SSE/Complex.h
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 //
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_COMPLEX_SSE_H
11 #define EIGEN_COMPLEX_SSE_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 //---------- float ----------
18 struct Packet2cf
19 {
20  EIGEN_STRONG_INLINE Packet2cf() {}
21  EIGEN_STRONG_INLINE explicit Packet2cf(const __m128& a) : v(a) {}
22  __m128 v;
23 };
24 
25 template<> struct packet_traits<std::complex<float> > : default_packet_traits
26 {
27  typedef Packet2cf type;
28  enum {
29  Vectorizable = 1,
30  AlignedOnScalar = 1,
31  size = 2,
32 
33  HasAdd = 1,
34  HasSub = 1,
35  HasMul = 1,
36  HasDiv = 1,
37  HasNegate = 1,
38  HasAbs = 0,
39  HasAbs2 = 0,
40  HasMin = 0,
41  HasMax = 0,
42  HasSetLinear = 0
43  };
44 };
45 
46 template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2}; };
47 
48 template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_add_ps(a.v,b.v)); }
49 template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_sub_ps(a.v,b.v)); }
50 template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a)
51 {
52  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
53  return Packet2cf(_mm_xor_ps(a.v,mask));
54 }
55 template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
56 {
57  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
58  return Packet2cf(_mm_xor_ps(a.v,mask));
59 }
60 
61 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
62 {
63  // TODO optimize it for SSE3 and 4
64  #ifdef EIGEN_VECTORIZE_SSE3
65  return Packet2cf(_mm_addsub_ps(_mm_mul_ps(_mm_moveldup_ps(a.v), b.v),
66  _mm_mul_ps(_mm_movehdup_ps(a.v),
67  vec4f_swizzle1(b.v, 1, 0, 3, 2))));
68 // return Packet2cf(_mm_addsub_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
69 // _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
70 // vec4f_swizzle1(b.v, 1, 0, 3, 2))));
71  #else
72  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x00000000,0x80000000,0x00000000));
73  return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
74  _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
75  vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));
76  #endif
77 }
78 
79 template<> EIGEN_STRONG_INLINE Packet2cf pand <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_and_ps(a.v,b.v)); }
80 template<> EIGEN_STRONG_INLINE Packet2cf por <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_or_ps(a.v,b.v)); }
81 template<> EIGEN_STRONG_INLINE Packet2cf pxor <Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_xor_ps(a.v,b.v)); }
82 template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(_mm_andnot_ps(a.v,b.v)); }
83 
84 template<> EIGEN_STRONG_INLINE Packet2cf pload <Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>(&real_ref(*from))); }
85 template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>(&real_ref(*from))); }
86 
87 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>& from)
88 {
89  Packet2cf res;
90  #if EIGEN_GNUC_AT_MOST(4,2)
91  // workaround annoying "may be used uninitialized in this function" warning with gcc 4.2
92  res.v = _mm_loadl_pi(_mm_set1_ps(0.0f), reinterpret_cast<const __m64*>(&from));
93  #else
94  res.v = _mm_loadl_pi(res.v, (const __m64*)&from);
95  #endif
96  return Packet2cf(_mm_movelh_ps(res.v,res.v));
97 }
98 
99 template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
100 
101 template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore(&real_ref(*to), from.v); }
102 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> * to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(&real_ref(*to), from.v); }
103 
104 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> * addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
105 
106 template<> EIGEN_STRONG_INLINE std::complex<float> pfirst<Packet2cf>(const Packet2cf& a)
107 {
108  #if EIGEN_GNUC_AT_MOST(4,3)
109  // Workaround gcc 4.2 ICE - this is not performance wise ideal, but who cares...
110  // This workaround also fix invalid code generation with gcc 4.3
111  EIGEN_ALIGN16 std::complex<float> res[2];
112  _mm_store_ps((float*)res, a.v);
113  return res[0];
114  #else
115  std::complex<float> res;
116  _mm_storel_pi((__m64*)&res, a.v);
117  return res;
118  #endif
119 }
120 
121 template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a) { return Packet2cf(_mm_castpd_ps(preverse(_mm_castps_pd(a.v)))); }
122 
123 template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
124 {
125  return pfirst(Packet2cf(_mm_add_ps(a.v, _mm_movehl_ps(a.v,a.v))));
126 }
127 
128 template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
129 {
130  return Packet2cf(_mm_add_ps(_mm_movelh_ps(vecs[0].v,vecs[1].v), _mm_movehl_ps(vecs[1].v,vecs[0].v)));
131 }
132 
133 template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
134 {
135  return pfirst(pmul(a, Packet2cf(_mm_movehl_ps(a.v,a.v))));
136 }
137 
138 template<int Offset>
139 struct palign_impl<Offset,Packet2cf>
140 {
141  static EIGEN_STRONG_INLINE void run(Packet2cf& first, const Packet2cf& second)
142  {
143  if (Offset==1)
144  {
145  first.v = _mm_movehl_ps(first.v, first.v);
146  first.v = _mm_movelh_ps(first.v, second.v);
147  }
148  }
149 };
150 
151 template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
152 {
153  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
154  { return padd(pmul(x,y),c); }
155 
156  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
157  {
158  #ifdef EIGEN_VECTORIZE_SSE3
159  return internal::pmul(a, pconj(b));
160  #else
161  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
162  return Packet2cf(_mm_add_ps(_mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v), mask),
163  _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
164  vec4f_swizzle1(b.v, 1, 0, 3, 2))));
165  #endif
166  }
167 };
168 
169 template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
170 {
171  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
172  { return padd(pmul(x,y),c); }
173 
174  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
175  {
176  #ifdef EIGEN_VECTORIZE_SSE3
177  return internal::pmul(pconj(a), b);
178  #else
179  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
180  return Packet2cf(_mm_add_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v),
181  _mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
182  vec4f_swizzle1(b.v, 1, 0, 3, 2)), mask)));
183  #endif
184  }
185 };
186 
187 template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
188 {
189  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
190  { return padd(pmul(x,y),c); }
191 
192  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
193  {
194  #ifdef EIGEN_VECTORIZE_SSE3
195  return pconj(internal::pmul(a, b));
196  #else
197  const __m128 mask = _mm_castsi128_ps(_mm_setr_epi32(0x00000000,0x80000000,0x00000000,0x80000000));
198  return Packet2cf(_mm_sub_ps(_mm_xor_ps(_mm_mul_ps(vec4f_swizzle1(a.v, 0, 0, 2, 2), b.v), mask),
199  _mm_mul_ps(vec4f_swizzle1(a.v, 1, 1, 3, 3),
200  vec4f_swizzle1(b.v, 1, 0, 3, 2))));
201  #endif
202  }
203 };
204 
205 template<> struct conj_helper<Packet4f, Packet2cf, false,false>
206 {
207  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet4f& x, const Packet2cf& y, const Packet2cf& c) const
208  { return padd(c, pmul(x,y)); }
209 
210  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet4f& x, const Packet2cf& y) const
211  { return Packet2cf(Eigen::internal::pmul(x, y.v)); }
212 };
213 
214 template<> struct conj_helper<Packet2cf, Packet4f, false,false>
215 {
216  EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet4f& y, const Packet2cf& c) const
217  { return padd(c, pmul(x,y)); }
218 
219  EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& x, const Packet4f& y) const
220  { return Packet2cf(Eigen::internal::pmul(x.v, y)); }
221 };
222 
223 template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
224 {
225  // TODO optimize it for SSE3 and 4
226  Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
227  __m128 s = _mm_mul_ps(b.v,b.v);
228  return Packet2cf(_mm_div_ps(res.v,_mm_add_ps(s,_mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(s), 0xb1)))));
229 }
230 
231 EIGEN_STRONG_INLINE Packet2cf pcplxflip/*<Packet2cf>*/(const Packet2cf& x)
232 {
233  return Packet2cf(vec4f_swizzle1(x.v, 1, 0, 3, 2));
234 }
235 
236 
237 //---------- double ----------
238 struct Packet1cd
239 {
240  EIGEN_STRONG_INLINE Packet1cd() {}
241  EIGEN_STRONG_INLINE explicit Packet1cd(const __m128d& a) : v(a) {}
242  __m128d v;
243 };
244 
245 template<> struct packet_traits<std::complex<double> > : default_packet_traits
246 {
247  typedef Packet1cd type;
248  enum {
249  Vectorizable = 1,
250  AlignedOnScalar = 0,
251  size = 1,
252 
253  HasAdd = 1,
254  HasSub = 1,
255  HasMul = 1,
256  HasDiv = 1,
257  HasNegate = 1,
258  HasAbs = 0,
259  HasAbs2 = 0,
260  HasMin = 0,
261  HasMax = 0,
262  HasSetLinear = 0
263  };
264 };
265 
266 template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1}; };
267 
268 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_add_pd(a.v,b.v)); }
269 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_sub_pd(a.v,b.v)); }
270 template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate(a.v)); }
271 template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a)
272 {
273  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
274  return Packet1cd(_mm_xor_pd(a.v,mask));
275 }
276 
277 template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
278 {
279  // TODO optimize it for SSE3 and 4
280  #ifdef EIGEN_VECTORIZE_SSE3
281  return Packet1cd(_mm_addsub_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
282  _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
283  vec2d_swizzle1(b.v, 1, 0))));
284  #else
285  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
286  return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
287  _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
288  vec2d_swizzle1(b.v, 1, 0)), mask)));
289  #endif
290 }
291 
292 template<> EIGEN_STRONG_INLINE Packet1cd pand <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_and_pd(a.v,b.v)); }
293 template<> EIGEN_STRONG_INLINE Packet1cd por <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_or_pd(a.v,b.v)); }
294 template<> EIGEN_STRONG_INLINE Packet1cd pxor <Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_xor_pd(a.v,b.v)); }
295 template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(_mm_andnot_pd(a.v,b.v)); }
296 
297 // FIXME force unaligned load, this is a temporary fix
298 template<> EIGEN_STRONG_INLINE Packet1cd pload <Packet1cd>(const std::complex<double>* from)
299 { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
300 template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from)
301 { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
302 template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>& from)
303 { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
304 
305 template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }
306 
307 // FIXME force unaligned store, this is a temporary fix
308 template<> EIGEN_STRONG_INLINE void pstore <std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((double*)to, from.v); }
309 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<double> >(std::complex<double> * to, const Packet1cd& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((double*)to, from.v); }
310 
311 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> * addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
312 
313 template<> EIGEN_STRONG_INLINE std::complex<double> pfirst<Packet1cd>(const Packet1cd& a)
314 {
315  EIGEN_ALIGN16 double res[2];
316  _mm_store_pd(res, a.v);
317  return std::complex<double>(res[0],res[1]);
318 }
319 
320 template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
321 
322 template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a)
323 {
324  return pfirst(a);
325 }
326 
327 template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs)
328 {
329  return vecs[0];
330 }
331 
332 template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a)
333 {
334  return pfirst(a);
335 }
336 
337 template<int Offset>
338 struct palign_impl<Offset,Packet1cd>
339 {
340  static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)
341  {
342  // FIXME is it sure we never have to align a Packet1cd?
343  // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...
344  }
345 };
346 
347 template<> struct conj_helper<Packet1cd, Packet1cd, false,true>
348 {
349  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
350  { return padd(pmul(x,y),c); }
351 
352  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
353  {
354  #ifdef EIGEN_VECTORIZE_SSE3
355  return internal::pmul(a, pconj(b));
356  #else
357  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
358  return Packet1cd(_mm_add_pd(_mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v), mask),
359  _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
360  vec2d_swizzle1(b.v, 1, 0))));
361  #endif
362  }
363 };
364 
365 template<> struct conj_helper<Packet1cd, Packet1cd, true,false>
366 {
367  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
368  { return padd(pmul(x,y),c); }
369 
370  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
371  {
372  #ifdef EIGEN_VECTORIZE_SSE3
373  return internal::pmul(pconj(a), b);
374  #else
375  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
376  return Packet1cd(_mm_add_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v),
377  _mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
378  vec2d_swizzle1(b.v, 1, 0)), mask)));
379  #endif
380  }
381 };
382 
383 template<> struct conj_helper<Packet1cd, Packet1cd, true,true>
384 {
385  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
386  { return padd(pmul(x,y),c); }
387 
388  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
389  {
390  #ifdef EIGEN_VECTORIZE_SSE3
391  return pconj(internal::pmul(a, b));
392  #else
393  const __m128d mask = _mm_castsi128_pd(_mm_set_epi32(0x80000000,0x0,0x0,0x0));
394  return Packet1cd(_mm_sub_pd(_mm_xor_pd(_mm_mul_pd(vec2d_swizzle1(a.v, 0, 0), b.v), mask),
395  _mm_mul_pd(vec2d_swizzle1(a.v, 1, 1),
396  vec2d_swizzle1(b.v, 1, 0))));
397  #endif
398  }
399 };
400 
401 template<> struct conj_helper<Packet2d, Packet1cd, false,false>
402 {
403  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet2d& x, const Packet1cd& y, const Packet1cd& c) const
404  { return padd(c, pmul(x,y)); }
405 
406  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet2d& x, const Packet1cd& y) const
407  { return Packet1cd(Eigen::internal::pmul(x, y.v)); }
408 };
409 
410 template<> struct conj_helper<Packet1cd, Packet2d, false,false>
411 {
412  EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet2d& y, const Packet1cd& c) const
413  { return padd(c, pmul(x,y)); }
414 
415  EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& x, const Packet2d& y) const
416  { return Packet1cd(Eigen::internal::pmul(x.v, y)); }
417 };
418 
419 template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
420 {
421  // TODO optimize it for SSE3 and 4
422  Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);
423  __m128d s = _mm_mul_pd(b.v,b.v);
424  return Packet1cd(_mm_div_pd(res.v, _mm_add_pd(s,_mm_shuffle_pd(s, s, 0x1))));
425 }
426 
427 EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
428 {
429  return Packet1cd(preverse(x.v));
430 }
431 
432 } // end namespace internal
433 
434 } // end namespace Eigen
435 
436 #endif // EIGEN_COMPLEX_SSE_H