subroutine r1f4kf ( ido, l1, cc, in1, ch, in2, wa1, wa2, wa3 )

!*****************************************************************************80
!
!! R1F4KF 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 ) l1

  real ( kind = 4 ) cc(in1,ido,l1,4)
  real ( kind = 4 ) ch(in2,ido,4,l1)
  real ( kind = 4 ) hsqt2
  integer ( kind = 4 ) i
  integer ( kind = 4 ) ic
  integer ( kind = 4 ) idp2
  integer ( kind = 4 ) k
  real ( kind = 4 ) wa1(ido)
  real ( kind = 4 ) wa2(ido)
  real ( kind = 4 ) wa3(ido)

  hsqt2 = sqrt ( 2.0E+00 ) / 2.0E+00

  do k = 1, l1
    ch(1,1,1,k)   = ( cc(1,1,k,2) + cc(1,1,k,4) ) &
                  + ( cc(1,1,k,1) + cc(1,1,k,3) )
    ch(1,ido,4,k) = ( cc(1,1,k,1) + cc(1,1,k,3) ) &
                  - ( cc(1,1,k,2) + cc(1,1,k,4) )
    ch(1,ido,2,k) = cc(1,1,k,1) - cc(1,1,k,3)
    ch(1,1,3,k)   = cc(1,1,k,4) - cc(1,1,k,2)
  end do

  if ( ido < 2 ) then
    return
  end if

  if ( 2 < ido ) then

    idp2 = ido + 2

    do k = 1, l1
      do i = 3, ido, 2
        ic = idp2 - i
        ch(1,i-1,1,k) = ((wa1(i-2)*cc(1,i-1,k,2)+wa1(i-1)* &
          cc(1,i,k,2))+(wa3(i-2)*cc(1,i-1,k,4)+wa3(i-1)* &
          cc(1,i,k,4)))+(cc(1,i-1,k,1)+(wa2(i-2)*cc(1,i-1,k,3)+ &
          wa2(i-1)*cc(1,i,k,3)))
        ch(1,ic-1,4,k) = (cc(1,i-1,k,1)+(wa2(i-2)*cc(1,i-1,k,3)+ &
          wa2(i-1)*cc(1,i,k,3)))-((wa1(i-2)*cc(1,i-1,k,2)+ &
          wa1(i-1)*cc(1,i,k,2))+(wa3(i-2)*cc(1,i-1,k,4)+ &
          wa3(i-1)*cc(1,i,k,4)))
        ch(1,i,1,k) = ((wa1(i-2)*cc(1,i,k,2)-wa1(i-1)* &
          cc(1,i-1,k,2))+(wa3(i-2)*cc(1,i,k,4)-wa3(i-1)* &
          cc(1,i-1,k,4)))+(cc(1,i,k,1)+(wa2(i-2)*cc(1,i,k,3)- &
          wa2(i-1)*cc(1,i-1,k,3)))
        ch(1,ic,4,k) = ((wa1(i-2)*cc(1,i,k,2)-wa1(i-1)* &
          cc(1,i-1,k,2))+(wa3(i-2)*cc(1,i,k,4)-wa3(i-1)* &
          cc(1,i-1,k,4)))-(cc(1,i,k,1)+(wa2(i-2)*cc(1,i,k,3)- &
          wa2(i-1)*cc(1,i-1,k,3)))
        ch(1,i-1,3,k) = ((wa1(i-2)*cc(1,i,k,2)-wa1(i-1)* &
          cc(1,i-1,k,2))-(wa3(i-2)*cc(1,i,k,4)-wa3(i-1)* &
          cc(1,i-1,k,4)))+(cc(1,i-1,k,1)-(wa2(i-2)*cc(1,i-1,k,3)+ &
          wa2(i-1)*cc(1,i,k,3)))
        ch(1,ic-1,2,k) = (cc(1,i-1,k,1)-(wa2(i-2)*cc(1,i-1,k,3)+ &
          wa2(i-1)*cc(1,i,k,3)))-((wa1(i-2)*cc(1,i,k,2)-wa1(i-1)* &
          cc(1,i-1,k,2))-(wa3(i-2)*cc(1,i,k,4)-wa3(i-1)* &
          cc(1,i-1,k,4)))
        ch(1,i,3,k) = ((wa3(i-2)*cc(1,i-1,k,4)+wa3(i-1)* &
          cc(1,i,k,4))-(wa1(i-2)*cc(1,i-1,k,2)+wa1(i-1)* &
          cc(1,i,k,2)))+(cc(1,i,k,1)-(wa2(i-2)*cc(1,i,k,3)- &
          wa2(i-1)*cc(1,i-1,k,3)))
        ch(1,ic,2,k) = ((wa3(i-2)*cc(1,i-1,k,4)+wa3(i-1)* &
          cc(1,i,k,4))-(wa1(i-2)*cc(1,i-1,k,2)+wa1(i-1)* &
          cc(1,i,k,2)))-(cc(1,i,k,1)-(wa2(i-2)*cc(1,i,k,3)- &
          wa2(i-1)*cc(1,i-1,k,3)))
       end do
    end do

    if ( mod ( ido, 2 ) == 1 ) then
      return
    end if

  end if

  do k = 1, l1
    ch(1,ido,1,k) = (hsqt2*(cc(1,ido,k,2)-cc(1,ido,k,4)))+ cc(1,ido,k,1)
    ch(1,ido,3,k) = cc(1,ido,k,1)-(hsqt2*(cc(1,ido,k,2)- cc(1,ido,k,4)))
    ch(1,1,2,k) = (-hsqt2*(cc(1,ido,k,2)+cc(1,ido,k,4)))- cc(1,ido,k,3)
    ch(1,1,4,k) = (-hsqt2*(cc(1,ido,k,2)+cc(1,ido,k,4)))+ cc(1,ido,k,3)
  end do

  return
end