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      1 // This file is part of Eigen, a lightweight C++ template library
      2 // for linear algebra.
      3 //
      4 // Copyright (C) 2010 Gael Guennebaud <gael.guennebaud (at) inria.fr>
      5 // Copyright (C) 2010-2016 Konstantinos Margaritis <markos (at) freevec.org>
      6 //
      7 // This Source Code Form is subject to the terms of the Mozilla
      8 // Public License v. 2.0. If a copy of the MPL was not distributed
      9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
     10 
     11 #ifndef EIGEN_COMPLEX32_ALTIVEC_H
     12 #define EIGEN_COMPLEX32_ALTIVEC_H
     13 
     14 namespace Eigen {
     15 
     16 namespace internal {
     17 
     18 static Packet4ui  p4ui_CONJ_XOR = vec_mergeh((Packet4ui)p4i_ZERO, (Packet4ui)p4f_MZERO);//{ 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
     19 #ifdef __VSX__
     20 #if defined(_BIG_ENDIAN)
     21 static Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2d_MZERO, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
     22 static Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_MZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
     23 #else
     24 static Packet2ul  p2ul_CONJ_XOR1 = (Packet2ul) vec_sld((Packet4ui) p2l_ZERO,  (Packet4ui) p2d_MZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
     25 static Packet2ul  p2ul_CONJ_XOR2 = (Packet2ul) vec_sld((Packet4ui) p2d_MZERO, (Packet4ui) p2l_ZERO, 8);//{ 0x8000000000000000, 0x0000000000000000 };
     26 #endif
     27 #endif
     28 
     29 //---------- float ----------
     30 struct Packet2cf
     31 {
     32   EIGEN_STRONG_INLINE explicit Packet2cf() : v(p4f_ZERO) {}
     33   EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
     34   Packet4f  v;
     35 };
     36 
     37 template<> struct packet_traits<std::complex<float> >  : default_packet_traits
     38 {
     39   typedef Packet2cf type;
     40   typedef Packet2cf half;
     41   enum {
     42     Vectorizable = 1,
     43     AlignedOnScalar = 1,
     44     size = 2,
     45     HasHalfPacket = 0,
     46 
     47     HasAdd    = 1,
     48     HasSub    = 1,
     49     HasMul    = 1,
     50     HasDiv    = 1,
     51     HasNegate = 1,
     52     HasAbs    = 0,
     53     HasAbs2   = 0,
     54     HasMin    = 0,
     55     HasMax    = 0,
     56 #ifdef __VSX__
     57     HasBlend  = 1,
     58 #endif
     59     HasSetLinear = 0
     60   };
     61 };
     62 
     63 template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };
     64 
     65 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
     66 {
     67   Packet2cf res;
     68   if((std::ptrdiff_t(&from) % 16) == 0)
     69     res.v = pload<Packet4f>((const float *)&from);
     70   else
     71     res.v = ploadu<Packet4f>((const float *)&from);
     72   res.v = vec_perm(res.v, res.v, p16uc_PSET64_HI);
     73   return res;
     74 }
     75 
     76 template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>*        from) { return Packet2cf(pload<Packet4f>((const float *) from)); }
     77 template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>*       from) { return Packet2cf(ploadu<Packet4f>((const float*) from)); }
     78 template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>*     from) { return pset1<Packet2cf>(*from); }
     79 
     80 template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { pstore((float*)to, from.v); }
     81 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { pstoreu((float*)to, from.v); }
     82 
     83 template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
     84 {
     85   std::complex<float> EIGEN_ALIGN16 af[2];
     86   af[0] = from[0*stride];
     87   af[1] = from[1*stride];
     88   return pload<Packet2cf>(af);
     89 }
     90 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
     91 {
     92   std::complex<float> EIGEN_ALIGN16 af[2];
     93   pstore<std::complex<float> >((std::complex<float> *) af, from);
     94   to[0*stride] = af[0];
     95   to[1*stride] = af[1];
     96 }
     97 
     98 template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v + b.v); }
     99 template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(a.v - b.v); }
    100 template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate(a.v)); }
    101 template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a) { return Packet2cf(pxor<Packet4f>(a.v, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR))); }
    102 
    103 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
    104 {
    105   Packet4f v1, v2;
    106 
    107   // Permute and multiply the real parts of a and b
    108   v1 = vec_perm(a.v, a.v, p16uc_PSET32_WODD);
    109   // Get the imaginary parts of a
    110   v2 = vec_perm(a.v, a.v, p16uc_PSET32_WEVEN);
    111   // multiply a_re * b
    112   v1 = vec_madd(v1, b.v, p4f_ZERO);
    113   // multiply a_im * b and get the conjugate result
    114   v2 = vec_madd(v2, b.v, p4f_ZERO);
    115   v2 = reinterpret_cast<Packet4f>(pxor(v2, reinterpret_cast<Packet4f>(p4ui_CONJ_XOR)));
    116   // permute back to a proper order
    117   v2 = vec_perm(v2, v2, p16uc_COMPLEX32_REV);
    118 
    119   return Packet2cf(padd<Packet4f>(v1, v2));
    120 }
    121 
    122 template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pand<Packet4f>(a.v, b.v)); }
    123 template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(por<Packet4f>(a.v, b.v)); }
    124 template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pxor<Packet4f>(a.v, b.v)); }
    125 template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(pandnot<Packet4f>(a.v, b.v)); }
    126 
    127 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr)    { EIGEN_PPC_PREFETCH(addr); }
    128 
    129 template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
    130 {
    131   std::complex<float> EIGEN_ALIGN16 res[2];
    132   pstore((float *)&res, a.v);
    133 
    134   return res[0];
    135 }
    136 
    137 template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
    138 {
    139   Packet4f rev_a;
    140   rev_a = vec_perm(a.v, a.v, p16uc_COMPLEX32_REV2);
    141   return Packet2cf(rev_a);
    142 }
    143 
    144 template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
    145 {
    146   Packet4f b;
    147   b = vec_sld(a.v, a.v, 8);
    148   b = padd<Packet4f>(a.v, b);
    149   return pfirst<Packet2cf>(Packet2cf(b));
    150 }
    151 
    152 template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
    153 {
    154   Packet4f b1, b2;
    155 #ifdef _BIG_ENDIAN
    156   b1 = vec_sld(vecs[0].v, vecs[1].v, 8);
    157   b2 = vec_sld(vecs[1].v, vecs[0].v, 8);
    158 #else
    159   b1 = vec_sld(vecs[1].v, vecs[0].v, 8);
    160   b2 = vec_sld(vecs[0].v, vecs[1].v, 8);
    161 #endif
    162   b2 = vec_sld(b2, b2, 8);
    163   b2 = padd<Packet4f>(b1, b2);
    164 
    165   return Packet2cf(b2);
    166 }
    167 
    168 template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
    169 {
    170   Packet4f b;
    171   Packet2cf prod;
    172   b = vec_sld(a.v, a.v, 8);
    173   prod = pmul<Packet2cf>(a, Packet2cf(b));
    174 
    175   return pfirst<Packet2cf>(prod);
    176 }
    177 
    178 template<int Offset>
    179 struct palign_impl<Offset,Packet2cf>
    180 {
    181   static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)
    182   {
    183     if (Offset==1)
    184     {
    185 #ifdef _BIG_ENDIAN
    186       first.v = vec_sld(first.v, second.v, 8);
    187 #else
    188       first.v = vec_sld(second.v, first.v, 8);
    189 #endif
    190     }
    191   }
    192 };
    193 
    194 template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
    195 {
    196   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
    197   { return padd(pmul(x,y),c); }
    198 
    199   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
    200   {
    201     return internal::pmul(a, pconj(b));
    202   }
    203 };
    204 
    205 template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
    206 {
    207   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
    208   { return padd(pmul(x,y),c); }
    209 
    210   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
    211   {
    212     return internal::pmul(pconj(a), b);
    213   }
    214 };
    215 
    216 template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
    217 {
    218   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
    219   { return padd(pmul(x,y),c); }
    220 
    221   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
    222   {
    223     return pconj(internal::pmul(a, b));
    224   }
    225 };
    226 
    227 template<> struct conj_helper<Packet4f, Packet2cf, false,false>
    228 {
    229   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet4f& x, const Packet2cf& y, const Packet2cf& c) const
    230   { return padd(c, pmul(x,y)); }
    231 
    232   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet4f& x, const Packet2cf& y) const
    233   { return Packet2cf(internal::pmul<Packet4f>(x, y.v)); }
    234 };
    235 
    236 template<> struct conj_helper<Packet2cf, Packet4f, false,false>
    237 {
    238   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet4f& y, const Packet2cf& c) const
    239   { return padd(c, pmul(x,y)); }
    240 
    241   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& x, const Packet4f& y) const
    242   { return Packet2cf(internal::pmul<Packet4f>(x.v, y)); }
    243 };
    244 
    245 template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
    246 {
    247   // TODO optimize it for AltiVec
    248   Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a, b);
    249   Packet4f s = pmul<Packet4f>(b.v, b.v);
    250   return Packet2cf(pdiv(res.v, padd<Packet4f>(s, vec_perm(s, s, p16uc_COMPLEX32_REV))));
    251 }
    252 
    253 template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& x)
    254 {
    255   return Packet2cf(vec_perm(x.v, x.v, p16uc_COMPLEX32_REV));
    256 }
    257 
    258 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2cf,2>& kernel)
    259 {
    260   Packet4f tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
    261   kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
    262   kernel.packet[0].v = tmp;
    263 }
    264 
    265 #ifdef __VSX__
    266 template<> EIGEN_STRONG_INLINE Packet2cf pblend(const Selector<2>& ifPacket, const Packet2cf& thenPacket, const Packet2cf& elsePacket) {
    267   Packet2cf result;
    268   result.v = reinterpret_cast<Packet4f>(pblend<Packet2d>(ifPacket, reinterpret_cast<Packet2d>(thenPacket.v), reinterpret_cast<Packet2d>(elsePacket.v)));
    269   return result;
    270 }
    271 #endif
    272 
    273 //---------- double ----------
    274 #ifdef __VSX__
    275 struct Packet1cd
    276 {
    277   EIGEN_STRONG_INLINE Packet1cd() {}
    278   EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
    279   Packet2d v;
    280 };
    281 
    282 template<> struct packet_traits<std::complex<double> >  : default_packet_traits
    283 {
    284   typedef Packet1cd type;
    285   typedef Packet1cd half;
    286   enum {
    287     Vectorizable = 1,
    288     AlignedOnScalar = 0,
    289     size = 1,
    290     HasHalfPacket = 0,
    291 
    292     HasAdd    = 1,
    293     HasSub    = 1,
    294     HasMul    = 1,
    295     HasDiv    = 1,
    296     HasNegate = 1,
    297     HasAbs    = 0,
    298     HasAbs2   = 0,
    299     HasMin    = 0,
    300     HasMax    = 0,
    301     HasSetLinear = 0
    302   };
    303 };
    304 
    305 template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
    306 
    307 template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from) { return Packet1cd(pload<Packet2d>((const double*)from)); }
    308 template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { return Packet1cd(ploadu<Packet2d>((const double*)from)); }
    309 template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { pstore((double*)to, from.v); }
    310 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> *   to, const Packet1cd& from) { pstoreu((double*)to, from.v); }
    311 
    312 template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)
    313 { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
    314 
    315 template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride)
    316 {
    317   std::complex<double> EIGEN_ALIGN16 af[2];
    318   af[0] = from[0*stride];
    319   af[1] = from[1*stride];
    320   return pload<Packet1cd>(af);
    321 }
    322 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride)
    323 {
    324   std::complex<double> EIGEN_ALIGN16 af[2];
    325   pstore<std::complex<double> >(af, from);
    326   to[0*stride] = af[0];
    327   to[1*stride] = af[1];
    328 }
    329 
    330 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v + b.v); }
    331 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(a.v - b.v); }
    332 template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(Packet2d(a.v))); }
    333 template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(pxor(a.v, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR2))); }
    334 
    335 template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
    336 {
    337   Packet2d a_re, a_im, v1, v2;
    338 
    339   // Permute and multiply the real parts of a and b
    340   a_re = vec_perm(a.v, a.v, p16uc_PSET64_HI);
    341   // Get the imaginary parts of a
    342   a_im = vec_perm(a.v, a.v, p16uc_PSET64_LO);
    343   // multiply a_re * b
    344   v1 = vec_madd(a_re, b.v, p2d_ZERO);
    345   // multiply a_im * b and get the conjugate result
    346   v2 = vec_madd(a_im, b.v, p2d_ZERO);
    347   v2 = reinterpret_cast<Packet2d>(vec_sld(reinterpret_cast<Packet4ui>(v2), reinterpret_cast<Packet4ui>(v2), 8));
    348   v2 = pxor(v2, reinterpret_cast<Packet2d>(p2ul_CONJ_XOR1));
    349 
    350   return Packet1cd(padd<Packet2d>(v1, v2));
    351 }
    352 
    353 template<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pand(a.v,b.v)); }
    354 template<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(por(a.v,b.v)); }
    355 template<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pxor(a.v,b.v)); }
    356 template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(pandnot(a.v, b.v)); }
    357 
    358 template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>*     from)  { return pset1<Packet1cd>(*from); }
    359 
    360 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr)    { EIGEN_PPC_PREFETCH(addr); }
    361 
    362 template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)
    363 {
    364   std::complex<double> EIGEN_ALIGN16 res[2];
    365   pstore<std::complex<double> >(res, a);
    366 
    367   return res[0];
    368 }
    369 
    370 template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
    371 
    372 template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
    373 template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)        { return vecs[0]; }
    374 
    375 template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
    376 
    377 template<int Offset>
    378 struct palign_impl<Offset,Packet1cd>
    379 {
    380   static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)
    381   {
    382     // FIXME is it sure we never have to align a Packet1cd?
    383     // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...
    384   }
    385 };
    386 
    387 template<> struct conj_helper<Packet1cd, Packet1cd, false,true>
    388 {
    389   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
    390   { return padd(pmul(x,y),c); }
    391 
    392   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
    393   {
    394     return internal::pmul(a, pconj(b));
    395   }
    396 };
    397 
    398 template<> struct conj_helper<Packet1cd, Packet1cd, true,false>
    399 {
    400   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
    401   { return padd(pmul(x,y),c); }
    402 
    403   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
    404   {
    405     return internal::pmul(pconj(a), b);
    406   }
    407 };
    408 
    409 template<> struct conj_helper<Packet1cd, Packet1cd, true,true>
    410 {
    411   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
    412   { return padd(pmul(x,y),c); }
    413 
    414   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
    415   {
    416     return pconj(internal::pmul(a, b));
    417   }
    418 };
    419 template<> struct conj_helper<Packet2d, Packet1cd, false,false>
    420 {
    421   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet2d& x, const Packet1cd& y, const Packet1cd& c) const
    422   { return padd(c, pmul(x,y)); }
    423 
    424   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet2d& x, const Packet1cd& y) const
    425   { return Packet1cd(internal::pmul<Packet2d>(x, y.v)); }
    426 };
    427 
    428 template<> struct conj_helper<Packet1cd, Packet2d, false,false>
    429 {
    430   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet2d& y, const Packet1cd& c) const
    431   { return padd(c, pmul(x,y)); }
    432 
    433   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& x, const Packet2d& y) const
    434   { return Packet1cd(internal::pmul<Packet2d>(x.v, y)); }
    435 };
    436 
    437 template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
    438 {
    439   // TODO optimize it for AltiVec
    440   Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);
    441   Packet2d s = pmul<Packet2d>(b.v, b.v);
    442   return Packet1cd(pdiv(res.v, padd<Packet2d>(s, vec_perm(s, s, p16uc_REVERSE64))));
    443 }
    444 
    445 EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
    446 {
    447   return Packet1cd(preverse(Packet2d(x.v)));
    448 }
    449 
    450 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
    451 {
    452   Packet2d tmp = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_HI);
    453   kernel.packet[1].v = vec_perm(kernel.packet[0].v, kernel.packet[1].v, p16uc_TRANSPOSE64_LO);
    454   kernel.packet[0].v = tmp;
    455 }
    456 #endif // __VSX__
    457 } // end namespace internal
    458 
    459 } // end namespace Eigen
    460 
    461 #endif // EIGEN_COMPLEX32_ALTIVEC_H
    462