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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@inria.fr>
5 // Copyright (C) 2010-2016 Konstantinos Margaritis <markos@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 {
Packet2cfPacket2cf32   EIGEN_STRONG_INLINE explicit Packet2cf() : v(p4f_ZERO) {}
Packet2cfPacket2cf33   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