xref: /aosp_15_r20/external/eigen/Eigen/src/Core/arch/GPU/PacketMath.h (revision bf2c37156dfe67e5dfebd6d394bad8b2ab5804d4)
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2014 Benoit Steiner <[email protected]>
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_GPU_H
11 #define EIGEN_PACKET_MATH_GPU_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 // Read-only data cached load available.
18 #if defined(EIGEN_HIP_DEVICE_COMPILE) || (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 350)
19 #define EIGEN_GPU_HAS_LDG 1
20 #endif
21 
22 // FP16 math available.
23 #if (defined(EIGEN_CUDA_ARCH) && EIGEN_CUDA_ARCH >= 530)
24 #define EIGEN_CUDA_HAS_FP16_ARITHMETIC 1
25 #endif
26 
27 #if defined(EIGEN_HIP_DEVICE_COMPILE) || defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
28 #define EIGEN_GPU_HAS_FP16_ARITHMETIC 1
29 #endif
30 
31 // Make sure this is only available when targeting a GPU: we don't want to
32 // introduce conflicts between these packet_traits definitions and the ones
33 // we'll use on the host side (SSE, AVX, ...)
34 #if defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
35 
36 template<> struct is_arithmetic<float4>  { enum { value = true }; };
37 template<> struct is_arithmetic<double2> { enum { value = true }; };
38 
39 template<> struct packet_traits<float> : default_packet_traits
40 {
41   typedef float4 type;
42   typedef float4 half;
43   enum {
44     Vectorizable = 1,
45     AlignedOnScalar = 1,
46     size=4,
47     HasHalfPacket = 0,
48 
49     HasDiv  = 1,
50     HasSin  = 0,
51     HasCos  = 0,
52     HasLog  = 1,
53     HasExp  = 1,
54     HasSqrt = 1,
55     HasRsqrt = 1,
56     HasLGamma = 1,
57     HasDiGamma = 1,
58     HasZeta = 1,
59     HasPolygamma = 1,
60     HasErf = 1,
61     HasErfc = 1,
62     HasNdtri = 1,
63     HasBessel = 1,
64     HasIGamma = 1,
65     HasIGammaDerA = 1,
66     HasGammaSampleDerAlpha = 1,
67     HasIGammac = 1,
68     HasBetaInc = 1,
69 
70     HasBlend = 0,
71     HasFloor = 1,
72   };
73 };
74 
75 template<> struct packet_traits<double> : default_packet_traits
76 {
77   typedef double2 type;
78   typedef double2 half;
79   enum {
80     Vectorizable = 1,
81     AlignedOnScalar = 1,
82     size=2,
83     HasHalfPacket = 0,
84 
85     HasDiv  = 1,
86     HasLog  = 1,
87     HasExp  = 1,
88     HasSqrt = 1,
89     HasRsqrt = 1,
90     HasLGamma = 1,
91     HasDiGamma = 1,
92     HasZeta = 1,
93     HasPolygamma = 1,
94     HasErf = 1,
95     HasErfc = 1,
96     HasNdtri = 1,
97     HasBessel = 1,
98     HasIGamma = 1,
99     HasIGammaDerA = 1,
100     HasGammaSampleDerAlpha = 1,
101     HasIGammac = 1,
102     HasBetaInc = 1,
103 
104     HasBlend = 0,
105     HasFloor = 1,
106   };
107 };
108 
109 
110 template<> struct unpacket_traits<float4>  { typedef float  type; enum {size=4, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef float4 half; };
111 template<> struct unpacket_traits<double2> { typedef double type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef double2 half; };
112 
113 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pset1<float4>(const float&  from) {
114   return make_float4(from, from, from, from);
115 }
116 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pset1<double2>(const double& from) {
117   return make_double2(from, from);
118 }
119 
120 // We need to distinguish ‘clang as the CUDA compiler’ from ‘clang as the host compiler,
121 // invoked by NVCC’ (e.g. on MacOS). The former needs to see both host and device implementation
122 // of the functions, while the latter can only deal with one of them.
123 #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
124 namespace {
125 
126 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_and(const float& a,
127                                                         const float& b) {
128   return __int_as_float(__float_as_int(a) & __float_as_int(b));
129 }
130 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_and(const double& a,
131                                                          const double& b) {
132   return __longlong_as_double(__double_as_longlong(a) &
133                               __double_as_longlong(b));
134 }
135 
136 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_or(const float& a,
137                                                        const float& b) {
138   return __int_as_float(__float_as_int(a) | __float_as_int(b));
139 }
140 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_or(const double& a,
141                                                         const double& b) {
142   return __longlong_as_double(__double_as_longlong(a) |
143                               __double_as_longlong(b));
144 }
145 
146 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_xor(const float& a,
147                                                         const float& b) {
148   return __int_as_float(__float_as_int(a) ^ __float_as_int(b));
149 }
150 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_xor(const double& a,
151                                                          const double& b) {
152   return __longlong_as_double(__double_as_longlong(a) ^
153                               __double_as_longlong(b));
154 }
155 
156 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float bitwise_andnot(const float& a,
157                                                            const float& b) {
158   return __int_as_float(__float_as_int(a) & ~__float_as_int(b));
159 }
160 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double bitwise_andnot(const double& a,
161                                                             const double& b) {
162   return __longlong_as_double(__double_as_longlong(a) &
163                               ~__double_as_longlong(b));
164 }
165 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float eq_mask(const float& a,
166                                                     const float& b) {
167   return __int_as_float(a == b ? 0xffffffffu : 0u);
168 }
169 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double eq_mask(const double& a,
170                                                      const double& b) {
171   return __longlong_as_double(a == b ? 0xffffffffffffffffull : 0ull);
172 }
173 
174 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float lt_mask(const float& a,
175                                                     const float& b) {
176   return __int_as_float(a < b ? 0xffffffffu : 0u);
177 }
178 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double lt_mask(const double& a,
179                                                      const double& b) {
180   return __longlong_as_double(a < b ? 0xffffffffffffffffull : 0ull);
181 }
182 
183 }  // namespace
184 
185 template <>
186 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pand<float4>(const float4& a,
187                                                           const float4& b) {
188   return make_float4(bitwise_and(a.x, b.x), bitwise_and(a.y, b.y),
189                      bitwise_and(a.z, b.z), bitwise_and(a.w, b.w));
190 }
191 template <>
192 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pand<double2>(const double2& a,
193                                                             const double2& b) {
194   return make_double2(bitwise_and(a.x, b.x), bitwise_and(a.y, b.y));
195 }
196 
197 template <>
198 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 por<float4>(const float4& a,
199                                                          const float4& b) {
200   return make_float4(bitwise_or(a.x, b.x), bitwise_or(a.y, b.y),
201                      bitwise_or(a.z, b.z), bitwise_or(a.w, b.w));
202 }
203 template <>
204 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 por<double2>(const double2& a,
205                                                            const double2& b) {
206   return make_double2(bitwise_or(a.x, b.x), bitwise_or(a.y, b.y));
207 }
208 
209 template <>
210 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pxor<float4>(const float4& a,
211                                                           const float4& b) {
212   return make_float4(bitwise_xor(a.x, b.x), bitwise_xor(a.y, b.y),
213                      bitwise_xor(a.z, b.z), bitwise_xor(a.w, b.w));
214 }
215 template <>
216 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pxor<double2>(const double2& a,
217                                                             const double2& b) {
218   return make_double2(bitwise_xor(a.x, b.x), bitwise_xor(a.y, b.y));
219 }
220 
221 template <>
222 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pandnot<float4>(const float4& a,
223                                                              const float4& b) {
224   return make_float4(bitwise_andnot(a.x, b.x), bitwise_andnot(a.y, b.y),
225                      bitwise_andnot(a.z, b.z), bitwise_andnot(a.w, b.w));
226 }
227 template <>
228 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
229 pandnot<double2>(const double2& a, const double2& b) {
230   return make_double2(bitwise_andnot(a.x, b.x), bitwise_andnot(a.y, b.y));
231 }
232 
233 template <>
234 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_eq<float4>(const float4& a,
235                                                              const float4& b) {
236   return make_float4(eq_mask(a.x, b.x), eq_mask(a.y, b.y), eq_mask(a.z, b.z),
237                      eq_mask(a.w, b.w));
238 }
239 template <>
240 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pcmp_lt<float4>(const float4& a,
241                                                              const float4& b) {
242   return make_float4(lt_mask(a.x, b.x), lt_mask(a.y, b.y), lt_mask(a.z, b.z),
243                      lt_mask(a.w, b.w));
244 }
245 template <>
246 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
247 pcmp_eq<double2>(const double2& a, const double2& b) {
248   return make_double2(eq_mask(a.x, b.x), eq_mask(a.y, b.y));
249 }
250 template <>
251 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
252 pcmp_lt<double2>(const double2& a, const double2& b) {
253   return make_double2(lt_mask(a.x, b.x), lt_mask(a.y, b.y));
254 }
255 #endif // defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
256 
257 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 plset<float4>(const float& a) {
258   return make_float4(a, a+1, a+2, a+3);
259 }
260 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 plset<double2>(const double& a) {
261   return make_double2(a, a+1);
262 }
263 
264 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 padd<float4>(const float4& a, const float4& b) {
265   return make_float4(a.x+b.x, a.y+b.y, a.z+b.z, a.w+b.w);
266 }
267 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 padd<double2>(const double2& a, const double2& b) {
268   return make_double2(a.x+b.x, a.y+b.y);
269 }
270 
271 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 psub<float4>(const float4& a, const float4& b) {
272   return make_float4(a.x-b.x, a.y-b.y, a.z-b.z, a.w-b.w);
273 }
274 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 psub<double2>(const double2& a, const double2& b) {
275   return make_double2(a.x-b.x, a.y-b.y);
276 }
277 
278 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pnegate(const float4& a) {
279   return make_float4(-a.x, -a.y, -a.z, -a.w);
280 }
281 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pnegate(const double2& a) {
282   return make_double2(-a.x, -a.y);
283 }
284 
285 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pconj(const float4& a) { return a; }
286 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pconj(const double2& a) { return a; }
287 
288 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmul<float4>(const float4& a, const float4& b) {
289   return make_float4(a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w);
290 }
291 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmul<double2>(const double2& a, const double2& b) {
292   return make_double2(a.x*b.x, a.y*b.y);
293 }
294 
295 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pdiv<float4>(const float4& a, const float4& b) {
296   return make_float4(a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w);
297 }
298 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pdiv<double2>(const double2& a, const double2& b) {
299   return make_double2(a.x/b.x, a.y/b.y);
300 }
301 
302 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmin<float4>(const float4& a, const float4& b) {
303   return make_float4(fminf(a.x, b.x), fminf(a.y, b.y), fminf(a.z, b.z), fminf(a.w, b.w));
304 }
305 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmin<double2>(const double2& a, const double2& b) {
306   return make_double2(fmin(a.x, b.x), fmin(a.y, b.y));
307 }
308 
309 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pmax<float4>(const float4& a, const float4& b) {
310   return make_float4(fmaxf(a.x, b.x), fmaxf(a.y, b.y), fmaxf(a.z, b.z), fmaxf(a.w, b.w));
311 }
312 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pmax<double2>(const double2& a, const double2& b) {
313   return make_double2(fmax(a.x, b.x), fmax(a.y, b.y));
314 }
315 
316 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pload<float4>(const float* from) {
317   return *reinterpret_cast<const float4*>(from);
318 }
319 
320 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 pload<double2>(const double* from) {
321   return *reinterpret_cast<const double2*>(from);
322 }
323 
324 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 ploadu<float4>(const float* from) {
325   return make_float4(from[0], from[1], from[2], from[3]);
326 }
327 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 ploadu<double2>(const double* from) {
328   return make_double2(from[0], from[1]);
329 }
330 
331 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 ploaddup<float4>(const float*   from) {
332   return make_float4(from[0], from[0], from[1], from[1]);
333 }
334 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2 ploaddup<double2>(const double*  from) {
335   return make_double2(from[0], from[0]);
336 }
337 
338 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<float>(float*   to, const float4& from) {
339   *reinterpret_cast<float4*>(to) = from;
340 }
341 
342 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<double>(double* to, const double2& from) {
343   *reinterpret_cast<double2*>(to) = from;
344 }
345 
346 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const float4& from) {
347   to[0] = from.x;
348   to[1] = from.y;
349   to[2] = from.z;
350   to[3] = from.w;
351 }
352 
353 template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const double2& from) {
354   to[0] = from.x;
355   to[1] = from.y;
356 }
357 
358 template<>
359 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Aligned>(const float* from) {
360 #if defined(EIGEN_GPU_HAS_LDG)
361   return __ldg((const float4*)from);
362 #else
363   return make_float4(from[0], from[1], from[2], from[3]);
364 #endif
365 }
366 template<>
367 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Aligned>(const double* from) {
368 #if defined(EIGEN_GPU_HAS_LDG)
369   return __ldg((const double2*)from);
370 #else
371   return make_double2(from[0], from[1]);
372 #endif
373 }
374 
375 template<>
376 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE float4 ploadt_ro<float4, Unaligned>(const float* from) {
377 #if defined(EIGEN_GPU_HAS_LDG)
378   return make_float4(__ldg(from+0), __ldg(from+1), __ldg(from+2), __ldg(from+3));
379 #else
380   return make_float4(from[0], from[1], from[2], from[3]);
381 #endif
382 }
383 template<>
384 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE double2 ploadt_ro<double2, Unaligned>(const double* from) {
385 #if defined(EIGEN_GPU_HAS_LDG)
386   return make_double2(__ldg(from+0), __ldg(from+1));
387 #else
388   return make_double2(from[0], from[1]);
389 #endif
390 }
391 
392 template<> EIGEN_DEVICE_FUNC inline float4 pgather<float, float4>(const float* from, Index stride) {
393   return make_float4(from[0*stride], from[1*stride], from[2*stride], from[3*stride]);
394 }
395 
396 template<> EIGEN_DEVICE_FUNC inline double2 pgather<double, double2>(const double* from, Index stride) {
397   return make_double2(from[0*stride], from[1*stride]);
398 }
399 
400 template<> EIGEN_DEVICE_FUNC inline void pscatter<float, float4>(float* to, const float4& from, Index stride) {
401   to[stride*0] = from.x;
402   to[stride*1] = from.y;
403   to[stride*2] = from.z;
404   to[stride*3] = from.w;
405 }
406 template<> EIGEN_DEVICE_FUNC inline void pscatter<double, double2>(double* to, const double2& from, Index stride) {
407   to[stride*0] = from.x;
408   to[stride*1] = from.y;
409 }
410 
411 template<> EIGEN_DEVICE_FUNC inline float  pfirst<float4>(const float4& a) {
412   return a.x;
413 }
414 template<> EIGEN_DEVICE_FUNC inline double pfirst<double2>(const double2& a) {
415   return a.x;
416 }
417 
418 template<> EIGEN_DEVICE_FUNC inline float  predux<float4>(const float4& a) {
419   return a.x + a.y + a.z + a.w;
420 }
421 template<> EIGEN_DEVICE_FUNC inline double predux<double2>(const double2& a) {
422   return a.x + a.y;
423 }
424 
425 template<> EIGEN_DEVICE_FUNC inline float  predux_max<float4>(const float4& a) {
426   return fmaxf(fmaxf(a.x, a.y), fmaxf(a.z, a.w));
427 }
428 template<> EIGEN_DEVICE_FUNC inline double predux_max<double2>(const double2& a) {
429   return fmax(a.x, a.y);
430 }
431 
432 template<> EIGEN_DEVICE_FUNC inline float  predux_min<float4>(const float4& a) {
433   return fminf(fminf(a.x, a.y), fminf(a.z, a.w));
434 }
435 template<> EIGEN_DEVICE_FUNC inline double predux_min<double2>(const double2& a) {
436   return fmin(a.x, a.y);
437 }
438 
439 template<> EIGEN_DEVICE_FUNC inline float  predux_mul<float4>(const float4& a) {
440   return a.x * a.y * a.z * a.w;
441 }
442 template<> EIGEN_DEVICE_FUNC inline double predux_mul<double2>(const double2& a) {
443   return a.x * a.y;
444 }
445 
446 template<> EIGEN_DEVICE_FUNC inline float4  pabs<float4>(const float4& a) {
447   return make_float4(fabsf(a.x), fabsf(a.y), fabsf(a.z), fabsf(a.w));
448 }
449 template<> EIGEN_DEVICE_FUNC inline double2 pabs<double2>(const double2& a) {
450   return make_double2(fabs(a.x), fabs(a.y));
451 }
452 
453 template<> EIGEN_DEVICE_FUNC inline float4  pfloor<float4>(const float4& a) {
454   return make_float4(floorf(a.x), floorf(a.y), floorf(a.z), floorf(a.w));
455 }
456 template<> EIGEN_DEVICE_FUNC inline double2 pfloor<double2>(const double2& a) {
457   return make_double2(floor(a.x), floor(a.y));
458 }
459 
460 EIGEN_DEVICE_FUNC inline void
461 ptranspose(PacketBlock<float4,4>& kernel) {
462   float tmp = kernel.packet[0].y;
463   kernel.packet[0].y = kernel.packet[1].x;
464   kernel.packet[1].x = tmp;
465 
466   tmp = kernel.packet[0].z;
467   kernel.packet[0].z = kernel.packet[2].x;
468   kernel.packet[2].x = tmp;
469 
470   tmp = kernel.packet[0].w;
471   kernel.packet[0].w = kernel.packet[3].x;
472   kernel.packet[3].x = tmp;
473 
474   tmp = kernel.packet[1].z;
475   kernel.packet[1].z = kernel.packet[2].y;
476   kernel.packet[2].y = tmp;
477 
478   tmp = kernel.packet[1].w;
479   kernel.packet[1].w = kernel.packet[3].y;
480   kernel.packet[3].y = tmp;
481 
482   tmp = kernel.packet[2].w;
483   kernel.packet[2].w = kernel.packet[3].z;
484   kernel.packet[3].z = tmp;
485 }
486 
487 EIGEN_DEVICE_FUNC inline void
488 ptranspose(PacketBlock<double2,2>& kernel) {
489   double tmp = kernel.packet[0].y;
490   kernel.packet[0].y = kernel.packet[1].x;
491   kernel.packet[1].x = tmp;
492 }
493 
494 #endif // defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
495 
496 // Packet4h2 must be defined in the macro without EIGEN_CUDA_ARCH, meaning
497 // its corresponding packet_traits<Eigen::half> must be visible on host.
498 #if defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
499 
500 typedef ulonglong2 Packet4h2;
501 template<> struct unpacket_traits<Packet4h2> { typedef Eigen::half type; enum {size=8, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef Packet4h2 half; };
502 template<> struct is_arithmetic<Packet4h2> { enum { value = true }; };
503 
504 template<> struct unpacket_traits<half2> { typedef Eigen::half type; enum {size=2, alignment=Aligned16, vectorizable=true, masked_load_available=false, masked_store_available=false}; typedef half2 half; };
505 template<> struct is_arithmetic<half2> { enum { value = true }; };
506 
507 template<> struct packet_traits<Eigen::half> : default_packet_traits
508 {
509   typedef Packet4h2 type;
510   typedef Packet4h2 half;
511   enum {
512     Vectorizable = 1,
513     AlignedOnScalar = 1,
514     size=8,
515     HasHalfPacket = 0,
516     HasAdd    = 1,
517     HasSub    = 1,
518     HasMul    = 1,
519     HasDiv    = 1,
520     HasSqrt   = 1,
521     HasRsqrt  = 1,
522     HasExp    = 1,
523     HasExpm1  = 1,
524     HasLog    = 1,
525     HasLog1p  = 1
526   };
527 };
528 
529 namespace {
530 // This is equivalent to make_half2, which is undocumented and doesn't seem to always exist.
531 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 combine_half(const __half& a, const __half& b) {
532 #if defined(EIGEN_GPU_COMPILE_PHASE)
533   return __halves2half2(a, b);
534 #else
535   // Round-about way since __halves2half2 is a __device__ function.
536   return __floats2half2_rn(__half2float(a), __half2float(b));
537 #endif
538 }
539 
540 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE __half get_half2_low(const half2& a) {
541 #if defined(EIGEN_GPU_COMPILE_PHASE)
542   return __low2half(a);
543 #else
544   return __float2half(__low2float(a));
545 #endif
546 }
547 
548 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE __half get_half2_high(const half2& a) {
549 #if defined(EIGEN_GPU_COMPILE_PHASE)
550   return __high2half(a);
551 #else
552   return __float2half(__high2float(a));
553 #endif
554 }
555 } // namespace
556 
557 template<>
558 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pset1<half2>(const Eigen::half& from) {
559 #if defined(EIGEN_GPU_COMPILE_PHASE)
560   return __half2half2(from);
561 #else
562   const float f = __half2float(from);
563   return __floats2half2_rn(f, f);
564 #endif
565 }
566 
567 template <>
568 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
569 pset1<Packet4h2>(const Eigen::half& from) {
570   Packet4h2 r;
571   half2* p_alias = reinterpret_cast<half2*>(&r);
572   p_alias[0] = pset1<half2>(from);
573   p_alias[1] = pset1<half2>(from);
574   p_alias[2] = pset1<half2>(from);
575   p_alias[3] = pset1<half2>(from);
576   return r;
577 }
578 
579 // We now need this visible on both host and device.
580 // #if defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
581 namespace {
582 
583 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pload(const Eigen::half* from) {
584   return *reinterpret_cast<const half2*>(from);
585 }
586 
587 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploadu(const Eigen::half* from) {
588   return combine_half(from[0], from[1]);
589 }
590 
591 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ploaddup(const Eigen::half*  from) {
592   return combine_half(from[0], from[0]);
593 }
594 
595 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(Eigen::half* to,
596                                                   const half2& from) {
597   *reinterpret_cast<half2*>(to) = from;
598 }
599 
600 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu(Eigen::half* to,
601                                                    const half2& from) {
602   to[0] = get_half2_low(from);
603   to[1] = get_half2_high(from);
604 }
605 
606 
607 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_aligned(
608     const Eigen::half* from) {
609 #if defined(EIGEN_GPU_HAS_LDG)
610   // Input is guaranteed to be properly aligned.
611   return __ldg(reinterpret_cast<const half2*>(from));
612 #else
613   return combine_half(*(from+0), *(from+1));
614 #endif
615 }
616 
617 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE half2 ploadt_ro_unaligned(
618     const Eigen::half* from) {
619 #if defined(EIGEN_GPU_HAS_LDG)
620   return __halves2half2(__ldg(from+0), __ldg(from+1));
621 #else
622   return combine_half(*(from+0), *(from+1));
623 #endif
624 }
625 
626 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pgather(const Eigen::half* from,
627                                                     Index stride) {
628   return combine_half(from[0*stride], from[1*stride]);
629 }
630 
631 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(
632     Eigen::half* to, const half2& from, Index stride) {
633   to[stride*0] = get_half2_low(from);
634   to[stride*1] = get_half2_high(from);
635 }
636 
637 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst(const half2& a) {
638   return get_half2_low(a);
639 }
640 
641 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pabs(const half2& a) {
642   half a1 = get_half2_low(a);
643   half a2 = get_half2_high(a);
644   half result1 = half_impl::raw_uint16_to_half(a1.x & 0x7FFF);
645   half result2 = half_impl::raw_uint16_to_half(a2.x & 0x7FFF);
646   return combine_half(result1, result2);
647 }
648 
649 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 ptrue(const half2& /*a*/) {
650   half true_half = half_impl::raw_uint16_to_half(0xffffu);
651   return pset1<half2>(true_half);
652 }
653 
654 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pzero(const half2& /*a*/) {
655   half false_half = half_impl::raw_uint16_to_half(0x0000u);
656   return pset1<half2>(false_half);
657 }
658 
659 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
660 ptranspose(PacketBlock<half2,2>& kernel) {
661   __half a1 = get_half2_low(kernel.packet[0]);
662   __half a2 = get_half2_high(kernel.packet[0]);
663   __half b1 = get_half2_low(kernel.packet[1]);
664   __half b2 = get_half2_high(kernel.packet[1]);
665   kernel.packet[0] = combine_half(a1, b1);
666   kernel.packet[1] = combine_half(a2, b2);
667 }
668 
669 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plset(const Eigen::half& a) {
670 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
671   return __halves2half2(a, __hadd(a, __float2half(1.0f)));
672 #else
673   float f = __half2float(a) + 1.0f;
674   return combine_half(a, __float2half(f));
675 #endif
676 }
677 
678 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pselect(const half2& mask,
679                                                     const half2& a,
680                                                     const half2& b) {
681   half mask_low = get_half2_low(mask);
682   half mask_high = get_half2_high(mask);
683   half result_low = mask_low == half(0) ? get_half2_low(b) : get_half2_low(a);
684   half result_high = mask_high == half(0) ? get_half2_high(b) : get_half2_high(a);
685   return combine_half(result_low, result_high);
686 }
687 
688 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_eq(const half2& a,
689                                                     const half2& b) {
690   half true_half = half_impl::raw_uint16_to_half(0xffffu);
691   half false_half = half_impl::raw_uint16_to_half(0x0000u);
692   half a1 = get_half2_low(a);
693   half a2 = get_half2_high(a);
694   half b1 = get_half2_low(b);
695   half b2 = get_half2_high(b);
696   half eq1 = __half2float(a1) == __half2float(b1) ? true_half : false_half;
697   half eq2 = __half2float(a2) == __half2float(b2) ? true_half : false_half;
698   return combine_half(eq1, eq2);
699 }
700 
701 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pcmp_lt(const half2& a,
702                                                     const half2& b) {
703   half true_half = half_impl::raw_uint16_to_half(0xffffu);
704   half false_half = half_impl::raw_uint16_to_half(0x0000u);
705   half a1 = get_half2_low(a);
706   half a2 = get_half2_high(a);
707   half b1 = get_half2_low(b);
708   half b2 = get_half2_high(b);
709   half eq1 = __half2float(a1) < __half2float(b1) ? true_half : false_half;
710   half eq2 = __half2float(a2) < __half2float(b2) ? true_half : false_half;
711   return combine_half(eq1, eq2);
712 }
713 
714 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pand(const half2& a,
715                                                  const half2& b) {
716   half a1 = get_half2_low(a);
717   half a2 = get_half2_high(a);
718   half b1 = get_half2_low(b);
719   half b2 = get_half2_high(b);
720   half result1 = half_impl::raw_uint16_to_half(a1.x & b1.x);
721   half result2 = half_impl::raw_uint16_to_half(a2.x & b2.x);
722   return combine_half(result1, result2);
723 }
724 
725 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 por(const half2& a,
726                                                 const half2& b) {
727   half a1 = get_half2_low(a);
728   half a2 = get_half2_high(a);
729   half b1 = get_half2_low(b);
730   half b2 = get_half2_high(b);
731   half result1 = half_impl::raw_uint16_to_half(a1.x | b1.x);
732   half result2 = half_impl::raw_uint16_to_half(a2.x | b2.x);
733   return combine_half(result1, result2);
734 }
735 
736 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pxor(const half2& a,
737                                                  const half2& b) {
738   half a1 = get_half2_low(a);
739   half a2 = get_half2_high(a);
740   half b1 = get_half2_low(b);
741   half b2 = get_half2_high(b);
742   half result1 = half_impl::raw_uint16_to_half(a1.x ^ b1.x);
743   half result2 = half_impl::raw_uint16_to_half(a2.x ^ b2.x);
744   return combine_half(result1, result2);
745 }
746 
747 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pandnot(const half2& a,
748                                                     const half2& b) {
749   half a1 = get_half2_low(a);
750   half a2 = get_half2_high(a);
751   half b1 = get_half2_low(b);
752   half b2 = get_half2_high(b);
753   half result1 = half_impl::raw_uint16_to_half(a1.x & ~b1.x);
754   half result2 = half_impl::raw_uint16_to_half(a2.x & ~b2.x);
755   return combine_half(result1, result2);
756 }
757 
758 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd(const half2& a,
759                                                  const half2& b) {
760 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
761   return __hadd2(a, b);
762 #else
763   float a1 = __low2float(a);
764   float a2 = __high2float(a);
765   float b1 = __low2float(b);
766   float b2 = __high2float(b);
767   float r1 = a1 + b1;
768   float r2 = a2 + b2;
769   return __floats2half2_rn(r1, r2);
770 #endif
771 }
772 
773 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psub(const half2& a,
774                                                  const half2& b) {
775 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
776   return __hsub2(a, b);
777 #else
778   float a1 = __low2float(a);
779   float a2 = __high2float(a);
780   float b1 = __low2float(b);
781   float b2 = __high2float(b);
782   float r1 = a1 - b1;
783   float r2 = a2 - b2;
784   return __floats2half2_rn(r1, r2);
785 #endif
786 }
787 
788 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pnegate(const half2& a) {
789 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
790   return __hneg2(a);
791 #else
792   float a1 = __low2float(a);
793   float a2 = __high2float(a);
794   return __floats2half2_rn(-a1, -a2);
795 #endif
796 }
797 
798 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pconj(const half2& a) { return a; }
799 
800 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul(const half2& a,
801                                                  const half2& b) {
802 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
803   return __hmul2(a, b);
804 #else
805   float a1 = __low2float(a);
806   float a2 = __high2float(a);
807   float b1 = __low2float(b);
808   float b2 = __high2float(b);
809   float r1 = a1 * b1;
810   float r2 = a2 * b2;
811   return __floats2half2_rn(r1, r2);
812 #endif
813 }
814 
815 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmadd(const half2& a,
816                                                   const half2& b,
817                                                   const half2& c) {
818 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
819    return __hfma2(a, b, c);
820 #else
821   float a1 = __low2float(a);
822   float a2 = __high2float(a);
823   float b1 = __low2float(b);
824   float b2 = __high2float(b);
825   float c1 = __low2float(c);
826   float c2 = __high2float(c);
827   float r1 = a1 * b1 + c1;
828   float r2 = a2 * b2 + c2;
829   return __floats2half2_rn(r1, r2);
830 #endif
831 }
832 
833 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv(const half2& a,
834                                                  const half2& b) {
835 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
836   return __h2div(a, b);
837 #else
838   float a1 = __low2float(a);
839   float a2 = __high2float(a);
840   float b1 = __low2float(b);
841   float b2 = __high2float(b);
842   float r1 = a1 / b1;
843   float r2 = a2 / b2;
844   return __floats2half2_rn(r1, r2);
845 #endif
846 }
847 
848 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin(const half2& a,
849                                                  const half2& b) {
850   float a1 = __low2float(a);
851   float a2 = __high2float(a);
852   float b1 = __low2float(b);
853   float b2 = __high2float(b);
854   __half r1 = a1 < b1 ? get_half2_low(a) : get_half2_low(b);
855   __half r2 = a2 < b2 ? get_half2_high(a) : get_half2_high(b);
856   return combine_half(r1, r2);
857 }
858 
859 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax(const half2& a,
860                                                  const half2& b) {
861   float a1 = __low2float(a);
862   float a2 = __high2float(a);
863   float b1 = __low2float(b);
864   float b2 = __high2float(b);
865   __half r1 = a1 > b1 ? get_half2_low(a) : get_half2_low(b);
866   __half r2 = a2 > b2 ? get_half2_high(a) : get_half2_high(b);
867   return combine_half(r1, r2);
868 }
869 
870 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux(const half2& a) {
871 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
872   return __hadd(__low2half(a), __high2half(a));
873 #else
874   float a1 = __low2float(a);
875   float a2 = __high2float(a);
876   return Eigen::half(__float2half(a1 + a2));
877 #endif
878 }
879 
880 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max(const half2& a) {
881 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
882   __half first = __low2half(a);
883   __half second = __high2half(a);
884   return __hgt(first, second) ? first : second;
885 #else
886   float a1 = __low2float(a);
887   float a2 = __high2float(a);
888   return a1 > a2 ? get_half2_low(a) : get_half2_high(a);
889 #endif
890 }
891 
892 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min(const half2& a) {
893 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
894   __half first = __low2half(a);
895   __half second = __high2half(a);
896   return __hlt(first, second) ? first : second;
897 #else
898   float a1 = __low2float(a);
899   float a2 = __high2float(a);
900   return a1 < a2 ? get_half2_low(a) : get_half2_high(a);
901 #endif
902 }
903 
904 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul(const half2& a) {
905 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
906   return __hmul(__low2half(a), __high2half(a));
907 #else
908   float a1 = __low2float(a);
909   float a2 = __high2float(a);
910   return Eigen::half(__float2half(a1 * a2));
911 #endif
912 }
913 
914 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog1p(const half2& a) {
915   float a1 = __low2float(a);
916   float a2 = __high2float(a);
917   float r1 = log1pf(a1);
918   float r2 = log1pf(a2);
919   return __floats2half2_rn(r1, r2);
920 }
921 
922 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexpm1(const half2& a) {
923   float a1 = __low2float(a);
924   float a2 = __high2float(a);
925   float r1 = expm1f(a1);
926   float r2 = expm1f(a2);
927   return __floats2half2_rn(r1, r2);
928 }
929 
930 #if (EIGEN_CUDA_SDK_VER >= 80000 && defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)) || \
931   defined(EIGEN_HIP_DEVICE_COMPILE)
932 
933 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
934 half2 plog(const half2& a) {
935   return h2log(a);
936 }
937 
938  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
939 half2 pexp(const half2& a) {
940   return h2exp(a);
941 }
942 
943  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
944 half2 psqrt(const half2& a) {
945   return h2sqrt(a);
946 }
947 
948  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
949 half2 prsqrt(const half2& a) {
950   return h2rsqrt(a);
951 }
952 
953 #else
954 
955 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 plog(const half2& a) {
956   float a1 = __low2float(a);
957   float a2 = __high2float(a);
958   float r1 = logf(a1);
959   float r2 = logf(a2);
960   return __floats2half2_rn(r1, r2);
961 }
962 
963 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pexp(const half2& a) {
964   float a1 = __low2float(a);
965   float a2 = __high2float(a);
966   float r1 = expf(a1);
967   float r2 = expf(a2);
968   return __floats2half2_rn(r1, r2);
969 }
970 
971 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 psqrt(const half2& a) {
972   float a1 = __low2float(a);
973   float a2 = __high2float(a);
974   float r1 = sqrtf(a1);
975   float r2 = sqrtf(a2);
976   return __floats2half2_rn(r1, r2);
977 }
978 
979 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 prsqrt(const half2& a) {
980   float a1 = __low2float(a);
981   float a2 = __high2float(a);
982   float r1 = rsqrtf(a1);
983   float r2 = rsqrtf(a2);
984   return __floats2half2_rn(r1, r2);
985 }
986 #endif
987 } // namespace
988 
989 template <>
990 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
991 pload<Packet4h2>(const Eigen::half* from) {
992   return *reinterpret_cast<const Packet4h2*>(from);
993 }
994 
995 // unaligned load;
996 template <>
997 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
998 ploadu<Packet4h2>(const Eigen::half* from) {
999   Packet4h2 r;
1000   half2* p_alias = reinterpret_cast<half2*>(&r);
1001   p_alias[0] = ploadu(from + 0);
1002   p_alias[1] = ploadu(from + 2);
1003   p_alias[2] = ploadu(from + 4);
1004   p_alias[3] = ploadu(from + 6);
1005   return r;
1006 }
1007 
1008 template <>
1009 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1010 ploaddup<Packet4h2>(const Eigen::half* from) {
1011   Packet4h2 r;
1012   half2* p_alias = reinterpret_cast<half2*>(&r);
1013   p_alias[0] = ploaddup(from + 0);
1014   p_alias[1] = ploaddup(from + 1);
1015   p_alias[2] = ploaddup(from + 2);
1016   p_alias[3] = ploaddup(from + 3);
1017   return r;
1018 }
1019 
1020 template <>
1021 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore<Eigen::half>(
1022     Eigen::half* to, const Packet4h2& from) {
1023   *reinterpret_cast<Packet4h2*>(to) = from;
1024 }
1025 
1026 template <>
1027 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstoreu<Eigen::half>(
1028     Eigen::half* to, const Packet4h2& from) {
1029   const half2* from_alias = reinterpret_cast<const half2*>(&from);
1030   pstoreu(to + 0,from_alias[0]);
1031   pstoreu(to + 2,from_alias[1]);
1032   pstoreu(to + 4,from_alias[2]);
1033   pstoreu(to + 6,from_alias[3]);
1034 }
1035 
1036 template <>
1037 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
1038 ploadt_ro<Packet4h2, Aligned>(const Eigen::half* from) {
1039 #if defined(EIGEN_GPU_HAS_LDG)
1040   Packet4h2 r;
1041   r = __ldg(reinterpret_cast<const Packet4h2*>(from));
1042   return r;
1043 #else
1044   Packet4h2 r;
1045   half2* r_alias = reinterpret_cast<half2*>(&r);
1046   r_alias[0] = ploadt_ro_aligned(from + 0);
1047   r_alias[1] = ploadt_ro_aligned(from + 2);
1048   r_alias[2] = ploadt_ro_aligned(from + 4);
1049   r_alias[3] = ploadt_ro_aligned(from + 6);
1050   return r;
1051 #endif
1052 }
1053 
1054 template <>
1055 EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet4h2
1056 ploadt_ro<Packet4h2, Unaligned>(const Eigen::half* from) {
1057   Packet4h2 r;
1058   half2* r_alias = reinterpret_cast<half2*>(&r);
1059   r_alias[0] = ploadt_ro_unaligned(from + 0);
1060   r_alias[1] = ploadt_ro_unaligned(from + 2);
1061   r_alias[2] = ploadt_ro_unaligned(from + 4);
1062   r_alias[3] = ploadt_ro_unaligned(from + 6);
1063   return r;
1064 }
1065 
1066 template <>
1067 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1068 pgather<Eigen::half, Packet4h2>(const Eigen::half* from, Index stride) {
1069   Packet4h2 r;
1070   half2* p_alias = reinterpret_cast<half2*>(&r);
1071   p_alias[0] = combine_half(from[0 * stride], from[1 * stride]);
1072   p_alias[1] = combine_half(from[2 * stride], from[3 * stride]);
1073   p_alias[2] = combine_half(from[4 * stride], from[5 * stride]);
1074   p_alias[3] = combine_half(from[6 * stride], from[7 * stride]);
1075   return r;
1076 }
1077 
1078 template <>
1079 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<Eigen::half, Packet4h2>(
1080     Eigen::half* to, const Packet4h2& from, Index stride) {
1081   const half2* from_alias = reinterpret_cast<const half2*>(&from);
1082   pscatter(to + stride * 0, from_alias[0], stride);
1083   pscatter(to + stride * 2, from_alias[1], stride);
1084   pscatter(to + stride * 4, from_alias[2], stride);
1085   pscatter(to + stride * 6, from_alias[3], stride);
1086 }
1087 
1088 template <>
1089 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half pfirst<Packet4h2>(
1090     const Packet4h2& a) {
1091   return pfirst(*(reinterpret_cast<const half2*>(&a)));
1092 }
1093 
1094 template <>
1095 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pabs<Packet4h2>(
1096     const Packet4h2& a) {
1097   Packet4h2 r;
1098   half2* p_alias = reinterpret_cast<half2*>(&r);
1099   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1100   p_alias[0] = pabs(a_alias[0]);
1101   p_alias[1] = pabs(a_alias[1]);
1102   p_alias[2] = pabs(a_alias[2]);
1103   p_alias[3] = pabs(a_alias[3]);
1104   return r;
1105 }
1106 
1107 template <>
1108 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 ptrue<Packet4h2>(
1109     const Packet4h2& /*a*/) {
1110   half true_half = half_impl::raw_uint16_to_half(0xffffu);
1111   return pset1<Packet4h2>(true_half);
1112 }
1113 
1114 template <>
1115 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pzero<Packet4h2>(const Packet4h2& /*a*/) {
1116   half false_half = half_impl::raw_uint16_to_half(0x0000u);
1117   return pset1<Packet4h2>(false_half);
1118 }
1119 
1120 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose_double(
1121     double* d_row0, double* d_row1, double* d_row2, double* d_row3,
1122     double* d_row4, double* d_row5, double* d_row6, double* d_row7) {
1123   double d_tmp;
1124   d_tmp = d_row0[1];
1125   d_row0[1] = d_row4[0];
1126   d_row4[0] = d_tmp;
1127 
1128   d_tmp = d_row1[1];
1129   d_row1[1] = d_row5[0];
1130   d_row5[0] = d_tmp;
1131 
1132   d_tmp = d_row2[1];
1133   d_row2[1] = d_row6[0];
1134   d_row6[0] = d_tmp;
1135 
1136   d_tmp = d_row3[1];
1137   d_row3[1] = d_row7[0];
1138   d_row7[0] = d_tmp;
1139 }
1140 
1141 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose_half2(
1142     half2* f_row0, half2* f_row1, half2* f_row2, half2* f_row3) {
1143   half2 f_tmp;
1144   f_tmp = f_row0[1];
1145   f_row0[1] = f_row2[0];
1146   f_row2[0] = f_tmp;
1147 
1148   f_tmp = f_row1[1];
1149   f_row1[1] = f_row3[0];
1150   f_row3[0] = f_tmp;
1151 }
1152 
1153 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
1154 ptranspose_half(half2& f0, half2& f1) {
1155   __half a1 = get_half2_low(f0);
1156   __half a2 = get_half2_high(f0);
1157   __half b1 = get_half2_low(f1);
1158   __half b2 = get_half2_high(f1);
1159   f0 = combine_half(a1, b1);
1160   f1 = combine_half(a2, b2);
1161 }
1162 
1163 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void
1164 ptranspose(PacketBlock<Packet4h2,8>& kernel) {
1165   double* d_row0 = reinterpret_cast<double*>(&kernel.packet[0]);
1166   double* d_row1 = reinterpret_cast<double*>(&kernel.packet[1]);
1167   double* d_row2 = reinterpret_cast<double*>(&kernel.packet[2]);
1168   double* d_row3 = reinterpret_cast<double*>(&kernel.packet[3]);
1169   double* d_row4 = reinterpret_cast<double*>(&kernel.packet[4]);
1170   double* d_row5 = reinterpret_cast<double*>(&kernel.packet[5]);
1171   double* d_row6 = reinterpret_cast<double*>(&kernel.packet[6]);
1172   double* d_row7 = reinterpret_cast<double*>(&kernel.packet[7]);
1173   ptranspose_double(d_row0, d_row1, d_row2, d_row3,
1174                     d_row4, d_row5, d_row6, d_row7);
1175 
1176 
1177   half2* f_row0 = reinterpret_cast<half2*>(d_row0);
1178   half2* f_row1 = reinterpret_cast<half2*>(d_row1);
1179   half2* f_row2 = reinterpret_cast<half2*>(d_row2);
1180   half2* f_row3 = reinterpret_cast<half2*>(d_row3);
1181   ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
1182   ptranspose_half(f_row0[0], f_row1[0]);
1183   ptranspose_half(f_row0[1], f_row1[1]);
1184   ptranspose_half(f_row2[0], f_row3[0]);
1185   ptranspose_half(f_row2[1], f_row3[1]);
1186 
1187   f_row0 = reinterpret_cast<half2*>(d_row0 + 1);
1188   f_row1 = reinterpret_cast<half2*>(d_row1 + 1);
1189   f_row2 = reinterpret_cast<half2*>(d_row2 + 1);
1190   f_row3 = reinterpret_cast<half2*>(d_row3 + 1);
1191   ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
1192   ptranspose_half(f_row0[0], f_row1[0]);
1193   ptranspose_half(f_row0[1], f_row1[1]);
1194   ptranspose_half(f_row2[0], f_row3[0]);
1195   ptranspose_half(f_row2[1], f_row3[1]);
1196 
1197   f_row0 = reinterpret_cast<half2*>(d_row4);
1198   f_row1 = reinterpret_cast<half2*>(d_row5);
1199   f_row2 = reinterpret_cast<half2*>(d_row6);
1200   f_row3 = reinterpret_cast<half2*>(d_row7);
1201   ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
1202   ptranspose_half(f_row0[0], f_row1[0]);
1203   ptranspose_half(f_row0[1], f_row1[1]);
1204   ptranspose_half(f_row2[0], f_row3[0]);
1205   ptranspose_half(f_row2[1], f_row3[1]);
1206 
1207   f_row0 = reinterpret_cast<half2*>(d_row4 + 1);
1208   f_row1 = reinterpret_cast<half2*>(d_row5 + 1);
1209   f_row2 = reinterpret_cast<half2*>(d_row6 + 1);
1210   f_row3 = reinterpret_cast<half2*>(d_row7 + 1);
1211   ptranspose_half2(f_row0, f_row1, f_row2, f_row3);
1212   ptranspose_half(f_row0[0], f_row1[0]);
1213   ptranspose_half(f_row0[1], f_row1[1]);
1214   ptranspose_half(f_row2[0], f_row3[0]);
1215   ptranspose_half(f_row2[1], f_row3[1]);
1216 
1217 }
1218 
1219 template <>
1220 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1221 plset<Packet4h2>(const Eigen::half& a) {
1222 #if defined(EIGEN_HIP_DEVICE_COMPILE)
1223 
1224   Packet4h2 r;
1225   half2* p_alias = reinterpret_cast<half2*>(&r);
1226   p_alias[0] = __halves2half2(a, __hadd(a, __float2half(1.0f)));
1227   p_alias[1] = __halves2half2(__hadd(a, __float2half(2.0f)),
1228                               __hadd(a, __float2half(3.0f)));
1229   p_alias[2] = __halves2half2(__hadd(a, __float2half(4.0f)),
1230                               __hadd(a, __float2half(5.0f)));
1231   p_alias[3] = __halves2half2(__hadd(a, __float2half(6.0f)),
1232                               __hadd(a, __float2half(7.0f)));
1233   return r;
1234 #elif defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
1235   Packet4h2 r;
1236   half2* r_alias = reinterpret_cast<half2*>(&r);
1237 
1238   half2 b = pset1<half2>(a);
1239   half2 c;
1240   half2 half_offset0 = __halves2half2(__float2half(0.0f),__float2half(2.0f));
1241   half2 half_offset1 = __halves2half2(__float2half(4.0f),__float2half(6.0f));
1242 
1243   c = __hadd2(b, half_offset0);
1244   r_alias[0] = plset(__low2half(c));
1245   r_alias[1] = plset(__high2half(c));
1246 
1247   c = __hadd2(b, half_offset1);
1248   r_alias[2] = plset(__low2half(c));
1249   r_alias[3] = plset(__high2half(c));
1250 
1251   return r;
1252 
1253 #else
1254   float f = __half2float(a);
1255   Packet4h2 r;
1256   half2* p_alias = reinterpret_cast<half2*>(&r);
1257   p_alias[0] = combine_half(a, __float2half(f + 1.0f));
1258   p_alias[1] = combine_half(__float2half(f + 2.0f), __float2half(f + 3.0f));
1259   p_alias[2] = combine_half(__float2half(f + 4.0f), __float2half(f + 5.0f));
1260   p_alias[3] = combine_half(__float2half(f + 6.0f), __float2half(f + 7.0f));
1261   return r;
1262 #endif
1263 }
1264 
1265 template <>
1266 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1267 pselect<Packet4h2>(const Packet4h2& mask, const Packet4h2& a,
1268                    const Packet4h2& b) {
1269   Packet4h2 r;
1270   half2* r_alias = reinterpret_cast<half2*>(&r);
1271   const half2* mask_alias = reinterpret_cast<const half2*>(&mask);
1272   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1273   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1274   r_alias[0] = pselect(mask_alias[0], a_alias[0], b_alias[0]);
1275   r_alias[1] = pselect(mask_alias[1], a_alias[1], b_alias[1]);
1276   r_alias[2] = pselect(mask_alias[2], a_alias[2], b_alias[2]);
1277   r_alias[3] = pselect(mask_alias[3], a_alias[3], b_alias[3]);
1278   return r;
1279 }
1280 
1281 template <>
1282 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1283 pcmp_eq<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
1284   Packet4h2 r;
1285   half2* r_alias = reinterpret_cast<half2*>(&r);
1286   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1287   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1288   r_alias[0] = pcmp_eq(a_alias[0], b_alias[0]);
1289   r_alias[1] = pcmp_eq(a_alias[1], b_alias[1]);
1290   r_alias[2] = pcmp_eq(a_alias[2], b_alias[2]);
1291   r_alias[3] = pcmp_eq(a_alias[3], b_alias[3]);
1292   return r;
1293 }
1294 
1295 template <>
1296 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pand<Packet4h2>(
1297     const Packet4h2& a, const Packet4h2& b) {
1298   Packet4h2 r;
1299   half2* r_alias = reinterpret_cast<half2*>(&r);
1300   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1301   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1302   r_alias[0] = pand(a_alias[0], b_alias[0]);
1303   r_alias[1] = pand(a_alias[1], b_alias[1]);
1304   r_alias[2] = pand(a_alias[2], b_alias[2]);
1305   r_alias[3] = pand(a_alias[3], b_alias[3]);
1306   return r;
1307 }
1308 
1309 template <>
1310 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 por<Packet4h2>(
1311     const Packet4h2& a, const Packet4h2& b) {
1312   Packet4h2 r;
1313   half2* r_alias = reinterpret_cast<half2*>(&r);
1314   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1315   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1316   r_alias[0] = por(a_alias[0], b_alias[0]);
1317   r_alias[1] = por(a_alias[1], b_alias[1]);
1318   r_alias[2] = por(a_alias[2], b_alias[2]);
1319   r_alias[3] = por(a_alias[3], b_alias[3]);
1320   return r;
1321 }
1322 
1323 template <>
1324 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pxor<Packet4h2>(
1325     const Packet4h2& a, const Packet4h2& b) {
1326   Packet4h2 r;
1327   half2* r_alias = reinterpret_cast<half2*>(&r);
1328   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1329   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1330   r_alias[0] = pxor(a_alias[0], b_alias[0]);
1331   r_alias[1] = pxor(a_alias[1], b_alias[1]);
1332   r_alias[2] = pxor(a_alias[2], b_alias[2]);
1333   r_alias[3] = pxor(a_alias[3], b_alias[3]);
1334   return r;
1335 }
1336 
1337 template <>
1338 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1339 pandnot<Packet4h2>(const Packet4h2& a, const Packet4h2& b) {
1340   Packet4h2 r;
1341   half2* r_alias = reinterpret_cast<half2*>(&r);
1342   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1343   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1344   r_alias[0] = pandnot(a_alias[0], b_alias[0]);
1345   r_alias[1] = pandnot(a_alias[1], b_alias[1]);
1346   r_alias[2] = pandnot(a_alias[2], b_alias[2]);
1347   r_alias[3] = pandnot(a_alias[3], b_alias[3]);
1348   return r;
1349 }
1350 
1351 template <>
1352 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 padd<Packet4h2>(
1353     const Packet4h2& a, const Packet4h2& b) {
1354   Packet4h2 r;
1355   half2* r_alias = reinterpret_cast<half2*>(&r);
1356   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1357   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1358   r_alias[0] = padd(a_alias[0], b_alias[0]);
1359   r_alias[1] = padd(a_alias[1], b_alias[1]);
1360   r_alias[2] = padd(a_alias[2], b_alias[2]);
1361   r_alias[3] = padd(a_alias[3], b_alias[3]);
1362   return r;
1363 }
1364 
1365 template <>
1366 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 psub<Packet4h2>(
1367     const Packet4h2& a, const Packet4h2& b) {
1368   Packet4h2 r;
1369   half2* r_alias = reinterpret_cast<half2*>(&r);
1370   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1371   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1372   r_alias[0] = psub(a_alias[0], b_alias[0]);
1373   r_alias[1] = psub(a_alias[1], b_alias[1]);
1374   r_alias[2] = psub(a_alias[2], b_alias[2]);
1375   r_alias[3] = psub(a_alias[3], b_alias[3]);
1376   return r;
1377 }
1378 
1379 template <>
1380 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pnegate(const Packet4h2& a) {
1381   Packet4h2 r;
1382   half2* r_alias = reinterpret_cast<half2*>(&r);
1383   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1384   r_alias[0] = pnegate(a_alias[0]);
1385   r_alias[1] = pnegate(a_alias[1]);
1386   r_alias[2] = pnegate(a_alias[2]);
1387   r_alias[3] = pnegate(a_alias[3]);
1388   return r;
1389 }
1390 
1391 template <>
1392 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pconj(const Packet4h2& a) {
1393   return a;
1394 }
1395 
1396 template <>
1397 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmul<Packet4h2>(
1398     const Packet4h2& a, const Packet4h2& b) {
1399   Packet4h2 r;
1400   half2* r_alias = reinterpret_cast<half2*>(&r);
1401   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1402   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1403   r_alias[0] = pmul(a_alias[0], b_alias[0]);
1404   r_alias[1] = pmul(a_alias[1], b_alias[1]);
1405   r_alias[2] = pmul(a_alias[2], b_alias[2]);
1406   r_alias[3] = pmul(a_alias[3], b_alias[3]);
1407   return r;
1408 }
1409 
1410 template <>
1411 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmadd<Packet4h2>(
1412     const Packet4h2& a, const Packet4h2& b, const Packet4h2& c) {
1413   Packet4h2 r;
1414   half2* r_alias = reinterpret_cast<half2*>(&r);
1415   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1416   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1417   const half2* c_alias = reinterpret_cast<const half2*>(&c);
1418   r_alias[0] = pmadd(a_alias[0], b_alias[0], c_alias[0]);
1419   r_alias[1] = pmadd(a_alias[1], b_alias[1], c_alias[1]);
1420   r_alias[2] = pmadd(a_alias[2], b_alias[2], c_alias[2]);
1421   r_alias[3] = pmadd(a_alias[3], b_alias[3], c_alias[3]);
1422   return r;
1423 }
1424 
1425 template <>
1426 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pdiv<Packet4h2>(
1427     const Packet4h2& a, const Packet4h2& b) {
1428   Packet4h2 r;
1429   half2* r_alias = reinterpret_cast<half2*>(&r);
1430   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1431   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1432   r_alias[0] = pdiv(a_alias[0], b_alias[0]);
1433   r_alias[1] = pdiv(a_alias[1], b_alias[1]);
1434   r_alias[2] = pdiv(a_alias[2], b_alias[2]);
1435   r_alias[3] = pdiv(a_alias[3], b_alias[3]);
1436   return r;
1437 }
1438 
1439 template <>
1440 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmin<Packet4h2>(
1441     const Packet4h2& a, const Packet4h2& b) {
1442   Packet4h2 r;
1443   half2* r_alias = reinterpret_cast<half2*>(&r);
1444   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1445   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1446   r_alias[0] = pmin(a_alias[0], b_alias[0]);
1447   r_alias[1] = pmin(a_alias[1], b_alias[1]);
1448   r_alias[2] = pmin(a_alias[2], b_alias[2]);
1449   r_alias[3] = pmin(a_alias[3], b_alias[3]);
1450   return r;
1451 }
1452 
1453 template <>
1454 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pmax<Packet4h2>(
1455     const Packet4h2& a, const Packet4h2& b) {
1456   Packet4h2 r;
1457   half2* r_alias = reinterpret_cast<half2*>(&r);
1458   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1459   const half2* b_alias = reinterpret_cast<const half2*>(&b);
1460   r_alias[0] = pmax(a_alias[0], b_alias[0]);
1461   r_alias[1] = pmax(a_alias[1], b_alias[1]);
1462   r_alias[2] = pmax(a_alias[2], b_alias[2]);
1463   r_alias[3] = pmax(a_alias[3], b_alias[3]);
1464   return r;
1465 }
1466 
1467 template <>
1468 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux<Packet4h2>(
1469     const Packet4h2& a) {
1470   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1471 
1472   return predux(a_alias[0]) + predux(a_alias[1]) +
1473          predux(a_alias[2]) + predux(a_alias[3]);
1474 }
1475 
1476 template <>
1477 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_max<Packet4h2>(
1478     const Packet4h2& a) {
1479   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1480   half2 m0 = combine_half(predux_max(a_alias[0]),
1481                             predux_max(a_alias[1]));
1482   half2 m1 = combine_half(predux_max(a_alias[2]),
1483                             predux_max(a_alias[3]));
1484   __half first  = predux_max(m0);
1485   __half second = predux_max(m1);
1486 #if defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
1487   return (__hgt(first, second) ? first : second);
1488 #else
1489   float ffirst  = __half2float(first);
1490   float fsecond = __half2float(second);
1491   return (ffirst > fsecond)? first: second;
1492 #endif
1493 }
1494 
1495 template <>
1496 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_min<Packet4h2>(
1497     const Packet4h2& a) {
1498   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1499   half2 m0 = combine_half(predux_min(a_alias[0]),
1500                             predux_min(a_alias[1]));
1501   half2 m1 = combine_half(predux_min(a_alias[2]),
1502                             predux_min(a_alias[3]));
1503   __half first  = predux_min(m0);
1504   __half second = predux_min(m1);
1505 #if defined(EIGEN_CUDA_HAS_FP16_ARITHMETIC)
1506   return (__hlt(first, second) ? first : second);
1507 #else
1508   float ffirst  = __half2float(first);
1509   float fsecond = __half2float(second);
1510   return (ffirst < fsecond)? first: second;
1511 #endif
1512 }
1513 
1514 // likely overflow/underflow
1515 template <>
1516 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet4h2>(
1517     const Packet4h2& a) {
1518   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1519   return predux_mul(pmul(pmul(a_alias[0], a_alias[1]),
1520                                        pmul(a_alias[2], a_alias[3])));
1521 }
1522 
1523 template <>
1524 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1525 plog1p<Packet4h2>(const Packet4h2& a) {
1526   Packet4h2 r;
1527   half2* r_alias = reinterpret_cast<half2*>(&r);
1528   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1529   r_alias[0] = plog1p(a_alias[0]);
1530   r_alias[1] = plog1p(a_alias[1]);
1531   r_alias[2] = plog1p(a_alias[2]);
1532   r_alias[3] = plog1p(a_alias[3]);
1533   return r;
1534 }
1535 
1536 template <>
1537 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1538 pexpm1<Packet4h2>(const Packet4h2& a) {
1539   Packet4h2 r;
1540   half2* r_alias = reinterpret_cast<half2*>(&r);
1541   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1542   r_alias[0] = pexpm1(a_alias[0]);
1543   r_alias[1] = pexpm1(a_alias[1]);
1544   r_alias[2] = pexpm1(a_alias[2]);
1545   r_alias[3] = pexpm1(a_alias[3]);
1546   return r;
1547 }
1548 
1549 template <>
1550 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 plog<Packet4h2>(const Packet4h2& a) {
1551   Packet4h2 r;
1552   half2* r_alias = reinterpret_cast<half2*>(&r);
1553   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1554   r_alias[0] = plog(a_alias[0]);
1555   r_alias[1] = plog(a_alias[1]);
1556   r_alias[2] = plog(a_alias[2]);
1557   r_alias[3] = plog(a_alias[3]);
1558   return r;
1559 }
1560 
1561 template <>
1562 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 pexp<Packet4h2>(const Packet4h2& a) {
1563   Packet4h2 r;
1564   half2* r_alias = reinterpret_cast<half2*>(&r);
1565   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1566   r_alias[0] = pexp(a_alias[0]);
1567   r_alias[1] = pexp(a_alias[1]);
1568   r_alias[2] = pexp(a_alias[2]);
1569   r_alias[3] = pexp(a_alias[3]);
1570   return r;
1571 }
1572 
1573 template <>
1574 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2 psqrt<Packet4h2>(const Packet4h2& a) {
1575   Packet4h2 r;
1576   half2* r_alias = reinterpret_cast<half2*>(&r);
1577   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1578   r_alias[0] = psqrt(a_alias[0]);
1579   r_alias[1] = psqrt(a_alias[1]);
1580   r_alias[2] = psqrt(a_alias[2]);
1581   r_alias[3] = psqrt(a_alias[3]);
1582   return r;
1583 }
1584 
1585 template <>
1586 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4h2
1587 prsqrt<Packet4h2>(const Packet4h2& a) {
1588   Packet4h2 r;
1589   half2* r_alias = reinterpret_cast<half2*>(&r);
1590   const half2* a_alias = reinterpret_cast<const half2*>(&a);
1591   r_alias[0] = prsqrt(a_alias[0]);
1592   r_alias[1] = prsqrt(a_alias[1]);
1593   r_alias[2] = prsqrt(a_alias[2]);
1594   r_alias[3] = prsqrt(a_alias[3]);
1595   return r;
1596 }
1597 
1598 // The following specialized padd, pmul, pdiv, pmin, pmax, pset1 are needed for
1599 // the implementation of GPU half reduction.
1600 template<>
1601 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 padd<half2>(const half2& a,
1602                                                         const half2& b) {
1603 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
1604   return __hadd2(a, b);
1605 #else
1606   float a1 = __low2float(a);
1607   float a2 = __high2float(a);
1608   float b1 = __low2float(b);
1609   float b2 = __high2float(b);
1610   float r1 = a1 + b1;
1611   float r2 = a2 + b2;
1612   return __floats2half2_rn(r1, r2);
1613 #endif
1614 }
1615 
1616 template<>
1617 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmul<half2>(const half2& a,
1618                                                         const half2& b) {
1619 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
1620   return __hmul2(a, b);
1621 #else
1622   float a1 = __low2float(a);
1623   float a2 = __high2float(a);
1624   float b1 = __low2float(b);
1625   float b2 = __high2float(b);
1626   float r1 = a1 * b1;
1627   float r2 = a2 * b2;
1628   return __floats2half2_rn(r1, r2);
1629 #endif
1630 }
1631 
1632 template<>
1633 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pdiv<half2>(const half2& a,
1634                                                         const half2& b) {
1635 #if defined(EIGEN_GPU_HAS_FP16_ARITHMETIC)
1636   return __h2div(a, b);
1637 #else
1638   float a1 = __low2float(a);
1639   float a2 = __high2float(a);
1640   float b1 = __low2float(b);
1641   float b2 = __high2float(b);
1642   float r1 = a1 / b1;
1643   float r2 = a2 / b2;
1644   return __floats2half2_rn(r1, r2);
1645 #endif
1646 }
1647 
1648 template<>
1649 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmin<half2>(const half2& a,
1650                                                         const half2& b) {
1651   float a1 = __low2float(a);
1652   float a2 = __high2float(a);
1653   float b1 = __low2float(b);
1654   float b2 = __high2float(b);
1655   __half r1 = a1 < b1 ? get_half2_low(a) : get_half2_low(b);
1656   __half r2 = a2 < b2 ? get_half2_high(a) : get_half2_high(b);
1657   return combine_half(r1, r2);
1658 }
1659 
1660 template<>
1661 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half2 pmax<half2>(const half2& a,
1662                                                         const half2& b) {
1663   float a1 = __low2float(a);
1664   float a2 = __high2float(a);
1665   float b1 = __low2float(b);
1666   float b2 = __high2float(b);
1667   __half r1 = a1 > b1 ? get_half2_low(a) : get_half2_low(b);
1668   __half r2 = a2 > b2 ? get_half2_high(a) : get_half2_high(b);
1669   return combine_half(r1, r2);
1670 }
1671 
1672 // #endif // defined(EIGEN_CUDA_ARCH) || defined(EIGEN_HIPCC) || (defined(EIGEN_CUDACC) && EIGEN_COMP_CLANG && !EIGEN_COMP_NVCC)
1673 
1674 #endif // defined(EIGEN_HAS_CUDA_FP16) || defined(EIGEN_HAS_HIP_FP16)
1675 
1676 #undef EIGEN_GPU_HAS_LDG
1677 #undef EIGEN_CUDA_HAS_FP16_ARITHMETIC
1678 #undef EIGEN_GPU_HAS_FP16_ARITHMETIC
1679 
1680 } // end namespace internal
1681 
1682 } // end namespace Eigen
1683 
1684 
1685 #endif // EIGEN_PACKET_MATH_GPU_H
1686