text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
  // Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
  //
  // 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/.
  
  #ifndef EIGEN_COMPLEX32_ALTIVEC_H
  #define EIGEN_COMPLEX32_ALTIVEC_H
  
  namespace Eigen {
  
  namespace internal {
  
  #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
  static Packet4ui  p4ui_CONJ_XOR = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 }; //vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);
  #endif
  
  static Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
  static Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 };
  
  struct Packet1cd
  {
    EIGEN_STRONG_INLINE Packet1cd() {}
    EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
    Packet2d v;
  };
  
  struct Packet2cf
  {
    EIGEN_STRONG_INLINE Packet2cf() {}
    EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
  #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
    union {
      Packet4f v;
      Packet1cd cd[2];
    };
  #else
    Packet4f v;
  #endif
  };
  
  template<> struct packet_traits<std::complex<float> >  : default_packet_traits
  {
    typedef Packet2cf type;
    typedef Packet2cf half;
    enum {
      Vectorizable = 1,
      AlignedOnScalar = 1,
      size = 2,
      HasHalfPacket = 0,
  
      HasAdd    = 1,
      HasSub    = 1,
      HasMul    = 1,
      HasDiv    = 1,
      HasNegate = 1,
      HasAbs    = 0,
      HasAbs2   = 0,
      HasMin    = 0,
      HasMax    = 0,
      HasBlend  = 1,
      HasSetLinear = 0
    };
  };
  
  
  template<> struct packet_traits<std::complex<double> >  : default_packet_traits
  {
    typedef Packet1cd type;
    typedef Packet1cd half;
    enum {
      Vectorizable = 1,
      AlignedOnScalar = 1,
      size = 1,
      HasHalfPacket = 0,
  
      HasAdd    = 1,
      HasSub    = 1,
      HasMul    = 1,
      HasDiv    = 1,
      HasNegate = 1,
      HasAbs    = 0,
      HasAbs2   = 0,
      HasMin    = 0,
      HasMax    = 0,
      HasSetLinear = 0
    };
  };
  
  template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float>  type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet2cf half; };
  template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet1cd half; };
  
  /* Forward declaration */
  EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel);
  
  /* complex<double> first */
  template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
  template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
  template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
  template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
  
  template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)
  { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
  
  template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride EIGEN_UNUSED)
  {
    return pload<Packet1cd>(from);
  }
  template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride EIGEN_UNUSED)
  {
    pstore<std::complex<double> >(to, from);
  }
  template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
  template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
  template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
  template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd((Packet2d)vec_xor((Packet2d)a.v, (Packet2d)p2ul_CONJ_XOR2)); }
  template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
  {
    Packet2d a_re, a_im, v1, v2;
  
    // Permute and multiply the real parts of a and b
    a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);
    // Get the imaginary parts of a
    a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);
    // multiply a_re * b
    v1 = vec_madd(a_re, b.v, p2d_ZERO);
    // multiply a_im * b and get the conjugate result
    v2 = vec_madd(a_im, b.v, p2d_ZERO);
    v2 = (Packet2d) vec_sld((Packet4ui)v2, (Packet4ui)v2, 8);
    v2 = (Packet2d) vec_xor((Packet2d)v2, (Packet2d) p2ul_CONJ_XOR1);
  
    return Packet1cd(v1 + v2);
  }
  template<> EIGEN_STRONG_INLINE Packet1cd pand    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v,b.v)); }
  template<> EIGEN_STRONG_INLINE Packet1cd por     <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_or(a.v,b.v)); }
  template<> EIGEN_STRONG_INLINE Packet1cd pxor    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_xor(a.v,b.v)); }
  template<> EIGEN_STRONG_INLINE Packet1cd pandnot <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v, vec_nor(b.v,b.v))); }
  template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from) {  return pset1<Packet1cd>(*from); }
  template<> EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b) {
    Packet2d eq = vec_cmpeq (a.v, b.v);
    Packet2d tmp = { eq[1], eq[0] };
    return (Packet1cd)pand<Packet2d>(eq, tmp);
  }
  
  template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
  
  template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)
  {
    std::complex<double> EIGEN_ALIGN16 res;
    pstore<std::complex<double> >(&res, a);
  
    return res;
  }
  
  template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
  template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
  {
    return pfirst(a);
  }
  template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
  {
    return pfirst(a);
  }
  EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet1cd,Packet2d)
  
  template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
  {
    return pdiv_complex(a, b);
  }
  
  EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
  {
    return Packet1cd(preverse(Packet2d(x.v)));
  }
  
  EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
  {
    Packet2d tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
    kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
    kernel.packet[0].v = tmp;
  }
  
  /* complex<float> follows */
  template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from)  { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
  template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from)  { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
  template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *     to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
  template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *     to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
  
  template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
  {
    std::complex<float> EIGEN_ALIGN16 res[2];
    pstore<std::complex<float> >(res, a);
  
    return res[0];
  }
  
  
  #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
  template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
  {
    Packet2cf res;
    res.cd[0] = Packet1cd(vec_ld2f((const float *)&from));
    res.cd[1] = res.cd[0];
    return res;
  }
  #else
  template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
  {
    Packet2cf res;
    if((std::ptrdiff_t(&from) % 16) == 0)
      res.v = pload<Packet4f>((const float *)&from);
    else
      res.v = ploadu<Packet4f>((const float *)&from);
    res.v = vec_perm(res.v, res.v, p16uc_PSET64_HI);
    return res;
  }
  #endif
  
  template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
  {
    std::complex<float> EIGEN_ALIGN16 af[2];
    af[0] = from[0*stride];
    af[1] = from[1*stride];
    return pload<Packet2cf>(af);
  }
  template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
  {
    std::complex<float> EIGEN_ALIGN16 af[2];
    pstore<std::complex<float> >((std::complex<float> *) af, from);
    to[0*stride] = af[0];
    to[1*stride] = af[1];
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v, b.v)); }
  template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v, b.v)); }
  template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(Packet4f(a.v))); }
  
  template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v,b.v)); }
  template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v,b.v)); }
  template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v,b.v)); }
  template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v,b.v)); }
  
  template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>*      from) {  return pset1<Packet2cf>(*from); }
  
  template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *     addr) { EIGEN_ZVECTOR_PREFETCH(addr); }
  
  
  #if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ < 12)
  
  template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
    Packet4f eq = pcmp_eq<Packet4f> (a.v, b.v);
    Packet2cf res;
    Packet2d tmp1 = { eq.v4f[0][1], eq.v4f[0][0] };
    Packet2d tmp2 = { eq.v4f[1][1], eq.v4f[1][0] };
    res.v.v4f[0] = pand<Packet2d>(eq.v4f[0], tmp1);
    res.v.v4f[1] = pand<Packet2d>(eq.v4f[1], tmp2);
    return res;
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
  {
    Packet2cf res;
    res.v.v4f[0] = pconj(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[0]))).v;
    res.v.v4f[1] = pconj(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[1]))).v;
    return res;
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
  {
    Packet2cf res;
    res.v.v4f[0] = pmul(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[0])), Packet1cd(reinterpret_cast<Packet2d>(b.v.v4f[0]))).v;
    res.v.v4f[1] = pmul(Packet1cd(reinterpret_cast<Packet2d>(a.v.v4f[1])), Packet1cd(reinterpret_cast<Packet2d>(b.v.v4f[1]))).v;
    return res;
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
  {
    Packet2cf res;
    res.cd[0] = a.cd[1];
    res.cd[1] = a.cd[0];
    return res;
  }
  
  template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
  {
    std::complex<float> res;
    Packet1cd b = padd<Packet1cd>(a.cd[0], a.cd[1]);
    vec_st2f(b.v, (float*)&res);
    return res;
  }
  
  template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
  {
    std::complex<float> res;
    Packet1cd b = pmul<Packet1cd>(a.cd[0], a.cd[1]);
    vec_st2f(b.v, (float*)&res);
    return res;
  }
  
  EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
  
  template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
  {
    return pdiv_complex(a, b);
  }
  
  EIGEN_STRONG_INLINE Packet2cf pcplxflip/*<Packet2cf>*/(const Packet2cf& x)
  {
    Packet2cf res;
    res.cd[0] = pcplxflip(x.cd[0]);
    res.cd[1] = pcplxflip(x.cd[1]);
    return res;
  }
  
  EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
  {
    Packet1cd tmp = kernel.packet[0].cd[1];
    kernel.packet[0].cd[1] = kernel.packet[1].cd[0];
    kernel.packet[1].cd[0] = tmp;
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
    Packet2cf result;
    const Selector<4> ifPacket4 = { ifPacket.select[0], ifPacket.select[0], ifPacket.select[1], ifPacket.select[1] };
    result.v = pblend<Packet4f>(ifPacket4, thenPacket.v, elsePacket.v);
    return result;
  }
  #else
  template<> EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
    Packet4f eq = vec_cmpeq (a.v, b.v);
    Packet4f tmp = { eq[1], eq[0], eq[3], eq[2] };
    return (Packet2cf)pand<Packet4f>(eq, tmp);
  }
  template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }
  template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
  {
    Packet4f a_re, a_im, prod, prod_im;
  
    // Permute and multiply the real parts of a and b
    a_re = vec_perm(a.v, a.v, p16uc_PSET32_WODD);
    
    // Get the imaginary parts of a
    a_im = vec_perm(a.v, a.v, p16uc_PSET32_WEVEN);
  
    // multiply a_im * b and get the conjugate result
    prod_im = a_im * b.v;
    prod_im = pxor<Packet4f>(prod_im, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR));
    // permute back to a proper order
    prod_im = vec_perm(prod_im, prod_im, p16uc_COMPLEX32_REV);
  
    // multiply a_re * b, add prod_im
    prod = pmadd<Packet4f>(a_re, b.v, prod_im);
   
    return Packet2cf(prod);
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
  {
    Packet4f rev_a;
    rev_a = vec_perm(a.v, a.v, p16uc_COMPLEX32_REV2);
    return Packet2cf(rev_a);
  }
  
  template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
  {
    Packet4f b;
    b = vec_sld(a.v, a.v, 8);
    b = padd<Packet4f>(a.v, b);
    return pfirst<Packet2cf>(Packet2cf(b));
  }
  
  template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
  {
    Packet4f b;
    Packet2cf prod;
    b = vec_sld(a.v, a.v, 8);
    prod = pmul<Packet2cf>(a, Packet2cf(b));
  
    return pfirst<Packet2cf>(prod);
  }
  
  EIGEN_MAKE_CONJ_HELPER_CPLX_REAL(Packet2cf,Packet4f)
  
  template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
  {
    return pdiv_complex(a, b);
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
  {
    return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX32_REV));
  }
  
  EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
  {
    Packet4f tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
    kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
    kernel.packet[0].v = tmp;
  }
  
  template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
    Packet2cf result;
    result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v)));
    return result;
  }
  #endif
  
  } // end namespace internal
  
  } // end namespace Eigen
  
  #endif // EIGEN_COMPLEX32_ALTIVEC_H
  