//#####################################################################
// Copyright (c) 2010-2011, Eftychios Sifakis.
//
// Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
//   * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
//   * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or
//     other materials provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
// SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//#####################################################################

#ifdef __INTEL_COMPILER
#pragma warning( disable : 592 )
#endif

// #define USE_ACCURATE_RSQRT_IN_JACOBI_CONJUGATION
// #define PERFORM_STRICT_QUATERNION_RENORMALIZATION

{ // Begin block : Scope of qV (if not maintained)

#ifndef COMPUTE_V_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvs;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vqvs;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vqvs;) 
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvx;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvx;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvx;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvy;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvy;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvy;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvz;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvz;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvz;)
#endif

{ // Begin block : Symmetric eigenanalysis

    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss11;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs11;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss21;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs21;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss31;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs31;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss22;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs22;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss32;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs32;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss33;)                  ENABLE_SSE_IMPLEMENTATION(__m128 Vs33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vs33;)

    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vqvs=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vqvs=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_xor_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_xor_ps(Vqvvx,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_xor_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_xor_ps(Vqvvy,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_xor_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_xor_ps(Vqvvz,Vqvvz);)

    //###########################################################
    // Compute normal equations matrix
    //###########################################################

    ENABLE_SCALAR_IMPLEMENTATION(Ss11.f=Sa11.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs11=_mm_mul_ps(Va11,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Vs11=_mm256_mul_ps(Va11,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa21.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va21,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va21,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss11.f=Stmp1.f+Ss11.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs11=_mm_add_ps(Vtmp1,Vs11);)                                   ENABLE_AVX_IMPLEMENTATION(Vs11=_mm256_add_ps(Vtmp1,Vs11);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa31.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va31,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va31,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss11.f=Stmp1.f+Ss11.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs11=_mm_add_ps(Vtmp1,Vs11);)                                   ENABLE_AVX_IMPLEMENTATION(Vs11=_mm256_add_ps(Vtmp1,Vs11);)

    ENABLE_SCALAR_IMPLEMENTATION(Ss21.f=Sa12.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs21=_mm_mul_ps(Va12,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Vs21=_mm256_mul_ps(Va12,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa22.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va22,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va22,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss21.f=Stmp1.f+Ss21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs21=_mm_add_ps(Vtmp1,Vs21);)                                   ENABLE_AVX_IMPLEMENTATION(Vs21=_mm256_add_ps(Vtmp1,Vs21);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa32.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va32,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va32,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss21.f=Stmp1.f+Ss21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs21=_mm_add_ps(Vtmp1,Vs21);)                                   ENABLE_AVX_IMPLEMENTATION(Vs21=_mm256_add_ps(Vtmp1,Vs21);)

    ENABLE_SCALAR_IMPLEMENTATION(Ss31.f=Sa13.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs31=_mm_mul_ps(Va13,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Vs31=_mm256_mul_ps(Va13,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa23.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va23,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va23,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss31.f=Stmp1.f+Ss31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs31=_mm_add_ps(Vtmp1,Vs31);)                                   ENABLE_AVX_IMPLEMENTATION(Vs31=_mm256_add_ps(Vtmp1,Vs31);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa33.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va33,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va33,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss31.f=Stmp1.f+Ss31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs31=_mm_add_ps(Vtmp1,Vs31);)                                   ENABLE_AVX_IMPLEMENTATION(Vs31=_mm256_add_ps(Vtmp1,Vs31);)

    ENABLE_SCALAR_IMPLEMENTATION(Ss22.f=Sa12.f*Sa12.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs22=_mm_mul_ps(Va12,Va12);)                                    ENABLE_AVX_IMPLEMENTATION(Vs22=_mm256_mul_ps(Va12,Va12);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa22.f*Sa22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va22,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va22,Va22);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss22.f=Stmp1.f+Ss22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs22=_mm_add_ps(Vtmp1,Vs22);)                                   ENABLE_AVX_IMPLEMENTATION(Vs22=_mm256_add_ps(Vtmp1,Vs22);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa32.f*Sa32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va32,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va32,Va32);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss22.f=Stmp1.f+Ss22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs22=_mm_add_ps(Vtmp1,Vs22);)                                   ENABLE_AVX_IMPLEMENTATION(Vs22=_mm256_add_ps(Vtmp1,Vs22);)

    ENABLE_SCALAR_IMPLEMENTATION(Ss32.f=Sa13.f*Sa12.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs32=_mm_mul_ps(Va13,Va12);)                                    ENABLE_AVX_IMPLEMENTATION(Vs32=_mm256_mul_ps(Va13,Va12);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa23.f*Sa22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va23,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va23,Va22);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss32.f=Stmp1.f+Ss32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs32=_mm_add_ps(Vtmp1,Vs32);)                                   ENABLE_AVX_IMPLEMENTATION(Vs32=_mm256_add_ps(Vtmp1,Vs32);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa33.f*Sa32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va33,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va33,Va32);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss32.f=Stmp1.f+Ss32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs32=_mm_add_ps(Vtmp1,Vs32);)                                   ENABLE_AVX_IMPLEMENTATION(Vs32=_mm256_add_ps(Vtmp1,Vs32);)

    ENABLE_SCALAR_IMPLEMENTATION(Ss33.f=Sa13.f*Sa13.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs33=_mm_mul_ps(Va13,Va13);)                                    ENABLE_AVX_IMPLEMENTATION(Vs33=_mm256_mul_ps(Va13,Va13);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa23.f*Sa23.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va23,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va23,Va23);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss33.f=Stmp1.f+Ss33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs33=_mm_add_ps(Vtmp1,Vs33);)                                   ENABLE_AVX_IMPLEMENTATION(Vs33=_mm256_add_ps(Vtmp1,Vs33);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa33.f*Sa33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va33,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va33,Va33);)
    ENABLE_SCALAR_IMPLEMENTATION(Ss33.f=Stmp1.f+Ss33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vs33=_mm_add_ps(Vtmp1,Vs33);)                                   ENABLE_AVX_IMPLEMENTATION(Vs33=_mm256_add_ps(Vtmp1,Vs33);)
    
    //###########################################################
    // Solve symmetric eigenproblem using Jacobi iteration
    //###########################################################

    for(int sweep=1;sweep<=4;sweep++){

        // First Jacobi conjugation

#define SS11 Ss11
#define SS21 Ss21
#define SS31 Ss31
#define SS22 Ss22
#define SS32 Ss32
#define SS33 Ss33
#define SQVVX Sqvvx
#define SQVVY Sqvvy
#define SQVVZ Sqvvz
#define STMP1 Stmp1
#define STMP2 Stmp2
#define STMP3 Stmp3

#define VS11 Vs11
#define VS21 Vs21
#define VS31 Vs31
#define VS22 Vs22
#define VS32 Vs32
#define VS33 Vs33
#define VQVVX Vqvvx
#define VQVVY Vqvvy
#define VQVVZ Vqvvz
#define VTMP1 Vtmp1
#define VTMP2 Vtmp2
#define VTMP3 Vtmp3

#include "Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp"

#undef SS11
#undef SS21
#undef SS31
#undef SS22
#undef SS32
#undef SS33
#undef SQVVX
#undef SQVVY
#undef SQVVZ
#undef STMP1
#undef STMP2
#undef STMP3

#undef VS11
#undef VS21
#undef VS31
#undef VS22
#undef VS32
#undef VS33
#undef VQVVX
#undef VQVVY
#undef VQVVZ
#undef VTMP1
#undef VTMP2
#undef VTMP3

        // Second Jacobi conjugation

#define SS11 Ss22
#define SS21 Ss32
#define SS31 Ss21
#define SS22 Ss33
#define SS32 Ss31
#define SS33 Ss11
#define SQVVX Sqvvy
#define SQVVY Sqvvz
#define SQVVZ Sqvvx
#define STMP1 Stmp2
#define STMP2 Stmp3
#define STMP3 Stmp1

#define VS11 Vs22
#define VS21 Vs32
#define VS31 Vs21
#define VS22 Vs33
#define VS32 Vs31
#define VS33 Vs11
#define VQVVX Vqvvy
#define VQVVY Vqvvz
#define VQVVZ Vqvvx
#define VTMP1 Vtmp2
#define VTMP2 Vtmp3
#define VTMP3 Vtmp1

#include "Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp"

#undef SS11
#undef SS21
#undef SS31
#undef SS22
#undef SS32
#undef SS33
#undef SQVVX
#undef SQVVY
#undef SQVVZ
#undef STMP1
#undef STMP2
#undef STMP3

#undef VS11
#undef VS21
#undef VS31
#undef VS22
#undef VS32
#undef VS33
#undef VQVVX
#undef VQVVY
#undef VQVVZ
#undef VTMP1
#undef VTMP2
#undef VTMP3

        // Third Jacobi conjugation

#define SS11 Ss33
#define SS21 Ss31
#define SS31 Ss32
#define SS22 Ss11
#define SS32 Ss21
#define SS33 Ss22
#define SQVVX Sqvvz
#define SQVVY Sqvvx
#define SQVVZ Sqvvy
#define STMP1 Stmp3
#define STMP2 Stmp1
#define STMP3 Stmp2

#define VS11 Vs33
#define VS21 Vs31
#define VS31 Vs32
#define VS22 Vs11
#define VS32 Vs21
#define VS33 Vs22
#define VQVVX Vqvvz
#define VQVVY Vqvvx
#define VQVVZ Vqvvy
#define VTMP1 Vtmp3
#define VTMP2 Vtmp1
#define VTMP3 Vtmp2

#include "Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp"

#undef SS11
#undef SS21
#undef SS31
#undef SS22
#undef SS32
#undef SS33
#undef SQVVX
#undef SQVVY
#undef SQVVZ
#undef STMP1
#undef STMP2
#undef STMP3

#undef VS11
#undef VS21
#undef VS31
#undef VS22
#undef VS32
#undef VS33
#undef VQVVX
#undef VQVVY
#undef VQVVZ
#undef VTMP1
#undef VTMP2
#undef VTMP3
    }

#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar S ="<<std::endl;
    std::cout<<std::setw(12)<<Ss11.f<<std::endl;
    std::cout<<std::setw(12)<<Ss21.f<<"  "<<std::setw(12)<<Ss22.f<<std::endl;
    std::cout<<std::setw(12)<<Ss31.f<<"  "<<std::setw(12)<<Ss32.f<<"  "<<std::setw(12)<<Ss33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vs11);S11=buf[0];
    _mm_storeu_ps(buf,Vs21);S21=buf[0];
    _mm_storeu_ps(buf,Vs31);S31=buf[0];
    _mm_storeu_ps(buf,Vs22);S22=buf[0];
    _mm_storeu_ps(buf,Vs32);S32=buf[0];
    _mm_storeu_ps(buf,Vs33);S33=buf[0];
    std::cout<<"Vector S ="<<std::endl;
    std::cout<<std::setw(12)<<S11<<std::endl;
    std::cout<<std::setw(12)<<S21<<"  "<<std::setw(12)<<S22<<std::endl;
    std::cout<<std::setw(12)<<S31<<"  "<<std::setw(12)<<S32<<"  "<<std::setw(12)<<S33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vs11);S11=buf[0];
    _mm256_storeu_ps(buf,Vs21);S21=buf[0];
    _mm256_storeu_ps(buf,Vs31);S31=buf[0];
    _mm256_storeu_ps(buf,Vs22);S22=buf[0];
    _mm256_storeu_ps(buf,Vs32);S32=buf[0];
    _mm256_storeu_ps(buf,Vs33);S33=buf[0];
    std::cout<<"Vector S ="<<std::endl;
    std::cout<<std::setw(12)<<S11<<std::endl;
    std::cout<<std::setw(12)<<S21<<"  "<<std::setw(12)<<S22<<std::endl;
    std::cout<<std::setw(12)<<S31<<"  "<<std::setw(12)<<S32<<"  "<<std::setw(12)<<S33<<std::endl;
#endif
#endif

} // End block : Symmetric eigenanalysis

    //###########################################################
    // Normalize quaternion for matrix V
    //###########################################################

#if !defined(USE_ACCURATE_RSQRT_IN_JACOBI_CONJUGATION) || defined(PERFORM_STRICT_QUATERNION_RENORMALIZATION)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvs.f*Sqvs.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvs,Vqvs);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvs,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvx,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvy.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvy,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvz.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvz,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=rsqrt(Stmp2.f);)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_rsqrt_ps(Vtmp2);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_rsqrt_ps(Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp1.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp1,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp1,Vone_half);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp2.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp2,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f-Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_sub_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_sub_ps(Vtmp1,Vtmp3);)

    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vqvvx,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vqvvx,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vqvvy,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vqvvy,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vqvvz,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vqvvz,Vtmp1);)

#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar qV ="<<std::endl;
    std::cout<<std::setw(12)<<Sqvs.f<<"  "<<std::setw(12)<<Sqvvx.f<<"  "<<std::setw(12)<<Sqvvy.f<<"  "<<std::setw(12)<<Sqvvz.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vqvs);QVS=buf[0];
    _mm_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    _mm_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    _mm_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    std::cout<<"Vector qV ="<<std::endl;
    std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vqvs);QVS=buf[0];
    _mm256_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    _mm256_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    _mm256_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    std::cout<<"Vector qV ="<<std::endl;
    std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
#endif
#endif

#endif

{ // Begin block : Conjugation with V

    //###########################################################
    // Transform quaternion to matrix V
    //###########################################################

#ifndef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv11;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv11;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv21;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv21;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv31;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv31;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv12;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv12;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv22;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv22;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv32;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv32;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv13;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv13;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv23;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv23;)
    ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv33;)                  ENABLE_VECTOR_IMPLEMENTATION(__m128 Vv33;)
#endif

    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvx,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvvy.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvvy,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sqvvz.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vqvvz,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sqvs.f*Sqvs.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_mul_ps(Vqvs,Vqvs);)                                    ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_mul_ps(Vqvs,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv11.f-Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_sub_ps(Vv11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_sub_ps(Vv11,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv33.f=Sv22.f-Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_sub_ps(Vv22,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_sub_ps(Vv22,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv33.f=Sv33.f+Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_add_ps(Vv33,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_add_ps(Vv33,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv22.f+Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_add_ps(Vv22,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_add_ps(Vv22,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv22.f-Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_sub_ps(Vv22,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_sub_ps(Vv22,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_add_ps(Vv11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_add_ps(Vv11,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f-Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_sub_ps(Vv11,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_sub_ps(Vv11,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f-Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_sub_ps(Vv11,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_sub_ps(Vv11,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f+Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vqvvx,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvvy.f+Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vqvvy,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sqvvz.f+Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vqvvz,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv32.f=Sqvs.f*Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_mul_ps(Vqvs,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_mul_ps(Vqvs,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv13.f=Sqvs.f*Stmp2.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_mul_ps(Vqvs,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_mul_ps(Vqvs,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv21.f=Sqvs.f*Stmp3.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_mul_ps(Vqvs,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_mul_ps(Vqvs,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvy.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvy,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvy,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvvz.f*Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvvz,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvvz,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sqvvx.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vqvvx,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vqvvx,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv12.f=Stmp1.f-Sv21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_sub_ps(Vtmp1,Vv21);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_sub_ps(Vtmp1,Vv21);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv23.f=Stmp2.f-Sv32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_sub_ps(Vtmp2,Vv32);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_sub_ps(Vtmp2,Vv32);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv31.f=Stmp3.f-Sv13.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_sub_ps(Vtmp3,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_sub_ps(Vtmp3,Vv13);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv21.f=Stmp1.f+Sv21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_add_ps(Vtmp1,Vv21);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_add_ps(Vtmp1,Vv21);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv32.f=Stmp2.f+Sv32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_add_ps(Vtmp2,Vv32);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_add_ps(Vtmp2,Vv32);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv13.f=Stmp3.f+Sv13.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_add_ps(Vtmp3,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_add_ps(Vtmp3,Vv13);)

#ifdef COMPUTE_V_AS_MATRIX
#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar V ="<<std::endl;
    std::cout<<std::setw(12)<<Sv11.f<<"  "<<std::setw(12)<<Sv12.f<<"  "<<std::setw(12)<<Sv13.f<<std::endl;
    std::cout<<std::setw(12)<<Sv21.f<<"  "<<std::setw(12)<<Sv22.f<<"  "<<std::setw(12)<<Sv23.f<<std::endl;
    std::cout<<std::setw(12)<<Sv31.f<<"  "<<std::setw(12)<<Sv32.f<<"  "<<std::setw(12)<<Sv33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vv11);V11=buf[0];
    _mm_storeu_ps(buf,Vv21);V21=buf[0];
    _mm_storeu_ps(buf,Vv31);V31=buf[0];
    _mm_storeu_ps(buf,Vv12);V12=buf[0];
    _mm_storeu_ps(buf,Vv22);V22=buf[0];
    _mm_storeu_ps(buf,Vv32);V32=buf[0];
    _mm_storeu_ps(buf,Vv13);V13=buf[0];
    _mm_storeu_ps(buf,Vv23);V23=buf[0];
    _mm_storeu_ps(buf,Vv33);V33=buf[0];
    std::cout<<"Vector V ="<<std::endl;
    std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vv11);V11=buf[0];
    _mm256_storeu_ps(buf,Vv21);V21=buf[0];
    _mm256_storeu_ps(buf,Vv31);V31=buf[0];
    _mm256_storeu_ps(buf,Vv12);V12=buf[0];
    _mm256_storeu_ps(buf,Vv22);V22=buf[0];
    _mm256_storeu_ps(buf,Vv32);V32=buf[0];
    _mm256_storeu_ps(buf,Vv13);V13=buf[0];
    _mm256_storeu_ps(buf,Vv23);V23=buf[0];
    _mm256_storeu_ps(buf,Vv33);V33=buf[0];
    std::cout<<"Vector V ="<<std::endl;
    std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
#endif
#endif
#endif

    //###########################################################
    // Multiply (from the right) with V
    //###########################################################

    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa12.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp2=Va12;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp2=Va12;)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa13.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp3=Va13;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp3=Va13;)
    ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sv12.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va12=_mm_mul_ps(Vv12,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_mul_ps(Vv12,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sv13.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va13=_mm_mul_ps(Vv13,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_mul_ps(Vv13,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sv11.f*Sa11.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va11=_mm_mul_ps(Vv11,Va11);)                                    ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_mul_ps(Vv11,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv21.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv21,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv21,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sa11.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va11=_mm_add_ps(Va11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_add_ps(Va11,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv31.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv31,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv31,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sa11.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va11=_mm_add_ps(Va11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_add_ps(Va11,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv22.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv22,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sa12.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va12=_mm_add_ps(Va12,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_add_ps(Va12,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv32.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv32,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv32,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sa12.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va12=_mm_add_ps(Va12,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_add_ps(Va12,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv23.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv23,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv23,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sa13.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va13=_mm_add_ps(Va13,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_add_ps(Va13,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv33.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv33,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv33,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sa13.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va13=_mm_add_ps(Va13,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_add_ps(Va13,Vtmp1);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa22.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp2=Va22;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp2=Va22;)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa23.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp3=Va23;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp3=Va23;)
    ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sv12.f*Sa21.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va22=_mm_mul_ps(Vv12,Va21);)                                    ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_mul_ps(Vv12,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sv13.f*Sa21.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va23=_mm_mul_ps(Vv13,Va21);)                                    ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_mul_ps(Vv13,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sv11.f*Sa21.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va21=_mm_mul_ps(Vv11,Va21);)                                    ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_mul_ps(Vv11,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv21.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv21,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv21,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sa21.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va21=_mm_add_ps(Va21,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_add_ps(Va21,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv31.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv31,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv31,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sa21.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va21=_mm_add_ps(Va21,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_add_ps(Va21,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv22.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv22,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sa22.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va22=_mm_add_ps(Va22,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_add_ps(Va22,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv32.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv32,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv32,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sa22.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va22=_mm_add_ps(Va22,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_add_ps(Va22,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv23.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv23,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv23,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sa23.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va23=_mm_add_ps(Va23,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_add_ps(Va23,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv33.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv33,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv33,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sa23.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va23=_mm_add_ps(Va23,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_add_ps(Va23,Vtmp1);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa32.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp2=Va32;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp2=Va32;)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa33.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vtmp3=Va33;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp3=Va33;)
    ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sv12.f*Sa31.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va32=_mm_mul_ps(Vv12,Va31);)                                    ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_mul_ps(Vv12,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sv13.f*Sa31.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va33=_mm_mul_ps(Vv13,Va31);)                                    ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_mul_ps(Vv13,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sv11.f*Sa31.f;)                                   ENABLE_SSE_IMPLEMENTATION(Va31=_mm_mul_ps(Vv11,Va31);)                                    ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_mul_ps(Vv11,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv21.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv21,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv21,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sa31.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va31=_mm_add_ps(Va31,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_add_ps(Va31,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv31.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv31,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv31,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sa31.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va31=_mm_add_ps(Va31,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_add_ps(Va31,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv22.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv22,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sa32.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va32=_mm_add_ps(Va32,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_add_ps(Va32,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv32.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv32,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv32,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sa32.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va32=_mm_add_ps(Va32,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_add_ps(Va32,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv23.f*Stmp2.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv23,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv23,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sa33.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va33=_mm_add_ps(Va33,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_add_ps(Va33,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sv33.f*Stmp3.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vv33,Vtmp3);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vv33,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sa33.f+Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va33=_mm_add_ps(Va33,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_add_ps(Va33,Vtmp1);)

#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar A (after multiplying with V) ="<<std::endl;
    std::cout<<std::setw(12)<<Sa11.f<<"  "<<std::setw(12)<<Sa12.f<<"  "<<std::setw(12)<<Sa13.f<<std::endl;
    std::cout<<std::setw(12)<<Sa21.f<<"  "<<std::setw(12)<<Sa22.f<<"  "<<std::setw(12)<<Sa23.f<<std::endl;
    std::cout<<std::setw(12)<<Sa31.f<<"  "<<std::setw(12)<<Sa32.f<<"  "<<std::setw(12)<<Sa33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Va11);A11=buf[0];
    _mm_storeu_ps(buf,Va21);A21=buf[0];
    _mm_storeu_ps(buf,Va31);A31=buf[0];
    _mm_storeu_ps(buf,Va12);A12=buf[0];
    _mm_storeu_ps(buf,Va22);A22=buf[0];
    _mm_storeu_ps(buf,Va32);A32=buf[0];
    _mm_storeu_ps(buf,Va13);A13=buf[0];
    _mm_storeu_ps(buf,Va23);A23=buf[0];
    _mm_storeu_ps(buf,Va33);A33=buf[0];
    std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Va11);A11=buf[0];
    _mm256_storeu_ps(buf,Va21);A21=buf[0];
    _mm256_storeu_ps(buf,Va31);A31=buf[0];
    _mm256_storeu_ps(buf,Va12);A12=buf[0];
    _mm256_storeu_ps(buf,Va22);A22=buf[0];
    _mm256_storeu_ps(buf,Va32);A32=buf[0];
    _mm256_storeu_ps(buf,Va13);A13=buf[0];
    _mm256_storeu_ps(buf,Va23);A23=buf[0];
    _mm256_storeu_ps(buf,Va33);A33=buf[0];
    std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
#endif
#endif

} // End block : Conjugation with V

} // End block : Scope of qV (if not maintained)

    //###########################################################
    // Permute columns such that the singular values are sorted
    //###########################################################

    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sa11.f*Sa11.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Va11,Va11);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Va11,Va11);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa21.f*Sa21.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va21,Va21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va21,Va21);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa31.f*Sa31.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va31,Va31);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va31,Va31);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sa12.f*Sa12.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Va12,Va12);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Va12,Va12);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa22.f*Sa22.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va22,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va22,Va22);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp2.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp2,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp2,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa32.f*Sa32.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va32,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va32,Va32);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp2.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp2,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp2,Vtmp4);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Sa13.f*Sa13.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Va13,Va13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Va13,Va13);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa23.f*Sa23.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va23,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va23,Va23);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp3.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vtmp3,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vtmp3,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sa33.f*Sa33.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Va33,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Va33,Va33);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp3.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vtmp3,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vtmp3,Vtmp4);)

    // Swap columns 1-2 if necessary

    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.ui=(Stmp1.f<Stmp2.f)?0xffffffff:0;)                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_cmplt_ps(Vtmp1,Vtmp2);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmp_ps(Vtmp1,Vtmp2, _CMP_LT_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmplt_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa11.ui^Sa12.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va11,Va12);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va11,Va12);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa11.ui=Sa11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va11=_mm_xor_ps(Va11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_xor_ps(Va11,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa12.ui=Sa12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va12=_mm_xor_ps(Va12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_xor_ps(Va12,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa21.ui^Sa22.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va21,Va22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va21,Va22);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa21.ui=Sa21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va21=_mm_xor_ps(Va21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_xor_ps(Va21,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa22.ui=Sa22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va22=_mm_xor_ps(Va22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_xor_ps(Va22,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa31.ui^Sa32.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va31,Va32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va31,Va32);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa31.ui=Sa31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va31=_mm_xor_ps(Va31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_xor_ps(Va31,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa32.ui=Sa32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va32=_mm_xor_ps(Va32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_xor_ps(Va32,Vtmp5);)

#ifdef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv11.ui^Sv12.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv11,Vv12);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv11,Vv12);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.ui=Sv11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_xor_ps(Vv11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_xor_ps(Vv11,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv12.ui=Sv12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_xor_ps(Vv12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_xor_ps(Vv12,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv21.ui^Sv22.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv21,Vv22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv21,Vv22);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv21.ui=Sv21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_xor_ps(Vv21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_xor_ps(Vv21,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv22.ui=Sv22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_xor_ps(Vv22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_xor_ps(Vv22,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv31.ui^Sv32.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv31,Vv32);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv31,Vv32);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv31.ui=Sv31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_xor_ps(Vv31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_xor_ps(Vv31,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv32.ui=Sv32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_xor_ps(Vv32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_xor_ps(Vv32,Vtmp5);)
#endif

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp1.ui^Stmp2.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=Stmp1.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_xor_ps(Vtmp1,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_xor_ps(Vtmp1,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=Stmp2.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_xor_ps(Vtmp2,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_xor_ps(Vtmp2,Vtmp5);)

    // If columns 1-2 have been swapped, negate 2nd column of A and V so that V is still a rotation

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=-2.;)                                            ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_set1_ps(-2.);)                                        ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_set1_ps(-2.);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=1.;)                                             ENABLE_SSE_IMPLEMENTATION(Vtmp4=Vone;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Stmp5.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Sa12.f=Sa12.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va12=_mm_mul_ps(Va12,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_mul_ps(Va12,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa22.f=Sa22.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va22=_mm_mul_ps(Va22,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_mul_ps(Va22,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa32.f=Sa32.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va32=_mm_mul_ps(Va32,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_mul_ps(Va32,Vtmp4);)

#ifdef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Sv12.f=Sv12.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_mul_ps(Vv12,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_mul_ps(Vv12,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv22.f=Sv22.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_mul_ps(Vv22,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_mul_ps(Vv22,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv32.f=Sv32.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_mul_ps(Vv32,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_mul_ps(Vv32,Vtmp4);)
#endif

    // If columns 1-2 have been swapped, also update quaternion representation of V (the quaternion may become un-normalized after this)

#ifdef COMPUTE_V_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp4,Vone_half);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vone_half);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f-Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_sub_ps(Vqvvz,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_sub_ps(Vqvvz,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Stmp5.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vqvs=Vtmp5;)                                                    ENABLE_AVX_IMPLEMENTATION(Vqvs=Vtmp5;)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vqvvy,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vqvvy,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f-Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_sub_ps(Vqvvx,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_sub_ps(Vqvvx,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Stmp5.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvvy=Vtmp5;)                                                   ENABLE_AVX_IMPLEMENTATION(Vqvvy=Vtmp5;)
#endif

    // Swap columns 1-3 if necessary

    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.ui=(Stmp1.f<Stmp3.f)?0xffffffff:0;)                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_cmplt_ps(Vtmp1,Vtmp3);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmp_ps(Vtmp1,Vtmp3, _CMP_LT_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmplt_ps(Vtmp1,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa11.ui^Sa13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va11,Va13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va11,Va13);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa11.ui=Sa11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va11=_mm_xor_ps(Va11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_xor_ps(Va11,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa13.ui=Sa13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va13=_mm_xor_ps(Va13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_xor_ps(Va13,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa21.ui^Sa23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va21,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va21,Va23);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa21.ui=Sa21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va21=_mm_xor_ps(Va21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_xor_ps(Va21,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa23.ui=Sa23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va23=_mm_xor_ps(Va23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_xor_ps(Va23,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa31.ui^Sa33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va31,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va31,Va33);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa31.ui=Sa31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va31=_mm_xor_ps(Va31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_xor_ps(Va31,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa33.ui=Sa33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va33=_mm_xor_ps(Va33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_xor_ps(Va33,Vtmp5);)

#ifdef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv11.ui^Sv13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv11,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv11,Vv13);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.ui=Sv11.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_xor_ps(Vv11,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_xor_ps(Vv11,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv13.ui=Sv13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_xor_ps(Vv13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_xor_ps(Vv13,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv21.ui^Sv23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv21,Vv23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv21,Vv23);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv21.ui=Sv21.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_xor_ps(Vv21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_xor_ps(Vv21,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv23.ui=Sv23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_xor_ps(Vv23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_xor_ps(Vv23,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv31.ui^Sv33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv31,Vv33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv31,Vv33);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv31.ui=Sv31.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_xor_ps(Vv31,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_xor_ps(Vv31,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv33.ui=Sv33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_xor_ps(Vv33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_xor_ps(Vv33,Vtmp5);)
#endif

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp1.ui^Stmp3.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp1,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=Stmp1.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_xor_ps(Vtmp1,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_xor_ps(Vtmp1,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.ui=Stmp3.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_xor_ps(Vtmp3,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_xor_ps(Vtmp3,Vtmp5);)

    // If columns 1-3 have been swapped, negate 1st column of A and V so that V is still a rotation

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=-2.;)                                            ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_set1_ps(-2.);)                                        ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_set1_ps(-2.);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=1.;)                                             ENABLE_SSE_IMPLEMENTATION(Vtmp4=Vone;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Stmp5.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Sa11.f=Sa11.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va11=_mm_mul_ps(Va11,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va11=_mm256_mul_ps(Va11,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa21.f=Sa21.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va21=_mm_mul_ps(Va21,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va21=_mm256_mul_ps(Va21,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa31.f=Sa31.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va31=_mm_mul_ps(Va31,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va31=_mm256_mul_ps(Va31,Vtmp4);)

#ifdef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Sv11.f=Sv11.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv11=_mm_mul_ps(Vv11,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv11=_mm256_mul_ps(Vv11,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv21.f=Sv21.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv21=_mm_mul_ps(Vv21,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv21=_mm256_mul_ps(Vv21,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv31.f=Sv31.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv31=_mm_mul_ps(Vv31,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv31=_mm256_mul_ps(Vv31,Vtmp4);)
#endif

    // If columns 1-3 have been swapped, also update quaternion representation of V (the quaternion may become un-normalized after this)

#ifdef COMPUTE_V_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp4,Vone_half);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vone_half);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f-Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_sub_ps(Vqvvy,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_sub_ps(Vqvvy,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Stmp5.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vqvs=Vtmp5;)                                                    ENABLE_AVX_IMPLEMENTATION(Vqvs=Vtmp5;)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vqvvx,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vqvvx,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f-Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_sub_ps(Vqvvz,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_sub_ps(Vqvvz,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Stmp5.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvvx=Vtmp5;)                                                   ENABLE_AVX_IMPLEMENTATION(Vqvvx=Vtmp5;)
#endif

    // Swap columns 2-3 if necessary

    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.ui=(Stmp2.f<Stmp3.f)?0xffffffff:0;)                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_cmplt_ps(Vtmp2,Vtmp3);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmp_ps(Vtmp2,Vtmp3, _CMP_LT_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_cmplt_ps(Vtmp2,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa12.ui^Sa13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va12,Va13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va12,Va13);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa12.ui=Sa12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va12=_mm_xor_ps(Va12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va12=_mm256_xor_ps(Va12,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa13.ui=Sa13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va13=_mm_xor_ps(Va13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_xor_ps(Va13,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa22.ui^Sa23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va22,Va23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va22,Va23);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa22.ui=Sa22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va22=_mm_xor_ps(Va22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va22=_mm256_xor_ps(Va22,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa23.ui=Sa23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va23=_mm_xor_ps(Va23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_xor_ps(Va23,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sa32.ui^Sa33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Va32,Va33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Va32,Va33);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa32.ui=Sa32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va32=_mm_xor_ps(Va32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va32=_mm256_xor_ps(Va32,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa33.ui=Sa33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Va33=_mm_xor_ps(Va33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_xor_ps(Va33,Vtmp5);)

#ifdef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv12.ui^Sv13.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv12,Vv13);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv12,Vv13);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv12.ui=Sv12.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv12=_mm_xor_ps(Vv12,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv12=_mm256_xor_ps(Vv12,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv13.ui=Sv13.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_xor_ps(Vv13,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_xor_ps(Vv13,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv22.ui^Sv23.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv22,Vv23);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv22,Vv23);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv22.ui=Sv22.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv22=_mm_xor_ps(Vv22,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv22=_mm256_xor_ps(Vv22,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv23.ui=Sv23.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_xor_ps(Vv23,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_xor_ps(Vv23,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Sv32.ui^Sv33.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vv32,Vv33);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vv32,Vv33);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv32.ui=Sv32.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv32=_mm_xor_ps(Vv32,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv32=_mm256_xor_ps(Vv32,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv33.ui=Sv33.ui^Stmp5.ui;)                               ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_xor_ps(Vv33,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_xor_ps(Vv33,Vtmp5);)
#endif

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp2.ui^Stmp3.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp2,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=Stmp2.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_xor_ps(Vtmp2,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_xor_ps(Vtmp2,Vtmp5);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.ui=Stmp3.ui^Stmp5.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_xor_ps(Vtmp3,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_xor_ps(Vtmp3,Vtmp5);)

    // If columns 2-3 have been swapped, negate 3rd column of A and V so that V is still a rotation

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=-2.;)                                            ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_set1_ps(-2.);)                                        ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_set1_ps(-2.);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=Stmp5.ui&Stmp4.ui;)                             ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_and_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_and_ps(Vtmp5,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=1.;)                                             ENABLE_SSE_IMPLEMENTATION(Vtmp4=Vone;)                                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Stmp5.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vtmp5);)

    ENABLE_SCALAR_IMPLEMENTATION(Sa13.f=Sa13.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va13=_mm_mul_ps(Va13,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va13=_mm256_mul_ps(Va13,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa23.f=Sa23.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va23=_mm_mul_ps(Va23,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va23=_mm256_mul_ps(Va23,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sa33.f=Sa33.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Va33=_mm_mul_ps(Va33,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Va33=_mm256_mul_ps(Va33,Vtmp4);)

#ifdef COMPUTE_V_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Sv13.f=Sv13.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv13=_mm_mul_ps(Vv13,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv13=_mm256_mul_ps(Vv13,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv23.f=Sv23.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv23=_mm_mul_ps(Vv23,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv23=_mm256_mul_ps(Vv23,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sv33.f=Sv33.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vv33=_mm_mul_ps(Vv33,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vv33=_mm256_mul_ps(Vv33,Vtmp4);)
#endif

    // If columns 2-3 have been swapped, also update quaternion representation of V (the quaternion may become un-normalized after this)

#ifdef COMPUTE_V_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp4,Vone_half);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vone_half);)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp4.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f-Sqvs.f;)                                 ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_sub_ps(Vqvvx,Vqvs);)                                  ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_sub_ps(Vqvvx,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Stmp5.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vqvs=Vtmp5;)                                                    ENABLE_AVX_IMPLEMENTATION(Vqvs=Vtmp5;)

    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp4.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp4,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp4,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f+Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_add_ps(Vtmp5,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_add_ps(Vtmp5,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vqvvz,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vqvvz,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f-Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_sub_ps(Vqvvy,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_sub_ps(Vqvvy,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Stmp5.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvvz=Vtmp5;)                                                   ENABLE_AVX_IMPLEMENTATION(Vqvvz=Vtmp5;)
#endif

#ifdef COMPUTE_V_AS_MATRIX
#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar V ="<<std::endl;
    std::cout<<std::setw(12)<<Sv11.f<<"  "<<std::setw(12)<<Sv12.f<<"  "<<std::setw(12)<<Sv13.f<<std::endl;
    std::cout<<std::setw(12)<<Sv21.f<<"  "<<std::setw(12)<<Sv22.f<<"  "<<std::setw(12)<<Sv23.f<<std::endl;
    std::cout<<std::setw(12)<<Sv31.f<<"  "<<std::setw(12)<<Sv32.f<<"  "<<std::setw(12)<<Sv33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vv11);V11=buf[0];
    _mm_storeu_ps(buf,Vv21);V21=buf[0];
    _mm_storeu_ps(buf,Vv31);V31=buf[0];
    _mm_storeu_ps(buf,Vv12);V12=buf[0];
    _mm_storeu_ps(buf,Vv22);V22=buf[0];
    _mm_storeu_ps(buf,Vv32);V32=buf[0];
    _mm_storeu_ps(buf,Vv13);V13=buf[0];
    _mm_storeu_ps(buf,Vv23);V23=buf[0];
    _mm_storeu_ps(buf,Vv33);V33=buf[0];
    std::cout<<"Vector V ="<<std::endl;
    std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vv11);V11=buf[0];
    _mm256_storeu_ps(buf,Vv21);V21=buf[0];
    _mm256_storeu_ps(buf,Vv31);V31=buf[0];
    _mm256_storeu_ps(buf,Vv12);V12=buf[0];
    _mm256_storeu_ps(buf,Vv22);V22=buf[0];
    _mm256_storeu_ps(buf,Vv32);V32=buf[0];
    _mm256_storeu_ps(buf,Vv13);V13=buf[0];
    _mm256_storeu_ps(buf,Vv23);V23=buf[0];
    _mm256_storeu_ps(buf,Vv33);V33=buf[0];
    std::cout<<"Vector V ="<<std::endl;
    std::cout<<std::setw(12)<<V11<<"  "<<std::setw(12)<<V12<<"  "<<std::setw(12)<<V13<<std::endl;
    std::cout<<std::setw(12)<<V21<<"  "<<std::setw(12)<<V22<<"  "<<std::setw(12)<<V23<<std::endl;
    std::cout<<std::setw(12)<<V31<<"  "<<std::setw(12)<<V32<<"  "<<std::setw(12)<<V33<<std::endl;
#endif
#endif
#endif

#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar A (after multiplying with V) ="<<std::endl;
    std::cout<<std::setw(12)<<Sa11.f<<"  "<<std::setw(12)<<Sa12.f<<"  "<<std::setw(12)<<Sa13.f<<std::endl;
    std::cout<<std::setw(12)<<Sa21.f<<"  "<<std::setw(12)<<Sa22.f<<"  "<<std::setw(12)<<Sa23.f<<std::endl;
    std::cout<<std::setw(12)<<Sa31.f<<"  "<<std::setw(12)<<Sa32.f<<"  "<<std::setw(12)<<Sa33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Va11);A11=buf[0];
    _mm_storeu_ps(buf,Va21);A21=buf[0];
    _mm_storeu_ps(buf,Va31);A31=buf[0];
    _mm_storeu_ps(buf,Va12);A12=buf[0];
    _mm_storeu_ps(buf,Va22);A22=buf[0];
    _mm_storeu_ps(buf,Va32);A32=buf[0];
    _mm_storeu_ps(buf,Va13);A13=buf[0];
    _mm_storeu_ps(buf,Va23);A23=buf[0];
    _mm_storeu_ps(buf,Va33);A33=buf[0];
    std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Va11);A11=buf[0];
    _mm256_storeu_ps(buf,Va21);A21=buf[0];
    _mm256_storeu_ps(buf,Va31);A31=buf[0];
    _mm256_storeu_ps(buf,Va12);A12=buf[0];
    _mm256_storeu_ps(buf,Va22);A22=buf[0];
    _mm256_storeu_ps(buf,Va32);A32=buf[0];
    _mm256_storeu_ps(buf,Va13);A13=buf[0];
    _mm256_storeu_ps(buf,Va23);A23=buf[0];
    _mm256_storeu_ps(buf,Va33);A33=buf[0];
    std::cout<<"Vector A (after multiplying with V) ="<<std::endl;
    std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
#endif
#endif

    //###########################################################
    // Re-normalize quaternion for matrix V
    //###########################################################

#ifdef COMPUTE_V_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sqvs.f*Sqvs.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vqvs,Vqvs);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vqvs,Vqvs);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvx.f*Sqvvx.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvx,Vqvvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvx,Vqvvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvy.f*Sqvvy.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvy,Vqvvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvy,Vqvvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sqvvz.f*Sqvvz.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vqvvz,Vqvvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vqvvz,Vqvvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=rsqrt(Stmp2.f);)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_rsqrt_ps(Vtmp2);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_rsqrt_ps(Vtmp2);)

#ifdef PERFORM_STRICT_QUATERNION_RENORMALIZATION
    ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp1.f*Sone_half.f;)                            ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp1,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp1,Vone_half);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp2.f*Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp2,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f-Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_sub_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_sub_ps(Vtmp1,Vtmp3);)
#endif

    ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f*Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vqvs,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vqvs,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sqvvx.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vqvvx,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vqvvx,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sqvvy.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vqvvy,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vqvvy,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sqvvz.f*Stmp1.f;)                                ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vqvvz,Vtmp1);)                                 ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vqvvz,Vtmp1);)

#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar qV ="<<std::endl;
    std::cout<<std::setw(12)<<Sqvs.f<<"  "<<std::setw(12)<<Sqvvx.f<<"  "<<std::setw(12)<<Sqvvy.f<<"  "<<std::setw(12)<<Sqvvz.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vqvs);QVS=buf[0];
    _mm_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    _mm_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    _mm_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    std::cout<<"Vector qV ="<<std::endl;
    std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vqvs);QVS=buf[0];
    _mm256_storeu_ps(buf,Vqvvx);QVVX=buf[0];
    _mm256_storeu_ps(buf,Vqvvy);QVVY=buf[0];
    _mm256_storeu_ps(buf,Vqvvz);QVVZ=buf[0];
    std::cout<<"Vector qV ="<<std::endl;
    std::cout<<std::setw(12)<<QVS<<"  "<<std::setw(12)<<QVVX<<"  "<<std::setw(12)<<QVVY<<"  "<<std::setw(12)<<QVVZ<<std::endl;
#endif
#endif
#endif

    //###########################################################
    // Construct QR factorization of A*V (=U*D) using Givens rotations
    //###########################################################

#ifdef COMPUTE_U_AS_MATRIX
    ENABLE_SCALAR_IMPLEMENTATION(Su11.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu11=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vu11=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Su21.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu21=_mm_xor_ps(Vu21,Vu21);)                                    ENABLE_AVX_IMPLEMENTATION(Vu21=_mm256_xor_ps(Vu21,Vu21);)
    ENABLE_SCALAR_IMPLEMENTATION(Su31.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu31=_mm_xor_ps(Vu31,Vu31);)                                    ENABLE_AVX_IMPLEMENTATION(Vu31=_mm256_xor_ps(Vu31,Vu31);)
    ENABLE_SCALAR_IMPLEMENTATION(Su12.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu12=_mm_xor_ps(Vu12,Vu12);)                                    ENABLE_AVX_IMPLEMENTATION(Vu12=_mm256_xor_ps(Vu12,Vu12);)
    ENABLE_SCALAR_IMPLEMENTATION(Su22.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu22=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vu22=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Su32.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu32=_mm_xor_ps(Vu32,Vu32);)                                    ENABLE_AVX_IMPLEMENTATION(Vu32=_mm256_xor_ps(Vu32,Vu32);)
    ENABLE_SCALAR_IMPLEMENTATION(Su13.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu13=_mm_xor_ps(Vu13,Vu13);)                                    ENABLE_AVX_IMPLEMENTATION(Vu13=_mm256_xor_ps(Vu13,Vu13);)
    ENABLE_SCALAR_IMPLEMENTATION(Su23.f=0.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu23=_mm_xor_ps(Vu23,Vu23);)                                    ENABLE_AVX_IMPLEMENTATION(Vu23=_mm256_xor_ps(Vu23,Vu23);)
    ENABLE_SCALAR_IMPLEMENTATION(Su33.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vu33=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vu33=Vone;)
#endif

#ifdef COMPUTE_U_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Squs.f=1.;)                                              ENABLE_SSE_IMPLEMENTATION(Vqus=Vone;)                                                     ENABLE_AVX_IMPLEMENTATION(Vqus=Vone;)
    ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_xor_ps(Vquvx,Vquvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_xor_ps(Vquvx,Vquvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_xor_ps(Vquvy,Vquvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_xor_ps(Vquvy,Vquvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_xor_ps(Vquvz,Vquvz);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_xor_ps(Vquvz,Vquvz);)
#endif

    // First Givens rotation

#define SAPIVOT Sa11
#define SANPIVOT Sa21
#define SA11 Sa11
#define SA21 Sa21
#define SA12 Sa12
#define SA22 Sa22
#define SA13 Sa13
#define SA23 Sa23
#define SU11 Su11
#define SU12 Su12
#define SU21 Su21
#define SU22 Su22
#define SU31 Su31
#define SU32 Su32

#define VAPIVOT Va11
#define VANPIVOT Va21
#define VA11 Va11
#define VA21 Va21
#define VA12 Va12
#define VA22 Va22
#define VA13 Va13
#define VA23 Va23
#define VU11 Vu11
#define VU12 Vu12
#define VU21 Vu21
#define VU22 Vu22
#define VU31 Vu31
#define VU32 Vu32

#include "Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp"
    
#undef SAPIVOT
#undef SANPIVOT
#undef SA11
#undef SA21
#undef SA12
#undef SA22
#undef SA13
#undef SA23
#undef SU11
#undef SU12
#undef SU21
#undef SU22
#undef SU31
#undef SU32

#undef VAPIVOT
#undef VANPIVOT
#undef VA11
#undef VA21
#undef VA12
#undef VA22
#undef VA13
#undef VA23
#undef VU11
#undef VU12
#undef VU21
#undef VU22
#undef VU31
#undef VU32

    // Update quaternion representation of U

#ifdef COMPUTE_U_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Sch.f;)                                           ENABLE_SSE_IMPLEMENTATION(Vqus=Vch;)                                                      ENABLE_AVX_IMPLEMENTATION(Vqus=Vch;)
    ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_xor_ps(Vquvx,Vquvx);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_xor_ps(Vquvx,Vquvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=0.;)                                             ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_xor_ps(Vquvy,Vquvy);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_xor_ps(Vquvy,Vquvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Ssh.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vquvz=Vsh;)                                                     ENABLE_AVX_IMPLEMENTATION(Vquvz=Vsh;)
#endif

    // Second Givens rotation

#define SAPIVOT Sa11
#define SANPIVOT Sa31
#define SA11 Sa11
#define SA21 Sa31
#define SA12 Sa12
#define SA22 Sa32
#define SA13 Sa13
#define SA23 Sa33
#define SU11 Su11
#define SU12 Su13
#define SU21 Su21
#define SU22 Su23
#define SU31 Su31
#define SU32 Su33

#define VAPIVOT Va11
#define VANPIVOT Va31
#define VA11 Va11
#define VA21 Va31
#define VA12 Va12
#define VA22 Va32
#define VA13 Va13
#define VA23 Va33
#define VU11 Vu11
#define VU12 Vu13
#define VU21 Vu21
#define VU22 Vu23
#define VU31 Vu31
#define VU32 Vu33

#include "Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp"
    
#undef SAPIVOT
#undef SANPIVOT
#undef SA11
#undef SA21
#undef SA12
#undef SA22
#undef SA13
#undef SA23
#undef SU11
#undef SU12
#undef SU21
#undef SU22
#undef SU31
#undef SU32

#undef VAPIVOT
#undef VANPIVOT
#undef VA11
#undef VA21
#undef VA12
#undef VA22
#undef VA13
#undef VA23
#undef VU11
#undef VU12
#undef VU21
#undef VU22
#undef VU31
#undef VU32

    // Update quaternion representation of U

#ifdef COMPUTE_U_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=Ssh.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_mul_ps(Vsh,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_mul_ps(Vsh,Vquvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Ssh.f*Squs.f;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vsh,Vqus);)                                      ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vsh,Vqus);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=Squvy.f-Ssh.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_sub_ps(Vquvy,Vsh);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_sub_ps(Vquvy,Vsh);)
    ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Sch.f*Squs.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vqus=_mm_mul_ps(Vch,Vqus);)                                     ENABLE_AVX_IMPLEMENTATION(Vqus=_mm256_mul_ps(Vch,Vqus);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Sch.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_mul_ps(Vch,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_mul_ps(Vch,Vquvz);)
#endif

    // Third Givens rotation

#define SAPIVOT Sa22
#define SANPIVOT Sa32
#define SA11 Sa21
#define SA21 Sa31
#define SA12 Sa22
#define SA22 Sa32
#define SA13 Sa23
#define SA23 Sa33
#define SU11 Su12
#define SU12 Su13
#define SU21 Su22
#define SU22 Su23
#define SU31 Su32
#define SU32 Su33

#define VAPIVOT Va22
#define VANPIVOT Va32
#define VA11 Va21
#define VA21 Va31
#define VA12 Va22
#define VA22 Va32
#define VA13 Va23
#define VA23 Va33
#define VU11 Vu12
#define VU12 Vu13
#define VU21 Vu22
#define VU22 Vu23
#define VU31 Vu32
#define VU32 Vu33

#include "Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp"
    
#undef SAPIVOT
#undef SANPIVOT
#undef SA11
#undef SA21
#undef SA12
#undef SA22
#undef SA13
#undef SA23
#undef SU11
#undef SU12
#undef SU21
#undef SU22
#undef SU31
#undef SU32

#undef VAPIVOT
#undef VANPIVOT
#undef VA11
#undef VA21
#undef VA12
#undef VA22
#undef VA13
#undef VA23
#undef VU11
#undef VU12
#undef VU21
#undef VU22
#undef VU31
#undef VU32

    // Update quaternion representation of U

#ifdef COMPUTE_U_AS_QUATERNION
    ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ssh.f*Squvx.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vsh,Vquvx);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vsh,Vquvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ssh.f*Squvy.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vsh,Vquvy);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vsh,Vquvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Ssh.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vsh,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vsh,Vquvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Ssh.f*Squs.f;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vsh,Vqus);)                                      ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vsh,Vqus);)
    ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Sch.f*Squs.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vqus=_mm_mul_ps(Vch,Vqus);)                                     ENABLE_AVX_IMPLEMENTATION(Vqus=_mm256_mul_ps(Vch,Vqus);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=Sch.f*Squvx.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_mul_ps(Vch,Vquvx);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_mul_ps(Vch,Vquvx);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=Sch.f*Squvy.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_mul_ps(Vch,Vquvy);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_mul_ps(Vch,Vquvy);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Sch.f*Squvz.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_mul_ps(Vch,Vquvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_mul_ps(Vch,Vquvz);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvx.f=Squvx.f+Ssh.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vquvx=_mm_add_ps(Vquvx,Vsh);)                                   ENABLE_AVX_IMPLEMENTATION(Vquvx=_mm256_add_ps(Vquvx,Vsh);)
    ENABLE_SCALAR_IMPLEMENTATION(Squs.f=Squs.f-Stmp1.f;)                                  ENABLE_SSE_IMPLEMENTATION(Vqus=_mm_sub_ps(Vqus,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(Vqus=_mm256_sub_ps(Vqus,Vtmp1);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvy.f=Squvy.f+Stmp3.f;)                                ENABLE_SSE_IMPLEMENTATION(Vquvy=_mm_add_ps(Vquvy,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvy=_mm256_add_ps(Vquvy,Vtmp3);)
    ENABLE_SCALAR_IMPLEMENTATION(Squvz.f=Squvz.f-Stmp2.f;)                                ENABLE_SSE_IMPLEMENTATION(Vquvz=_mm_sub_ps(Vquvz,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vquvz=_mm256_sub_ps(Vquvz,Vtmp2);)
#endif

#ifdef COMPUTE_U_AS_MATRIX
#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar U ="<<std::endl;
    std::cout<<std::setw(12)<<Su11.f<<"  "<<std::setw(12)<<Su12.f<<"  "<<std::setw(12)<<Su13.f<<std::endl;
    std::cout<<std::setw(12)<<Su21.f<<"  "<<std::setw(12)<<Su22.f<<"  "<<std::setw(12)<<Su23.f<<std::endl;
    std::cout<<std::setw(12)<<Su31.f<<"  "<<std::setw(12)<<Su32.f<<"  "<<std::setw(12)<<Su33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vu11);U11=buf[0];
    _mm_storeu_ps(buf,Vu21);U21=buf[0];
    _mm_storeu_ps(buf,Vu31);U31=buf[0];
    _mm_storeu_ps(buf,Vu12);U12=buf[0];
    _mm_storeu_ps(buf,Vu22);U22=buf[0];
    _mm_storeu_ps(buf,Vu32);U32=buf[0];
    _mm_storeu_ps(buf,Vu13);U13=buf[0];
    _mm_storeu_ps(buf,Vu23);U23=buf[0];
    _mm_storeu_ps(buf,Vu33);U33=buf[0];
    std::cout<<"Vector U ="<<std::endl;
    std::cout<<std::setw(12)<<U11<<"  "<<std::setw(12)<<U12<<"  "<<std::setw(12)<<U13<<std::endl;
    std::cout<<std::setw(12)<<U21<<"  "<<std::setw(12)<<U22<<"  "<<std::setw(12)<<U23<<std::endl;
    std::cout<<std::setw(12)<<U31<<"  "<<std::setw(12)<<U32<<"  "<<std::setw(12)<<U33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vu11);U11=buf[0];
    _mm256_storeu_ps(buf,Vu21);U21=buf[0];
    _mm256_storeu_ps(buf,Vu31);U31=buf[0];
    _mm256_storeu_ps(buf,Vu12);U12=buf[0];
    _mm256_storeu_ps(buf,Vu22);U22=buf[0];
    _mm256_storeu_ps(buf,Vu32);U32=buf[0];
    _mm256_storeu_ps(buf,Vu13);U13=buf[0];
    _mm256_storeu_ps(buf,Vu23);U23=buf[0];
    _mm256_storeu_ps(buf,Vu33);U33=buf[0];
    std::cout<<"Vector U ="<<std::endl;
    std::cout<<std::setw(12)<<U11<<"  "<<std::setw(12)<<U12<<"  "<<std::setw(12)<<U13<<std::endl;
    std::cout<<std::setw(12)<<U21<<"  "<<std::setw(12)<<U22<<"  "<<std::setw(12)<<U23<<std::endl;
    std::cout<<std::setw(12)<<U31<<"  "<<std::setw(12)<<U32<<"  "<<std::setw(12)<<U33<<std::endl;
#endif
#endif
#endif

#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar A (after multiplying with U-transpose and V) ="<<std::endl;
    std::cout<<std::setw(12)<<Sa11.f<<"  "<<std::setw(12)<<Sa12.f<<"  "<<std::setw(12)<<Sa13.f<<std::endl;
    std::cout<<std::setw(12)<<Sa21.f<<"  "<<std::setw(12)<<Sa22.f<<"  "<<std::setw(12)<<Sa23.f<<std::endl;
    std::cout<<std::setw(12)<<Sa31.f<<"  "<<std::setw(12)<<Sa32.f<<"  "<<std::setw(12)<<Sa33.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Va11);A11=buf[0];
    _mm_storeu_ps(buf,Va21);A21=buf[0];
    _mm_storeu_ps(buf,Va31);A31=buf[0];
    _mm_storeu_ps(buf,Va12);A12=buf[0];
    _mm_storeu_ps(buf,Va22);A22=buf[0];
    _mm_storeu_ps(buf,Va32);A32=buf[0];
    _mm_storeu_ps(buf,Va13);A13=buf[0];
    _mm_storeu_ps(buf,Va23);A23=buf[0];
    _mm_storeu_ps(buf,Va33);A33=buf[0];
    std::cout<<"Vector A (after multiplying with U-transpose and V) ="<<std::endl;
    std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Va11);A11=buf[0];
    _mm256_storeu_ps(buf,Va21);A21=buf[0];
    _mm256_storeu_ps(buf,Va31);A31=buf[0];
    _mm256_storeu_ps(buf,Va12);A12=buf[0];
    _mm256_storeu_ps(buf,Va22);A22=buf[0];
    _mm256_storeu_ps(buf,Va32);A32=buf[0];
    _mm256_storeu_ps(buf,Va13);A13=buf[0];
    _mm256_storeu_ps(buf,Va23);A23=buf[0];
    _mm256_storeu_ps(buf,Va33);A33=buf[0];
    std::cout<<"Vector A (after multiplying with U-transpose and V) ="<<std::endl;
    std::cout<<std::setw(12)<<A11<<"  "<<std::setw(12)<<A12<<"  "<<std::setw(12)<<A13<<std::endl;
    std::cout<<std::setw(12)<<A21<<"  "<<std::setw(12)<<A22<<"  "<<std::setw(12)<<A23<<std::endl;
    std::cout<<std::setw(12)<<A31<<"  "<<std::setw(12)<<A32<<"  "<<std::setw(12)<<A33<<std::endl;
#endif
#endif

#ifdef COMPUTE_U_AS_QUATERNION
#ifdef PRINT_DEBUGGING_OUTPUT
#ifdef USE_SCALAR_IMPLEMENTATION
    std::cout<<"Scalar qU ="<<std::endl;
    std::cout<<std::setw(12)<<Squs.f<<"  "<<std::setw(12)<<Squvx.f<<"  "<<std::setw(12)<<Squvy.f<<"  "<<std::setw(12)<<Squvz.f<<std::endl;
#endif
#ifdef USE_SSE_IMPLEMENTATION
    _mm_storeu_ps(buf,Vqus);QUS=buf[0];
    _mm_storeu_ps(buf,Vquvx);QUVX=buf[0];
    _mm_storeu_ps(buf,Vquvy);QUVY=buf[0];
    _mm_storeu_ps(buf,Vquvz);QUVZ=buf[0];
    std::cout<<"Vector qU ="<<std::endl;
    std::cout<<std::setw(12)<<QUS<<"  "<<std::setw(12)<<QUVX<<"  "<<std::setw(12)<<QUVY<<"  "<<std::setw(12)<<QUVZ<<std::endl;
#endif
#ifdef USE_AVX_IMPLEMENTATION
    _mm256_storeu_ps(buf,Vqus);QUS=buf[0];
    _mm256_storeu_ps(buf,Vquvx);QUVX=buf[0];
    _mm256_storeu_ps(buf,Vquvy);QUVY=buf[0];
    _mm256_storeu_ps(buf,Vquvz);QUVZ=buf[0];
    std::cout<<"Vector qU ="<<std::endl;
    std::cout<<std::setw(12)<<QUS<<"  "<<std::setw(12)<<QUVX<<"  "<<std::setw(12)<<QUVY<<"  "<<std::setw(12)<<QUVZ<<std::endl;
#endif
#endif
#endif

#ifdef __INTEL_COMPILER
#pragma warning( default : 592 )
#endif