER :: routineN = 'get_fft_scratch', &
                                     routineP = moduleN//':'//routineN

      INTEGER :: coord(2), DIM(2), handle, i, ix, iz, lg, lmax, m1, m2, &
                 mcx2, mcy3, mcz1, mcz2, mg, mmax, mx1, mx2, my1, my3, mz1, mz2, mz3, &
                 nbx, nbz, nm, nmax, nmray, nn, np, nx, ny, nyzray, nz, pos(2)
      INTEGER, DIMENSION(3)                    :: pcoord
      LOGICAL                                  :: equal
      LOGICAL, DIMENSION(2)                    :: dims
      TYPE(fft_scratch_pool_type), POINTER     :: fft_scratch_current, &
                                                  fft_scratch_last, &
                                                  fft_scratch_new
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
      INTEGER                   :: ierr
      INTEGER(KIND=C_SIZE_T)    :: length
      TYPE(C_PTR)               :: cptr_r1buf, cptr_tbuf, &
                                   cptr_p2buf, cptr_p3buf, cptr_p4buf, cptr_p5buf, cptr_p7buf
      INTEGER(KIND=C_INT), PARAMETER :: cudaHostAllocDefault = 0
#endif
      CALL timeset(routineN, handle)

      ! this is the place to check that the scratch_pool does not grow without limits
      ! before we add a new scratch check the size of the pool and release some of the list if needed
      CALL resize_fft_scratch_pool()

      ! get the required scratch
      tick_fft_pool = tick_fft_pool+1
      fft_scratch_current => fft_scratch_first
      DO
         IF (ASSOCIATED(fft_scratch_current)) THEN
            IF (fft_scratch_current%fft_scratch%in_use) THEN
               fft_scratch_last => fft_scratch_current
               fft_scratch_current => fft_scratch_current%fft_scratch_next
               CYCLE
            END IF
            IF (tf_type /= fft_scratch_current%fft_scratch%tf_type) THEN
               fft_scratch_last => fft_scratch_current
               fft_scratch_current => fft_scratch_current%fft_scratch_next
               CYCLE
            END IF
            IF (.NOT. ALL(n == fft_scratch_current%fft_scratch%nfft)) THEN
               fft_scratch_last => fft_scratch_current
               fft_scratch_current => fft_scratch_current%fft_scratch_next
               CYCLE
            END IF
            IF (PRESENT(fft_sizes)) THEN
               IF (fft_sizes%gs_group /= fft_scratch_current%fft_scratch%group) THEN
                  fft_scratch_last => fft_scratch_current
                  fft_scratch_current => fft_scratch_current%fft_scratch_next
                  CYCLE
               END IF
               CALL is_equal(fft_sizes, fft_scratch_current%fft_scratch%sizes, equal)
               IF (.NOT. equal) THEN
                  fft_scratch_last => fft_scratch_current
                  fft_scratch_current => fft_scratch_current%fft_scratch_next
                  CYCLE
               ENDIF
            END IF
            ! Success
            fft_scratch => fft_scratch_current%fft_scratch
            fft_scratch_current%fft_scratch%in_use = .TRUE.
            EXIT
         ELSE
            ! We cannot find the scratch type in this pool
            ! Generate a new scratch set
            ALLOCATE (fft_scratch_new)
            ALLOCATE (fft_scratch_new%fft_scratch)
            fft_scratch_new%fft_scratch%group = 0
            NULLIFY (fft_scratch_new%fft_scratch%ziptr)
            NULLIFY (fft_scratch_new%fft_scratch%zoptr)
            NULLIFY (fft_scratch_new%fft_scratch%p1buf)
            NULLIFY (fft_scratch_new%fft_scratch%p2buf)
            NULLIFY (fft_scratch_new%fft_scratch%p3buf)
            NULLIFY (fft_scratch_new%fft_scratch%p4buf)
            NULLIFY (fft_scratch_new%fft_scratch%p5buf)
            NULLIFY (fft_scratch_new%fft_scratch%p6buf)
            NULLIFY (fft_scratch_new%fft_scratch%p7buf)
            NULLIFY (fft_scratch_new%fft_scratch%r1buf)
            NULLIFY (fft_scratch_new%fft_scratch%r2buf)
            NULLIFY (fft_scratch_new%fft_scratch%tbuf)
            NULLIFY (fft_scratch_new%fft_scratch%a1buf)
            NULLIFY (fft_scratch_new%fft_scratch%a2buf)
            NULLIFY (fft_scratch_new%fft_scratch%a3buf)
            NULLIFY (fft_scratch_new%fft_scratch%a4buf)
            NULLIFY (fft_scratch_new%fft_scratch%a5buf)
            NULLIFY (fft_scratch_new%fft_scratch%a6buf)
            NULLIFY (fft_scratch_new%fft_scratch%scount, fft_scratch_new%fft_scratch%rcount, &
                     fft_scratch_new%fft_scratch%sdispl, fft_scratch_new%fft_scratch%rdispl)
            NULLIFY (fft_scratch_new%fft_scratch%rr, &
                     fft_scratch_new%fft_scratch%ss, fft_scratch_new%fft_scratch%tt)
            NULLIFY (fft_scratch_new%fft_scratch%xzbuf, fft_scratch_new%fft_scratch%yzbuf, &
                     fft_scratch_new%fft_scratch%xzbuf_sgl, fft_scratch_new%fft_scratch%yzbuf_sgl)
            NULLIFY (fft_scratch_new%fft_scratch%pgcube)
            NULLIFY (fft_scratch_new%fft_scratch%pgrid)
            NULLIFY (fft_scratch_new%fft_scratch%xcor, fft_scratch_new%fft_scratch%zcor)
            NULLIFY (fft_scratch_new%fft_scratch%pzcoord)
            NULLIFY (fft_scratch_new%fft_scratch%xzcount, fft_scratch_new%fft_scratch%yzcount)
            NULLIFY (fft_scratch_new%fft_scratch%xzdispl, fft_scratch_new%fft_scratch%yzdispl)
            NULLIFY (fft_scratch_new%fft_scratch%rbuf1, fft_scratch_new%fft_scratch%rbuf2, &
                     fft_scratch_new%fft_scratch%rbuf3, fft_scratch_new%fft_scratch%rbuf4)
            NULLIFY (fft_scratch_new%fft_scratch%rbuf5, fft_scratch_new%fft_scratch%rbuf6)
            fft_scratch_new%fft_scratch%in = 0
            fft_scratch_new%fft_scratch%rsratio = 1._dp
            DO i = 1, 6
               fft_scratch_new%fft_scratch%fft_plan(i)%valid = .FALSE.
            END DO

            fft_scratch_new%fft_scratch%cart_sub_comm = mp_comm_null

            IF (tf_type .NE. 400) THEN
               fft_scratch_new%fft_scratch%sizes = fft_sizes
               np = fft_sizes%numtask
               ALLOCATE (fft_scratch_new%fft_scratch%scount(0:np-1), fft_scratch_new%fft_scratch%rcount(0:np-1), &
                         fft_scratch_new%fft_scratch%sdispl(0:np-1), fft_scratch_new%fft_scratch%rdispl(0:np-1), &
                         fft_scratch_new%fft_scratch%pgcube(0:np-1, 2))
            END IF

            SELECT CASE (tf_type)
            CASE DEFAULT
               CPABORT("")
            CASE (100) ! fft3d_pb: full cube distribution
               mx1 = fft_sizes%mx1
               my1 = fft_sizes%my1
               mx2 = fft_sizes%mx2
               mz2 = fft_sizes%mz2
               my3 = fft_sizes%my3
               mz3 = fft_sizes%mz3
               ALLOCATE (fft_scratch_new%fft_scratch%a1buf(mx1*my1, n(3)))
               ALLOCATE (fft_scratch_new%fft_scratch%a2buf(n(3), mx1*my1))
               ALLOCATE (fft_scratch_new%fft_scratch%a3buf(mx2*mz2, n(2)))
               ALLOCATE (fft_scratch_new%fft_scratch%a4buf(n(2), mx2*mz2))
               ALLOCATE (fft_scratch_new%fft_scratch%a5buf(my3*mz3, n(1)))
               ALLOCATE (fft_scratch_new%fft_scratch%a6buf(n(1), my3*mz3))
               fft_scratch_new%fft_scratch%group = fft_sizes%gs_group

               CALL mp_environ(nn, dim, pos, fft_sizes%rs_group)
               CALL mp_cart_rank(fft_sizes%rs_group, pos, fft_scratch_new%fft_scratch%mip)
               fft_scratch_new%fft_scratch%dim = dim
               fft_scratch_new%fft_scratch%pos = pos
               mcz1 = fft_sizes%mcz1
               mcx2 = fft_sizes%mcx2
               mcz2 = fft_sizes%mcz2
               mcy3 = fft_sizes%mcy3
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf1(mx2*my1*mcz2, 0:DIM(2)-1))
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf2(mx1*my1*mcz2, 0:DIM(2)-1))
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf3(mx2*mz3*mcy3, 0:DIM(1)-1))
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf4(mx2*mz2*mcy3, 0:DIM(1)-1))

               dims = (/.TRUE., .FALSE./)
               CALL mp_cart_sub(fft_sizes%rs_group, dims, fft_scratch_new%fft_scratch%cart_sub_comm(1))
               dims = (/.FALSE., .TRUE./)
               CALL mp_cart_sub(fft_sizes%rs_group, dims, fft_scratch_new%fft_scratch%cart_sub_comm(2))

               !initialise pgcube
               DO i = 0, DIM(1)-1
                  coord = (/i, pos(2)/)
                  CALL mp_cart_rank(fft_sizes%rs_group, coord, fft_scratch_new%fft_scratch%pgcube(i, 1))
               END DO
               DO i = 0, DIM(2)-1
                  coord = (/pos(1), i/)
                  CALL mp_cart_rank(fft_sizes%rs_group, coord, fft_scratch_new%fft_scratch%pgcube(i, 2))
               END DO

               !set up fft plans
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(1), fft_type, FWFFT, .TRUE., n(3), mx1*my1, &
                                        fft_scratch_new%fft_scratch%a1buf, fft_scratch_new%fft_scratch%a2buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(2), fft_type, FWFFT, .TRUE., n(2), mx2*mz2, &
                                        fft_scratch_new%fft_scratch%a3buf, fft_scratch_new%fft_scratch%a4buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(3), fft_type, FWFFT, .TRUE., n(1), my3*mz3, &
                                        fft_scratch_new%fft_scratch%a5buf, fft_scratch_new%fft_scratch%a6buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(4), fft_type, BWFFT, .TRUE., n(1), my3*mz3, &
                                        fft_scratch_new%fft_scratch%a6buf, fft_scratch_new%fft_scratch%a5buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(5), fft_type, BWFFT, .TRUE., n(2), mx2*mz2, &
                                        fft_scratch_new%fft_scratch%a4buf, fft_scratch_new%fft_scratch%a3buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(6), fft_type, BWFFT, .TRUE., n(3), mx1*my1, &
                                        fft_scratch_new%fft_scratch%a2buf, fft_scratch_new%fft_scratch%a1buf, fft_plan_style)

            CASE (101) ! fft3d_pb: full cube distribution (dim 1)
               mx1 = fft_sizes%mx1
               my1 = fft_sizes%my1
               mz1 = fft_sizes%mz1
               my3 = fft_sizes%my3
               mz3 = fft_sizes%mz3
               ALLOCATE (fft_scratch_new%fft_scratch%a1buf(mx1*my1, n(3)))
               ALLOCATE (fft_scratch_new%fft_scratch%a2buf(n(3), mx1*my1))
               fft_scratch_new%fft_scratch%group = fft_sizes%gs_group
               ALLOCATE (fft_scratch_new%fft_scratch%a3buf(mx1*mz1, n(2)))
               ALLOCATE (fft_scratch_new%fft_scratch%a4buf(n(2), mx1*mz1))
               ALLOCATE (fft_scratch_new%fft_scratch%a5buf(my3*mz3, n(1)))
               ALLOCATE (fft_scratch_new%fft_scratch%a6buf(n(1), my3*mz3))

               CALL mp_environ(nn, dim, pos, fft_sizes%rs_group)
               CALL mp_cart_rank(fft_sizes%rs_group, pos, fft_scratch_new%fft_scratch%mip)
               fft_scratch_new%fft_scratch%dim = dim
               fft_scratch_new%fft_scratch%pos = pos
               mcy3 = fft_sizes%mcy3
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf5(mx1*mz3*mcy3, 0:DIM(1)-1))
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf6(mx1*mz1*mcy3, 0:DIM(1)-1))

               !set up fft plans
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(1), fft_type, FWFFT, .TRUE., n(3), mx1*my1, &
                                        fft_scratch_new%fft_scratch%a1buf, fft_scratch_new%fft_scratch%a3buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(2), fft_type, FWFFT, .TRUE., n(2), mx1*mz1, &
                                        fft_scratch_new%fft_scratch%a3buf, fft_scratch_new%fft_scratch%a4buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(3), fft_type, FWFFT, .TRUE., n(1), my3*mz3, &
                                        fft_scratch_new%fft_scratch%a5buf, fft_scratch_new%fft_scratch%a6buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(4), fft_type, BWFFT, .TRUE., n(1), my3*mz3, &
                                        fft_scratch_new%fft_scratch%a6buf, fft_scratch_new%fft_scratch%a5buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(5), fft_type, BWFFT, .TRUE., n(2), mx1*mz1, &
                                        fft_scratch_new%fft_scratch%a4buf, fft_scratch_new%fft_scratch%a3buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(6), fft_type, BWFFT, .TRUE., n(3), mx1*my1, &
                                        fft_scratch_new%fft_scratch%a3buf, fft_scratch_new%fft_scratch%a1buf, fft_plan_style)

            CASE (200) ! fft3d_ps: plane distribution
               nx = fft_sizes%nx
               ny = fft_sizes%ny
               nz = fft_sizes%nz
               mx2 = fft_sizes%mx2
               lmax = fft_sizes%lmax
               mmax = fft_sizes%mmax
               lg = fft_sizes%lg
               mg = fft_sizes%mg
               np = fft_sizes%numtask
               nmray = fft_sizes%nmray
               nyzray = fft_sizes%nyzray
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
               length = INT(2*dp_size*MAX(mmax, 1)*MAX(lmax, 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_r1buf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_r1buf, fft_scratch_new%fft_scratch%r1buf, (/MAX(mmax, 1), MAX(lmax, 1)/))
               length = INT(2*dp_size*MAX(ny, 1)*MAX(nz, 1)*MAX(nx, 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_tbuf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_tbuf, fft_scratch_new%fft_scratch%tbuf, (/MAX(ny, 1), MAX(nz, 1), MAX(nx, 1)/))
#else
               ALLOCATE (fft_scratch_new%fft_scratch%r1buf(mmax, lmax))
               ALLOCATE (fft_scratch_new%fft_scratch%tbuf(ny, nz, nx))
#endif
               fft_scratch_new%fft_scratch%group = fft_sizes%gs_group
               ALLOCATE (fft_scratch_new%fft_scratch%r2buf(lg, mg))
               nm = nmray*mx2
               IF (alltoall_sgl) THEN
                  ALLOCATE (fft_scratch_new%fft_scratch%ss(mmax, lmax))
                  ALLOCATE (fft_scratch_new%fft_scratch%tt(nm, 0:np-1))
               ELSE
                  ALLOCATE (fft_scratch_new%fft_scratch%rr(nm, 0:np-1))
               END IF

               !set up fft plans
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(1), fft_type, FWFFT, .TRUE., nz, nx*ny, &
                                        fft_scratch_new%fft_scratch%tbuf, fft_scratch_new%fft_scratch%r1buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(2), fft_type, FWFFT, .TRUE., ny, nx*nz, &
                                        fft_scratch_new%fft_scratch%r1buf, fft_scratch_new%fft_scratch%tbuf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(3), fft_type, FWFFT, .TRUE., n(1), nyzray, &
                                        fft_scratch_new%fft_scratch%r1buf, fft_scratch_new%fft_scratch%r2buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(4), fft_type, BWFFT, .TRUE., n(1), nyzray, &
                                        fft_scratch_new%fft_scratch%r2buf, fft_scratch_new%fft_scratch%r1buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(5), fft_type, BWFFT, .TRUE., ny, nx*nz, &
                                        fft_scratch_new%fft_scratch%tbuf, fft_scratch_new%fft_scratch%r1buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(6), fft_type, BWFFT, .TRUE., nz, nx*ny, &
                                        fft_scratch_new%fft_scratch%r1buf, fft_scratch_new%fft_scratch%tbuf, fft_plan_style)

            CASE (300) ! fft3d_ps: block distribution
               mx1 = fft_sizes%mx1
               mx2 = fft_sizes%mx2
               my1 = fft_sizes%my1
               mz2 = fft_sizes%mz2
               mcx2 = fft_sizes%mcx2
               lg = fft_sizes%lg
               mg = fft_sizes%mg
               nmax = fft_sizes%nmax
               nmray = fft_sizes%nmray
               nyzray = fft_sizes%nyzray
               m1 = fft_sizes%r_dim(1)
               m2 = fft_sizes%r_dim(2)
               nbx = fft_sizes%nbx
               nbz = fft_sizes%nbz
               ALLOCATE (fft_scratch_new%fft_scratch%p1buf(mx1*my1, n(3)))
               ALLOCATE (fft_scratch_new%fft_scratch%p6buf(lg, mg))
#if defined ( __PW_CUDA ) && !defined ( __PW_CUDA_NO_HOSTALLOC )
               length = INT(2*dp_size*MAX(n(3), 1)*MAX(mx1*my1, 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_p2buf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_p2buf, fft_scratch_new%fft_scratch%p2buf, (/MAX(n(3), 1), MAX(mx1*my1, 1)/))
               length = INT(2*dp_size*MAX(mx2*mz2, 1)*MAX(n(2), 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_p3buf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_p3buf, fft_scratch_new%fft_scratch%p3buf, (/MAX(mx2*mz2, 1), MAX(n(2), 1)/))
               length = INT(2*dp_size*MAX(n(2), 1)*MAX(mx2*mz2, 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_p4buf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_p4buf, fft_scratch_new%fft_scratch%p4buf, (/MAX(n(2), 1), MAX(mx2*mz2, 1)/))
               length = INT(2*dp_size*MAX(nyzray, 1)*MAX(n(1), 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_p5buf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_p5buf, fft_scratch_new%fft_scratch%p5buf, (/MAX(nyzray, 1), MAX(n(1), 1)/))
               length = INT(2*dp_size*MAX(mg, 1)*MAX(lg, 1), KIND=C_SIZE_T)
               ierr = cudaHostAlloc(cptr_p7buf, length, cudaHostAllocDefault)
               CPASSERT(ierr == 0)
               CALL c_f_pointer(cptr_p7buf, fft_scratch_new%fft_scratch%p7buf, (/MAX(mg, 1), MAX(lg, 1)/))
#else
               ALLOCATE (fft_scratch_new%fft_scratch%p2buf(n(3), mx1*my1))
               ALLOCATE (fft_scratch_new%fft_scratch%p3buf(mx2*mz2, n(2)))
               ALLOCATE (fft_scratch_new%fft_scratch%p4buf(n(2), mx2*mz2))
               ALLOCATE (fft_scratch_new%fft_scratch%p5buf(nyzray, n(1)))
               ALLOCATE (fft_scratch_new%fft_scratch%p7buf(mg, lg))
#endif
               IF (alltoall_sgl) THEN
                  ALLOCATE (fft_scratch_new%fft_scratch%yzbuf_sgl(mg*lg))
                  ALLOCATE (fft_scratch_new%fft_scratch%xzbuf_sgl(n(2)*mx2*mz2))
               ELSE
                  ALLOCATE (fft_scratch_new%fft_scratch%yzbuf(mg*lg))
                  ALLOCATE (fft_scratch_new%fft_scratch%xzbuf(n(2)*mx2*mz2))
               END IF
               ALLOCATE (fft_scratch_new%fft_scratch%pgrid(0:m1-1, 0:m2-1))
               ALLOCATE (fft_scratch_new%fft_scratch%xcor(nbx))
               ALLOCATE (fft_scratch_new%fft_scratch%zcor(nbz))
               ALLOCATE (fft_scratch_new%fft_scratch%pzcoord(0:np-1))
               ALLOCATE (fft_scratch_new%fft_scratch%xzcount(0:np-1), &
                         fft_scratch_new%fft_scratch%yzcount(0:np-1))
               ALLOCATE (fft_scratch_new%fft_scratch%xzdispl(0:np-1), &
                         fft_scratch_new%fft_scratch%yzdispl(0:np-1))
               fft_scratch_new%fft_scratch%in = 0
               fft_scratch_new%fft_scratch%rsratio = 1._dp
               fft_scratch_new%fft_scratch%group = fft_sizes%gs_group

               CALL mp_environ(nn, dim, pos, fft_sizes%rs_group)
               CALL mp_cart_rank(fft_sizes%rs_group, pos, fft_scratch_new%fft_scratch%mip)
               fft_scratch_new%fft_scratch%dim = dim
               fft_scratch_new%fft_scratch%pos = pos
               mcz1 = fft_sizes%mcz1
               mcz2 = fft_sizes%mcz2
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf1(mx2*my1*mcz2, 0:DIM(2)-1))
               ALLOCATE (fft_scratch_new%fft_scratch%rbuf2(mx1*my1*mcz2, 0:DIM(2)-1))

               dims = (/.FALSE., .TRUE./)
               CALL mp_cart_sub(fft_sizes%rs_group, dims, fft_scratch_new%fft_scratch%cart_sub_comm(2))

               !initialise pgcube
               DO i = 0, DIM(2)-1
                  coord = (/pos(1), i/)
                  CALL mp_cart_rank(fft_sizes%rs_group, coord, fft_scratch_new%fft_scratch%pgcube(i, 2))
               END DO

               !initialise pgrid
               DO ix = 0, m1-1
                  DO iz = 0, m2-1
                     coord = (/ix, iz/)
                     CALL mp_cart_rank(fft_sizes%rs_group, coord, fft_scratch_new%fft_scratch%pgrid(ix, iz))
                  END DO
               END DO

               !initialise pzcoord
               DO i = 0, np-1
                  CALL mp_cart_coords(fft_sizes%rs_group, i, pcoord)
                  fft_scratch_new%fft_scratch%pzcoord(i) = pcoord(2)
               END DO

               !set up fft plans
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(1), fft_type, FWFFT, .TRUE., n(3), mx1*my1, &
                                        fft_scratch_new%fft_scratch%p1buf, fft_scratch_new%fft_scratch%p2buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(2), fft_type, FWFFT, .TRUE., n(2), mx2*mz2, &
                                        fft_scratch_new%fft_scratch%p3buf, fft_scratch_new%fft_scratch%p4buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(3), fft_type, FWFFT, .TRUE., n(1), nyzray, &
                                        fft_scratch_new%fft_scratch%p5buf, fft_scratch_new%fft_scratch%p6buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(4), fft_type, BWFFT, .TRUE., n(1), nyzray, &
                                        fft_scratch_new%fft_scratch%p6buf, fft_scratch_new%fft_scratch%p7buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(5), fft_type, BWFFT, .TRUE., n(2), mx2*mz2, &
                                        fft_scratch_new%fft_scratch%p4buf, fft_scratch_new%fft_scratch%p3buf, fft_plan_style)
               CALL fft_create_plan_1dm(fft_scratch_new%fft_scratch%fft_plan(6), fft_type, BWFFT, .TRUE., n(3), mx1*my1, &
                                        fft_scratch_new%fft_scratch%p3buf, fft_scratch_new%fft_scratch%p1buf, fft_plan_style)

            CASE (400) ! serial FFT
               np = 0
               ALLOCATE (fft_scratch_new%fft_scratch%ziptr(n(1), n(2), n(3)))
               ALLOCATE (fft_scratch_new%fft_scratch%zoptr(n(1), n(2), n(3)))

               !in place plans
               CALL fft_create_plan_3d(fft_scratch_new%fft_scratch%fft_plan(1), fft_type, .TRUE., FWFFT, n, &
                                       fft_scratch_new%fft_scratch%ziptr, fft_scratch_new%fft_scratch%ziptr, fft_plan_style)
               CALL fft_create_plan_3d(fft_scratch_new%fft_scratch%fft_plan(2), fft_type, .TRUE., BWFFT, n, &
                                       fft_scratch_new%fft_scratch%ziptr, fft_scratch_new%fft_scratch%ziptr, fft_plan_style)
               ! out of place plans
               CALL fft_create_plan_3d(fft_scratch_new%fft_scratch%fft_plan(3), fft_type, .FALSE., FWFFT, n, &
                                       fft_scratch_new%fft_scratch%ziptr, fft_scratch_new%fft_scratch%zoptr, fft_plan_style)
               CALL fft_create_plan_3d(fft_scratch_new%fft_scratch%fft_plan(4), fft_type, .FALSE., BWFFT, n, &
                                       fft_scratch_new%fft_scratch%ziptr, fft_scratch_new%fft_scratch%zoptr, fft_plan_style)

            END SELECT

            NULLIFY (fft_scratch_new%fft_scratch_next)
            fft_scratch_new%fft_scratch%fft_scratch_id = &
               fft_scratch_last%fft_scratch%fft_scratch_id+1
            fft_scratch_new%fft_scratch%in_use = .TRUE.
            fft_scratch_new%fft_scratch%nfft = n
            fft_scratch_last%fft_scratch_next => fft_scratch_new
            fft_scratch_new%fft_scratch%tf_type = tf_type
            fft_scratch => fft_scratch_new%fft_scratch
            EXIT

         END IF
      END DO

      fft_scratch%last_tick = tick_fft_pool

      CALL timestop(handle)

   END SUBROUTINE get_fft_scratch

! **************************************************************************************************
!> \brief ...
!> \param fft_scratch ...
! **************************************************************************************************
   SUBROUTINE release_fft_scratch(fft_scratch)

      TYPE(fft_scratch_type), POINTER                    :: fft_scratch

      CHARACTER(len=*), PARAMETER :: routineN = 'release_fft_scratch', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: scratch_id
      TYPE(fft_scratch_pool_type), POINTER               :: fft_scratch_current

      scratch_id = fft_scratch%fft_scratch_id

      fft_scratch_current => fft_scratch_first
      DO
         IF (ASSOCIATED(fft_scratch_current)) THEN
            IF (scratch_id == fft_scratch_current%fft_scratch%fft_scratch_id) THEN
               fft_scratch%in_use = .FALSE.
               NULLIFY (fft_scratch)
               EXIT
            END IF
            fft_scratch_current => fft_scratch_current%fft_scratch_next
         ELSE
            ! We cannot find the scratch type in this pool
            CPABORT("")
            EXIT
         END IF
      END DO

   END SUBROUTINE release_fft_scratch

! **************************************************************************************************
!> \brief ...
!> \param rs ...
!> \param scount ...
!> \param sdispl ...
!> \param rq ...
!> \param rcount ...
!> \param rdispl ...
!> \param group ...
! **************************************************************************************************
   SUBROUTINE sparse_alltoall(rs, scount, sdispl, rq, rcount, rdispl, group)
      COMPLEX(KIND=dp), DIMENSION(:), POINTER            :: rs
      INTEGER, DIMENSION(:), POINTER                     :: scount, sdispl
      COMPLEX(KIND=dp), DIMENSION(:), POINTER            :: rq
      INTEGER, DIMENSION(:), POINTER                     :: rcount, rdispl
      INTEGER, INTENT(IN)                                :: group

      COMPLEX(KIND=dp), DIMENSION(:), POINTER            :: msgin, msgout
      INTEGER                                            :: ip, n, nr, ns, pos, rn, sn
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: rreq, sreq

      CALL mp_sync(group)
      CALL mp_environ(n, pos, group)
      ALLOCATE (sreq(0:n-1))
      ALLOCATE (rreq(0:n-1))
      nr = 0
      DO ip = 0, n-1
         IF (rcount(ip) == 0) CYCLE
         IF (ip == pos) CYCLE
         msgout => rq(rdispl(ip)+1:rdispl(ip)+rcount(ip))
         CALL mp_irecv(msgout, ip, group, rn)
         nr = nr+1
         rreq(nr-1) = rn
      END DO
      ns = 0
      DO ip = 0, n-1
         IF (scount(ip) == 0) CYCLE
         IF (ip == pos) CYCLE
         msgin => rs(sdispl(ip)+1:sdispl(ip)+scount(ip))
         CALL mp_isend(msgin, ip, group, sn)
         ns = ns+1
         sreq(ns-1) = sn
      END DO
      IF (rcount(pos) /= 0) THEN
         IF (rcount(pos) /= scount(pos)) CPABORT("")
         rq(rdispl(pos)+1:rdispl(pos)+rcount(pos)) = rs(sdispl(pos)+1:sdispl(pos)+scount(pos))
      END IF
      CALL mp_waitall(sreq(0:ns-1))
      CALL mp_waitall(rreq(0:nr-1))
      DEALLOCATE (sreq)
      DEALLOCATE (rreq)
      CALL mp_sync(group)

   END SUBROUTINE sparse_alltoall

! **************************************************************************************************
!> \brief  test data structures for equality. It is assumed that if they are
!>         different for one mpi task they are different for all (??)
!> \param fft_size_1 ...
!> \param fft_size_2 ...
!> \param equal ...
! **************************************************************************************************
   SUBROUTINE is_equal(fft_size_1, fft_size_2, equal)
      TYPE(fft_scratch_sizes)                            :: fft_size_1, fft_size_2
      LOGICAL                                            :: equal

      equal = .TRUE.

      equal = equal .AND. fft_size_1%nx == fft_size_2%nx
      equal = equal .AND. fft_size_1%ny == fft_size_2%ny
      equal = equal .AND. fft_size_1%nz == fft_size_2%nz

      equal = equal .AND. fft_size_1%lmax == fft_size_2%lmax
      equal = equal .AND. fft_size_1%mmax == fft_size_2%mmax
      equal = equal .AND. fft_size_1%nmax == fft_size_2%nmax

      equal = equal .AND. fft_size_1%mx1 == fft_size_2%mx1
      equal = equal .AND. fft_size_1%mx2 == fft_size_2%mx2
      equal = equal .AND. fft_size_1%mx3 == fft_size_2%mx3

      equal = equal .AND. fft_size_1%my1 == fft_size_2%my1
      equal = equal .AND. fft_size_1%my2 == fft_size_2%my2
      equal = equal .AND. fft_size_1%my3 == fft_size_2%my3

      equal = equal .AND. fft_size_1%mcz1 == fft_size_2%mcz1
      equal = equal .AND. fft_size_1%mcx2 == fft_size_2%mcx2
      equal = equal .AND. fft_size_1%mcz2 == fft_size_2%mcz2
      equal = equal .AND. fft_size_1%mcy3 == fft_size_2%mcy3

      equal = equal .AND. fft_size_1%lg == fft_size_2%lg
      equal = equal .AND. fft_size_1%mg == fft_size_2%mg

      equal = equal .AND. fft_size_1%nbx == fft_size_2%nbx
      equal = equal .AND. fft_size_1%nbz == fft_size_2%nbz

      equal = equal .AND. fft_size_1%nmray == fft_size_2%nmray
      equal = equal .AND. fft_size_1%nyzray == fft_size_2%nyzray

      equal = equal .AND. fft_size_1%gs_group == fft_size_2%gs_group
      equal = equal .AND. fft_size_1%rs_group == fft_size_2%rs_group

      equal = equal .AND. ALL(fft_size_1%g_pos == fft_size_2%g_pos)
      equal = equal .AND. ALL(fft_size_1%r_pos == fft_size_2%r_pos)
      equal = equal .AND. ALL(fft_size_1%r_dim == fft_size_2%r_dim)

      equal = equal .AND. fft_size_1%numtask == fft_size_2%numtask

   END SUBROUTINE is_equal

END MODULE fft_tools

