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      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2008-2016 Konstantinos Margaritis <markos (at) freevec.org>
      5 //
      6 // This Source Code Form is subject to the terms of the Mozilla
      7 // Public License v. 2.0. If a copy of the MPL was not distributed
      8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
      9 
     10 #ifndef EIGEN_PACKET_MATH_ALTIVEC_H
     11 #define EIGEN_PACKET_MATH_ALTIVEC_H
     12 
     13 namespace Eigen {
     14 
     15 namespace internal {
     16 
     17 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
     18 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
     19 #endif
     20 
     21 #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
     22 #define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
     23 #endif
     24 
     25 #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
     26 #define EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
     27 #endif
     28 
     29 // NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
     30 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
     31 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS  32
     32 #endif
     33 
     34 typedef __vector float          Packet4f;
     35 typedef __vector int            Packet4i;
     36 typedef __vector unsigned int   Packet4ui;
     37 typedef __vector __bool int     Packet4bi;
     38 typedef __vector short int      Packet8i;
     39 typedef __vector unsigned char  Packet16uc;
     40 
     41 // We don't want to write the same code all the time, but we need to reuse the constants
     42 // and it doesn't really work to declare them global, so we define macros instead
     43 
     44 #define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
     45   Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(vec_splat_s32(X))
     46 
     47 #define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
     48   Packet4i p4i_##NAME = vec_splat_s32(X)
     49 
     50 #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
     51   Packet4f p4f_##NAME = pset1<Packet4f>(X)
     52 
     53 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
     54   Packet4i p4i_##NAME = pset1<Packet4i>(X)
     55 
     56 #define _EIGEN_DECLARE_CONST_Packet2d(NAME,X) \
     57   Packet2d p2d_##NAME = pset1<Packet2d>(X)
     58 
     59 #define _EIGEN_DECLARE_CONST_Packet2l(NAME,X) \
     60   Packet2l p2l_##NAME = pset1<Packet2l>(X)
     61 
     62 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
     63   const Packet4f p4f_##NAME = reinterpret_cast<Packet4f>(pset1<Packet4i>(X))
     64 
     65 #define DST_CHAN 1
     66 #define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
     67 
     68 
     69 // These constants are endian-agnostic
     70 static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0); //{ 0.0, 0.0, 0.0, 0.0}
     71 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0); //{ 0, 0, 0, 0,}
     72 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1); //{ 1, 1, 1, 1}
     73 static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16); //{ -16, -16, -16, -16}
     74 static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1); //{ -1, -1, -1, -1}
     75 static Packet4f p4f_MZERO = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1); //{ 0x80000000, 0x80000000, 0x80000000, 0x80000000}
     76 #ifndef __VSX__
     77 static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0); //{ 1.0, 1.0, 1.0, 1.0}
     78 #endif
     79 
     80 static Packet4f p4f_COUNTDOWN = { 0.0, 1.0, 2.0, 3.0 };
     81 static Packet4i p4i_COUNTDOWN = { 0, 1, 2, 3 };
     82 
     83 static Packet16uc p16uc_REVERSE32 = { 12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3 };
     84 static Packet16uc p16uc_DUPLICATE32_HI = { 0,1,2,3, 0,1,2,3, 4,5,6,7, 4,5,6,7 };
     85 
     86 // Mask alignment
     87 #ifdef __PPC64__
     88 #define _EIGEN_MASK_ALIGNMENT	0xfffffffffffffff0
     89 #else
     90 #define _EIGEN_MASK_ALIGNMENT	0xfffffff0
     91 #endif
     92 
     93 #define _EIGEN_ALIGNED_PTR(x)	((std::ptrdiff_t)(x) & _EIGEN_MASK_ALIGNMENT)
     94 
     95 // Handle endianness properly while loading constants
     96 // Define global static constants:
     97 #ifdef _BIG_ENDIAN
     98 static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
     99 #ifdef __VSX__
    100 static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
    101 #endif
    102 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 };
    103 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 };
    104 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};
    105 #else
    106 static Packet16uc p16uc_FORWARD = p16uc_REVERSE32;
    107 static Packet16uc p16uc_REVERSE64 = { 8,9,10,11, 12,13,14,15, 0,1,2,3, 4,5,6,7 };
    108 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 };
    109 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 };
    110 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};
    111 #endif // _BIG_ENDIAN
    112 
    113 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 };
    114 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 };
    115 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};
    116 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};
    117 
    118 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 };
    119 
    120 #ifdef _BIG_ENDIAN
    121 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 };
    122 #else
    123 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 };
    124 #endif // _BIG_ENDIAN
    125 
    126 #if EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
    127   #define EIGEN_PPC_PREFETCH(ADDR) __builtin_prefetch(ADDR);
    128 #else
    129   #define EIGEN_PPC_PREFETCH(ADDR) asm( "   dcbt [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
    130 #endif
    131 
    132 template<> struct packet_traits<float>  : default_packet_traits
    133 {
    134   typedef Packet4f type;
    135   typedef Packet4f half;
    136   enum {
    137     Vectorizable = 1,
    138     AlignedOnScalar = 1,
    139     size=4,
    140     HasHalfPacket = 1,
    141 
    142     HasAdd  = 1,
    143     HasSub  = 1,
    144     HasMul  = 1,
    145     HasDiv  = 1,
    146     HasMin  = 1,
    147     HasMax  = 1,
    148     HasAbs  = 1,
    149     HasSin  = 0,
    150     HasCos  = 0,
    151     HasLog  = 0,
    152     HasExp  = 1,
    153 #ifdef __VSX__
    154     HasSqrt = 1,
    155 #if !EIGEN_COMP_CLANG
    156     HasRsqrt = 1,
    157 #else
    158     HasRsqrt = 0,
    159 #endif
    160 #else
    161     HasSqrt = 0,
    162     HasRsqrt = 0,
    163 #endif
    164     HasRound = 1,
    165     HasFloor = 1,
    166     HasCeil = 1,
    167     HasNegate = 1,
    168     HasBlend = 1
    169   };
    170 };
    171 template<> struct packet_traits<int>    : default_packet_traits
    172 {
    173   typedef Packet4i type;
    174   typedef Packet4i half;
    175   enum {
    176     Vectorizable = 1,
    177     AlignedOnScalar = 1,
    178     size = 4,
    179     HasHalfPacket = 0,
    180 
    181     HasAdd  = 1,
    182     HasSub  = 1,
    183     HasMul  = 1,
    184     HasDiv  = 0,
    185     HasBlend = 1
    186   };
    187 };
    188 
    189 
    190 template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };
    191 template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
    192 
    193 inline std::ostream & operator <<(std::ostream & s, const Packet16uc & v)
    194 {
    195   union {
    196     Packet16uc   v;
    197     unsigned char n[16];
    198   } vt;
    199   vt.v = v;
    200   for (int i=0; i< 16; i++)
    201     s << (int)vt.n[i] << ", ";
    202   return s;
    203 }
    204 
    205 inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
    206 {
    207   union {
    208     Packet4f   v;
    209     float n[4];
    210   } vt;
    211   vt.v = v;
    212   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
    213   return s;
    214 }
    215 
    216 inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
    217 {
    218   union {
    219     Packet4i   v;
    220     int n[4];
    221   } vt;
    222   vt.v = v;
    223   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
    224   return s;
    225 }
    226 
    227 inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
    228 {
    229   union {
    230     Packet4ui   v;
    231     unsigned int n[4];
    232   } vt;
    233   vt.v = v;
    234   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
    235   return s;
    236 }
    237 
    238 // Need to define them first or we get specialization after instantiation errors
    239 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from)
    240 {
    241   EIGEN_DEBUG_ALIGNED_LOAD
    242 #ifdef __VSX__
    243   return vec_vsx_ld(0, from);
    244 #else
    245   return vec_ld(0, from);
    246 #endif
    247 }
    248 
    249 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from)
    250 {
    251   EIGEN_DEBUG_ALIGNED_LOAD
    252 #ifdef __VSX__
    253   return vec_vsx_ld(0, from);
    254 #else
    255   return vec_ld(0, from);
    256 #endif
    257 }
    258 
    259 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from)
    260 {
    261   EIGEN_DEBUG_ALIGNED_STORE
    262 #ifdef __VSX__
    263   vec_vsx_st(from, 0, to);
    264 #else
    265   vec_st(from, 0, to);
    266 #endif
    267 }
    268 
    269 template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from)
    270 {
    271   EIGEN_DEBUG_ALIGNED_STORE
    272 #ifdef __VSX__
    273   vec_vsx_st(from, 0, to);
    274 #else
    275   vec_st(from, 0, to);
    276 #endif
    277 }
    278 
    279 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) {
    280   Packet4f v = {from, from, from, from};
    281   return v;
    282 }
    283 
    284 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
    285   Packet4i v = {from, from, from, from};
    286   return v;
    287 }
    288 template<> EIGEN_STRONG_INLINE void
    289 pbroadcast4<Packet4f>(const float *a,
    290                       Packet4f& a0, Packet4f& a1, Packet4f& a2, Packet4f& a3)
    291 {
    292   a3 = pload<Packet4f>(a);
    293   a0 = vec_splat(a3, 0);
    294   a1 = vec_splat(a3, 1);
    295   a2 = vec_splat(a3, 2);
    296   a3 = vec_splat(a3, 3);
    297 }
    298 template<> EIGEN_STRONG_INLINE void
    299 pbroadcast4<Packet4i>(const int *a,
    300                       Packet4i& a0, Packet4i& a1, Packet4i& a2, Packet4i& a3)
    301 {
    302   a3 = pload<Packet4i>(a);
    303   a0 = vec_splat(a3, 0);
    304   a1 = vec_splat(a3, 1);
    305   a2 = vec_splat(a3, 2);
    306   a3 = vec_splat(a3, 3);
    307 }
    308 
    309 template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
    310 {
    311   float EIGEN_ALIGN16 af[4];
    312   af[0] = from[0*stride];
    313   af[1] = from[1*stride];
    314   af[2] = from[2*stride];
    315   af[3] = from[3*stride];
    316  return pload<Packet4f>(af);
    317 }
    318 template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int, Packet4i>(const int* from, Index stride)
    319 {
    320   int EIGEN_ALIGN16 ai[4];
    321   ai[0] = from[0*stride];
    322   ai[1] = from[1*stride];
    323   ai[2] = from[2*stride];
    324   ai[3] = from[3*stride];
    325  return pload<Packet4i>(ai);
    326 }
    327 template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
    328 {
    329   float EIGEN_ALIGN16 af[4];
    330   pstore<float>(af, from);
    331   to[0*stride] = af[0];
    332   to[1*stride] = af[1];
    333   to[2*stride] = af[2];
    334   to[3*stride] = af[3];
    335 }
    336 template<> EIGEN_DEVICE_FUNC inline void pscatter<int, Packet4i>(int* to, const Packet4i& from, Index stride)
    337 {
    338   int EIGEN_ALIGN16 ai[4];
    339   pstore<int>((int *)ai, from);
    340   to[0*stride] = ai[0];
    341   to[1*stride] = ai[1];
    342   to[2*stride] = ai[2];
    343   to[3*stride] = ai[3];
    344 }
    345 
    346 template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) { return pset1<Packet4f>(a) + p4f_COUNTDOWN; }
    347 template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int& a)   { return pset1<Packet4i>(a) + p4i_COUNTDOWN; }
    348 
    349 template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return a + b; }
    350 template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return a + b; }
    351 
    352 template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return a - b; }
    353 template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return a - b; }
    354 
    355 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return p4f_ZERO - a; }
    356 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return p4i_ZERO - a; }
    357 
    358 template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
    359 template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
    360 
    361 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b, p4f_MZERO); }
    362 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return a * b; }
    363 
    364 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
    365 {
    366 #ifndef __VSX__  // VSX actually provides a div instruction
    367   Packet4f t, y_0, y_1;
    368 
    369   // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
    370   y_0 = vec_re(b);
    371 
    372   // Do one Newton-Raphson iteration to get the needed accuracy
    373   t   = vec_nmsub(y_0, b, p4f_ONE);
    374   y_1 = vec_madd(y_0, t, y_0);
    375 
    376   return vec_madd(a, y_1, p4f_MZERO);
    377 #else
    378   return vec_div(a, b);
    379 #endif
    380 }
    381 
    382 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
    383 { eigen_assert(false && "packet integer division are not supported by AltiVec");
    384   return pset1<Packet4i>(0);
    385 }
    386 
    387 // for some weird raisons, it has to be overloaded for packet of integers
    388 template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a,b,c); }
    389 template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return a*b + c; }
    390 
    391 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_min(a, b); }
    392 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
    393 
    394 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_max(a, b); }
    395 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
    396 
    397 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
    398 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
    399 
    400 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
    401 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
    402 
    403 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
    404 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
    405 
    406 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
    407 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }
    408 
    409 template<> EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) { return vec_round(a); }
    410 template<> EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const  Packet4f& a) { return vec_ceil(a); }
    411 template<> EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) { return vec_floor(a); }
    412 
    413 #ifdef _BIG_ENDIAN
    414 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
    415 {
    416   EIGEN_DEBUG_ALIGNED_LOAD
    417   Packet16uc MSQ, LSQ;
    418   Packet16uc mask;
    419   MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
    420   LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
    421   mask = vec_lvsl(0, from);                        // create the permute mask
    422   return (Packet4f) vec_perm(MSQ, LSQ, mask);           // align the data
    423 
    424 }
    425 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
    426 {
    427   EIGEN_DEBUG_ALIGNED_LOAD
    428   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
    429   Packet16uc MSQ, LSQ;
    430   Packet16uc mask;
    431   MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
    432   LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
    433   mask = vec_lvsl(0, from);                        // create the permute mask
    434   return (Packet4i) vec_perm(MSQ, LSQ, mask);    // align the data
    435 }
    436 #else
    437 // We also need ot redefine little endian loading of Packet4i/Packet4f using VSX
    438 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
    439 {
    440   EIGEN_DEBUG_UNALIGNED_LOAD
    441   return (Packet4i) vec_vsx_ld((long)from & 15, (const int*) _EIGEN_ALIGNED_PTR(from));
    442 }
    443 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
    444 {
    445   EIGEN_DEBUG_UNALIGNED_LOAD
    446   return (Packet4f) vec_vsx_ld((long)from & 15, (const float*) _EIGEN_ALIGNED_PTR(from));
    447 }
    448 #endif
    449 
    450 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
    451 {
    452   Packet4f p;
    453   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet4f>(from);
    454   else                                  p = ploadu<Packet4f>(from);
    455   return vec_perm(p, p, p16uc_DUPLICATE32_HI);
    456 }
    457 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
    458 {
    459   Packet4i p;
    460   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet4i>(from);
    461   else                                  p = ploadu<Packet4i>(from);
    462   return vec_perm(p, p, p16uc_DUPLICATE32_HI);
    463 }
    464 
    465 #ifdef _BIG_ENDIAN
    466 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from)
    467 {
    468   EIGEN_DEBUG_UNALIGNED_STORE
    469   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
    470   // Warning: not thread safe!
    471   Packet16uc MSQ, LSQ, edges;
    472   Packet16uc edgeAlign, align;
    473 
    474   MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
    475   LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
    476   edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
    477   edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges
    478   align = vec_lvsr( 0, to );                                // permute map to misalign data
    479   MSQ = vec_perm(edges,(Packet16uc)from,align);             // misalign the data (MSQ)
    480   LSQ = vec_perm((Packet16uc)from,edges,align);             // misalign the data (LSQ)
    481   vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
    482   vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
    483 }
    484 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from)
    485 {
    486   EIGEN_DEBUG_UNALIGNED_STORE
    487   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
    488   // Warning: not thread safe!
    489   Packet16uc MSQ, LSQ, edges;
    490   Packet16uc edgeAlign, align;
    491 
    492   MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
    493   LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
    494   edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
    495   edges=vec_perm(LSQ, MSQ, edgeAlign);                      // extract the edges
    496   align = vec_lvsr( 0, to );                                // permute map to misalign data
    497   MSQ = vec_perm(edges, (Packet16uc) from, align);          // misalign the data (MSQ)
    498   LSQ = vec_perm((Packet16uc) from, edges, align);          // misalign the data (LSQ)
    499   vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
    500   vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
    501 }
    502 #else
    503 // We also need ot redefine little endian loading of Packet4i/Packet4f using VSX
    504 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*       to, const Packet4i& from)
    505 {
    506   EIGEN_DEBUG_ALIGNED_STORE
    507   vec_vsx_st(from, (long)to & 15, (int*) _EIGEN_ALIGNED_PTR(to));
    508 }
    509 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*   to, const Packet4f& from)
    510 {
    511   EIGEN_DEBUG_ALIGNED_STORE
    512   vec_vsx_st(from, (long)to & 15, (float*) _EIGEN_ALIGNED_PTR(to));
    513 }
    514 #endif
    515 
    516 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr)    { EIGEN_PPC_PREFETCH(addr); }
    517 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr)    { EIGEN_PPC_PREFETCH(addr); }
    518 
    519 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; }
    520 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x; vec_ste(a, 0, &x); return x; }
    521 
    522 template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
    523 {
    524   return reinterpret_cast<Packet4f>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32));
    525 }
    526 template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
    527 {
    528   return reinterpret_cast<Packet4i>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE32)); }
    529 
    530 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
    531 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
    532 
    533 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
    534 {
    535   Packet4f b, sum;
    536   b   = vec_sld(a, a, 8);
    537   sum = a + b;
    538   b   = vec_sld(sum, sum, 4);
    539   sum += b;
    540   return pfirst(sum);
    541 }
    542 
    543 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
    544 {
    545   Packet4f v[4], sum[4];
    546 
    547   // It's easier and faster to transpose then add as columns
    548   // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
    549   // Do the transpose, first set of moves
    550   v[0] = vec_mergeh(vecs[0], vecs[2]);
    551   v[1] = vec_mergel(vecs[0], vecs[2]);
    552   v[2] = vec_mergeh(vecs[1], vecs[3]);
    553   v[3] = vec_mergel(vecs[1], vecs[3]);
    554   // Get the resulting vectors
    555   sum[0] = vec_mergeh(v[0], v[2]);
    556   sum[1] = vec_mergel(v[0], v[2]);
    557   sum[2] = vec_mergeh(v[1], v[3]);
    558   sum[3] = vec_mergel(v[1], v[3]);
    559 
    560   // Now do the summation:
    561   // Lines 0+1
    562   sum[0] = sum[0] + sum[1];
    563   // Lines 2+3
    564   sum[1] = sum[2] + sum[3];
    565   // Add the results
    566   sum[0] = sum[0] + sum[1];
    567 
    568   return sum[0];
    569 }
    570 
    571 template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
    572 {
    573   Packet4i sum;
    574   sum = vec_sums(a, p4i_ZERO);
    575 #ifdef _BIG_ENDIAN
    576   sum = vec_sld(sum, p4i_ZERO, 12);
    577 #else
    578   sum = vec_sld(p4i_ZERO, sum, 4);
    579 #endif
    580   return pfirst(sum);
    581 }
    582 
    583 template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
    584 {
    585   Packet4i v[4], sum[4];
    586 
    587   // It's easier and faster to transpose then add as columns
    588   // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
    589   // Do the transpose, first set of moves
    590   v[0] = vec_mergeh(vecs[0], vecs[2]);
    591   v[1] = vec_mergel(vecs[0], vecs[2]);
    592   v[2] = vec_mergeh(vecs[1], vecs[3]);
    593   v[3] = vec_mergel(vecs[1], vecs[3]);
    594   // Get the resulting vectors
    595   sum[0] = vec_mergeh(v[0], v[2]);
    596   sum[1] = vec_mergel(v[0], v[2]);
    597   sum[2] = vec_mergeh(v[1], v[3]);
    598   sum[3] = vec_mergel(v[1], v[3]);
    599 
    600   // Now do the summation:
    601   // Lines 0+1
    602   sum[0] = sum[0] + sum[1];
    603   // Lines 2+3
    604   sum[1] = sum[2] + sum[3];
    605   // Add the results
    606   sum[0] = sum[0] + sum[1];
    607 
    608   return sum[0];
    609 }
    610 
    611 // Other reduction functions:
    612 // mul
    613 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
    614 {
    615   Packet4f prod;
    616   prod = pmul(a, vec_sld(a, a, 8));
    617   return pfirst(pmul(prod, vec_sld(prod, prod, 4)));
    618 }
    619 
    620 template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
    621 {
    622   EIGEN_ALIGN16 int aux[4];
    623   pstore(aux, a);
    624   return aux[0] * aux[1] * aux[2] * aux[3];
    625 }
    626 
    627 // min
    628 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
    629 {
    630   Packet4f b, res;
    631   b = vec_min(a, vec_sld(a, a, 8));
    632   res = vec_min(b, vec_sld(b, b, 4));
    633   return pfirst(res);
    634 }
    635 
    636 template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
    637 {
    638   Packet4i b, res;
    639   b = vec_min(a, vec_sld(a, a, 8));
    640   res = vec_min(b, vec_sld(b, b, 4));
    641   return pfirst(res);
    642 }
    643 
    644 // max
    645 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
    646 {
    647   Packet4f b, res;
    648   b = vec_max(a, vec_sld(a, a, 8));
    649   res = vec_max(b, vec_sld(b, b, 4));
    650   return pfirst(res);
    651 }
    652 
    653 template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
    654 {
    655   Packet4i b, res;
    656   b = vec_max(a, vec_sld(a, a, 8));
    657   res = vec_max(b, vec_sld(b, b, 4));
    658   return pfirst(res);
    659 }
    660 
    661 template<int Offset>
    662 struct palign_impl<Offset,Packet4f>
    663 {
    664   static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
    665   {
    666 #ifdef _BIG_ENDIAN
    667     switch (Offset % 4) {
    668     case 1:
    669       first = vec_sld(first, second, 4); break;
    670     case 2:
    671       first = vec_sld(first, second, 8); break;
    672     case 3:
    673       first = vec_sld(first, second, 12); break;
    674     }
    675 #else
    676     switch (Offset % 4) {
    677     case 1:
    678       first = vec_sld(second, first, 12); break;
    679     case 2:
    680       first = vec_sld(second, first, 8); break;
    681     case 3:
    682       first = vec_sld(second, first, 4); break;
    683     }
    684 #endif
    685   }
    686 };
    687 
    688 template<int Offset>
    689 struct palign_impl<Offset,Packet4i>
    690 {
    691   static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
    692   {
    693 #ifdef _BIG_ENDIAN
    694     switch (Offset % 4) {
    695     case 1:
    696       first = vec_sld(first, second, 4); break;
    697     case 2:
    698       first = vec_sld(first, second, 8); break;
    699     case 3:
    700       first = vec_sld(first, second, 12); break;
    701     }
    702 #else
    703     switch (Offset % 4) {
    704     case 1:
    705       first = vec_sld(second, first, 12); break;
    706     case 2:
    707       first = vec_sld(second, first, 8); break;
    708     case 3:
    709       first = vec_sld(second, first, 4); break;
    710     }
    711 #endif
    712   }
    713 };
    714 
    715 EIGEN_DEVICE_FUNC inline void
    716 ptranspose(PacketBlock<Packet4f,4>& kernel) {
    717   Packet4f t0, t1, t2, t3;
    718   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
    719   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
    720   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
    721   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
    722   kernel.packet[0] = vec_mergeh(t0, t2);
    723   kernel.packet[1] = vec_mergel(t0, t2);
    724   kernel.packet[2] = vec_mergeh(t1, t3);
    725   kernel.packet[3] = vec_mergel(t1, t3);
    726 }
    727 
    728 EIGEN_DEVICE_FUNC inline void
    729 ptranspose(PacketBlock<Packet4i,4>& kernel) {
    730   Packet4i t0, t1, t2, t3;
    731   t0 = vec_mergeh(kernel.packet[0], kernel.packet[2]);
    732   t1 = vec_mergel(kernel.packet[0], kernel.packet[2]);
    733   t2 = vec_mergeh(kernel.packet[1], kernel.packet[3]);
    734   t3 = vec_mergel(kernel.packet[1], kernel.packet[3]);
    735   kernel.packet[0] = vec_mergeh(t0, t2);
    736   kernel.packet[1] = vec_mergel(t0, t2);
    737   kernel.packet[2] = vec_mergeh(t1, t3);
    738   kernel.packet[3] = vec_mergel(t1, t3);
    739 }
    740 
    741 template<> EIGEN_STRONG_INLINE Packet4i pblend(const Selector<4>& ifPacket, const Packet4i& thenPacket, const Packet4i& elsePacket) {
    742   Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
    743   Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));
    744   return vec_sel(elsePacket, thenPacket, mask);
    745 }
    746 
    747 template<> EIGEN_STRONG_INLINE Packet4f pblend(const Selector<4>& ifPacket, const Packet4f& thenPacket, const Packet4f& elsePacket) {
    748   Packet4ui select = { ifPacket.select[0], ifPacket.select[1], ifPacket.select[2], ifPacket.select[3] };
    749   Packet4ui mask = reinterpret_cast<Packet4ui>(vec_cmpeq(reinterpret_cast<Packet4ui>(select), reinterpret_cast<Packet4ui>(p4i_ONE)));
    750   return vec_sel(elsePacket, thenPacket, mask);
    751 }
    752 
    753 
    754 //---------- double ----------
    755 #ifdef __VSX__
    756 typedef __vector double              Packet2d;
    757 typedef __vector unsigned long long  Packet2ul;
    758 typedef __vector long long           Packet2l;
    759 #if EIGEN_COMP_CLANG
    760 typedef Packet2ul                    Packet2bl;
    761 #else
    762 typedef __vector __bool long         Packet2bl;
    763 #endif
    764 
    765 static Packet2l  p2l_ONE  = { 1, 1 };
    766 static Packet2l  p2l_ZERO = reinterpret_cast<Packet2l>(p4i_ZERO);
    767 static Packet2d  p2d_ONE  = { 1.0, 1.0 };
    768 static Packet2d  p2d_ZERO = reinterpret_cast<Packet2d>(p4f_ZERO);
    769 static Packet2d  p2d_MZERO = { -0.0, -0.0 };
    770 
    771 #ifdef _BIG_ENDIAN
    772 static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ZERO), reinterpret_cast<Packet4f>(p2d_ONE), 8));
    773 #else
    774 static Packet2d p2d_COUNTDOWN = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(p2d_ONE), reinterpret_cast<Packet4f>(p2d_ZERO), 8));
    775 #endif
    776 
    777 template<int index> Packet2d vec_splat_dbl(Packet2d& a);
    778 
    779 template<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<0>(Packet2d& a)
    780 {
    781   return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_HI));
    782 }
    783 
    784 template<> EIGEN_STRONG_INLINE Packet2d vec_splat_dbl<1>(Packet2d& a)
    785 {
    786   return reinterpret_cast<Packet2d>(vec_perm(a, a, p16uc_PSET64_LO));
    787 }
    788 
    789 template<> struct packet_traits<double> : default_packet_traits
    790 {
    791   typedef Packet2d type;
    792   typedef Packet2d half;
    793   enum {
    794     Vectorizable = 1,
    795     AlignedOnScalar = 1,
    796     size=2,
    797     HasHalfPacket = 1,
    798 
    799     HasAdd  = 1,
    800     HasSub  = 1,
    801     HasMul  = 1,
    802     HasDiv  = 1,
    803     HasMin  = 1,
    804     HasMax  = 1,
    805     HasAbs  = 1,
    806     HasSin  = 0,
    807     HasCos  = 0,
    808     HasLog  = 0,
    809     HasExp  = 1,
    810     HasSqrt = 1,
    811     HasRsqrt = 1,
    812     HasRound = 1,
    813     HasFloor = 1,
    814     HasCeil = 1,
    815     HasNegate = 1,
    816     HasBlend = 1
    817   };
    818 };
    819 
    820 template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
    821 
    822 inline std::ostream & operator <<(std::ostream & s, const Packet2l & v)
    823 {
    824   union {
    825     Packet2l   v;
    826     int64_t n[2];
    827   } vt;
    828   vt.v = v;
    829   s << vt.n[0] << ", " << vt.n[1];
    830   return s;
    831 }
    832 
    833 inline std::ostream & operator <<(std::ostream & s, const Packet2d & v)
    834 {
    835   union {
    836     Packet2d   v;
    837     double n[2];
    838   } vt;
    839   vt.v = v;
    840   s << vt.n[0] << ", " << vt.n[1];
    841   return s;
    842 }
    843 
    844 // Need to define them first or we get specialization after instantiation errors
    845 template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from)
    846 {
    847   EIGEN_DEBUG_ALIGNED_LOAD
    848 #ifdef __VSX__
    849   return vec_vsx_ld(0, from);
    850 #else
    851   return vec_ld(0, from);
    852 #endif
    853 }
    854 
    855 template<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from)
    856 {
    857   EIGEN_DEBUG_ALIGNED_STORE
    858 #ifdef __VSX__
    859   vec_vsx_st(from, 0, to);
    860 #else
    861   vec_st(from, 0, to);
    862 #endif
    863 }
    864 
    865 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) {
    866   Packet2d v = {from, from};
    867   return v;
    868 }
    869 
    870 template<> EIGEN_STRONG_INLINE void
    871 pbroadcast4<Packet2d>(const double *a,
    872                       Packet2d& a0, Packet2d& a1, Packet2d& a2, Packet2d& a3)
    873 {
    874   a1 = pload<Packet2d>(a);
    875   a0 = vec_splat_dbl<0>(a1);
    876   a1 = vec_splat_dbl<1>(a1);
    877   a3 = pload<Packet2d>(a+2);
    878   a2 = vec_splat_dbl<0>(a3);
    879   a3 = vec_splat_dbl<1>(a3);
    880 }
    881 
    882 template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
    883 {
    884   double EIGEN_ALIGN16 af[2];
    885   af[0] = from[0*stride];
    886   af[1] = from[1*stride];
    887  return pload<Packet2d>(af);
    888 }
    889 template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
    890 {
    891   double EIGEN_ALIGN16 af[2];
    892   pstore<double>(af, from);
    893   to[0*stride] = af[0];
    894   to[1*stride] = af[1];
    895 }
    896 
    897 template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) { return pset1<Packet2d>(a) + p2d_COUNTDOWN; }
    898 
    899 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return a + b; }
    900 
    901 template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return a - b; }
    902 
    903 template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return p2d_ZERO - a; }
    904 
    905 template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
    906 
    907 template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_madd(a,b,p2d_MZERO); }
    908 template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_div(a,b); }
    909 
    910 // for some weird raisons, it has to be overloaded for packet of integers
    911 template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vec_madd(a, b, c); }
    912 
    913 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_min(a, b); }
    914 
    915 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_max(a, b); }
    916 
    917 template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, b); }
    918 
    919 template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_or(a, b); }
    920 
    921 template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_xor(a, b); }
    922 
    923 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return vec_and(a, vec_nor(b, b)); }
    924 
    925 template<> EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) { return vec_round(a); }
    926 template<> EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const  Packet2d& a) { return vec_ceil(a); }
    927 template<> EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) { return vec_floor(a); }
    928 
    929 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
    930 {
    931   EIGEN_DEBUG_ALIGNED_LOAD
    932   return (Packet2d) vec_vsx_ld((long)from & 15, (const double*) _EIGEN_ALIGNED_PTR(from));
    933 }
    934 
    935 template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)
    936 {
    937   Packet2d p;
    938   if((std::ptrdiff_t(from) % 16) == 0)  p = pload<Packet2d>(from);
    939   else                                  p = ploadu<Packet2d>(from);
    940   return vec_splat_dbl<0>(p);
    941 }
    942 
    943 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from)
    944 {
    945   EIGEN_DEBUG_ALIGNED_STORE
    946   vec_vsx_st((Packet4f)from, (long)to & 15, (float*) _EIGEN_ALIGNED_PTR(to));
    947 }
    948 
    949 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_PPC_PREFETCH(addr); }
    950 
    951 template<> EIGEN_STRONG_INLINE double  pfirst<Packet2d>(const Packet2d& a) { double EIGEN_ALIGN16 x[2]; pstore<double>(x, a); return x[0]; }
    952 
    953 template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
    954 {
    955   return reinterpret_cast<Packet2d>(vec_perm(reinterpret_cast<Packet16uc>(a), reinterpret_cast<Packet16uc>(a), p16uc_REVERSE64));
    956 }
    957 template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vec_abs(a); }
    958 
    959 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
    960 {
    961   Packet2d b, sum;
    962   b   = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(a), reinterpret_cast<Packet4f>(a), 8));
    963   sum = a + b;
    964   return pfirst<Packet2d>(sum);
    965 }
    966 
    967 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
    968 {
    969   Packet2d v[2], sum;
    970   v[0] = vecs[0] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[0]), reinterpret_cast<Packet4f>(vecs[0]), 8));
    971   v[1] = vecs[1] + reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(vecs[1]), reinterpret_cast<Packet4f>(vecs[1]), 8));
    972 
    973 #ifdef _BIG_ENDIAN
    974   sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[0]), reinterpret_cast<Packet4f>(v[1]), 8));
    975 #else
    976   sum = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4f>(v[1]), reinterpret_cast<Packet4f>(v[0]), 8));
    977 #endif
    978 
    979   return sum;
    980 }
    981 // Other reduction functions:
    982 // mul
    983 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
    984 {
    985   return pfirst(pmul(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
    986 }
    987 
    988 // min
    989 template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
    990 {
    991   return pfirst(pmin(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
    992 }
    993 
    994 // max
    995 template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
    996 {
    997   return pfirst(pmax(a, reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(a), reinterpret_cast<Packet4ui>(a), 8))));
    998 }
    999 
   1000 template<int Offset>
   1001 struct palign_impl<Offset,Packet2d>
   1002 {
   1003   static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
   1004   {
   1005     if (Offset == 1)
   1006 #ifdef _BIG_ENDIAN
   1007       first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(first), reinterpret_cast<Packet4ui>(second), 8));
   1008 #else
   1009       first = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(second), reinterpret_cast<Packet4ui>(first), 8));
   1010 #endif
   1011   }
   1012 };
   1013 
   1014 EIGEN_DEVICE_FUNC inline void
   1015 ptranspose(PacketBlock<Packet2d,2>& kernel) {
   1016   Packet2d t0, t1;
   1017   t0 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_HI);
   1018   t1 = vec_perm(kernel.packet[0], kernel.packet[1], p16uc_TRANSPOSE64_LO);
   1019   kernel.packet[0] = t0;
   1020   kernel.packet[1] = t1;
   1021 }
   1022 
   1023 template<> EIGEN_STRONG_INLINE Packet2d pblend(const Selector<2>& ifPacket, const Packet2d& thenPacket, const Packet2d& elsePacket) {
   1024   Packet2l select = { ifPacket.select[0], ifPacket.select[1] };
   1025   Packet2bl mask = vec_cmpeq(reinterpret_cast<Packet2d>(select), reinterpret_cast<Packet2d>(p2l_ONE));
   1026   return vec_sel(elsePacket, thenPacket, mask);
   1027 }
   1028 #endif // __VSX__
   1029 } // end namespace internal
   1030 
   1031 } // end namespace Eigen
   1032 
   1033 #endif // EIGEN_PACKET_MATH_ALTIVEC_H
   1034