Merged kmargar/eigen/tip into default, Altivec/VSX port should be working ok now.

6 files changed, 468 insertions, 327 deletions

diff --git a/Eigen/src/Core/arch/AltiVec/Complex.h b/Eigen/src/Core/arch/AltiVec/Complex.h
index 58c296171..45213f791 100644
--- a/Eigen/src/Core/arch/AltiVec/Complex.h
+++ b/Eigen/src/Core/arch/AltiVec/Complex.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010-2016 Konstantinos Margaritis <markos@freevec.org>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -15,18 +16,20 @@ namespace Eigen {
 namespace internal {
 
 static Packet4ui  p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_ZERO_);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
-#ifdef _BIG_ENDIAN
+#ifdef __VSX__
+#if defined(_BIG_ENDIAN)
 static Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
 static Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 };
 #else
 static Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_ZERO_, 8);//{ 0x8000000000000000, 0x0000000000000000 };
 static Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2d_ZERO_, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
 #endif
+#endif
 
 //---------- float ----------
 struct Packet2cf
 {
-  EIGEN_STRONG_INLINE Packet2cf() {}
+  EIGEN_STRONG_INLINE explicit Packet2cf() : v(p4f_ZERO) {}
   EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
   Packet4f  v;
 };
@@ -39,6 +42,7 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 2,
+    HasHalfPacket = 0,
 
     HasAdd    = 1,
     HasSub    = 1,
@@ -49,6 +53,9 @@ template<> struct packet_traits<std::complex<float> >  : default_packet_traits
     HasAbs2   = 0,
     HasMin    = 0,
     HasMax    = 0,
+#ifdef __VSX__
+    HasBlend  = 1,
+#endif
     HasSetLinear = 0
   };
 };
@@ -58,7 +65,6 @@ template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type;
 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
 {
   Packet2cf res;
-  /* On AltiVec we cannot load 64-bit registers, so wa have to take care of alignment */
   if((ptrdiff_t(&from) % 16) == 0)
     res.v = pload<Packet4f>((const float *)&from);
   else
@@ -67,26 +73,32 @@ template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<flo
   return res;
 }
 
+template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>*        from) { return Packet2cf(pload<Packet4f>((const float *) from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>*       from) { return Packet2cf(ploadu<Packet4f>((const float*) from)); }
+template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>*     from) { return pset1<Packet2cf>(*from); }
+
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { pstore((float*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { pstoreu((float*)to, from.v); }
+
 template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
 {
   std::complex<float> EIGEN_ALIGN16 af[2];
   af[0] = from[0*stride];
   af[1] = from[1*stride];
-  return Packet2cf(vec_ld(0, (const float*)af));
+  return pload<Packet2cf>(af);
 }
 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
 {
   std::complex<float> EIGEN_ALIGN16 af[2];
-  vec_st(from.v, 0, (float*)af);
+  pstore<std::complex<float> >((std::complex<float> *) af, from);
   to[0*stride] = af[0];
   to[1*stride] = af[1];
 }
 
-
-template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_add(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_sub(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v + b.v); }
+template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v - b.v); }
 template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); }
-template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf((Packet4f)vec_xor((Packet4ui)a.v, p4ui_CONJ_XOR)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }
 
 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
 {
@@ -100,30 +112,19 @@ template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, con
   v1 = vec_madd(v1, b.v, p4f_ZERO);
   // multiply a_im * b and get the conjugate result
   v2 = vec_madd(v2, b.v, p4f_ZERO);
-  v2 = (Packet4f) vec_xor((Packet4ui)v2, p4ui_CONJ_XOR);
+  v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR)));
   // permute back to a proper order
   v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV);
   
-  return Packet2cf(vec_add(v1, v2));
+  return Packet2cf(padd<Packet4f>(v1, v2));
 }
 
-template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_or(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_xor(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(vec_and(a.v, vec_nor(b.v,b.v))); }
+template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v, b.v)); }
+template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v, b.v)); }
 
-template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
-template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
-
-template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>*     from)
-{
-  return pset1<Packet2cf>(*from);
-}
-
-template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
-template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
-
-template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { vec_dstt((float *)addr, DST_CTRL(2,2,32), DST_CHAN); }
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr)    { EIGEN_PPC_PREFETCH(addr); }
 
 template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
 {
@@ -143,23 +144,23 @@ template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
 template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
 {
   Packet4f b;
-  b = (Packet4f) vec_sld(a.v, a.v, 8);
-  b = padd(a.v, b);
-  return pfirst(Packet2cf(b));
+  b = vec_sld(a.v, a.v, 8);
+  b = padd<Packet4f>(a.v, b);
+  return pfirst<Packet2cf>(Packet2cf(b));
 }
 
 template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
 {
   Packet4f b1, b2;
 #ifdef _BIG_ENDIAN  
-  b1 = (Packet4f) vec_sld(vecs[0].v, vecs[1].v, 8);
-  b2 = (Packet4f) vec_sld(vecs[1].v, vecs[0].v, 8);
+  b1 = vec_sld(vecs[0].v, vecs[1].v, 8);
+  b2 = vec_sld(vecs[1].v, vecs[0].v, 8);
 #else
-  b1 = (Packet4f) vec_sld(vecs[1].v, vecs[0].v, 8);
-  b2 = (Packet4f) vec_sld(vecs[0].v, vecs[1].v, 8);
+  b1 = vec_sld(vecs[1].v, vecs[0].v, 8);
+  b2 = vec_sld(vecs[0].v, vecs[1].v, 8);
 #endif
-  b2 = (Packet4f) vec_sld(b2, b2, 8);
-  b2 = padd(b1, b2);
+  b2 = vec_sld(b2, b2, 8);
+  b2 = padd<Packet4f>(b1, b2);
 
   return Packet2cf(b2);
 }
@@ -168,10 +169,10 @@ template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const P
 {
   Packet4f b;
   Packet2cf prod;
-  b = (Packet4f) vec_sld(a.v, a.v, 8);
-  prod = pmul(a, Packet2cf(b));
+  b = vec_sld(a.v, a.v, 8);
+  prod = pmul<Packet2cf>(a, Packet2cf(b));
 
-  return pfirst(prod);
+  return pfirst<Packet2cf>(prod);
 }
 
 template<int Offset>
@@ -223,12 +224,30 @@ template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
   }
 };
 
+template<> struct conj_helper<Packet4f, Packet2cf, false,false>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet4f& x, const Packet2cf& y, const Packet2cf& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet4f& x, const Packet2cf& y) const
+  { return Packet2cf(internal::pmul<Packet4f>(x, y.v)); }
+};
+
+template<> struct conj_helper<Packet2cf, Packet4f, false,false>
+{
+  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet4f& y, const Packet2cf& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& x, const Packet4f& y) const
+  { return Packet2cf(internal::pmul<Packet4f>(x.v, y)); }
+};
+
 template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
 {
   // TODO optimize it for AltiVec
-  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
-  Packet4f s = vec_madd(b.v, b.v, p4f_ZERO);
-  return Packet2cf(pdiv(res.v, vec_add(s,vec_perm(s, s, p16uc_COMPLEX32_REV))));
+  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a, b);
+  Packet4f s = pmul<Packet4f>(b.v, b.v);
+  return Packet2cf(pdiv(res.v, padd<Packet4f>(s, vec_perm(s, s, p16uc_COMPLEX32_REV))));
 }
 
 template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
@@ -243,6 +262,14 @@ EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
   kernel.packet[0].v = tmp;
 }
 
+#ifdef __VSX__
+template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
+  Packet2cf result;
+  result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v)));
+  return result;
+}
+#endif
+
 //---------- double ----------
 #ifdef __VSX__
 struct Packet1cd
@@ -277,10 +304,10 @@ template<> struct packet_traits<std::complex<double> >  : default_packet_traits
 
 template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
 
-template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
-template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
-template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
-template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { return Packet1cd(pload<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { return Packet1cd(ploadu<Packet2d>((const double*)from)); }
+template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { pstore((double*)to, from.v); }
+template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { pstoreu((double*)to, from.v); }
 
 template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)
 { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
@@ -300,10 +327,10 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1c
   to[1*stride] = af[1];
 }
 
-template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_add(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_sub(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
+template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
 template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
-template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd((Packet2d)vec_xor((Packet2d)a.v, (Packet2d)p2ul_CONJ_XOR2)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2))); }
 
 template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
 {
@@ -317,23 +344,20 @@ template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, con
   v1 = vec_madd(a_re, b.v, p2d_ZERO);
   // multiply a_im * b and get the conjugate result
   v2 = vec_madd(a_im, b.v, p2d_ZERO);
-  v2 = (Packet2d) vec_sld((Packet4ui)v2, (Packet4ui)v2, 8);
-  v2 = (Packet2d) vec_xor((Packet2d)v2, (Packet2d) p2ul_CONJ_XOR1);
+  v2 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8));
+  v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1));
 
-  return Packet1cd(vec_add(v1, v2));
+  return Packet1cd(padd<Packet2d>(v1, v2));
 }
 
-template<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_or(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_xor(a.v,b.v)); }
-template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(vec_and(a.v, vec_nor(b.v,b.v))); }
+template<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pand(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(por(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pxor(a.v,b.v)); }
+template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pandnot(a.v, b.v)); }
 
-template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from)
-{
-  return pset1<Packet1cd>(*from);
-}
+template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from)  { return pset1<Packet1cd>(*from); }
 
-template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { vec_dstt((long *)addr, DST_CTRL(2,2,32), DST_CHAN); }
+template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr)    { EIGEN_PPC_PREFETCH(addr); }
 
 template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)
 {
@@ -345,20 +369,10 @@ template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Pac
 
 template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
 
-template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
-{
-  return pfirst(a);
-}
+template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
+template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)        { return vecs[0]; }
 
-template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)
-{
-  return vecs[0];
-}
-
-template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
-{
-  return pfirst(a);
-}
+template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
 
 template<int Offset>
 struct palign_impl<Offset,Packet1cd>
@@ -402,13 +416,30 @@ template<> struct conj_helper<Packet1cd, Packet1cd, true,true>
     return pconj(internal::pmul(a, b));
   }
 };
+template<> struct conj_helper<Packet2d, Packet1cd, false,false>
+{
+  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet2d& x, const Packet1cd& y, const Packet1cd& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet2d& x, const Packet1cd& y) const
+  { return Packet1cd(internal::pmul<Packet2d>(x, y.v)); }
+};
+
+template<> struct conj_helper<Packet1cd, Packet2d, false,false>
+{
+  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet2d& y, const Packet1cd& c) const
+  { return padd(c, pmul(x,y)); }
+
+  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& x, const Packet2d& y) const
+  { return Packet1cd(internal::pmul<Packet2d>(x.v, y)); }
+};
 
 template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
 {
   // TODO optimize it for AltiVec
   Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);
-  Packet2d s = vec_madd(b.v, b.v, p2d_ZERO_);
-  return Packet1cd(pdiv(res.v, vec_add(s,vec_perm(s, s, p16uc_REVERSE64))));
+  Packet2d s = pmul<Packet2d>(b.v, b.v);
+  return Packet1cd(pdiv(res.v, padd<Packet2d>(s, vec_perm(s, s, p16uc_REVERSE64))));
 }
 
 EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
diff --git a/Eigen/src/Core/arch/AltiVec/MathFunctions.h b/Eigen/src/Core/arch/AltiVec/MathFunctions.h
index 9e37e93f8..5511245dd 100644
--- a/Eigen/src/Core/arch/AltiVec/MathFunctions.h
+++ b/Eigen/src/Core/arch/AltiVec/MathFunctions.h
@@ -3,6 +3,7 @@
 //
 // Copyright (C) 2007 Julien Pommier
 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -19,38 +20,79 @@ namespace Eigen {
 
 namespace internal {
 
-template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
-Packet4f plog<Packet4f>(const Packet4f& _x)
-{
-  Packet4f x = _x;
-  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
-  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
-  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
-  _EIGEN_DECLARE_CONST_Packet4i(23, 23);
+static _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
+static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
+static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
+static _EIGEN_DECLARE_CONST_Packet4i(23, 23);
 
-  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
+static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
 
-  /* the smallest non denormalized float number */
-  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos,  0x00800000);
-  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf,     0xff800000); // -1.f/0.f
-  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan,     0xffffffff);
+/* the smallest non denormalized float number */
+static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos,  0x00800000);
+static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf,     0xff800000); // -1.f/0.f
+static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan,     0xffffffff);
   
-  /* natural logarithm computed for 4 simultaneous float
-    return NaN for x <= 0
-  */
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
+/* natural logarithm computed for 4 simultaneous float
+  return NaN for x <= 0
+*/
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
+
+static _EIGEN_DECLARE_CONST_Packet4f(exp_hi,  88.3762626647950f);
+static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
+
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
+
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
+static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
+
+#ifdef __VSX__
+static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
+static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
+static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
 
+static _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);
+static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
+
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
+
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
+
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
+
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
+static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
+
+static Packet2l p2l_1023 = { 1023, 1023 };
+static Packet2ul p2ul_52 = { 52, 52 };
+
+#endif
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f plog<Packet4f>(const Packet4f& _x)
+{
+  Packet4f x = _x;
 
   Packet4i emm0;
 
@@ -112,36 +154,17 @@ template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
 Packet4f pexp<Packet4f>(const Packet4f& _x)
 {
   Packet4f x = _x;
-  _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
-  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
-  _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
-  _EIGEN_DECLARE_CONST_Packet4i(23, 23);
-
-
-  _EIGEN_DECLARE_CONST_Packet4f(exp_hi,  88.3762626647950f);
-  _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
-
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
-
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
-  _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
 
   Packet4f tmp, fx;
   Packet4i emm0;
 
   // clamp x
-  x = vec_max(vec_min(x, p4f_exp_hi), p4f_exp_lo);
+  x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
 
-  /* express exp(x) as exp(g + n*log(2)) */
+  // express exp(x) as exp(g + n*log(2))
   fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
 
-  fx = vec_floor(fx);
+  fx = pfloor(fx);
 
   tmp = pmul(fx, p4f_cephes_exp_C1);
   Packet4f z = pmul(fx, p4f_cephes_exp_C2);
@@ -171,14 +194,44 @@ Packet4f pexp<Packet4f>(const Packet4f& _x)
                  isnumber_mask);
 }
 
+#ifndef EIGEN_COMP_CLANG
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f prsqrt<Packet4f>(const Packet4f& x)
+{
+  return  vec_rsqrt(x);
+}
+#endif
+
 #ifdef __VSX__
+#ifndef EIGEN_COMP_CLANG
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d prsqrt<Packet2d>(const Packet2d& x)
+{
+  return  vec_rsqrt(x);
+}
+#endif
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet4f psqrt<Packet4f>(const Packet4f& x)
+{
+  return  vec_sqrt(x);
+}
+
+template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
+Packet2d psqrt<Packet2d>(const Packet2d& x)
+{
+  return  vec_sqrt(x);
+}
+
 // VSX support varies between different compilers and even different
 // versions of the same compiler.  For gcc version >= 4.9.3, we can use
 // vec_cts to efficiently convert Packet2d to Packet2l.  Otherwise, use
 // a slow version that works with older compilers. 
+// Update: apparently vec_cts/vec_ctf intrinsics for 64-bit doubles
+// are buggy, https://gcc.gnu.org/bugzilla/show_bug.cgi?id=70963
 static inline Packet2l ConvertToPacket2l(const Packet2d& x) {
-#if EIGEN_GNUC_AT_LEAST(5, 0) || \
-    (EIGEN_GNUC_AT(4, 9) && __GNUC_PATCHLEVEL__ >= 3)
+#if EIGEN_GNUC_AT_LEAST(5, 4) || \
+    (EIGEN_GNUC_AT(6, 1) && __GNUC_PATCHLEVEL__ >= 1)
   return vec_cts(x, 0);    // TODO: check clang version.
 #else
   double tmp[2];
@@ -194,36 +247,16 @@ Packet2d pexp<Packet2d>(const Packet2d& _x)
 {
   Packet2d x = _x;
 
-  _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
-  _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
-  _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
-
-  _EIGEN_DECLARE_CONST_Packet2d(exp_hi,  709.437);
-  _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
-
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
-
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
-
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
-
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
-  _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
-
   Packet2d tmp, fx;
   Packet2l emm0;
 
   // clamp x
   x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
+
   /* express exp(x) as exp(g + n*log(2)) */
-  fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
+  fx = pmadd(x, p2d_cephes_LOG2EF, p2d_half);
 
-  fx = vec_floor(fx);
+  fx = pfloor(fx);
 
   tmp = pmul(fx, p2d_cephes_exp_C1);
   Packet2d z = pmul(fx, p2d_cephes_exp_C2);
@@ -249,9 +282,6 @@ Packet2d pexp<Packet2d>(const Packet2d& _x)
   emm0 = ConvertToPacket2l(fx);
 
 #ifdef __POWER8_VECTOR__ 
-  static const Packet2l p2l_1023 = { 1023, 1023 };
-  static const Packet2ul p2ul_52 = { 52, 52 };
-
   emm0 = vec_add(emm0, p2l_1023);
   emm0 = vec_sl(emm0, p2ul_52);
 #else
diff --git a/Eigen/src/Core/arch/AltiVec/PacketMath.h b/Eigen/src/Core/arch/AltiVec/PacketMath.h
index 0dbbc2e42..cbfef3503 100755
--- a/Eigen/src/Core/arch/AltiVec/PacketMath.h
+++ b/Eigen/src/Core/arch/AltiVec/PacketMath.h
@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2008-2014 Konstantinos Margaritis <markos@freevec.org>
+// Copyright (C) 2008-2016 Konstantinos Margaritis <markos@freevec.org>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
@@ -42,7 +42,7 @@ typedef __vector unsigned char  Packet16uc;
 // and it doesn't really work to declare them global, so we define macros instead
 
 #define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
-  Packet4f p4f_##NAME = (Packet4f) vec_splat_s32(X)
+  Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(vec_splat_s32(X))
 
 #define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
   Packet4i p4i_##NAME = vec_splat_s32(X)
@@ -69,13 +69,13 @@ typedef __vector unsigned char  Packet16uc;
 // These constants are endian-agnostic
 static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0); //{ 0.0, 0.0, 0.0, 0.0}
 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}
-#ifndef __VSX__
 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1); //{ 1, 1, 1, 1}
-static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0}
-#endif
 static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16); //{ -16, -16, -16, -16}
 static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1); //{ -1, -1, -1, -1}
 static Packet4f p4f_ZERO_ = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1); //{ 0x80000000, 0x80000000, 0x80000000, 0x80000000}
+#ifndef __VSX__
+static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0}
+#endif
 
 static Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 };
 static Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };
@@ -95,8 +95,10 @@ static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
 // Handle endianness properly while loading constants
 // Define global static constants:
 #ifdef _BIG_ENDIAN
-static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0); 
+static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
+#ifdef __VSX__
 static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
+#endif
 static Packet16uc p16uc_PSET32_WODD   = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
 static Packet16uc p16uc_PSET32_WEVEN  = vec_sld(p16uc_DUPLICATE32_HI, (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 4,5,6,7, 4,5,6,7, 12,13,14,15, 12,13,14,15 };
 static Packet16uc p16uc_HALF64_0_16 = vec_sld((Packet16uc)p4i_ZERO, vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 3), 8);      //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
@@ -110,8 +112,8 @@ static Packet16uc p16uc_HALF64_0_16 = vec_sld(vec_splat((Packet16uc) vec_abs(p4i
 
 static Packet16uc p16uc_PSET64_HI = (Packet16uc) vec_mergeh((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 0,1,2,3, 4,5,6,7, 0,1,2,3, 4,5,6,7 };
 static Packet16uc p16uc_PSET64_LO = (Packet16uc) vec_mergel((Packet4ui)p16uc_PSET32_WODD, (Packet4ui)p16uc_PSET32_WEVEN);     //{ 8,9,10,11, 12,13,14,15, 8,9,10,11, 12,13,14,15 };
-static Packet16uc p16uc_TRANSPOSE64_HI = vec_add(p16uc_PSET64_HI, p16uc_HALF64_0_16);                                         //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
-static Packet16uc p16uc_TRANSPOSE64_LO = vec_add(p16uc_PSET64_LO, p16uc_HALF64_0_16);                                         //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};
+static Packet16uc p16uc_TRANSPOSE64_HI = p16uc_PSET64_HI + p16uc_HALF64_0_16;                                         //{ 0,1,2,3, 4,5,6,7, 16,17,18,19, 20,21,22,23};
+static Packet16uc p16uc_TRANSPOSE64_LO = p16uc_PSET64_LO + p16uc_HALF64_0_16;                                         //{ 8,9,10,11, 12,13,14,15, 24,25,26,27, 28,29,30,31};
 
 static Packet16uc p16uc_COMPLEX32_REV = vec_sld(p16uc_REVERSE32, p16uc_REVERSE32, 8);                                         //{ 4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11 };
 
@@ -121,6 +123,12 @@ static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8
 static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_PSET64_HI, p16uc_PSET64_LO, 8);                                            //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
 #endif // _BIG_ENDIAN
 
+#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
+  #define EIGEN_PPC_PREFETCH(ADDR) __builtin_prefetch(ADDR);
+#else
+  #define EIGEN_PPC_PREFETCH(ADDR) asm( "   dcbt [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
+#endif
+
 template<> struct packet_traits<float>  : default_packet_traits
 {
   typedef Packet4f type;
@@ -129,15 +137,35 @@ template<> struct packet_traits<float>  : default_packet_traits
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size=4,
-    HasHalfPacket=0,
+    HasHalfPacket = 1,
 
-    // FIXME check the Has*
+    HasAdd  = 1,
+    HasSub  = 1,
+    HasMul  = 1,
     HasDiv  = 1,
+    HasMin  = 1,
+    HasMax  = 1,
+    HasAbs  = 1,
     HasSin  = 0,
     HasCos  = 0,
-    HasLog  = 1,
+    HasLog  = 0,
     HasExp  = 1,
-    HasSqrt = 0
+#ifdef __VSX__
+    HasSqrt = 1,
+#if !EIGEN_COMP_CLANG
+    HasRsqrt = 1,
+#else
+    HasRsqrt = 0,
+#endif
+#else
+    HasSqrt = 0,
+    HasRsqrt = 0,
+#endif
+    HasRound = 1,
+    HasFloor = 1,
+    HasCeil = 1,
+    HasNegate = 1,
+    HasBlend = 1
   };
 };
 template<> struct packet_traits<int>    : default_packet_traits
@@ -145,10 +173,16 @@ template<> struct packet_traits<int>    : default_packet_traits
   typedef Packet4i type;
   typedef Packet4i half;
   enum {
-    // FIXME check the Has*
     Vectorizable = 1,
     AlignedOnScalar = 1,
-    size=4
+    size = 4,
+    HasHalfPacket = 0,
+
+    HasAdd  = 1,
+    HasSub  = 1,
+    HasMul  = 1,
+    HasDiv  = 0,
+    HasBlend = 1
   };
 };
 
@@ -200,41 +234,56 @@ inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
   return s;
 }
-/*
-inline std::ostream & operator <<(std::ostream & s, const Packetbi & v)
+
+// Need to define them first or we get specialization after instantiation errors
+template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
 {
-  union {
-    Packet4bi v;
-    unsigned int n[4];
-  } vt;
-  vt.v = v;
-  s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
-  return s;
-}*/
+  EIGEN_DEBUG_ALIGNED_LOAD
+#ifdef __VSX__
+  return vec_vsx_ld(0, from);
+#else
+  return vec_ld(0, from);
+#endif
+}
 
+template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from)
+{
+  EIGEN_DEBUG_ALIGNED_LOAD
+#ifdef __VSX__
+  return vec_vsx_ld(0, from);
+#else
+  return vec_ld(0, from);
+#endif
+}
 
-// Need to define them first or we get specialization after instantiation errors
-template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
-template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
+template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from)
+{
+  EIGEN_DEBUG_ALIGNED_STORE
+#ifdef __VSX__
+  vec_vsx_st(from, 0, to);
+#else
+  vec_st(from, 0, to);
+#endif
+}
 
-template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
-template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
+template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from)
+{
+  EIGEN_DEBUG_ALIGNED_STORE
+#ifdef __VSX__
+  vec_vsx_st(from, 0, to);
+#else
+  vec_st(from, 0, to);
+#endif
+}
 
 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) {
-  // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
-  float EIGEN_ALIGN16 af[4];
-  af[0] = from;
-  Packet4f vc = pload<Packet4f>(af);
-  vc = vec_splat(vc, 0);
-  return vc;
+  Packet4f v = {from, from, from, from};
+  return v;
 }
 
 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
-  int EIGEN_ALIGN16 ai[4];
-  ai[0] = from;
-  Packet4i vc = pload<Packet4i>(ai);
-  vc = vec_splat(vc, 0);
-  return vc;
+  Packet4i v = {from, from, from, from};
+  return v;
 }
 template<> EIGEN_STRONG_INLINE void
 pbroadcast4<Packet4f>(const float *a,
@@ -294,58 +343,24 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const
   to[3*stride] = ai[3];
 }
 
-template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return vec_add(pset1<Packet4f>(a), p4f_COUNTDOWN); }
-template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)   { return vec_add(pset1<Packet4i>(a), p4i_COUNTDOWN); }
+template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return pset1<Packet4f>(a) + p4f_COUNTDOWN; }
+template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)   { return pset1<Packet4i>(a) + p4i_COUNTDOWN; }
 
-template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_add(a,b); }
-template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_add(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return a + b; }
+template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return a + b; }
 
-template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_sub(a,b); }
-template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_sub(a,b); }
+template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return a - b; }
+template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return a - b; }
 
-template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return psub<Packet4f>(p4f_ZERO, a); }
-template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return psub<Packet4i>(p4i_ZERO, a); }
+template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return p4f_ZERO - a; }
+template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return p4i_ZERO - a; }
 
 template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& 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 vec_madd(a,b,p4f_ZERO); }
-/* Commented out: it's actually slower than processing it scalar
- *
-template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
-{
-  // Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec
-  //Set up constants, variables
-  Packet4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel;
-
-  // Get the absolute values
-  a1  = vec_abs(a);
-  b1  = vec_abs(b);
-
-  // Get the signs using xor
-  Packet4bi sgn = (Packet4bi) vec_cmplt(vec_xor(a, b), p4i_ZERO);
-
-  // Do the multiplication for the asbolute values.
-  bswap = (Packet4i) vec_rl((Packet4ui) b1, (Packet4ui) p4i_MINUS16 );
-  low_prod = vec_mulo((Packet8i) a1, (Packet8i)b1);
-  high_prod = vec_msum((Packet8i) a1, (Packet8i) bswap, p4i_ZERO);
-  high_prod = (Packet4i) vec_sl((Packet4ui) high_prod, (Packet4ui) p4i_MINUS16);
-  prod = vec_add( low_prod, high_prod );
+template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b, p4f_ZERO); }
+template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return a * b; }
 
-  // NOR the product and select only the negative elements according to the sign mask
-  prod_ = vec_nor(prod, prod);
-  prod_ = vec_sel(p4i_ZERO, prod_, sgn);
-
-  // Add 1 to the result to get the negative numbers
-  v1sel = vec_sel(p4i_ZERO, p4i_ONE, sgn);
-  prod_ = vec_add(prod_, v1sel);
-
-  // Merge the results back to the final vector.
-  prod = vec_sel(prod, prod_, sgn);
-
-  return prod;
-}
-*/
 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
 #ifndef __VSX__  // VSX actually provides a div instruction
@@ -370,8 +385,8 @@ template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, co
 }
 
 // for some weird raisons, it has to be overloaded for packet of integers
-template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); }
-template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
+template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a,b,c); }
+template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return a*b + c; }
 
 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_min(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
@@ -391,6 +406,10 @@ template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const
 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }
 
+template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return vec_round(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const  Packet4f& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }
+
 #ifdef _BIG_ENDIAN
 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
 {
@@ -418,12 +437,12 @@ template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
 // We also need ot redefine little endian loading of Packet4i/Packet4f using VSX
 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
 {
-  EIGEN_DEBUG_ALIGNED_LOAD
+  EIGEN_DEBUG_UNALIGNED_LOAD
   return (Packet4i) vec_vsx_ld((long)from & 15, (const int*) _EIGEN_ALIGNED_PTR(from));
 }
 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
 {
-  EIGEN_DEBUG_ALIGNED_LOAD
+  EIGEN_DEBUG_UNALIGNED_LOAD
   return (Packet4f) vec_vsx_ld((long)from & 15, (const float*) _EIGEN_ALIGNED_PTR(from));
 }
 #endif
@@ -494,16 +513,19 @@ template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet4f&
 }
 #endif
 
-#ifndef __VSX__
-template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
-template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
-#endif
+template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr)    { EIGEN_PPC_PREFETCH(addr); }
+template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr)    { EIGEN_PPC_PREFETCH(addr); }
 
-template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
-template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
+template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; }
+template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; }
 
-template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return (Packet4f)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE32); }
-template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return (Packet4i)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE32); }
+template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
+{
+  return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
+}
+template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
+{
+  return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32)); }
 
 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); }
@@ -511,10 +533,10 @@ template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs
 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
 {
   Packet4f b, sum;
-  b   = (Packet4f) vec_sld(a, a, 8);
-  sum = vec_add(a, b);
-  b   = (Packet4f) vec_sld(sum, sum, 4);
-  sum = vec_add(sum, b);
+  b   = vec_sld(a, a, 8);
+  sum = a + b;
+  b   = vec_sld(sum, sum, 4);
+  sum += b;
   return pfirst(sum);
 }
 
@@ -537,11 +559,11 @@ template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
 
   // Now do the summation:
   // Lines 0+1
-  sum[0] = vec_add(sum[0], sum[1]);
+  sum[0] = sum[0] + sum[1];
   // Lines 2+3
-  sum[1] = vec_add(sum[2], sum[3]);
+  sum[1] = sum[2] + sum[3];
   // Add the results
-  sum[0] = vec_add(sum[0], sum[1]);
+  sum[0] = sum[0] + sum[1];
 
   return sum[0];
 }
@@ -577,11 +599,11 @@ template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
 
   // Now do the summation:
   // Lines 0+1
-  sum[0] = vec_add(sum[0], sum[1]);
+  sum[0] = sum[0] + sum[1];
   // Lines 2+3
-  sum[1] = vec_add(sum[2], sum[3]);
+  sum[1] = sum[2] + sum[3];
   // Add the results
-  sum[0] = vec_add(sum[0], sum[1]);
+  sum[0] = sum[0] + sum[1];
 
   return sum[0];
 }
@@ -591,8 +613,8 @@ template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
 {
   Packet4f prod;
-  prod = pmul(a, (Packet4f)vec_sld(a, a, 8));
-  return pfirst(pmul(prod, (Packet4f)vec_sld(prod, prod, 4)));
+  prod = pmul(a, vec_sld(a, a, 8));
+  return pfirst(pmul(prod, vec_sld(prod, prod, 4)));
 }
 
 template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
@@ -716,33 +738,52 @@ ptranspose(PacketBlock<Packet4i,4>& kernel) {
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
+template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
+  Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
+  Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));
+  return vec_sel(elsePacket, thenPacket, mask);
+}
+
+template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
+  Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
+  Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));
+  return vec_sel(elsePacket, thenPacket, mask);
+}
+
 
 //---------- double ----------
 #ifdef __VSX__
 typedef __vector double              Packet2d;
 typedef __vector unsigned long long  Packet2ul;
 typedef __vector long long           Packet2l;
+#if EIGEN_COMP_CLANG
+typedef Packet2ul                    Packet2bl;
+#else
+typedef __vector __bool long         Packet2bl;
+#endif
 
-static Packet2l p2l_ZERO = (Packet2l) p4i_ZERO;
-static Packet2d p2d_ONE = { 1.0, 1.0 }; 
-static Packet2d p2d_ZERO = (Packet2d) p4f_ZERO;
-static Packet2d p2d_ZERO_ = { -0.0, -0.0 };
+static Packet2l  p2l_ONE  = { 1, 1 };
+static Packet2l  p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);
+static Packet2d  p2d_ONE  = { 1.0, 1.0 }; 
+static Packet2d  p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO);
+static Packet2d  p2d_ZERO_ = { -0.0, -0.0 };
 
 #ifdef _BIG_ENDIAN
-static Packet2d p2d_COUNTDOWN = (Packet2d) vec_sld((Packet16uc) p2d_ZERO, (Packet16uc) p2d_ONE, 8);
+static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ZERO), reinterpret_cast<Packet4f>(p2d_ONE), 8));
 #else
-static Packet2d p2d_COUNTDOWN = (Packet2d) vec_sld((Packet16uc) p2d_ONE, (Packet16uc) p2d_ZERO, 8);
+static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8));
 #endif
 
-static EIGEN_STRONG_INLINE Packet2d vec_splat_dbl(Packet2d& a, int index)
+template<int index> Packet2d vec_splat_dbl(Packet2d& a);
+
+template<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<0>(Packet2d& a)
 {
-  switch (index) {
-  case 0:
-    return (Packet2d) vec_perm(a, a, p16uc_PSET64_HI);
-  case 1:
-    return (Packet2d) vec_perm(a, a, p16uc_PSET64_LO);
-  }
-  return a;
+  return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_HI));
+}
+
+template<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<1>(Packet2d& a)
+{
+  return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_LO));
 }
 
 template<> struct packet_traits<double> : default_packet_traits
@@ -753,16 +794,41 @@ template<> struct packet_traits<double> : default_packet_traits
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size=2,
-    HasHalfPacket = 0,
+    HasHalfPacket = 1,
 
+    HasAdd  = 1,
+    HasSub  = 1,
+    HasMul  = 1,
     HasDiv  = 1,
+    HasMin  = 1,
+    HasMax  = 1,
+    HasAbs  = 1,
+    HasSin  = 0,
+    HasCos  = 0,
+    HasLog  = 0,
     HasExp  = 1,
-    HasSqrt = 0
+    HasSqrt = 1,
+    HasRsqrt = 1,
+    HasRound = 1,
+    HasFloor = 1,
+    HasCeil = 1,
+    HasNegate = 1,
+    HasBlend = 1
   };
 };
 
 template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
 
+inline std::ostream & operator <<(std::ostream & s, const Packet2l & v)
+{
+  union {
+    Packet2l   v;
+    int64_t n[2];
+  } vt;
+  vt.v = v;
+  s << vt.n[0] << ", " << vt.n[1];
+  return s;
+}
 
 inline std::ostream & operator <<(std::ostream & s, const Packet2d & v)
 {
@@ -776,28 +842,43 @@ inline std::ostream & operator <<(std::ostream & s, const Packet2d & v)
 }
 
 // Need to define them first or we get specialization after instantiation errors
-template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return (Packet2d) vec_ld(0, (const float *) from); } //FIXME
+template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
+{
+  EIGEN_DEBUG_ALIGNED_LOAD
+#ifdef __VSX__
+  return vec_vsx_ld(0, from);
+#else
+  return vec_ld(0, from);
+#endif
+}
 
-template<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st((Packet4f)from, 0, (float *)to); }
+template<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from)
+{
+  EIGEN_DEBUG_ALIGNED_STORE
+#ifdef __VSX__
+  vec_vsx_st(from, 0, to);
+#else
+  vec_st(from, 0, to);
+#endif
+}
 
 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) {
-  double EIGEN_ALIGN16 af[2];
-  af[0] = from;
-  Packet2d vc = pload<Packet2d>(af);
-  vc = vec_splat_dbl(vc, 0);
-  return vc;
+  Packet2d v = {from, from};
+  return v;
 }
+
 template<> EIGEN_STRONG_INLINE void
 pbroadcast4<Packet2d>(const double *a,
                       Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
 {
   a1 = pload<Packet2d>(a);
-  a0 = vec_splat_dbl(a1, 0);
-  a1 = vec_splat_dbl(a1, 1);
+  a0 = vec_splat_dbl<0>(a1);
+  a1 = vec_splat_dbl<1>(a1);
   a3 = pload<Packet2d>(a+2);
-  a2 = vec_splat_dbl(a3, 0);
-  a3 = vec_splat_dbl(a3, 1);
+  a2 = vec_splat_dbl<0>(a3);
+  a3 = vec_splat_dbl<1>(a3);
 }
+
 template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
 {
   double EIGEN_ALIGN16 af[2];
@@ -812,13 +893,14 @@ template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to,
   to[0*stride] = af[0];
   to[1*stride] = af[1];
 }
-template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return vec_add(pset1<Packet2d>(a), p2d_COUNTDOWN); }
 
-template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_add(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return pset1<Packet2d>(a) + p2d_COUNTDOWN; }
+
+template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return a + b; }
 
-template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_sub(a,b); }
+template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return a - b; }
 
-template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return psub<Packet2d>(p2d_ZERO, a); }
+template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return p2d_ZERO - a; }
 
 template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
 
@@ -840,17 +922,22 @@ template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const
 
 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }
 
+template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const  Packet2d& a) { return vec_ceil(a); }
+template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }
+
 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
 {
   EIGEN_DEBUG_ALIGNED_LOAD
-  return (Packet2d) vec_vsx_ld((long)from & 15, (const float*) _EIGEN_ALIGNED_PTR(from));
+  return (Packet2d) vec_vsx_ld((long)from & 15, (const double*) _EIGEN_ALIGNED_PTR(from));
 }
+
 template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)
 {
   Packet2d p;
   if((ptrdiff_t(from) % 16) == 0)  p = pload<Packet2d>(from);
   else                             p = ploadu<Packet2d>(from);
-  return vec_perm(p, p, p16uc_PSET64_HI);
+  return vec_splat_dbl<0>(p);
 }
 
 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from)
@@ -859,32 +946,34 @@ template<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d&
   vec_vsx_st((Packet4f)from, (long)to & 15, (float*) _EIGEN_ALIGNED_PTR(to));
 }
 
-template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { vec_dstt((const float *) addr, DST_CTRL(2,2,32), DST_CHAN); }
+template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); }
 
-template<> EIGEN_STRONG_INLINE double  pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore(x, a); return x[0]; }
-
-template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) { return (Packet2d)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE64); }
+template<> EIGEN_STRONG_INLINE double  pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore<double>(x, a); return x[0]; }
 
+template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
+{
+  return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));
+}
 template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); }
 
 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
 {
   Packet2d b, sum;
-  b   = (Packet2d) vec_sld((Packet4ui) a, (Packet4ui)a, 8);
-  sum = vec_add(a, b);
-  return pfirst(sum);
+  b   = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8));
+  sum = a + b;
+  return pfirst<Packet2d>(sum);
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
 {
   Packet2d v[2], sum;
-  v[0] = vec_add(vecs[0], (Packet2d) vec_sld((Packet4ui) vecs[0], (Packet4ui) vecs[0], 8));
-  v[1] = vec_add(vecs[1], (Packet2d) vec_sld((Packet4ui) vecs[1], (Packet4ui) vecs[1], 8));
+  v[0] = vecs[0] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[0]), reinterpret_cast<Packet4f>(vecs[0]), 8));
+  v[1] = vecs[1] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[1]), reinterpret_cast<Packet4f>(vecs[1]), 8));
  
 #ifdef _BIG_ENDIAN
- sum = (Packet2d) vec_sld((Packet4ui) v[0], (Packet4ui) v[1], 8);
+  sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[0]), reinterpret_cast<Packet4f>(v[1]), 8));
 #else
-  sum = (Packet2d) vec_sld((Packet4ui) v[1], (Packet4ui) v[0], 8);
+  sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[1]), reinterpret_cast<Packet4f>(v[0]), 8));
 #endif
 
   return sum;
@@ -893,19 +982,19 @@ template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
 // mul
 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
 {
-  return pfirst(pmul(a, (Packet2d)vec_sld((Packet4ui) a, (Packet4ui) a, 8)));
+  return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
 }
 
 // min
 template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
 {
-  return pfirst(vec_min(a, (Packet2d) vec_sld((Packet4ui) a, (Packet4ui) a, 8)));
+  return pfirst(pmin(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
 }
 
 // max
 template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
 {
-  return pfirst(vec_max(a, (Packet2d) vec_sld((Packet4ui) a, (Packet4ui) a, 8)));
+  return pfirst(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
 }
 
 template<int Offset>
@@ -915,9 +1004,9 @@ struct palign_impl<Offset,Packet2d>
   {
     if (Offset == 1)
 #ifdef _BIG_ENDIAN
-      first = (Packet2d) vec_sld((Packet4ui) first, (Packet4ui) second, 8);
+      first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(first), reinterpret_cast<Packet4ui>(second), 8));
 #else
-      first = (Packet2d) vec_sld((Packet4ui) second, (Packet4ui) first, 8);
+      first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(second), reinterpret_cast<Packet4ui>(first), 8));
 #endif
   }
 };
@@ -931,6 +1020,11 @@ ptranspose(PacketBlock<Packet2d,2>& kernel) {
   kernel.packet[1] = t1;
 }
 
+template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
+  Packet2l select = { ifPacket.select[0], ifPacket.select[1] };
+  Packet2bl mask = vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE));
+  return vec_sel(elsePacket, thenPacket, mask);
+}
 #endif // __VSX__
 } // end namespace internal
 
diff --git a/Eigen/src/Core/arch/NEON/Complex.h b/Eigen/src/Core/arch/NEON/Complex.h
index aa9797885..3e121dce5 100644
--- a/Eigen/src/Core/arch/NEON/Complex.h
+++ b/Eigen/src/Core/arch/NEON/Complex.h
@@ -2,6 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
diff --git a/Eigen/src/Core/arch/NEON/PacketMath.h b/Eigen/src/Core/arch/NEON/PacketMath.h
index e1247696d..2a8f58d74 100644
--- a/Eigen/src/Core/arch/NEON/PacketMath.h
+++ b/Eigen/src/Core/arch/NEON/PacketMath.h
@@ -2,7 +2,7 @@
 // for linear algebra.
 //
 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2010 Konstantinos Margaritis <markos@codex.gr>
+// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
 // Heavily based on Gael's SSE version.
 //
 // This Source Code Form is subject to the terms of the Mozilla
diff --git a/Eigen/src/Core/arch/ZVector/Complex.h b/Eigen/src/Core/arch/ZVector/Complex.h
index 9a8735ac1..e9d83eca6 100644
--- a/Eigen/src/Core/arch/ZVector/Complex.h
+++ b/Eigen/src/Core/arch/ZVector/Complex.h
@@ -57,21 +57,6 @@ template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<
 template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)
 { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
 
-template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride)
-{
-  std::complex<double> EIGEN_ALIGN16 af[2];
-  af[0] = from[0*stride];
-  af[1] = from[1*stride];
-  return pload<Packet1cd>(af);
-}
-template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride)
-{
-  std::complex<double> EIGEN_ALIGN16 af[2];
-  pstore<std::complex<double> >(af, from);
-  to[0*stride] = af[0];
-  to[1*stride] = af[1];
-}
-
 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
 template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }