subroutine cmfgkf ( lot, ido, ip, l1, lid, na, cc, cc1, im1, in1, &
  ch, ch1, im2, in2, wa )

!*****************************************************************************80
!
!! CMFGKF is an FFTPACK5 auxiliary routine.
!
!
!    Copyright (C) 1995-2004, Scientific Computing Division,
!    University Corporation for Atmospheric Research
!
!  Modified:
!
!    27 March 2009
!
!  Author:
!
!    Paul Swarztrauber
!    Richard Valent
!
!  Reference:
!
!    Paul Swarztrauber,
!    Vectorizing the Fast Fourier Transforms,
!    in Parallel Computations,
!    edited by G. Rodrigue,
!    Academic Press, 1982.
!
!    Paul Swarztrauber,
!    Fast Fourier Transform Algorithms for Vector Computers,
!    Parallel Computing, pages 45-63, 1984.
!
!  Parameters:
!
  implicit none

  integer ( kind = 4 ) ido
  integer ( kind = 4 ) in1
  integer ( kind = 4 ) in2
  integer ( kind = 4 ) ip
  integer ( kind = 4 ) l1
  integer ( kind = 4 ) lid

  real ( kind = 4 ) cc(2,in1,l1,ip,ido)
  real ( kind = 4 ) cc1(2,in1,lid,ip)
  real ( kind = 4 ) ch(2,in2,l1,ido,ip)
  real ( kind = 4 ) ch1(2,in2,lid,ip)
  real ( kind = 4 ) chold1
  real ( kind = 4 ) chold2
  integer ( kind = 4 ) i
  integer ( kind = 4 ) idlj
  integer ( kind = 4 ) im1
  integer ( kind = 4 ) im2
  integer ( kind = 4 ) ipp2
  integer ( kind = 4 ) ipph
  integer ( kind = 4 ) j
  integer ( kind = 4 ) jc
  integer ( kind = 4 ) k
  integer ( kind = 4 ) ki
  integer ( kind = 4 ) l
  integer ( kind = 4 ) lc
  integer ( kind = 4 ) lot
  integer ( kind = 4 ) m1
  integer ( kind = 4 ) m1d
  integer ( kind = 4 ) m2
  integer ( kind = 4 ) m2s
  integer ( kind = 4 ) na
  real ( kind = 4 ) sn
  real ( kind = 4 ) wa(ido,ip-1,2)
  real ( kind = 4 ) wai
  real ( kind = 4 ) war

  m1d = ( lot - 1 ) * im1 + 1
  m2s = 1 - im2
  ipp2 = ip + 2
  ipph = ( ip + 1 ) / 2

  do ki = 1, lid
    m2 = m2s
    do m1 = 1, m1d, im1
      m2 = m2 + im2
      ch1(1,m2,ki,1) = cc1(1,m1,ki,1)
      ch1(2,m2,ki,1) = cc1(2,m1,ki,1)
    end do
  end do

  do j = 2, ipph
    jc = ipp2 - j
    do ki = 1, lid
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        ch1(1,m2,ki,j) =  cc1(1,m1,ki,j) + cc1(1,m1,ki,jc)
        ch1(1,m2,ki,jc) = cc1(1,m1,ki,j) - cc1(1,m1,ki,jc)
        ch1(2,m2,ki,j) =  cc1(2,m1,ki,j) + cc1(2,m1,ki,jc)
        ch1(2,m2,ki,jc) = cc1(2,m1,ki,j) - cc1(2,m1,ki,jc)
      end do
    end do
  end do

  do j = 2, ipph
    do ki = 1, lid
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        cc1(1,m1,ki,1) = cc1(1,m1,ki,1) + ch1(1,m2,ki,j)
        cc1(2,m1,ki,1) = cc1(2,m1,ki,1) + ch1(2,m2,ki,j)
      end do
    end do
  end do

  do l = 2, ipph

    lc = ipp2 - l

    do ki = 1, lid
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        cc1(1,m1,ki,l)  = ch1(1,m2,ki,1) + wa(1,l-1,1) * ch1(1,m2,ki,2)
        cc1(1,m1,ki,lc) =                - wa(1,l-1,2) * ch1(1,m2,ki,ip)
        cc1(2,m1,ki,l)  = ch1(2,m2,ki,1) + wa(1,l-1,1) * ch1(2,m2,ki,2)
        cc1(2,m1,ki,lc) =                - wa(1,l-1,2) * ch1(2,m2,ki,ip)
      end do
    end do

    do j = 3, ipph
      jc = ipp2 - j
      idlj = mod ( ( l - 1 ) * ( j - 1 ), ip )
      war = wa(1,idlj,1)
      wai = -wa(1,idlj,2)
      do ki = 1, lid
        m2 = m2s
        do m1 = 1, m1d, im1
          m2 = m2 + im2
          cc1(1,m1,ki,l)  = cc1(1,m1,ki,l)  + war * ch1(1,m2,ki,j)
          cc1(1,m1,ki,lc) = cc1(1,m1,ki,lc) + wai * ch1(1,m2,ki,jc)
          cc1(2,m1,ki,l)  = cc1(2,m1,ki,l)  + war * ch1(2,m2,ki,j)
          cc1(2,m1,ki,lc) = cc1(2,m1,ki,lc) + wai * ch1(2,m2,ki,jc)
        end do
      end do
    end do

  end do

  if ( 1 < ido ) then

    do ki = 1, lid
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        ch1(1,m2,ki,1) = cc1(1,m1,ki,1)
        ch1(2,m2,ki,1) = cc1(2,m1,ki,1)
      end do
    end do

    do j = 2, ipph
      jc = ipp2 - j
      do ki = 1, lid
        m2 = m2s
        do m1 = 1, m1d, im1
          m2 = m2 + im2
          ch1(1,m2,ki,j)  = cc1(1,m1,ki,j) - cc1(2,m1,ki,jc)
          ch1(2,m2,ki,j)  = cc1(2,m1,ki,j) + cc1(1,m1,ki,jc)
          ch1(1,m2,ki,jc) = cc1(1,m1,ki,j) + cc1(2,m1,ki,jc)
          ch1(2,m2,ki,jc) = cc1(2,m1,ki,j) - cc1(1,m1,ki,jc)
        end do
      end do
    end do

    do i = 1, ido
      do k = 1, l1
        m2 = m2s
        do m1 = 1, m1d, im1
          m2 = m2 + im2
          cc(1,m1,k,1,i) = ch(1,m2,k,i,1)
          cc(2,m1,k,1,i) = ch(2,m2,k,i,1)
        end do
      end do
    end do

    do j = 2, ip
      do k = 1, l1
        m2 = m2s
        do m1 = 1, m1d, im1
          m2 = m2 + im2
          cc(1,m1,k,j,1) = ch(1,m2,k,1,j)
          cc(2,m1,k,j,1) = ch(2,m2,k,1,j)
        end do
      end do
    end do

    do j = 2, ip
      do i = 2, ido
        do k = 1, l1
          m2 = m2s
          do m1 = 1, m1d, im1
            m2 = m2 + im2
            cc(1,m1,k,j,i) = wa(i,j-1,1) * ch(1,m2,k,i,j) &
                           + wa(i,j-1,2) * ch(2,m2,k,i,j)
            cc(2,m1,k,j,i) = wa(i,j-1,1) * ch(2,m2,k,i,j) &
                           - wa(i,j-1,2) * ch(1,m2,k,i,j)
          end do
        end do
      end do
    end do

  else if ( na == 1 ) then

    sn = 1.0E+00 / real ( ip * l1, kind = 4 )

    do ki = 1, lid
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        ch1(1,m2,ki,1) = sn * cc1(1,m1,ki,1)
        ch1(2,m2,ki,1) = sn * cc1(2,m1,ki,1)
      end do
    end do

    do j = 2, ipph
      jc = ipp2 - j
      do ki = 1, lid
        m2 = m2s
        do m1 = 1, m1d, im1
          m2 = m2 + im2
          ch1(1,m2,ki,j)  = sn * ( cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) )
          ch1(2,m2,ki,j)  = sn * ( cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) )
          ch1(1,m2,ki,jc) = sn * ( cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) )
          ch1(2,m2,ki,jc) = sn * ( cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) )
        end do
      end do
    end do

  else

    sn = 1.0E+00 / real ( ip * l1, kind = 4 )

    do ki = 1, lid
      m2 = m2s
      do m1 = 1, m1d, im1
        m2 = m2 + im2
        cc1(1,m1,ki,1) = sn * cc1(1,m1,ki,1)
        cc1(2,m1,ki,1) = sn * cc1(2,m1,ki,1)
      end do
    end do

    do j = 2, ipph
      jc = ipp2 - j
      do ki = 1, lid
        do m1 = 1, m1d, im1
          chold1 = sn * ( cc1(1,m1,ki,j) - cc1(2,m1,ki,jc) )
          chold2 = sn * ( cc1(1,m1,ki,j) + cc1(2,m1,ki,jc) )
          cc1(1,m1,ki,j) = chold1
          cc1(2,m1,ki,jc) = sn * ( cc1(2,m1,ki,j) - cc1(1,m1,ki,jc) )
          cc1(2,m1,ki,j)  = sn * ( cc1(2,m1,ki,j) + cc1(1,m1,ki,jc) )
          cc1(1,m1,ki,jc) = chold2
        end do
      end do
    end do

  end if

  return
end