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>
  //
  // 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_PACKET_MATH_SSE_H
  #define EIGEN_PACKET_MATH_SSE_H
  
  namespace Eigen {
  
  namespace internal {
  
  #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
  #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
  #endif
  
  #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
  #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))
  #endif
  
  #ifdef __FMA__
  #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
  #define EIGEN_HAS_SINGLE_INSTRUCTION_MADD 1
  #endif
  #endif
  
  #if (defined EIGEN_VECTORIZE_AVX) && (EIGEN_COMP_GNUC_STRICT || EIGEN_COMP_MINGW) && (__GXX_ABI_VERSION < 1004)
  // With GCC's default ABI version, a __m128 or __m256 are the same types and therefore we cannot
  // have overloads for both types without linking error.
  // One solution is to increase ABI version using -fabi-version=4 (or greater).
  // Otherwise, we workaround this inconvenience by wrapping 128bit types into the following helper
  // structure:
  template<typename T>
  struct eigen_packet_wrapper
  {
    EIGEN_ALWAYS_INLINE operator T&() { return m_val; }
    EIGEN_ALWAYS_INLINE operator const T&() const { return m_val; }
    EIGEN_ALWAYS_INLINE eigen_packet_wrapper() {}
    EIGEN_ALWAYS_INLINE eigen_packet_wrapper(const T &v) : m_val(v) {}
    EIGEN_ALWAYS_INLINE eigen_packet_wrapper& operator=(const T &v) {
      m_val = v;
      return *this;
    }
  
    T m_val;
  };
  typedef eigen_packet_wrapper<__m128>  Packet4f;
  typedef eigen_packet_wrapper<__m128i> Packet4i;
  typedef eigen_packet_wrapper<__m128d> Packet2d;
  #else
  typedef __m128  Packet4f;
  typedef __m128i Packet4i;
  typedef __m128d Packet2d;
  #endif
  
  template<> struct is_arithmetic<__m128>  { enum { value = true }; };
  template<> struct is_arithmetic<__m128i> { enum { value = true }; };
  template<> struct is_arithmetic<__m128d> { enum { value = true }; };
  
  #define vec4f_swizzle1(v,p,q,r,s) \
    (_mm_castsi128_ps(_mm_shuffle_epi32( _mm_castps_si128(v), ((s)<<6|(r)<<4|(q)<<2|(p)))))
  
  #define vec4i_swizzle1(v,p,q,r,s) \
    (_mm_shuffle_epi32( v, ((s)<<6|(r)<<4|(q)<<2|(p))))
  
  #define vec2d_swizzle1(v,p,q) \
    (_mm_castsi128_pd(_mm_shuffle_epi32( _mm_castpd_si128(v), ((q*2+1)<<6|(q*2)<<4|(p*2+1)<<2|(p*2)))))
  
  #define vec4f_swizzle2(a,b,p,q,r,s) \
    (_mm_shuffle_ps( (a), (b), ((s)<<6|(r)<<4|(q)<<2|(p))))
  
  #define vec4i_swizzle2(a,b,p,q,r,s) \
    (_mm_castps_si128( (_mm_shuffle_ps( _mm_castsi128_ps(a), _mm_castsi128_ps(b), ((s)<<6|(r)<<4|(q)<<2|(p))))))
  
  #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
    const Packet4f p4f_##NAME = pset1<Packet4f>(X)
  
  #define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
    const Packet2d p2d_##NAME = pset1<Packet2d>(X)
  
  #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
    const Packet4f p4f_##NAME = _mm_castsi128_ps(pset1<Packet4i>(X))
  
  #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
    const Packet4i p4i_##NAME = pset1<Packet4i>(X)
  
  
  // 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<float>  : default_packet_traits
  {
    typedef Packet4f type;
    typedef Packet4f half;
    enum {
      Vectorizable = 1,
      AlignedOnScalar = 1,
      size=4,
      HasHalfPacket = 0,
  
      HasDiv  = 1,
      HasSin  = EIGEN_FAST_MATH,
      HasCos  = EIGEN_FAST_MATH,
      HasLog  = 1,
      HasExp  = 1,
      HasSqrt = 1,
      HasRsqrt = 1,
      HasTanh  = EIGEN_FAST_MATH,
      HasBlend = 1
  
  #ifdef EIGEN_VECTORIZE_SSE4_1
      ,
      HasRound = 1,
      HasFloor = 1,
      HasCeil = 1
  #endif
    };
  };
  template<> struct packet_traits<double> : default_packet_traits
  {
    typedef Packet2d type;
    typedef Packet2d half;
    enum {
      Vectorizable = 1,
      AlignedOnScalar = 1,
      size=2,
      HasHalfPacket = 0,
  
      HasDiv  = 1,
      HasExp  = 1,
      HasSqrt = 1,
      HasRsqrt = 1,
      HasBlend = 1
  
  #ifdef EIGEN_VECTORIZE_SSE4_1
      ,
      HasRound = 1,
      HasFloor = 1,
      HasCeil = 1
  #endif
    };
  };
  #endif
  template<> struct packet_traits<int>    : default_packet_traits
  {
    typedef Packet4i type;
    typedef Packet4i half;
    enum {
      Vectorizable = 1,
      AlignedOnScalar = 1,
      size=4,
  
      HasBlend = 1
    };
  };
  
  template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };
  template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
  template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
  
  #ifndef EIGEN_VECTORIZE_AVX
  template<> struct scalar_div_cost<float,true> { enum { value = 7 }; };
  template<> struct scalar_div_cost<double,true> { enum { value = 8 }; };
  #endif
  
  #if EIGEN_COMP_MSVC==1500
  // Workaround MSVC 9 internal compiler error.
  // TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode
  // TODO: let's check whether there does not exist a better fix, like adding a pset0() function. (it crashed on pset1(0)).
  template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return _mm_set_ps(from,from,from,from); }
  template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set_pd(from,from); }
  template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set_epi32(from,from,from,from); }
  #else
  template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return _mm_set_ps1(from); }
  template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
  template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set1_epi32(from); }
  #endif
  
  // GCC generates a shufps instruction for _mm_set1_ps/_mm_load1_ps instead of the more efficient pshufd instruction.
  // However, using inrinsics for pset1 makes gcc to generate crappy code in some cases (see bug 203)
  // Using inline assembly is also not an option because then gcc fails to reorder properly the instructions.
  // Therefore, we introduced the pload1 functions to be used in product kernels for which bug 203 does not apply.
  // Also note that with AVX, we want it to generate a vbroadcastss.
  #if EIGEN_COMP_GNUC_STRICT && (!defined __AVX__)
  template<> EIGEN_STRONG_INLINE Packet4f pload1<Packet4f>(const float *from) {
    return vec4f_swizzle1(_mm_load_ss(from),0,0,0,0);
  }
  #endif
  
  template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }
  template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }
  template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a),_mm_set_epi32(3,2,1,0)); }
  
  template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }
  
  template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
  {
    const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
    return _mm_xor_ps(a,mask);
  }
  template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
  {
    const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));
    return _mm_xor_pd(a,mask);
  }
  template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
  {
    return psub(Packet4i(_mm_setr_epi32(0,0,0,0)), a);
  }
  
  template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
  template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
  template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
  
  template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_mullo_epi32(a,b);
  #else
    // this version is slightly faster than 4 scalar products
    return vec4i_swizzle1(
              vec4i_swizzle2(
                _mm_mul_epu32(a,b),
                _mm_mul_epu32(vec4i_swizzle1(a,1,0,3,2),
                              vec4i_swizzle1(b,1,0,3,2)),
                0,2,0,2),
              0,2,1,3);
  #endif
  }
  
  template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }
  
  // for some weird raisons, it has to be overloaded for packet of integers
  template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
  #ifdef __FMA__
  template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return _mm_fmadd_ps(a,b,c); }
  template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return _mm_fmadd_pd(a,b,c); }
  #endif
  
  template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) {
  #if EIGEN_COMP_GNUC
    // There appears to be a bug in GCC, by which the optimizer may
    // flip the argument order in calls to _mm_min_ps, so we have to
    // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
    // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
    Packet4f res = b;
    asm("minps %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
    return res;
  #else
    // Arguments are reversed to match NaN propagation behavior of std::min.
    return _mm_min_ps(b, a);
  #endif
  }
  template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) {
  #if EIGEN_COMP_GNUC
    // There appears to be a bug in GCC, by which the optimizer may
    // flip the argument order in calls to _mm_min_pd, so we have to
    // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
    // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
    Packet2d res = b;
    asm("minpd %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
    return res;
  #else
    // Arguments are reversed to match NaN propagation behavior of std::min.
    return _mm_min_pd(b, a);
  #endif
  }
  template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_min_epi32(a,b);
  #else
    // after some bench, this version *is* faster than a scalar implementation
    Packet4i mask = _mm_cmplt_epi32(a,b);
    return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
  #endif
  }
  
  template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) {
  #if EIGEN_COMP_GNUC
    // There appears to be a bug in GCC, by which the optimizer may
    // flip the argument order in calls to _mm_max_ps, so we have to
    // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
    // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
    Packet4f res = b;
    asm("maxps %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
    return res;
  #else
    // Arguments are reversed to match NaN propagation behavior of std::max.
    return _mm_max_ps(b, a);
  #endif
  }
  template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) {
  #if EIGEN_COMP_GNUC
    // There appears to be a bug in GCC, by which the optimizer may
    // flip the argument order in calls to _mm_max_pd, so we have to
    // resort to inline ASM here. This is supposed to be fixed in gcc6.3,
    // see also: https://gcc.gnu.org/bugzilla/show_bug.cgi?id=72867
    Packet2d res = b;
    asm("maxpd %[a], %[res]" : [res] "+x" (res) : [a] "x" (a));
    return res;
  #else
    // Arguments are reversed to match NaN propagation behavior of std::max.
    return _mm_max_pd(b, a);
  #endif
  }
  template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_max_epi32(a,b);
  #else
    // after some bench, this version *is* faster than a scalar implementation
    Packet4i mask = _mm_cmpgt_epi32(a,b);
    return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
  #endif
  }
  
  #ifdef EIGEN_VECTORIZE_SSE4_1
  template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return _mm_round_ps(a, 0); }
  template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return _mm_round_pd(a, 0); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) { return _mm_ceil_ps(a); }
  template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) { return _mm_ceil_pd(a); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return _mm_floor_ps(a); }
  template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return _mm_floor_pd(a); }
  #endif
  
  template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
  
  template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(a,b); }
  template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(a,b); }
  template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(a,b); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*   from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
  template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double*  from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
  template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const __m128i*>(from)); }
  
  #if EIGEN_COMP_MSVC
    template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*  from) {
      EIGEN_DEBUG_UNALIGNED_LOAD
      #if (EIGEN_COMP_MSVC==1600)
      // NOTE Some version of MSVC10 generates bad code when using _mm_loadu_ps
      // (i.e., it does not generate an unaligned load!!
      __m128 res = _mm_loadl_pi(_mm_set1_ps(0.0f), (const __m64*)(from));
      res = _mm_loadh_pi(res, (const __m64*)(from+2));
      return res;
      #else
      return _mm_loadu_ps(from);
      #endif
    }
  #else
  // NOTE: with the code below, MSVC's compiler crashes!
  
  template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
  {
    EIGEN_DEBUG_UNALIGNED_LOAD
    return _mm_loadu_ps(from);
  }
  #endif
  
  template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
  {
    EIGEN_DEBUG_UNALIGNED_LOAD
    return _mm_loadu_pd(from);
  }
  template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
  {
    EIGEN_DEBUG_UNALIGNED_LOAD
    return _mm_loadu_si128(reinterpret_cast<const __m128i*>(from));
  }
  
  
  template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
  {
    return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);
  }
  template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*  from)
  { return pset1<Packet2d>(from[0]); }
  template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
  {
    Packet4i tmp;
    tmp = _mm_loadl_epi64(reinterpret_cast<const __m128i*>(from));
    return vec4i_swizzle1(tmp, 0, 0, 1, 1);
  }
  
  template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }
  template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }
  template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<__m128i*>(to), from); }
  
  template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_pd(to, from); }
  template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_ps(to, from); }
  template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm_storeu_si128(reinterpret_cast<__m128i*>(to), from); }
  
  template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
  {
   return _mm_set_ps(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
  }
  template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
  {
   return _mm_set_pd(from[1*stride], from[0*stride]);
  }
  template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
  {
   return _mm_set_epi32(from[3*stride], from[2*stride], from[1*stride], from[0*stride]);
   }
  
  template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
  {
    to[stride*0] = _mm_cvtss_f32(from);
    to[stride*1] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 1));
    to[stride*2] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 2));
    to[stride*3] = _mm_cvtss_f32(_mm_shuffle_ps(from, from, 3));
  }
  template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
  {
    to[stride*0] = _mm_cvtsd_f64(from);
    to[stride*1] = _mm_cvtsd_f64(_mm_shuffle_pd(from, from, 1));
  }
  template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
  {
    to[stride*0] = _mm_cvtsi128_si32(from);
    to[stride*1] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 1));
    to[stride*2] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 2));
    to[stride*3] = _mm_cvtsi128_si32(_mm_shuffle_epi32(from, 3));
  }
  
  // some compilers might be tempted to perform multiple moves instead of using a vector path.
  template<> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)
  {
    Packet4f pa = _mm_set_ss(a);
    pstore(to, Packet4f(vec4f_swizzle1(pa,0,0,0,0)));
  }
  // some compilers might be tempted to perform multiple moves instead of using a vector path.
  template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)
  {
    Packet2d pa = _mm_set_sd(a);
    pstore(to, Packet2d(vec2d_swizzle1(pa,0,0)));
  }
  
  #ifndef EIGEN_VECTORIZE_AVX
  template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
  template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
  template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const void*)(addr), _MM_HINT_T0); }
  #endif
  
  #if EIGEN_COMP_MSVC_STRICT && EIGEN_OS_WIN64
  // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
  // Direct of the struct members fixed bug #62.
  template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
  template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
  template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
  #elif EIGEN_COMP_MSVC_STRICT
  // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
  template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
  template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
  template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
  #else
  template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
  template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
  template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
  #endif
  
  template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
  { return _mm_shuffle_ps(a,a,0x1B); }
  template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
  { return _mm_shuffle_pd(a,a,0x1); }
  template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
  { return _mm_shuffle_epi32(a,0x1B); }
  
  template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)
  {
    const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
    return _mm_and_ps(a,mask);
  }
  template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)
  {
    const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
    return _mm_and_pd(a,mask);
  }
  template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
  {
    #ifdef EIGEN_VECTORIZE_SSSE3
    return _mm_abs_epi32(a);
    #else
    Packet4i aux = _mm_srai_epi32(a,31);
    return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);
    #endif
  }
  
  // with AVX, the default implementations based on pload1 are faster
  #ifndef __AVX__
  template<> EIGEN_STRONG_INLINE void
  pbroadcast4<Packet4f>(const float *a,
                        Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
  {
    a3 = pload<Packet4f>(a);
    a0 = vec4f_swizzle1(a3, 0,0,0,0);
    a1 = vec4f_swizzle1(a3, 1,1,1,1);
    a2 = vec4f_swizzle1(a3, 2,2,2,2);
    a3 = vec4f_swizzle1(a3, 3,3,3,3);
  }
  template<> EIGEN_STRONG_INLINE void
  pbroadcast4<Packet2d>(const double *a,
                        Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
  {
  #ifdef EIGEN_VECTORIZE_SSE3
    a0 = _mm_loaddup_pd(a+0);
    a1 = _mm_loaddup_pd(a+1);
    a2 = _mm_loaddup_pd(a+2);
    a3 = _mm_loaddup_pd(a+3);
  #else
    a1 = pload<Packet2d>(a);
    a0 = vec2d_swizzle1(a1, 0,0);
    a1 = vec2d_swizzle1(a1, 1,1);
    a3 = pload<Packet2d>(a+2);
    a2 = vec2d_swizzle1(a3, 0,0);
    a3 = vec2d_swizzle1(a3, 1,1);
  #endif
  }
  #endif
  
  EIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)
  {
    vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));
    vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));
    vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));
    vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));
  }
  
  #ifdef EIGEN_VECTORIZE_SSE3
  template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
  {
    return _mm_hadd_ps(_mm_hadd_ps(vecs[0], vecs[1]),_mm_hadd_ps(vecs[2], vecs[3]));
  }
  
  template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
  {
    return _mm_hadd_pd(vecs[0], vecs[1]);
  }
  
  #else
  template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
  {
    Packet4f tmp0, tmp1, tmp2;
    tmp0 = _mm_unpacklo_ps(vecs[0], vecs[1]);
    tmp1 = _mm_unpackhi_ps(vecs[0], vecs[1]);
    tmp2 = _mm_unpackhi_ps(vecs[2], vecs[3]);
    tmp0 = _mm_add_ps(tmp0, tmp1);
    tmp1 = _mm_unpacklo_ps(vecs[2], vecs[3]);
    tmp1 = _mm_add_ps(tmp1, tmp2);
    tmp2 = _mm_movehl_ps(tmp1, tmp0);
    tmp0 = _mm_movelh_ps(tmp0, tmp1);
    return _mm_add_ps(tmp0, tmp2);
  }
  
  template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
  {
    return _mm_add_pd(_mm_unpacklo_pd(vecs[0], vecs[1]), _mm_unpackhi_pd(vecs[0], vecs[1]));
  }
  #endif  // SSE3
  
  template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
  {
    // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures
    // (from Nehalem to Haswell)
  // #ifdef EIGEN_VECTORIZE_SSE3
  //   Packet4f tmp = _mm_add_ps(a, vec4f_swizzle1(a,2,3,2,3));
  //   return pfirst<Packet4f>(_mm_hadd_ps(tmp, tmp));
  // #else
    Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));
    return pfirst<Packet4f>(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
  // #endif
  }
  
  template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
  {
    // Disable SSE3 _mm_hadd_pd that is extremely slow on all existing Intel's architectures
    // (from Nehalem to Haswell)
  // #ifdef EIGEN_VECTORIZE_SSE3
  //   return pfirst<Packet2d>(_mm_hadd_pd(a, a));
  // #else
    return pfirst<Packet2d>(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));
  // #endif
  }
  
  #ifdef EIGEN_VECTORIZE_SSSE3
  template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
  {
    return _mm_hadd_epi32(_mm_hadd_epi32(vecs[0], vecs[1]),_mm_hadd_epi32(vecs[2], vecs[3]));
  }
  template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
  {
    Packet4i tmp0 = _mm_hadd_epi32(a,a);
    return pfirst<Packet4i>(_mm_hadd_epi32(tmp0,tmp0));
  }
  #else
  template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
  {
    Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));
    return pfirst(tmp) + pfirst<Packet4i>(_mm_shuffle_epi32(tmp, 1));
  }
  
  template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
  {
    Packet4i tmp0, tmp1, tmp2;
    tmp0 = _mm_unpacklo_epi32(vecs[0], vecs[1]);
    tmp1 = _mm_unpackhi_epi32(vecs[0], vecs[1]);
    tmp2 = _mm_unpackhi_epi32(vecs[2], vecs[3]);
    tmp0 = _mm_add_epi32(tmp0, tmp1);
    tmp1 = _mm_unpacklo_epi32(vecs[2], vecs[3]);
    tmp1 = _mm_add_epi32(tmp1, tmp2);
    tmp2 = _mm_unpacklo_epi64(tmp0, tmp1);
    tmp0 = _mm_unpackhi_epi64(tmp0, tmp1);
    return _mm_add_epi32(tmp0, tmp2);
  }
  #endif
  // Other reduction functions:
  
  // mul
  template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
  {
    Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
    return pfirst<Packet4f>(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
  }
  template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
  {
    return pfirst<Packet2d>(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
  }
  template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
  {
    // after some experiments, it is seems this is the fastest way to implement it
    // for GCC (eg., reusing pmul is very slow !)
    // TODO try to call _mm_mul_epu32 directly
    EIGEN_ALIGN16 int aux[4];
    pstore(aux, a);
    return  (aux[0] * aux[1]) * (aux[2] * aux[3]);;
  }
  
  // min
  template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
  {
    Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));
    return pfirst<Packet4f>(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
  }
  template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
  {
    return pfirst<Packet2d>(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));
  }
  template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    Packet4i tmp = _mm_min_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0,0,3,2)));
    return pfirst<Packet4i>(_mm_min_epi32(tmp,_mm_shuffle_epi32(tmp, 1)));
  #else
    // after some experiments, it is seems this is the fastest way to implement it
    // for GCC (eg., it does not like using std::min after the pstore !!)
    EIGEN_ALIGN16 int aux[4];
    pstore(aux, a);
    int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
    int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
    return aux0<aux2 ? aux0 : aux2;
  #endif // EIGEN_VECTORIZE_SSE4_1
  }
  
  // max
  template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
  {
    Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));
    return pfirst<Packet4f>(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
  }
  template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
  {
    return pfirst<Packet2d>(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));
  }
  template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    Packet4i tmp = _mm_max_epi32(a, _mm_shuffle_epi32(a, _MM_SHUFFLE(0,0,3,2)));
    return pfirst<Packet4i>(_mm_max_epi32(tmp,_mm_shuffle_epi32(tmp, 1)));
  #else
    // after some experiments, it is seems this is the fastest way to implement it
    // for GCC (eg., it does not like using std::min after the pstore !!)
    EIGEN_ALIGN16 int aux[4];
    pstore(aux, a);
    int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
    int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
    return aux0>aux2 ? aux0 : aux2;
  #endif // EIGEN_VECTORIZE_SSE4_1
  }
  
  #if EIGEN_COMP_GNUC
  // template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f&  a, const Packet4f&  b, const Packet4f&  c)
  // {
  //   Packet4f res = b;
  //   asm("mulps %[a], %[b] \n\taddps %[c], %[b]" : [b] "+x" (res) : [a] "x" (a), [c] "x" (c));
  //   return res;
  // }
  // EIGEN_STRONG_INLINE Packet4i _mm_alignr_epi8(const Packet4i&  a, const Packet4i&  b, const int i)
  // {
  //   Packet4i res = a;
  //   asm("palignr %[i], %[a], %[b] " : [b] "+x" (res) : [a] "x" (a), [i] "i" (i));
  //   return res;
  // }
  #endif
  
  #ifdef EIGEN_VECTORIZE_SSSE3
  // SSSE3 versions
  template<int Offset>
  struct palign_impl<Offset,Packet4f>
  {
    static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
    {
      if (Offset!=0)
        first = _mm_castsi128_ps(_mm_alignr_epi8(_mm_castps_si128(second), _mm_castps_si128(first), Offset*4));
    }
  };
  
  template<int Offset>
  struct palign_impl<Offset,Packet4i>
  {
    static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
    {
      if (Offset!=0)
        first = _mm_alignr_epi8(second,first, Offset*4);
    }
  };
  
  template<int Offset>
  struct palign_impl<Offset,Packet2d>
  {
    static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
    {
      if (Offset==1)
        first = _mm_castsi128_pd(_mm_alignr_epi8(_mm_castpd_si128(second), _mm_castpd_si128(first), 8));
    }
  };
  #else
  // SSE2 versions
  template<int Offset>
  struct palign_impl<Offset,Packet4f>
  {
    static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
    {
      if (Offset==1)
      {
        first = _mm_move_ss(first,second);
        first = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(first),0x39));
      }
      else if (Offset==2)
      {
        first = _mm_movehl_ps(first,first);
        first = _mm_movelh_ps(first,second);
      }
      else if (Offset==3)
      {
        first = _mm_move_ss(first,second);
        first = _mm_shuffle_ps(first,second,0x93);
      }
    }
  };
  
  template<int Offset>
  struct palign_impl<Offset,Packet4i>
  {
    static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
    {
      if (Offset==1)
      {
        first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
        first = _mm_shuffle_epi32(first,0x39);
      }
      else if (Offset==2)
      {
        first = _mm_castps_si128(_mm_movehl_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(first)));
        first = _mm_castps_si128(_mm_movelh_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
      }
      else if (Offset==3)
      {
        first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
        first = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second),0x93));
      }
    }
  };
  
  template<int Offset>
  struct palign_impl<Offset,Packet2d>
  {
    static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
    {
      if (Offset==1)
      {
        first = _mm_castps_pd(_mm_movehl_ps(_mm_castpd_ps(first),_mm_castpd_ps(first)));
        first = _mm_castps_pd(_mm_movelh_ps(_mm_castpd_ps(first),_mm_castpd_ps(second)));
      }
    }
  };
  #endif
  
  EIGEN_DEVICE_FUNC inline void
  ptranspose(PacketBlock<Packet4f,4>& kernel) {
    _MM_TRANSPOSE4_PS(kernel.packet[0], kernel.packet[1], kernel.packet[2], kernel.packet[3]);
  }
  
  EIGEN_DEVICE_FUNC inline void
  ptranspose(PacketBlock<Packet2d,2>& kernel) {
    __m128d tmp = _mm_unpackhi_pd(kernel.packet[0], kernel.packet[1]);
    kernel.packet[0] = _mm_unpacklo_pd(kernel.packet[0], kernel.packet[1]);
    kernel.packet[1] = tmp;
  }
  
  EIGEN_DEVICE_FUNC inline void
  ptranspose(PacketBlock<Packet4i,4>& kernel) {
    __m128i T0 = _mm_unpacklo_epi32(kernel.packet[0], kernel.packet[1]);
    __m128i T1 = _mm_unpacklo_epi32(kernel.packet[2], kernel.packet[3]);
    __m128i T2 = _mm_unpackhi_epi32(kernel.packet[0], kernel.packet[1]);
    __m128i T3 = _mm_unpackhi_epi32(kernel.packet[2], kernel.packet[3]);
  
    kernel.packet[0] = _mm_unpacklo_epi64(T0, T1);
    kernel.packet[1] = _mm_unpackhi_epi64(T0, T1);
    kernel.packet[2] = _mm_unpacklo_epi64(T2, T3);
    kernel.packet[3] = _mm_unpackhi_epi64(T2, T3);
  }
  
  template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
    const __m128i zero = _mm_setzero_si128();
    const __m128i select = _mm_set_epi32(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
    __m128i false_mask = _mm_cmpeq_epi32(select, zero);
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blendv_epi8(thenPacket, elsePacket, false_mask);
  #else
    return _mm_or_si128(_mm_andnot_si128(false_mask, thenPacket), _mm_and_si128(false_mask, elsePacket));
  #endif
  }
  template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
    const __m128 zero = _mm_setzero_ps();
    const __m128 select = _mm_set_ps(ifPacket.select[3], ifPacket.select[2], ifPacket.select[1], ifPacket.select[0]);
    __m128 false_mask = _mm_cmpeq_ps(select, zero);
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blendv_ps(thenPacket, elsePacket, false_mask);
  #else
    return _mm_or_ps(_mm_andnot_ps(false_mask, thenPacket), _mm_and_ps(false_mask, elsePacket));
  #endif
  }
  template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
    const __m128d zero = _mm_setzero_pd();
    const __m128d select = _mm_set_pd(ifPacket.select[1], ifPacket.select[0]);
    __m128d false_mask = _mm_cmpeq_pd(select, zero);
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blendv_pd(thenPacket, elsePacket, false_mask);
  #else
    return _mm_or_pd(_mm_andnot_pd(false_mask, thenPacket), _mm_and_pd(false_mask, elsePacket));
  #endif
  }
  
  template<> EIGEN_STRONG_INLINE Packet4f pinsertfirst(const Packet4f& a, float b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blend_ps(a,pset1<Packet4f>(b),1);
  #else
    return _mm_move_ss(a, _mm_load_ss(&b));
  #endif
  }
  
  template<> EIGEN_STRONG_INLINE Packet2d pinsertfirst(const Packet2d& a, double b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blend_pd(a,pset1<Packet2d>(b),1);
  #else
    return _mm_move_sd(a, _mm_load_sd(&b));
  #endif
  }
  
  template<> EIGEN_STRONG_INLINE Packet4f pinsertlast(const Packet4f& a, float b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blend_ps(a,pset1<Packet4f>(b),(1<<3));
  #else
    const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x0,0x0,0x0,0xFFFFFFFF));
    return _mm_or_ps(_mm_andnot_ps(mask, a), _mm_and_ps(mask, pset1<Packet4f>(b)));
  #endif
  }
  
  template<> EIGEN_STRONG_INLINE Packet2d pinsertlast(const Packet2d& a, double b)
  {
  #ifdef EIGEN_VECTORIZE_SSE4_1
    return _mm_blend_pd(a,pset1<Packet2d>(b),(1<<1));
  #else
    const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x0,0xFFFFFFFF,0xFFFFFFFF));
    return _mm_or_pd(_mm_andnot_pd(mask, a), _mm_and_pd(mask, pset1<Packet2d>(b)));
  #endif
  }
  
  // Scalar path for pmadd with FMA to ensure consistency with vectorized path.
  #ifdef __FMA__
  template<> EIGEN_STRONG_INLINE float pmadd(const float& a, const float& b, const float& c) {
    return ::fmaf(a,b,c);
  }
  template<> EIGEN_STRONG_INLINE double pmadd(const double& a, const double& b, const double& c) {
    return ::fma(a,b,c);
  }
  #endif
  
  } // end namespace internal
  
  } // end namespace Eigen
  
  #if EIGEN_COMP_PGI
  // PGI++ does not define the following intrinsics in C++ mode.
  static inline __m128  _mm_castpd_ps   (__m128d x) { return reinterpret_cast<__m128&>(x);  }
  static inline __m128i _mm_castpd_si128(__m128d x) { return reinterpret_cast<__m128i&>(x); }
  static inline __m128d _mm_castps_pd   (__m128  x) { return reinterpret_cast<__m128d&>(x); }
  static inline __m128i _mm_castps_si128(__m128  x) { return reinterpret_cast<__m128i&>(x); }
  static inline __m128  _mm_castsi128_ps(__m128i x) { return reinterpret_cast<__m128&>(x);  }
  static inline __m128d _mm_castsi128_pd(__m128i x) { return reinterpret_cast<__m128d&>(x); }
  #endif
  
  #endif // EIGEN_PACKET_MATH_SSE_H
  