diff --git a/Eigen/Core b/Eigen/Core
index 61cc646aa..4bbde063a 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -163,11 +163,11 @@ using std::ptrdiff_t;
   #include "src/Core/arch/SSE/PacketMath.h"
   #include "src/Core/arch/SSE/TypeCasting.h"
   #include "src/Core/arch/SSE/Complex.h"
-  #include "src/Core/arch/SSE/MathFunctions.h"
   #include "src/Core/arch/AVX/PacketMath.h"
   #include "src/Core/arch/AVX/TypeCasting.h"
-  #include "src/Core/arch/AVX/MathFunctions.h"
   #include "src/Core/arch/AVX/Complex.h"
+  #include "src/Core/arch/SSE/MathFunctions.h"
+  #include "src/Core/arch/AVX/MathFunctions.h"
 #elif defined EIGEN_VECTORIZE_SSE
   #include "src/Core/arch/SSE/PacketMath.h"
   #include "src/Core/arch/SSE/TypeCasting.h"
diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index c24268443..cc044de22 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -219,7 +219,13 @@ pxor(const Packet& a, const Packet& b) { return a ^ b; }
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
 pandnot(const Packet& a, const Packet& b) { return a & (!b); }
 
-/** \internal \returns \a a shifted by N bits */
+/** \internal \returns \a a shifted by N bits to the right */
+template<int N> EIGEN_DEVICE_FUNC inline int
+pshiftright(const int& a) { return a >> N; }
+template<int N> EIGEN_DEVICE_FUNC inline long int
+pshiftright(const long int& a) { return a >> N; }
+
+/** \internal \returns \a a shifted by N bits to the left */
 template<int N> EIGEN_DEVICE_FUNC inline int
 pshiftleft(const int& a) { return a << N; }
 template<int N> EIGEN_DEVICE_FUNC inline long int
@@ -654,41 +660,17 @@ pinsertlast(const Packet& a, typename unpacket_traits<Packet>::type b)
  * Some generic implementations to be used by implementors
 ***************************************************************************/
 
-/** \internal shift the bits by n and cast the result to the initial type, i.e.:
-  *   return float(reinterpret_cast<uint>(a) >> n)
-  */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pshiftright_and_cast(Packet a, int n);
-
 /** Default implementation of pfrexp for float.
-  * It is expected to be called by implementers of template<> pfrexp,
-  * and the above pshiftright_and_cast function must be implemented.
+  * It is expected to be called by implementers of template<> pfrexp.
   */
 template<typename Packet> EIGEN_STRONG_INLINE Packet
-pfrexp_float(const Packet& a, Packet& exponent) {
-  const Packet cst_126f = pset1<Packet>(126.0f);
-  const Packet cst_half = pset1<Packet>(0.5f);
-  const Packet cst_inv_mant_mask  = pset1frombits<Packet>(~0x7f800000u);
-  exponent = psub(pshiftright_and_cast(a,23), cst_126f);
-  return por(pand(a, cst_inv_mant_mask), cst_half);
-}
-
-/** \internal shift the bits by n and cast the result to the initial type, i.e.:
-  *   return reinterpret_cast<float>(int(a) >> n)
-  */
-template<typename Packet> EIGEN_DEVICE_FUNC inline Packet
-pcast_and_shiftleft(Packet a, int n);
+pfrexp_float(const Packet& a, Packet& exponent);
 
 /** Default implementation of pldexp for float.
-  * It is expected to be called by implementers of template<> pldexp,
-  * and the above pcast_and_shiftleft function must be implemented.
+  * It is expected to be called by implementers of template<> pldexp.
   */
 template<typename Packet> EIGEN_STRONG_INLINE Packet
-pldexp_float(Packet a, Packet exponent) {
-  const Packet cst_127 = pset1<Packet>(127.f);
-  // return a * 2^exponent
-  return pmul(a, pcast_and_shiftleft(padd(exponent, cst_127), 23));
-}
+pldexp_float(Packet a, Packet exponent);
 
 } // end namespace internal
 
diff --git a/Eigen/src/Core/arch/AVX/PacketMath.h b/Eigen/src/Core/arch/AVX/PacketMath.h
index 969f68d79..4c1abe43f 100644
--- a/Eigen/src/Core/arch/AVX/PacketMath.h
+++ b/Eigen/src/Core/arch/AVX/PacketMath.h
@@ -256,7 +256,17 @@ template<> EIGEN_STRONG_INLINE Packet8f pselect<Packet8f>(const Packet8f& mask,
 template<> EIGEN_STRONG_INLINE Packet4d pselect<Packet4d>(const Packet4d& mask, const Packet4d& a, const Packet4d& b)
 { return _mm256_blendv_pd(b,a,mask); }
 
-template<int N> EIGEN_STRONG_INLINE Packet8i pshiftleft(const Packet8i& a) {
+template<int N> EIGEN_STRONG_INLINE Packet8i pshiftright(Packet8i a) {
+#ifdef EIGEN_VECTORIZE_AVX2
+  return _mm256_srli_epi32(a, N);
+#else
+  __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(a, 0), N);
+  __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(a, 1), N);
+  return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1);
+#endif
+}
+
+template<int N> EIGEN_STRONG_INLINE Packet8i pshiftleft(Packet8i a) {
 #ifdef EIGEN_VECTORIZE_AVX2
   return _mm256_slli_epi32(a, N);
 #else
@@ -409,33 +419,10 @@ template<> EIGEN_STRONG_INLINE Packet4d pabs(const Packet4d& a)
   return _mm256_and_pd(a,mask);
 }
 
-template<> EIGEN_STRONG_INLINE Packet8f pshiftright_and_cast<Packet8f>(Packet8f v, int n)
-{
-#ifdef EIGEN_VECTORIZE_AVX2
-  return _mm256_cvtepi32_ps(_mm256_srli_epi32(_mm256_castps_si256(v), n));
-#else
-  __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 0), n);
-  __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 1), n);
-  return _mm256_cvtepi32_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1));
-#endif
-}
-
 template<> EIGEN_STRONG_INLINE Packet8f pfrexp<Packet8f>(const Packet8f& a, Packet8f& exponent) {
   return pfrexp_float(a,exponent);
 }
 
-template<> EIGEN_STRONG_INLINE Packet8f pcast_and_shiftleft<Packet8f>(Packet8f v, int n)
-{
-  Packet8i vi = _mm256_cvttps_epi32(v);
-#ifdef EIGEN_VECTORIZE_AVX2
-  return _mm256_castsi256_ps(_mm256_slli_epi32(vi, n));
-#else
-  __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(vi, 0), n);
-  __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(vi, 1), n);
-  return _mm256_castsi256_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1));
-#endif
-}
-
 template<> EIGEN_STRONG_INLINE Packet8f pldexp<Packet8f>(const Packet8f& a, const Packet8f& exponent) {
   return pldexp_float(a,exponent);
 }
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index d64550d8a..446065fb7 100755
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -187,8 +187,19 @@ template<> struct packet_traits<int>    : default_packet_traits
 };
 
 
-template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };
-template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
+template<> struct unpacket_traits<Packet4f>
+{
+  typedef float     type;
+  typedef Packet4f  half;
+  typedef Packet4i  integer_packet;
+  enum {size=4, alignment=Aligned16};
+};
+template<> struct unpacket_traits<Packet4i>
+{
+  typedef int       type;
+  typedef Packet4i  half;
+  enum {size=4, alignment=Aligned16};
+};
 
 inline std::ostream & operator <<(std::ostream & s, const Packet16uc & v)
 {
@@ -567,21 +578,15 @@ template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
 
-template<> EIGEN_STRONG_INLINE Packet4f pshiftright_and_cast(Packet4f a, int n) {
-  return vec_ctf(vec_sr(reinterpret_cast<Packet4i>(a),
-                        reinterpret_cast<Packet4ui>(pset1<Packet4i>(n))),0);
-}
+template<int N> EIGEN_STRONG_INLINE Packet4i pshiftright(Packet4i a)
+{ return vec_sr(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
+template<int N> EIGEN_STRONG_INLINE Packet4i pshiftleft(Packet4i a)
+{ return vec_sl(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
   return pfrexp_float(a,exponent);
 }
 
-template<> EIGEN_STRONG_INLINE Packet4f pcast_and_shiftleft<Packet4f>(Packet4f v, int n)
-{
-  Packet4i vi = vec_cts(v,0);
-  return reinterpret_cast<Packet4f>(vec_sl(vi, reinterpret_cast<Packet4ui>(pset1<Packet4i>(n))));
-}
-
 template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
   return pldexp_float(a,exponent);
 }
@@ -807,6 +812,43 @@ template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, cons
 }
 
 
+template <>
+struct type_casting_traits<float, int> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 1
+  };
+};
+
+template <>
+struct type_casting_traits<int, float> {
+  enum {
+    VectorizedCast = 1,
+    SrcCoeffRatio = 1,
+    TgtCoeffRatio = 1
+  };
+};
+
+
+template<> EIGEN_STRONG_INLINE Packet4i pcast<Packet4f, Packet4i>(const Packet4f& a) {
+  return vec_cts(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
+  return vec_ctf(a,0);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet4f>(const Packet4f& a) {
+  return reinterpret_cast<Packet4i>(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f,Packet4i>(const Packet4i& a) {
+  return reinterpret_cast<Packet4f>(a);
+}
+
+
+
 //---------- double ----------
 #ifdef __VSX__
 typedef __vector double              Packet2d;
diff --git a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
index 067d1dbe0..465f9bc3e 100644
--- a/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
+++ b/Eigen/src/Core/arch/Default/GenericPacketMathFunctions.h
@@ -16,6 +16,26 @@
 namespace Eigen {
 namespace internal {
 
+template<typename Packet> EIGEN_STRONG_INLINE Packet
+pfrexp_float(const Packet& a, Packet& exponent) {
+  typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+  const Packet cst_126f = pset1<Packet>(126.0f);
+  const Packet cst_half = pset1<Packet>(0.5f);
+  const Packet cst_inv_mant_mask  = pset1frombits<Packet>(~0x7f800000u);
+  exponent = psub(pcast<PacketI,Packet>(pshiftright<23>(preinterpret<PacketI>(a))), cst_126f);
+  return por(pand(a, cst_inv_mant_mask), cst_half);
+}
+
+template<typename Packet> EIGEN_STRONG_INLINE Packet
+pldexp_float(Packet a, Packet exponent)
+{
+  typedef typename unpacket_traits<Packet>::integer_packet PacketI;
+  const Packet cst_127 = pset1<Packet>(127.f);
+  // return a * 2^exponent
+  PacketI ei = pcast<Packet,PacketI>(padd(exponent, cst_127));
+  return pmul(a, preinterpret<Packet>(pshiftleft<23>(ei)));
+}
+
 // Natural logarithm
 // Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2)
 // and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index dc432f0d2..0a50153c7 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -140,8 +140,19 @@ EIGEN_STRONG_INLINE void        vst1q_f32(float* to, float32x4_t from) { ::vst1q
 EIGEN_STRONG_INLINE void        vst1_f32 (float* to, float32x2_t from) { ::vst1_f32 ((float32_t*)to,from); }
 #endif
 
-template<> struct unpacket_traits<Packet4f> { typedef float   type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };
-template<> struct unpacket_traits<Packet4i> { typedef int32_t type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
+template<> struct unpacket_traits<Packet4f>
+{
+  typedef float     type;
+  typedef Packet4f  half;
+  typedef Packet4i  integer_packet;
+  enum {size=4, alignment=Aligned16};
+};
+template<> struct unpacket_traits<Packet4i>
+{
+  typedef int32_t   type;
+  typedef Packet4i  half;
+  enum {size=4, alignment=Aligned16};
+};
 
 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return vdupq_n_f32(from); }
 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int32_t&    from)   { return vdupq_n_s32(from); }
@@ -294,6 +305,9 @@ template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, con
 }
 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vbicq_s32(a,b); }
 
+template<int N> EIGEN_STRONG_INLINE Packet4i pshiftright(Packet4i a) { return vshrq_n_s32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i pshiftleft(Packet4i a) { return vshlq_n_s32(a,N); }
+
 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*    from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); }
 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int32_t*  from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); }
 
@@ -384,20 +398,10 @@ template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); }
 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); }
 
-template<> EIGEN_STRONG_INLINE Packet4f pshiftright_and_cast(Packet4f a, int n) {
-  return vcvtq_f32_s32(vshrq_n_s32(vreinterpretq_s32_f32(a),n));
-}
-
 template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
   return pfrexp_float(a,exponent);
 }
 
-template<> EIGEN_STRONG_INLINE Packet4f pcast_and_shiftleft<Packet4f>(Packet4f v, int n)
-{
-  Packet4i vi = vcvtq_s32_f32(v);
-  return vreinterpretq_f32_s32(vshlq_n_s32(vi, n));
-}
-
 template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
   return pldexp_float(a,exponent);
 }
diff --git a/Eigen/src/Core/arch/NEON/TypeCasting.h b/Eigen/src/Core/arch/NEON/TypeCasting.h
index 95d1fd0e4..20dbe1332 100644
--- a/Eigen/src/Core/arch/NEON/TypeCasting.h
+++ b/Eigen/src/Core/arch/NEON/TypeCasting.h
@@ -41,6 +41,14 @@ template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i
   return vcvtq_f32_s32(a);
 }
 
+template<> EIGEN_STRONG_INLINE Packet4i preinterpret<Packet4i,Packet4f>(const Packet4f& a) {
+  return vreinterpretq_s32_f32(a);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f preinterpret<Packet4f,Packet4i>(const Packet4i& a) {
+  return vreinterpretq_f32_s32(a);
+}
+
 } // end namespace internal
 
 } // end namespace Eigen
diff --git a/Eigen/src/Core/arch/SSE/PacketMath.h b/Eigen/src/Core/arch/SSE/PacketMath.h
index fbc69ef1f..800eb4d86 100755
--- a/Eigen/src/Core/arch/SSE/PacketMath.h
+++ b/Eigen/src/Core/arch/SSE/PacketMath.h
@@ -370,7 +370,8 @@ template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, con
 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(b,a); }
 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(b,a); }
 
-template<int N> EIGEN_STRONG_INLINE Packet4i pshiftleft(const Packet4i& a) { return _mm_slli_epi32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i pshiftright(Packet4i a) { return _mm_srli_epi32(a,N); }
+template<int N> EIGEN_STRONG_INLINE Packet4i pshiftleft(Packet4i a) { return _mm_slli_epi32(a,N); }
 
 #ifdef EIGEN_VECTORIZE_SSE4_1
 template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return _mm_round_ps(a, 0); }
@@ -569,20 +570,10 @@ template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
   #endif
 }
 
-template<> EIGEN_STRONG_INLINE Packet4f pshiftright_and_cast(Packet4f a, int n) {
-  return _mm_cvtepi32_ps(_mm_srli_epi32(_mm_castps_si128(a),n));
-}
-
 template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
   return pfrexp_float(a,exponent);
 }
 
-template<> EIGEN_STRONG_INLINE Packet4f pcast_and_shiftleft<Packet4f>(Packet4f v, int n)
-{
-  Packet4i vi = _mm_cvttps_epi32(v);
-  return _mm_castsi128_ps(_mm_slli_epi32(vi, n));
-}
-
 template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
   return pldexp_float(a,exponent);
 }