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>
//
// 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_COMPLEX_SSE_H
#define EIGEN_COMPLEX_SSE_H
 
// IWYU pragma: private
#include "../../InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
//---------- float ----------
struct Packet2cf {
  EIGEN_STRONG_INLINE Packet2cf() {}
  EIGEN_STRONG_INLINE explicit Packet2cf(const __m128& a) : v(a) {}
  Packet4f v;
};
 
// Use the packet_traits defined in AVX/PacketMath.h instead if we're going
// to leverage AVX instructions.
#ifndef EIGEN_VECTORIZE_AVX
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,
    HasNegate = 1,
    HasSqrt = 1,
    HasLog = 1,
    HasExp = 1,
    HasAbs = 0,
    HasAbs2 = 0,
    HasMin = 0,
    HasMax = 0,
    HasSetLinear = 0,
  };
};
#endif
 
template <>
struct unpacket_traits<Packet2cf> {
  typedef std::complex<float> type;
  typedef Packet2cf half;
  typedef Packet4f as_real;
  enum {
    size = 2,
    alignment = Aligned16,
    vectorizable = true,
    masked_load_available = false,
    masked_store_available = false
  };
};
 
template <>
EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(_mm_add_ps(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(_mm_sub_ps(a.v, b.v));
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) {
  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000, 0x80000000, 0x80000000, 0x80000000));
  return Packet2cf(_mm_xor_ps(a.v, mask));
}
template <>
EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) {
  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000, 0x80000000, 0x00000000, 0x80000000));
  return Packet2cf(_mm_xor_ps(a.v, mask));
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) {
#ifdef EIGEN_VECTORIZE_SSE3
  __m128 tmp1 = _mm_mul_ps(_mm_movehdup_ps(a.v), vec4f_swizzle1(b.v, 1, 0, 3, 2));
  __m128 tmp2 = _mm_moveldup_ps(a.v);
#else
  __m128 tmp1 = _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3), vec4f_swizzle1(b.v, 1, 0, 3, 2));
  __m128 tmp2 = vec4f_swizzle1(a.v, 0, 0, 2, 2);
#endif
#ifdef EIGEN_VECTORIZE_FMA
  __m128 result = _mm_fmaddsub_ps(tmp2, b.v, tmp1);
#else
#ifdef EIGEN_VECTORIZE_SSE3
  __m128 result = _mm_addsub_ps(_mm_mul_ps(tmp2, b.v), tmp1);
#else
  const __m128 mask = _mm_setr_ps(-0.0f, 0.0f, -0.0f, 0.0f);
  __m128 result = _mm_add_ps(_mm_mul_ps(tmp2, b.v), _mm_xor_ps(tmp1, mask));
#endif
#endif
  return Packet2cf(result);
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf ptrue<Packet2cf>(const Packet2cf& a) {
  return Packet2cf(ptrue(Packet4f(a.v)));
}
template <>
EIGEN_STRONG_INLINE Packet2cf pand<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(_mm_and_ps(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet2cf por<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(_mm_or_ps(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet2cf pxor<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(_mm_xor_ps(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) {
  return Packet2cf(_mm_andnot_ps(b.v, a.v));
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(_mm_load_ps(&numext::real_ref(*from)));
}
template <>
EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(_mm_loadu_ps(&numext::real_ref(*from)));
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from) {
  const float re = std::real(from);
  const float im = std::imag(from);
  return Packet2cf(_mm_set_ps(im, re, im, re));
}
 
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) {
  EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(&numext::real_ref(*to), from.v);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet2cf& from) {
  EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_ps(&numext::real_ref(*to), from.v);
}
 
template <>
EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from,
                                                                           Index stride) {
  return Packet2cf(_mm_set_ps(std::imag(from[1 * stride]), std::real(from[1 * stride]), std::imag(from[0 * stride]),
                              std::real(from[0 * stride])));
}
 
template <>
EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from,
                                                                       Index stride) {
  to[stride * 0] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 0)),
                                       _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 1)));
  to[stride * 1] = std::complex<float>(_mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 2)),
                                       _mm_cvtss_f32(_mm_shuffle_ps(from.v, from.v, 3)));
}
 
template <>
EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float>* addr) {
  _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0);
}
 
template <>
EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a) {
  alignas(alignof(__m64)) std::complex<float> res;
  _mm_storel_pi((__m64*)&res, a.v);
  return res;
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) {
  return Packet2cf(_mm_castpd_ps(preverse(Packet2d(_mm_castps_pd(a.v)))));
}
 
template <>
EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a) {
  return pfirst(Packet2cf(_mm_add_ps(a.v, _mm_movehl_ps(a.v, a.v))));
}
 
template <>
EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a) {
  return pfirst(pmul(a, Packet2cf(_mm_movehl_ps(a.v, a.v))));
}
 
EIGEN_STRONG_INLINE Packet2cf pcplxflip /* <Packet2cf> */ (const Packet2cf& x) {
  return Packet2cf(vec4f_swizzle1(x.v, 1, 0, 3, 2));
}
 
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);
}
 
//---------- double ----------
struct Packet1cd {
  EIGEN_STRONG_INLINE Packet1cd() {}
  EIGEN_STRONG_INLINE explicit Packet1cd(const __m128d& a) : v(a) {}
  Packet2d v;
};
 
// Use the packet_traits defined in AVX/PacketMath.h instead if we're going
// to leverage AVX instructions.
#ifndef EIGEN_VECTORIZE_AVX
template <>
struct packet_traits<std::complex<double> > : default_packet_traits {
  typedef Packet1cd type;
  typedef Packet1cd half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 0,
    size = 1,
 
    HasAdd = 1,
    HasSub = 1,
    HasMul = 1,
    HasDiv = 1,
    HasNegate = 1,
    HasSqrt = 1,
    HasLog = 1,
    HasAbs = 0,
    HasAbs2 = 0,
    HasMin = 0,
    HasMax = 0,
    HasSetLinear = 0
  };
};
#endif
 
template <>
struct unpacket_traits<Packet1cd> {
  typedef std::complex<double> type;
  typedef Packet1cd half;
  typedef Packet2d as_real;
  enum {
    size = 1,
    alignment = Aligned16,
    vectorizable = true,
    masked_load_available = false,
    masked_store_available = false
  };
};
 
template <>
EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(_mm_add_pd(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(_mm_sub_pd(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) {
  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000, 0x0, 0x0, 0x0));
  return Packet1cd(_mm_xor_pd(a.v, mask));
}
 
template <>
EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) {
  __m128d tmp1 = _mm_mul_pd(_mm_unpackhi_pd(a.v, a.v), vec2d_swizzle1(b.v, 1, 0));
#ifdef EIGEN_VECTORIZE_SSE3
  __m128d tmp2 = _mm_movedup_pd(a.v);
#else
  __m128d tmp2 = _mm_unpacklo_pd(a.v, a.v);
#endif
#ifdef EIGEN_VECTORIZE_FMA
  __m128d result = _mm_fmaddsub_pd(tmp2, b.v, tmp1);
#else
#ifdef EIGEN_VECTORIZE_SSE3
  __m128d result = _mm_addsub_pd(_mm_mul_pd(tmp2, b.v), tmp1);
#else
  const __m128d mask = _mm_setr_pd(-0.0, 0.0);
  __m128d result = _mm_add_pd(_mm_mul_pd(tmp2, b.v), _mm_xor_pd(tmp1, mask));
#endif
#endif
  return Packet1cd(result);
}
 
template <>
EIGEN_STRONG_INLINE Packet1cd ptrue<Packet1cd>(const Packet1cd& a) {
  return Packet1cd(ptrue(Packet2d(a.v)));
}
template <>
EIGEN_STRONG_INLINE Packet1cd pand<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(_mm_and_pd(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd por<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(_mm_or_pd(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd pxor<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(_mm_xor_pd(a.v, b.v));
}
template <>
EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) {
  return Packet1cd(_mm_andnot_pd(b.v, a.v));
}
 
// FIXME force unaligned load, this is a temporary fix
template <>
EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(_mm_load_pd((const double*)from));
}
template <>
EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(_mm_loadu_pd((const double*)from));
}
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_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) {
  return pset1<Packet1cd>(*from);
}
 
// FIXME force unaligned store, this is a temporary fix
template <>
EIGEN_STRONG_INLINE void pstore<std::complex<double> >(std::complex<double>* to, const Packet1cd& from) {
  EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd((double*)to, from.v);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double>* to, const Packet1cd& from) {
  EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_pd((double*)to, from.v);
}
 
template <>
EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double>* addr) {
  _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0);
}
 
template <>
EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a) {
  EIGEN_ALIGN16 double res[2];
  _mm_store_pd(res, a.v);
  return std::complex<double>(res[0], res[1]);
}
 
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_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet2cf, 2>& kernel) {
  __m128d w1 = _mm_castps_pd(kernel.packet[0].v);
  __m128d w2 = _mm_castps_pd(kernel.packet[1].v);
 
  __m128 tmp = _mm_castpd_ps(_mm_unpackhi_pd(w1, w2));
  kernel.packet[0].v = _mm_castpd_ps(_mm_unpacklo_pd(w1, w2));
  kernel.packet[1].v = tmp;
}
 
template <>
EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf& a, const Packet2cf& b) {
  __m128 eq = _mm_cmpeq_ps(a.v, b.v);
  return Packet2cf(pand<Packet4f>(eq, vec4f_swizzle1(eq, 1, 0, 3, 2)));
}
 
template <>
EIGEN_STRONG_INLINE Packet1cd pcmp_eq(const Packet1cd& a, const Packet1cd& b) {
  __m128d eq = _mm_cmpeq_pd(a.v, b.v);
  return Packet1cd(pand<Packet2d>(eq, vec2d_swizzle1(eq, 1, 0)));
}
 
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<Packet2cf>(a);
}
 
#ifdef EIGEN_VECTORIZE_FMA
// std::complex<float>
template <>
EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& a, const Packet2cf& b, const Packet2cf& c) {
  __m128 a_odd = _mm_movehdup_ps(a.v);
  __m128 a_even = _mm_moveldup_ps(a.v);
  __m128 b_swap = _mm_permute_ps(b.v, _MM_SHUFFLE(2, 3, 0, 1));
  __m128 result = _mm_fmaddsub_ps(a_even, b.v, _mm_fmaddsub_ps(a_odd, b_swap, c.v));
  return Packet2cf(result);
}
template <>
EIGEN_STRONG_INLINE Packet2cf pmsub(const Packet2cf& a, const Packet2cf& b, const Packet2cf& c) {
  __m128 a_odd = _mm_movehdup_ps(a.v);
  __m128 a_even = _mm_moveldup_ps(a.v);
  __m128 b_swap = _mm_permute_ps(b.v, _MM_SHUFFLE(2, 3, 0, 1));
  __m128 result = _mm_fmaddsub_ps(a_even, b.v, _mm_fmsubadd_ps(a_odd, b_swap, c.v));
  return Packet2cf(result);
}
template <>
EIGEN_STRONG_INLINE Packet2cf pnmadd(const Packet2cf& a, const Packet2cf& b, const Packet2cf& c) {
  return pnegate(pmsub(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet2cf pnmsub(const Packet2cf& a, const Packet2cf& b, const Packet2cf& c) {
  return pnegate(pmadd(a, b, c));
}
// std::complex<double>
template <>
EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& a, const Packet1cd& b, const Packet1cd& c) {
  __m128d a_odd = _mm_permute_pd(a.v, 0x3);
  __m128d a_even = _mm_movedup_pd(a.v);
  __m128d b_swap = _mm_permute_pd(b.v, 0x1);
  __m128d result = _mm_fmaddsub_pd(a_even, b.v, _mm_fmaddsub_pd(a_odd, b_swap, c.v));
  return Packet1cd(result);
}
template <>
EIGEN_STRONG_INLINE Packet1cd pmsub(const Packet1cd& a, const Packet1cd& b, const Packet1cd& c) {
  __m128d a_odd = _mm_permute_pd(a.v, 0x3);
  __m128d a_even = _mm_movedup_pd(a.v);
  __m128d b_swap = _mm_permute_pd(b.v, 0x1);
  __m128d result = _mm_fmaddsub_pd(a_even, b.v, _mm_fmsubadd_pd(a_odd, b_swap, c.v));
  return Packet1cd(result);
}
template <>
EIGEN_STRONG_INLINE Packet1cd pnmadd(const Packet1cd& a, const Packet1cd& b, const Packet1cd& c) {
  return pnegate(pmsub(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet1cd pnmsub(const Packet1cd& a, const Packet1cd& b, const Packet1cd& c) {
  return pnegate(pmadd(a, b, c));
}
#endif
}  // end namespace internal
}  // end namespace Eigen
 
#endif  // EIGEN_COMPLEX_SSE_H