radf3 Subroutine

      subroutine radf3(ido, l1, cc, ch, wa1, wa2)
         use fftpack_kind, only: dp => rk
         implicit none
         integer, intent(in) :: ido, l1
         real(dp), intent(in) :: cc(ido, l1, 3), wa1(*), wa2(*)
         real(dp), intent(out) :: ch(ido, 3, l1)
         real(dp) :: ci2, cr2, di2, di3, dr2, dr3, &
                     ti2, ti3, tr2, tr3
         integer :: i, ic, idp2, k
         real(dp), parameter :: taur = -0.5_dp
         ! note: original comment said this was -sqrt(3)/2 but value was 0.86602540378443864676d0
         real(dp), parameter :: taui = sqrt(3.0_dp)/2.0_dp
         do k = 1, l1
            cr2 = cc(1, k, 2) + cc(1, k, 3)
            ch(1, 1, k) = cc(1, k, 1) + cr2
            ch(1, 3, k) = taui*(cc(1, k, 3) - cc(1, k, 2))
            ch(ido, 2, k) = cc(1, k, 1) + taur*cr2
         end do
         if (ido == 1) return
         idp2 = ido + 2
         do k = 1, l1
            do i = 3, ido, 2
               ic = idp2 - i
               dr2 = wa1(i - 2)*cc(i - 1, k, 2) + wa1(i - 1)*cc(i, k, 2)
               di2 = wa1(i - 2)*cc(i, k, 2) - wa1(i - 1)*cc(i - 1, k, 2)
               dr3 = wa2(i - 2)*cc(i - 1, k, 3) + wa2(i - 1)*cc(i, k, 3)
               di3 = wa2(i - 2)*cc(i, k, 3) - wa2(i - 1)*cc(i - 1, k, 3)
               cr2 = dr2 + dr3
               ci2 = di2 + di3
               ch(i - 1, 1, k) = cc(i - 1, k, 1) + cr2
               ch(i, 1, k) = cc(i, k, 1) + ci2
               tr2 = cc(i - 1, k, 1) + taur*cr2
               ti2 = cc(i, k, 1) + taur*ci2
               tr3 = taui*(di2 - di3)
               ti3 = taui*(dr3 - dr2)
               ch(i - 1, 3, k) = tr2 + tr3
               ch(ic - 1, 2, k) = tr2 - tr3
               ch(i, 3, k) = ti2 + ti3
               ch(ic, 2, k) = ti3 - ti2
            end do
         end do
      end subroutine radf3