Added support for AVX to Eigen.

10 files changed, 928 insertions, 33 deletions

diff --git a/Eigen/src/Core/DenseStorage.h b/Eigen/src/Core/DenseStorage.h
index b9dd75ade..2342b08a1 100644
--- a/Eigen/src/Core/DenseStorage.h
+++ b/Eigen/src/Core/DenseStorage.h
@@ -83,7 +83,7 @@ struct plain_array
 template <typename T, int Size, int MatrixOrArrayOptions>
 struct plain_array<T, Size, MatrixOrArrayOptions, 16>
 {
-  EIGEN_USER_ALIGN16 T array[Size];
+  EIGEN_USER_ALIGN32 T array[Size];
 
   EIGEN_DEVICE_FUNC
   plain_array() 
@@ -102,7 +102,7 @@ struct plain_array<T, Size, MatrixOrArrayOptions, 16>
 template <typename T, int MatrixOrArrayOptions, int Alignment>
 struct plain_array<T, 0, MatrixOrArrayOptions, Alignment>
 {
-  EIGEN_USER_ALIGN16 T array[1];
+  EIGEN_USER_ALIGN32 T array[1];
   EIGEN_DEVICE_FUNC plain_array() {}
   EIGEN_DEVICE_FUNC plain_array(constructor_without_unaligned_array_assert) {}
 };
diff --git a/Eigen/src/Core/Redux.h b/Eigen/src/Core/Redux.h
index b2c775d90..5b82c9a65 100644
--- a/Eigen/src/Core/Redux.h
+++ b/Eigen/src/Core/Redux.h
@@ -303,10 +303,15 @@ struct redux_impl<Func, Derived, LinearVectorizedTraversal, CompleteUnrolling>
   static EIGEN_STRONG_INLINE Scalar run(const Derived& mat, const Func& func)
   {
     eigen_assert(mat.rows()>0 && mat.cols()>0 && "you are using an empty matrix");
-    Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
-    if (VectorizedSize != Size)
-      res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
-    return res;
+    if (VectorizedSize > 0) {
+      Scalar res = func.predux(redux_vec_unroller<Func, Derived, 0, Size / PacketSize>::run(mat,func));
+      if (VectorizedSize != Size)
+        res = func(res,redux_novec_unroller<Func, Derived, VectorizedSize, Size-VectorizedSize>::run(mat,func));
+      return res;
+    }
+    else {
+      return redux_novec_unroller<Func, Derived, 0, Size>::run(mat,func);
+    }
   }
 };
 
diff --git a/Eigen/src/Core/arch/AVX/CMakeLists.txt b/Eigen/src/Core/arch/AVX/CMakeLists.txt
new file mode 100644
index 000000000..bdb71ab99
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/CMakeLists.txt
@@ -0,0 +1,6 @@
+FILE(GLOB Eigen_Core_arch_AVX_SRCS "*.h")
+
+INSTALL(FILES
+  ${Eigen_Core_arch_AVX_SRCS}
+  DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/Core/arch/AVX COMPONENT Devel
+)
diff --git a/Eigen/src/Core/arch/AVX/Complex.h b/Eigen/src/Core/arch/AVX/Complex.h
new file mode 100644
index 000000000..9fb44ecab
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/Complex.h
@@ -0,0 +1,443 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner (benoit.steiner.goog@gmail.com)
+//
+// 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_AVX_H
+#define EIGEN_COMPLEX_AVX_H
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- float ----------
+struct Packet4cf
+{
+  EIGEN_STRONG_INLINE Packet4cf() {}
+  EIGEN_STRONG_INLINE explicit Packet4cf(const __m256& a) : v(a) {}
+  __m256  v;
+};
+
+template<> struct packet_traits<std::complex<float> >  : default_packet_traits
+{
+  typedef Packet4cf type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size = 4,
+
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasDiv    = 1,
+    HasNegate = 1,
+    HasAbs    = 0,
+    HasAbs2   = 0,
+    HasMin    = 0,
+    HasMax    = 0,
+    HasSetLinear = 0
+  };
+};
+
+template<> struct unpacket_traits<Packet4cf> { typedef std::complex<float> type; enum {size=4}; };
+
+template<> EIGEN_STRONG_INLINE Packet4cf padd<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_add_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf psub<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_sub_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf pnegate(const Packet4cf& a)
+{
+  return Packet4cf(pnegate(a.v));
+}
+template<> EIGEN_STRONG_INLINE Packet4cf pconj(const Packet4cf& a)
+{
+  const __m256 mask = _mm256_castsi256_ps(_mm256_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000,0x00000000,0x80000000));
+  return Packet4cf(_mm256_xor_ps(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf pmul<Packet4cf>(const Packet4cf& a, const Packet4cf& b)
+{
+  __m256 tmp1 = _mm256_mul_ps(_mm256_moveldup_ps(a.v), b.v);
+  __m256 tmp2 = _mm256_mul_ps(_mm256_movehdup_ps(a.v), _mm256_permute_ps(b.v, _MM_SHUFFLE(2,3,0,1)));
+  __m256 result = _mm256_addsub_ps(tmp1, tmp2);
+  return Packet4cf(result);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf pand   <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_and_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf por    <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_or_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf pxor   <Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_xor_ps(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet4cf pandnot<Packet4cf>(const Packet4cf& a, const Packet4cf& b) { return Packet4cf(_mm256_andnot_ps(a.v,b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet4cf pload <Packet4cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet4cf(pload<Packet8f>(&numext::real_ref(*from))); }
+template<> EIGEN_STRONG_INLINE Packet4cf ploadu<Packet4cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet4cf(ploadu<Packet8f>(&numext::real_ref(*from))); }
+
+
+template<> EIGEN_STRONG_INLINE Packet4cf pset1<Packet4cf>(const std::complex<float>& from)
+{
+  __m256 result;
+  for (int i = 0; i < 8; i+=2) {
+    result[i] = std::real(from);
+    result[i+1] = std::imag(from);
+  }
+  return Packet4cf(result);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf ploaddup<Packet4cf>(const std::complex<float>* from)
+{
+  __m256 result;
+  for (int i = 0; i < 2; ++i) {
+    result[4*i] = std::real(from[i]);
+    result[4*i+1] = std::imag(from[i]);
+    result[4*i+2] = std::real(from[i]);
+    result[4*i+3] = std::imag(from[i]);
+  }
+  return Packet4cf(result);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float>* to, const Packet4cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&numext::real_ref(*to), from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float>* to, const Packet4cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&numext::real_ref(*to), from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float>* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+
+
+template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet4cf>(const Packet4cf& a)
+{
+  return std::complex<float>(a.v[0], a.v[1]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf preverse(const Packet4cf& a) {
+  __m256 result;
+  result[0] = a.v[6];
+  result[1] = a.v[7];
+  result[2] = a.v[4];
+  result[3] = a.v[5];
+  result[4] = a.v[2];
+  result[5] = a.v[3];
+  result[6] = a.v[0];
+  result[7] = a.v[1];
+  return Packet4cf(result);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet4cf>(const Packet4cf& a)
+{
+  return std::complex<float>(a.v[0]+a.v[2]+a.v[4]+a.v[6], a.v[1]+a.v[3]+a.v[5]+a.v[7]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf preduxp<Packet4cf>(const Packet4cf* vecs)
+{
+  __m256 result = _mm256_setzero_ps();
+  for (int i = 0; i < 4; ++i) {
+    for (int j = 0; j < 8; j+=2) {
+      result[2*i] += vecs[i].v[j];
+      result[2*i+1] += vecs[i].v[j+1];
+    }
+  }
+  return Packet4cf(result);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet4cf>(const Packet4cf& a)
+{
+  std::complex<float> result(a.v[0], a.v[1]);
+  for (int i = 2; i < 8; i+=2) {
+    result *= std::complex<float>(a.v[i], a.v[i+1]);
+  }
+  return result;
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet4cf>
+{
+  static EIGEN_STRONG_INLINE void run(Packet4cf& first, const Packet4cf& second)
+  {
+    if (Offset==0) return;
+    for (int i = 0; i < 4-Offset; ++i)
+    {
+      first.v[2*i] = first.v[2*(i+Offset)];
+      first.v[2*i+1] = first.v[2*(i+Offset)+1];
+    }
+    for (int i = 4-Offset; i < 4; ++i)
+    {
+      first.v[2*i] = second.v[2*(i-4+Offset)];
+      first.v[2*i+1] = second.v[2*(i-4+Offset)+1];
+    }
+  }
+};
+
+template<> struct conj_helper<Packet4cf, Packet4cf, false,true>
+{
+  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet4cf& y, const Packet4cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& a, const Packet4cf& b) const
+  {
+    return internal::pmul(a, pconj(b));
+  }
+};
+
+template<> struct conj_helper<Packet4cf, Packet4cf, true,false>
+{
+  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet4cf& y, const Packet4cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& a, const Packet4cf& b) const
+  {
+    return internal::pmul(pconj(a), b);
+  }
+};
+
+template<> struct conj_helper<Packet4cf, Packet4cf, true,true>
+{
+  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet4cf& y, const Packet4cf& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& a, const Packet4cf& b) const
+  {
+    return pconj(internal::pmul(a, b));
+  }
+};
+
+template<> struct conj_helper<Packet8f, Packet4cf, false,false>
+{
+  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet8f& x, const Packet4cf& y, const Packet4cf& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet8f& x, const Packet4cf& y) const
+  { return Packet4cf(Eigen::internal::pmul(x, y.v)); }
+};
+
+template<> struct conj_helper<Packet4cf, Packet8f, false,false>
+{
+  EIGEN_STRONG_INLINE Packet4cf pmadd(const Packet4cf& x, const Packet8f& y, const Packet4cf& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet4cf pmul(const Packet4cf& x, const Packet8f& y) const
+  { return Packet4cf(Eigen::internal::pmul(x.v, y)); }
+};
+
+template<> EIGEN_STRONG_INLINE Packet4cf pdiv<Packet4cf>(const Packet4cf& a, const Packet4cf& b)
+{
+  Packet4cf res;
+  for (int i = 0; i < 8; i+=2) {
+    std::complex<float> result = std::complex<float>(a.v[i], a.v[i+1]) / std::complex<float>(b.v[i], b.v[i+1]);
+    res.v[i] = std::real(result);
+    res.v[i+1] = std::imag(result);
+  }
+  return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet4cf pcplxflip<Packet4cf>(const Packet4cf& x)
+{
+  Packet4cf res;
+  for (int i = 0; i < 8; i+=2) {
+    res.v[i] = x.v[i+1];
+    res.v[i+1] = x.v[i];
+  }
+  return res;
+}
+
+//---------- double ----------
+struct Packet2cd
+{
+  EIGEN_STRONG_INLINE Packet2cd() {}
+  EIGEN_STRONG_INLINE explicit Packet2cd(const __m256d& a) : v(a) {}
+  __m256d  v;
+};
+
+template<> struct packet_traits<std::complex<double> >  : default_packet_traits
+{
+  typedef Packet2cd type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 0,
+    size = 2,
+
+    HasAdd    = 1,
+    HasSub    = 1,
+    HasMul    = 1,
+    HasDiv    = 1,
+    HasNegate = 1,
+    HasAbs    = 0,
+    HasAbs2   = 0,
+    HasMin    = 0,
+    HasMax    = 0,
+    HasSetLinear = 0
+  };
+};
+
+template<> struct unpacket_traits<Packet2cd> { typedef std::complex<double> type; enum {size=2}; };
+
+template<> EIGEN_STRONG_INLINE Packet2cd padd<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_add_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd psub<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_sub_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pnegate(const Packet2cd& a) { return Packet2cd(pnegate(a.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pconj(const Packet2cd& a)
+{
+  const __m256d mask = _mm256_castsi256_pd(_mm256_set_epi32(0x80000000,0x0,0x0,0x0,0x80000000,0x0,0x0,0x0));
+  return Packet2cd(_mm256_xor_pd(a.v,mask));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd pmul<Packet2cd>(const Packet2cd& a, const Packet2cd& b)
+{
+  __m256d tmp1 = _mm256_mul_pd(_mm256_permute_pd(a.v, 0), b.v);
+  // FIXME: _mm256_permute_pd(b.v, _MM_SHUFFLE2(1,0) won't work as expected, figure out an alternative.
+  __m256d op = {b.v[1], b.v[0], b.v[3], b.v[2]};
+  __m256d tmp2 = _mm256_mul_pd(_mm256_permute_pd(a.v, 15), op);
+  __m256d result = _mm256_addsub_pd(tmp1, tmp2);
+
+  return Packet2cd(result);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd pand   <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_and_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd por    <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_or_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pxor   <Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_xor_pd(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cd pandnot<Packet2cd>(const Packet2cd& a, const Packet2cd& b) { return Packet2cd(_mm256_andnot_pd(a.v,b.v)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cd pload <Packet2cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_ALIGNED_LOAD return Packet2cd(pload<Packet4d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet2cd ploadu<Packet2cd>(const std::complex<double>* from)
+{ EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cd(ploadu<Packet4d>((const double*)from)); }
+
+template<> EIGEN_STRONG_INLINE Packet2cd pset1<Packet2cd>(const std::complex<double>&  from)
+{
+  __m256d result;
+  for (int i = 0; i < 4; i+=2) {
+    result[i] = std::real(from);
+    result[i+1] = std::imag(from);
+  }
+  return Packet2cd(result);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd ploaddup<Packet2cd>(const std::complex<double>* from) { return pset1<Packet2cd>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet2cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet2cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+
+template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet2cd>(const Packet2cd& a)
+{
+  return std::complex<double>(a.v[0],a.v[1]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd preverse(const Packet2cd& a) {
+  __m256d result;
+  result[0] = a.v[2];
+  result[1] = a.v[3];
+  result[2] = a.v[0];
+  result[3] = a.v[1];
+  return Packet2cd(result);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet2cd>(const Packet2cd& a)
+{
+  return std::complex<double>(a.v[0]+a.v[2], a.v[1]+a.v[3]);
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd preduxp<Packet2cd>(const Packet2cd* vecs)
+{
+  __m256d result = _mm256_setzero_pd();
+  for (int i = 0; i < 2; ++i) {
+    for (int j = 0; j < 4; j+=2) {
+      result[2*i] += vecs[i].v[j];
+      result[2*i+1] += vecs[i].v[j+1];
+    }
+  }
+  return Packet2cd(result);
+}
+
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet2cd>(const Packet2cd& a)
+{
+  return std::complex<double>(a.v[0], a.v[1]) * std::complex<double>(a.v[2], a.v[3]);
+}
+
+template<int Offset>
+struct palign_impl<Offset,Packet2cd>
+{
+  static EIGEN_STRONG_INLINE void run(Packet2cd& first, const Packet2cd& second)
+  {
+    if (Offset==0) return;
+    first.v[0] = first.v[2];
+    first.v[1] = first.v[3];
+    first.v[2] = second.v[0];
+    first.v[3] = second.v[1];
+  }
+};
+
+template<> struct conj_helper<Packet2cd, Packet2cd, false,true>
+{
+  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet2cd& y, const Packet2cd& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& a, const Packet2cd& b) const
+  {
+    return internal::pmul(a, pconj(b));
+  }
+};
+
+template<> struct conj_helper<Packet2cd, Packet2cd, true,false>
+{
+  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet2cd& y, const Packet2cd& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& a, const Packet2cd& b) const
+  {
+    return internal::pmul(pconj(a), b);
+  }
+};
+
+template<> struct conj_helper<Packet2cd, Packet2cd, true,true>
+{
+  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet2cd& y, const Packet2cd& c) const
+  { return padd(pmul(x,y),c); }
+
+  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& a, const Packet2cd& b) const
+  {
+    return pconj(internal::pmul(a, b));
+  }
+};
+
+template<> struct conj_helper<Packet4d, Packet2cd, false,false>
+{
+  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet4d& x, const Packet2cd& y, const Packet2cd& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet4d& x, const Packet2cd& y) const
+  { return Packet2cd(Eigen::internal::pmul(x, y.v)); }
+};
+
+template<> struct conj_helper<Packet2cd, Packet4d, false,false>
+{
+  EIGEN_STRONG_INLINE Packet2cd pmadd(const Packet2cd& x, const Packet4d& y, const Packet2cd& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet2cd pmul(const Packet2cd& x, const Packet4d& y) const
+  { return Packet2cd(Eigen::internal::pmul(x.v, y)); }
+};
+
+template<> EIGEN_STRONG_INLINE Packet2cd pdiv<Packet2cd>(const Packet2cd& a, const Packet2cd& b)
+{
+  Packet2cd res;
+  for (int i = 0; i < 4; i+=2) {
+    std::complex<double> result = std::complex<double>(a.v[i], a.v[i+1]) / std::complex<double>(b.v[i], b.v[i+1]);
+    res.v[i] = std::real(result);
+    res.v[i+1] = std::imag(result);
+  }
+  return res;
+}
+
+template<> EIGEN_STRONG_INLINE Packet2cd pcplxflip<Packet2cd>(const Packet2cd& x)
+{
+  Packet2cd res;
+  for (int i = 0; i < 4; i+=2) {
+    res.v[i] = x.v[i+1];
+    res.v[i+1] = x.v[i];
+  }
+  return res;
+}
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_COMPLEX_AVX_H
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
new file mode 100644
index 000000000..244e63e74
--- /dev/null
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -0,0 +1,423 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner (benoit.steiner.goog@gmail.com)
+//
+// 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_AVX_H
+#define EIGEN_PACKET_MATH_AVX_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
+
+typedef __m256  Packet8f;
+typedef __m256i Packet8i;
+typedef __m256d Packet4d;
+
+template<> struct is_arithmetic<__m256>  { enum { value = true }; };
+template<> struct is_arithmetic<__m256i> { enum { value = true }; };
+template<> struct is_arithmetic<__m256d> { enum { value = true }; };
+
+#define _EIGEN_DECLARE_CONST_Packet8f(NAME,X) \
+  const Packet8f p8f_##NAME = pset1<Packet8f>(X)
+
+#define _EIGEN_DECLARE_CONST_Packet4d(NAME,X) \
+  const Packet4d p4d_##NAME = pset1<Packet4d>(X)
+
+
+template<> struct packet_traits<float>  : default_packet_traits
+{
+  typedef Packet8f type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=8,
+
+    HasDiv  = 1,
+    HasSin  = 0,
+    HasCos  = 0,
+    HasLog  = 0,
+    HasExp  = 0,
+    HasSqrt = 0
+  };
+ };
+template<> struct packet_traits<double> : default_packet_traits
+{
+  typedef Packet4d type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=4,
+
+    HasDiv  = 1,
+    HasExp  = 0
+  };
+};
+
+/* Proper support for integers is only provided by AVX2. In the meantime, we'll
+   use SSE instructions and packets to deal with integers.
+template<> struct packet_traits<int>    : default_packet_traits
+{
+  typedef Packet8i type;
+  enum {
+    Vectorizable = 1,
+    AlignedOnScalar = 1,
+    size=8
+  };
+};
+*/
+
+template<> struct unpacket_traits<Packet8f> { typedef float  type; enum {size=8}; };
+template<> struct unpacket_traits<Packet4d> { typedef double type; enum {size=4}; };
+template<> struct unpacket_traits<Packet8i> { typedef int    type; enum {size=8}; };
+
+template<> EIGEN_STRONG_INLINE Packet8f pset1<Packet8f>(const float&  from) { return _mm256_set1_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet4d pset1<Packet4d>(const double& from) { return _mm256_set1_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet8i pset1<Packet8i>(const int&    from) { return _mm256_set1_epi32(from); }
+
+template<> EIGEN_STRONG_INLINE Packet8f plset<float>(const float& a) { return _mm256_add_ps(_mm256_set1_ps(a), _mm256_set_ps(7.0,6.0,5.0,4.0,3.0,2.0,1.0,0.0)); }
+template<> EIGEN_STRONG_INLINE Packet4d plset<double>(const double& a) { return _mm256_add_pd(_mm256_set1_pd(a), _mm256_set_pd(3.0,2.0,1.0,0.0)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f padd<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_add_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d padd<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_add_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f psub<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_sub_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d psub<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_sub_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pnegate(const Packet8f& a)
+{
+  return _mm256_sub_ps(_mm256_set1_ps(0.0),a);
+}
+template<> EIGEN_STRONG_INLINE Packet4d pnegate(const Packet4d& a)
+{
+  return _mm256_sub_pd(_mm256_set1_pd(0.0),a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pconj(const Packet8f& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet4d pconj(const Packet4d& a) { return a; }
+template<> EIGEN_STRONG_INLINE Packet8i pconj(const Packet8i& a) { return a; }
+
+template<> EIGEN_STRONG_INLINE Packet8f pmul<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_mul_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pmul<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_mul_pd(a,b); }
+
+
+template<> EIGEN_STRONG_INLINE Packet8f pdiv<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_div_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pdiv<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_div_pd(a,b); }
+template<> EIGEN_STRONG_INLINE Packet8i pdiv<Packet8i>(const Packet8i& /*a*/, const Packet8i& /*b*/)
+{ eigen_assert(false && "packet integer division are not supported by AVX");
+  return pset1<Packet8i>(0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet8f pmin<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_min_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pmin<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_min_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pmax<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_max_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pmax<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_max_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pand<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_and_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pand<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_and_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f por<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_or_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d por<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_or_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pxor<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_xor_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pxor<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_xor_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pandnot<Packet8f>(const Packet8f& a, const Packet8f& b) { return _mm256_andnot_ps(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4d pandnot<Packet4d>(const Packet4d& a, const Packet4d& b) { return _mm256_andnot_pd(a,b); }
+
+template<> EIGEN_STRONG_INLINE Packet8f pload<Packet8f>(const float*   from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet4d pload<Packet4d>(const double*  from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet8i pload<Packet8i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm256_load_si256(reinterpret_cast<const __m256i*>(from)); }
+
+template<> EIGEN_STRONG_INLINE Packet8f ploadu<Packet8f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_ps(from); }
+template<> EIGEN_STRONG_INLINE Packet4d ploadu<Packet4d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_pd(from); }
+template<> EIGEN_STRONG_INLINE Packet8i ploadu<Packet8i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from)); }
+
+// Loads 4 floats from memory a returns the packet {a0, a0  a1, a1, a2, a2, a3, a3}
+template<> EIGEN_STRONG_INLINE Packet8f ploaddup<Packet8f>(const float* from)
+{
+  Packet8f tmp  = ploadu<Packet8f>(from);
+  Packet8f tmp1 = _mm256_permute_ps(tmp, _MM_SHUFFLE(3,3,2,2));
+  Packet8f tmp2 = _mm256_permute_ps(tmp, _MM_SHUFFLE(1,1,0,0));
+  return _mm256_blend_ps(_mm256_permute2f128_ps(tmp1,tmp1,1),tmp2,15);
+}
+// Loads 2 doubles from memory a returns the packet {a0, a0  a1, a1}
+template<> EIGEN_STRONG_INLINE Packet4d ploaddup<Packet4d>(const double* from)
+{
+  Packet4d tmp = ploadu<Packet4d>(from);
+  Packet4d tmp1  = _mm256_permute_pd(tmp,0);
+  Packet4d tmp2  = _mm256_permute_pd(tmp,3);
+  return _mm256_blend_pd(tmp1,_mm256_permute2f128_pd(tmp2,tmp2,1),12);
+}
+
+template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet8f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet4d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_store_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet8i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet8f& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_ps(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet4d& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_pd(to, from); }
+template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet8i& from) { EIGEN_DEBUG_UNALIGNED_STORE _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from); }
+
+template<> EIGEN_STRONG_INLINE void pstore1<Packet8f>(float* to, const float& a)
+{
+  Packet8f pa = pset1<Packet8f>(a);
+  pstore(to, pa);
+}
+template<> EIGEN_STRONG_INLINE void pstore1<Packet4d>(double* to, const double& a)
+{
+  Packet4d pa = pset1<Packet4d>(a);
+  pstore(to, pa);
+}
+template<> EIGEN_STRONG_INLINE void pstore1<Packet8i>(int* to, const int& a)
+{
+  Packet8i pa = pset1<Packet8i>(a);
+  pstore(to, pa);
+}
+
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+
+template<> EIGEN_STRONG_INLINE float  pfirst<Packet8f>(const Packet8f& a) {
+  return _mm_cvtss_f32(_mm256_castps256_ps128(a));
+}
+template<> EIGEN_STRONG_INLINE double pfirst<Packet4d>(const Packet4d& a) {
+  return _mm_cvtsd_f64(_mm256_castpd256_pd128(a));
+}
+template<> EIGEN_STRONG_INLINE int    pfirst<Packet8i>(const Packet8i& a) {
+  return _mm_cvtsi128_si32(_mm256_castsi256_si128(a));
+}
+
+
+template<> EIGEN_STRONG_INLINE Packet8f preverse(const Packet8f& a)
+{
+  __m256 tmp = _mm256_shuffle_ps(a,a,0x1b);
+  return _mm256_permute2f128_ps(tmp, tmp, 1);
+}
+template<> EIGEN_STRONG_INLINE Packet4d preverse(const Packet4d& a)
+{
+   __m256d tmp = _mm256_shuffle_pd(a,a,5);
+  return _mm256_permute2f128_pd(tmp, tmp, 1);
+
+  __m256d swap_halves = _mm256_permute2f128_pd(a,a,1);
+    return _mm256_permute_pd(swap_halves,5);
+}
+
+// pabs should be ok
+template<> EIGEN_STRONG_INLINE Packet8f pabs(const Packet8f& a)
+{
+  const Packet8f mask = _mm256_castsi256_ps(_mm256_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
+  return _mm256_and_ps(a,mask);
+}
+template<> EIGEN_STRONG_INLINE Packet4d pabs(const Packet4d& a)
+{
+  const Packet4d mask = _mm256_castsi256_pd(_mm256_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
+  return _mm256_and_pd(a,mask);
+}
+
+// preduxp should be ok
+// FIXME: why is this ok? why isn't the simply implementation working as expected?
+template<> EIGEN_STRONG_INLINE Packet8f preduxp<Packet8f>(const Packet8f* vecs)
+{
+    __m256 hsum1 = _mm256_hadd_ps(vecs[0], vecs[1]);
+    __m256 hsum2 = _mm256_hadd_ps(vecs[2], vecs[3]);
+    __m256 hsum3 = _mm256_hadd_ps(vecs[4], vecs[5]);
+    __m256 hsum4 = _mm256_hadd_ps(vecs[6], vecs[7]);
+
+    __m256 hsum5 = _mm256_hadd_ps(hsum1, hsum1);
+    __m256 hsum6 = _mm256_hadd_ps(hsum2, hsum2);
+    __m256 hsum7 = _mm256_hadd_ps(hsum3, hsum3);
+    __m256 hsum8 = _mm256_hadd_ps(hsum4, hsum4);
+
+    __m256 perm1 =  _mm256_permute2f128_ps(hsum5, hsum5, 0x23);
+    __m256 perm2 =  _mm256_permute2f128_ps(hsum6, hsum6, 0x23);
+    __m256 perm3 =  _mm256_permute2f128_ps(hsum7, hsum7, 0x23);
+    __m256 perm4 =  _mm256_permute2f128_ps(hsum8, hsum8, 0x23);
+
+    __m256 sum1 = _mm256_add_ps(perm1, hsum5);
+    __m256 sum2 = _mm256_add_ps(perm2, hsum6);
+    __m256 sum3 = _mm256_add_ps(perm3, hsum7);
+    __m256 sum4 = _mm256_add_ps(perm4, hsum8);
+
+    __m256 blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
+    __m256 blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
+
+    __m256 final = _mm256_blend_ps(blend1, blend2, 0xf0);
+    return final;
+}
+template<> EIGEN_STRONG_INLINE Packet4d preduxp<Packet4d>(const Packet4d* vecs)
+{
+ Packet4d tmp0, tmp1;
+
+  tmp0 = _mm256_hadd_pd(vecs[0], vecs[1]);
+  tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));
+
+  tmp1 = _mm256_hadd_pd(vecs[2], vecs[3]);
+  tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
+
+  return _mm256_blend_pd(tmp0, tmp1, 0xC);
+}
+
+template<> EIGEN_STRONG_INLINE float predux<Packet8f>(const Packet8f& a)
+{
+  Packet8f tmp0 = _mm256_hadd_ps(a,_mm256_permute2f128_ps(a,a,1));
+  tmp0 = _mm256_hadd_ps(tmp0,tmp0);
+  return pfirst(_mm256_hadd_ps(tmp0, tmp0));
+}
+template<> EIGEN_STRONG_INLINE double predux<Packet4d>(const Packet4d& a)
+{
+  Packet4d tmp0 = _mm256_hadd_pd(a,_mm256_permute2f128_pd(a,a,1));
+  return pfirst(_mm256_hadd_pd(tmp0,tmp0));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_mul<Packet8f>(const Packet8f& a)
+{
+  Packet8f tmp;
+  tmp = _mm256_mul_ps(a, _mm256_permute2f128_ps(a,a,1));
+  tmp = _mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp,tmp,_MM_SHUFFLE(1,0,3,2)));
+  return pfirst(_mm256_mul_ps(tmp, _mm256_shuffle_ps(tmp,tmp,1)));
+}
+template<> EIGEN_STRONG_INLINE double predux_mul<Packet4d>(const Packet4d& a)
+{
+  Packet4d tmp;
+  tmp = _mm256_mul_pd(a, _mm256_permute2f128_pd(a,a,1));
+  return pfirst(_mm256_mul_pd(tmp, _mm256_shuffle_pd(tmp,tmp,1)));
+}
+
+template<> EIGEN_STRONG_INLINE float predux_min<Packet8f>(const Packet8f& a)
+{
+  float result = a[0];
+  for (int i = 1; i < 8; ++i) {
+    if (a[i] < result) result = a[i];
+  }
+  return result;
+}
+template<> EIGEN_STRONG_INLINE double predux_min<Packet4d>(const Packet4d& a)
+{
+  double result = a[0];
+  for (int i = 1; i < 4; ++i) {
+    if (a[i] < result) result = a[i];
+  }
+  return result;
+}
+
+template<> EIGEN_STRONG_INLINE float predux_max<Packet8f>(const Packet8f& a)
+{
+  float result = a[0];
+  for (int i = 1; i < 8; ++i) {
+    if (a[i] > result) result = a[i];
+  }
+  return result;
+}
+
+template<> EIGEN_STRONG_INLINE double predux_max<Packet4d>(const Packet4d& a)
+{
+  double result = a[0];
+  for (int i = 1; i < 4; ++i) {
+    if (a[i] > result) result = a[i];
+  }
+  return result;
+}
+
+
+template<int Offset>
+struct palign_impl<Offset,Packet8f>
+{
+  static EIGEN_STRONG_INLINE void run(Packet8f& first, const Packet8f& second)
+  {
+    if (Offset==1)
+    {
+      first = _mm256_blend_ps(first, second, 1);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(0,3,2,1));
+      first = _mm256_blend_ps(tmp, _mm256_permute2f128_ps (tmp, tmp, 1), 0x88);
+    }
+    else if (Offset==2)
+    {
+      first = _mm256_blend_ps(first, second, 3);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(1,0,3,2));
+      first = _mm256_blend_ps(tmp, _mm256_permute2f128_ps (tmp, tmp, 1), 0xcc);
+    }
+    else if (Offset==3)
+    {
+      first = _mm256_blend_ps(first, second, 7);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(2,1,0,3));
+      first = _mm256_blend_ps(tmp, _mm256_permute2f128_ps (tmp, tmp, 1), 0xee);
+    }
+    else if (Offset==4)
+    {
+      first = _mm256_blend_ps(first, second, 15);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(3,2,1,0));
+      first = _mm256_permute_ps(_mm256_permute2f128_ps (tmp, tmp, 1), _MM_SHUFFLE(3,2,1,0));
+    }
+    else if (Offset==5)
+    {
+      first = _mm256_blend_ps(first, second, 31);
+      first = _mm256_permute2f128_ps(first, first, 1);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(0,3,2,1));
+      first = _mm256_permute2f128_ps(tmp, tmp, 1);
+      first = _mm256_blend_ps(tmp, first, 0x88);
+    }
+    else if (Offset==6)
+    {
+      first = _mm256_blend_ps(first, second, 63);
+      first = _mm256_permute2f128_ps(first, first, 1);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(1,0,3,2));
+      first = _mm256_permute2f128_ps(tmp, tmp, 1);
+      first = _mm256_blend_ps(tmp, first, 0xcc);
+    }
+    else if (Offset==7)
+    {
+      first = _mm256_blend_ps(first, second, 127);
+      first = _mm256_permute2f128_ps(first, first, 1);
+      Packet8f tmp = _mm256_permute_ps (first, _MM_SHUFFLE(2,1,0,3));
+      first = _mm256_permute2f128_ps(tmp, tmp, 1);
+      first = _mm256_blend_ps(tmp, first, 0xee);
+    }
+  }
+};
+
+template<int Offset>
+struct palign_impl<Offset,Packet4d>
+{
+  static EIGEN_STRONG_INLINE void run(Packet4d& first, const Packet4d& second)
+  {
+    if (Offset==1)
+    {
+      first = _mm256_blend_pd(first, second, 1);
+      __m256d tmp = _mm256_permute_pd(first, 5);
+      first = _mm256_permute2f128_pd(tmp, tmp, 1);
+      first = _mm256_blend_pd(tmp, first, 0xA);
+    }
+    else if (Offset==2)
+    {
+      first = _mm256_blend_pd(first, second, 3);
+      first = _mm256_permute2f128_pd(first, first, 1);
+    }
+    else if (Offset==3)
+    {
+      first = _mm256_blend_pd(first, second, 7);
+      __m256d tmp = _mm256_permute_pd(first, 5);
+      first = _mm256_permute2f128_pd(tmp, tmp, 1);
+      first = _mm256_blend_pd(tmp, first, 5);
+    }
+  }
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_PACKET_MATH_AVX_H
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index f5a3dab52..e913af650 100644
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -58,6 +58,9 @@ template<> struct is_arithmetic<__m128d> { enum { value = true }; };
   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;
@@ -87,6 +90,7 @@ template<> struct packet_traits<double> : default_packet_traits
     HasSqrt = 1
   };
 };
+#endif
 template<> struct packet_traits<int>    : default_packet_traits
 {
   typedef Packet4i type;
@@ -115,8 +119,10 @@ template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { re
 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set1_epi32(from); }
 #endif
 
+#ifndef EIGEN_VECTORIZE_AVX
 template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }
 template<> EIGEN_STRONG_INLINE Packet2d plset<double>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }
+#endif
 template<> EIGEN_STRONG_INLINE Packet4i plset<int>(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); }
@@ -331,9 +337,11 @@ template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double&
   pstore(to, vec2d_swizzle1(pa,0,0));
 }
 
+#ifndef EIGEN_VECTORIZE_AVX
 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
+#endif
 
 #if defined(_MSC_VER) && defined(_WIN64) && !defined(__INTEL_COMPILER)
 // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
diff --git a/Eigen/src/Core/products/GeneralMatrixMatrix.h b/Eigen/src/Core/products/GeneralMatrixMatrix.h
index 3f5ffcf51..eb399a824 100644
--- a/Eigen/src/Core/products/GeneralMatrixMatrix.h
+++ b/Eigen/src/Core/products/GeneralMatrixMatrix.h
@@ -286,9 +286,9 @@ class gemm_blocking_space<StorageOrder,_LhsScalar,_RhsScalar,MaxRows, MaxCols, M
       SizeW = MaxDepth * Traits::WorkSpaceFactor
     };
 
-    EIGEN_ALIGN16 LhsScalar m_staticA[SizeA];
-    EIGEN_ALIGN16 RhsScalar m_staticB[SizeB];
-    EIGEN_ALIGN16 RhsScalar m_staticW[SizeW];
+    EIGEN_ALIGN32 LhsScalar m_staticA[SizeA];
+    EIGEN_ALIGN32 RhsScalar m_staticB[SizeB];
+    EIGEN_ALIGN32 RhsScalar m_staticW[SizeW];
 
   public:
 
diff --git a/Eigen/src/Core/products/GeneralMatrixVector.h b/Eigen/src/Core/products/GeneralMatrixVector.h
index c8697c913..7f35cc53a 100644
--- a/Eigen/src/Core/products/GeneralMatrixVector.h
+++ b/Eigen/src/Core/products/GeneralMatrixVector.h
@@ -141,7 +141,8 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,ColMajor,Co
   // find how many columns do we have to skip to be aligned with the result (if possible)
   Index skipColumns = 0;
   // if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
-  if( (size_t(lhs)%sizeof(LhsScalar)) || (size_t(res)%sizeof(ResScalar)) )
+  // TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.
+  if( (size_t(lhs)%sizeof(LhsScalar)) || (size_t(res)%sizeof(ResScalar)) || LhsPacketSize > 4)
   {
     alignedSize = 0;
     alignedStart = 0;
@@ -404,7 +405,9 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,RowMajor,Co
   // find how many rows do we have to skip to be aligned with rhs (if possible)
   Index skipRows = 0;
   // if the data cannot be aligned (TODO add some compile time tests when possible, e.g. for floats)
-  if( (sizeof(LhsScalar)!=sizeof(RhsScalar)) || (size_t(lhs)%sizeof(LhsScalar)) || (size_t(rhs)%sizeof(RhsScalar)) )
+  // TODO: extend the code to support aligned loads whenever possible when LhsPacketSize > 4.
+  if( (sizeof(LhsScalar)!=sizeof(RhsScalar)) || (size_t(lhs)%sizeof(LhsScalar)) || (size_t(rhs)%sizeof(RhsScalar)) ||
+      (LhsPacketSize > 4))
   {
     alignedSize = 0;
     alignedStart = 0;
@@ -446,7 +449,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,RowMajor,Co
   Index rowBound = ((rows-skipRows)/rowsAtOnce)*rowsAtOnce + skipRows;
   for (Index i=skipRows; i<rowBound; i+=rowsAtOnce)
   {
-    EIGEN_ALIGN16 ResScalar tmp0 = ResScalar(0);
+    EIGEN_ALIGN32 ResScalar tmp0 = ResScalar(0);
     ResScalar tmp1 = ResScalar(0), tmp2 = ResScalar(0), tmp3 = ResScalar(0);
 
     // this helps the compiler generating good binary code
@@ -555,7 +558,7 @@ EIGEN_DONT_INLINE void general_matrix_vector_product<Index,LhsScalar,RowMajor,Co
   {
     for (Index i=start; i<end; ++i)
     {
-      EIGEN_ALIGN16 ResScalar tmp0 = ResScalar(0);
+      EIGEN_ALIGN32 ResScalar tmp0 = ResScalar(0);
       ResPacket ptmp0 = pset1<ResPacket>(tmp0);
       const LhsScalar* lhs0 = lhs + i*lhsStride;
       // process first unaligned result's coeffs
diff --git a/Eigen/src/Core/util/Macros.h b/Eigen/src/Core/util/Macros.h
index debc04f3f..787f800b8 100644
--- a/Eigen/src/Core/util/Macros.h
+++ b/Eigen/src/Core/util/Macros.h
@@ -72,7 +72,11 @@
   #endif
   #define EIGEN_ALIGN 0
 #else
-  #define EIGEN_ALIGN 1
+  #if !defined(EIGEN_DONT_VECTORIZE) && defined(__AVX__)
+    #define EIGEN_ALIGN 32
+  #else
+    #define EIGEN_ALIGN 16
+  #endif
 #endif
 
 // EIGEN_ALIGN_STATICALLY is the true test whether we want to align arrays on the stack or not. It takes into account both the user choice to explicitly disable
@@ -281,13 +285,16 @@
 #endif
 
 #define EIGEN_ALIGN16 EIGEN_ALIGN_TO_BOUNDARY(16)
+#define EIGEN_ALIGN32 EIGEN_ALIGN_TO_BOUNDARY(32)
 
 #if EIGEN_ALIGN_STATICALLY
 #define EIGEN_USER_ALIGN_TO_BOUNDARY(n) EIGEN_ALIGN_TO_BOUNDARY(n)
 #define EIGEN_USER_ALIGN16 EIGEN_ALIGN16
+#define EIGEN_USER_ALIGN32 EIGEN_ALIGN32
 #else
 #define EIGEN_USER_ALIGN_TO_BOUNDARY(n)
 #define EIGEN_USER_ALIGN16
+#define EIGEN_USER_ALIGN32
 #endif
 
 #ifdef EIGEN_DONT_USE_RESTRICT_KEYWORD
diff --git a/Eigen/src/Core/util/Memory.h b/Eigen/src/Core/util/Memory.h
index d177e8b5a..76bdb6cfc 100644
--- a/Eigen/src/Core/util/Memory.h
+++ b/Eigen/src/Core/util/Memory.h
@@ -32,7 +32,7 @@
 // page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
 // quite safe, at least within the context of glibc, to equate 64-bit with LP64.
 #if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 8) || __GLIBC__>2) \
- && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ )
+ && defined(__LP64__) && ! defined( __SANITIZE_ADDRESS__ ) && (EIGEN_ALIGN == 16)
   #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
 #else
   #define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
@@ -42,14 +42,14 @@
 //   See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
 // FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
 //   See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
-#if defined(__FreeBSD__) && !defined(__arm__) && !defined(__mips__)
+#if defined(__FreeBSD__) && !defined(__arm__) && !defined(__mips__) && (EIGEN_ALIGN == 16)
   #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
 #else
   #define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
 #endif
 
-#if defined(__APPLE__) \
- || defined(_WIN64) \
+#if (defined(__APPLE__) && (EIGEN_ALIGN == 16)) \
+ || (defined(_WIN64) && (EIGEN_ALIGN == 16))   \
  || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED \
  || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
   #define EIGEN_MALLOC_ALREADY_ALIGNED 1
@@ -73,7 +73,7 @@
   #define EIGEN_HAS_POSIX_MEMALIGN 0
 #endif
 
-#ifdef EIGEN_VECTORIZE_SSE
+#if defined EIGEN_VECTORIZE_SSE || defined EIGEN_VECTORIZE_AVX
   #define EIGEN_HAS_MM_MALLOC 1
 #else
   #define EIGEN_HAS_MM_MALLOC 0
@@ -105,9 +105,9 @@ inline void throw_std_bad_alloc()
   */
 inline void* handmade_aligned_malloc(std::size_t size)
 {
-  void *original = std::malloc(size+16);
+  void *original = std::malloc(size+EIGEN_ALIGN);
   if (original == 0) return 0;
-  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_ALIGN-1))) + EIGEN_ALIGN);
   *(reinterpret_cast<void**>(aligned) - 1) = original;
   return aligned;
 }
@@ -128,9 +128,9 @@ inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t =
   if (ptr == 0) return handmade_aligned_malloc(size);
   void *original = *(reinterpret_cast<void**>(ptr) - 1);
   std::ptrdiff_t previous_offset = static_cast<char *>(ptr)-static_cast<char *>(original);
-  original = std::realloc(original,size+16);
+  original = std::realloc(original,size+EIGEN_ALIGN);
   if (original == 0) return 0;
-  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(15))) + 16);
+  void *aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_ALIGN-1))) + EIGEN_ALIGN);
   void *previous_aligned = static_cast<char *>(original)+previous_offset;
   if(aligned!=previous_aligned)
     std::memmove(aligned, previous_aligned, size);
@@ -208,7 +208,7 @@ inline void check_that_malloc_is_allowed()
 {}
 #endif
 
-/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 bytes alignment.
+/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 or 32 bytes alignment depending on the requirements.
   * On allocation error, the returned pointer is null, and std::bad_alloc is thrown.
   */
 inline void* aligned_malloc(size_t size)
@@ -221,11 +221,11 @@ inline void* aligned_malloc(size_t size)
   #elif EIGEN_MALLOC_ALREADY_ALIGNED
     result = std::malloc(size);
   #elif EIGEN_HAS_POSIX_MEMALIGN
-    if(posix_memalign(&result, 16, size)) result = 0;
+    if(posix_memalign(&result, EIGEN_ALIGN, size)) result = 0;
   #elif EIGEN_HAS_MM_MALLOC
-    result = _mm_malloc(size, 16);
+    result = _mm_malloc(size, EIGEN_ALIGN);
   #elif defined(_MSC_VER) && (!defined(_WIN32_WCE))
-    result = _aligned_malloc(size, 16);
+    result = _aligned_malloc(size, EIGEN_ALIGN);
   #else
     result = handmade_aligned_malloc(size);
   #endif
@@ -275,12 +275,12 @@ inline void* aligned_realloc(void *ptr, size_t new_size, size_t old_size)
   // implements _mm_malloc/_mm_free based on the corresponding _aligned_
   // functions. This may not always be the case and we just try to be safe.
   #if defined(_MSC_VER) && defined(_mm_free)
-    result = _aligned_realloc(ptr,new_size,16);
+    result = _aligned_realloc(ptr,new_size,EIGEN_ALIGN);
   #else
     result = generic_aligned_realloc(ptr,new_size,old_size);
   #endif
 #elif defined(_MSC_VER)
-  result = _aligned_realloc(ptr,new_size,16);
+  result = _aligned_realloc(ptr,new_size,EIGEN_ALIGN);
 #else
   result = handmade_aligned_realloc(ptr,new_size,old_size);
 #endif
@@ -607,9 +607,9 @@ template<typename T> class aligned_stack_memory_handler
   * The underlying stack allocation function can controlled with the EIGEN_ALLOCA preprocessor token.
   */
 #ifdef EIGEN_ALLOCA
-
-  #ifdef __arm__
-    #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((reinterpret_cast<size_t>(EIGEN_ALLOCA(SIZE+16)) & ~(size_t(15))) + 16)
+  // The native alloca() that comes with llvm aligns buffer on 16 bytes even when AVX is enabled.
+  #if defined(__arm__) || EIGEN_ALIGN > 16
+    #define EIGEN_ALIGNED_ALLOCA(SIZE) reinterpret_cast<void*>((reinterpret_cast<size_t>(EIGEN_ALLOCA(SIZE+EIGEN_ALIGN)) & ~(size_t(EIGEN_ALIGN-1))) + EIGEN_ALIGN)
   #else
     #define EIGEN_ALIGNED_ALLOCA EIGEN_ALLOCA
   #endif
@@ -679,7 +679,7 @@ template<typename T> class aligned_stack_memory_handler
 
 #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
 #define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar,Size) \
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%16==0)))
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(((Size)!=Eigen::Dynamic) && ((sizeof(Scalar)*(Size))%EIGEN_ALIGN==0)))
 
 /****************************************************************************/