Complex.h

// 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) 2010-2016 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/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_COMPLEX32_ALTIVEC_H
#define EIGEN_COMPLEX32_ALTIVEC_H
 
// IWYU pragma: private
#include "../../InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
EIGEN_GCC_FAST_MATH_COMPLEX_VECTORIZE_WORKAROUND_PUSH
 
inline Packet4ui p4ui_CONJ_XOR() {
  return vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);  //{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
}
#ifdef EIGEN_VECTORIZE_VSX
#if defined(_BIG_ENDIAN)
inline Packet2ul p2ul_CONJ_XOR1() {
  return (Packet2ul)vec_sld((Packet4ui)p2d_MZERO, (Packet4ui)p2l_ZERO,
                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
}
inline Packet2ul p2ul_CONJ_XOR2() {
  return (Packet2ul)vec_sld((Packet4ui)p2l_ZERO, (Packet4ui)p2d_MZERO,
                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
}
#else
inline Packet2ul p2ul_CONJ_XOR1() {
  return (Packet2ul)vec_sld((Packet4ui)p2l_ZERO, (Packet4ui)p2d_MZERO,
                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
}
inline Packet2ul p2ul_CONJ_XOR2() {
  return (Packet2ul)vec_sld((Packet4ui)p2d_MZERO, (Packet4ui)p2l_ZERO,
                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
}
#endif
#endif
 
//---------- float ----------
struct Packet2cf {
  EIGEN_STRONG_INLINE explicit Packet2cf() {}
  EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
 
  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) {
    Packet4f v1, v2;
 
    // Permute and multiply the real parts of a and b
    v1 = vec_perm(a.v, a.v, p16uc_PSET32_WODD);
    // Get the imaginary parts of a
    v2 = vec_perm(a.v, a.v, p16uc_PSET32_WEVEN);
    // multiply a_re * b
    v1 = vec_madd(v1, b.v, p4f_ZERO);
    // multiply a_im * b and get the conjugate result
    v2 = vec_madd(v2, b.v, p4f_ZERO);
    v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR())));
    // permute back to a proper order
    v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV);
 
    return Packet2cf(padd<Packet4f>(v1, v2));
  }
 
  EIGEN_STRONG_INLINE Packet2cf& operator*=(const Packet2cf& b) {
    v = pmul(Packet2cf(*this), b).v;
    return *this;
  }
  EIGEN_STRONG_INLINE Packet2cf operator*(const Packet2cf& b) const { return Packet2cf(*this) *= b; }
 
  EIGEN_STRONG_INLINE Packet2cf& operator+=(const Packet2cf& b) {
    v = padd(v, b.v);
    return *this;
  }
  EIGEN_STRONG_INLINE Packet2cf operator+(const Packet2cf& b) const { return Packet2cf(*this) += b; }
  EIGEN_STRONG_INLINE Packet2cf& operator-=(const Packet2cf& b) {
    v = psub(v, b.v);
    return *this;
  }
  EIGEN_STRONG_INLINE Packet2cf operator-(const Packet2cf& b) const { return Packet2cf(*this) -= b; }
  EIGEN_STRONG_INLINE Packet2cf operator-(void) const { return Packet2cf(-v); }
 
  Packet4f v;
};
 
template <>
struct packet_traits<std::complex<float> > : default_packet_traits {
  typedef Packet2cf type;
  typedef Packet2cf half;
  typedef Packet4f as_real;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 2,
 
    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasNegate = 1,
    HasAbs = 0,
    HasAbs2 = 0,
    HasMin = 0,
    HasMax = 0,
    HasSqrt = 1,
    HasLog = 1,
    HasExp = 1,
    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;
  typedef Packet4f as_real;
};
 
template <>
EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from) {
  Packet2cf res;
#ifdef EIGEN_VECTORIZE_VSX
  // Load a single std::complex<float> from memory and duplicate
  //
  // Using pload would read past the end of the reference in this case
  // Using vec_xl_len + vec_splat, generates poor assembly
  __asm__("lxvdsx %x0,%y1" : "=wa"(res.v) : "Z"(from));
#else
  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);
#endif
  return res;
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) {
  return Packet2cf(pload<Packet4f>((const float*)from));
}
template <>
EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) {
  return Packet2cf(ploadu<Packet4f>((const float*)from));
}
template <>
EIGEN_ALWAYS_INLINE Packet2cf pload_partial<Packet2cf>(const std::complex<float>* from, const Index n,
                                                       const Index offset) {
  return Packet2cf(pload_partial<Packet4f>((const float*)from, n * 2, offset * 2));
}
template <>
EIGEN_ALWAYS_INLINE Packet2cf ploadu_partial<Packet2cf>(const std::complex<float>* from, const Index n,
                                                        const Index offset) {
  return Packet2cf(ploadu_partial<Packet4f>((const float*)from, n * 2, offset * 2));
}
template <>
EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) {
  return pset1<Packet2cf>(*from);
}
 
template <>
EIGEN_STRONG_INLINE void pstore<std::complex<float> >(std::complex<float>* to, const Packet2cf& from) {
  pstore((float*)to, from.v);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet2cf& from) {
  pstoreu((float*)to, from.v);
}
template <>
EIGEN_ALWAYS_INLINE void pstore_partial<std::complex<float> >(std::complex<float>* to, const Packet2cf& from,
                                                              const Index n, const Index offset) {
  pstore_partial((float*)to, from.v, n * 2, offset * 2);
}
template <>
EIGEN_ALWAYS_INLINE void pstoreu_partial<std::complex<float> >(std::complex<float>* to, const Packet2cf& from,
                                                               const Index n, const Index offset) {
  pstoreu_partial((float*)to, from.v, n * 2, offset * 2);
}
 
EIGEN_STRONG_INLINE Packet2cf pload2(const std::complex<float>& from0, const std::complex<float>& from1) {
  Packet4f res0, res1;
#ifdef EIGEN_VECTORIZE_VSX
  // Load two std::complex<float> from memory and combine
  __asm__("lxsdx %x0,%y1" : "=wa"(res0) : "Z"(from0));
  __asm__("lxsdx %x0,%y1" : "=wa"(res1) : "Z"(from1));
#ifdef _BIG_ENDIAN
  __asm__("xxpermdi %x0, %x1, %x2, 0" : "=wa"(res0) : "wa"(res0), "wa"(res1));
#else
  __asm__("xxpermdi %x0, %x2, %x1, 0" : "=wa"(res0) : "wa"(res0), "wa"(res1));
#endif
#else
  *reinterpret_cast<std::complex<float>*>(&res0) = from0;
  *reinterpret_cast<std::complex<float>*>(&res1) = from1;
  res0 = vec_perm(res0, res1, p16uc_TRANSPOSE64_HI);
#endif
  return Packet2cf(res0);
}
 
template <>
EIGEN_ALWAYS_INLINE Packet2cf pload_ignore<Packet2cf>(const std::complex<float>* from) {
  Packet2cf res;
  res.v = pload_ignore<Packet4f>(reinterpret_cast<const float*>(from));
  return res;
}
 
template <typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet pgather_complex_size2(const Scalar* from, Index stride,
                                                                   const Index n = 2) {
  eigen_internal_assert(n <= unpacket_traits<Packet>::size && "number of elements will gather past end of packet");
  EIGEN_ALIGN16 Scalar af[2];
  for (Index i = 0; i < n; i++) {
    af[i] = from[i * stride];
  }
  return pload_ignore<Packet>(af);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from,
                                                                                        Index stride) {
  return pgather_complex_size2<std::complex<float>, Packet2cf>(from, stride);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet2cf
pgather_partial<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride, const Index n) {
  return pgather_complex_size2<std::complex<float>, Packet2cf>(from, stride, n);
}
template <typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_complex_size2(Scalar* to, const Packet& from, Index stride,
                                                                  const Index n = 2) {
  eigen_internal_assert(n <= unpacket_traits<Packet>::size && "number of elements will scatter past end of packet");
  EIGEN_ALIGN16 Scalar af[2];
  pstore<Scalar>((Scalar*)af, from);
  for (Index i = 0; i < n; i++) {
    to[i * stride] = af[i];
  }
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to,
                                                                                    const Packet2cf& from,
                                                                                    Index stride) {
  pscatter_complex_size2<std::complex<float>, Packet2cf>(to, from, stride);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<std::complex<float>, Packet2cf>(std::complex<float>* to,
                                                                                            const Packet2cf& from,
                                                                                            Index stride,
                                                                                            const Index n) {
  pscatter_complex_size2<std::complex<float>, Packet2cf>(to, from, stride, n);
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(a.v + b.v);
}
template <>
EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(a.v - b.v);
}
template <>
EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) {
  return Packet2cf(pnegate(a.v));
}
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 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 void prefetch<std::complex<float> >(const std::complex<float>* addr) {
  EIGEN_PPC_PREFETCH(addr);
}
 
template <>
EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a) {
  EIGEN_ALIGN16 std::complex<float> res[2];
  pstore((float*)&res, a.v);
 
  return res[0];
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) {
  Packet4f rev_a;
  rev_a = vec_sld(a.v, a.v, 8);
  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) {
#ifdef EIGEN_VECTORIZE_VSX
  Packet4f tmp = reinterpret_cast<Packet4f>(
      vec_mergeh(reinterpret_cast<Packet2d>(kernel.packet[0].v), reinterpret_cast<Packet2d>(kernel.packet[1].v)));
  kernel.packet[1].v = reinterpret_cast<Packet4f>(
      vec_mergel(reinterpret_cast<Packet2d>(kernel.packet[0].v), reinterpret_cast<Packet2d>(kernel.packet[1].v)));
#else
  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);
#endif
  kernel.packet[0].v = tmp;
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
  Packet4f eq = reinterpret_cast<Packet4f>(vec_cmpeq(a.v, b.v));
  return Packet2cf(vec_and(eq, vec_perm(eq, eq, p16uc_COMPLEX32_REV)));
}
 
EIGEN_INSTANTIATE_COMPLEX_MATH_FUNCS(Packet2cf)
 
//---------- double ----------
#ifdef EIGEN_VECTORIZE_VSX
struct Packet1cd {
  EIGEN_STRONG_INLINE Packet1cd() {}
  EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
 
  EIGEN_STRONG_INLINE Packet1cd pmul(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 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8));
    v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1()));
 
    return Packet1cd(padd<Packet2d>(v1, v2));
  }
 
  EIGEN_STRONG_INLINE Packet1cd& operator*=(const Packet1cd& b) {
    v = pmul(Packet1cd(*this), b).v;
    return *this;
  }
  EIGEN_STRONG_INLINE Packet1cd operator*(const Packet1cd& b) const { return Packet1cd(*this) *= b; }
 
  EIGEN_STRONG_INLINE Packet1cd& operator+=(const Packet1cd& b) {
    v = padd(v, b.v);
    return *this;
  }
  EIGEN_STRONG_INLINE Packet1cd operator+(const Packet1cd& b) const { return Packet1cd(*this) += b; }
  EIGEN_STRONG_INLINE Packet1cd& operator-=(const Packet1cd& b) {
    v = psub(v, b.v);
    return *this;
  }
  EIGEN_STRONG_INLINE Packet1cd operator-(const Packet1cd& b) const { return Packet1cd(*this) -= b; }
  EIGEN_STRONG_INLINE Packet1cd operator-(void) const { return Packet1cd(-v); }
 
  Packet2d v;
};
 
template <>
struct packet_traits<std::complex<double> > : default_packet_traits {
  typedef Packet1cd type;
  typedef Packet1cd half;
  typedef Packet2d as_real;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 0,
    size = 1,
 
    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasNegate = 1,
    HasAbs = 0,
    HasAbs2 = 0,
    HasMin = 0,
    HasMax = 0,
    HasSqrt = 1,
    HasLog = 1,
    HasSetLinear = 0
  };
};
 
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;
  typedef Packet2d as_real;
};
 
template <>
EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from) {
  return Packet1cd(pload<Packet2d>((const double*)from));
}
template <>
EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) {
  return Packet1cd(ploadu<Packet2d>((const double*)from));
}
template <>
EIGEN_ALWAYS_INLINE Packet1cd pload_partial<Packet1cd>(const std::complex<double>* from, const Index n,
                                                       const Index offset) {
  return Packet1cd(pload_partial<Packet2d>((const double*)from, n * 2, offset * 2));
}
template <>
EIGEN_ALWAYS_INLINE Packet1cd ploadu_partial<Packet1cd>(const std::complex<double>* from, const Index n,
                                                        const Index offset) {
  return Packet1cd(ploadu_partial<Packet2d>((const double*)from, n * 2, offset * 2));
}
template <>
EIGEN_STRONG_INLINE void pstore<std::complex<double> >(std::complex<double>* to, const Packet1cd& from) {
  pstore((double*)to, from.v);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double>* to, const Packet1cd& from) {
  pstoreu((double*)to, from.v);
}
template <>
EIGEN_ALWAYS_INLINE void pstore_partial<std::complex<double> >(std::complex<double>* to, const Packet1cd& from,
                                                               const Index n, const Index offset) {
  pstore_partial((double*)to, from.v, n * 2, offset * 2);
}
template <>
EIGEN_ALWAYS_INLINE void pstoreu_partial<std::complex<double> >(std::complex<double>* to, const Packet1cd& from,
                                                                const Index n, const Index offset) {
  pstoreu_partial((double*)to, from.v, n * 2, offset * 2);
}
 
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 EIGEN_ALWAYS_INLINE Packet1cd
pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index) {
  return pload<Packet1cd>(from);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet1cd
pgather_partial<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index, const Index) {
  return pload<Packet1cd>(from);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to,
                                                                                     const Packet1cd& from, Index) {
  pstore<std::complex<double> >(to, from);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void pscatter_partial<std::complex<double>, Packet1cd>(std::complex<double>* to,
                                                                                             const Packet1cd& from,
                                                                                             Index, const Index) {
  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(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2())));
}
 
template <>
EIGEN_STRONG_INLINE Packet1cd pand<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(pand(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd por<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(por(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd pxor<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(pxor(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(pandnot(a.v, b.v));
}
 
template <>
EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double>* addr) {
  EIGEN_PPC_PREFETCH(addr);
}
 
template <>
EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a) {
  EIGEN_ALIGN16 std::complex<double> res[1];
  pstore<std::complex<double> >(res, a);
 
  return res[0];
}
 
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_mergeh(kernel.packet[0].v, kernel.packet[1].v);
  kernel.packet[1].v = vec_mergel(kernel.packet[0].v, kernel.packet[1].v);
  kernel.packet[0].v = tmp;
}
 
template <>
EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b) {
  // Compare real and imaginary parts of a and b to get the mask vector:
  // [re(a)==re(b), im(a)==im(b)]
  Packet2d eq = reinterpret_cast<Packet2d>(vec_cmpeq(a.v, b.v));
  // Swap real/imag elements in the mask in to get:
  // [im(a)==im(b), re(a)==re(b)]
  Packet2d eq_swapped =
      reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(eq), reinterpret_cast<Packet4ui>(eq), 8));
  // Return re(a)==re(b) & im(a)==im(b) by computing bitwise AND of eq and eq_swapped
  return Packet1cd(vec_and(eq, eq_swapped));
}
 
EIGEN_INSTANTIATE_COMPLEX_MATH_FUNCS_NO_EXP(Packet1cd)
 
#endif  // __VSX__
 
EIGEN_GCC_FAST_MATH_COMPLEX_VECTORIZE_WORKAROUND_POP
}  // end namespace internal
 
}  // end namespace Eigen
 
#endif  // EIGEN_COMPLEX32_ALTIVEC_H