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 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // 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
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 #ifndef EIGEN_PACKET_MATH_ALTIVEC_H
 #define EIGEN_PACKET_MATH_ALTIVEC_H
 
 namespace RivetEigen {
 
 namespace internal {
 
 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
 #endif
 
 #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
 #define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
 #endif
 
 // NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS  32
 #endif
 
 typedef __vector float                   Packet4f;
 typedef __vector int                     Packet4i;
 typedef __vector unsigned int            Packet4ui;
 typedef __vector __bool int              Packet4bi;
 typedef __vector short int               Packet8s;
 typedef __vector unsigned short int      Packet8us;
 typedef __vector signed char             Packet16c;
 typedef __vector unsigned char           Packet16uc;
 typedef eigen_packet_wrapper<__vector unsigned short int,0> Packet8bf;
 
 // We don't want to write the same code all the time, but we need to reuse the constants
 // 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 = {X, X, X, X}
 
 #define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
   Packet4i p4i_##NAME = vec_splat_s32(X)
 
 #define _EIGEN_DECLARE_CONST_FAST_Packet4ui(NAME,X) \
   Packet4ui p4ui_##NAME = {X, X, X, X}
 
 #define _EIGEN_DECLARE_CONST_FAST_Packet8us(NAME,X) \
   Packet8us p8us_##NAME = {X, X, X, X, X, X, X, X}
 
 #define _EIGEN_DECLARE_CONST_FAST_Packet16uc(NAME,X) \
   Packet16uc p16uc_##NAME = {X, X, X, X, X, X, X, X, X, X, X, X, X, X, X, X}
 
 #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
   Packet4f p4f_##NAME = pset1<Packet4f>(X)
 
 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
   Packet4i p4i_##NAME = pset1<Packet4i>(X)
 
 #define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
   Packet2d p2d_##NAME = pset1<Packet2d>(X)
 
 #define _EIGEN_DECLARE_CONST_Packet2l(NAME,X) \
   Packet2l p2l_##NAME = pset1<Packet2l>(X)
 
 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
   const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))
 
 #define DST_CHAN 1
 #define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
 #define __UNPACK_TYPE__(PACKETNAME) typename unpacket_traits<PACKETNAME>::type 
 
 // 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,}
 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1); //{ 1, 1, 1, 1}
 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 _EIGEN_DECLARE_CONST_FAST_Packet4ui(SIGN, 0x80000000u);
 static _EIGEN_DECLARE_CONST_FAST_Packet4ui(PREV0DOT5, 0x3EFFFFFFu);
 static _EIGEN_DECLARE_CONST_FAST_Packet8us(ONE,1); //{ 1, 1, 1, 1, 1, 1, 1, 1}
 static _EIGEN_DECLARE_CONST_FAST_Packet16uc(ONE,1);
 static Packet4f p4f_MZERO = (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 };
 static Packet8s  p8s_COUNTDOWN  = { 0, 1, 2, 3, 4, 5, 6, 7 };
 static Packet8us p8us_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7 };
 
 static Packet16c  p16c_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7,
                                     8, 9, 10, 11, 12, 13, 14, 15};
 static Packet16uc p16uc_COUNTDOWN = { 0, 1, 2, 3, 4, 5, 6, 7, 
                                     8, 9, 10, 11, 12, 13, 14, 15};
 
 static Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };
 static Packet16uc p16uc_REVERSE16 = { 14,15, 12,13, 10,11, 8,9, 6,7, 4,5, 2,3, 0,1 };
 static Packet16uc p16uc_REVERSE8 = { 15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 };
 
 static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
 static Packet16uc p16uc_DUPLICATE16_HI = { 0,1,0,1, 2,3,2,3, 4,5,4,5, 6,7,6,7 };
 static Packet16uc p16uc_DUPLICATE8_HI = { 0,0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, 7,7 };
 static const Packet16uc p16uc_DUPLICATE16_EVEN= { 0,1 ,0,1, 4,5, 4,5, 8,9, 8,9, 12,13, 12,13 };
 static const Packet16uc p16uc_DUPLICATE16_ODD = { 2,3 ,2,3, 6,7, 6,7, 10,11, 10,11, 14,15, 14,15 };
 
 static Packet16uc p16uc_QUADRUPLICATE16_HI = { 0,1,0,1,0,1,0,1, 2,3,2,3,2,3,2,3 };
 
 // Handle endianness properly while loading constants
 // Define global static constants:
 #ifdef _BIG_ENDIAN
 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};
 #else
 static Packet16uc p16uc_FORWARD = p16uc_REVERSE32;
 static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
 static Packet16uc p16uc_PSET32_WODD = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 1), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 3), 8);//{ 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 };
 static Packet16uc p16uc_PSET32_WEVEN = vec_sld((Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 0), (Packet16uc) vec_splat((Packet4ui)p16uc_FORWARD, 2), 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(vec_splat((Packet16uc) vec_abs(p4i_MINUS16), 0), (Packet16uc)p4i_ZERO, 8);      //{ 0,0,0,0, 0,0,0,0, 16,16,16,16, 16,16,16,16};
 #endif // _BIG_ENDIAN
 
 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 = 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 };
 
 #ifdef _BIG_ENDIAN
 static Packet16uc p16uc_COMPLEX32_REV2 = vec_sld(p16uc_FORWARD, p16uc_FORWARD, 8);                                            //{ 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
 #else
 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;
   typedef Packet4f half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 4,
     HasHalfPacket = 1,
 
     HasAdd = 1,
     HasSub = 1,
     HasMul = 1,
     HasDiv = 1,
     HasMin = 1,
     HasMax = 1,
     HasAbs = 1,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
     HasLog = 1,
     HasExp = 1,
 #ifdef __VSX__
     HasSqrt = 1,
 #if !EIGEN_COMP_CLANG
     HasRsqrt = 1,
 #else
     HasRsqrt = 0,
 #endif
 #else
     HasSqrt = 0,
     HasRsqrt = 0,
     HasTanh = EIGEN_FAST_MATH,
     HasErf = EIGEN_FAST_MATH,
 #endif
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
     HasRint = 1,
     HasNegate = 1,
     HasBlend = 1
   };
 };
 template <>
 struct packet_traits<bfloat16> : default_packet_traits {
   typedef Packet8bf type;
   typedef Packet8bf half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 0,
 
     HasAdd = 1,
     HasSub = 1,
     HasMul = 1,
     HasDiv = 1,
     HasMin = 1,
     HasMax = 1,
     HasAbs = 1,
     HasSin = EIGEN_FAST_MATH,
     HasCos = EIGEN_FAST_MATH,
     HasLog = 1,
     HasExp = 1,
 #ifdef __VSX__
     HasSqrt = 1,
 #if !EIGEN_COMP_CLANG
     HasRsqrt = 1,
 #else
     HasRsqrt = 0,
 #endif
 #else
     HasSqrt = 0,
     HasRsqrt = 0,
     HasTanh = EIGEN_FAST_MATH,
     HasErf = EIGEN_FAST_MATH,
 #endif
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
     HasRint = 1,
     HasNegate = 1,
     HasBlend = 1
   };
 };
 
 template <>
 struct packet_traits<int> : default_packet_traits {
   typedef Packet4i type;
   typedef Packet4i half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 4,
     HasHalfPacket = 0,
 
     HasAdd   = 1,
     HasSub   = 1,
     HasShift = 1,
     HasMul   = 1,
     HasDiv   = 0,
     HasBlend = 1
   };
 };
 
 template <>
 struct packet_traits<short int> : default_packet_traits {
   typedef Packet8s type;
   typedef Packet8s half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 0,
 
     HasAdd  = 1,
     HasSub  = 1,
     HasMul  = 1,
     HasDiv  = 0,
     HasBlend = 1
   };
 };
 
 template <>
 struct packet_traits<unsigned short int> : default_packet_traits {
   typedef Packet8us type;
   typedef Packet8us half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 8,
     HasHalfPacket = 0,
 
     HasAdd  = 1,
     HasSub  = 1,
     HasMul  = 1,
     HasDiv  = 0,
     HasBlend = 1
   };
 };
 
 template <>
 struct packet_traits<signed char> : default_packet_traits {
   typedef Packet16c type;
   typedef Packet16c half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 16,
     HasHalfPacket = 0,
 
     HasAdd  = 1,
     HasSub  = 1,
     HasMul  = 1,
     HasDiv  = 0,
     HasBlend = 1
   };
 };
 
 template <>
 struct packet_traits<unsigned char> : default_packet_traits {
   typedef Packet16uc type;
   typedef Packet16uc half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size = 16,
     HasHalfPacket = 0,
 
     HasAdd  = 1,
     HasSub  = 1,
     HasMul  = 1,
     HasDiv  = 0,
     HasBlend = 1
   };
 };
 
 template<> struct unpacket_traits<Packet4f>
 {
   typedef float     type;
   typedef Packet4f  half;
   typedef Packet4i  integer_packet;
   enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 template<> struct unpacket_traits<Packet4i>
 {
   typedef int       type;
   typedef Packet4i  half;
   enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 template<> struct unpacket_traits<Packet8s>
 {
   typedef short int type;
   typedef Packet8s  half;
   enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 template<> struct unpacket_traits<Packet8us>
 {
   typedef unsigned short int type;
   typedef Packet8us          half;
   enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 
 template<> struct unpacket_traits<Packet16c>
 {
   typedef signed char type;
   typedef Packet16c  half;
   enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 template<> struct unpacket_traits<Packet16uc>
 {
   typedef unsigned char type;
   typedef Packet16uc  half;
   enum {size=16, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 
 template<> struct unpacket_traits<Packet8bf>
 {
   typedef bfloat16 type;
   typedef Packet8bf          half;
   enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false};
 };
 inline std::ostream & operator <<(std::ostream & s, const Packet16c & v)
 {
   union {
     Packet16c   v;
     signed char n[16];
   } vt;
   vt.v = v;
   for (int i=0; i< 16; i++)
     s << vt.n[i] << ", ";
   return s;
 }
 
 inline std::ostream & operator <<(std::ostream & s, const Packet16uc & v)
 {
   union {
     Packet16uc   v;
     unsigned char n[16];
   } vt;
   vt.v = v;
   for (int i=0; i< 16; i++)
     s << vt.n[i] << ", ";
   return s;
 }
 
 inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
 {
   union {
     Packet4f   v;
     float n[4];
   } vt;
   vt.v = v;
   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
   return s;
 }
 
 inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
 {
   union {
     Packet4i   v;
     int n[4];
   } vt;
   vt.v = v;
   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
   return s;
 }
 
 inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
 {
   union {
     Packet4ui   v;
     unsigned int n[4];
   } vt;
   vt.v = v;
   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
   return s;
 }
 
 template <typename Packet>
 EIGEN_STRONG_INLINE Packet pload_common(const __UNPACK_TYPE__(Packet)* from)
 {
   // some versions of GCC throw "unused-but-set-parameter".
   // ignoring these warnings for now.
   EIGEN_UNUSED_VARIABLE(from);
   EIGEN_DEBUG_ALIGNED_LOAD
 #ifdef __VSX__
   return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(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)
 {
   return pload_common<Packet4f>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from)
 {
   return pload_common<Packet4i>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8s pload<Packet8s>(const short int* from)
 {
   return pload_common<Packet8s>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8us pload<Packet8us>(const unsigned short int* from)
 {
   return pload_common<Packet8us>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16c pload<Packet16c>(const signed char*     from)
 {
   return pload_common<Packet16c>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16uc pload<Packet16uc>(const unsigned char*     from)
 {
   return pload_common<Packet16uc>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pload<Packet8bf>(const bfloat16*     from)
 {
   return pload_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
 }
 
 template <typename Packet>
 EIGEN_STRONG_INLINE void pstore_common(__UNPACK_TYPE__(Packet)* to, const Packet& from){
   // some versions of GCC throw "unused-but-set-parameter" (float *to).
   // ignoring these warnings for now.
   EIGEN_UNUSED_VARIABLE(to);
   EIGEN_DEBUG_ALIGNED_STORE
 #ifdef __VSX__
   vec_xst(from, 0, to);
 #else
   vec_st(from, 0, to);
 #endif
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from)
 {
   pstore_common<Packet4f>(to, from);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from)
 {
   pstore_common<Packet4i>(to, from);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<short int>(short int*       to, const Packet8s& from)
 {
   pstore_common<Packet8s>(to, from);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<unsigned short int>(unsigned short int*       to, const Packet8us& from)
 {
   pstore_common<Packet8us>(to, from);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16*       to, const Packet8bf& from)
 {
   pstore_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<signed char>(signed char*       to, const Packet16c& from)
 {
   pstore_common<Packet16c>(to, from);
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<unsigned char>(unsigned char*       to, const Packet16uc& from)
 {
   pstore_common<Packet16uc>(to, from);
 }
 
 template<typename Packet>
 EIGEN_STRONG_INLINE Packet pset1_size4(const __UNPACK_TYPE__(Packet)& from)
 {
   Packet v = {from, from, from, from};
   return v;
 }
 
 template<typename Packet>
 EIGEN_STRONG_INLINE Packet pset1_size8(const __UNPACK_TYPE__(Packet)& from)
 {
   Packet v = {from, from, from, from, from, from, from, from};
   return v;
 }
 
 template<typename Packet>
 EIGEN_STRONG_INLINE Packet pset1_size16(const __UNPACK_TYPE__(Packet)& from)
 {
   Packet v = {from, from, from, from, from, from, from, from, from, from, from, from, from, from, from, from};
   return v;
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) {
   return pset1_size4<Packet4f>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
   return pset1_size4<Packet4i>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8s pset1<Packet8s>(const short int&    from)   {
   return pset1_size8<Packet8s>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8us pset1<Packet8us>(const unsigned short int&    from)   {
   return pset1_size8<Packet8us>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16c pset1<Packet16c>(const signed char&    from)   {
   return pset1_size16<Packet16c>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16uc pset1<Packet16uc>(const unsigned char&    from)   {
   return pset1_size16<Packet16uc>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(unsigned int from) {
   return reinterpret_cast<Packet4f>(pset1<Packet4i>(from));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pset1<Packet8bf>(const bfloat16&    from)   {
   return pset1_size8<Packet8us>(reinterpret_cast<const unsigned short int&>(from));
 }
 
 template<typename Packet> EIGEN_STRONG_INLINE void
 pbroadcast4_common(const __UNPACK_TYPE__(Packet) *a,
                       Packet& a0, Packet& a1, Packet& a2, Packet& a3)
 {
   a3 = pload<Packet>(a);
   a0 = vec_splat(a3, 0);
   a1 = vec_splat(a3, 1);
   a2 = vec_splat(a3, 2);
   a3 = vec_splat(a3, 3);
 }
 
 template<> EIGEN_STRONG_INLINE void
 pbroadcast4<Packet4f>(const float *a,
                       Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
 {
   pbroadcast4_common<Packet4f>(a, a0, a1, a2, a3);
 }
 template<> EIGEN_STRONG_INLINE void
 pbroadcast4<Packet4i>(const int *a,
                       Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)
 {
   pbroadcast4_common<Packet4i>(a, a0, a1, a2, a3);
 }
 
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_common(const __UNPACK_TYPE__(Packet)* from, Index stride)
 {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[4];
   a[0] = from[0*stride];
   a[1] = from[1*stride];
   a[2] = from[2*stride];
   a[3] = from[3*stride];
   return pload<Packet>(a);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
 {
   return pgather_common<Packet4f>(from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
 {
   return pgather_common<Packet4i>(from, stride);
 }
 
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_size8(const __UNPACK_TYPE__(Packet)* from, Index stride)
 {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[8];
   a[0] = from[0*stride];
   a[1] = from[1*stride];
   a[2] = from[2*stride];
   a[3] = from[3*stride];
   a[4] = from[4*stride];
   a[5] = from[5*stride];
   a[6] = from[6*stride];
   a[7] = from[7*stride];
   return pload<Packet>(a);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet8s pgather<short int, Packet8s>(const short int* from, Index stride)
 {
   return pgather_size8<Packet8s>(from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet8us pgather<unsigned short int, Packet8us>(const unsigned short int* from, Index stride)
 {
   return pgather_size8<Packet8us>(from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet8bf pgather<bfloat16, Packet8bf>(const bfloat16* from, Index stride)
 {
   return pgather_size8<Packet8bf>(from, stride);
 }
 
 template<typename Packet> EIGEN_DEVICE_FUNC inline Packet pgather_size16(const __UNPACK_TYPE__(Packet)* from, Index stride)
 {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[16];
   a[0] = from[0*stride];
   a[1] = from[1*stride];
   a[2] = from[2*stride];
   a[3] = from[3*stride];
   a[4] = from[4*stride];
   a[5] = from[5*stride];
   a[6] = from[6*stride];
   a[7] = from[7*stride];
   a[8] = from[8*stride];
   a[9] = from[9*stride];
   a[10] = from[10*stride];
   a[11] = from[11*stride];
   a[12] = from[12*stride];
   a[13] = from[13*stride];
   a[14] = from[14*stride];
   a[15] = from[15*stride];
   return pload<Packet>(a);
 }
 
 
 template<> EIGEN_DEVICE_FUNC inline Packet16c pgather<signed char, Packet16c>(const signed char* from, Index stride)
 {
   return pgather_size16<Packet16c>(from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet16uc pgather<unsigned char, Packet16uc>(const unsigned char* from, Index stride)
 {
   return pgather_size16<Packet16uc>(from, stride);
 }
 
 template<typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_size4(__UNPACK_TYPE__(Packet)* to, const Packet& from, Index stride)
 {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[4];
   pstore<__UNPACK_TYPE__(Packet)>(a, from);
   to[0*stride] = a[0];
   to[1*stride] = a[1];
   to[2*stride] = a[2];
   to[3*stride] = a[3];
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
 {
   pscatter_size4<Packet4f>(to, from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
 {
   pscatter_size4<Packet4i>(to, from, stride);
 }
 
 template<typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_size8(__UNPACK_TYPE__(Packet)* to, const Packet& from, Index stride)
 {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[8];
   pstore<__UNPACK_TYPE__(Packet)>(a, from);
   to[0*stride] = a[0];
   to[1*stride] = a[1];
   to[2*stride] = a[2];
   to[3*stride] = a[3];
   to[4*stride] = a[4];
   to[5*stride] = a[5];
   to[6*stride] = a[6];
   to[7*stride] = a[7];
 }
 
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<short int, Packet8s>(short int* to, const Packet8s& from, Index stride)
 {
   pscatter_size8<Packet8s>(to, from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<unsigned short int, Packet8us>(unsigned short int* to, const Packet8us& from, Index stride)
 {
   pscatter_size8<Packet8us>(to, from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<bfloat16, Packet8bf>(bfloat16* to, const Packet8bf& from, Index stride)
 {
   pscatter_size8<Packet8bf>(to, from, stride);
 }
 
 template<typename Packet> EIGEN_DEVICE_FUNC inline void pscatter_size16(__UNPACK_TYPE__(Packet)* to, const Packet& from, Index stride)
 {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) a[16];
   pstore<__UNPACK_TYPE__(Packet)>(a, from);
   to[0*stride] = a[0];
   to[1*stride] = a[1];
   to[2*stride] = a[2];
   to[3*stride] = a[3];
   to[4*stride] = a[4];
   to[5*stride] = a[5];
   to[6*stride] = a[6];
   to[7*stride] = a[7];
   to[8*stride] = a[8];
   to[9*stride] = a[9];
   to[10*stride] = a[10];
   to[11*stride] = a[11];
   to[12*stride] = a[12];
   to[13*stride] = a[13];
   to[14*stride] = a[14];
   to[15*stride] = a[15];
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<signed char, Packet16c>(signed char* to, const Packet16c& from, Index stride)
 {
   pscatter_size16<Packet16c>(to, from, stride);
 }
 
 template<> EIGEN_DEVICE_FUNC inline void pscatter<unsigned char, Packet16uc>(unsigned char* to, const Packet16uc& from, Index stride)
 {
   pscatter_size16<Packet16uc>(to, from, stride);
 }
 
 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 Packet8s   plset<Packet8s>(const short int& a) { return pset1<Packet8s>(a) + p8s_COUNTDOWN; }
 template<> EIGEN_STRONG_INLINE Packet8us  plset<Packet8us>(const unsigned short int& a) { return pset1<Packet8us>(a) + p8us_COUNTDOWN; }
 template<> EIGEN_STRONG_INLINE Packet16c  plset<Packet16c>(const signed char& a)   { return pset1<Packet16c>(a) + p16c_COUNTDOWN; }
 template<> EIGEN_STRONG_INLINE Packet16uc plset<Packet16uc>(const unsigned char& a)   { return pset1<Packet16uc>(a) + p16uc_COUNTDOWN; }
 
 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 Packet4ui   padd<Packet4ui>  (const Packet4ui&   a, const Packet4ui&   b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet8s   padd<Packet8s>  (const Packet8s&   a, const Packet8s&   b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet8us  padd<Packet8us> (const Packet8us&  a, const Packet8us&  b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet16c  padd<Packet16c> (const Packet16c&  a, const Packet16c&  b) { return a + b; }
 template<> EIGEN_STRONG_INLINE Packet16uc padd<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return 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 Packet8s   psub<Packet8s>  (const Packet8s&   a, const Packet8s&   b) { return a - b; }
 template<> EIGEN_STRONG_INLINE Packet8us  psub<Packet8us> (const Packet8us&  a, const Packet8us&  b) { return a - b; }
 template<> EIGEN_STRONG_INLINE Packet16c  psub<Packet16c> (const Packet16c&  a, const Packet16c&  b) { return a - b; }
 template<> EIGEN_STRONG_INLINE Packet16uc psub<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return a - b; }
 
 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_MZERO); }
 template<> EIGEN_STRONG_INLINE Packet4i   pmul<Packet4i>  (const Packet4i&   a, const Packet4i&   b) { return a * b; }
 template<> EIGEN_STRONG_INLINE Packet8s   pmul<Packet8s>  (const Packet8s&   a, const Packet8s&   b) { return vec_mul(a,b); }
 template<> EIGEN_STRONG_INLINE Packet8us  pmul<Packet8us> (const Packet8us&  a, const Packet8us&  b) { return vec_mul(a,b); }
 template<> EIGEN_STRONG_INLINE Packet16c  pmul<Packet16c> (const Packet16c&  a, const Packet16c&  b) { return vec_mul(a,b); }
 template<> EIGEN_STRONG_INLINE Packet16uc pmul<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_mul(a,b); }
 
 
 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
 #ifndef __VSX__  // VSX actually provides a div instruction
   Packet4f t, y_0, y_1;
 
   // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
   y_0 = vec_re(b);
 
   // Do one Newton-Raphson iteration to get the needed accuracy
   t   = vec_nmsub(y_0, b, p4f_ONE);
   y_1 = vec_madd(y_0, t, y_0);
 
   return vec_madd(a, y_1, p4f_MZERO);
 #else
   return vec_div(a, b);
 #endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
 { eigen_assert(false && "packet integer division are not supported by AltiVec");
   return pset1<Packet4i>(0);
 }
 
 // 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 a*b + c; }
 template<> EIGEN_STRONG_INLINE Packet8s pmadd(const Packet8s& a, const Packet8s& b, const Packet8s& c) { return vec_madd(a,b,c); }
 template<> EIGEN_STRONG_INLINE Packet8us pmadd(const Packet8us& a, const Packet8us& b, const Packet8us& c) { return vec_madd(a,b,c); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
   #ifdef __VSX__
   // NOTE: about 10% slower than vec_min, but consistent with std::min and SSE regarding NaN
   Packet4f ret;
   __asm__ ("xvcmpgesp %x0,%x1,%x2\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
   return ret;
   #else
   return vec_min(a, b);
   #endif
 }
 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8s pmin<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_min(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8us pmin<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_min(a, b); }
 template<> EIGEN_STRONG_INLINE Packet16c pmin<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_min(a, b); }
 template<> EIGEN_STRONG_INLINE Packet16uc pmin<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_min(a, b); }
 
 
 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b)
 {
   #ifdef __VSX__
   // NOTE: about 10% slower than vec_max, but consistent with std::max and SSE regarding NaN
   Packet4f ret;
   __asm__ ("xvcmpgtsp %x0,%x2,%x1\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
   return ret;
   #else
   return vec_max(a, b);
   #endif
 }
 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8s pmax<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_max(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8us pmax<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_max(a, b); }
 template<> EIGEN_STRONG_INLINE Packet16c pmax<Packet16c>(const Packet16c& a, const Packet16c& b) { return vec_max(a, b); }
 template<> EIGEN_STRONG_INLINE Packet16uc pmax<Packet16uc>(const Packet16uc& a, const Packet16uc& b) { return vec_max(a, b); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_eq(const Packet4f& a, const Packet4f& b) { return reinterpret_cast<Packet4f>(vec_cmpeq(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f& a, const Packet4f& b) {
   Packet4f c = reinterpret_cast<Packet4f>(vec_cmpge(a,b));
   return vec_nor(c,c);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_le(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_lt(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet4i pcmp_eq(const Packet4i& a, const Packet4i& b) { return reinterpret_cast<Packet4i>(vec_cmpeq(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8s pcmp_le(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8s pcmp_lt(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8s pcmp_eq(const Packet8s& a, const Packet8s& b) { return reinterpret_cast<Packet8s>(vec_cmpeq(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8us pcmp_le(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8us pcmp_lt(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet8us pcmp_eq(const Packet8us& a, const Packet8us& b) { return reinterpret_cast<Packet8us>(vec_cmpeq(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16c pcmp_le(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16c pcmp_lt(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16c pcmp_eq(const Packet16c& a, const Packet16c& b) { return reinterpret_cast<Packet16c>(vec_cmpeq(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16uc pcmp_le(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16uc pcmp_lt(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet16uc pcmp_eq(const Packet16uc& a, const Packet16uc& b) { return reinterpret_cast<Packet16uc>(vec_cmpeq(a,b)); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4ui pand<Packet4ui>(const Packet4ui& a, const Packet4ui& b) { return vec_and(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8us pand<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_and(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8bf pand<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   return pand<Packet8us>(a, b);
 }
 
 
 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8s por<Packet8s>(const Packet8s& a, const Packet8s& b) { return vec_or(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8us por<Packet8us>(const Packet8us& a, const Packet8us& b) { return vec_or(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8bf por<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   return por<Packet8us>(a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
 template<> EIGEN_STRONG_INLINE Packet8bf pxor<Packet8bf>(const Packet8bf& a, const Packet8bf& b) { 
   return pxor<Packet8us>(a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_andc(a, b); }
 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_andc(a, b); }
 
 template<> EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b) {
   return vec_sel(b, a, reinterpret_cast<Packet4ui>(mask));
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a)
 {
     Packet4f t = vec_add(reinterpret_cast<Packet4f>(vec_or(vec_and(reinterpret_cast<Packet4ui>(a), p4ui_SIGN), p4ui_PREV0DOT5)), a);
     Packet4f res;
 
 #ifdef __VSX__
     __asm__("xvrspiz %x0, %x1\n\t"
         : "=&wa" (res)
         : "wa" (t));
 #else
     __asm__("vrfiz %0, %1\n\t"
         : "=v" (res)
         : "v" (t));
 #endif
 
     return res;
 }
 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); }
 template<> EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a)
 {
     Packet4f res;
 
     __asm__("xvrspic %x0, %x1\n\t"
         : "=&wa" (res)
         : "wa" (a));
 
     return res;
 }
 
 template<typename Packet> EIGEN_STRONG_INLINE Packet ploadu_common(const __UNPACK_TYPE__(Packet)* from)
 {
   EIGEN_DEBUG_ALIGNED_LOAD
 #ifdef _BIG_ENDIAN
   Packet16uc MSQ, LSQ;
   Packet16uc mask;
   MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
   LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
   mask = vec_lvsl(0, from);                        // create the permute mask
   //TODO: Add static_cast here
   return (Packet) vec_perm(MSQ, LSQ, mask);           // align the data
 #else
   EIGEN_DEBUG_UNALIGNED_LOAD
   return vec_xl(0, const_cast<__UNPACK_TYPE__(Packet)*>(from));
 #endif
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
 {
   return ploadu_common<Packet4f>(from);
 }
 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
 {
   return ploadu_common<Packet4i>(from);
 }
 template<> EIGEN_STRONG_INLINE Packet8s ploadu<Packet8s>(const short int* from)
 {
   return ploadu_common<Packet8s>(from);
 }
 template<> EIGEN_STRONG_INLINE Packet8us ploadu<Packet8us>(const unsigned short int* from)
 {
   return ploadu_common<Packet8us>(from);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf ploadu<Packet8bf>(const bfloat16* from)
 {
   return ploadu_common<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
 }
 template<> EIGEN_STRONG_INLINE Packet16c ploadu<Packet16c>(const signed char* from)
 {
   return ploadu_common<Packet16c>(from);
 }
 template<> EIGEN_STRONG_INLINE Packet16uc ploadu<Packet16uc>(const unsigned char* from)
 {
   return ploadu_common<Packet16uc>(from);
 }
 
 template<typename Packet> EIGEN_STRONG_INLINE Packet ploaddup_common(const __UNPACK_TYPE__(Packet)*   from)
 {
   Packet p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet>(from);
   else                                  p = ploadu<Packet>(from);
   return vec_perm(p, p, p16uc_DUPLICATE32_HI);
 }
 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
 {
   return ploaddup_common<Packet4f>(from);
 }
 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
 {
   return ploaddup_common<Packet4i>(from);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8s ploaddup<Packet8s>(const short int*     from)
 {
   Packet8s p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet8s>(from);
   else                                  p = ploadu<Packet8s>(from);
   return vec_perm(p, p, p16uc_DUPLICATE16_HI);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8us ploaddup<Packet8us>(const unsigned short int*     from)
 {
   Packet8us p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet8us>(from);
   else                                  p = ploadu<Packet8us>(from);
   return vec_perm(p, p, p16uc_DUPLICATE16_HI);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8s ploadquad<Packet8s>(const short int*     from)
 {
   Packet8s p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet8s>(from);
   else                                  p = ploadu<Packet8s>(from);
   return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8us ploadquad<Packet8us>(const unsigned short int*     from)
 {
   Packet8us p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet8us>(from);
   else                                  p = ploadu<Packet8us>(from);
   return vec_perm(p, p, p16uc_QUADRUPLICATE16_HI);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf ploadquad<Packet8bf>(const bfloat16*     from)
 {
   return ploadquad<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
 }
 
 template<> EIGEN_STRONG_INLINE Packet16c ploaddup<Packet16c>(const signed char*     from)
 {
   Packet16c p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet16c>(from);
   else                                  p = ploadu<Packet16c>(from);
   return vec_perm(p, p, p16uc_DUPLICATE8_HI);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16uc ploaddup<Packet16uc>(const unsigned char*     from)
 {
   Packet16uc p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet16uc>(from);
   else                                  p = ploadu<Packet16uc>(from);
   return vec_perm(p, p, p16uc_DUPLICATE8_HI);
 }
 
 template<typename Packet> EIGEN_STRONG_INLINE void pstoreu_common(__UNPACK_TYPE__(Packet)*  to, const Packet& from)
 {
   EIGEN_DEBUG_UNALIGNED_STORE
 #ifdef _BIG_ENDIAN
   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
   // Warning: not thread safe!
   Packet16uc MSQ, LSQ, edges;
   Packet16uc edgeAlign, align;
 
   MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
   LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
   edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
   edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges
   align = vec_lvsr( 0, to );                                // permute map to misalign data
   MSQ = vec_perm(edges,(Packet16uc)from,align);             // misalign the data (MSQ)
   LSQ = vec_perm((Packet16uc)from,edges,align);             // misalign the data (LSQ)
   vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
   vec_st( MSQ, 0, (unsigned char *)to );                   // Store the MSQ part second
 #else
   vec_xst(from, 0, to);
 #endif
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from)
 {
   pstoreu_common<Packet4f>(to, from);
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from)
 {
   pstoreu_common<Packet4i>(to, from);
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<short int>(short int*      to, const Packet8s& from)
 {
   pstoreu_common<Packet8s>(to, from);
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<unsigned short int>(unsigned short int*      to, const Packet8us& from)
 {
   pstoreu_common<Packet8us>(to, from);
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16*      to, const Packet8bf& from)
 {
   pstoreu_common<Packet8us>(reinterpret_cast<unsigned short int*>(to), from);
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<signed char>(signed char*      to, const Packet16c& from)
 {
   pstoreu_common<Packet16c>(to, from);
 }
 template<> EIGEN_STRONG_INLINE void pstoreu<unsigned char>(unsigned char*      to, const Packet16uc& from)
 {
   pstoreu_common<Packet16uc>(to, from);
 }
 
 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) { EIGEN_ALIGN16 float x; vec_ste(a, 0, &x); return x; }
 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { EIGEN_ALIGN16 int   x; vec_ste(a, 0, &x); return x; }
 
 template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) pfirst_common(const Packet& a) {
   EIGEN_ALIGN16 __UNPACK_TYPE__(Packet) x;
   vec_ste(a, 0, &x);
   return x;
 }
 
 template<> EIGEN_STRONG_INLINE short int pfirst<Packet8s>(const Packet8s& a) {
   return pfirst_common<Packet8s>(a);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned short int pfirst<Packet8us>(const Packet8us& a) {
   return pfirst_common<Packet8us>(a);
 }
 
 template<> EIGEN_STRONG_INLINE signed char pfirst<Packet16c>(const Packet16c& a)
 {
   return pfirst_common<Packet16c>(a);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned char pfirst<Packet16uc>(const Packet16uc& a)
 {
   return pfirst_common<Packet16uc>(a);
 }
 
 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 Packet8s preverse(const Packet8s& a)
 {
   return reinterpret_cast<Packet8s>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE16));
 }
 template<> EIGEN_STRONG_INLINE Packet8us preverse(const Packet8us& a)
 {
   return reinterpret_cast<Packet8us>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE16));
 }
 template<> EIGEN_STRONG_INLINE Packet16c preverse(const Packet16c& a)
 {
   return vec_perm(a, a, p16uc_REVERSE8);
 }
 template<> EIGEN_STRONG_INLINE Packet16uc preverse(const Packet16uc& a)
 {
   return vec_perm(a, a, p16uc_REVERSE8);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf preverse(const Packet8bf& a)
 {
   return preverse<Packet8us>(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 Packet8s pabs(const Packet8s& a) { return vec_abs(a); }
 template<> EIGEN_STRONG_INLINE Packet8us pabs(const Packet8us& a) { return a; }
 template<> EIGEN_STRONG_INLINE Packet16c pabs(const Packet16c& a) { return vec_abs(a); }
 template<> EIGEN_STRONG_INLINE Packet16uc pabs(const Packet16uc& a) { return a; }
 template<> EIGEN_STRONG_INLINE Packet8bf  pabs(const Packet8bf& a) {
   _EIGEN_DECLARE_CONST_FAST_Packet8us(abs_mask,0x7FFF);
   return pand<Packet8us>(p8us_abs_mask, a);
 }
 
 template<int N> EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a)
 { return vec_sra(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
 template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i& a)
 { return vec_sr(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
 template<int N> EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i& a)
 { return vec_sl(a,reinterpret_cast<Packet4ui>(pset1<Packet4i>(N))); }
 template<int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_left(const Packet4f& a)
 {
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
   Packet4ui r = vec_sl(reinterpret_cast<Packet4ui>(a), p4ui_mask);
   return reinterpret_cast<Packet4f>(r);
 }
 
 template<int N> EIGEN_STRONG_INLINE Packet4f plogical_shift_right(const Packet4f& a)
 {
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
   Packet4ui r = vec_sr(reinterpret_cast<Packet4ui>(a), p4ui_mask);
   return reinterpret_cast<Packet4f>(r);
 }
 
 template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_right(const Packet4ui& a)
 {
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
   return vec_sr(a, p4ui_mask);
 }
 
 template<int N> EIGEN_STRONG_INLINE Packet4ui plogical_shift_left(const Packet4ui& a)
 {
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mask, N);
   return vec_sl(a, p4ui_mask);
 }
 
 template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_left(const Packet8us& a)
 {
   const _EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
   return vec_sl(a, p8us_mask);
 }
 template<int N> EIGEN_STRONG_INLINE Packet8us plogical_shift_right(const Packet8us& a)
 {
   const _EIGEN_DECLARE_CONST_FAST_Packet8us(mask, N);
   return vec_sr(a, p8us_mask);
 }
 
 EIGEN_STRONG_INLINE Packet4f Bf16ToF32Even(const Packet8bf& bf){
   return plogical_shift_left<16>(reinterpret_cast<Packet4f>(bf.m_val));
 }
 
 EIGEN_STRONG_INLINE Packet4f Bf16ToF32Odd(const Packet8bf& bf){
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
   return pand<Packet4f>(
     reinterpret_cast<Packet4f>(bf.m_val),
     reinterpret_cast<Packet4f>(p4ui_high_mask)
   );
 }
 
 // Simple interleaving of bool masks, prevents true values from being
 // converted to NaNs.
 EIGEN_STRONG_INLINE Packet8bf F32ToBf16Bool(Packet4f even, Packet4f odd) {
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(high_mask, 0xFFFF0000);
   Packet4f bf_odd, bf_even;
   bf_odd = pand(reinterpret_cast<Packet4f>(p4ui_high_mask), odd);
   bf_even = plogical_shift_right<16>(even);
   return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
 }
 
 EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f){
   Packet4ui input = reinterpret_cast<Packet4ui>(p4f);
   Packet4ui lsb = plogical_shift_right<16>(input);
   lsb = pand<Packet4ui>(lsb, reinterpret_cast<Packet4ui>(p4i_ONE));
 
   _EIGEN_DECLARE_CONST_FAST_Packet4ui(BIAS,0x7FFFu);
   Packet4ui rounding_bias = padd<Packet4ui>(lsb, p4ui_BIAS);
   input = padd<Packet4ui>(input, rounding_bias);
 
   //Test NaN and Subnormal - Begin
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(exp_mask, 0x7F800000);
   Packet4ui exp = pand<Packet4ui>(p4ui_exp_mask, reinterpret_cast<Packet4ui>(p4f));
 
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(mantissa_mask, 0x7FFFFF);
   Packet4ui mantissa = pand<Packet4ui>(p4ui_mantissa_mask, reinterpret_cast<Packet4ui>(p4f));
 
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(max_exp, 0x7F800000);
   Packet4bi is_max_exp = vec_cmpeq(exp, p4ui_max_exp);
   Packet4bi is_zero_exp = vec_cmpeq(exp, reinterpret_cast<Packet4ui>(p4i_ZERO));
 
   Packet4bi is_mant_zero = vec_cmpeq(mantissa, reinterpret_cast<Packet4ui>(p4i_ZERO));
   Packet4ui nan_selector = pandnot<Packet4ui>(
       reinterpret_cast<Packet4ui>(is_max_exp),
       reinterpret_cast<Packet4ui>(is_mant_zero)
   );
 
   Packet4ui subnormal_selector = pandnot<Packet4ui>(
       reinterpret_cast<Packet4ui>(is_zero_exp),
       reinterpret_cast<Packet4ui>(is_mant_zero)
   );
 
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(nan, 0x7FC00000);
   input = vec_sel(input, p4ui_nan, nan_selector);
   input = vec_sel(input, reinterpret_cast<Packet4ui>(p4f), subnormal_selector);
   //Test NaN and Subnormal - End
 
   input = plogical_shift_right<16>(input);
   return reinterpret_cast<Packet8us>(input);
 }
 
 EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f even, Packet4f odd){
   Packet4f bf_odd, bf_even;
   bf_odd = reinterpret_cast<Packet4f>(F32ToBf16(odd).m_val);
   bf_odd = plogical_shift_left<16>(bf_odd);
   bf_even = reinterpret_cast<Packet4f>(F32ToBf16(even).m_val);
   return reinterpret_cast<Packet8us>(por<Packet4f>(bf_even, bf_odd));
 }
 #define BF16_TO_F32_UNARY_OP_WRAPPER(OP, A) \
   Packet4f a_even = Bf16ToF32Even(A);\
   Packet4f a_odd = Bf16ToF32Odd(A);\
   Packet4f op_even = OP(a_even);\
   Packet4f op_odd = OP(a_odd);\
   return F32ToBf16(op_even, op_odd);\
 
 #define BF16_TO_F32_BINARY_OP_WRAPPER(OP, A, B) \
   Packet4f a_even = Bf16ToF32Even(A);\
   Packet4f a_odd = Bf16ToF32Odd(A);\
   Packet4f b_even = Bf16ToF32Even(B);\
   Packet4f b_odd = Bf16ToF32Odd(B);\
   Packet4f op_even = OP(a_even, b_even);\
   Packet4f op_odd = OP(a_odd, b_odd);\
   return F32ToBf16(op_even, op_odd);\
 
 #define BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(OP, A, B) \
   Packet4f a_even = Bf16ToF32Even(A);\
   Packet4f a_odd = Bf16ToF32Odd(A);\
   Packet4f b_even = Bf16ToF32Even(B);\
   Packet4f b_odd = Bf16ToF32Odd(B);\
   Packet4f op_even = OP(a_even, b_even);\
   Packet4f op_odd = OP(a_odd, b_odd);\
   return F32ToBf16Bool(op_even, op_odd);\
 
 template<> EIGEN_STRONG_INLINE Packet8bf padd<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(padd<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pmul<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(pmul<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pdiv<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(pdiv<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pnegate<Packet8bf>(const Packet8bf& a) {
   BF16_TO_F32_UNARY_OP_WRAPPER(pnegate<Packet4f>, a);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf psub<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(psub<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf psqrt<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(vec_sqrt, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf prsqrt<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(prsqrt<Packet4f>, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pexp<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pexp_float, a);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
   return pldexp_generic(a,exponent);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pldexp<Packet8bf> (const Packet8bf& a, const Packet8bf& exponent){
   BF16_TO_F32_BINARY_OP_WRAPPER(pldexp<Packet4f>, a, exponent);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
   return pfrexp_generic(a,exponent);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pfrexp<Packet8bf> (const Packet8bf& a, Packet8bf& e){
   Packet4f a_even = Bf16ToF32Even(a);
   Packet4f a_odd = Bf16ToF32Odd(a);
   Packet4f e_even;
   Packet4f e_odd;
   Packet4f op_even = pfrexp<Packet4f>(a_even, e_even);
   Packet4f op_odd = pfrexp<Packet4f>(a_odd, e_odd);
   e = F32ToBf16(e_even, e_odd);
   return F32ToBf16(op_even, op_odd);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf psin<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(psin_float, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pcos<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pcos_float, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf plog<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(plog_float, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pfloor<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pfloor<Packet4f>, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pceil<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pceil<Packet4f>, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pround<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(pround<Packet4f>, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf print<Packet8bf> (const Packet8bf& a){
   BF16_TO_F32_UNARY_OP_WRAPPER(print<Packet4f>, a);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pmadd(const Packet8bf& a, const Packet8bf& b, const Packet8bf& c) {
   Packet4f a_even = Bf16ToF32Even(a);
   Packet4f a_odd = Bf16ToF32Odd(a);
   Packet4f b_even = Bf16ToF32Even(b);
   Packet4f b_odd = Bf16ToF32Odd(b);
   Packet4f c_even = Bf16ToF32Even(c);
   Packet4f c_odd = Bf16ToF32Odd(c);
   Packet4f pmadd_even = pmadd<Packet4f>(a_even, b_even, c_even);
   Packet4f pmadd_odd = pmadd<Packet4f>(a_odd, b_odd, c_odd);
   return F32ToBf16(pmadd_even, pmadd_odd);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pmin<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(pmin<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pmax<Packet8bf>(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER(pmax<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_lt<Packet4f>, a, b);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pcmp_lt_or_nan(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_lt_or_nan<Packet4f>, a, b);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pcmp_le(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_le<Packet4f>, a, b);
 }
 template<> EIGEN_STRONG_INLINE Packet8bf pcmp_eq(const Packet8bf& a, const Packet8bf& b) {
   BF16_TO_F32_BINARY_OP_WRAPPER_BOOL(pcmp_eq<Packet4f>, a, b);
 }
 
 template<> EIGEN_STRONG_INLINE bfloat16 pfirst(const Packet8bf& a) {
   return RivetEigen::bfloat16_impl::raw_uint16_to_bfloat16((pfirst<Packet8us>(a)));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf ploaddup<Packet8bf>(const  bfloat16*     from)
 {
   return ploaddup<Packet8us>(reinterpret_cast<const unsigned short int*>(from));
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf plset<Packet8bf>(const bfloat16& a) {
   bfloat16 countdown[8] = { bfloat16(0), bfloat16(1), bfloat16(2), bfloat16(3),
                             bfloat16(4), bfloat16(5), bfloat16(6), bfloat16(7) };
   return padd<Packet8bf>(pset1<Packet8bf>(a), pload<Packet8bf>(countdown));
 }
 
 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
 {
   Packet4f b, sum;
   b   = vec_sld(a, a, 8);
   sum = a + b;
   b   = vec_sld(sum, sum, 4);
   sum += b;
   return pfirst(sum);
 }
 
 template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
 {
   Packet4i sum;
   sum = vec_sums(a, p4i_ZERO);
 #ifdef _BIG_ENDIAN
   sum = vec_sld(sum, p4i_ZERO, 12);
 #else
   sum = vec_sld(p4i_ZERO, sum, 4);
 #endif
   return pfirst(sum);
 }
 
 template<> EIGEN_STRONG_INLINE bfloat16 predux<Packet8bf>(const Packet8bf& a)
 {
   float redux_even = predux<Packet4f>(Bf16ToF32Even(a));
   float redux_odd  = predux<Packet4f>(Bf16ToF32Odd(a));
   float f32_result = redux_even + redux_odd;
   return bfloat16(f32_result);
 }
 template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size8(const Packet& a)
 {
   union{
     Packet v;
     __UNPACK_TYPE__(Packet) n[8];
   } vt;
   vt.v = a;
 
   EIGEN_ALIGN16 int first_loader[4] = { vt.n[0], vt.n[1], vt.n[2], vt.n[3] };
   EIGEN_ALIGN16 int second_loader[4] = { vt.n[4], vt.n[5], vt.n[6], vt.n[7] };
   Packet4i first_half  = pload<Packet4i>(first_loader);
   Packet4i second_half = pload<Packet4i>(second_loader);
 
   return static_cast<__UNPACK_TYPE__(Packet)>(predux(first_half) + predux(second_half));
 }
 
 template<> EIGEN_STRONG_INLINE short int predux<Packet8s>(const Packet8s& a)
 {
   return predux_size8<Packet8s>(a);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned short int predux<Packet8us>(const Packet8us& a)
 {
   return predux_size8<Packet8us>(a);
 }
 
 template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_size16(const Packet& a)
 {
   union{
     Packet v;
     __UNPACK_TYPE__(Packet) n[16];
   } vt;
   vt.v = a;
 
   EIGEN_ALIGN16 int first_loader[4] = { vt.n[0], vt.n[1], vt.n[2], vt.n[3] };
   EIGEN_ALIGN16 int second_loader[4] = { vt.n[4], vt.n[5], vt.n[6], vt.n[7] };
   EIGEN_ALIGN16 int third_loader[4] = { vt.n[8], vt.n[9], vt.n[10], vt.n[11] };
   EIGEN_ALIGN16 int fourth_loader[4] = { vt.n[12], vt.n[13], vt.n[14], vt.n[15] };
 
   Packet4i first_quarter = pload<Packet4i>(first_loader);
   Packet4i second_quarter = pload<Packet4i>(second_loader);
   Packet4i third_quarter = pload<Packet4i>(third_loader);
   Packet4i fourth_quarter = pload<Packet4i>(fourth_loader);
 
   return static_cast<__UNPACK_TYPE__(Packet)>(predux(first_quarter) + predux(second_quarter)
                           + predux(third_quarter) + predux(fourth_quarter));
 }
 
 template<> EIGEN_STRONG_INLINE signed char predux<Packet16c>(const Packet16c& a)
 {
   return predux_size16<Packet16c>(a);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned char predux<Packet16uc>(const Packet16uc& a)
 {
   return predux_size16<Packet16uc>(a);
 }
 
 // Other reduction functions:
 // mul
 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
 {
   Packet4f prod;
   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)
 {
   EIGEN_ALIGN16 int aux[4];
   pstore(aux, a);
   return aux[0] * aux[1] * aux[2] * aux[3];
 }
 
 template<> EIGEN_STRONG_INLINE short int predux_mul<Packet8s>(const Packet8s& a)
 {
   Packet8s pair, quad, octo;
 
   pair = vec_mul(a, vec_sld(a, a, 8));
   quad = vec_mul(pair, vec_sld(pair, pair, 4));
   octo = vec_mul(quad, vec_sld(quad, quad, 2));
 
   return pfirst(octo);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned short int predux_mul<Packet8us>(const Packet8us& a)
 {
   Packet8us pair, quad, octo;
 
   pair = vec_mul(a, vec_sld(a, a, 8));
   quad = vec_mul(pair, vec_sld(pair, pair, 4));
   octo = vec_mul(quad, vec_sld(quad, quad, 2));
 
   return pfirst(octo);
 }
 
 template<> EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet8bf>(const Packet8bf& a)
 {
   float redux_even = predux_mul<Packet4f>(Bf16ToF32Even(a));
   float redux_odd  = predux_mul<Packet4f>(Bf16ToF32Odd(a));
   float f32_result = redux_even * redux_odd;
   return bfloat16(f32_result);
 }
 
 
 template<> EIGEN_STRONG_INLINE signed char predux_mul<Packet16c>(const Packet16c& a)
 {
   Packet16c pair, quad, octo, result;
 
   pair = vec_mul(a, vec_sld(a, a, 8));
   quad = vec_mul(pair, vec_sld(pair, pair, 4));
   octo = vec_mul(quad, vec_sld(quad, quad, 2));
   result = vec_mul(octo, vec_sld(octo, octo, 1));
 
   return pfirst(result);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned char predux_mul<Packet16uc>(const Packet16uc& a)
 {
   Packet16uc pair, quad, octo, result;
 
   pair = vec_mul(a, vec_sld(a, a, 8));
   quad = vec_mul(pair, vec_sld(pair, pair, 4));
   octo = vec_mul(quad, vec_sld(quad, quad, 2));
   result = vec_mul(octo, vec_sld(octo, octo, 1));
 
   return pfirst(result);
 }
 
 // min
 template<typename Packet> EIGEN_STRONG_INLINE
 __UNPACK_TYPE__(Packet) predux_min4(const Packet& a)
 {
   Packet b, res;
   b = vec_min(a, vec_sld(a, a, 8));
   res = vec_min(b, vec_sld(b, b, 4));
   return pfirst(res);
 }
 
 
 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
 {
   return predux_min4<Packet4f>(a);
 }
 
 template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
 {
   return predux_min4<Packet4i>(a);
 }
 
 template<> EIGEN_STRONG_INLINE bfloat16 predux_min<Packet8bf>(const Packet8bf& a)
 {
   float redux_even = predux_min<Packet4f>(Bf16ToF32Even(a));
   float redux_odd  = predux_min<Packet4f>(Bf16ToF32Odd(a));
   float f32_result = (std::min)(redux_even, redux_odd);
   return bfloat16(f32_result);
 }
 
 template<> EIGEN_STRONG_INLINE short int predux_min<Packet8s>(const Packet8s& a)
 {
   Packet8s pair, quad, octo;
   
   //pair = { Min(a0,a4), Min(a1,a5), Min(a2,a6), Min(a3,a7) }
   pair = vec_min(a, vec_sld(a, a, 8)); 
 
   //quad = { Min(a0, a4, a2, a6), Min(a1, a5, a3, a7) }
   quad = vec_min(pair, vec_sld(pair, pair, 4));
 
   //octo = { Min(a0, a4, a2, a6, a1, a5, a3, a7) }
   octo = vec_min(quad, vec_sld(quad, quad, 2));
   return pfirst(octo);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned short int predux_min<Packet8us>(const Packet8us& a)
 {
   Packet8us pair, quad, octo;
   
   //pair = { Min(a0,a4), Min(a1,a5), Min(a2,a6), Min(a3,a7) }
   pair = vec_min(a, vec_sld(a, a, 8)); 
 
   //quad = { Min(a0, a4, a2, a6), Min(a1, a5, a3, a7) }
   quad = vec_min(pair, vec_sld(pair, pair, 4));
 
   //octo = { Min(a0, a4, a2, a6, a1, a5, a3, a7) }
   octo = vec_min(quad, vec_sld(quad, quad, 2));
   return pfirst(octo);
 }
 
 template<> EIGEN_STRONG_INLINE signed char predux_min<Packet16c>(const Packet16c& a)
 {
   Packet16c pair, quad, octo, result;
 
   pair = vec_min(a, vec_sld(a, a, 8));
   quad = vec_min(pair, vec_sld(pair, pair, 4));
   octo = vec_min(quad, vec_sld(quad, quad, 2));
   result = vec_min(octo, vec_sld(octo, octo, 1));
 
   return pfirst(result);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned char predux_min<Packet16uc>(const Packet16uc& a)
 {
   Packet16uc pair, quad, octo, result;
 
   pair = vec_min(a, vec_sld(a, a, 8));
   quad = vec_min(pair, vec_sld(pair, pair, 4));
   octo = vec_min(quad, vec_sld(quad, quad, 2));
   result = vec_min(octo, vec_sld(octo, octo, 1));
 
   return pfirst(result);
 }
 // max
 template<typename Packet> EIGEN_STRONG_INLINE __UNPACK_TYPE__(Packet) predux_max4(const Packet& a)
 {
   Packet b, res;
   b = vec_max(a, vec_sld(a, a, 8));
   res = vec_max(b, vec_sld(b, b, 4));
   return pfirst(res);
 }
 
 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
 {
   return predux_max4<Packet4f>(a);
 }
 
 template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
 {
   return predux_max4<Packet4i>(a);
 }
 
 template<> EIGEN_STRONG_INLINE bfloat16 predux_max<Packet8bf>(const Packet8bf& a)
 {
   float redux_even = predux_max<Packet4f>(Bf16ToF32Even(a));
   float redux_odd  = predux_max<Packet4f>(Bf16ToF32Odd(a));
   float f32_result = (std::max)(redux_even, redux_odd);
   return bfloat16(f32_result);
 }
 
 template<> EIGEN_STRONG_INLINE short int predux_max<Packet8s>(const Packet8s& a)
 {
   Packet8s pair, quad, octo;
   
   //pair = { Max(a0,a4), Max(a1,a5), Max(a2,a6), Max(a3,a7) }
   pair = vec_max(a, vec_sld(a, a, 8)); 
 
   //quad = { Max(a0, a4, a2, a6), Max(a1, a5, a3, a7) }
   quad = vec_max(pair, vec_sld(pair, pair, 4));
 
   //octo = { Max(a0, a4, a2, a6, a1, a5, a3, a7) }
   octo = vec_max(quad, vec_sld(quad, quad, 2));
   return pfirst(octo);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned short int predux_max<Packet8us>(const Packet8us& a)
 {
   Packet8us pair, quad, octo;
   
   //pair = { Max(a0,a4), Max(a1,a5), Max(a2,a6), Max(a3,a7) }
   pair = vec_max(a, vec_sld(a, a, 8)); 
 
   //quad = { Max(a0, a4, a2, a6), Max(a1, a5, a3, a7) }
   quad = vec_max(pair, vec_sld(pair, pair, 4));
 
   //octo = { Max(a0, a4, a2, a6, a1, a5, a3, a7) }
   octo = vec_max(quad, vec_sld(quad, quad, 2));
   return pfirst(octo);
 }
 
 template<> EIGEN_STRONG_INLINE signed char predux_max<Packet16c>(const Packet16c& a)
 {
   Packet16c pair, quad, octo, result;
 
   pair = vec_max(a, vec_sld(a, a, 8));
   quad = vec_max(pair, vec_sld(pair, pair, 4));
   octo = vec_max(quad, vec_sld(quad, quad, 2));
   result = vec_max(octo, vec_sld(octo, octo, 1));
 
   return pfirst(result);
 }
 
 template<> EIGEN_STRONG_INLINE unsigned char predux_max<Packet16uc>(const Packet16uc& a)
 {
   Packet16uc pair, quad, octo, result;
 
   pair = vec_max(a, vec_sld(a, a, 8));
   quad = vec_max(pair, vec_sld(pair, pair, 4));
   octo = vec_max(quad, vec_sld(quad, quad, 2));
   result = vec_max(octo, vec_sld(octo, octo, 1));
 
   return pfirst(result);
 }
 
 template<> EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x)
 {
   return vec_any_ne(x, pzero(x));
 }
 
 template <typename T> EIGEN_DEVICE_FUNC inline void
 ptranpose_common(PacketBlock<T,4>& kernel){
   T t0, t1, t2, t3;
   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
   kernel.packet[0] = vec_mergeh(t0, t2);
   kernel.packet[1] = vec_mergel(t0, t2);
   kernel.packet[2] = vec_mergeh(t1, t3);
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet4f,4>& kernel) {
   ptranpose_common<Packet4f>(kernel);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet4i,4>& kernel) {
   ptranpose_common<Packet4i>(kernel);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8s,4>& kernel) {
   Packet8s t0, t1, t2, t3;
   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
   kernel.packet[0] = vec_mergeh(t0, t2);
   kernel.packet[1] = vec_mergel(t0, t2);
   kernel.packet[2] = vec_mergeh(t1, t3);
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8us,4>& kernel) {
   Packet8us t0, t1, t2, t3;
   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
   kernel.packet[0] = vec_mergeh(t0, t2);
   kernel.packet[1] = vec_mergel(t0, t2);
   kernel.packet[2] = vec_mergeh(t1, t3);
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8bf,4>& kernel) {
   Packet8us t0, t1, t2, t3;
 
   t0 = vec_mergeh(kernel.packet[0].m_val, kernel.packet[2].m_val);
   t1 = vec_mergel(kernel.packet[0].m_val, kernel.packet[2].m_val);
   t2 = vec_mergeh(kernel.packet[1].m_val, kernel.packet[3].m_val);
   t3 = vec_mergel(kernel.packet[1].m_val, kernel.packet[3].m_val);
   kernel.packet[0] = vec_mergeh(t0, t2);
   kernel.packet[1] = vec_mergel(t0, t2);
   kernel.packet[2] = vec_mergeh(t1, t3);
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet16c,4>& kernel) {
   Packet16c t0, t1, t2, t3;
   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
   kernel.packet[0] = vec_mergeh(t0, t2);
   kernel.packet[1] = vec_mergel(t0, t2);
   kernel.packet[2] = vec_mergeh(t1, t3);
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet16uc,4>& kernel) {
   Packet16uc t0, t1, t2, t3;
   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
   kernel.packet[0] = vec_mergeh(t0, t2);
   kernel.packet[1] = vec_mergel(t0, t2);
   kernel.packet[2] = vec_mergeh(t1, t3);
   kernel.packet[3] = vec_mergel(t1, t3);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8s,8>& kernel) {
   Packet8s v[8], sum[8];
 
   v[0] = vec_mergeh(kernel.packet[0], kernel.packet[4]);
   v[1] = vec_mergel(kernel.packet[0], kernel.packet[4]);
   v[2] = vec_mergeh(kernel.packet[1], kernel.packet[5]);
   v[3] = vec_mergel(kernel.packet[1], kernel.packet[5]);
   v[4] = vec_mergeh(kernel.packet[2], kernel.packet[6]);
   v[5] = vec_mergel(kernel.packet[2], kernel.packet[6]);
   v[6] = vec_mergeh(kernel.packet[3], kernel.packet[7]);
   v[7] = vec_mergel(kernel.packet[3], kernel.packet[7]);
   sum[0] = vec_mergeh(v[0], v[4]);
   sum[1] = vec_mergel(v[0], v[4]);
   sum[2] = vec_mergeh(v[1], v[5]);
   sum[3] = vec_mergel(v[1], v[5]);
   sum[4] = vec_mergeh(v[2], v[6]);
   sum[5] = vec_mergel(v[2], v[6]);
   sum[6] = vec_mergeh(v[3], v[7]);
   sum[7] = vec_mergel(v[3], v[7]);
 
   kernel.packet[0] = vec_mergeh(sum[0], sum[4]);
   kernel.packet[1] = vec_mergel(sum[0], sum[4]);
   kernel.packet[2] = vec_mergeh(sum[1], sum[5]);
   kernel.packet[3] = vec_mergel(sum[1], sum[5]);
   kernel.packet[4] = vec_mergeh(sum[2], sum[6]);
   kernel.packet[5] = vec_mergel(sum[2], sum[6]);
   kernel.packet[6] = vec_mergeh(sum[3], sum[7]);
   kernel.packet[7] = vec_mergel(sum[3], sum[7]);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8us,8>& kernel) {
   Packet8us v[8], sum[8];
 
   v[0] = vec_mergeh(kernel.packet[0], kernel.packet[4]);
   v[1] = vec_mergel(kernel.packet[0], kernel.packet[4]);
   v[2] = vec_mergeh(kernel.packet[1], kernel.packet[5]);
   v[3] = vec_mergel(kernel.packet[1], kernel.packet[5]);
   v[4] = vec_mergeh(kernel.packet[2], kernel.packet[6]);
   v[5] = vec_mergel(kernel.packet[2], kernel.packet[6]);
   v[6] = vec_mergeh(kernel.packet[3], kernel.packet[7]);
   v[7] = vec_mergel(kernel.packet[3], kernel.packet[7]);
   sum[0] = vec_mergeh(v[0], v[4]);
   sum[1] = vec_mergel(v[0], v[4]);
   sum[2] = vec_mergeh(v[1], v[5]);
   sum[3] = vec_mergel(v[1], v[5]);
   sum[4] = vec_mergeh(v[2], v[6]);
   sum[5] = vec_mergel(v[2], v[6]);
   sum[6] = vec_mergeh(v[3], v[7]);
   sum[7] = vec_mergel(v[3], v[7]);
 
   kernel.packet[0] = vec_mergeh(sum[0], sum[4]);
   kernel.packet[1] = vec_mergel(sum[0], sum[4]);
   kernel.packet[2] = vec_mergeh(sum[1], sum[5]);
   kernel.packet[3] = vec_mergel(sum[1], sum[5]);
   kernel.packet[4] = vec_mergeh(sum[2], sum[6]);
   kernel.packet[5] = vec_mergel(sum[2], sum[6]);
   kernel.packet[6] = vec_mergeh(sum[3], sum[7]);
   kernel.packet[7] = vec_mergel(sum[3], sum[7]);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet8bf,8>& kernel) {
   Packet8bf v[8], sum[8];
 
   v[0] = vec_mergeh(kernel.packet[0].m_val, kernel.packet[4].m_val);
   v[1] = vec_mergel(kernel.packet[0].m_val, kernel.packet[4].m_val);
   v[2] = vec_mergeh(kernel.packet[1].m_val, kernel.packet[5].m_val);
   v[3] = vec_mergel(kernel.packet[1].m_val, kernel.packet[5].m_val);
   v[4] = vec_mergeh(kernel.packet[2].m_val, kernel.packet[6].m_val);
   v[5] = vec_mergel(kernel.packet[2].m_val, kernel.packet[6].m_val);
   v[6] = vec_mergeh(kernel.packet[3].m_val, kernel.packet[7].m_val);
   v[7] = vec_mergel(kernel.packet[3].m_val, kernel.packet[7].m_val);
   sum[0] = vec_mergeh(v[0].m_val, v[4].m_val);
   sum[1] = vec_mergel(v[0].m_val, v[4].m_val);
   sum[2] = vec_mergeh(v[1].m_val, v[5].m_val);
   sum[3] = vec_mergel(v[1].m_val, v[5].m_val);
   sum[4] = vec_mergeh(v[2].m_val, v[6].m_val);
   sum[5] = vec_mergel(v[2].m_val, v[6].m_val);
   sum[6] = vec_mergeh(v[3].m_val, v[7].m_val);
   sum[7] = vec_mergel(v[3].m_val, v[7].m_val);
 
   kernel.packet[0] = vec_mergeh(sum[0].m_val, sum[4].m_val);
   kernel.packet[1] = vec_mergel(sum[0].m_val, sum[4].m_val);
   kernel.packet[2] = vec_mergeh(sum[1].m_val, sum[5].m_val);
   kernel.packet[3] = vec_mergel(sum[1].m_val, sum[5].m_val);
   kernel.packet[4] = vec_mergeh(sum[2].m_val, sum[6].m_val);
   kernel.packet[5] = vec_mergel(sum[2].m_val, sum[6].m_val);
   kernel.packet[6] = vec_mergeh(sum[3].m_val, sum[7].m_val);
   kernel.packet[7] = vec_mergel(sum[3].m_val, sum[7].m_val);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet16c,16>& kernel) {
   Packet16c step1[16], step2[16], step3[16];
 
   step1[0] = vec_mergeh(kernel.packet[0], kernel.packet[8]);
   step1[1] = vec_mergel(kernel.packet[0], kernel.packet[8]);
   step1[2] = vec_mergeh(kernel.packet[1], kernel.packet[9]);
   step1[3] = vec_mergel(kernel.packet[1], kernel.packet[9]);
   step1[4] = vec_mergeh(kernel.packet[2], kernel.packet[10]);
   step1[5] = vec_mergel(kernel.packet[2], kernel.packet[10]);
   step1[6] = vec_mergeh(kernel.packet[3], kernel.packet[11]);
   step1[7] = vec_mergel(kernel.packet[3], kernel.packet[11]);
   step1[8] = vec_mergeh(kernel.packet[4], kernel.packet[12]);
   step1[9] = vec_mergel(kernel.packet[4], kernel.packet[12]);
   step1[10] = vec_mergeh(kernel.packet[5], kernel.packet[13]);
   step1[11] = vec_mergel(kernel.packet[5], kernel.packet[13]);
   step1[12] = vec_mergeh(kernel.packet[6], kernel.packet[14]);
   step1[13] = vec_mergel(kernel.packet[6], kernel.packet[14]);
   step1[14] = vec_mergeh(kernel.packet[7], kernel.packet[15]);
   step1[15] = vec_mergel(kernel.packet[7], kernel.packet[15]);
 
   step2[0]  = vec_mergeh(step1[0], step1[8]);
   step2[1]  = vec_mergel(step1[0], step1[8]);
   step2[2]  = vec_mergeh(step1[1], step1[9]);
   step2[3]  = vec_mergel(step1[1], step1[9]);
   step2[4]  = vec_mergeh(step1[2], step1[10]);
   step2[5]  = vec_mergel(step1[2], step1[10]);
   step2[6]  = vec_mergeh(step1[3], step1[11]);
   step2[7]  = vec_mergel(step1[3], step1[11]);
   step2[8]  = vec_mergeh(step1[4], step1[12]);
   step2[9]  = vec_mergel(step1[4], step1[12]);
   step2[10] = vec_mergeh(step1[5], step1[13]);
   step2[11] = vec_mergel(step1[5], step1[13]);
   step2[12] = vec_mergeh(step1[6], step1[14]);
   step2[13] = vec_mergel(step1[6], step1[14]);
   step2[14] = vec_mergeh(step1[7], step1[15]);
   step2[15] = vec_mergel(step1[7], step1[15]);
 
   step3[0]  = vec_mergeh(step2[0], step2[8]);
   step3[1]  = vec_mergel(step2[0], step2[8]);
   step3[2]  = vec_mergeh(step2[1], step2[9]);
   step3[3]  = vec_mergel(step2[1], step2[9]);
   step3[4]  = vec_mergeh(step2[2], step2[10]);
   step3[5]  = vec_mergel(step2[2], step2[10]);
   step3[6]  = vec_mergeh(step2[3], step2[11]);
   step3[7]  = vec_mergel(step2[3], step2[11]);
   step3[8]  = vec_mergeh(step2[4], step2[12]);
   step3[9]  = vec_mergel(step2[4], step2[12]);
   step3[10] = vec_mergeh(step2[5], step2[13]);
   step3[11] = vec_mergel(step2[5], step2[13]);
   step3[12] = vec_mergeh(step2[6], step2[14]);
   step3[13] = vec_mergel(step2[6], step2[14]);
   step3[14] = vec_mergeh(step2[7], step2[15]);
   step3[15] = vec_mergel(step2[7], step2[15]);
 
   kernel.packet[0]  = vec_mergeh(step3[0], step3[8]);
   kernel.packet[1]  = vec_mergel(step3[0], step3[8]);
   kernel.packet[2]  = vec_mergeh(step3[1], step3[9]);
   kernel.packet[3]  = vec_mergel(step3[1], step3[9]);
   kernel.packet[4]  = vec_mergeh(step3[2], step3[10]);
   kernel.packet[5]  = vec_mergel(step3[2], step3[10]);
   kernel.packet[6]  = vec_mergeh(step3[3], step3[11]);
   kernel.packet[7]  = vec_mergel(step3[3], step3[11]);
   kernel.packet[8]  = vec_mergeh(step3[4], step3[12]);
   kernel.packet[9]  = vec_mergel(step3[4], step3[12]);
   kernel.packet[10] = vec_mergeh(step3[5], step3[13]);
   kernel.packet[11] = vec_mergel(step3[5], step3[13]);
   kernel.packet[12] = vec_mergeh(step3[6], step3[14]);
   kernel.packet[13] = vec_mergel(step3[6], step3[14]);
   kernel.packet[14] = vec_mergeh(step3[7], step3[15]);
   kernel.packet[15] = vec_mergel(step3[7], step3[15]);
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet16uc,16>& kernel) {
   Packet16uc step1[16], step2[16], step3[16];
 
   step1[0] = vec_mergeh(kernel.packet[0], kernel.packet[8]);
   step1[1] = vec_mergel(kernel.packet[0], kernel.packet[8]);
   step1[2] = vec_mergeh(kernel.packet[1], kernel.packet[9]);
   step1[3] = vec_mergel(kernel.packet[1], kernel.packet[9]);
   step1[4] = vec_mergeh(kernel.packet[2], kernel.packet[10]);
   step1[5] = vec_mergel(kernel.packet[2], kernel.packet[10]);
   step1[6] = vec_mergeh(kernel.packet[3], kernel.packet[11]);
   step1[7] = vec_mergel(kernel.packet[3], kernel.packet[11]);
   step1[8] = vec_mergeh(kernel.packet[4], kernel.packet[12]);
   step1[9] = vec_mergel(kernel.packet[4], kernel.packet[12]);
   step1[10] = vec_mergeh(kernel.packet[5], kernel.packet[13]);
   step1[11] = vec_mergel(kernel.packet[5], kernel.packet[13]);
   step1[12] = vec_mergeh(kernel.packet[6], kernel.packet[14]);
   step1[13] = vec_mergel(kernel.packet[6], kernel.packet[14]);
   step1[14] = vec_mergeh(kernel.packet[7], kernel.packet[15]);
   step1[15] = vec_mergel(kernel.packet[7], kernel.packet[15]);
 
   step2[0]  = vec_mergeh(step1[0], step1[8]);
   step2[1]  = vec_mergel(step1[0], step1[8]);
   step2[2]  = vec_mergeh(step1[1], step1[9]);
   step2[3]  = vec_mergel(step1[1], step1[9]);
   step2[4]  = vec_mergeh(step1[2], step1[10]);
   step2[5]  = vec_mergel(step1[2], step1[10]);
   step2[6]  = vec_mergeh(step1[3], step1[11]);
   step2[7]  = vec_mergel(step1[3], step1[11]);
   step2[8]  = vec_mergeh(step1[4], step1[12]);
   step2[9]  = vec_mergel(step1[4], step1[12]);
   step2[10] = vec_mergeh(step1[5], step1[13]);
   step2[11] = vec_mergel(step1[5], step1[13]);
   step2[12] = vec_mergeh(step1[6], step1[14]);
   step2[13] = vec_mergel(step1[6], step1[14]);
   step2[14] = vec_mergeh(step1[7], step1[15]);
   step2[15] = vec_mergel(step1[7], step1[15]);
 
   step3[0]  = vec_mergeh(step2[0], step2[8]);
   step3[1]  = vec_mergel(step2[0], step2[8]);
   step3[2]  = vec_mergeh(step2[1], step2[9]);
   step3[3]  = vec_mergel(step2[1], step2[9]);
   step3[4]  = vec_mergeh(step2[2], step2[10]);
   step3[5]  = vec_mergel(step2[2], step2[10]);
   step3[6]  = vec_mergeh(step2[3], step2[11]);
   step3[7]  = vec_mergel(step2[3], step2[11]);
   step3[8]  = vec_mergeh(step2[4], step2[12]);
   step3[9]  = vec_mergel(step2[4], step2[12]);
   step3[10] = vec_mergeh(step2[5], step2[13]);
   step3[11] = vec_mergel(step2[5], step2[13]);
   step3[12] = vec_mergeh(step2[6], step2[14]);
   step3[13] = vec_mergel(step2[6], step2[14]);
   step3[14] = vec_mergeh(step2[7], step2[15]);
   step3[15] = vec_mergel(step2[7], step2[15]);
 
   kernel.packet[0]  = vec_mergeh(step3[0], step3[8]);
   kernel.packet[1]  = vec_mergel(step3[0], step3[8]);
   kernel.packet[2]  = vec_mergeh(step3[1], step3[9]);
   kernel.packet[3]  = vec_mergel(step3[1], step3[9]);
   kernel.packet[4]  = vec_mergeh(step3[2], step3[10]);
   kernel.packet[5]  = vec_mergel(step3[2], step3[10]);
   kernel.packet[6]  = vec_mergeh(step3[3], step3[11]);
   kernel.packet[7]  = vec_mergel(step3[3], step3[11]);
   kernel.packet[8]  = vec_mergeh(step3[4], step3[12]);
   kernel.packet[9]  = vec_mergel(step3[4], step3[12]);
   kernel.packet[10] = vec_mergeh(step3[5], step3[13]);
   kernel.packet[11] = vec_mergel(step3[5], step3[13]);
   kernel.packet[12] = vec_mergeh(step3[6], step3[14]);
   kernel.packet[13] = vec_mergel(step3[6], step3[14]);
   kernel.packet[14] = vec_mergeh(step3[7], step3[15]);
   kernel.packet[15] = vec_mergel(step3[7], step3[15]);
 }
 
 template<typename Packet> EIGEN_STRONG_INLINE
 Packet pblend4(const Selector<4>& ifPacket, const Packet& thenPacket, const Packet& 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 Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
   return pblend4<Packet4i>(ifPacket, thenPacket, elsePacket);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
   return pblend4<Packet4f>(ifPacket, thenPacket, elsePacket);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8s pblend(const Selector<8>& ifPacket, const Packet8s& thenPacket, const Packet8s& elsePacket) {
   Packet8us select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
                        ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7] };
   Packet8us mask = reinterpret_cast<Packet8us>(vec_cmpeq(select, p8us_ONE));
   Packet8s result = vec_sel(elsePacket, thenPacket, mask);
   return result;
 }
 
 template<> EIGEN_STRONG_INLINE Packet8us pblend(const Selector<8>& ifPacket, const Packet8us& thenPacket, const Packet8us& elsePacket) {
   Packet8us select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
                        ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7] };
   Packet8us mask = reinterpret_cast<Packet8us>(vec_cmpeq(reinterpret_cast<Packet8us>(select), p8us_ONE));
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pblend(const Selector<8>& ifPacket, const Packet8bf& thenPacket, const Packet8bf& elsePacket) {
   return pblend<Packet8us>(ifPacket, thenPacket, elsePacket);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16c pblend(const Selector<16>& ifPacket, const Packet16c& thenPacket, const Packet16c& elsePacket) {
   Packet16uc select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
                        ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7],
                        ifPacket.select[8], ifPacket.select[9], ifPacket.select[10], ifPacket.select[11],
                        ifPacket.select[12], ifPacket.select[13], ifPacket.select[14], ifPacket.select[15] };
 
   Packet16uc mask = reinterpret_cast<Packet16uc>(vec_cmpeq(reinterpret_cast<Packet16uc>(select), p16uc_ONE));
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
 template<> EIGEN_STRONG_INLINE Packet16uc pblend(const Selector<16>& ifPacket, const Packet16uc& thenPacket, const Packet16uc& elsePacket) {
   Packet16uc select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3],
                        ifPacket.select[4], ifPacket.select[5], ifPacket.select[6], ifPacket.select[7],
                        ifPacket.select[8], ifPacket.select[9], ifPacket.select[10], ifPacket.select[11],
                        ifPacket.select[12], ifPacket.select[13], ifPacket.select[14], ifPacket.select[15] };
 
   Packet16uc mask = reinterpret_cast<Packet16uc>(vec_cmpeq(reinterpret_cast<Packet16uc>(select), p16uc_ONE));
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
 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 <>
 struct type_casting_traits<bfloat16, unsigned short int> {
   enum {
     VectorizedCast = 1,
     SrcCoeffRatio = 1,
     TgtCoeffRatio = 1
   };
 };
 
 template <>
 struct type_casting_traits<unsigned short int, bfloat16> {
   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 Packet4ui pcast<Packet4f, Packet4ui>(const Packet4f& a) {
   return vec_ctu(a,0);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4i, Packet4f>(const Packet4i& a) {
   return vec_ctf(a,0);
 }
 
 template<> EIGEN_STRONG_INLINE Packet4f pcast<Packet4ui, Packet4f>(const Packet4ui& a) {
   return vec_ctf(a,0);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8us pcast<Packet8bf, Packet8us>(const Packet8bf& a) {
   Packet4f float_even = Bf16ToF32Even(a);
   Packet4f float_odd = Bf16ToF32Odd(a);
   Packet4ui int_even = pcast<Packet4f, Packet4ui>(float_even);
   Packet4ui int_odd = pcast<Packet4f, Packet4ui>(float_odd);
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
   Packet4ui low_even = pand<Packet4ui>(int_even, p4ui_low_mask);
   Packet4ui low_odd = pand<Packet4ui>(int_odd, p4ui_low_mask);
 
   //Check values that are bigger than USHRT_MAX (0xFFFF)
   Packet4bi overflow_selector;
   if(vec_any_gt(int_even, p4ui_low_mask)){
     overflow_selector = vec_cmpgt(int_even, p4ui_low_mask);
     low_even = vec_sel(low_even, p4ui_low_mask, overflow_selector);
   }
   if(vec_any_gt(int_odd, p4ui_low_mask)){
     overflow_selector = vec_cmpgt(int_odd, p4ui_low_mask);
     low_odd = vec_sel(low_even, p4ui_low_mask, overflow_selector);
   }
 
   low_odd = plogical_shift_left<16>(low_odd);
 
   Packet4ui int_final = por<Packet4ui>(low_even, low_odd);
   return reinterpret_cast<Packet8us>(int_final);
 }
 
 template<> EIGEN_STRONG_INLINE Packet8bf pcast<Packet8us, Packet8bf>(const Packet8us& a) {
   //short -> int -> float -> bfloat16
   const _EIGEN_DECLARE_CONST_FAST_Packet4ui(low_mask, 0x0000FFFF);
   Packet4ui int_cast = reinterpret_cast<Packet4ui>(a);
   Packet4ui int_even = pand<Packet4ui>(int_cast, p4ui_low_mask);
   Packet4ui int_odd = plogical_shift_right<16>(int_cast);
   Packet4f float_even = pcast<Packet4ui, Packet4f>(int_even);
   Packet4f float_odd = pcast<Packet4ui, Packet4f>(int_odd);
   return F32ToBf16(float_even, float_odd);
 }
 
 
 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;
 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_ONE  = { 1, 1 };
 static Packet2l  p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);
 static Packet2ul p2ul_SIGN = { 0x8000000000000000ull, 0x8000000000000000ull };
 static Packet2ul p2ul_PREV0DOT5 = { 0x3FDFFFFFFFFFFFFFull, 0x3FDFFFFFFFFFFFFFull };
 static Packet2d  p2d_ONE  = { 1.0, 1.0 };
 static Packet2d  p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO);
 static Packet2d  p2d_MZERO = { numext::bit_cast<double>(0x8000000000000000ull),
                                numext::bit_cast<double>(0x8000000000000000ull) };
 
 #ifdef _BIG_ENDIAN
 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 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8));
 #endif
 
 template<int index> Packet2d vec_splat_dbl(Packet2d& a)
 {
   return vec_splat(a, index);
 }
 
 template<> struct packet_traits<double> : default_packet_traits
 {
   typedef Packet2d type;
   typedef Packet2d half;
   enum {
     Vectorizable = 1,
     AlignedOnScalar = 1,
     size=2,
     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 = 1,
     HasRsqrt = 1,
     HasRound = 1,
     HasFloor = 1,
     HasCeil = 1,
     HasRint = 1,
     HasNegate = 1,
     HasBlend = 1
   };
 };
 
 template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; 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)
 {
   union {
     Packet2d   v;
     double n[2];
   } vt;
   vt.v = v;
   s << vt.n[0] << ", " << vt.n[1];
   return s;
 }
 
 // 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 vec_xl(0, const_cast<double *>(from)); // cast needed by Clang
 }
 
 template<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from)
 {
   EIGEN_DEBUG_ALIGNED_STORE
   vec_xst(from, 0, to);
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) {
   Packet2d v = {from, from};
   return v;
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(unsigned long from) {
   Packet2l v = {static_cast<long long>(from), static_cast<long long>(from)};
   return reinterpret_cast<Packet2d>(v);
 }
 
 template<> EIGEN_STRONG_INLINE void
 pbroadcast4<Packet2d>(const double *a,
                       Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
 {
   //This way is faster than vec_splat (at least for doubles in Power 9)
   a0 = pset1<Packet2d>(a[0]);
   a1 = pset1<Packet2d>(a[1]);
   a2 = pset1<Packet2d>(a[2]);
   a3 = pset1<Packet2d>(a[3]);
 }
 
 template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
 {
   EIGEN_ALIGN16 double af[2];
   af[0] = from[0*stride];
   af[1] = from[1*stride];
  return pload<Packet2d>(af);
 }
 template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
 {
   EIGEN_ALIGN16 double af[2];
   pstore<double>(af, from);
   to[0*stride] = af[0];
   to[1*stride] = af[1];
 }
 
 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 a - b; }
 
 template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return p2d_ZERO - a; }
 
 template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
 
 template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_madd(a,b,p2d_MZERO); }
 template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_div(a,b); }
 
 // for some weird raisons, it has to be overloaded for packet of integers
 template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }
 
 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b)
 {
   // NOTE: about 10% slower than vec_min, but consistent with std::min and SSE regarding NaN
   Packet2d ret;
   __asm__ ("xvcmpgedp %x0,%x1,%x2\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
   return ret;
  }
 
 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b)
 {
   // NOTE: about 10% slower than vec_max, but consistent with std::max and SSE regarding NaN
   Packet2d ret;
   __asm__ ("xvcmpgtdp %x0,%x2,%x1\n\txxsel %x0,%x1,%x2,%x0" : "=&wa" (ret) : "wa" (a), "wa" (b));
   return ret;
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmple(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmplt(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) { return reinterpret_cast<Packet2d>(vec_cmpeq(a,b)); }
 template<> EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) {
   Packet2d c = reinterpret_cast<Packet2d>(vec_cmpge(a,b));
   return vec_nor(c,c);
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }
 
 template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }
 
 template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }
 
 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)
 {
     Packet2d t = vec_add(reinterpret_cast<Packet2d>(vec_or(vec_and(reinterpret_cast<Packet2ul>(a), p2ul_SIGN), p2ul_PREV0DOT5)), a);
     Packet2d res;
 
     __asm__("xvrdpiz %x0, %x1\n\t"
         : "=&wa" (res)
         : "wa" (t));
 
     return res;
 }
 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 print<Packet2d>(const Packet2d& a)
 {
     Packet2d res;
 
     __asm__("xvrdpic %x0, %x1\n\t"
         : "=&wa" (res)
         : "wa" (a));
 
     return res;
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
 {
   EIGEN_DEBUG_UNALIGNED_LOAD
   return vec_xl(0, const_cast<double*>(from));
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)
 {
   Packet2d p;
   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet2d>(from);
   else                                  p = ploadu<Packet2d>(from);
   return vec_splat_dbl<0>(p);
 }
 
 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from)
 {
   EIGEN_DEBUG_UNALIGNED_STORE
   vec_xst(from, 0, to);
 }
 
 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); }
 
 template<> EIGEN_STRONG_INLINE double  pfirst<Packet2d>(const Packet2d& a) { EIGEN_ALIGN16 double 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); }
 
 // 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
 template<>
 inline Packet2l pcast<Packet2d, Packet2l>(const Packet2d& x) {
 #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];
   memcpy(tmp, &x, sizeof(tmp));
   Packet2l l = { static_cast<long long>(tmp[0]),
                  static_cast<long long>(tmp[1]) };
   return l;
 #endif
 }
 
 template<>
 inline Packet2d pcast<Packet2l, Packet2d>(const Packet2l& x) {
   unsigned long long tmp[2];
   memcpy(tmp, &x, sizeof(tmp));
   Packet2d d = { static_cast<double>(tmp[0]),
                  static_cast<double>(tmp[1]) };
   return d;
 }
 
 
 // Packet2l shifts.
 // For POWER8 we simply use vec_sr/l. 
 //
 // Things are more complicated for POWER7. There is actually a
 // vec_xxsxdi intrinsic but it is not supported by some gcc versions.
 // So we need to shift by N % 32 and rearrage bytes.
 #ifdef __POWER8_VECTOR__
 
 template<int N>
 EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) {
   const Packet2ul shift = { N, N };
   return vec_sl(a, shift); 
 }
 
 template<int N>
 EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) {
   const Packet2ul shift = { N, N };
   return vec_sr(a, shift); 
 }
 
 #else
 
 // Shifts [A, B, C, D] to [B, 0, D, 0].
 // Used to implement left shifts for Packet2l.
 EIGEN_ALWAYS_INLINE Packet4i shift_even_left(const Packet4i& a) {
   static const Packet16uc perm = {
       0x14, 0x15, 0x16, 0x17, 0x00, 0x01, 0x02, 0x03, 
       0x1c, 0x1d, 0x1e, 0x1f, 0x08, 0x09, 0x0a, 0x0b };
   #ifdef  _BIG_ENDIAN
     return vec_perm(p4i_ZERO, a, perm);
   #else
     return vec_perm(a, p4i_ZERO, perm);
   #endif
 }
 
 // Shifts [A, B, C, D] to [0, A, 0, C].
 // Used to implement right shifts for Packet2l.
 EIGEN_ALWAYS_INLINE Packet4i shift_odd_right(const Packet4i& a) {
   static const Packet16uc perm = {
       0x04, 0x05, 0x06, 0x07, 0x10, 0x11, 0x12, 0x13, 
       0x0c, 0x0d, 0x0e, 0x0f, 0x18, 0x19, 0x1a, 0x1b };
   #ifdef  _BIG_ENDIAN
     return vec_perm(p4i_ZERO, a, perm);
   #else
     return vec_perm(a, p4i_ZERO, perm);
   #endif
 }
 
 template<int N, typename EnableIf = void>
 struct plogical_shift_left_impl;
 
 template<int N>
 struct plogical_shift_left_impl<N, typename enable_if<(N < 32) && (N >= 0)>::type> {
   static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
     static const unsigned n = static_cast<unsigned>(N);
     const Packet4ui shift = {n, n, n, n};
     const Packet4i ai = reinterpret_cast<Packet4i>(a);
     static const unsigned m = static_cast<unsigned>(32 - N);
     const Packet4ui shift_right = {m, m, m, m};
     const Packet4i out_hi = vec_sl(ai, shift);
     const Packet4i out_lo = shift_even_left(vec_sr(ai, shift_right));
     return reinterpret_cast<Packet2l>(por<Packet4i>(out_hi, out_lo));
   }
 };
 
 template<int N>
 struct plogical_shift_left_impl<N, typename enable_if<(N >= 32)>::type> {
   static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
     static const unsigned m = static_cast<unsigned>(N - 32);
     const Packet4ui shift = {m, m, m, m};
     const Packet4i ai = reinterpret_cast<Packet4i>(a);
     return reinterpret_cast<Packet2l>(shift_even_left(vec_sl(ai, shift)));
   }
 };
 
 template<int N>
 EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) {
   return plogical_shift_left_impl<N>::run(a); 
 }
 
 template<int N, typename EnableIf = void>
 struct plogical_shift_right_impl;
 
 template<int N>
 struct plogical_shift_right_impl<N, typename enable_if<(N < 32) && (N >= 0)>::type> {
   static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
     static const unsigned n = static_cast<unsigned>(N);
     const Packet4ui shift = {n, n, n, n};
     const Packet4i ai = reinterpret_cast<Packet4i>(a);
     static const unsigned m = static_cast<unsigned>(32 - N);
     const Packet4ui shift_left = {m, m, m, m};
     const Packet4i out_lo = vec_sr(ai, shift);
     const Packet4i out_hi = shift_odd_right(vec_sl(ai, shift_left));
     return reinterpret_cast<Packet2l>(por<Packet4i>(out_hi, out_lo));
   }
 };
 
 template<int N>
 struct plogical_shift_right_impl<N, typename enable_if<(N >= 32)>::type> {
   static EIGEN_STRONG_INLINE Packet2l run(const Packet2l& a) {
     static const unsigned m = static_cast<unsigned>(N - 32);
     const Packet4ui shift = {m, m, m, m};
     const Packet4i ai = reinterpret_cast<Packet4i>(a);
     return reinterpret_cast<Packet2l>(shift_odd_right(vec_sr(ai, shift)));
   }
 };
 
 template<int N>
 EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) {
   return plogical_shift_right_impl<N>::run(a); 
 }
 #endif
 
 template<> EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent) {
   // Clamp exponent to [-2099, 2099]
   const Packet2d max_exponent = pset1<Packet2d>(2099.0);
   const Packet2l e = pcast<Packet2d, Packet2l>(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
 
   // Split 2^e into four factors and multiply:
   const Packet2l  bias = { 1023, 1023 };
   Packet2l b = plogical_shift_right<2>(e);  // floor(e/4)
   Packet2d c = reinterpret_cast<Packet2d>(plogical_shift_left<52>(b + bias));
   Packet2d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
   b = psub(psub(psub(e, b), b), b);  // e - 3b
   c = reinterpret_cast<Packet2d>(plogical_shift_left<52>(b + bias)); // 2^(e - 3b)
   out = pmul(out, c); // a * 2^e
   return out;
 }
 
 
 // Extract exponent without existence of Packet2l.
 template<>
 EIGEN_STRONG_INLINE  
 Packet2d pfrexp_generic_get_biased_exponent(const Packet2d& a) {
   return pcast<Packet2l, Packet2d>(plogical_shift_right<52>(reinterpret_cast<Packet2l>(pabs(a))));
 }
 
 template<> EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d> (const Packet2d& a, Packet2d& exponent) {
   return pfrexp_generic(a, exponent);
 }
 
 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
 {
   Packet2d b, sum;
   b   = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8));
   sum = a + b;
   return pfirst<Packet2d>(sum);
 }
 
 // Other reduction functions:
 // mul
 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
 {
   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(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(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
 }
 
 EIGEN_DEVICE_FUNC inline void
 ptranspose(PacketBlock<Packet2d,2>& kernel) {
   Packet2d t0, t1;
   t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);
   t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);
   kernel.packet[0] = t0;
   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 = reinterpret_cast<Packet2bl>( vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE)) );
   return vec_sel(elsePacket, thenPacket, mask);
 }
 
 
 #endif // __VSX__
 } // end namespace internal
 
 } // end namespace RivetEigen
 
 #endif // EIGEN_PACKET_MATH_ALTIVEC_H