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) 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_ZVECTOR_H
#define EIGEN_COMPLEX32_ZVECTOR_H

// IWYU pragma: private
#include "../../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
inline Packet4ui p4ui_CONJ_XOR() {
  return Packet4ui {0x00000000, 0x80000000, 0x00000000, 0x80000000};  // vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);
}
#endif

inline Packet2ul p2ul_CONJ_XOR1() {
  return (Packet2ul)vec_sld((Packet4ui)p2d_ZERO_, (Packet4ui)p2l_ZERO,
                            8);  //{ 0x8000000000000000, 0x0000000000000000 };
}
inline Packet2ul p2ul_CONJ_XOR2() {
  return (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,

    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasLog = 1,
    HasExp = 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,

    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasLog = 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;
  typedef Packet4f as_real;
};
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;
};

/* 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) {
  EIGEN_ALIGN16 std::complex<double> 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);
}

template <>
EIGEN_STRONG_INLINE Packet1cd psqrt<Packet1cd>(const Packet1cd& a) {
  return psqrt_complex<Packet1cd>(a);
}

template <>
EIGEN_STRONG_INLINE Packet2cf psqrt<Packet2cf>(const Packet2cf& a) {
  return psqrt_complex<Packet2cf>(a);
}

template <>
EIGEN_STRONG_INLINE Packet1cd plog<Packet1cd>(const Packet1cd& a) {
  return plog_complex<Packet1cd>(a);
}
template <>
EIGEN_STRONG_INLINE Packet2cf plog<Packet2cf>(const Packet2cf& a) {
  return plog_complex<Packet2cf>(a);
}

template <>
EIGEN_STRONG_INLINE Packet2cf pexp<Packet2cf>(const Packet2cf& a) {
  return pexp_complex(a);
}

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) {
  EIGEN_ALIGN16 std::complex<float> 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) {
  EIGEN_ALIGN16 std::complex<float> 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) {
  EIGEN_ALIGN16 std::complex<float> 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_ZVECTOR_H