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 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_COMPLEX_NEON_H
12 #define EIGEN_COMPLEX_NEON_H
13 
14 namespace Eigen {
15 
16 namespace internal {
17 
p4ui_CONJ_XOR()18 inline uint32x4_t p4ui_CONJ_XOR() {
19 // See bug 1325, clang fails to call vld1q_u64.
20 #if EIGEN_COMP_CLANG
21   uint32x4_t ret = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
22   return ret;
23 #else
24   static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000, 0x00000000, 0x80000000 };
25   return vld1q_u32( conj_XOR_DATA );
26 #endif
27 }
28 
p2ui_CONJ_XOR()29 inline uint32x2_t p2ui_CONJ_XOR() {
30   static const uint32_t conj_XOR_DATA[] = { 0x00000000, 0x80000000 };
31   return vld1_u32( conj_XOR_DATA );
32 }
33 
34 //---------- float ----------
35 struct Packet2cf
36 {
Packet2cfPacket2cf37   EIGEN_STRONG_INLINE Packet2cf() {}
Packet2cfPacket2cf38   EIGEN_STRONG_INLINE explicit Packet2cf(const Packet4f& a) : v(a) {}
39   Packet4f  v;
40 };
41 
42 template<> struct packet_traits<std::complex<float> >  : default_packet_traits
43 {
44   typedef Packet2cf type;
45   typedef Packet2cf half;
46   enum {
47     Vectorizable = 1,
48     AlignedOnScalar = 1,
49     size = 2,
50     HasHalfPacket = 0,
51 
52     HasAdd    = 1,
53     HasSub    = 1,
54     HasMul    = 1,
55     HasDiv    = 1,
56     HasNegate = 1,
57     HasAbs    = 0,
58     HasAbs2   = 0,
59     HasMin    = 0,
60     HasMax    = 0,
61     HasSetLinear = 0
62   };
63 };
64 
65 template<> struct unpacket_traits<Packet2cf> { typedef std::complex<float> type; enum {size=2, alignment=Aligned16}; typedef Packet2cf half; };
66 
67 template<> EIGEN_STRONG_INLINE Packet2cf pset1<Packet2cf>(const std::complex<float>&  from)
68 {
69   float32x2_t r64;
70   r64 = vld1_f32((float *)&from);
71 
72   return Packet2cf(vcombine_f32(r64, r64));
73 }
74 
75 template<> EIGEN_STRONG_INLINE Packet2cf padd<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(padd<Packet4f>(a.v,b.v)); }
76 template<> EIGEN_STRONG_INLINE Packet2cf psub<Packet2cf>(const Packet2cf& a, const Packet2cf& b) { return Packet2cf(psub<Packet4f>(a.v,b.v)); }
77 template<> EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf& a) { return Packet2cf(pnegate<Packet4f>(a.v)); }
78 template<> EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf& a)
79 {
80   Packet4ui b = vreinterpretq_u32_f32(a.v);
81   return Packet2cf(vreinterpretq_f32_u32(veorq_u32(b, p4ui_CONJ_XOR())));
82 }
83 
84 template<> EIGEN_STRONG_INLINE Packet2cf pmul<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
85 {
86   Packet4f v1, v2;
87 
88   // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
89   v1 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 0), vdup_lane_f32(vget_high_f32(a.v), 0));
90   // Get the imag values of a | a1_im | a1_im | a2_im | a2_im |
91   v2 = vcombine_f32(vdup_lane_f32(vget_low_f32(a.v), 1), vdup_lane_f32(vget_high_f32(a.v), 1));
92   // Multiply the real a with b
93   v1 = vmulq_f32(v1, b.v);
94   // Multiply the imag a with b
95   v2 = vmulq_f32(v2, b.v);
96   // Conjugate v2
97   v2 = vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(v2), p4ui_CONJ_XOR()));
98   // Swap real/imag elements in v2.
99   v2 = vrev64q_f32(v2);
100   // Add and return the result
101   return Packet2cf(vaddq_f32(v1, v2));
102 }
103 
104 template<> EIGEN_STRONG_INLINE Packet2cf pand   <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
105 {
106   return Packet2cf(vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
107 }
108 template<> EIGEN_STRONG_INLINE Packet2cf por    <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
109 {
110   return Packet2cf(vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
111 }
112 template<> EIGEN_STRONG_INLINE Packet2cf pxor   <Packet2cf>(const Packet2cf& a, const Packet2cf& b)
113 {
114   return Packet2cf(vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
115 }
116 template<> EIGEN_STRONG_INLINE Packet2cf pandnot<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
117 {
118   return Packet2cf(vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a.v),vreinterpretq_u32_f32(b.v))));
119 }
120 
121 template<> EIGEN_STRONG_INLINE Packet2cf pload<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet2cf(pload<Packet4f>((const float*)from)); }
122 template<> EIGEN_STRONG_INLINE Packet2cf ploadu<Packet2cf>(const std::complex<float>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet2cf(ploadu<Packet4f>((const float*)from)); }
123 
124 template<> EIGEN_STRONG_INLINE Packet2cf ploaddup<Packet2cf>(const std::complex<float>* from) { return pset1<Packet2cf>(*from); }
125 
126 template<> EIGEN_STRONG_INLINE void pstore <std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_ALIGNED_STORE pstore((float*)to, from.v); }
127 template<> EIGEN_STRONG_INLINE void pstoreu<std::complex<float> >(std::complex<float> *   to, const Packet2cf& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu((float*)to, from.v); }
128 
129 template<> EIGEN_DEVICE_FUNC inline Packet2cf pgather<std::complex<float>, Packet2cf>(const std::complex<float>* from, Index stride)
130 {
131   Packet4f res = pset1<Packet4f>(0.f);
132   res = vsetq_lane_f32(std::real(from[0*stride]), res, 0);
133   res = vsetq_lane_f32(std::imag(from[0*stride]), res, 1);
134   res = vsetq_lane_f32(std::real(from[1*stride]), res, 2);
135   res = vsetq_lane_f32(std::imag(from[1*stride]), res, 3);
136   return Packet2cf(res);
137 }
138 
139 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<float>, Packet2cf>(std::complex<float>* to, const Packet2cf& from, Index stride)
140 {
141   to[stride*0] = std::complex<float>(vgetq_lane_f32(from.v, 0), vgetq_lane_f32(from.v, 1));
142   to[stride*1] = std::complex<float>(vgetq_lane_f32(from.v, 2), vgetq_lane_f32(from.v, 3));
143 }
144 
145 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<float> >(const std::complex<float> *   addr) { EIGEN_ARM_PREFETCH((float *)addr); }
146 
147 template<> EIGEN_STRONG_INLINE std::complex<float>  pfirst<Packet2cf>(const Packet2cf& a)
148 {
149   std::complex<float> EIGEN_ALIGN16 x[2];
150   vst1q_f32((float *)x, a.v);
151   return x[0];
152 }
153 
154 template<> EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf& a)
155 {
156   float32x2_t a_lo, a_hi;
157   Packet4f a_r128;
158 
159   a_lo = vget_low_f32(a.v);
160   a_hi = vget_high_f32(a.v);
161   a_r128 = vcombine_f32(a_hi, a_lo);
162 
163   return Packet2cf(a_r128);
164 }
165 
166 template<> EIGEN_STRONG_INLINE Packet2cf pcplxflip<Packet2cf>(const Packet2cf& a)
167 {
168   return Packet2cf(vrev64q_f32(a.v));
169 }
170 
171 template<> EIGEN_STRONG_INLINE std::complex<float> predux<Packet2cf>(const Packet2cf& a)
172 {
173   float32x2_t a1, a2;
174   std::complex<float> s;
175 
176   a1 = vget_low_f32(a.v);
177   a2 = vget_high_f32(a.v);
178   a2 = vadd_f32(a1, a2);
179   vst1_f32((float *)&s, a2);
180 
181   return s;
182 }
183 
184 template<> EIGEN_STRONG_INLINE Packet2cf preduxp<Packet2cf>(const Packet2cf* vecs)
185 {
186   Packet4f sum1, sum2, sum;
187 
188   // Add the first two 64-bit float32x2_t of vecs[0]
189   sum1 = vcombine_f32(vget_low_f32(vecs[0].v), vget_low_f32(vecs[1].v));
190   sum2 = vcombine_f32(vget_high_f32(vecs[0].v), vget_high_f32(vecs[1].v));
191   sum = vaddq_f32(sum1, sum2);
192 
193   return Packet2cf(sum);
194 }
195 
196 template<> EIGEN_STRONG_INLINE std::complex<float> predux_mul<Packet2cf>(const Packet2cf& a)
197 {
198   float32x2_t a1, a2, v1, v2, prod;
199   std::complex<float> s;
200 
201   a1 = vget_low_f32(a.v);
202   a2 = vget_high_f32(a.v);
203    // Get the real values of a | a1_re | a1_re | a2_re | a2_re |
204   v1 = vdup_lane_f32(a1, 0);
205   // Get the real values of a | a1_im | a1_im | a2_im | a2_im |
206   v2 = vdup_lane_f32(a1, 1);
207   // Multiply the real a with b
208   v1 = vmul_f32(v1, a2);
209   // Multiply the imag a with b
210   v2 = vmul_f32(v2, a2);
211   // Conjugate v2
212   v2 = vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(v2), p2ui_CONJ_XOR()));
213   // Swap real/imag elements in v2.
214   v2 = vrev64_f32(v2);
215   // Add v1, v2
216   prod = vadd_f32(v1, v2);
217 
218   vst1_f32((float *)&s, prod);
219 
220   return s;
221 }
222 
223 template<int Offset>
224 struct palign_impl<Offset,Packet2cf>
225 {
226   EIGEN_STRONG_INLINE static void run(Packet2cf& first, const Packet2cf& second)
227   {
228     if (Offset==1)
229     {
230       first.v = vextq_f32(first.v, second.v, 2);
231     }
232   }
233 };
234 
235 template<> struct conj_helper<Packet2cf, Packet2cf, false,true>
236 {
237   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
238   { return padd(pmul(x,y),c); }
239 
240   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
241   {
242     return internal::pmul(a, pconj(b));
243   }
244 };
245 
246 template<> struct conj_helper<Packet2cf, Packet2cf, true,false>
247 {
248   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
249   { return padd(pmul(x,y),c); }
250 
251   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
252   {
253     return internal::pmul(pconj(a), b);
254   }
255 };
256 
257 template<> struct conj_helper<Packet2cf, Packet2cf, true,true>
258 {
259   EIGEN_STRONG_INLINE Packet2cf pmadd(const Packet2cf& x, const Packet2cf& y, const Packet2cf& c) const
260   { return padd(pmul(x,y),c); }
261 
262   EIGEN_STRONG_INLINE Packet2cf pmul(const Packet2cf& a, const Packet2cf& b) const
263   {
264     return pconj(internal::pmul(a, b));
265   }
266 };
267 
268 template<> EIGEN_STRONG_INLINE Packet2cf pdiv<Packet2cf>(const Packet2cf& a, const Packet2cf& b)
269 {
270   // TODO optimize it for NEON
271   Packet2cf res = conj_helper<Packet2cf,Packet2cf,false,true>().pmul(a,b);
272   Packet4f s, rev_s;
273 
274   // this computes the norm
275   s = vmulq_f32(b.v, b.v);
276   rev_s = vrev64q_f32(s);
277 
278   return Packet2cf(pdiv(res.v, vaddq_f32(s,rev_s)));
279 }
280 
281 EIGEN_DEVICE_FUNC inline void
282 ptranspose(PacketBlock<Packet2cf,2>& kernel) {
283   Packet4f tmp = vcombine_f32(vget_high_f32(kernel.packet[0].v), vget_high_f32(kernel.packet[1].v));
284   kernel.packet[0].v = vcombine_f32(vget_low_f32(kernel.packet[0].v), vget_low_f32(kernel.packet[1].v));
285   kernel.packet[1].v = tmp;
286 }
287 
288 //---------- double ----------
289 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
290 
291 // See bug 1325, clang fails to call vld1q_u64.
292 #if EIGEN_COMP_CLANG
293   static uint64x2_t p2ul_CONJ_XOR = {0x0, 0x8000000000000000};
294 #else
295   const uint64_t  p2ul_conj_XOR_DATA[] = { 0x0, 0x8000000000000000 };
296   static uint64x2_t p2ul_CONJ_XOR = vld1q_u64( p2ul_conj_XOR_DATA );
297 #endif
298 
299 struct Packet1cd
300 {
301   EIGEN_STRONG_INLINE Packet1cd() {}
302   EIGEN_STRONG_INLINE explicit Packet1cd(const Packet2d& a) : v(a) {}
303   Packet2d v;
304 };
305 
306 template<> struct packet_traits<std::complex<double> >  : default_packet_traits
307 {
308   typedef Packet1cd type;
309   typedef Packet1cd half;
310   enum {
311     Vectorizable = 1,
312     AlignedOnScalar = 0,
313     size = 1,
314     HasHalfPacket = 0,
315 
316     HasAdd    = 1,
317     HasSub    = 1,
318     HasMul    = 1,
319     HasDiv    = 1,
320     HasNegate = 1,
321     HasAbs    = 0,
322     HasAbs2   = 0,
323     HasMin    = 0,
324     HasMax    = 0,
325     HasSetLinear = 0
326   };
327 };
328 
329 template<> struct unpacket_traits<Packet1cd> { typedef std::complex<double> type; enum {size=1, alignment=Aligned16}; typedef Packet1cd half; };
330 
331 template<> EIGEN_STRONG_INLINE Packet1cd pload<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_ALIGNED_LOAD return Packet1cd(pload<Packet2d>((const double*)from)); }
332 template<> EIGEN_STRONG_INLINE Packet1cd ploadu<Packet1cd>(const std::complex<double>* from) { EIGEN_DEBUG_UNALIGNED_LOAD return Packet1cd(ploadu<Packet2d>((const double*)from)); }
333 
334 template<> EIGEN_STRONG_INLINE Packet1cd pset1<Packet1cd>(const std::complex<double>&  from)
335 { /* here we really have to use unaligned loads :( */ return ploadu<Packet1cd>(&from); }
336 
337 template<> EIGEN_STRONG_INLINE Packet1cd padd<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(padd<Packet2d>(a.v,b.v)); }
338 template<> EIGEN_STRONG_INLINE Packet1cd psub<Packet1cd>(const Packet1cd& a, const Packet1cd& b) { return Packet1cd(psub<Packet2d>(a.v,b.v)); }
339 template<> EIGEN_STRONG_INLINE Packet1cd pnegate(const Packet1cd& a) { return Packet1cd(pnegate<Packet2d>(a.v)); }
340 template<> EIGEN_STRONG_INLINE Packet1cd pconj(const Packet1cd& a) { return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v), p2ul_CONJ_XOR))); }
341 
342 template<> EIGEN_STRONG_INLINE Packet1cd pmul<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
343 {
344   Packet2d v1, v2;
345 
346   // Get the real values of a
347   v1 = vdupq_lane_f64(vget_low_f64(a.v), 0);
348   // Get the imag values of a
349   v2 = vdupq_lane_f64(vget_high_f64(a.v), 0);
350   // Multiply the real a with b
351   v1 = vmulq_f64(v1, b.v);
352   // Multiply the imag a with b
353   v2 = vmulq_f64(v2, b.v);
354   // Conjugate v2
355   v2 = vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(v2), p2ul_CONJ_XOR));
356   // Swap real/imag elements in v2.
357   v2 = preverse<Packet2d>(v2);
358   // Add and return the result
359   return Packet1cd(vaddq_f64(v1, v2));
360 }
361 
362 template<> EIGEN_STRONG_INLINE Packet1cd pand   <Packet1cd>(const Packet1cd& a, const Packet1cd& b)
363 {
364   return Packet1cd(vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));
365 }
366 template<> EIGEN_STRONG_INLINE Packet1cd por    <Packet1cd>(const Packet1cd& a, const Packet1cd& b)
367 {
368   return Packet1cd(vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));
369 }
370 template<> EIGEN_STRONG_INLINE Packet1cd pxor   <Packet1cd>(const Packet1cd& a, const Packet1cd& b)
371 {
372   return Packet1cd(vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));
373 }
374 template<> EIGEN_STRONG_INLINE Packet1cd pandnot<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
375 {
376   return Packet1cd(vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a.v),vreinterpretq_u64_f64(b.v))));
377 }
378 
379 template<> EIGEN_STRONG_INLINE Packet1cd ploaddup<Packet1cd>(const std::complex<double>* from) { return pset1<Packet1cd>(*from); }
380 
381 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); }
382 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); }
383 
384 template<> EIGEN_STRONG_INLINE void prefetch<std::complex<double> >(const std::complex<double> *   addr) { EIGEN_ARM_PREFETCH((double *)addr); }
385 
386 template<> EIGEN_DEVICE_FUNC inline Packet1cd pgather<std::complex<double>, Packet1cd>(const std::complex<double>* from, Index stride)
387 {
388   Packet2d res = pset1<Packet2d>(0.0);
389   res = vsetq_lane_f64(std::real(from[0*stride]), res, 0);
390   res = vsetq_lane_f64(std::imag(from[0*stride]), res, 1);
391   return Packet1cd(res);
392 }
393 
394 template<> EIGEN_DEVICE_FUNC inline void pscatter<std::complex<double>, Packet1cd>(std::complex<double>* to, const Packet1cd& from, Index stride)
395 {
396   to[stride*0] = std::complex<double>(vgetq_lane_f64(from.v, 0), vgetq_lane_f64(from.v, 1));
397 }
398 
399 
400 template<> EIGEN_STRONG_INLINE std::complex<double>  pfirst<Packet1cd>(const Packet1cd& a)
401 {
402   std::complex<double> EIGEN_ALIGN16 res;
403   pstore<std::complex<double> >(&res, a);
404 
405   return res;
406 }
407 
408 template<> EIGEN_STRONG_INLINE Packet1cd preverse(const Packet1cd& a) { return a; }
409 
410 template<> EIGEN_STRONG_INLINE std::complex<double> predux<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
411 
412 template<> EIGEN_STRONG_INLINE Packet1cd preduxp<Packet1cd>(const Packet1cd* vecs) { return vecs[0]; }
413 
414 template<> EIGEN_STRONG_INLINE std::complex<double> predux_mul<Packet1cd>(const Packet1cd& a) { return pfirst(a); }
415 
416 template<int Offset>
417 struct palign_impl<Offset,Packet1cd>
418 {
419   static EIGEN_STRONG_INLINE void run(Packet1cd& /*first*/, const Packet1cd& /*second*/)
420   {
421     // FIXME is it sure we never have to align a Packet1cd?
422     // Even though a std::complex<double> has 16 bytes, it is not necessarily aligned on a 16 bytes boundary...
423   }
424 };
425 
426 template<> struct conj_helper<Packet1cd, Packet1cd, false,true>
427 {
428   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
429   { return padd(pmul(x,y),c); }
430 
431   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
432   {
433     return internal::pmul(a, pconj(b));
434   }
435 };
436 
437 template<> struct conj_helper<Packet1cd, Packet1cd, true,false>
438 {
439   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
440   { return padd(pmul(x,y),c); }
441 
442   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
443   {
444     return internal::pmul(pconj(a), b);
445   }
446 };
447 
448 template<> struct conj_helper<Packet1cd, Packet1cd, true,true>
449 {
450   EIGEN_STRONG_INLINE Packet1cd pmadd(const Packet1cd& x, const Packet1cd& y, const Packet1cd& c) const
451   { return padd(pmul(x,y),c); }
452 
453   EIGEN_STRONG_INLINE Packet1cd pmul(const Packet1cd& a, const Packet1cd& b) const
454   {
455     return pconj(internal::pmul(a, b));
456   }
457 };
458 
459 template<> EIGEN_STRONG_INLINE Packet1cd pdiv<Packet1cd>(const Packet1cd& a, const Packet1cd& b)
460 {
461   // TODO optimize it for NEON
462   Packet1cd res = conj_helper<Packet1cd,Packet1cd,false,true>().pmul(a,b);
463   Packet2d s = pmul<Packet2d>(b.v, b.v);
464   Packet2d rev_s = preverse<Packet2d>(s);
465 
466   return Packet1cd(pdiv(res.v, padd<Packet2d>(s,rev_s)));
467 }
468 
469 EIGEN_STRONG_INLINE Packet1cd pcplxflip/*<Packet1cd>*/(const Packet1cd& x)
470 {
471   return Packet1cd(preverse(Packet2d(x.v)));
472 }
473 
474 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet1cd,2>& kernel)
475 {
476   Packet2d tmp = vcombine_f64(vget_high_f64(kernel.packet[0].v), vget_high_f64(kernel.packet[1].v));
477   kernel.packet[0].v = vcombine_f64(vget_low_f64(kernel.packet[0].v), vget_low_f64(kernel.packet[1].v));
478   kernel.packet[1].v = tmp;
479 }
480 #endif // EIGEN_ARCH_ARM64
481 
482 } // end namespace internal
483 
484 } // end namespace Eigen
485 
486 #endif // EIGEN_COMPLEX_NEON_H
487