text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
  // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
  
  #include "main.h"
  
  // using namespace Eigen;
  
  namespace Eigen {
  namespace internal {
  template<typename T> T negate(const T& x) { return -x; }
  }
  }
  
  template<typename Scalar> bool isApproxAbs(const Scalar& a, const Scalar& b, const typename NumTraits<Scalar>::Real& refvalue)
  {
    return internal::isMuchSmallerThan(a-b, refvalue);
  }
  
  template<typename Scalar> bool areApproxAbs(const Scalar* a, const Scalar* b, int size, const typename NumTraits<Scalar>::Real& refvalue)
  {
    for (int i=0; i<size; ++i)
    {
      if (!isApproxAbs(a[i],b[i],refvalue))
      {
        std::cout << "[" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != " << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "\n";
        return false;
      }
    }
    return true;
  }
  
  template<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int size)
  {
    for (int i=0; i<size; ++i)
    {
      if (!internal::isApprox(a[i],b[i]))
      {
        std::cout << "[" << Map<const Matrix<Scalar,1,Dynamic> >(a,size) << "]" << " != " << Map<const Matrix<Scalar,1,Dynamic> >(b,size) << "\n";
        return false;
      }
    }
    return true;
  }
  
  
  #define CHECK_CWISE2(REFOP, POP) { \
    for (int i=0; i<PacketSize; ++i) \
      ref[i] = REFOP(data1[i], data1[i+PacketSize]); \
    internal::pstore(data2, POP(internal::pload<Packet>(data1), internal::pload<Packet>(data1+PacketSize))); \
    VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
  }
  
  #define CHECK_CWISE1(REFOP, POP) { \
    for (int i=0; i<PacketSize; ++i) \
      ref[i] = REFOP(data1[i]); \
    internal::pstore(data2, POP(internal::pload<Packet>(data1))); \
    VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
  }
  
  template<bool Cond,typename Packet>
  struct packet_helper
  {
    template<typename T>
    inline Packet load(const T* from) const { return internal::pload<Packet>(from); }
  
    template<typename T>
    inline void store(T* to, const Packet& x) const { internal::pstore(to,x); }
  };
  
  template<typename Packet>
  struct packet_helper<false,Packet>
  {
    template<typename T>
    inline T load(const T* from) const { return *from; }
  
    template<typename T>
    inline void store(T* to, const T& x) const { *to = x; }
  };
  
  #define CHECK_CWISE1_IF(COND, REFOP, POP) if(COND) { \
    packet_helper<COND,Packet> h; \
    for (int i=0; i<PacketSize; ++i) \
      ref[i] = REFOP(data1[i]); \
    h.store(data2, POP(h.load(data1))); \
    VERIFY(areApprox(ref, data2, PacketSize) && #POP); \
  }
  
  #define REF_ADD(a,b) ((a)+(b))
  #define REF_SUB(a,b) ((a)-(b))
  #define REF_MUL(a,b) ((a)*(b))
  #define REF_DIV(a,b) ((a)/(b))
  
  template<typename Scalar> void packetmath()
  {
    typedef typename internal::packet_traits<Scalar>::type Packet;
    const int PacketSize = internal::packet_traits<Scalar>::size;
    typedef typename NumTraits<Scalar>::Real RealScalar;
  
    const int size = PacketSize*4;
    EIGEN_ALIGN16 Scalar data1[internal::packet_traits<Scalar>::size*4];
    EIGEN_ALIGN16 Scalar data2[internal::packet_traits<Scalar>::size*4];
    EIGEN_ALIGN16 Packet packets[PacketSize*2];
    EIGEN_ALIGN16 Scalar ref[internal::packet_traits<Scalar>::size*4];
    RealScalar refvalue = 0;
    for (int i=0; i<size; ++i)
    {
      data1[i] = internal::random<Scalar>()/RealScalar(PacketSize);
      data2[i] = internal::random<Scalar>()/RealScalar(PacketSize);
      refvalue = (std::max)(refvalue,internal::abs(data1[i]));
    }
  
    internal::pstore(data2, internal::pload<Packet>(data1));
    VERIFY(areApprox(data1, data2, PacketSize) && "aligned load/store");
  
    for (int offset=0; offset<PacketSize; ++offset)
    {
      internal::pstore(data2, internal::ploadu<Packet>(data1+offset));
      VERIFY(areApprox(data1+offset, data2, PacketSize) && "internal::ploadu");
    }
  
    for (int offset=0; offset<PacketSize; ++offset)
    {
      internal::pstoreu(data2+offset, internal::pload<Packet>(data1));
      VERIFY(areApprox(data1, data2+offset, PacketSize) && "internal::pstoreu");
    }
  
    for (int offset=0; offset<PacketSize; ++offset)
    {
      packets[0] = internal::pload<Packet>(data1);
      packets[1] = internal::pload<Packet>(data1+PacketSize);
           if (offset==0) internal::palign<0>(packets[0], packets[1]);
      else if (offset==1) internal::palign<1>(packets[0], packets[1]);
      else if (offset==2) internal::palign<2>(packets[0], packets[1]);
      else if (offset==3) internal::palign<3>(packets[0], packets[1]);
      internal::pstore(data2, packets[0]);
  
      for (int i=0; i<PacketSize; ++i)
        ref[i] = data1[i+offset];
  
      typedef Matrix<Scalar, PacketSize, 1> Vector;
      VERIFY(areApprox(ref, data2, PacketSize) && "internal::palign");
    }
  
    CHECK_CWISE2(REF_ADD,  internal::padd);
    CHECK_CWISE2(REF_SUB,  internal::psub);
    CHECK_CWISE2(REF_MUL,  internal::pmul);
    #ifndef EIGEN_VECTORIZE_ALTIVEC
    if (!internal::is_same<Scalar,int>::value)
      CHECK_CWISE2(REF_DIV,  internal::pdiv);
    #endif
    CHECK_CWISE1(internal::negate, internal::pnegate);
    CHECK_CWISE1(internal::conj, internal::pconj);
  
    for(int offset=0;offset<3;++offset)
    {
      for (int i=0; i<PacketSize; ++i)
        ref[i] = data1[offset];
      internal::pstore(data2, internal::pset1<Packet>(data1[offset]));
      VERIFY(areApprox(ref, data2, PacketSize) && "internal::pset1");
    }
    
    VERIFY(internal::isApprox(data1[0], internal::pfirst(internal::pload<Packet>(data1))) && "internal::pfirst");
    
    if(PacketSize>1)
    {
      for(int offset=0;offset<4;++offset)
      {
        for(int i=0;i<PacketSize/2;++i)
          ref[2*i+0] = ref[2*i+1] = data1[offset+i];
        internal::pstore(data2,internal::ploaddup<Packet>(data1+offset));
        VERIFY(areApprox(ref, data2, PacketSize) && "ploaddup");
      }
    }
  
    ref[0] = 0;
    for (int i=0; i<PacketSize; ++i)
      ref[0] += data1[i];
    VERIFY(isApproxAbs(ref[0], internal::predux(internal::pload<Packet>(data1)), refvalue) && "internal::predux");
  
    ref[0] = 1;
    for (int i=0; i<PacketSize; ++i)
      ref[0] *= data1[i];
    VERIFY(internal::isApprox(ref[0], internal::predux_mul(internal::pload<Packet>(data1))) && "internal::predux_mul");
  
    for (int j=0; j<PacketSize; ++j)
    {
      ref[j] = 0;
      for (int i=0; i<PacketSize; ++i)
        ref[j] += data1[i+j*PacketSize];
      packets[j] = internal::pload<Packet>(data1+j*PacketSize);
    }
    internal::pstore(data2, internal::preduxp(packets));
    VERIFY(areApproxAbs(ref, data2, PacketSize, refvalue) && "internal::preduxp");
  
    for (int i=0; i<PacketSize; ++i)
      ref[i] = data1[PacketSize-i-1];
    internal::pstore(data2, internal::preverse(internal::pload<Packet>(data1)));
    VERIFY(areApprox(ref, data2, PacketSize) && "internal::preverse");
  }
  
  template<typename Scalar> void packetmath_real()
  {
    typedef typename internal::packet_traits<Scalar>::type Packet;
    const int PacketSize = internal::packet_traits<Scalar>::size;
  
    const int size = PacketSize*4;
    EIGEN_ALIGN16 Scalar data1[internal::packet_traits<Scalar>::size*4];
    EIGEN_ALIGN16 Scalar data2[internal::packet_traits<Scalar>::size*4];
    EIGEN_ALIGN16 Scalar ref[internal::packet_traits<Scalar>::size*4];
  
    for (int i=0; i<size; ++i)
    {
      data1[i] = internal::random<Scalar>(-1e3,1e3);
      data2[i] = internal::random<Scalar>(-1e3,1e3);
    }
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSin, internal::sin, internal::psin);
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasCos, internal::cos, internal::pcos);
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasTan, internal::tan, internal::ptan);
    
    for (int i=0; i<size; ++i)
    {
      data1[i] = internal::random<Scalar>(-1,1);
      data2[i] = internal::random<Scalar>(-1,1);
    }
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasASin, internal::asin, internal::pasin);
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasACos, internal::acos, internal::pacos);
  
    for (int i=0; i<size; ++i)
    {
      data1[i] = internal::random<Scalar>(-87,88);
      data2[i] = internal::random<Scalar>(-87,88);
    }
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasExp, internal::exp, internal::pexp);
  
    for (int i=0; i<size; ++i)
    {
      data1[i] = internal::random<Scalar>(0,1e6);
      data2[i] = internal::random<Scalar>(0,1e6);
    }
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLog, internal::log, internal::plog);
    CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSqrt, internal::sqrt, internal::psqrt);
  
    ref[0] = data1[0];
    for (int i=0; i<PacketSize; ++i)
      ref[0] = (std::min)(ref[0],data1[i]);
    VERIFY(internal::isApprox(ref[0], internal::predux_min(internal::pload<Packet>(data1))) && "internal::predux_min");
  
    CHECK_CWISE2((std::min), internal::pmin);
    CHECK_CWISE2((std::max), internal::pmax);
    CHECK_CWISE1(internal::abs, internal::pabs);
  
    ref[0] = data1[0];
    for (int i=0; i<PacketSize; ++i)
      ref[0] = (std::max)(ref[0],data1[i]);
    VERIFY(internal::isApprox(ref[0], internal::predux_max(internal::pload<Packet>(data1))) && "internal::predux_max");
    
    for (int i=0; i<PacketSize; ++i)
      ref[i] = data1[0]+Scalar(i);
    internal::pstore(data2, internal::plset(data1[0]));
    VERIFY(areApprox(ref, data2, PacketSize) && "internal::plset");
  }
  
  template<typename Scalar,bool ConjLhs,bool ConjRhs> void test_conj_helper(Scalar* data1, Scalar* data2, Scalar* ref, Scalar* pval)
  {
    typedef typename internal::packet_traits<Scalar>::type Packet;
    const int PacketSize = internal::packet_traits<Scalar>::size;
    
    internal::conj_if<ConjLhs> cj0;
    internal::conj_if<ConjRhs> cj1;
    internal::conj_helper<Scalar,Scalar,ConjLhs,ConjRhs> cj;
    internal::conj_helper<Packet,Packet,ConjLhs,ConjRhs> pcj;
    
    for(int i=0;i<PacketSize;++i)
    {
      ref[i] = cj0(data1[i]) * cj1(data2[i]);
      VERIFY(internal::isApprox(ref[i], cj.pmul(data1[i],data2[i])) && "conj_helper pmul");
    }
    internal::pstore(pval,pcj.pmul(internal::pload<Packet>(data1),internal::pload<Packet>(data2)));
    VERIFY(areApprox(ref, pval, PacketSize) && "conj_helper pmul");
    
    for(int i=0;i<PacketSize;++i)
    {
      Scalar tmp = ref[i];
      ref[i] += cj0(data1[i]) * cj1(data2[i]);
      VERIFY(internal::isApprox(ref[i], cj.pmadd(data1[i],data2[i],tmp)) && "conj_helper pmadd");
    }
    internal::pstore(pval,pcj.pmadd(internal::pload<Packet>(data1),internal::pload<Packet>(data2),internal::pload<Packet>(pval)));
    VERIFY(areApprox(ref, pval, PacketSize) && "conj_helper pmadd");
  }
  
  template<typename Scalar> void packetmath_complex()
  {
    typedef typename internal::packet_traits<Scalar>::type Packet;
    const int PacketSize = internal::packet_traits<Scalar>::size;
  
    const int size = PacketSize*4;
    EIGEN_ALIGN16 Scalar data1[PacketSize*4];
    EIGEN_ALIGN16 Scalar data2[PacketSize*4];
    EIGEN_ALIGN16 Scalar ref[PacketSize*4];
    EIGEN_ALIGN16 Scalar pval[PacketSize*4];
  
    for (int i=0; i<size; ++i)
    {
      data1[i] = internal::random<Scalar>() * Scalar(1e2);
      data2[i] = internal::random<Scalar>() * Scalar(1e2);
    }
    
    test_conj_helper<Scalar,false,false> (data1,data2,ref,pval);
    test_conj_helper<Scalar,false,true>  (data1,data2,ref,pval);
    test_conj_helper<Scalar,true,false>  (data1,data2,ref,pval);
    test_conj_helper<Scalar,true,true>   (data1,data2,ref,pval);
    
    {
      for(int i=0;i<PacketSize;++i)
        ref[i] = Scalar(std::imag(data1[i]),std::real(data1[i]));
      internal::pstore(pval,internal::pcplxflip(internal::pload<Packet>(data1)));
      VERIFY(areApprox(ref, pval, PacketSize) && "pcplxflip");
    }
    
    
  }
  
  void test_packetmath()
  {
    for(int i = 0; i < g_repeat; i++) {
      CALL_SUBTEST_1( packetmath<float>() );
      CALL_SUBTEST_2( packetmath<double>() );
      CALL_SUBTEST_3( packetmath<int>() );
      CALL_SUBTEST_1( packetmath<std::complex<float> >() );
      CALL_SUBTEST_2( packetmath<std::complex<double> >() );
  
      CALL_SUBTEST_1( packetmath_real<float>() );
      CALL_SUBTEST_2( packetmath_real<double>() );
  
      CALL_SUBTEST_1( packetmath_complex<std::complex<float> >() );
      CALL_SUBTEST_2( packetmath_complex<std::complex<double> >() );
    }
  }
  