elpa2_kernels_real.F90 35.1 KB
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!    This file is part of ELPA.
!
!    The ELPA library was originally created by the ELPA consortium,
!    consisting of the following organizations:
!
!    - Max Planck Computing and Data Facility (MPCDF), formerly known as
!      Rechenzentrum Garching der Max-Planck-Gesellschaft (RZG),
!    - Bergische Universität Wuppertal, Lehrstuhl für angewandte
!      Informatik,
!    - Technische Universität München, Lehrstuhl für Informatik mit
!      Schwerpunkt Wissenschaftliches Rechnen ,
!    - Fritz-Haber-Institut, Berlin, Abt. Theorie,
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!    - Max-Plack-Institut für Mathematik in den Naturwissenschaften,
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!      Leipzig, Abt. Komplexe Strukutren in Biologie und Kognition,
!      and
!    - IBM Deutschland GmbH
!
!
!    More information can be found here:
!    http://elpa.mpcdf.mpg.de/
!
!    ELPA is free software: you can redistribute it and/or modify
!    it under the terms of the version 3 of the license of the
!    GNU Lesser General Public License as published by the Free
!    Software Foundation.
!
!    ELPA is distributed in the hope that it will be useful,
!    but WITHOUT ANY WARRANTY; without even the implied warranty of
!    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!    GNU Lesser General Public License for more details.
!
!    You should have received a copy of the GNU Lesser General Public License
!    along with ELPA.  If not, see <http://www.gnu.org/licenses/>
!
!    ELPA reflects a substantial effort on the part of the original
!    ELPA consortium, and we ask you to respect the spirit of the
!    license that we chose: i.e., please contribute any changes you
!    may have back to the original ELPA library distribution, and keep
!    any derivatives of ELPA under the same license that we chose for
!    the original distribution, the GNU Lesser General Public License.
!
!
! --------------------------------------------------------------------------------------------------
!
! This file contains the compute intensive kernels for the Householder transformations.
! It should be compiled with the highest possible optimization level.
!
! On Intel use -O3 -xSSE4.2 (or the SSE level fitting to your CPU)
!
! Copyright of the original code rests with the authors inside the ELPA
! consortium. The copyright of any additional modifications shall rest
! with their original authors, but shall adhere to the licensing terms
! distributed along with the original code in the file "COPYING".
!
! --------------------------------------------------------------------------------------------------
#include "config-f90.h"

#ifdef DESPERATELY_WANT_ASSUMED_SIZE
#define PACK_REAL_TO_COMPLEX
#else
#undef PACK_REAL_TO_COMPLEX
#endif

#ifndef DESPERATELY_WANT_ASSUMED_SIZE
module real_generic_kernel

  private
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  public double_hh_trafo_generic_double

#ifdef WANT_SINGLE_PRECISION_REAL
  public double_hh_trafo_generic_single
#endif

  contains
#endif

  ! the intel compiler creates a temp copy of array q!
  ! this should be prevented if possible without using assumed size arrays
  subroutine double_hh_trafo_generic_double(q, hh, nb, nq, ldq, ldh)
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    use iso_c_binding
    implicit none

    integer(kind=ik), intent(in)      :: nb, nq, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
    real(kind=rk8), intent(inout)      :: q(ldq,*)
    real(kind=rk8), intent(in)         :: hh(ldh,*)
#else
    real(kind=rk8), intent(inout)      :: q(1:ldq,1:nb+1)
    real(kind=rk8), intent(in)         :: hh(1:ldh,1:6)
#endif

    real(kind=rk8)                     :: s
    integer(kind=ik)                  :: i

!    equivalence(q(1,1),q_complex(1,1))

    ! Safety only:
#ifdef HAVE_DETAILED_TIMINGS
    call timer%start("kernel generic: double_hh_trafo_generic_double")
#endif
    if(mod(ldq,4) /= 0) STOP 'double_hh_trafo: ldq not divisible by 4!'

    ! Calculate dot product of the two Householder vectors

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    s = hh(2,2)*1.0
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    do i=3,nb
       s = s+hh(i,2)*hh(i-1,1)
    enddo

    ! Do the Householder transformations

#ifndef DESPERATELY_WANT_ASSUMED_SIZE
!    ! assign real data to compplex pointer
!    call c_f_pointer(c_loc(q), q_complex, [size(q,dim=1)/2,size(q,dim=2)])
#endif
    ! Always a multiple of 4 Q-rows is transformed, even if nq is smaller

    do i=1,nq-8,12
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
       call hh_trafo_kernel_12_generic_double(q(i,1),hh, nb, ldq, ldh, s)
#else
       call hh_trafo_kernel_12_generic_double(q(i:ldq,1:nb+1),hh(1:ldh,1:2), nb, ldq, ldh, s)
#endif
    enddo

    ! i > nq-8 now, i.e. at most 8 rows remain

    if(nq-i+1 > 4) then
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
       call hh_trafo_kernel_8_generic_double(q(i,1),hh, nb, ldq, ldh, s)
#else
       call hh_trafo_kernel_8_generic_double(q(i:ldq,1:nb+1), hh(1:ldh,1:2), nb, ldq, ldh, s)
#endif

    else if(nq-i+1 > 0) then
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
       call hh_trafo_kernel_4_generic_double(q(i,1),hh, nb, ldq, ldh, s)
#else
       call hh_trafo_kernel_4_generic_double(q(i:ldq,1:+nb+1),hh(1:ldh,1:2), nb, ldq, ldh, s)
#endif

    endif
#ifdef HAVE_DETAILED_TIMINGS
    call timer%stop("kernel generic: double_hh_trafo_generic_double")
#endif
  end subroutine double_hh_trafo_generic_double

  ! --------------------------------------------------------------------------------------------------
  ! The following kernels perform the Householder transformation on Q for 12/8/4 rows.
  ! Please note that Q is declared complex*16 here.
  ! This is a hint for compilers that packed arithmetic can be used for Q
  ! (relevant for Intel SSE and BlueGene double hummer CPUs).
  ! --------------------------------------------------------------------------------------------------

  subroutine hh_trafo_kernel_12_generic_double(q, hh, nb, ldq, ldh, s)
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    implicit none

    integer(kind=ik), intent(in)    :: nb, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
    complex(kind=ck8), intent(inout) :: q(ldq/2,*)
    real(kind=rk8), intent(in)       :: hh(ldh,*)
#else
    real(kind=rk8), intent(inout)    :: q(:,:)
    real(kind=rk8), intent(in)       :: hh(ldh,2)
#endif
    real(kind=rk8), intent(in)       :: s

#ifdef PACK_REAL_TO_COMPLEX
    complex(kind=ck8)                :: x1, x2, x3, x4, x5, x6, y1, y2, y3, y4, y5, y6
#else
    real(kind=rk8)                   :: x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, &
                                       y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12
#endif
    real(kind=rk8)                   :: h1, h2, tau1, tau2
    integer(kind=ik)                :: i

#ifdef HAVE_DETAILED_TIMINGS
    call timer%start("kernel generic: hh_trafo_kernel_12_generic_double")
#endif
    x1  = q(1,2)
    x2  = q(2,2)
    x3  = q(3,2)
    x4  = q(4,2)
    x5  = q(5,2)
    x6  = q(6,2)
#ifndef PACK_REAL_TO_COMPLEX
    x7  = q(7,2)
    x8  = q(8,2)
    x9  = q(9,2)
    x10 = q(10,2)
    x11 = q(11,2)
    x12 = q(12,2)
#endif

    y1  = q(1 ,1) + q(1, 2)*hh(2,2)
    y2  = q(2 ,1) + q(2, 2)*hh(2,2)
    y3  = q(3 ,1) + q(3, 2)*hh(2,2)
    y4  = q(4 ,1) + q(4, 2)*hh(2,2)
    y5  = q(5 ,1) + q(5, 2)*hh(2,2)
    y6  = q(6 ,1) + q(6, 2)*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    y7  = q(7 ,1) + q(7, 2)*hh(2,2)
    y8  = q(8 ,1) + q(8, 2)*hh(2,2)
    y9  = q(9 ,1) + q(9, 2)*hh(2,2)
    y10 = q(10,1) + q(10,2)*hh(2,2)
    y11 = q(11,1) + q(11,2)*hh(2,2)
    y12 = q(12,1) + q(12,2)*hh(2,2)
#endif

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#if defined(SSE_ALIGNED)
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    !DEC$ VECTOR ALIGNED
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#endif
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    do i=3,nb
       h1  = hh(i-1,1)
       h2  = hh(i,2)
       x1  = x1 + q(1, i)*h1
       y1  = y1 + q(1, i)*h2
       x2  = x2 + q(2, i)*h1
       y2  = y2 + q(2, i)*h2
       x3  = x3 + q(3, i)*h1
       y3  = y3 + q(3, i)*h2
       x4  = x4 + q(4, i)*h1
       y4  = y4 + q(4, i)*h2
       x5  = x5 + q(5, i)*h1
       y5  = y5 + q(5, i)*h2
       x6  = x6 + q(6, i)*h1
       y6  = y6 + q(6, i)*h2
#ifndef PACK_REAL_TO_COMPLEX
       x7  = x7  + q(7, i)*h1
       y7  = y7  + q(7, i)*h2
       x8  = x8  + q(8, i)*h1
       y8  = y8  + q(8, i)*h2
       x9  = x9  + q(9, i)*h1
       y9  = y9  + q(9, i)*h2
       x10 = x10 + q(10,i)*h1
       y10 = y10 + q(10,i)*h2
       x11 = x11 + q(11,i)*h1
       y11 = y11 + q(11,i)*h2
       x12 = x12 + q(12,i)*h1
       y12 = y12 + q(12,i)*h2
#endif
    enddo

    x1  = x1  + q(1,nb+1)*hh(nb,1)
    x2  = x2  + q(2,nb+1)*hh(nb,1)
    x3  = x3  + q(3,nb+1)*hh(nb,1)
    x4  = x4  + q(4,nb+1)*hh(nb,1)
    x5  = x5  + q(5,nb+1)*hh(nb,1)
    x6  = x6  + q(6,nb+1)*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    x7  = x7  + q(7, nb+1)*hh(nb,1)
    x8  = x8  + q(8, nb+1)*hh(nb,1)
    x9  = x9  + q(9, nb+1)*hh(nb,1)
    x10 = x10 + q(10,nb+1)*hh(nb,1)
    x11 = x11 + q(11,nb+1)*hh(nb,1)
    x12 = x12 + q(12,nb+1)*hh(nb,1)

#endif

    tau1 = hh(1,1)
    tau2 = hh(1,2)

    h1  = -tau1
    x1  = x1 *h1
    x2  = x2 *h1
    x3  = x3 *h1
    x4  = x4 *h1
    x5  = x5 *h1
    x6  = x6 *h1
#ifndef PACK_REAL_TO_COMPLEX
    x7  = x7 *h1
    x8  = x8 *h1
    x9  = x9 *h1
    x10 = x10*h1
    x11 = x11*h1
    x12 = x12*h1
#endif

    h1  = -tau2
    h2  = -tau2*s
    y1  = y1 *h1 + x1 *h2
    y2  = y2 *h1 + x2 *h2
    y3  = y3 *h1 + x3 *h2
    y4  = y4 *h1 + x4 *h2
    y5  = y5 *h1 + x5 *h2
    y6  = y6 *h1 + x6 *h2
#ifndef PACK_REAL_TO_COMPLEX
    y7  = y7 *h1 + x7 *h2
    y8  = y8 *h1 + x8 *h2
    y9  = y9 *h1 + x9 *h2
    y10 = y10*h1 + x10*h2
    y11 = y11*h1 + x11*h2
    y12 = y12*h1 + x12*h2
#endif
    q(1,1)  = q(1, 1) + y1
    q(2,1)  = q(2, 1) + y2
    q(3,1)  = q(3, 1) + y3
    q(4,1)  = q(4, 1) + y4
    q(5,1)  = q(5, 1) + y5
    q(6,1)  = q(6, 1) + y6
#ifndef PACK_REAL_TO_COMPLEX
    q(7 ,1) = q(7, 1) + y7
    q(8 ,1) = q(8, 1) + y8
    q(9 ,1) = q(9, 1) + y9
    q(10,1) = q(10,1) + y10
    q(11,1) = q(11,1) + y11
    q(12,1) = q(12,1) + y12
#endif

    q(1, 2) = q(1, 2) + x1  + y1 *hh(2,2)
    q(2, 2) = q(2, 2) + x2  + y2 *hh(2,2)
    q(3, 2) = q(3, 2) + x3  + y3 *hh(2,2)
    q(4, 2) = q(4, 2) + x4  + y4 *hh(2,2)
    q(5, 2) = q(5, 2) + x5  + y5 *hh(2,2)
    q(6, 2) = q(6, 2) + x6  + y6 *hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    q(7, 2) = q(7, 2) + x7  + y7 *hh(2,2)
    q(8, 2) = q(8, 2) + x8  + y8 *hh(2,2)
    q(9, 2) = q(9, 2) + x9  + y9 *hh(2,2)
    q(10,2) = q(10,2) + x10 + y10*hh(2,2)
    q(11,2) = q(11,2) + x11 + y11*hh(2,2)
    q(12,2) = q(12,2) + x12 + y12*hh(2,2)
#endif
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#if defined(SSE_ALIGNED)
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    !DEC$ VECTOR ALIGNED
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#endif
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    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       q(1, i) = q(1,i)  + x1 *h1 + y1 *h2
       q(2, i) = q(2,i)  + x2 *h1 + y2 *h2
       q(3, i) = q(3,i)  + x3 *h1 + y3 *h2
       q(4, i) = q(4,i)  + x4 *h1 + y4 *h2
       q(5, i) = q(5,i)  + x5 *h1 + y5 *h2
       q(6, i) = q(6,i)  + x6 *h1 + y6 *h2
#ifndef PACK_REAL_TO_COMPLEX
       q(7, i) = q(7, i) + x7 *h1 + y7 *h2
       q(8, i) = q(8, i) + x8 *h1 + y8 *h2
       q(9, i) = q(9, i) + x9 *h1 + y9 *h2
       q(10,i) = q(10,i) + x10*h1 + y10*h2
       q(11,i) = q(11,i) + x11*h1 + y11*h2
       q(12,i) = q(12,i) + x12*h1 + y12*h2
#endif
    enddo

    q(1, nb+1) = q(1, nb+1) + x1 *hh(nb,1)
    q(2, nb+1) = q(2, nb+1) + x2 *hh(nb,1)
    q(3, nb+1) = q(3, nb+1) + x3 *hh(nb,1)
    q(4, nb+1) = q(4, nb+1) + x4 *hh(nb,1)
    q(5, nb+1) = q(5, nb+1) + x5 *hh(nb,1)
    q(6, nb+1) = q(6, nb+1) + x6 *hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    q(7, nb+1) = q(7, nb+1) + x7 *hh(nb,1)
    q(8, nb+1) = q(8, nb+1) + x8 *hh(nb,1)
    q(9, nb+1) = q(9, nb+1) + x9 *hh(nb,1)
    q(10,nb+1) = q(10,nb+1) + x10*hh(nb,1)
    q(11,nb+1) = q(11,nb+1) + x11*hh(nb,1)
    q(12,nb+1) = q(12,nb+1) + x12*hh(nb,1)
#endif


#ifdef HAVE_DETAILED_TIMINGS
    call timer%stop("kernel generic: hh_trafo_kernel_12_generic_double")
#endif
  end subroutine hh_trafo_kernel_12_generic_double

  ! --------------------------------------------------------------------------------------------------

  subroutine hh_trafo_kernel_8_generic_double(q, hh, nb, ldq, ldh, s)
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    implicit none

    integer(kind=ik), intent(in)     :: nb, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
    complex(kind=ck8), intent(inout)  :: q(ldq/2,*)
    real(kind=rk8), intent(in)        :: hh(ldh,*)
#else
    real(kind=rk8),   intent(inout)   :: q(:,:)
    real(kind=rk8), intent(in)        :: hh(ldh,2)
#endif
    real(kind=rk8), intent(in)        :: s
#ifdef PACK_REAL_TO_COMPLEX
    complex(kind=ck8)                 :: x1, x2, x3, x4, y1, y2, y3, y4
#else
    real(kind=rk8)                    :: x1, x2, x3, x4, x5, x6, x7, x8, &
                                        y1, y2, y3, y4, y5, y6, y7, y8
#endif
    real(kind=rk8)                    :: h1, h2, tau1, tau2
    integer(kind=ik)                 :: i

#ifdef HAVE_DETAILED_TIMINGS
    call timer%start("kernel generic: hh_trafo_kernel_8_generic_double")
#endif
    x1 = q(1,2)
    x2 = q(2,2)
    x3 = q(3,2)
    x4 = q(4,2)
#ifndef PACK_REAL_TO_COMPLEX
    x5 = q(5,2)
    x6 = q(6,2)
    x7 = q(7,2)
    x8 = q(8,2)
#endif

    y1 = q(1,1) + q(1,2)*hh(2,2)
    y2 = q(2,1) + q(2,2)*hh(2,2)
    y3 = q(3,1) + q(3,2)*hh(2,2)
    y4 = q(4,1) + q(4,2)*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    y5 = q(5,1) + q(5,2)*hh(2,2)
    y6 = q(6,1) + q(6,2)*hh(2,2)
    y7 = q(7,1) + q(7,2)*hh(2,2)
    y8 = q(8,1) + q(8,2)*hh(2,2)
#endif

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#if defined(SSE_ALIGNED)
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    !DEC$ VECTOR ALIGNED
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#endif

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    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       x1 = x1 + q(1,i)*h1
       y1 = y1 + q(1,i)*h2
       x2 = x2 + q(2,i)*h1
       y2 = y2 + q(2,i)*h2
       x3 = x3 + q(3,i)*h1
       y3 = y3 + q(3,i)*h2
       x4 = x4 + q(4,i)*h1
       y4 = y4 + q(4,i)*h2
#ifndef PACK_REAL_TO_COMPLEX
       x5 = x5 + q(5,i)*h1
       y5 = y5 + q(5,i)*h2
       x6 = x6 + q(6,i)*h1
       y6 = y6 + q(6,i)*h2
       x7 = x7 + q(7,i)*h1
       y7 = y7 + q(7,i)*h2
       x8 = x8 + q(8,i)*h1
       y8 = y8 + q(8,i)*h2
#endif
    enddo

    x1 = x1 + q(1,nb+1)*hh(nb,1)
    x2 = x2 + q(2,nb+1)*hh(nb,1)
    x3 = x3 + q(3,nb+1)*hh(nb,1)
    x4 = x4 + q(4,nb+1)*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    x5 = x5 + q(5,nb+1)*hh(nb,1)
    x6 = x6 + q(6,nb+1)*hh(nb,1)
    x7 = x7 + q(7,nb+1)*hh(nb,1)
    x8 = x8 + q(8,nb+1)*hh(nb,1)
#endif

    tau1 = hh(1,1)
    tau2 = hh(1,2)

    h1 = -tau1
    x1 = x1*h1
    x2 = x2*h1
    x3 = x3*h1
    x4 = x4*h1
#ifndef PACK_REAL_TO_COMPLEX
    x5 = x5*h1
    x6 = x6*h1
    x7 = x7*h1
    x8 = x8*h1
#endif
    h1 = -tau2
    h2 = -tau2*s
    y1 = y1*h1 + x1*h2
    y2 = y2*h1 + x2*h2
    y3 = y3*h1 + x3*h2
    y4 = y4*h1 + x4*h2
#ifndef PACK_REAL_TO_COMPLEX
    y5 = y5*h1 + x5*h2
    y6 = y6*h1 + x6*h2
    y7 = y7*h1 + x7*h2
    y8 = y8*h1 + x8*h2
#endif
    q(1,1) = q(1,1) + y1
    q(2,1) = q(2,1) + y2
    q(3,1) = q(3,1) + y3
    q(4,1) = q(4,1) + y4
#ifndef PACK_REAL_TO_COMPLEX
    q(5,1) = q(5,1) + y5
    q(6,1) = q(6,1) + y6
    q(7,1) = q(7,1) + y7
    q(8,1) = q(8,1) + y8
#endif
    q(1,2) = q(1,2) + x1 + y1*hh(2,2)
    q(2,2) = q(2,2) + x2 + y2*hh(2,2)
    q(3,2) = q(3,2) + x3 + y3*hh(2,2)
    q(4,2) = q(4,2) + x4 + y4*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    q(5,2) = q(5,2) + x5 + y5*hh(2,2)
    q(6,2) = q(6,2) + x6 + y6*hh(2,2)
    q(7,2) = q(7,2) + x7 + y7*hh(2,2)
    q(8,2) = q(8,2) + x8 + y8*hh(2,2)
#endif

513
#if defined(SSE_ALIGNED)
514
    !DEC$ VECTOR ALIGNED
515
#endif
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    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       q(1,i) = q(1,i) + x1*h1 + y1*h2
       q(2,i) = q(2,i) + x2*h1 + y2*h2
       q(3,i) = q(3,i) + x3*h1 + y3*h2
       q(4,i) = q(4,i) + x4*h1 + y4*h2
#ifndef PACK_REAL_TO_COMPLEX
       q(5,i) = q(5,i) + x5*h1 + y5*h2
       q(6,i) = q(6,i) + x6*h1 + y6*h2
       q(7,i) = q(7,i) + x7*h1 + y7*h2
       q(8,i) = q(8,i) + x8*h1 + y8*h2
#endif
    enddo

    q(1,nb+1) = q(1,nb+1) + x1*hh(nb,1)
    q(2,nb+1) = q(2,nb+1) + x2*hh(nb,1)
    q(3,nb+1) = q(3,nb+1) + x3*hh(nb,1)
    q(4,nb+1) = q(4,nb+1) + x4*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    q(5,nb+1) = q(5,nb+1) + x5*hh(nb,1)
    q(6,nb+1) = q(6,nb+1) + x6*hh(nb,1)
    q(7,nb+1) = q(7,nb+1) + x7*hh(nb,1)
    q(8,nb+1) = q(8,nb+1) + x8*hh(nb,1)
#endif

#ifdef HAVE_DETAILED_TIMINGS
    call timer%stop("kernel generic: hh_trafo_kernel_8_generic_double")
#endif

  end subroutine hh_trafo_kernel_8_generic_double

  ! --------------------------------------------------------------------------------------------------

  subroutine hh_trafo_kernel_4_generic_double(q, hh, nb, ldq, ldh, s)
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    implicit none

    integer(kind=ik), intent(in)    :: nb, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
    complex(kind=ck8), intent(inout) :: q(ldq/2,*)
    real(kind=rk8), intent(in)       :: hh(ldh,*)
#else
    real(kind=rk8), intent(inout)    :: q(:,:) !q(1:ldq/2,1:nb+1)
    real(kind=rk8), intent(in)       :: hh(ldh,2)
#endif
    real(kind=rk8), intent(in)       :: s

#ifdef PACK_REAL_TO_COMPLEX
    complex(kind=ck8)                :: x1, x2, y1, y2
#else
    real(kind=rk8)                   :: x1, x2, x3, x4, y1, y2, y3, y4
#endif
    real(kind=rk8)                   :: h1, h2, tau1, tau2
    integer(kind=ik)                :: i

#ifdef HAVE_DETAILED_TIMINGS
    call timer%start("kernel generic: hh_trafo_kernel_4_generic_double")
#endif
    x1 = q(1,2)
    x2 = q(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    x3 = q(3,2)
    x4 = q(4,2)
#endif

    y1 = q(1,1) + q(1,2)*hh(2,2)
    y2 = q(2,1) + q(2,2)*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    y3 = q(3,1) + q(3,2)*hh(2,2)
    y4 = q(4,1) + q(4,2)*hh(2,2)
#endif

592
#if defined(SSE_ALIGNED)
593
    !DEC$ VECTOR ALIGNED
594
#endif
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    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       x1 = x1 + q(1,i)*h1
       y1 = y1 + q(1,i)*h2
       x2 = x2 + q(2,i)*h1
       y2 = y2 + q(2,i)*h2
#ifndef PACK_REAL_TO_COMPLEX
       x3 = x3 + q(3,i)*h1
       y3 = y3 + q(3,i)*h2
       x4 = x4 + q(4,i)*h1
       y4 = y4 + q(4,i)*h2
#endif
    enddo

    x1 = x1 + q(1,nb+1)*hh(nb,1)
    x2 = x2 + q(2,nb+1)*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    x3 = x3 + q(3,nb+1)*hh(nb,1)
    x4 = x4 + q(4,nb+1)*hh(nb,1)
#endif

    tau1 = hh(1,1)
    tau2 = hh(1,2)

    h1 = -tau1
    x1 = x1*h1
    x2 = x2*h1
#ifndef PACK_REAL_TO_COMPLEX
    x3 = x3*h1
    x4 = x4*h1
#endif
    h1 = -tau2
    h2 = -tau2*s
    y1 = y1*h1 + x1*h2
    y2 = y2*h1 + x2*h2
#ifndef PACK_REAL_TO_COMPLEX
    y3 = y3*h1 + x3*h2
    y4 = y4*h1 + x4*h2
#endif

    q(1,1) = q(1,1) + y1
    q(2,1) = q(2,1) + y2
#ifndef PACK_REAL_TO_COMPLEX
    q(3,1) = q(3,1) + y3
    q(4,1) = q(4,1) + y4
#endif
    q(1,2) = q(1,2) + x1 + y1*hh(2,2)
    q(2,2) = q(2,2) + x2 + y2*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    q(3,2) = q(3,2) + x3 + y3*hh(2,2)
    q(4,2) = q(4,2) + x4 + y4*hh(2,2)
#endif

649
#if defined(SSE_ALIGNED)
650
    !DEC$ VECTOR ALIGNED
651
#endif
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    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       q(1,i) = q(1,i) + x1*h1 + y1*h2
       q(2,i) = q(2,i) + x2*h1 + y2*h2
#ifndef PACK_REAL_TO_COMPLEX
       q(3,i) = q(3,i) + x3*h1 + y3*h2
       q(4,i) = q(4,i) + x4*h1 + y4*h2
#endif
    enddo

    q(1,nb+1) = q(1,nb+1) + x1*hh(nb,1)
    q(2,nb+1) = q(2,nb+1) + x2*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    q(3,nb+1) = q(3,nb+1) + x3*hh(nb,1)
    q(4,nb+1) = q(4,nb+1) + x4*hh(nb,1)
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#endif

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#ifdef HAVE_DETAILED_TIMINGS
    call timer%stop("kernel generic: hh_trafo_kernel_4_generic_double")
#endif

  end subroutine hh_trafo_kernel_4_generic_double

#ifdef WANT_SINGLE_PRECISION_REAL
! single precision implementation at the moment duplicated


680 681
  ! the intel compiler creates a temp copy of array q!
  ! this should be prevented if possible without using assumed size arrays
682
  subroutine double_hh_trafo_generic_single(q, hh, nb, nq, ldq, ldh)
683 684 685 686 687 688 689 690 691
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    use iso_c_binding
    implicit none

    integer(kind=ik), intent(in)      :: nb, nq, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
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    real(kind=rk4), intent(inout)      :: q(ldq,*)
    real(kind=rk4), intent(in)         :: hh(ldh,*)
694
#else
695 696
    real(kind=rk4), intent(inout)      :: q(1:ldq,1:nb+1)
    real(kind=rk4), intent(in)         :: hh(1:ldh,1:6)
697 698
#endif

699
    real(kind=rk4)                     :: s
700 701 702 703 704 705
    integer(kind=ik)                  :: i

!    equivalence(q(1,1),q_complex(1,1))

    ! Safety only:
#ifdef HAVE_DETAILED_TIMINGS
706
    call timer%start("kernel generic: double_hh_trafo_generic_single")
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#endif
    if(mod(ldq,4) /= 0) STOP 'double_hh_trafo: ldq not divisible by 4!'

    ! Calculate dot product of the two Householder vectors

    s = hh(2,2)*1
    do i=3,nb
       s = s+hh(i,2)*hh(i-1,1)
    enddo

    ! Do the Householder transformations

#ifndef DESPERATELY_WANT_ASSUMED_SIZE
!    ! assign real data to compplex pointer
!    call c_f_pointer(c_loc(q), q_complex, [size(q,dim=1)/2,size(q,dim=2)])
#endif
    ! Always a multiple of 4 Q-rows is transformed, even if nq is smaller

    do i=1,nq-8,12
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
727
       call hh_trafo_kernel_12_generic_single(q(i,1),hh, nb, ldq, ldh, s)
728
#else
729
       call hh_trafo_kernel_12_generic_single(q(i:ldq,1:nb+1),hh(1:ldh,1:2), nb, ldq, ldh, s)
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#endif
    enddo

    ! i > nq-8 now, i.e. at most 8 rows remain

    if(nq-i+1 > 4) then
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
737
       call hh_trafo_kernel_8_generic_single(q(i,1),hh, nb, ldq, ldh, s)
738
#else
739
       call hh_trafo_kernel_8_generic_single(q(i:ldq,1:nb+1), hh(1:ldh,1:2), nb, ldq, ldh, s)
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#endif

    else if(nq-i+1 > 0) then
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
744
       call hh_trafo_kernel_4_generic_single(q(i,1),hh, nb, ldq, ldh, s)
745
#else
746
       call hh_trafo_kernel_4_generic_single(q(i:ldq,1:+nb+1),hh(1:ldh,1:2), nb, ldq, ldh, s)
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#endif

    endif
#ifdef HAVE_DETAILED_TIMINGS
751
    call timer%stop("kernel generic: double_hh_trafo_generic_single")
752
#endif
753
  end subroutine double_hh_trafo_generic_single
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  ! --------------------------------------------------------------------------------------------------
  ! The following kernels perform the Householder transformation on Q for 12/8/4 rows.
  ! Please note that Q is declared complex*16 here.
  ! This is a hint for compilers that packed arithmetic can be used for Q
  ! (relevant for Intel SSE and BlueGene double hummer CPUs).
  ! --------------------------------------------------------------------------------------------------

762
  subroutine hh_trafo_kernel_12_generic_single(q, hh, nb, ldq, ldh, s)
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    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    implicit none

    integer(kind=ik), intent(in)    :: nb, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
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    complex(kind=ck4), intent(inout) :: q(ldq/2,*)
    real(kind=rk4), intent(in)       :: hh(ldh,*)
773
#else
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    real(kind=rk4), intent(inout)    :: q(:,:)
    real(kind=rk4), intent(in)       :: hh(ldh,2)
776
#endif
777
    real(kind=rk4), intent(in)       :: s
778 779

#ifdef PACK_REAL_TO_COMPLEX
780
    complex(kind=ck4)                :: x1, x2, x3, x4, x5, x6, y1, y2, y3, y4, y5, y6
781
#else
782
    real(kind=rk4)                   :: x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, &
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                                       y1, y2, y3, y4, y5, y6, y7, y8, y9, y10, y11, y12
#endif
785 786
    real(kind=rk4)                   :: h1, h2, tau1, tau2
    integer(kind=ik)                 :: i
787 788

#ifdef HAVE_DETAILED_TIMINGS
789
    call timer%start("kernel generic: hh_trafo_kernel_12_generic_single")
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#endif
    x1  = q(1,2)
    x2  = q(2,2)
    x3  = q(3,2)
    x4  = q(4,2)
    x5  = q(5,2)
    x6  = q(6,2)
#ifndef PACK_REAL_TO_COMPLEX
    x7  = q(7,2)
    x8  = q(8,2)
    x9  = q(9,2)
    x10 = q(10,2)
    x11 = q(11,2)
    x12 = q(12,2)
#endif

    y1  = q(1 ,1) + q(1, 2)*hh(2,2)
    y2  = q(2 ,1) + q(2, 2)*hh(2,2)
    y3  = q(3 ,1) + q(3, 2)*hh(2,2)
    y4  = q(4 ,1) + q(4, 2)*hh(2,2)
    y5  = q(5 ,1) + q(5, 2)*hh(2,2)
    y6  = q(6 ,1) + q(6, 2)*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    y7  = q(7 ,1) + q(7, 2)*hh(2,2)
    y8  = q(8 ,1) + q(8, 2)*hh(2,2)
    y9  = q(9 ,1) + q(9, 2)*hh(2,2)
    y10 = q(10,1) + q(10,2)*hh(2,2)
    y11 = q(11,1) + q(11,2)*hh(2,2)
    y12 = q(12,1) + q(12,2)*hh(2,2)
#endif


    !DEC$ VECTOR ALIGNED
    do i=3,nb
       h1  = hh(i-1,1)
       h2  = hh(i,2)
       x1  = x1 + q(1, i)*h1
       y1  = y1 + q(1, i)*h2
       x2  = x2 + q(2, i)*h1
       y2  = y2 + q(2, i)*h2
       x3  = x3 + q(3, i)*h1
       y3  = y3 + q(3, i)*h2
       x4  = x4 + q(4, i)*h1
       y4  = y4 + q(4, i)*h2
       x5  = x5 + q(5, i)*h1
       y5  = y5 + q(5, i)*h2
       x6  = x6 + q(6, i)*h1
       y6  = y6 + q(6, i)*h2
#ifndef PACK_REAL_TO_COMPLEX
       x7  = x7  + q(7, i)*h1
       y7  = y7  + q(7, i)*h2
       x8  = x8  + q(8, i)*h1
       y8  = y8  + q(8, i)*h2
       x9  = x9  + q(9, i)*h1
       y9  = y9  + q(9, i)*h2
       x10 = x10 + q(10,i)*h1
       y10 = y10 + q(10,i)*h2
       x11 = x11 + q(11,i)*h1
       y11 = y11 + q(11,i)*h2
       x12 = x12 + q(12,i)*h1
       y12 = y12 + q(12,i)*h2
#endif
    enddo

    x1  = x1  + q(1,nb+1)*hh(nb,1)
    x2  = x2  + q(2,nb+1)*hh(nb,1)
    x3  = x3  + q(3,nb+1)*hh(nb,1)
    x4  = x4  + q(4,nb+1)*hh(nb,1)
    x5  = x5  + q(5,nb+1)*hh(nb,1)
    x6  = x6  + q(6,nb+1)*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    x7  = x7  + q(7, nb+1)*hh(nb,1)
    x8  = x8  + q(8, nb+1)*hh(nb,1)
    x9  = x9  + q(9, nb+1)*hh(nb,1)
    x10 = x10 + q(10,nb+1)*hh(nb,1)
    x11 = x11 + q(11,nb+1)*hh(nb,1)
    x12 = x12 + q(12,nb+1)*hh(nb,1)

#endif

    tau1 = hh(1,1)
    tau2 = hh(1,2)

    h1  = -tau1
    x1  = x1 *h1
    x2  = x2 *h1
    x3  = x3 *h1
    x4  = x4 *h1
    x5  = x5 *h1
    x6  = x6 *h1
#ifndef PACK_REAL_TO_COMPLEX
    x7  = x7 *h1
    x8  = x8 *h1
    x9  = x9 *h1
    x10 = x10*h1
    x11 = x11*h1
    x12 = x12*h1
#endif

    h1  = -tau2
    h2  = -tau2*s
    y1  = y1 *h1 + x1 *h2
    y2  = y2 *h1 + x2 *h2
    y3  = y3 *h1 + x3 *h2
    y4  = y4 *h1 + x4 *h2
    y5  = y5 *h1 + x5 *h2
    y6  = y6 *h1 + x6 *h2
#ifndef PACK_REAL_TO_COMPLEX
    y7  = y7 *h1 + x7 *h2
    y8  = y8 *h1 + x8 *h2
    y9  = y9 *h1 + x9 *h2
    y10 = y10*h1 + x10*h2
    y11 = y11*h1 + x11*h2
    y12 = y12*h1 + x12*h2
#endif
    q(1,1)  = q(1, 1) + y1
    q(2,1)  = q(2, 1) + y2
    q(3,1)  = q(3, 1) + y3
    q(4,1)  = q(4, 1) + y4
    q(5,1)  = q(5, 1) + y5
    q(6,1)  = q(6, 1) + y6
#ifndef PACK_REAL_TO_COMPLEX
    q(7 ,1) = q(7, 1) + y7
    q(8 ,1) = q(8, 1) + y8
    q(9 ,1) = q(9, 1) + y9
    q(10,1) = q(10,1) + y10
    q(11,1) = q(11,1) + y11
    q(12,1) = q(12,1) + y12
#endif

    q(1, 2) = q(1, 2) + x1  + y1 *hh(2,2)
    q(2, 2) = q(2, 2) + x2  + y2 *hh(2,2)
    q(3, 2) = q(3, 2) + x3  + y3 *hh(2,2)
    q(4, 2) = q(4, 2) + x4  + y4 *hh(2,2)
    q(5, 2) = q(5, 2) + x5  + y5 *hh(2,2)
    q(6, 2) = q(6, 2) + x6  + y6 *hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    q(7, 2) = q(7, 2) + x7  + y7 *hh(2,2)
    q(8, 2) = q(8, 2) + x8  + y8 *hh(2,2)
    q(9, 2) = q(9, 2) + x9  + y9 *hh(2,2)
    q(10,2) = q(10,2) + x10 + y10*hh(2,2)
    q(11,2) = q(11,2) + x11 + y11*hh(2,2)
    q(12,2) = q(12,2) + x12 + y12*hh(2,2)
#endif
    !DEC$ VECTOR ALIGNED
    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       q(1, i) = q(1,i)  + x1 *h1 + y1 *h2
       q(2, i) = q(2,i)  + x2 *h1 + y2 *h2
       q(3, i) = q(3,i)  + x3 *h1 + y3 *h2
       q(4, i) = q(4,i)  + x4 *h1 + y4 *h2
       q(5, i) = q(5,i)  + x5 *h1 + y5 *h2
       q(6, i) = q(6,i)  + x6 *h1 + y6 *h2
#ifndef PACK_REAL_TO_COMPLEX
       q(7, i) = q(7, i) + x7 *h1 + y7 *h2
       q(8, i) = q(8, i) + x8 *h1 + y8 *h2
       q(9, i) = q(9, i) + x9 *h1 + y9 *h2
       q(10,i) = q(10,i) + x10*h1 + y10*h2
       q(11,i) = q(11,i) + x11*h1 + y11*h2
       q(12,i) = q(12,i) + x12*h1 + y12*h2
#endif
    enddo

    q(1, nb+1) = q(1, nb+1) + x1 *hh(nb,1)
    q(2, nb+1) = q(2, nb+1) + x2 *hh(nb,1)
    q(3, nb+1) = q(3, nb+1) + x3 *hh(nb,1)
    q(4, nb+1) = q(4, nb+1) + x4 *hh(nb,1)
    q(5, nb+1) = q(5, nb+1) + x5 *hh(nb,1)
    q(6, nb+1) = q(6, nb+1) + x6 *hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    q(7, nb+1) = q(7, nb+1) + x7 *hh(nb,1)
    q(8, nb+1) = q(8, nb+1) + x8 *hh(nb,1)
    q(9, nb+1) = q(9, nb+1) + x9 *hh(nb,1)
    q(10,nb+1) = q(10,nb+1) + x10*hh(nb,1)
    q(11,nb+1) = q(11,nb+1) + x11*hh(nb,1)
    q(12,nb+1) = q(12,nb+1) + x12*hh(nb,1)
#endif


#ifdef HAVE_DETAILED_TIMINGS
971
    call timer%stop("kernel generic: hh_trafo_kernel_12_generic_single")
972
#endif
973
  end subroutine hh_trafo_kernel_12_generic_single
974 975 976

  ! --------------------------------------------------------------------------------------------------

977
  subroutine hh_trafo_kernel_8_generic_single(q, hh, nb, ldq, ldh, s)
978 979 980 981 982 983 984 985
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    implicit none

    integer(kind=ik), intent(in)     :: nb, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
986 987
    complex(kind=ck4), intent(inout)  :: q(ldq/2,*)
    real(kind=rk4), intent(in)        :: hh(ldh,*)
988
#else
989 990
    real(kind=rk4),   intent(inout)   :: q(:,:)
    real(kind=rk4), intent(in)        :: hh(ldh,2)
991
#endif
992
    real(kind=rk4), intent(in)        :: s
993
#ifdef PACK_REAL_TO_COMPLEX
994
    complex(kind=ck4)                 :: x1, x2, x3, x4, y1, y2, y3, y4
995
#else
996
    real(kind=rk4)                    :: x1, x2, x3, x4, x5, x6, x7, x8, &
997 998
                                        y1, y2, y3, y4, y5, y6, y7, y8
#endif
999 1000
    real(kind=rk4)                    :: h1, h2, tau1, tau2
    integer(kind=ik)                  :: i
1001 1002

#ifdef HAVE_DETAILED_TIMINGS
1003
    call timer%start("kernel generic: hh_trafo_kernel_8_generic_single")
1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137
#endif
    x1 = q(1,2)
    x2 = q(2,2)
    x3 = q(3,2)
    x4 = q(4,2)
#ifndef PACK_REAL_TO_COMPLEX
    x5 = q(5,2)
    x6 = q(6,2)
    x7 = q(7,2)
    x8 = q(8,2)
#endif

    y1 = q(1,1) + q(1,2)*hh(2,2)
    y2 = q(2,1) + q(2,2)*hh(2,2)
    y3 = q(3,1) + q(3,2)*hh(2,2)
    y4 = q(4,1) + q(4,2)*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    y5 = q(5,1) + q(5,2)*hh(2,2)
    y6 = q(6,1) + q(6,2)*hh(2,2)
    y7 = q(7,1) + q(7,2)*hh(2,2)
    y8 = q(8,1) + q(8,2)*hh(2,2)
#endif

    !DEC$ VECTOR ALIGNED
    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       x1 = x1 + q(1,i)*h1
       y1 = y1 + q(1,i)*h2
       x2 = x2 + q(2,i)*h1
       y2 = y2 + q(2,i)*h2
       x3 = x3 + q(3,i)*h1
       y3 = y3 + q(3,i)*h2
       x4 = x4 + q(4,i)*h1
       y4 = y4 + q(4,i)*h2
#ifndef PACK_REAL_TO_COMPLEX
       x5 = x5 + q(5,i)*h1
       y5 = y5 + q(5,i)*h2
       x6 = x6 + q(6,i)*h1
       y6 = y6 + q(6,i)*h2
       x7 = x7 + q(7,i)*h1
       y7 = y7 + q(7,i)*h2
       x8 = x8 + q(8,i)*h1
       y8 = y8 + q(8,i)*h2
#endif
    enddo

    x1 = x1 + q(1,nb+1)*hh(nb,1)
    x2 = x2 + q(2,nb+1)*hh(nb,1)
    x3 = x3 + q(3,nb+1)*hh(nb,1)
    x4 = x4 + q(4,nb+1)*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    x5 = x5 + q(5,nb+1)*hh(nb,1)
    x6 = x6 + q(6,nb+1)*hh(nb,1)
    x7 = x7 + q(7,nb+1)*hh(nb,1)
    x8 = x8 + q(8,nb+1)*hh(nb,1)
#endif

    tau1 = hh(1,1)
    tau2 = hh(1,2)

    h1 = -tau1
    x1 = x1*h1
    x2 = x2*h1
    x3 = x3*h1
    x4 = x4*h1
#ifndef PACK_REAL_TO_COMPLEX
    x5 = x5*h1
    x6 = x6*h1
    x7 = x7*h1
    x8 = x8*h1
#endif
    h1 = -tau2
    h2 = -tau2*s
    y1 = y1*h1 + x1*h2
    y2 = y2*h1 + x2*h2
    y3 = y3*h1 + x3*h2
    y4 = y4*h1 + x4*h2
#ifndef PACK_REAL_TO_COMPLEX
    y5 = y5*h1 + x5*h2
    y6 = y6*h1 + x6*h2
    y7 = y7*h1 + x7*h2
    y8 = y8*h1 + x8*h2
#endif
    q(1,1) = q(1,1) + y1
    q(2,1) = q(2,1) + y2
    q(3,1) = q(3,1) + y3
    q(4,1) = q(4,1) + y4
#ifndef PACK_REAL_TO_COMPLEX
    q(5,1) = q(5,1) + y5
    q(6,1) = q(6,1) + y6
    q(7,1) = q(7,1) + y7
    q(8,1) = q(8,1) + y8
#endif
    q(1,2) = q(1,2) + x1 + y1*hh(2,2)
    q(2,2) = q(2,2) + x2 + y2*hh(2,2)
    q(3,2) = q(3,2) + x3 + y3*hh(2,2)
    q(4,2) = q(4,2) + x4 + y4*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    q(5,2) = q(5,2) + x5 + y5*hh(2,2)
    q(6,2) = q(6,2) + x6 + y6*hh(2,2)
    q(7,2) = q(7,2) + x7 + y7*hh(2,2)
    q(8,2) = q(8,2) + x8 + y8*hh(2,2)
#endif


    !DEC$ VECTOR ALIGNED
    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       q(1,i) = q(1,i) + x1*h1 + y1*h2
       q(2,i) = q(2,i) + x2*h1 + y2*h2
       q(3,i) = q(3,i) + x3*h1 + y3*h2
       q(4,i) = q(4,i) + x4*h1 + y4*h2
#ifndef PACK_REAL_TO_COMPLEX
       q(5,i) = q(5,i) + x5*h1 + y5*h2
       q(6,i) = q(6,i) + x6*h1 + y6*h2
       q(7,i) = q(7,i) + x7*h1 + y7*h2
       q(8,i) = q(8,i) + x8*h1 + y8*h2
#endif
    enddo

    q(1,nb+1) = q(1,nb+1) + x1*hh(nb,1)
    q(2,nb+1) = q(2,nb+1) + x2*hh(nb,1)
    q(3,nb+1) = q(3,nb+1) + x3*hh(nb,1)
    q(4,nb+1) = q(4,nb+1) + x4*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    q(5,nb+1) = q(5,nb+1) + x5*hh(nb,1)
    q(6,nb+1) = q(6,nb+1) + x6*hh(nb,1)
    q(7,nb+1) = q(7,nb+1) + x7*hh(nb,1)
    q(8,nb+1) = q(8,nb+1) + x8*hh(nb,1)
#endif

#ifdef HAVE_DETAILED_TIMINGS
1138
    call timer%stop("kernel generic: hh_trafo_kernel_8_generic_single")
1139 1140
#endif

1141
  end subroutine hh_trafo_kernel_8_generic_single
1142 1143 1144

  ! --------------------------------------------------------------------------------------------------

1145
  subroutine hh_trafo_kernel_4_generic_single(q, hh, nb, ldq, ldh, s)
1146 1147 1148 1149 1150 1151 1152 1153
    use precision
#ifdef HAVE_DETAILED_TIMINGS
    use timings
#endif
    implicit none

    integer(kind=ik), intent(in)    :: nb, ldq, ldh
#ifdef DESPERATELY_WANT_ASSUMED_SIZE
1154 1155
    complex(kind=ck4), intent(inout) :: q(ldq/2,*)
    real(kind=rk4), intent(in)       :: hh(ldh,*)
1156
#else
1157 1158
    real(kind=rk4), intent(inout)    :: q(:,:) !q(1:ldq/2,1:nb+1)
    real(kind=rk4), intent(in)       :: hh(ldh,2)
1159
#endif
1160
    real(kind=rk4), intent(in)       :: s
1161 1162

#ifdef PACK_REAL_TO_COMPLEX
1163
    complex(kind=ck4)                :: x1, x2, y1, y2
1164
#else
1165
    real(kind=rk4)                   :: x1, x2, x3, x4, y1, y2, y3, y4
1166
#endif
1167
    real(kind=rk4)                   :: h1, h2, tau1, tau2
1168
    integer(kind=ik)                 :: i
1169 1170

#ifdef HAVE_DETAILED_TIMINGS
1171
    call timer%start("kernel generic: hh_trafo_kernel_4_generic_single")
1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261
#endif
    x1 = q(1,2)
    x2 = q(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    x3 = q(3,2)
    x4 = q(4,2)
#endif

    y1 = q(1,1) + q(1,2)*hh(2,2)
    y2 = q(2,1) + q(2,2)*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    y3 = q(3,1) + q(3,2)*hh(2,2)
    y4 = q(4,1) + q(4,2)*hh(2,2)
#endif

    !DEC$ VECTOR ALIGNED
    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       x1 = x1 + q(1,i)*h1
       y1 = y1 + q(1,i)*h2
       x2 = x2 + q(2,i)*h1
       y2 = y2 + q(2,i)*h2
#ifndef PACK_REAL_TO_COMPLEX
       x3 = x3 + q(3,i)*h1
       y3 = y3 + q(3,i)*h2
       x4 = x4 + q(4,i)*h1
       y4 = y4 + q(4,i)*h2
#endif
    enddo

    x1 = x1 + q(1,nb+1)*hh(nb,1)
    x2 = x2 + q(2,nb+1)*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    x3 = x3 + q(3,nb+1)*hh(nb,1)
    x4 = x4 + q(4,nb+1)*hh(nb,1)
#endif

    tau1 = hh(1,1)
    tau2 = hh(1,2)

    h1 = -tau1
    x1 = x1*h1
    x2 = x2*h1
#ifndef PACK_REAL_TO_COMPLEX
    x3 = x3*h1
    x4 = x4*h1
#endif
    h1 = -tau2
    h2 = -tau2*s
    y1 = y1*h1 + x1*h2
    y2 = y2*h1 + x2*h2
#ifndef PACK_REAL_TO_COMPLEX
    y3 = y3*h1 + x3*h2
    y4 = y4*h1 + x4*h2
#endif

    q(1,1) = q(1,1) + y1
    q(2,1) = q(2,1) + y2
#ifndef PACK_REAL_TO_COMPLEX
    q(3,1) = q(3,1) + y3
    q(4,1) = q(4,1) + y4
#endif
    q(1,2) = q(1,2) + x1 + y1*hh(2,2)
    q(2,2) = q(2,2) + x2 + y2*hh(2,2)
#ifndef PACK_REAL_TO_COMPLEX
    q(3,2) = q(3,2) + x3 + y3*hh(2,2)
    q(4,2) = q(4,2) + x4 + y4*hh(2,2)
#endif

    !DEC$ VECTOR ALIGNED
    do i=3,nb
       h1 = hh(i-1,1)
       h2 = hh(i,2)
       q(1,i) = q(1,i) + x1*h1 + y1*h2
       q(2,i) = q(2,i) + x2*h1 + y2*h2
#ifndef PACK_REAL_TO_COMPLEX
       q(3,i) = q(3,i) + x3*h1 + y3*h2
       q(4,i) = q(4,i) + x4*h1 + y4*h2
#endif
    enddo

    q(1,nb+1) = q(1,nb+1) + x1*hh(nb,1)
    q(2,nb+1) = q(2,nb+1) + x2*hh(nb,1)
#ifndef PACK_REAL_TO_COMPLEX
    q(3,nb+1) = q(3,nb+1) + x3*hh(nb,1)
    q(4,nb+1) = q(4,nb+1) + x4*hh(nb,1)
#endif

#ifdef HAVE_DETAILED_TIMINGS
1262
    call timer%stop("kernel generic: hh_trafo_kernel_4_generic_single")
1263 1264
#endif

1265 1266 1267 1268
  end subroutine hh_trafo_kernel_4_generic_single

#endif /* WANT_SINGLE_PRECISION_REAL */

1269 1270 1271 1272
#ifndef DESPERATELY_WANT_ASSUMED_SIZE
end module real_generic_kernel
#endif
! --------------------------------------------------------------------------------------------------