AVX512/PacketMath.h
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2016 Benoit Steiner (benoit.steiner.goog@gmail.com)
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_AVX512_H
11 #define EIGEN_PACKET_MATH_AVX512_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
18 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
19 #endif
20 
21 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
22 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
23 #endif
24 
25 #ifdef EIGEN_VECTORIZE_FMA
26 #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
27 #define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
28 #endif
29 #endif
30 
31 typedef __m512 Packet16f;
32 typedef __m512i Packet16i;
33 typedef __m512d Packet8d;
34 typedef eigen_packet_wrapper<__m256i, 1> Packet16h;
35 typedef eigen_packet_wrapper<__m256i, 2> Packet16bf;
36 
37 template <>
38 struct is_arithmetic<__m512> {
39  enum { value = true };
40 };
41 template <>
42 struct is_arithmetic<__m512i> {
43  enum { value = true };
44 };
45 template <>
46 struct is_arithmetic<__m512d> {
47  enum { value = true };
48 };
49 
50 template<> struct is_arithmetic<Packet16h> { enum { value = true }; };
51 
52 template <>
53 struct packet_traits<half> : default_packet_traits {
54  typedef Packet16h type;
55  // There is no half-size packet for Packet16h.
56  typedef Packet16h half;
57  enum {
58  Vectorizable = 1,
59  AlignedOnScalar = 1,
60  size = 16,
61  HasHalfPacket = 1,
62 
63  HasCmp = 1,
64  HasAdd = 1,
65  HasSub = 1,
66  HasMul = 1,
67  HasDiv = 1,
68  HasNegate = 1,
69  HasAbs = 1,
70  HasAbs2 = 0,
71  HasMin = 1,
72  HasMax = 1,
73  HasConj = 1,
74  HasSetLinear = 0,
75  HasLog = 1,
76  HasLog1p = 1,
77  HasExpm1 = 1,
78  HasExp = 1,
79  HasSqrt = 1,
80  HasRsqrt = 1,
81  HasSin = EIGEN_FAST_MATH,
82  HasCos = EIGEN_FAST_MATH,
83  HasTanh = EIGEN_FAST_MATH,
84  HasErf = EIGEN_FAST_MATH,
85  HasBlend = 0,
86  HasRound = 1,
87  HasFloor = 1,
88  HasCeil = 1,
89  HasRint = 1,
90  HasBessel = 1,
91  HasNdtri = 1
92  };
93 };
94 
95 template<> struct packet_traits<float> : default_packet_traits
96 {
97  typedef Packet16f type;
98  typedef Packet8f half;
99  enum {
100  Vectorizable = 1,
101  AlignedOnScalar = 1,
102  size = 16,
103  HasHalfPacket = 1,
104 
105  HasAbs = 1,
106  HasMin = 1,
107  HasMax = 1,
108  HasConj = 1,
109  HasBlend = 0,
110  HasSin = EIGEN_FAST_MATH,
111  HasCos = EIGEN_FAST_MATH,
112 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
113  HasLog = 1,
114  HasLog1p = 1,
115  HasExpm1 = 1,
116  HasNdtri = 1,
117  HasBessel = 1,
118  HasExp = 1,
119  HasSqrt = EIGEN_FAST_MATH,
120  HasRsqrt = EIGEN_FAST_MATH,
121  HasTanh = EIGEN_FAST_MATH,
122  HasErf = EIGEN_FAST_MATH,
123 #endif
124  HasCmp = 1,
125  HasDiv = 1,
126  HasRound = 1,
127  HasFloor = 1,
128  HasCeil = 1,
129  HasRint = 1
130  };
131  };
132 template<> struct packet_traits<double> : default_packet_traits
133 {
134  typedef Packet8d type;
135  typedef Packet4d half;
136  enum {
137  Vectorizable = 1,
138  AlignedOnScalar = 1,
139  size = 8,
140  HasHalfPacket = 1,
141 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
142  HasLog = 1,
143  HasExp = 1,
144  HasSqrt = EIGEN_FAST_MATH,
145  HasRsqrt = EIGEN_FAST_MATH,
146 #endif
147  HasCmp = 1,
148  HasDiv = 1,
149  HasRound = 1,
150  HasFloor = 1,
151  HasCeil = 1,
152  HasRint = 1
153  };
154 };
155 
156 /* TODO Implement AVX512 for integers
157 template<> struct packet_traits<int> : default_packet_traits
158 {
159  typedef Packet16i type;
160  enum {
161  Vectorizable = 1,
162  AlignedOnScalar = 1,
163  size=8
164  };
165 };
166 */
167 
168 template <>
169 struct unpacket_traits<Packet16f> {
170  typedef float type;
171  typedef Packet8f half;
172  typedef Packet16i integer_packet;
173  typedef uint16_t mask_t;
174  enum { size = 16, alignment=Aligned64, vectorizable=true, masked_load_available=true, masked_store_available=true };
175 };
176 template <>
177 struct unpacket_traits<Packet8d> {
178  typedef double type;
179  typedef Packet4d half;
180  enum { size = 8, alignment=Aligned64, vectorizable=true, masked_load_available=false, masked_store_available=false };
181 };
182 template <>
183 struct unpacket_traits<Packet16i> {
184  typedef int type;
185  typedef Packet8i half;
186  enum { size = 16, alignment=Aligned64, vectorizable=false, masked_load_available=false, masked_store_available=false };
187 };
188 
189 template<>
190 struct unpacket_traits<Packet16h> {
191  typedef Eigen::half type;
192  typedef Packet8h half;
193  enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
194 };
195 
196 template <>
197 EIGEN_STRONG_INLINE Packet16f pset1<Packet16f>(const float& from) {
198  return _mm512_set1_ps(from);
199 }
200 template <>
201 EIGEN_STRONG_INLINE Packet8d pset1<Packet8d>(const double& from) {
202  return _mm512_set1_pd(from);
203 }
204 template <>
205 EIGEN_STRONG_INLINE Packet16i pset1<Packet16i>(const int& from) {
206  return _mm512_set1_epi32(from);
207 }
208 
209 template <>
210 EIGEN_STRONG_INLINE Packet16f pset1frombits<Packet16f>(unsigned int from) {
211  return _mm512_castsi512_ps(_mm512_set1_epi32(from));
212 }
213 
214 template <>
215 EIGEN_STRONG_INLINE Packet8d pset1frombits<Packet8d>(const numext::uint64_t from) {
216  return _mm512_castsi512_pd(_mm512_set1_epi64(from));
217 }
218 
219 template<> EIGEN_STRONG_INLINE Packet16f pzero(const Packet16f& /*a*/) { return _mm512_setzero_ps(); }
220 template<> EIGEN_STRONG_INLINE Packet8d pzero(const Packet8d& /*a*/) { return _mm512_setzero_pd(); }
221 template<> EIGEN_STRONG_INLINE Packet16i pzero(const Packet16i& /*a*/) { return _mm512_setzero_si512(); }
222 
223 template<> EIGEN_STRONG_INLINE Packet16f peven_mask(const Packet16f& /*a*/) {
224  return _mm512_castsi512_ps(_mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1,
225  0, -1, 0, -1, 0, -1, 0, -1));
226 }
227 template<> EIGEN_STRONG_INLINE Packet16i peven_mask(const Packet16i& /*a*/) {
228  return _mm512_set_epi32(0, -1, 0, -1, 0, -1, 0, -1,
229  0, -1, 0, -1, 0, -1, 0, -1);
230 }
231 template<> EIGEN_STRONG_INLINE Packet8d peven_mask(const Packet8d& /*a*/) {
232  return _mm512_castsi512_pd(_mm512_set_epi32(0, 0, -1, -1, 0, 0, -1, -1,
233  0, 0, -1, -1, 0, 0, -1, -1));
234 }
235 
236 template <>
237 EIGEN_STRONG_INLINE Packet16f pload1<Packet16f>(const float* from) {
238  return _mm512_broadcastss_ps(_mm_load_ps1(from));
239 }
240 template <>
241 EIGEN_STRONG_INLINE Packet8d pload1<Packet8d>(const double* from) {
242  return _mm512_set1_pd(*from);
243 }
244 
245 template <>
246 EIGEN_STRONG_INLINE Packet16f plset<Packet16f>(const float& a) {
247  return _mm512_add_ps(
248  _mm512_set1_ps(a),
249  _mm512_set_ps(15.0f, 14.0f, 13.0f, 12.0f, 11.0f, 10.0f, 9.0f, 8.0f, 7.0f, 6.0f, 5.0f,
250  4.0f, 3.0f, 2.0f, 1.0f, 0.0f));
251 }
252 template <>
253 EIGEN_STRONG_INLINE Packet8d plset<Packet8d>(const double& a) {
254  return _mm512_add_pd(_mm512_set1_pd(a),
255  _mm512_set_pd(7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0));
256 }
257 
258 template <>
259 EIGEN_STRONG_INLINE Packet16f padd<Packet16f>(const Packet16f& a,
260  const Packet16f& b) {
261  return _mm512_add_ps(a, b);
262 }
263 template <>
264 EIGEN_STRONG_INLINE Packet8d padd<Packet8d>(const Packet8d& a,
265  const Packet8d& b) {
266  return _mm512_add_pd(a, b);
267 }
268 template <>
269 EIGEN_STRONG_INLINE Packet16i padd<Packet16i>(const Packet16i& a,
270  const Packet16i& b) {
271  return _mm512_add_epi32(a, b);
272 }
273 
274 template <>
275 EIGEN_STRONG_INLINE Packet16f psub<Packet16f>(const Packet16f& a,
276  const Packet16f& b) {
277  return _mm512_sub_ps(a, b);
278 }
279 template <>
280 EIGEN_STRONG_INLINE Packet8d psub<Packet8d>(const Packet8d& a,
281  const Packet8d& b) {
282  return _mm512_sub_pd(a, b);
283 }
284 template <>
285 EIGEN_STRONG_INLINE Packet16i psub<Packet16i>(const Packet16i& a,
286  const Packet16i& b) {
287  return _mm512_sub_epi32(a, b);
288 }
289 
290 template <>
291 EIGEN_STRONG_INLINE Packet16f pnegate(const Packet16f& a) {
292  return _mm512_sub_ps(_mm512_set1_ps(0.0), a);
293 }
294 template <>
295 EIGEN_STRONG_INLINE Packet8d pnegate(const Packet8d& a) {
296  return _mm512_sub_pd(_mm512_set1_pd(0.0), a);
297 }
298 
299 template <>
300 EIGEN_STRONG_INLINE Packet16f pconj(const Packet16f& a) {
301  return a;
302 }
303 template <>
304 EIGEN_STRONG_INLINE Packet8d pconj(const Packet8d& a) {
305  return a;
306 }
307 template <>
308 EIGEN_STRONG_INLINE Packet16i pconj(const Packet16i& a) {
309  return a;
310 }
311 
312 template <>
313 EIGEN_STRONG_INLINE Packet16f pmul<Packet16f>(const Packet16f& a,
314  const Packet16f& b) {
315  return _mm512_mul_ps(a, b);
316 }
317 template <>
318 EIGEN_STRONG_INLINE Packet8d pmul<Packet8d>(const Packet8d& a,
319  const Packet8d& b) {
320  return _mm512_mul_pd(a, b);
321 }
322 template <>
323 EIGEN_STRONG_INLINE Packet16i pmul<Packet16i>(const Packet16i& a,
324  const Packet16i& b) {
325  return _mm512_mullo_epi32(a, b);
326 }
327 
328 template <>
329 EIGEN_STRONG_INLINE Packet16f pdiv<Packet16f>(const Packet16f& a,
330  const Packet16f& b) {
331  return _mm512_div_ps(a, b);
332 }
333 template <>
334 EIGEN_STRONG_INLINE Packet8d pdiv<Packet8d>(const Packet8d& a,
335  const Packet8d& b) {
336  return _mm512_div_pd(a, b);
337 }
338 
339 #ifdef EIGEN_VECTORIZE_FMA
340 template <>
341 EIGEN_STRONG_INLINE Packet16f pmadd(const Packet16f& a, const Packet16f& b,
342  const Packet16f& c) {
343  return _mm512_fmadd_ps(a, b, c);
344 }
345 template <>
346 EIGEN_STRONG_INLINE Packet8d pmadd(const Packet8d& a, const Packet8d& b,
347  const Packet8d& c) {
348  return _mm512_fmadd_pd(a, b, c);
349 }
350 #endif
351 
352 template <>
353 EIGEN_DEVICE_FUNC inline Packet16f pselect(const Packet16f& mask,
354  const Packet16f& a,
355  const Packet16f& b) {
356  __mmask16 mask16 = _mm512_cmp_epi32_mask(
357  _mm512_castps_si512(mask), _mm512_setzero_epi32(), _MM_CMPINT_EQ);
358  return _mm512_mask_blend_ps(mask16, a, b);
359 }
360 
361 template <>
362 EIGEN_DEVICE_FUNC inline Packet8d pselect(const Packet8d& mask,
363  const Packet8d& a,
364  const Packet8d& b) {
365  __mmask8 mask8 = _mm512_cmp_epi64_mask(_mm512_castpd_si512(mask),
366  _mm512_setzero_epi32(), _MM_CMPINT_EQ);
367  return _mm512_mask_blend_pd(mask8, a, b);
368 }
369 
370 template <>
371 EIGEN_STRONG_INLINE Packet16f pmin<Packet16f>(const Packet16f& a,
372  const Packet16f& b) {
373  // Arguments are reversed to match NaN propagation behavior of std::min.
374  return _mm512_min_ps(b, a);
375 }
376 template <>
377 EIGEN_STRONG_INLINE Packet8d pmin<Packet8d>(const Packet8d& a,
378  const Packet8d& b) {
379  // Arguments are reversed to match NaN propagation behavior of std::min.
380  return _mm512_min_pd(b, a);
381 }
382 
383 template <>
384 EIGEN_STRONG_INLINE Packet16f pmax<Packet16f>(const Packet16f& a,
385  const Packet16f& b) {
386  // Arguments are reversed to match NaN propagation behavior of std::max.
387  return _mm512_max_ps(b, a);
388 }
389 template <>
390 EIGEN_STRONG_INLINE Packet8d pmax<Packet8d>(const Packet8d& a,
391  const Packet8d& b) {
392  // Arguments are reversed to match NaN propagation behavior of std::max.
393  return _mm512_max_pd(b, a);
394 }
395 
396 // Add specializations for min/max with prescribed NaN progation.
397 template<>
398 EIGEN_STRONG_INLINE Packet16f pmin<PropagateNumbers, Packet16f>(const Packet16f& a, const Packet16f& b) {
399  return pminmax_propagate_numbers(a, b, pmin<Packet16f>);
400 }
401 template<>
402 EIGEN_STRONG_INLINE Packet8d pmin<PropagateNumbers, Packet8d>(const Packet8d& a, const Packet8d& b) {
403  return pminmax_propagate_numbers(a, b, pmin<Packet8d>);
404 }
405 template<>
406 EIGEN_STRONG_INLINE Packet16f pmax<PropagateNumbers, Packet16f>(const Packet16f& a, const Packet16f& b) {
407  return pminmax_propagate_numbers(a, b, pmax<Packet16f>);
408 }
409 template<>
410 EIGEN_STRONG_INLINE Packet8d pmax<PropagateNumbers, Packet8d>(const Packet8d& a, const Packet8d& b) {
411  return pminmax_propagate_numbers(a, b, pmax<Packet8d>);
412 }
413 template<>
414 EIGEN_STRONG_INLINE Packet16f pmin<PropagateNaN, Packet16f>(const Packet16f& a, const Packet16f& b) {
415  return pminmax_propagate_nan(a, b, pmin<Packet16f>);
416 }
417 template<>
418 EIGEN_STRONG_INLINE Packet8d pmin<PropagateNaN, Packet8d>(const Packet8d& a, const Packet8d& b) {
419  return pminmax_propagate_nan(a, b, pmin<Packet8d>);
420 }
421 template<>
422 EIGEN_STRONG_INLINE Packet16f pmax<PropagateNaN, Packet16f>(const Packet16f& a, const Packet16f& b) {
423  return pminmax_propagate_nan(a, b, pmax<Packet16f>);
424 }
425 template<>
426 EIGEN_STRONG_INLINE Packet8d pmax<PropagateNaN, Packet8d>(const Packet8d& a, const Packet8d& b) {
427  return pminmax_propagate_nan(a, b, pmax<Packet8d>);
428 }
429 
430 
431 #ifdef EIGEN_VECTORIZE_AVX512DQ
432 template<int I_> EIGEN_STRONG_INLINE Packet8f extract256(Packet16f x) { return _mm512_extractf32x8_ps(x,I_); }
433 template<int I_> EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x) { return _mm512_extractf64x2_pd(x,I_); }
434 EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) { return _mm512_insertf32x8(_mm512_castps256_ps512(a),b,1); }
435 #else
436 // AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512
437 template<int I_> EIGEN_STRONG_INLINE Packet8f extract256(Packet16f x) {
438  return _mm256_castsi256_ps(_mm512_extracti64x4_epi64( _mm512_castps_si512(x),I_));
439 }
440 
441 // AVX512F does not define _mm512_extractf64x2_pd to extract _m128 from _m512
442 template<int I_> EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x) {
443  return _mm_castsi128_pd(_mm512_extracti32x4_epi32( _mm512_castpd_si512(x),I_));
444 }
445 
446 EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b) {
447  return _mm512_castsi512_ps(_mm512_inserti64x4(_mm512_castsi256_si512(_mm256_castps_si256(a)),
448  _mm256_castps_si256(b),1));
449 }
450 #endif
451 
452 // Helper function for bit packing snippet of low precision comparison.
453 // It packs the flags from 32x16 to 16x16.
454 EIGEN_STRONG_INLINE __m256i Pack32To16(Packet16f rf) {
455  // Split data into small pieces and handle with AVX instructions
456  // to guarantee internal order of vector.
457  // Operation:
458  // dst[15:0] := Saturate16(rf[31:0])
459  // dst[31:16] := Saturate16(rf[63:32])
460  // ...
461  // dst[255:240] := Saturate16(rf[255:224])
462  __m256i lo = _mm256_castps_si256(extract256<0>(rf));
463  __m256i hi = _mm256_castps_si256(extract256<1>(rf));
464  __m128i result_lo = _mm_packs_epi32(_mm256_extractf128_si256(lo, 0),
465  _mm256_extractf128_si256(lo, 1));
466  __m128i result_hi = _mm_packs_epi32(_mm256_extractf128_si256(hi, 0),
467  _mm256_extractf128_si256(hi, 1));
468  return _mm256_insertf128_si256(_mm256_castsi128_si256(result_lo), result_hi, 1);
469 }
470 
471 template <>
472 EIGEN_STRONG_INLINE Packet16f pcmp_eq(const Packet16f& a, const Packet16f& b) {
473  __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_EQ_OQ);
474  return _mm512_castsi512_ps(
475  _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
476 }
477 template<> EIGEN_STRONG_INLINE Packet16f pcmp_le(const Packet16f& a, const Packet16f& b) {
478  __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LE_OQ);
479  return _mm512_castsi512_ps(
480  _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
481 }
482 
483 template<> EIGEN_STRONG_INLINE Packet16f pcmp_lt(const Packet16f& a, const Packet16f& b) {
484  __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_LT_OQ);
485  return _mm512_castsi512_ps(
486  _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
487 }
488 
489 template<> EIGEN_STRONG_INLINE Packet16f pcmp_lt_or_nan(const Packet16f& a, const Packet16f& b) {
490  __mmask16 mask = _mm512_cmp_ps_mask(a, b, _CMP_NGE_UQ);
491  return _mm512_castsi512_ps(
492  _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu));
493 }
494 
495 template<> EIGEN_STRONG_INLINE Packet16i pcmp_eq(const Packet16i& a, const Packet16i& b) {
496  __mmask16 mask = _mm512_cmp_epi32_mask(a, b, _CMP_EQ_OQ);
497  return _mm512_mask_set1_epi32(_mm512_set1_epi32(0), mask, 0xffffffffu);
498 }
499 
500 
501 template <>
502 EIGEN_STRONG_INLINE Packet8d pcmp_eq(const Packet8d& a, const Packet8d& b) {
503  __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_EQ_OQ);
504  return _mm512_castsi512_pd(
505  _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
506 }
507 template <>
508 EIGEN_STRONG_INLINE Packet8d pcmp_le(const Packet8d& a, const Packet8d& b) {
509  __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LE_OQ);
510  return _mm512_castsi512_pd(
511  _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
512 }
513 template <>
514 EIGEN_STRONG_INLINE Packet8d pcmp_lt(const Packet8d& a, const Packet8d& b) {
515  __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_LT_OQ);
516  return _mm512_castsi512_pd(
517  _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
518 }
519 template <>
520 EIGEN_STRONG_INLINE Packet8d pcmp_lt_or_nan(const Packet8d& a, const Packet8d& b) {
521  __mmask8 mask = _mm512_cmp_pd_mask(a, b, _CMP_NGE_UQ);
522  return _mm512_castsi512_pd(
523  _mm512_mask_set1_epi64(_mm512_set1_epi64(0), mask, 0xffffffffffffffffu));
524 }
525 
526 template<> EIGEN_STRONG_INLINE Packet16f print<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_CUR_DIRECTION); }
527 template<> EIGEN_STRONG_INLINE Packet8d print<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_CUR_DIRECTION); }
528 
529 template<> EIGEN_STRONG_INLINE Packet16f pceil<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_POS_INF); }
530 template<> EIGEN_STRONG_INLINE Packet8d pceil<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_POS_INF); }
531 
532 template<> EIGEN_STRONG_INLINE Packet16f pfloor<Packet16f>(const Packet16f& a) { return _mm512_roundscale_ps(a, _MM_FROUND_TO_NEG_INF); }
533 template<> EIGEN_STRONG_INLINE Packet8d pfloor<Packet8d>(const Packet8d& a) { return _mm512_roundscale_pd(a, _MM_FROUND_TO_NEG_INF); }
534 
535 template <>
536 EIGEN_STRONG_INLINE Packet16i ptrue<Packet16i>(const Packet16i& /*a*/) {
537  return _mm512_set1_epi32(0xffffffffu);
538 }
539 
540 template <>
541 EIGEN_STRONG_INLINE Packet16f ptrue<Packet16f>(const Packet16f& a) {
542  return _mm512_castsi512_ps(ptrue<Packet16i>(_mm512_castps_si512(a)));
543 }
544 
545 template <>
546 EIGEN_STRONG_INLINE Packet8d ptrue<Packet8d>(const Packet8d& a) {
547  return _mm512_castsi512_pd(ptrue<Packet16i>(_mm512_castpd_si512(a)));
548 }
549 
550 template <>
551 EIGEN_STRONG_INLINE Packet16i pand<Packet16i>(const Packet16i& a,
552  const Packet16i& b) {
553  return _mm512_and_si512(a,b);
554 }
555 
556 template <>
557 EIGEN_STRONG_INLINE Packet16f pand<Packet16f>(const Packet16f& a,
558  const Packet16f& b) {
559 #ifdef EIGEN_VECTORIZE_AVX512DQ
560  return _mm512_and_ps(a, b);
561 #else
562  return _mm512_castsi512_ps(pand(_mm512_castps_si512(a),_mm512_castps_si512(b)));
563 #endif
564 }
565 template <>
566 EIGEN_STRONG_INLINE Packet8d pand<Packet8d>(const Packet8d& a,
567  const Packet8d& b) {
568 #ifdef EIGEN_VECTORIZE_AVX512DQ
569  return _mm512_and_pd(a, b);
570 #else
571  Packet8d res = _mm512_undefined_pd();
572  Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);
573  Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);
574  res = _mm512_insertf64x4(res, _mm256_and_pd(lane0_a, lane0_b), 0);
575 
576  Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);
577  Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);
578  return _mm512_insertf64x4(res, _mm256_and_pd(lane1_a, lane1_b), 1);
579 #endif
580 }
581 
582 template <>
583 EIGEN_STRONG_INLINE Packet16i por<Packet16i>(const Packet16i& a, const Packet16i& b) {
584  return _mm512_or_si512(a, b);
585 }
586 
587 template <>
588 EIGEN_STRONG_INLINE Packet16f por<Packet16f>(const Packet16f& a, const Packet16f& b) {
589 #ifdef EIGEN_VECTORIZE_AVX512DQ
590  return _mm512_or_ps(a, b);
591 #else
592  return _mm512_castsi512_ps(por(_mm512_castps_si512(a),_mm512_castps_si512(b)));
593 #endif
594 }
595 
596 template <>
597 EIGEN_STRONG_INLINE Packet8d por<Packet8d>(const Packet8d& a,
598  const Packet8d& b) {
599 #ifdef EIGEN_VECTORIZE_AVX512DQ
600  return _mm512_or_pd(a, b);
601 #else
602  return _mm512_castsi512_pd(por(_mm512_castpd_si512(a),_mm512_castpd_si512(b)));
603 #endif
604 }
605 
606 template <>
607 EIGEN_STRONG_INLINE Packet16i pxor<Packet16i>(const Packet16i& a, const Packet16i& b) {
608  return _mm512_xor_si512(a, b);
609 }
610 
611 template <>
612 EIGEN_STRONG_INLINE Packet16f pxor<Packet16f>(const Packet16f& a, const Packet16f& b) {
613 #ifdef EIGEN_VECTORIZE_AVX512DQ
614  return _mm512_xor_ps(a, b);
615 #else
616  return _mm512_castsi512_ps(pxor(_mm512_castps_si512(a),_mm512_castps_si512(b)));
617 #endif
618 }
619 
620 template <>
621 EIGEN_STRONG_INLINE Packet8d pxor<Packet8d>(const Packet8d& a, const Packet8d& b) {
622 #ifdef EIGEN_VECTORIZE_AVX512DQ
623  return _mm512_xor_pd(a, b);
624 #else
625  return _mm512_castsi512_pd(pxor(_mm512_castpd_si512(a),_mm512_castpd_si512(b)));
626 #endif
627 }
628 
629 template <>
630 EIGEN_STRONG_INLINE Packet16i pandnot<Packet16i>(const Packet16i& a, const Packet16i& b) {
631  return _mm512_andnot_si512(b, a);
632 }
633 
634 template <>
635 EIGEN_STRONG_INLINE Packet16f pandnot<Packet16f>(const Packet16f& a, const Packet16f& b) {
636 #ifdef EIGEN_VECTORIZE_AVX512DQ
637  return _mm512_andnot_ps(b, a);
638 #else
639  return _mm512_castsi512_ps(pandnot(_mm512_castps_si512(a),_mm512_castps_si512(b)));
640 #endif
641 }
642 template <>
643 EIGEN_STRONG_INLINE Packet8d pandnot<Packet8d>(const Packet8d& a,const Packet8d& b) {
644 #ifdef EIGEN_VECTORIZE_AVX512DQ
645  return _mm512_andnot_pd(b, a);
646 #else
647  return _mm512_castsi512_pd(pandnot(_mm512_castpd_si512(a),_mm512_castpd_si512(b)));
648 #endif
649 }
650 
651 template<> EIGEN_STRONG_INLINE Packet16f pround<Packet16f>(const Packet16f& a)
652 {
653  // Work-around for default std::round rounding mode.
654  const Packet16f mask = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x80000000u));
655  const Packet16f prev0dot5 = pset1frombits<Packet16f>(static_cast<numext::uint32_t>(0x3EFFFFFFu));
656  return _mm512_roundscale_ps(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
657 }
658 template<> EIGEN_STRONG_INLINE Packet8d pround<Packet8d>(const Packet8d& a)
659 {
660  // Work-around for default std::round rounding mode.
661  const Packet8d mask = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x8000000000000000ull));
662  const Packet8d prev0dot5 = pset1frombits<Packet8d>(static_cast<numext::uint64_t>(0x3FDFFFFFFFFFFFFFull));
663  return _mm512_roundscale_pd(padd(por(pand(a, mask), prev0dot5), a), _MM_FROUND_TO_ZERO);
664 }
665 
666 template<int N> EIGEN_STRONG_INLINE Packet16i parithmetic_shift_right(Packet16i a) {
667  return _mm512_srai_epi32(a, N);
668 }
669 
670 template<int N> EIGEN_STRONG_INLINE Packet16i plogical_shift_right(Packet16i a) {
671  return _mm512_srli_epi32(a, N);
672 }
673 
674 template<int N> EIGEN_STRONG_INLINE Packet16i plogical_shift_left(Packet16i a) {
675  return _mm512_slli_epi32(a, N);
676 }
677 
678 template <>
679 EIGEN_STRONG_INLINE Packet16f pload<Packet16f>(const float* from) {
680  EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_ps(from);
681 }
682 template <>
683 EIGEN_STRONG_INLINE Packet8d pload<Packet8d>(const double* from) {
684  EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_pd(from);
685 }
686 template <>
687 EIGEN_STRONG_INLINE Packet16i pload<Packet16i>(const int* from) {
688  EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_si512(
689  reinterpret_cast<const __m512i*>(from));
690 }
691 
692 template <>
693 EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from) {
694  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_ps(from);
695 }
696 template <>
697 EIGEN_STRONG_INLINE Packet8d ploadu<Packet8d>(const double* from) {
698  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_pd(from);
699 }
700 template <>
701 EIGEN_STRONG_INLINE Packet16i ploadu<Packet16i>(const int* from) {
702  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_si512(
703  reinterpret_cast<const __m512i*>(from));
704 }
705 
706 template <>
707 EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from, uint16_t umask) {
708  __mmask16 mask = static_cast<__mmask16>(umask);
709  EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_maskz_loadu_ps(mask, from);
710 }
711 
712 // Loads 8 floats from memory a returns the packet
713 // {a0, a0 a1, a1, a2, a2, a3, a3, a4, a4, a5, a5, a6, a6, a7, a7}
714 template <>
715 EIGEN_STRONG_INLINE Packet16f ploaddup<Packet16f>(const float* from) {
716  // an unaligned load is required here as there is no requirement
717  // on the alignment of input pointer 'from'
718  __m256i low_half = _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
719  __m512 even_elements = _mm512_castsi512_ps(_mm512_cvtepu32_epi64(low_half));
720  __m512 pairs = _mm512_permute_ps(even_elements, _MM_SHUFFLE(2, 2, 0, 0));
721  return pairs;
722 }
723 
724 #ifdef EIGEN_VECTORIZE_AVX512DQ
725 // FIXME: this does not look optimal, better load a Packet4d and shuffle...
726 // Loads 4 doubles from memory a returns the packet {a0, a0 a1, a1, a2, a2, a3,
727 // a3}
728 template <>
729 EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) {
730  __m512d x = _mm512_setzero_pd();
731  x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[0]), 0);
732  x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[1]), 1);
733  x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[2]), 2);
734  x = _mm512_insertf64x2(x, _mm_loaddup_pd(&from[3]), 3);
735  return x;
736 }
737 #else
738 template <>
739 EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) {
740  __m512d x = _mm512_setzero_pd();
741  x = _mm512_mask_broadcastsd_pd(x, 0x3<<0, _mm_load_sd(from+0));
742  x = _mm512_mask_broadcastsd_pd(x, 0x3<<2, _mm_load_sd(from+1));
743  x = _mm512_mask_broadcastsd_pd(x, 0x3<<4, _mm_load_sd(from+2));
744  x = _mm512_mask_broadcastsd_pd(x, 0x3<<6, _mm_load_sd(from+3));
745  return x;
746 }
747 #endif
748 
749 // Loads 4 floats from memory a returns the packet
750 // {a0, a0 a0, a0, a1, a1, a1, a1, a2, a2, a2, a2, a3, a3, a3, a3}
751 template <>
752 EIGEN_STRONG_INLINE Packet16f ploadquad<Packet16f>(const float* from) {
753  Packet16f tmp = _mm512_castps128_ps512(ploadu<Packet4f>(from));
754  const Packet16i scatter_mask = _mm512_set_epi32(3,3,3,3, 2,2,2,2, 1,1,1,1, 0,0,0,0);
755  return _mm512_permutexvar_ps(scatter_mask, tmp);
756 }
757 
758 // Loads 2 doubles from memory a returns the packet
759 // {a0, a0 a0, a0, a1, a1, a1, a1}
760 template <>
761 EIGEN_STRONG_INLINE Packet8d ploadquad<Packet8d>(const double* from) {
762  __m256d lane0 = _mm256_set1_pd(*from);
763  __m256d lane1 = _mm256_set1_pd(*(from+1));
764  __m512d tmp = _mm512_undefined_pd();
765  tmp = _mm512_insertf64x4(tmp, lane0, 0);
766  return _mm512_insertf64x4(tmp, lane1, 1);
767 }
768 
769 template <>
770 EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet16f& from) {
771  EIGEN_DEBUG_ALIGNED_STORE _mm512_store_ps(to, from);
772 }
773 template <>
774 EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet8d& from) {
775  EIGEN_DEBUG_ALIGNED_STORE _mm512_store_pd(to, from);
776 }
777 template <>
778 EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet16i& from) {
779  EIGEN_DEBUG_ALIGNED_STORE _mm512_storeu_si512(reinterpret_cast<__m512i*>(to),
780  from);
781 }
782 
783 template <>
784 EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from) {
785  EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_ps(to, from);
786 }
787 template <>
788 EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet8d& from) {
789  EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_pd(to, from);
790 }
791 template <>
792 EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet16i& from) {
793  EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_si512(
794  reinterpret_cast<__m512i*>(to), from);
795 }
796 template <>
797 EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from, uint16_t umask) {
798  __mmask16 mask = static_cast<__mmask16>(umask);
799  EIGEN_DEBUG_UNALIGNED_STORE return _mm512_mask_storeu_ps(to, mask, from);
800 }
801 
802 template <>
803 EIGEN_DEVICE_FUNC inline Packet16f pgather<float, Packet16f>(const float* from,
804  Index stride) {
805  Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
806  Packet16i stride_multiplier =
807  _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
808  Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
809 
810  return _mm512_i32gather_ps(indices, from, 4);
811 }
812 template <>
813 EIGEN_DEVICE_FUNC inline Packet8d pgather<double, Packet8d>(const double* from,
814  Index stride) {
815  Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride));
816  Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
817  Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
818 
819  return _mm512_i32gather_pd(indices, from, 8);
820 }
821 
822 template <>
823 EIGEN_DEVICE_FUNC inline void pscatter<float, Packet16f>(float* to,
824  const Packet16f& from,
825  Index stride) {
826  Packet16i stride_vector = _mm512_set1_epi32(convert_index<int>(stride));
827  Packet16i stride_multiplier =
828  _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
829  Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
830  _mm512_i32scatter_ps(to, indices, from, 4);
831 }
832 template <>
833 EIGEN_DEVICE_FUNC inline void pscatter<double, Packet8d>(double* to,
834  const Packet8d& from,
835  Index stride) {
836  Packet8i stride_vector = _mm256_set1_epi32(convert_index<int>(stride));
837  Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
838  Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
839  _mm512_i32scatter_pd(to, indices, from, 8);
840 }
841 
842 template <>
843 EIGEN_STRONG_INLINE void pstore1<Packet16f>(float* to, const float& a) {
844  Packet16f pa = pset1<Packet16f>(a);
845  pstore(to, pa);
846 }
847 template <>
848 EIGEN_STRONG_INLINE void pstore1<Packet8d>(double* to, const double& a) {
849  Packet8d pa = pset1<Packet8d>(a);
850  pstore(to, pa);
851 }
852 template <>
853 EIGEN_STRONG_INLINE void pstore1<Packet16i>(int* to, const int& a) {
854  Packet16i pa = pset1<Packet16i>(a);
855  pstore(to, pa);
856 }
857 
858 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
859 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
860 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((SsePrefetchPtrType)(addr), _MM_HINT_T0); }
861 
862 template <>
863 EIGEN_STRONG_INLINE float pfirst<Packet16f>(const Packet16f& a) {
864  return _mm_cvtss_f32(_mm512_extractf32x4_ps(a, 0));
865 }
866 template <>
867 EIGEN_STRONG_INLINE double pfirst<Packet8d>(const Packet8d& a) {
868  return _mm_cvtsd_f64(_mm256_extractf128_pd(_mm512_extractf64x4_pd(a, 0), 0));
869 }
870 template <>
871 EIGEN_STRONG_INLINE int pfirst<Packet16i>(const Packet16i& a) {
872  return _mm_extract_epi32(_mm512_extracti32x4_epi32(a, 0), 0);
873 }
874 
875 template<> EIGEN_STRONG_INLINE Packet16f preverse(const Packet16f& a)
876 {
877  return _mm512_permutexvar_ps(_mm512_set_epi32(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), a);
878 }
879 
880 template<> EIGEN_STRONG_INLINE Packet8d preverse(const Packet8d& a)
881 {
882  return _mm512_permutexvar_pd(_mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7), a);
883 }
884 
885 template<> EIGEN_STRONG_INLINE Packet16f pabs(const Packet16f& a)
886 {
887  // _mm512_abs_ps intrinsic not found, so hack around it
888  return _mm512_castsi512_ps(_mm512_and_si512(_mm512_castps_si512(a), _mm512_set1_epi32(0x7fffffff)));
889 }
890 template <>
891 EIGEN_STRONG_INLINE Packet8d pabs(const Packet8d& a) {
892  // _mm512_abs_ps intrinsic not found, so hack around it
893  return _mm512_castsi512_pd(_mm512_and_si512(_mm512_castpd_si512(a),
894  _mm512_set1_epi64(0x7fffffffffffffff)));
895 }
896 
897 template<>
898 EIGEN_STRONG_INLINE Packet16f pfrexp<Packet16f>(const Packet16f& a, Packet16f& exponent){
899  return pfrexp_generic(a, exponent);
900 }
901 
902 // Extract exponent without existence of Packet8l.
903 template<>
904 EIGEN_STRONG_INLINE
905 Packet8d pfrexp_generic_get_biased_exponent(const Packet8d& a) {
906  const Packet8d cst_exp_mask = pset1frombits<Packet8d>(static_cast<uint64_t>(0x7ff0000000000000ull));
907  #ifdef EIGEN_VECTORIZE_AVX512DQ
908  return _mm512_cvtepi64_pd(_mm512_srli_epi64(_mm512_castpd_si512(pand(a, cst_exp_mask)), 52));
909  #else
910  return _mm512_cvtepi32_pd(_mm512_cvtepi64_epi32(_mm512_srli_epi64(_mm512_castpd_si512(pand(a, cst_exp_mask)), 52)));
911  #endif
912 }
913 
914 template<>
915 EIGEN_STRONG_INLINE Packet8d pfrexp<Packet8d>(const Packet8d& a, Packet8d& exponent) {
916  return pfrexp_generic(a, exponent);
917 }
918 
919 template<> EIGEN_STRONG_INLINE Packet16f pldexp<Packet16f>(const Packet16f& a, const Packet16f& exponent) {
920  return pldexp_generic(a, exponent);
921 }
922 
923 template<> EIGEN_STRONG_INLINE Packet8d pldexp<Packet8d>(const Packet8d& a, const Packet8d& exponent) {
924  // Clamp exponent to [-2099, 2099]
925  const Packet8d max_exponent = pset1<Packet8d>(2099.0);
926  const Packet8i e = _mm512_cvtpd_epi32(pmin(pmax(exponent, pnegate(max_exponent)), max_exponent));
927 
928  // Split 2^e into four factors and multiply.
929  const Packet8i bias = pset1<Packet8i>(1023);
930  Packet8i b = parithmetic_shift_right<2>(e); // floor(e/4)
931 
932  // 2^b
933  const Packet8i permute_idx = _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7);
934  Packet8i hi = _mm256_permutevar8x32_epi32(padd(b, bias), permute_idx);
935  Packet8i lo = _mm256_slli_epi64(hi, 52);
936  hi = _mm256_slli_epi64(_mm256_srli_epi64(hi, 32), 52);
937  Packet8d c = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1));
938  Packet8d out = pmul(pmul(pmul(a, c), c), c); // a * 2^(3b)
939 
940  // 2^(e - 3b)
941  b = psub(psub(psub(e, b), b), b); // e - 3b
942  hi = _mm256_permutevar8x32_epi32(padd(b, bias), permute_idx);
943  lo = _mm256_slli_epi64(hi, 52);
944  hi = _mm256_slli_epi64(_mm256_srli_epi64(hi, 32), 52);
945  c = _mm512_castsi512_pd(_mm512_inserti64x4(_mm512_castsi256_si512(lo), hi, 1));
946  out = pmul(out, c); // a * 2^e
947  return out;
948 }
949 
950 #ifdef EIGEN_VECTORIZE_AVX512DQ
951 // AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512
952 #define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT) \
953  __m256 OUTPUT##_0 = _mm512_extractf32x8_ps(INPUT, 0); \
954  __m256 OUTPUT##_1 = _mm512_extractf32x8_ps(INPUT, 1)
955 #else
956 #define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT) \
957  __m256 OUTPUT##_0 = _mm256_insertf128_ps( \
958  _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 0)), \
959  _mm512_extractf32x4_ps(INPUT, 1), 1); \
960  __m256 OUTPUT##_1 = _mm256_insertf128_ps( \
961  _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 2)), \
962  _mm512_extractf32x4_ps(INPUT, 3), 1);
963 #endif
964 
965 #ifdef EIGEN_VECTORIZE_AVX512DQ
966 #define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \
967  OUTPUT = _mm512_insertf32x8(_mm512_castps256_ps512(INPUTA), INPUTB, 1);
968 #else
969 #define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \
970  OUTPUT = _mm512_undefined_ps(); \
971  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 0), 0); \
972  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 1), 1); \
973  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 0), 2); \
974  OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 1), 3);
975 #endif
976 
977 template <>
978 EIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) {
979 #ifdef EIGEN_VECTORIZE_AVX512DQ
980  __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
981  __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
982  Packet8f x = _mm256_add_ps(lane0, lane1);
983  return predux<Packet8f>(x);
984 #else
985  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
986  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
987  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
988  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
989  __m128 sum = _mm_add_ps(_mm_add_ps(lane0, lane1), _mm_add_ps(lane2, lane3));
990  sum = _mm_hadd_ps(sum, sum);
991  sum = _mm_hadd_ps(sum, _mm_permute_ps(sum, 1));
992  return _mm_cvtss_f32(sum);
993 #endif
994 }
995 template <>
996 EIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) {
997  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
998  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
999  __m256d sum = _mm256_add_pd(lane0, lane1);
1000  __m256d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1));
1001  return _mm_cvtsd_f64(_mm256_castpd256_pd128(_mm256_hadd_pd(tmp0, tmp0)));
1002 }
1003 
1004 template <>
1005 EIGEN_STRONG_INLINE Packet8f predux_half_dowto4<Packet16f>(const Packet16f& a) {
1006 #ifdef EIGEN_VECTORIZE_AVX512DQ
1007  __m256 lane0 = _mm512_extractf32x8_ps(a, 0);
1008  __m256 lane1 = _mm512_extractf32x8_ps(a, 1);
1009  return _mm256_add_ps(lane0, lane1);
1010 #else
1011  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
1012  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
1013  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
1014  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
1015  __m128 sum0 = _mm_add_ps(lane0, lane2);
1016  __m128 sum1 = _mm_add_ps(lane1, lane3);
1017  return _mm256_insertf128_ps(_mm256_castps128_ps256(sum0), sum1, 1);
1018 #endif
1019 }
1020 template <>
1021 EIGEN_STRONG_INLINE Packet4d predux_half_dowto4<Packet8d>(const Packet8d& a) {
1022  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
1023  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
1024  return _mm256_add_pd(lane0, lane1);
1025 }
1026 
1027 template <>
1028 EIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) {
1029 //#ifdef EIGEN_VECTORIZE_AVX512DQ
1030 #if 0
1031  Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
1032  Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
1033  Packet8f res = pmul(lane0, lane1);
1034  res = pmul(res, _mm256_permute2f128_ps(res, res, 1));
1035  res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
1036  return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
1037 #else
1038  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
1039  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
1040  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
1041  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
1042  __m128 res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));
1043  res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
1044  return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
1045 #endif
1046 }
1047 template <>
1048 EIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) {
1049  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
1050  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
1051  __m256d res = pmul(lane0, lane1);
1052  res = pmul(res, _mm256_permute2f128_pd(res, res, 1));
1053  return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1)));
1054 }
1055 
1056 template <>
1057 EIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) {
1058  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
1059  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
1060  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
1061  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
1062  __m128 res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));
1063  res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
1064  return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
1065 }
1066 template <>
1067 EIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) {
1068  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
1069  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
1070  __m256d res = _mm256_min_pd(lane0, lane1);
1071  res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1));
1072  return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1)));
1073 }
1074 
1075 template <>
1076 EIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) {
1077  __m128 lane0 = _mm512_extractf32x4_ps(a, 0);
1078  __m128 lane1 = _mm512_extractf32x4_ps(a, 1);
1079  __m128 lane2 = _mm512_extractf32x4_ps(a, 2);
1080  __m128 lane3 = _mm512_extractf32x4_ps(a, 3);
1081  __m128 res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));
1082  res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
1083  return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
1084 }
1085 
1086 template <>
1087 EIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) {
1088  __m256d lane0 = _mm512_extractf64x4_pd(a, 0);
1089  __m256d lane1 = _mm512_extractf64x4_pd(a, 1);
1090  __m256d res = _mm256_max_pd(lane0, lane1);
1091  res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1));
1092  return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1)));
1093 }
1094 
1095 template<> EIGEN_STRONG_INLINE bool predux_any(const Packet16f& x)
1096 {
1097  Packet16i xi = _mm512_castps_si512(x);
1098  __mmask16 tmp = _mm512_test_epi32_mask(xi,xi);
1099  return !_mm512_kortestz(tmp,tmp);
1100 }
1101 
1102 
1103 
1104 #define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE) \
1105  EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]);
1106 
1107 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 16>& kernel) {
1108  __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
1109  __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
1110  __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
1111  __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
1112  __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4], kernel.packet[5]);
1113  __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4], kernel.packet[5]);
1114  __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6], kernel.packet[7]);
1115  __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6], kernel.packet[7]);
1116  __m512 T8 = _mm512_unpacklo_ps(kernel.packet[8], kernel.packet[9]);
1117  __m512 T9 = _mm512_unpackhi_ps(kernel.packet[8], kernel.packet[9]);
1118  __m512 T10 = _mm512_unpacklo_ps(kernel.packet[10], kernel.packet[11]);
1119  __m512 T11 = _mm512_unpackhi_ps(kernel.packet[10], kernel.packet[11]);
1120  __m512 T12 = _mm512_unpacklo_ps(kernel.packet[12], kernel.packet[13]);
1121  __m512 T13 = _mm512_unpackhi_ps(kernel.packet[12], kernel.packet[13]);
1122  __m512 T14 = _mm512_unpacklo_ps(kernel.packet[14], kernel.packet[15]);
1123  __m512 T15 = _mm512_unpackhi_ps(kernel.packet[14], kernel.packet[15]);
1124  __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
1125  __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
1126  __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
1127  __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
1128  __m512 S4 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(1, 0, 1, 0));
1129  __m512 S5 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(3, 2, 3, 2));
1130  __m512 S6 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(1, 0, 1, 0));
1131  __m512 S7 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(3, 2, 3, 2));
1132  __m512 S8 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(1, 0, 1, 0));
1133  __m512 S9 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(3, 2, 3, 2));
1134  __m512 S10 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(1, 0, 1, 0));
1135  __m512 S11 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(3, 2, 3, 2));
1136  __m512 S12 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(1, 0, 1, 0));
1137  __m512 S13 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(3, 2, 3, 2));
1138  __m512 S14 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(1, 0, 1, 0));
1139  __m512 S15 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(3, 2, 3, 2));
1140 
1141  EIGEN_EXTRACT_8f_FROM_16f(S0, S0);
1142  EIGEN_EXTRACT_8f_FROM_16f(S1, S1);
1143  EIGEN_EXTRACT_8f_FROM_16f(S2, S2);
1144  EIGEN_EXTRACT_8f_FROM_16f(S3, S3);
1145  EIGEN_EXTRACT_8f_FROM_16f(S4, S4);
1146  EIGEN_EXTRACT_8f_FROM_16f(S5, S5);
1147  EIGEN_EXTRACT_8f_FROM_16f(S6, S6);
1148  EIGEN_EXTRACT_8f_FROM_16f(S7, S7);
1149  EIGEN_EXTRACT_8f_FROM_16f(S8, S8);
1150  EIGEN_EXTRACT_8f_FROM_16f(S9, S9);
1151  EIGEN_EXTRACT_8f_FROM_16f(S10, S10);
1152  EIGEN_EXTRACT_8f_FROM_16f(S11, S11);
1153  EIGEN_EXTRACT_8f_FROM_16f(S12, S12);
1154  EIGEN_EXTRACT_8f_FROM_16f(S13, S13);
1155  EIGEN_EXTRACT_8f_FROM_16f(S14, S14);
1156  EIGEN_EXTRACT_8f_FROM_16f(S15, S15);
1157 
1158  PacketBlock<Packet8f, 32> tmp;
1159 
1160  tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S4_0, 0x20);
1161  tmp.packet[1] = _mm256_permute2f128_ps(S1_0, S5_0, 0x20);
1162  tmp.packet[2] = _mm256_permute2f128_ps(S2_0, S6_0, 0x20);
1163  tmp.packet[3] = _mm256_permute2f128_ps(S3_0, S7_0, 0x20);
1164  tmp.packet[4] = _mm256_permute2f128_ps(S0_0, S4_0, 0x31);
1165  tmp.packet[5] = _mm256_permute2f128_ps(S1_0, S5_0, 0x31);
1166  tmp.packet[6] = _mm256_permute2f128_ps(S2_0, S6_0, 0x31);
1167  tmp.packet[7] = _mm256_permute2f128_ps(S3_0, S7_0, 0x31);
1168 
1169  tmp.packet[8] = _mm256_permute2f128_ps(S0_1, S4_1, 0x20);
1170  tmp.packet[9] = _mm256_permute2f128_ps(S1_1, S5_1, 0x20);
1171  tmp.packet[10] = _mm256_permute2f128_ps(S2_1, S6_1, 0x20);
1172  tmp.packet[11] = _mm256_permute2f128_ps(S3_1, S7_1, 0x20);
1173  tmp.packet[12] = _mm256_permute2f128_ps(S0_1, S4_1, 0x31);
1174  tmp.packet[13] = _mm256_permute2f128_ps(S1_1, S5_1, 0x31);
1175  tmp.packet[14] = _mm256_permute2f128_ps(S2_1, S6_1, 0x31);
1176  tmp.packet[15] = _mm256_permute2f128_ps(S3_1, S7_1, 0x31);
1177 
1178  // Second set of _m256 outputs
1179  tmp.packet[16] = _mm256_permute2f128_ps(S8_0, S12_0, 0x20);
1180  tmp.packet[17] = _mm256_permute2f128_ps(S9_0, S13_0, 0x20);
1181  tmp.packet[18] = _mm256_permute2f128_ps(S10_0, S14_0, 0x20);
1182  tmp.packet[19] = _mm256_permute2f128_ps(S11_0, S15_0, 0x20);
1183  tmp.packet[20] = _mm256_permute2f128_ps(S8_0, S12_0, 0x31);
1184  tmp.packet[21] = _mm256_permute2f128_ps(S9_0, S13_0, 0x31);
1185  tmp.packet[22] = _mm256_permute2f128_ps(S10_0, S14_0, 0x31);
1186  tmp.packet[23] = _mm256_permute2f128_ps(S11_0, S15_0, 0x31);
1187 
1188  tmp.packet[24] = _mm256_permute2f128_ps(S8_1, S12_1, 0x20);
1189  tmp.packet[25] = _mm256_permute2f128_ps(S9_1, S13_1, 0x20);
1190  tmp.packet[26] = _mm256_permute2f128_ps(S10_1, S14_1, 0x20);
1191  tmp.packet[27] = _mm256_permute2f128_ps(S11_1, S15_1, 0x20);
1192  tmp.packet[28] = _mm256_permute2f128_ps(S8_1, S12_1, 0x31);
1193  tmp.packet[29] = _mm256_permute2f128_ps(S9_1, S13_1, 0x31);
1194  tmp.packet[30] = _mm256_permute2f128_ps(S10_1, S14_1, 0x31);
1195  tmp.packet[31] = _mm256_permute2f128_ps(S11_1, S15_1, 0x31);
1196 
1197  // Pack them into the output
1198  PACK_OUTPUT(kernel.packet, tmp.packet, 0, 16);
1199  PACK_OUTPUT(kernel.packet, tmp.packet, 1, 16);
1200  PACK_OUTPUT(kernel.packet, tmp.packet, 2, 16);
1201  PACK_OUTPUT(kernel.packet, tmp.packet, 3, 16);
1202 
1203  PACK_OUTPUT(kernel.packet, tmp.packet, 4, 16);
1204  PACK_OUTPUT(kernel.packet, tmp.packet, 5, 16);
1205  PACK_OUTPUT(kernel.packet, tmp.packet, 6, 16);
1206  PACK_OUTPUT(kernel.packet, tmp.packet, 7, 16);
1207 
1208  PACK_OUTPUT(kernel.packet, tmp.packet, 8, 16);
1209  PACK_OUTPUT(kernel.packet, tmp.packet, 9, 16);
1210  PACK_OUTPUT(kernel.packet, tmp.packet, 10, 16);
1211  PACK_OUTPUT(kernel.packet, tmp.packet, 11, 16);
1212 
1213  PACK_OUTPUT(kernel.packet, tmp.packet, 12, 16);
1214  PACK_OUTPUT(kernel.packet, tmp.packet, 13, 16);
1215  PACK_OUTPUT(kernel.packet, tmp.packet, 14, 16);
1216  PACK_OUTPUT(kernel.packet, tmp.packet, 15, 16);
1217 }
1218 #define PACK_OUTPUT_2(OUTPUT, INPUT, INDEX, STRIDE) \
1219  EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[2 * INDEX], \
1220  INPUT[2 * INDEX + STRIDE]);
1221 
1222 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 4>& kernel) {
1223  __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
1224  __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
1225  __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
1226  __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
1227 
1228  __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
1229  __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
1230  __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
1231  __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
1232 
1233  EIGEN_EXTRACT_8f_FROM_16f(S0, S0);
1234  EIGEN_EXTRACT_8f_FROM_16f(S1, S1);
1235  EIGEN_EXTRACT_8f_FROM_16f(S2, S2);
1236  EIGEN_EXTRACT_8f_FROM_16f(S3, S3);
1237 
1238  PacketBlock<Packet8f, 8> tmp;
1239 
1240  tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S1_0, 0x20);
1241  tmp.packet[1] = _mm256_permute2f128_ps(S2_0, S3_0, 0x20);
1242  tmp.packet[2] = _mm256_permute2f128_ps(S0_0, S1_0, 0x31);
1243  tmp.packet[3] = _mm256_permute2f128_ps(S2_0, S3_0, 0x31);
1244 
1245  tmp.packet[4] = _mm256_permute2f128_ps(S0_1, S1_1, 0x20);
1246  tmp.packet[5] = _mm256_permute2f128_ps(S2_1, S3_1, 0x20);
1247  tmp.packet[6] = _mm256_permute2f128_ps(S0_1, S1_1, 0x31);
1248  tmp.packet[7] = _mm256_permute2f128_ps(S2_1, S3_1, 0x31);
1249 
1250  PACK_OUTPUT_2(kernel.packet, tmp.packet, 0, 1);
1251  PACK_OUTPUT_2(kernel.packet, tmp.packet, 1, 1);
1252  PACK_OUTPUT_2(kernel.packet, tmp.packet, 2, 1);
1253  PACK_OUTPUT_2(kernel.packet, tmp.packet, 3, 1);
1254 }
1255 
1256 #define PACK_OUTPUT_SQ_D(OUTPUT, INPUT, INDEX, STRIDE) \
1257  OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX], 0); \
1258  OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX + STRIDE], 1);
1259 
1260 #define PACK_OUTPUT_D(OUTPUT, INPUT, INDEX, STRIDE) \
1261  OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX)], 0); \
1262  OUTPUT[INDEX] = \
1263  _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX) + STRIDE], 1);
1264 
1265 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 4>& kernel) {
1266  __m512d T0 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0);
1267  __m512d T1 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0xff);
1268  __m512d T2 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0);
1269  __m512d T3 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0xff);
1270 
1271  PacketBlock<Packet4d, 8> tmp;
1272 
1273  tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
1274  _mm512_extractf64x4_pd(T2, 0), 0x20);
1275  tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
1276  _mm512_extractf64x4_pd(T3, 0), 0x20);
1277  tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
1278  _mm512_extractf64x4_pd(T2, 0), 0x31);
1279  tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
1280  _mm512_extractf64x4_pd(T3, 0), 0x31);
1281 
1282  tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
1283  _mm512_extractf64x4_pd(T2, 1), 0x20);
1284  tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
1285  _mm512_extractf64x4_pd(T3, 1), 0x20);
1286  tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
1287  _mm512_extractf64x4_pd(T2, 1), 0x31);
1288  tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
1289  _mm512_extractf64x4_pd(T3, 1), 0x31);
1290 
1291  PACK_OUTPUT_D(kernel.packet, tmp.packet, 0, 1);
1292  PACK_OUTPUT_D(kernel.packet, tmp.packet, 1, 1);
1293  PACK_OUTPUT_D(kernel.packet, tmp.packet, 2, 1);
1294  PACK_OUTPUT_D(kernel.packet, tmp.packet, 3, 1);
1295 }
1296 
1297 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 8>& kernel) {
1298  __m512d T0 = _mm512_unpacklo_pd(kernel.packet[0], kernel.packet[1]);
1299  __m512d T1 = _mm512_unpackhi_pd(kernel.packet[0], kernel.packet[1]);
1300  __m512d T2 = _mm512_unpacklo_pd(kernel.packet[2], kernel.packet[3]);
1301  __m512d T3 = _mm512_unpackhi_pd(kernel.packet[2], kernel.packet[3]);
1302  __m512d T4 = _mm512_unpacklo_pd(kernel.packet[4], kernel.packet[5]);
1303  __m512d T5 = _mm512_unpackhi_pd(kernel.packet[4], kernel.packet[5]);
1304  __m512d T6 = _mm512_unpacklo_pd(kernel.packet[6], kernel.packet[7]);
1305  __m512d T7 = _mm512_unpackhi_pd(kernel.packet[6], kernel.packet[7]);
1306 
1307  PacketBlock<Packet4d, 16> tmp;
1308 
1309  tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
1310  _mm512_extractf64x4_pd(T2, 0), 0x20);
1311  tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
1312  _mm512_extractf64x4_pd(T3, 0), 0x20);
1313  tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
1314  _mm512_extractf64x4_pd(T2, 0), 0x31);
1315  tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
1316  _mm512_extractf64x4_pd(T3, 0), 0x31);
1317 
1318  tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
1319  _mm512_extractf64x4_pd(T2, 1), 0x20);
1320  tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
1321  _mm512_extractf64x4_pd(T3, 1), 0x20);
1322  tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
1323  _mm512_extractf64x4_pd(T2, 1), 0x31);
1324  tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
1325  _mm512_extractf64x4_pd(T3, 1), 0x31);
1326 
1327  tmp.packet[8] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0),
1328  _mm512_extractf64x4_pd(T6, 0), 0x20);
1329  tmp.packet[9] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0),
1330  _mm512_extractf64x4_pd(T7, 0), 0x20);
1331  tmp.packet[10] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0),
1332  _mm512_extractf64x4_pd(T6, 0), 0x31);
1333  tmp.packet[11] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0),
1334  _mm512_extractf64x4_pd(T7, 0), 0x31);
1335 
1336  tmp.packet[12] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1),
1337  _mm512_extractf64x4_pd(T6, 1), 0x20);
1338  tmp.packet[13] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1),
1339  _mm512_extractf64x4_pd(T7, 1), 0x20);
1340  tmp.packet[14] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1),
1341  _mm512_extractf64x4_pd(T6, 1), 0x31);
1342  tmp.packet[15] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1),
1343  _mm512_extractf64x4_pd(T7, 1), 0x31);
1344 
1345  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 0, 8);
1346  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 1, 8);
1347  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 2, 8);
1348  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 3, 8);
1349 
1350  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 4, 8);
1351  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 5, 8);
1352  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 6, 8);
1353  PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 7, 8);
1354 }
1355 template <>
1356 EIGEN_STRONG_INLINE Packet16f pblend(const Selector<16>& /*ifPacket*/,
1357  const Packet16f& /*thenPacket*/,
1358  const Packet16f& /*elsePacket*/) {
1359  assert(false && "To be implemented");
1360  return Packet16f();
1361 }
1362 template <>
1363 EIGEN_STRONG_INLINE Packet8d pblend(const Selector<8>& ifPacket,
1364  const Packet8d& thenPacket,
1365  const Packet8d& elsePacket) {
1366  __mmask8 m = (ifPacket.select[0] )
1367  | (ifPacket.select[1]<<1)
1368  | (ifPacket.select[2]<<2)
1369  | (ifPacket.select[3]<<3)
1370  | (ifPacket.select[4]<<4)
1371  | (ifPacket.select[5]<<5)
1372  | (ifPacket.select[6]<<6)
1373  | (ifPacket.select[7]<<7);
1374  return _mm512_mask_blend_pd(m, elsePacket, thenPacket);
1375 }
1376 
1377 // Packet math for Eigen::half
1378 template<> EIGEN_STRONG_INLINE Packet16h pset1<Packet16h>(const Eigen::half& from) {
1379  return _mm256_set1_epi16(from.x);
1380 }
1381 
1382 template<> EIGEN_STRONG_INLINE Eigen::half pfirst<Packet16h>(const Packet16h& from) {
1383  return half_impl::raw_uint16_to_half(static_cast<unsigned short>(_mm256_extract_epi16(from, 0)));
1384 }
1385 
1386 template<> EIGEN_STRONG_INLINE Packet16h pload<Packet16h>(const Eigen::half* from) {
1387  return _mm256_load_si256(reinterpret_cast<const __m256i*>(from));
1388 }
1389 
1390 template<> EIGEN_STRONG_INLINE Packet16h ploadu<Packet16h>(const Eigen::half* from) {
1391  return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
1392 }
1393 
1394 template<> EIGEN_STRONG_INLINE void pstore<half>(Eigen::half* to, const Packet16h& from) {
1395  // (void*) -> workaround clang warning:
1396  // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32
1397  _mm256_store_si256((__m256i*)(void*)to, from);
1398 }
1399 
1400 template<> EIGEN_STRONG_INLINE void pstoreu<half>(Eigen::half* to, const Packet16h& from) {
1401  // (void*) -> workaround clang warning:
1402  // cast from 'Eigen::half *' to '__m256i *' increases required alignment from 2 to 32
1403  _mm256_storeu_si256((__m256i*)(void*)to, from);
1404 }
1405 
1406 template<> EIGEN_STRONG_INLINE Packet16h
1407 ploaddup<Packet16h>(const Eigen::half* from) {
1408  unsigned short a = from[0].x;
1409  unsigned short b = from[1].x;
1410  unsigned short c = from[2].x;
1411  unsigned short d = from[3].x;
1412  unsigned short e = from[4].x;
1413  unsigned short f = from[5].x;
1414  unsigned short g = from[6].x;
1415  unsigned short h = from[7].x;
1416  return _mm256_set_epi16(h, h, g, g, f, f, e, e, d, d, c, c, b, b, a, a);
1417 }
1418 
1419 template<> EIGEN_STRONG_INLINE Packet16h
1420 ploadquad(const Eigen::half* from) {
1421  unsigned short a = from[0].x;
1422  unsigned short b = from[1].x;
1423  unsigned short c = from[2].x;
1424  unsigned short d = from[3].x;
1425  return _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a);
1426 }
1427 
1428 EIGEN_STRONG_INLINE Packet16f half2float(const Packet16h& a) {
1429 #ifdef EIGEN_HAS_FP16_C
1430  return _mm512_cvtph_ps(a);
1431 #else
1432  EIGEN_ALIGN64 half aux[16];
1433  pstore(aux, a);
1434  float f0(aux[0]);
1435  float f1(aux[1]);
1436  float f2(aux[2]);
1437  float f3(aux[3]);
1438  float f4(aux[4]);
1439  float f5(aux[5]);
1440  float f6(aux[6]);
1441  float f7(aux[7]);
1442  float f8(aux[8]);
1443  float f9(aux[9]);
1444  float fa(aux[10]);
1445  float fb(aux[11]);
1446  float fc(aux[12]);
1447  float fd(aux[13]);
1448  float fe(aux[14]);
1449  float ff(aux[15]);
1450 
1451  return _mm512_set_ps(
1452  ff, fe, fd, fc, fb, fa, f9, f8, f7, f6, f5, f4, f3, f2, f1, f0);
1453 #endif
1454 }
1455 
1456 EIGEN_STRONG_INLINE Packet16h float2half(const Packet16f& a) {
1457 #ifdef EIGEN_HAS_FP16_C
1458  return _mm512_cvtps_ph(a, _MM_FROUND_TO_NEAREST_INT|_MM_FROUND_NO_EXC);
1459 #else
1460  EIGEN_ALIGN64 float aux[16];
1461  pstore(aux, a);
1462  half h0(aux[0]);
1463  half h1(aux[1]);
1464  half h2(aux[2]);
1465  half h3(aux[3]);
1466  half h4(aux[4]);
1467  half h5(aux[5]);
1468  half h6(aux[6]);
1469  half h7(aux[7]);
1470  half h8(aux[8]);
1471  half h9(aux[9]);
1472  half ha(aux[10]);
1473  half hb(aux[11]);
1474  half hc(aux[12]);
1475  half hd(aux[13]);
1476  half he(aux[14]);
1477  half hf(aux[15]);
1478 
1479  return _mm256_set_epi16(
1480  hf.x, he.x, hd.x, hc.x, hb.x, ha.x, h9.x, h8.x,
1481  h7.x, h6.x, h5.x, h4.x, h3.x, h2.x, h1.x, h0.x);
1482 #endif
1483 }
1484 
1485 template<> EIGEN_STRONG_INLINE Packet16h ptrue(const Packet16h& a) {
1486  return ptrue(Packet8i(a));
1487 }
1488 
1489 template <>
1490 EIGEN_STRONG_INLINE Packet16h pabs(const Packet16h& a) {
1491  const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000));
1492  return _mm256_andnot_si256(sign_mask, a);
1493 }
1494 
1495 template <>
1496 EIGEN_STRONG_INLINE Packet16h pmin<Packet16h>(const Packet16h& a,
1497  const Packet16h& b) {
1498  return float2half(pmin<Packet16f>(half2float(a), half2float(b)));
1499 }
1500 
1501 template <>
1502 EIGEN_STRONG_INLINE Packet16h pmax<Packet16h>(const Packet16h& a,
1503  const Packet16h& b) {
1504  return float2half(pmax<Packet16f>(half2float(a), half2float(b)));
1505 }
1506 
1507 template <>
1508 EIGEN_STRONG_INLINE Packet16h plset<Packet16h>(const half& a) {
1509  return float2half(plset<Packet16f>(static_cast<float>(a)));
1510 }
1511 
1512 template<> EIGEN_STRONG_INLINE Packet16h por(const Packet16h& a,const Packet16h& b) {
1513  // in some cases Packet8i is a wrapper around __m256i, so we need to
1514  // cast to Packet8i to call the correct overload.
1515  return por(Packet8i(a),Packet8i(b));
1516 }
1517 template<> EIGEN_STRONG_INLINE Packet16h pxor(const Packet16h& a,const Packet16h& b) {
1518  return pxor(Packet8i(a),Packet8i(b));
1519 }
1520 template<> EIGEN_STRONG_INLINE Packet16h pand(const Packet16h& a,const Packet16h& b) {
1521  return pand(Packet8i(a),Packet8i(b));
1522 }
1523 template<> EIGEN_STRONG_INLINE Packet16h pandnot(const Packet16h& a,const Packet16h& b) {
1524  return pandnot(Packet8i(a),Packet8i(b));
1525 }
1526 
1527 template<> EIGEN_STRONG_INLINE Packet16h pselect(const Packet16h& mask, const Packet16h& a, const Packet16h& b) {
1528  return _mm256_blendv_epi8(b, a, mask);
1529 }
1530 
1531 template<> EIGEN_STRONG_INLINE Packet16h pround<Packet16h>(const Packet16h& a) {
1532  return float2half(pround<Packet16f>(half2float(a)));
1533 }
1534 
1535 template<> EIGEN_STRONG_INLINE Packet16h print<Packet16h>(const Packet16h& a) {
1536  return float2half(print<Packet16f>(half2float(a)));
1537 }
1538 
1539 template<> EIGEN_STRONG_INLINE Packet16h pceil<Packet16h>(const Packet16h& a) {
1540  return float2half(pceil<Packet16f>(half2float(a)));
1541 }
1542 
1543 template<> EIGEN_STRONG_INLINE Packet16h pfloor<Packet16h>(const Packet16h& a) {
1544  return float2half(pfloor<Packet16f>(half2float(a)));
1545 }
1546 
1547 template<> EIGEN_STRONG_INLINE Packet16h pcmp_eq(const Packet16h& a,const Packet16h& b) {
1548  Packet16f af = half2float(a);
1549  Packet16f bf = half2float(b);
1550  return Pack32To16(pcmp_eq(af, bf));
1551 }
1552 
1553 template<> EIGEN_STRONG_INLINE Packet16h pcmp_le(const Packet16h& a,const Packet16h& b) {
1554  return Pack32To16(pcmp_le(half2float(a), half2float(b)));
1555 }
1556 
1557 template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt(const Packet16h& a,const Packet16h& b) {
1558  return Pack32To16(pcmp_lt(half2float(a), half2float(b)));
1559 }
1560 
1561 template<> EIGEN_STRONG_INLINE Packet16h pcmp_lt_or_nan(const Packet16h& a,const Packet16h& b) {
1562  return Pack32To16(pcmp_lt_or_nan(half2float(a), half2float(b)));
1563 }
1564 
1565 template<> EIGEN_STRONG_INLINE Packet16h pconj(const Packet16h& a) { return a; }
1566 
1567 template<> EIGEN_STRONG_INLINE Packet16h pnegate(const Packet16h& a) {
1568  Packet16h sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
1569  return _mm256_xor_si256(a, sign_mask);
1570 }
1571 
1572 template<> EIGEN_STRONG_INLINE Packet16h padd<Packet16h>(const Packet16h& a, const Packet16h& b) {
1573  Packet16f af = half2float(a);
1574  Packet16f bf = half2float(b);
1575  Packet16f rf = padd(af, bf);
1576  return float2half(rf);
1577 }
1578 
1579 template<> EIGEN_STRONG_INLINE Packet16h psub<Packet16h>(const Packet16h& a, const Packet16h& b) {
1580  Packet16f af = half2float(a);
1581  Packet16f bf = half2float(b);
1582  Packet16f rf = psub(af, bf);
1583  return float2half(rf);
1584 }
1585 
1586 template<> EIGEN_STRONG_INLINE Packet16h pmul<Packet16h>(const Packet16h& a, const Packet16h& b) {
1587  Packet16f af = half2float(a);
1588  Packet16f bf = half2float(b);
1589  Packet16f rf = pmul(af, bf);
1590  return float2half(rf);
1591 }
1592 
1593 template<> EIGEN_STRONG_INLINE Packet16h pdiv<Packet16h>(const Packet16h& a, const Packet16h& b) {
1594  Packet16f af = half2float(a);
1595  Packet16f bf = half2float(b);
1596  Packet16f rf = pdiv(af, bf);
1597  return float2half(rf);
1598 }
1599 
1600 template<> EIGEN_STRONG_INLINE half predux<Packet16h>(const Packet16h& from) {
1601  Packet16f from_float = half2float(from);
1602  return half(predux(from_float));
1603 }
1604 
1605 template <>
1606 EIGEN_STRONG_INLINE Packet8h predux_half_dowto4<Packet16h>(const Packet16h& a) {
1607  Packet8h lane0 = _mm256_extractf128_si256(a, 0);
1608  Packet8h lane1 = _mm256_extractf128_si256(a, 1);
1609  return padd<Packet8h>(lane0, lane1);
1610 }
1611 
1612 template<> EIGEN_STRONG_INLINE Eigen::half predux_max<Packet16h>(const Packet16h& a) {
1613  Packet16f af = half2float(a);
1614  float reduced = predux_max<Packet16f>(af);
1615  return Eigen::half(reduced);
1616 }
1617 
1618 template<> EIGEN_STRONG_INLINE Eigen::half predux_min<Packet16h>(const Packet16h& a) {
1619  Packet16f af = half2float(a);
1620  float reduced = predux_min<Packet16f>(af);
1621  return Eigen::half(reduced);
1622 }
1623 
1624 template<> EIGEN_STRONG_INLINE half predux_mul<Packet16h>(const Packet16h& from) {
1625  Packet16f from_float = half2float(from);
1626  return half(predux_mul(from_float));
1627 }
1628 
1629 template<> EIGEN_STRONG_INLINE Packet16h preverse(const Packet16h& a)
1630 {
1631  __m128i m = _mm_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1);
1632  return _mm256_insertf128_si256(
1633  _mm256_castsi128_si256(_mm_shuffle_epi8(_mm256_extractf128_si256(a,1),m)),
1634  _mm_shuffle_epi8(_mm256_extractf128_si256(a,0),m), 1);
1635 }
1636 
1637 template<> EIGEN_STRONG_INLINE Packet16h pgather<Eigen::half, Packet16h>(const Eigen::half* from, Index stride)
1638 {
1639  return _mm256_set_epi16(
1640  from[15*stride].x, from[14*stride].x, from[13*stride].x, from[12*stride].x,
1641  from[11*stride].x, from[10*stride].x, from[9*stride].x, from[8*stride].x,
1642  from[7*stride].x, from[6*stride].x, from[5*stride].x, from[4*stride].x,
1643  from[3*stride].x, from[2*stride].x, from[1*stride].x, from[0*stride].x);
1644 }
1645 
1646 template<> EIGEN_STRONG_INLINE void pscatter<half, Packet16h>(half* to, const Packet16h& from, Index stride)
1647 {
1648  EIGEN_ALIGN64 half aux[16];
1649  pstore(aux, from);
1650  to[stride*0] = aux[0];
1651  to[stride*1] = aux[1];
1652  to[stride*2] = aux[2];
1653  to[stride*3] = aux[3];
1654  to[stride*4] = aux[4];
1655  to[stride*5] = aux[5];
1656  to[stride*6] = aux[6];
1657  to[stride*7] = aux[7];
1658  to[stride*8] = aux[8];
1659  to[stride*9] = aux[9];
1660  to[stride*10] = aux[10];
1661  to[stride*11] = aux[11];
1662  to[stride*12] = aux[12];
1663  to[stride*13] = aux[13];
1664  to[stride*14] = aux[14];
1665  to[stride*15] = aux[15];
1666 }
1667 
1668 EIGEN_STRONG_INLINE void
1669 ptranspose(PacketBlock<Packet16h,16>& kernel) {
1670  __m256i a = kernel.packet[0];
1671  __m256i b = kernel.packet[1];
1672  __m256i c = kernel.packet[2];
1673  __m256i d = kernel.packet[3];
1674  __m256i e = kernel.packet[4];
1675  __m256i f = kernel.packet[5];
1676  __m256i g = kernel.packet[6];
1677  __m256i h = kernel.packet[7];
1678  __m256i i = kernel.packet[8];
1679  __m256i j = kernel.packet[9];
1680  __m256i k = kernel.packet[10];
1681  __m256i l = kernel.packet[11];
1682  __m256i m = kernel.packet[12];
1683  __m256i n = kernel.packet[13];
1684  __m256i o = kernel.packet[14];
1685  __m256i p = kernel.packet[15];
1686 
1687  __m256i ab_07 = _mm256_unpacklo_epi16(a, b);
1688  __m256i cd_07 = _mm256_unpacklo_epi16(c, d);
1689  __m256i ef_07 = _mm256_unpacklo_epi16(e, f);
1690  __m256i gh_07 = _mm256_unpacklo_epi16(g, h);
1691  __m256i ij_07 = _mm256_unpacklo_epi16(i, j);
1692  __m256i kl_07 = _mm256_unpacklo_epi16(k, l);
1693  __m256i mn_07 = _mm256_unpacklo_epi16(m, n);
1694  __m256i op_07 = _mm256_unpacklo_epi16(o, p);
1695 
1696  __m256i ab_8f = _mm256_unpackhi_epi16(a, b);
1697  __m256i cd_8f = _mm256_unpackhi_epi16(c, d);
1698  __m256i ef_8f = _mm256_unpackhi_epi16(e, f);
1699  __m256i gh_8f = _mm256_unpackhi_epi16(g, h);
1700  __m256i ij_8f = _mm256_unpackhi_epi16(i, j);
1701  __m256i kl_8f = _mm256_unpackhi_epi16(k, l);
1702  __m256i mn_8f = _mm256_unpackhi_epi16(m, n);
1703  __m256i op_8f = _mm256_unpackhi_epi16(o, p);
1704 
1705  __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);
1706  __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);
1707  __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07);
1708  __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07);
1709  __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07);
1710  __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07);
1711  __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07);
1712  __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07);
1713 
1714  __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);
1715  __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);
1716  __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f);
1717  __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f);
1718  __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f);
1719  __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f);
1720  __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f);
1721  __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f);
1722 
1723  __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03);
1724  __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03);
1725  __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03);
1726  __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03);
1727  __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47);
1728  __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47);
1729  __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47);
1730  __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47);
1731  __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b);
1732  __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b);
1733  __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b);
1734  __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b);
1735  __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf);
1736  __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf);
1737  __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf);
1738  __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf);
1739 
1740  // NOTE: no unpacklo/hi instr in this case, so using permute instr.
1741  __m256i a_p_0 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20);
1742  __m256i a_p_1 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20);
1743  __m256i a_p_2 = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20);
1744  __m256i a_p_3 = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20);
1745  __m256i a_p_4 = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20);
1746  __m256i a_p_5 = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20);
1747  __m256i a_p_6 = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20);
1748  __m256i a_p_7 = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20);
1749  __m256i a_p_8 = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31);
1750  __m256i a_p_9 = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31);
1751  __m256i a_p_a = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31);
1752  __m256i a_p_b = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31);
1753  __m256i a_p_c = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31);
1754  __m256i a_p_d = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31);
1755  __m256i a_p_e = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31);
1756  __m256i a_p_f = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31);
1757 
1758  kernel.packet[0] = a_p_0;
1759  kernel.packet[1] = a_p_1;
1760  kernel.packet[2] = a_p_2;
1761  kernel.packet[3] = a_p_3;
1762  kernel.packet[4] = a_p_4;
1763  kernel.packet[5] = a_p_5;
1764  kernel.packet[6] = a_p_6;
1765  kernel.packet[7] = a_p_7;
1766  kernel.packet[8] = a_p_8;
1767  kernel.packet[9] = a_p_9;
1768  kernel.packet[10] = a_p_a;
1769  kernel.packet[11] = a_p_b;
1770  kernel.packet[12] = a_p_c;
1771  kernel.packet[13] = a_p_d;
1772  kernel.packet[14] = a_p_e;
1773  kernel.packet[15] = a_p_f;
1774 }
1775 
1776 EIGEN_STRONG_INLINE void
1777 ptranspose(PacketBlock<Packet16h,8>& kernel) {
1778  EIGEN_ALIGN64 half in[8][16];
1779  pstore<half>(in[0], kernel.packet[0]);
1780  pstore<half>(in[1], kernel.packet[1]);
1781  pstore<half>(in[2], kernel.packet[2]);
1782  pstore<half>(in[3], kernel.packet[3]);
1783  pstore<half>(in[4], kernel.packet[4]);
1784  pstore<half>(in[5], kernel.packet[5]);
1785  pstore<half>(in[6], kernel.packet[6]);
1786  pstore<half>(in[7], kernel.packet[7]);
1787 
1788  EIGEN_ALIGN64 half out[8][16];
1789 
1790  for (int i = 0; i < 8; ++i) {
1791  for (int j = 0; j < 8; ++j) {
1792  out[i][j] = in[j][2*i];
1793  }
1794  for (int j = 0; j < 8; ++j) {
1795  out[i][j+8] = in[j][2*i+1];
1796  }
1797  }
1798 
1799  kernel.packet[0] = pload<Packet16h>(out[0]);
1800  kernel.packet[1] = pload<Packet16h>(out[1]);
1801  kernel.packet[2] = pload<Packet16h>(out[2]);
1802  kernel.packet[3] = pload<Packet16h>(out[3]);
1803  kernel.packet[4] = pload<Packet16h>(out[4]);
1804  kernel.packet[5] = pload<Packet16h>(out[5]);
1805  kernel.packet[6] = pload<Packet16h>(out[6]);
1806  kernel.packet[7] = pload<Packet16h>(out[7]);
1807 }
1808 
1809 EIGEN_STRONG_INLINE void
1810 ptranspose(PacketBlock<Packet16h,4>& kernel) {
1811  EIGEN_ALIGN64 half in[4][16];
1812  pstore<half>(in[0], kernel.packet[0]);
1813  pstore<half>(in[1], kernel.packet[1]);
1814  pstore<half>(in[2], kernel.packet[2]);
1815  pstore<half>(in[3], kernel.packet[3]);
1816 
1817  EIGEN_ALIGN64 half out[4][16];
1818 
1819  for (int i = 0; i < 4; ++i) {
1820  for (int j = 0; j < 4; ++j) {
1821  out[i][j] = in[j][4*i];
1822  }
1823  for (int j = 0; j < 4; ++j) {
1824  out[i][j+4] = in[j][4*i+1];
1825  }
1826  for (int j = 0; j < 4; ++j) {
1827  out[i][j+8] = in[j][4*i+2];
1828  }
1829  for (int j = 0; j < 4; ++j) {
1830  out[i][j+12] = in[j][4*i+3];
1831  }
1832  }
1833 
1834  kernel.packet[0] = pload<Packet16h>(out[0]);
1835  kernel.packet[1] = pload<Packet16h>(out[1]);
1836  kernel.packet[2] = pload<Packet16h>(out[2]);
1837  kernel.packet[3] = pload<Packet16h>(out[3]);
1838 }
1839 
1840 template <> struct is_arithmetic<Packet16bf> { enum { value = true }; };
1841 
1842 template <>
1843 struct packet_traits<bfloat16> : default_packet_traits {
1844  typedef Packet16bf type;
1845  typedef Packet8bf half;
1846  enum {
1847  Vectorizable = 1,
1848  AlignedOnScalar = 1,
1849  size = 16,
1850  HasHalfPacket = 1,
1851  HasBlend = 0,
1852  HasInsert = 1,
1853  HasSin = EIGEN_FAST_MATH,
1854  HasCos = EIGEN_FAST_MATH,
1855 #if EIGEN_GNUC_AT_LEAST(5, 3) || (!EIGEN_COMP_GNUC_STRICT)
1856 #ifdef EIGEN_VECTORIZE_AVX512DQ
1857  HasLog = 1, // Currently fails test with bad accuracy.
1858  HasLog1p = 1,
1859  HasExpm1 = 1,
1860  HasNdtri = 1,
1861  HasBessel = 1,
1862 #endif
1863  HasExp = 1,
1864  HasSqrt = EIGEN_FAST_MATH,
1865  HasRsqrt = EIGEN_FAST_MATH,
1866  HasTanh = EIGEN_FAST_MATH,
1867  HasErf = EIGEN_FAST_MATH,
1868 #endif
1869  HasCmp = 1,
1870  HasDiv = 1
1871  };
1872 };
1873 
1874 template <>
1875 struct unpacket_traits<Packet16bf>
1876 {
1877  typedef bfloat16 type;
1878  enum {size=16, alignment=Aligned32, vectorizable=true, masked_load_available=false, masked_store_available=false};
1879  typedef Packet8bf half;
1880 };
1881 
1882 template <>
1883 EIGEN_STRONG_INLINE Packet16bf pset1<Packet16bf>(const bfloat16& from) {
1884  return _mm256_set1_epi16(from.value);
1885 }
1886 
1887 template <>
1888 EIGEN_STRONG_INLINE bfloat16 pfirst<Packet16bf>(const Packet16bf& from) {
1889  bfloat16 t;
1890  t.value = static_cast<unsigned short>(_mm256_extract_epi16(from, 0));
1891  return t;
1892 }
1893 
1894 template <>
1895 EIGEN_STRONG_INLINE Packet16bf pload<Packet16bf>(const bfloat16* from) {
1896  return _mm256_load_si256(reinterpret_cast<const __m256i*>(from));
1897 }
1898 
1899 template <>
1900 EIGEN_STRONG_INLINE Packet16bf ploadu<Packet16bf>(const bfloat16* from) {
1901  return _mm256_loadu_si256(reinterpret_cast<const __m256i*>(from));
1902 }
1903 
1904 template <>
1905 EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to,
1906  const Packet16bf& from) {
1907  _mm256_store_si256(reinterpret_cast<__m256i*>(to), from);
1908 }
1909 
1910 template <>
1911 EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to,
1912  const Packet16bf& from) {
1913  _mm256_storeu_si256(reinterpret_cast<__m256i*>(to), from);
1914 }
1915 
1916 template<> EIGEN_STRONG_INLINE Packet16bf
1917 ploaddup<Packet16bf>(const bfloat16* from) {
1918  Packet16bf r;
1919  unsigned short a = from[0].value;
1920  unsigned short b = from[1].value;
1921  unsigned short c = from[2].value;
1922  unsigned short d = from[3].value;
1923  unsigned short e = from[4].value;
1924  unsigned short f = from[5].value;
1925  unsigned short g = from[6].value;
1926  unsigned short h = from[7].value;
1927  return _mm256_set_epi16(h, h, g, g, f, f, e, e, d, d, c, c, b, b, a, a);
1928 }
1929 
1930 template<> EIGEN_STRONG_INLINE Packet16bf
1931 ploadquad(const bfloat16* from) {
1932  Packet16bf r;
1933  unsigned short a = from[0].value;
1934  unsigned short b = from[1].value;
1935  unsigned short c = from[2].value;
1936  unsigned short d = from[3].value;
1937  return _mm256_set_epi16(d, d, d, d, c, c, c, c, b, b, b, b, a, a, a, a);
1938 }
1939 
1940 EIGEN_STRONG_INLINE Packet16f Bf16ToF32(const Packet16bf& a) {
1941  return _mm512_castsi512_ps(_mm512_slli_epi32(_mm512_cvtepu16_epi32(a), 16));
1942 }
1943 
1944 // Convert float to bfloat16 according to round-to-nearest-even/denormals algorithm.
1945 EIGEN_STRONG_INLINE Packet16bf F32ToBf16(const Packet16f& a) {
1946  Packet16bf r;
1947 
1948 #if defined(EIGEN_VECTORIZE_AVX512BF16) && EIGEN_GNUC_AT_LEAST(10, 1)
1949  // Since GCC 10.1 supports avx512bf16 and C style explicit cast
1950  // (C++ static_cast is not supported yet), do converion via intrinsic
1951  // and register path for performance.
1952  r = (__m256i)(_mm512_cvtneps_pbh(a));
1953 
1954 #else
1955  __m512i t;
1956  __m512i input = _mm512_castps_si512(a);
1957  __m512i nan = _mm512_set1_epi32(0x7fc0);
1958 
1959  // uint32_t lsb = (input >> 16) & 1;
1960  t = _mm512_and_si512(_mm512_srli_epi32(input, 16), _mm512_set1_epi32(1));
1961  // uint32_t rounding_bias = 0x7fff + lsb;
1962  t = _mm512_add_epi32(t, _mm512_set1_epi32(0x7fff));
1963  // input += rounding_bias;
1964  t = _mm512_add_epi32(t, input);
1965  // input = input >> 16;
1966  t = _mm512_srli_epi32(t, 16);
1967 
1968  // Check NaN before converting back to bf16
1969  __mmask16 mask = _mm512_cmp_ps_mask(a, a, _CMP_ORD_Q);
1970 
1971  t = _mm512_mask_blend_epi32(mask, nan, t);
1972  // output.value = static_cast<uint16_t>(input);
1973  r = _mm512_cvtepi32_epi16(t);
1974 #endif // EIGEN_VECTORIZE_AVX512BF16
1975 
1976  return r;
1977 }
1978 
1979 template <>
1980 EIGEN_STRONG_INLINE Packet16bf ptrue(const Packet16bf& a) {
1981  return ptrue<Packet8i>(a);
1982 }
1983 
1984 template <>
1985 EIGEN_STRONG_INLINE Packet16bf por(const Packet16bf& a, const Packet16bf& b) {
1986  return por<Packet8i>(a, b);
1987 }
1988 
1989 template <>
1990 EIGEN_STRONG_INLINE Packet16bf pxor(const Packet16bf& a, const Packet16bf& b) {
1991  return pxor<Packet8i>(a, b);
1992 }
1993 
1994 template <>
1995 EIGEN_STRONG_INLINE Packet16bf pand(const Packet16bf& a, const Packet16bf& b) {
1996  return pand<Packet8i>(a, b);
1997 }
1998 
1999 template <>
2000 EIGEN_STRONG_INLINE Packet16bf pandnot(const Packet16bf& a,
2001  const Packet16bf& b) {
2002  return pandnot<Packet8i>(a, b);
2003 }
2004 
2005 template <>
2006 EIGEN_STRONG_INLINE Packet16bf pselect(const Packet16bf& mask,
2007  const Packet16bf& a,
2008  const Packet16bf& b) {
2009  // Input mask is expected to be all 0/1, handle it with 8-bit
2010  // intrinsic for performance.
2011  return _mm256_blendv_epi8(b, a, mask);
2012 }
2013 
2014 template<> EIGEN_STRONG_INLINE Packet16bf pround<Packet16bf>(const Packet16bf& a)
2015 {
2016  return F32ToBf16(pround<Packet16f>(Bf16ToF32(a)));
2017 }
2018 
2019 template<> EIGEN_STRONG_INLINE Packet16bf print<Packet16bf>(const Packet16bf& a) {
2020  return F32ToBf16(print<Packet16f>(Bf16ToF32(a)));
2021 }
2022 
2023 template<> EIGEN_STRONG_INLINE Packet16bf pceil<Packet16bf>(const Packet16bf& a) {
2024  return F32ToBf16(pceil<Packet16f>(Bf16ToF32(a)));
2025 }
2026 
2027 template<> EIGEN_STRONG_INLINE Packet16bf pfloor<Packet16bf>(const Packet16bf& a) {
2028  return F32ToBf16(pfloor<Packet16f>(Bf16ToF32(a)));
2029 }
2030 
2031 template <>
2032 EIGEN_STRONG_INLINE Packet16bf pcmp_eq(const Packet16bf& a,
2033  const Packet16bf& b) {
2034  return Pack32To16(pcmp_eq(Bf16ToF32(a), Bf16ToF32(b)));
2035 }
2036 
2037 template <>
2038 EIGEN_STRONG_INLINE Packet16bf pcmp_le(const Packet16bf& a,
2039  const Packet16bf& b) {
2040  return Pack32To16(pcmp_le(Bf16ToF32(a), Bf16ToF32(b)));
2041 }
2042 
2043 template <>
2044 EIGEN_STRONG_INLINE Packet16bf pcmp_lt(const Packet16bf& a,
2045  const Packet16bf& b) {
2046  return Pack32To16(pcmp_lt(Bf16ToF32(a), Bf16ToF32(b)));
2047 }
2048 
2049 template <>
2050 EIGEN_STRONG_INLINE Packet16bf pcmp_lt_or_nan(const Packet16bf& a,
2051  const Packet16bf& b) {
2052  return Pack32To16(pcmp_lt_or_nan(Bf16ToF32(a), Bf16ToF32(b)));
2053 }
2054 
2055 template <>
2056 EIGEN_STRONG_INLINE Packet16bf pnegate(const Packet16bf& a) {
2057  Packet16bf sign_mask = _mm256_set1_epi16(static_cast<unsigned short>(0x8000));
2058  return _mm256_xor_si256(a, sign_mask);
2059 }
2060 
2061 template <>
2062 EIGEN_STRONG_INLINE Packet16bf pconj(const Packet16bf& a) {
2063  return a;
2064 }
2065 
2066 template <>
2067 EIGEN_STRONG_INLINE Packet16bf pabs(const Packet16bf& a) {
2068  const __m256i sign_mask = _mm256_set1_epi16(static_cast<numext::uint16_t>(0x8000));
2069  return _mm256_andnot_si256(sign_mask, a);
2070 }
2071 
2072 template <>
2073 EIGEN_STRONG_INLINE Packet16bf padd<Packet16bf>(const Packet16bf& a,
2074  const Packet16bf& b) {
2075  return F32ToBf16(padd<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
2076 }
2077 
2078 template <>
2079 EIGEN_STRONG_INLINE Packet16bf psub<Packet16bf>(const Packet16bf& a,
2080  const Packet16bf& b) {
2081  return F32ToBf16(psub<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
2082 }
2083 
2084 template <>
2085 EIGEN_STRONG_INLINE Packet16bf pmul<Packet16bf>(const Packet16bf& a,
2086  const Packet16bf& b) {
2087  return F32ToBf16(pmul<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
2088 }
2089 
2090 template <>
2091 EIGEN_STRONG_INLINE Packet16bf pdiv<Packet16bf>(const Packet16bf& a,
2092  const Packet16bf& b) {
2093  return F32ToBf16(pdiv<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
2094 }
2095 
2096 template <>
2097 EIGEN_STRONG_INLINE Packet16bf pmin<Packet16bf>(const Packet16bf& a,
2098  const Packet16bf& b) {
2099  return F32ToBf16(pmin<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
2100 }
2101 
2102 template <>
2103 EIGEN_STRONG_INLINE Packet16bf pmax<Packet16bf>(const Packet16bf& a,
2104  const Packet16bf& b) {
2105  return F32ToBf16(pmax<Packet16f>(Bf16ToF32(a), Bf16ToF32(b)));
2106 }
2107 
2108 template <>
2109 EIGEN_STRONG_INLINE Packet16bf plset<Packet16bf>(const bfloat16& a) {
2110  return F32ToBf16(plset<Packet16f>(static_cast<float>(a)));
2111 }
2112 
2113 template <>
2114 EIGEN_STRONG_INLINE Packet8bf predux_half_dowto4<Packet16bf>(const Packet16bf& a) {
2115  Packet8bf lane0 = _mm256_extractf128_si256(a, 0);
2116  Packet8bf lane1 = _mm256_extractf128_si256(a, 1);
2117  return padd<Packet8bf>(lane0, lane1);
2118 }
2119 
2120 template <>
2121 EIGEN_STRONG_INLINE bfloat16 predux<Packet16bf>(const Packet16bf& p) {
2122  return static_cast<bfloat16>(predux<Packet16f>(Bf16ToF32(p)));
2123 }
2124 
2125 template <>
2126 EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet16bf>(const Packet16bf& from) {
2127  return static_cast<bfloat16>(predux_mul<Packet16f>(Bf16ToF32(from)));
2128 }
2129 
2130 template <>
2131 EIGEN_STRONG_INLINE bfloat16 predux_min<Packet16bf>(const Packet16bf& from) {
2132  return static_cast<bfloat16>(predux_min<Packet16f>(Bf16ToF32(from)));
2133 }
2134 
2135 template <>
2136 EIGEN_STRONG_INLINE bfloat16 predux_max<Packet16bf>(const Packet16bf& from) {
2137  return static_cast<bfloat16>(predux_max<Packet16f>(Bf16ToF32(from)));
2138 }
2139 
2140 template <>
2141 EIGEN_STRONG_INLINE Packet16bf preverse(const Packet16bf& a) {
2142  __m256i m = _mm256_setr_epi8(14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1,
2143  14,15,12,13,10,11,8,9,6,7,4,5,2,3,0,1);
2144 
2145  Packet16bf res;
2146  // Swap hi and lo first because shuffle is in 128-bit lanes.
2147  res = _mm256_permute2x128_si256(a, a, 1);
2148  // Shuffle 8-bit values in src within 2*128-bit lanes.
2149  return _mm256_shuffle_epi8(res, m);
2150 }
2151 
2152 template <>
2153 EIGEN_STRONG_INLINE Packet16bf pgather<bfloat16, Packet16bf>(const bfloat16* from,
2154  Index stride) {
2155  return _mm256_set_epi16(
2156  from[15*stride].value, from[14*stride].value, from[13*stride].value, from[12*stride].value,
2157  from[11*stride].value, from[10*stride].value, from[9*stride].value, from[8*stride].value,
2158  from[7*stride].value, from[6*stride].value, from[5*stride].value, from[4*stride].value,
2159  from[3*stride].value, from[2*stride].value, from[1*stride].value, from[0*stride].value);
2160 }
2161 
2162 template <>
2163 EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet16bf>(bfloat16* to,
2164  const Packet16bf& from,
2165  Index stride) {
2166  EIGEN_ALIGN64 bfloat16 aux[16];
2167  pstore(aux, from);
2168  to[stride*0] = aux[0];
2169  to[stride*1] = aux[1];
2170  to[stride*2] = aux[2];
2171  to[stride*3] = aux[3];
2172  to[stride*4] = aux[4];
2173  to[stride*5] = aux[5];
2174  to[stride*6] = aux[6];
2175  to[stride*7] = aux[7];
2176  to[stride*8] = aux[8];
2177  to[stride*9] = aux[9];
2178  to[stride*10] = aux[10];
2179  to[stride*11] = aux[11];
2180  to[stride*12] = aux[12];
2181  to[stride*13] = aux[13];
2182  to[stride*14] = aux[14];
2183  to[stride*15] = aux[15];
2184 }
2185 
2186 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,16>& kernel) {
2187  __m256i a = kernel.packet[0];
2188  __m256i b = kernel.packet[1];
2189  __m256i c = kernel.packet[2];
2190  __m256i d = kernel.packet[3];
2191  __m256i e = kernel.packet[4];
2192  __m256i f = kernel.packet[5];
2193  __m256i g = kernel.packet[6];
2194  __m256i h = kernel.packet[7];
2195  __m256i i = kernel.packet[8];
2196  __m256i j = kernel.packet[9];
2197  __m256i k = kernel.packet[10];
2198  __m256i l = kernel.packet[11];
2199  __m256i m = kernel.packet[12];
2200  __m256i n = kernel.packet[13];
2201  __m256i o = kernel.packet[14];
2202  __m256i p = kernel.packet[15];
2203 
2204  __m256i ab_07 = _mm256_unpacklo_epi16(a, b);
2205  __m256i cd_07 = _mm256_unpacklo_epi16(c, d);
2206  __m256i ef_07 = _mm256_unpacklo_epi16(e, f);
2207  __m256i gh_07 = _mm256_unpacklo_epi16(g, h);
2208  __m256i ij_07 = _mm256_unpacklo_epi16(i, j);
2209  __m256i kl_07 = _mm256_unpacklo_epi16(k, l);
2210  __m256i mn_07 = _mm256_unpacklo_epi16(m, n);
2211  __m256i op_07 = _mm256_unpacklo_epi16(o, p);
2212 
2213  __m256i ab_8f = _mm256_unpackhi_epi16(a, b);
2214  __m256i cd_8f = _mm256_unpackhi_epi16(c, d);
2215  __m256i ef_8f = _mm256_unpackhi_epi16(e, f);
2216  __m256i gh_8f = _mm256_unpackhi_epi16(g, h);
2217  __m256i ij_8f = _mm256_unpackhi_epi16(i, j);
2218  __m256i kl_8f = _mm256_unpackhi_epi16(k, l);
2219  __m256i mn_8f = _mm256_unpackhi_epi16(m, n);
2220  __m256i op_8f = _mm256_unpackhi_epi16(o, p);
2221 
2222  __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);
2223  __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);
2224  __m256i efgh_03 = _mm256_unpacklo_epi32(ef_07, gh_07);
2225  __m256i efgh_47 = _mm256_unpackhi_epi32(ef_07, gh_07);
2226  __m256i ijkl_03 = _mm256_unpacklo_epi32(ij_07, kl_07);
2227  __m256i ijkl_47 = _mm256_unpackhi_epi32(ij_07, kl_07);
2228  __m256i mnop_03 = _mm256_unpacklo_epi32(mn_07, op_07);
2229  __m256i mnop_47 = _mm256_unpackhi_epi32(mn_07, op_07);
2230 
2231  __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);
2232  __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);
2233  __m256i efgh_8b = _mm256_unpacklo_epi32(ef_8f, gh_8f);
2234  __m256i efgh_cf = _mm256_unpackhi_epi32(ef_8f, gh_8f);
2235  __m256i ijkl_8b = _mm256_unpacklo_epi32(ij_8f, kl_8f);
2236  __m256i ijkl_cf = _mm256_unpackhi_epi32(ij_8f, kl_8f);
2237  __m256i mnop_8b = _mm256_unpacklo_epi32(mn_8f, op_8f);
2238  __m256i mnop_cf = _mm256_unpackhi_epi32(mn_8f, op_8f);
2239 
2240  __m256i abcdefgh_01 = _mm256_unpacklo_epi64(abcd_03, efgh_03);
2241  __m256i abcdefgh_23 = _mm256_unpackhi_epi64(abcd_03, efgh_03);
2242  __m256i ijklmnop_01 = _mm256_unpacklo_epi64(ijkl_03, mnop_03);
2243  __m256i ijklmnop_23 = _mm256_unpackhi_epi64(ijkl_03, mnop_03);
2244  __m256i abcdefgh_45 = _mm256_unpacklo_epi64(abcd_47, efgh_47);
2245  __m256i abcdefgh_67 = _mm256_unpackhi_epi64(abcd_47, efgh_47);
2246  __m256i ijklmnop_45 = _mm256_unpacklo_epi64(ijkl_47, mnop_47);
2247  __m256i ijklmnop_67 = _mm256_unpackhi_epi64(ijkl_47, mnop_47);
2248  __m256i abcdefgh_89 = _mm256_unpacklo_epi64(abcd_8b, efgh_8b);
2249  __m256i abcdefgh_ab = _mm256_unpackhi_epi64(abcd_8b, efgh_8b);
2250  __m256i ijklmnop_89 = _mm256_unpacklo_epi64(ijkl_8b, mnop_8b);
2251  __m256i ijklmnop_ab = _mm256_unpackhi_epi64(ijkl_8b, mnop_8b);
2252  __m256i abcdefgh_cd = _mm256_unpacklo_epi64(abcd_cf, efgh_cf);
2253  __m256i abcdefgh_ef = _mm256_unpackhi_epi64(abcd_cf, efgh_cf);
2254  __m256i ijklmnop_cd = _mm256_unpacklo_epi64(ijkl_cf, mnop_cf);
2255  __m256i ijklmnop_ef = _mm256_unpackhi_epi64(ijkl_cf, mnop_cf);
2256 
2257  // NOTE: no unpacklo/hi instr in this case, so using permute instr.
2258  kernel.packet[0] = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x20);
2259  kernel.packet[1] = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x20);
2260  kernel.packet[2] = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x20);
2261  kernel.packet[3] = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x20);
2262  kernel.packet[4] = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x20);
2263  kernel.packet[5] = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x20);
2264  kernel.packet[6] = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x20);
2265  kernel.packet[7] = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x20);
2266  kernel.packet[8] = _mm256_permute2x128_si256(abcdefgh_01, ijklmnop_01, 0x31);
2267  kernel.packet[9] = _mm256_permute2x128_si256(abcdefgh_23, ijklmnop_23, 0x31);
2268  kernel.packet[10] = _mm256_permute2x128_si256(abcdefgh_45, ijklmnop_45, 0x31);
2269  kernel.packet[11] = _mm256_permute2x128_si256(abcdefgh_67, ijklmnop_67, 0x31);
2270  kernel.packet[12] = _mm256_permute2x128_si256(abcdefgh_89, ijklmnop_89, 0x31);
2271  kernel.packet[13] = _mm256_permute2x128_si256(abcdefgh_ab, ijklmnop_ab, 0x31);
2272  kernel.packet[14] = _mm256_permute2x128_si256(abcdefgh_cd, ijklmnop_cd, 0x31);
2273  kernel.packet[15] = _mm256_permute2x128_si256(abcdefgh_ef, ijklmnop_ef, 0x31);
2274 }
2275 
2276 EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16bf,4>& kernel) {
2277  __m256i a = kernel.packet[0];
2278  __m256i b = kernel.packet[1];
2279  __m256i c = kernel.packet[2];
2280  __m256i d = kernel.packet[3];
2281 
2282  __m256i ab_07 = _mm256_unpacklo_epi16(a, b);
2283  __m256i cd_07 = _mm256_unpacklo_epi16(c, d);
2284  __m256i ab_8f = _mm256_unpackhi_epi16(a, b);
2285  __m256i cd_8f = _mm256_unpackhi_epi16(c, d);
2286 
2287  __m256i abcd_03 = _mm256_unpacklo_epi32(ab_07, cd_07);
2288  __m256i abcd_47 = _mm256_unpackhi_epi32(ab_07, cd_07);
2289  __m256i abcd_8b = _mm256_unpacklo_epi32(ab_8f, cd_8f);
2290  __m256i abcd_cf = _mm256_unpackhi_epi32(ab_8f, cd_8f);
2291 
2292  // NOTE: no unpacklo/hi instr in this case, so using permute instr.
2293  kernel.packet[0] = _mm256_permute2x128_si256(abcd_03, abcd_47, 0x20);
2294  kernel.packet[1] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x20);
2295  kernel.packet[2] = _mm256_permute2x128_si256(abcd_03, abcd_47, 0x31);
2296  kernel.packet[3] = _mm256_permute2x128_si256(abcd_8b, abcd_cf, 0x31);
2297 }
2298 
2299 } // end namespace internal
2300 
2301 } // end namespace Eigen
2302 
2303 #endif // EIGEN_PACKET_MATH_AVX512_H
Eigen::internal::eigen_packet_wrapper
Definition: GenericPacketMath.h:159
Eigen::internal::Packet4d
__m256d Packet4d
Definition: AVX/PacketMath.h:33
S1
static double S1[]
Definition: shichi.c:61
Eigen::internal::pmax< Packet16h >
EIGEN_STRONG_INLINE Packet16h pmax< Packet16h >(const Packet16h &a, const Packet16h &b)
Definition: AVX512/PacketMath.h:1502
Eigen::internal::pmul< Packet16f >
EIGEN_STRONG_INLINE Packet16f pmul< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:313
Eigen::internal::pcmp_eq
EIGEN_STRONG_INLINE Packet2cf pcmp_eq(const Packet2cf &a, const Packet2cf &b)
Definition: AltiVec/Complex.h:231
Eigen::internal::unpacket_traits< Packet8d >::type
double type
Definition: AVX512/PacketMath.h:178
EIGEN_DEVICE_FUNC
#define EIGEN_DEVICE_FUNC
Definition: Macros.h:976
Eigen::internal::predux< Packet16h >
EIGEN_STRONG_INLINE half predux< Packet16h >(const Packet16h &from)
Definition: AVX512/PacketMath.h:1600
Eigen::internal::packet_traits::HasAbs
@ HasAbs
Definition: GenericPacketMath.h:121
Eigen
Namespace containing all symbols from the Eigen library.
Definition: jet.h:637
Eigen::internal::packet_traits< double >::half
Packet4d half
Definition: AVX512/PacketMath.h:135
Eigen::internal::psub< Packet8d >
EIGEN_STRONG_INLINE Packet8d psub< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:280
Eigen::internal::pmax< Packet16f >
EIGEN_STRONG_INLINE Packet16f pmax< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:384
Eigen::internal::pxor< Packet8d >
EIGEN_STRONG_INLINE Packet8d pxor< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:621
Eigen::internal::pset1< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pset1< Packet16bf >(const bfloat16 &from)
Definition: AVX512/PacketMath.h:1883
Eigen::internal::psub< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf psub< Packet16bf >(const Packet16bf &a, const Packet16bf &b)
Definition: AVX512/PacketMath.h:2079
Eigen::internal::default_packet_traits::HasLog
@ HasLog
Definition: GenericPacketMath.h:70
Eigen::internal::pand< Packet8d >
EIGEN_STRONG_INLINE Packet8d pand< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:566
Eigen::internal::pceil< Packet16h >
EIGEN_STRONG_INLINE Packet16h pceil< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1539
Eigen::internal::packet_traits::HasSub
@ HasSub
Definition: GenericPacketMath.h:118
Eigen::internal::packet_traits::size
@ size
Definition: GenericPacketMath.h:112
Eigen::internal::plset< Packet16h >
EIGEN_STRONG_INLINE Packet16h plset< Packet16h >(const half &a)
Definition: AVX512/PacketMath.h:1508
Eigen::internal::predux_min< Packet8d >
EIGEN_STRONG_INLINE double predux_min< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:1067
e
Array< double, 1, 3 > e(1./3., 0.5, 2.)
d
static const double d[K][N]
Definition: igam.h:11
Eigen::internal::pload1< Packet16f >
EIGEN_STRONG_INLINE Packet16f pload1< Packet16f >(const float *from)
Definition: AVX512/PacketMath.h:237
screwPose2::xi
Vector xi
Definition: testPose2.cpp:148
Eigen::internal::pmin< PropagateNaN, Packet16f >
EIGEN_STRONG_INLINE Packet16f pmin< PropagateNaN, Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:414
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const double h0
Definition: testGPSFactor.cpp:41
Eigen::internal::peven_mask
EIGEN_STRONG_INLINE Packet8f peven_mask(const Packet8f &)
Definition: AVX/PacketMath.h:252
Eigen::internal::pdiv< Packet16h >
EIGEN_STRONG_INLINE Packet16h pdiv< Packet16h >(const Packet16h &a, const Packet16h &b)
Definition: AVX512/PacketMath.h:1593
Eigen::internal::predux_max< Packet16bf >
EIGEN_STRONG_INLINE bfloat16 predux_max< Packet16bf >(const Packet16bf &from)
Definition: AVX512/PacketMath.h:2136
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Definition: GenericPacketMath.h:1014
Eigen::internal::pstore1< Packet8d >
EIGEN_STRONG_INLINE void pstore1< Packet8d >(double *to, const double &a)
Definition: AVX512/PacketMath.h:848
Eigen::internal::predux_mul< Packet16h >
EIGEN_STRONG_INLINE half predux_mul< Packet16h >(const Packet16h &from)
Definition: AVX512/PacketMath.h:1624
Eigen::internal::pdiv< Packet8d >
EIGEN_STRONG_INLINE Packet8d pdiv< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:334
Eigen::internal::pmax< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pmax< Packet16bf >(const Packet16bf &a, const Packet16bf &b)
Definition: AVX512/PacketMath.h:2103
c
Scalar Scalar * c
Definition: benchVecAdd.cpp:17
Eigen::bfloat16_impl::__bfloat16_raw::value
unsigned short value
Definition: BFloat16.h:36
Eigen::internal::pload< Packet8d >
EIGEN_STRONG_INLINE Packet8d pload< Packet8d >(const double *from)
Definition: AVX512/PacketMath.h:683
b
Scalar * b
Definition: benchVecAdd.cpp:17
Eigen::internal::print< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf print< Packet16bf >(const Packet16bf &a)
Definition: AVX512/PacketMath.h:2019
Eigen::internal::plset< Packet16f >
EIGEN_STRONG_INLINE Packet16f plset< Packet16f >(const float &a)
Definition: AVX512/PacketMath.h:246
Eigen::internal::pcmp_lt
EIGEN_STRONG_INLINE Packet4f pcmp_lt(const Packet4f &a, const Packet4f &b)
Definition: AltiVec/PacketMath.h:868
Eigen::internal::pstore< bfloat16 >
EIGEN_STRONG_INLINE void pstore< bfloat16 >(bfloat16 *to, const Packet8bf &from)
Definition: AltiVec/PacketMath.h:511
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::uint32_t uint32_t
Definition: Meta.h:56
Eigen::internal::pscatter< bfloat16, Packet16bf >
EIGEN_STRONG_INLINE void pscatter< bfloat16, Packet16bf >(bfloat16 *to, const Packet16bf &from, Index stride)
Definition: AVX512/PacketMath.h:2163
Eigen::internal::pfirst
EIGEN_STRONG_INLINE bfloat16 pfirst(const Packet8bf &a)
Definition: AltiVec/PacketMath.h:1429
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@ HasLog1p
Definition: GenericPacketMath.h:71
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eigen_packet_wrapper< __m256i, 2 > Packet16bf
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Definition: GenericPacketMath.h:1027
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EIGEN_STRONG_INLINE Packet8d pset1frombits< Packet8d >(const numext::uint64_t from)
Definition: AVX512/PacketMath.h:215
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EIGEN_STRONG_INLINE Packet8d ploadu< Packet8d >(const double *from)
Definition: AVX512/PacketMath.h:697
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Definition: GenericPacketMath.h:106
Eigen::internal::pstore< half >
EIGEN_STRONG_INLINE void pstore< half >(Eigen::half *to, const Packet16h &from)
Definition: AVX512/PacketMath.h:1394
Eigen::internal::parithmetic_shift_right
EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i &a)
Definition: AltiVec/PacketMath.h:1187
Eigen::internal::pset1< Packet16f >
EIGEN_STRONG_INLINE Packet16f pset1< Packet16f >(const float &from)
Definition: AVX512/PacketMath.h:197
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EIGEN_STRONG_INLINE Packet16i pandnot< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:630
Eigen::internal::pmin< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pmin< Packet16bf >(const Packet16bf &a, const Packet16bf &b)
Definition: AVX512/PacketMath.h:2097
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EIGEN_STRONG_INLINE Packet2cf preverse(const Packet2cf &a)
Definition: AltiVec/Complex.h:184
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Packet8f half
Definition: AVX512/PacketMath.h:98
Eigen::internal::predux_mul
EIGEN_DEVICE_FUNC unpacket_traits< Packet >::type predux_mul(const Packet &a)
Definition: GenericPacketMath.h:882
f2
double f2(const Vector2 &x)
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Definition: GenericPacketMath.h:1018
Eigen::internal::pmin< Packet16f >
EIGEN_STRONG_INLINE Packet16f pmin< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:371
T3
static const Pose3 T3(Rot3::Rodrigues(-90, 0, 0), Point3(1, 2, 3))
Eigen::internal::packet_traits::HasMin
@ HasMin
Definition: GenericPacketMath.h:123
Eigen::internal::pset1frombits< Packet16f >
EIGEN_STRONG_INLINE Packet16f pset1frombits< Packet16f >(unsigned int from)
Definition: AVX512/PacketMath.h:210
Eigen::internal::psub< Packet16i >
EIGEN_STRONG_INLINE Packet16i psub< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:285
Eigen::internal::predux_half_dowto4< Packet16h >
EIGEN_STRONG_INLINE Packet8h predux_half_dowto4< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1606
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Definition: AVX512/PacketMath.h:184
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bool select[N]
Definition: GenericPacketMath.h:1031
Eigen::internal::pround< Packet16f >
EIGEN_STRONG_INLINE Packet16f pround< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:651
Eigen::internal::pmax< PropagateNaN, Packet16f >
EIGEN_STRONG_INLINE Packet16f pmax< PropagateNaN, Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:422
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EIGEN_DEVICE_FUNC Packet pdiv(const Packet &a, const Packet &b)
Definition: GenericPacketMath.h:244
PACK_OUTPUT
#define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE)
Definition: AVX512/PacketMath.h:1104
Eigen::internal::pminmax_propagate_numbers
EIGEN_STRONG_INLINE Packet pminmax_propagate_numbers(const Packet &a, const Packet &b, Op op)
Definition: SSE/PacketMath.h:546
Eigen::internal::pfloor< Packet16h >
EIGEN_STRONG_INLINE Packet16h pfloor< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1543
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EIGEN_STRONG_INLINE Packet16f pxor< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:612
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EIGEN_STRONG_INLINE Packet8d ploadquad< Packet8d >(const double *from)
Definition: AVX512/PacketMath.h:761
Eigen::internal::predux_half_dowto4< Packet8d >
EIGEN_STRONG_INLINE Packet4d predux_half_dowto4< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:1021
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EIGEN_STRONG_INLINE Packet2cf pconj(const Packet2cf &a)
Definition: AltiVec/Complex.h:167
Eigen::internal::ploadquad
EIGEN_STRONG_INLINE Packet16h ploadquad(const Eigen::half *from)
Definition: AVX512/PacketMath.h:1420
Eigen::internal::pmul< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pmul< Packet16bf >(const Packet16bf &a, const Packet16bf &b)
Definition: AVX512/PacketMath.h:2085
res
cout<< "Here is the matrix m:"<< endl<< m<< endl;Matrix< ptrdiff_t, 3, 1 > res
Definition: PartialRedux_count.cpp:3
Eigen::internal::prefetch< float >
EIGEN_STRONG_INLINE void prefetch< float >(const float *addr)
Definition: AltiVec/PacketMath.h:1117
Eigen::internal::ploadu< Packet4f >
EIGEN_STRONG_INLINE Packet4f ploadu< Packet4f >(const float *from)
Definition: AltiVec/PacketMath.h:968
h
const double h
Definition: testSimpleHelicopter.cpp:19
Eigen::internal::pfirst< Packet16f >
EIGEN_STRONG_INLINE float pfirst< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:863
Eigen::internal::pstoreu< int >
EIGEN_STRONG_INLINE void pstoreu< int >(int *to, const Packet4i &from)
Definition: AltiVec/PacketMath.h:1092
Eigen::internal::pfirst< Packet8d >
EIGEN_STRONG_INLINE double pfirst< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:867
Eigen::internal::pfrexp< Packet8d >
EIGEN_STRONG_INLINE Packet8d pfrexp< Packet8d >(const Packet8d &a, Packet8d &exponent)
Definition: AVX512/PacketMath.h:915
Eigen::internal::unpacket_traits::vectorizable
@ vectorizable
Definition: GenericPacketMath.h:140
Eigen::internal::default_packet_traits::HasBlend
@ HasBlend
Definition: GenericPacketMath.h:60
Eigen::internal::default_packet_traits::HasCos
@ HasCos
Definition: GenericPacketMath.h:76
Eigen::internal::predux_min< Packet16h >
EIGEN_STRONG_INLINE Eigen::half predux_min< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1618
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Definition: GenericPacketMath.h:42
Eigen::internal::pand< Packet8i >
EIGEN_STRONG_INLINE Packet8i pand< Packet8i >(const Packet8i &a, const Packet8i &b)
Definition: AVX/PacketMath.h:491
Eigen::internal::pset1< Packet16i >
EIGEN_STRONG_INLINE Packet16i pset1< Packet16i >(const int &from)
Definition: AVX512/PacketMath.h:205
Eigen::internal::pfloor< Packet8d >
EIGEN_STRONG_INLINE Packet8d pfloor< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:533
Eigen::internal::predux< Packet16f >
EIGEN_STRONG_INLINE float predux< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:978
Eigen::internal::ploaddup< Packet16f >
EIGEN_STRONG_INLINE Packet16f ploaddup< Packet16f >(const float *from)
Definition: AVX512/PacketMath.h:715
Eigen::internal::Packet16i
__m512i Packet16i
Definition: AVX512/PacketMath.h:32
Eigen::bfloat16
Definition: BFloat16.h:58
x3
Pose3 x3(Rot3::Ypr(M_PI/4.0, 0.0, 0.0), l2)
Eigen::internal::pldexp< Packet8d >
EIGEN_STRONG_INLINE Packet8d pldexp< Packet8d >(const Packet8d &a, const Packet8d &exponent)
Definition: AVX512/PacketMath.h:923
hc
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Definition: Tridiagonalization_householderCoefficients.cpp:5
Eigen::internal::packet_traits< half >::half
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Definition: AVX512/PacketMath.h:56
f6
Vector6 f6(const double x1, const double x2, const double x3, const double x4, const double x5, const double x6)
Definition: testNumericalDerivative.cpp:139
Eigen::internal::pmin< Packet16h >
EIGEN_STRONG_INLINE Packet16h pmin< Packet16h >(const Packet16h &a, const Packet16h &b)
Definition: AVX512/PacketMath.h:1496
Eigen::internal::pxor
EIGEN_STRONG_INLINE Packet8h pxor(const Packet8h &a, const Packet8h &b)
Definition: AVX/PacketMath.h:1047
Eigen::internal::packet_traits::HasHalfPacket
@ HasHalfPacket
Definition: GenericPacketMath.h:114
test_eigen_tensor.indices
indices
Definition: test_eigen_tensor.py:31
EIGEN_DEBUG_UNALIGNED_STORE
#define EIGEN_DEBUG_UNALIGNED_STORE
Definition: GenericPacketMath.h:39
Eigen::internal::is_arithmetic::value
@ value
Definition: Meta.h:133
Eigen::internal::unpacket_traits::masked_store_available
@ masked_store_available
Definition: GenericPacketMath.h:142
Eigen::numext::uint64_t
::uint64_t uint64_t
Definition: Meta.h:58
Eigen::internal::pload< Packet16i >
EIGEN_STRONG_INLINE Packet16i pload< Packet16i >(const int *from)
Definition: AVX512/PacketMath.h:687
Eigen::internal::predux_mul< Packet16f >
EIGEN_STRONG_INLINE float predux_mul< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:1028
n
int n
Definition: BiCGSTAB_simple.cpp:1
Eigen::internal::Packet16f
__m512 Packet16f
Definition: AVX512/PacketMath.h:31
Eigen::internal::predux< Packet8d >
EIGEN_STRONG_INLINE double predux< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:996
Eigen::internal::packet_traits< bfloat16 >::type
Packet16bf type
Definition: AVX512/PacketMath.h:1844
Eigen::internal::padd< Packet16f >
EIGEN_STRONG_INLINE Packet16f padd< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:259
Eigen::internal::print< Packet8d >
EIGEN_STRONG_INLINE Packet8d print< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:527
Eigen::internal::unpacket_traits::size
@ size
Definition: GenericPacketMath.h:138
EIGEN_EXTRACT_8f_FROM_16f
#define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT)
Definition: AVX512/PacketMath.h:956
Eigen::internal::plogical_shift_left
EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i &a)
Definition: AltiVec/PacketMath.h:1191
Eigen::internal::unpacket_traits< Packet16h >::type
Eigen::half type
Definition: AVX512/PacketMath.h:191
T4
static const Similarity3 T4(R, P, s)
Eigen::internal::unpacket_traits::alignment
@ alignment
Definition: GenericPacketMath.h:139
Eigen::internal::por< Packet8d >
EIGEN_STRONG_INLINE Packet8d por< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:597
Eigen::numext::uint16_t
::uint16_t uint16_t
Definition: Meta.h:54
Eigen::internal::pstore< double >
EIGEN_STRONG_INLINE void pstore< double >(double *to, const Packet4d &from)
Definition: AVX/PacketMath.h:623
Eigen::internal::predux_half_dowto4< Packet16f >
EIGEN_STRONG_INLINE Packet8f predux_half_dowto4< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:1005
EIGEN_ALIGN64
#define EIGEN_ALIGN64
Definition: ConfigureVectorization.h:155
Eigen::internal::unpacket_traits< Packet8d >::half
Packet4d half
Definition: AVX512/PacketMath.h:179
Eigen::internal::pdiv< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pdiv< Packet16bf >(const Packet16bf &a, const Packet16bf &b)
Definition: AVX512/PacketMath.h:2091
j
std::ptrdiff_t j
Definition: tut_arithmetic_redux_minmax.cpp:2
Eigen::internal::packet_traits::HasConj
@ HasConj
Definition: GenericPacketMath.h:125
Eigen::internal::default_packet_traits::HasSin
@ HasSin
Definition: GenericPacketMath.h:75
S2
Symmetric< 2 > S2
Definition: testGroup.cpp:80
Eigen::internal::pxor< Packet16i >
EIGEN_STRONG_INLINE Packet16i pxor< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:607
Eigen::internal::ptrue< Packet8d >
EIGEN_STRONG_INLINE Packet8d ptrue< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:546
Eigen::internal::psub< Packet16h >
EIGEN_STRONG_INLINE Packet16h psub< Packet16h >(const Packet16h &a, const Packet16h &b)
Definition: AVX512/PacketMath.h:1579
Eigen::internal::Packet8d
__m512d Packet8d
Definition: AVX512/PacketMath.h:33
Eigen::internal::packet_traits::AlignedOnScalar
@ AlignedOnScalar
Definition: GenericPacketMath.h:113
Eigen::internal::default_packet_traits::HasNdtri
@ HasNdtri
Definition: GenericPacketMath.h:90
T6
static const Similarity3 T6(Rot3(), Point3(1, 1, 0), 2)
Eigen::internal::pgather< double, Packet8d >
EIGEN_DEVICE_FUNC Packet8d pgather< double, Packet8d >(const double *from, Index stride)
Definition: AVX512/PacketMath.h:813
Eigen::internal::predux_max< Packet16f >
EIGEN_STRONG_INLINE float predux_max< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:1076
Eigen::internal::pnegate
EIGEN_STRONG_INLINE Packet2cf pnegate(const Packet2cf &a)
Definition: AltiVec/Complex.h:166
Eigen::internal::ploaddup< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf ploaddup< Packet16bf >(const bfloat16 *from)
Definition: AVX512/PacketMath.h:1917
Eigen::internal::default_packet_traits::HasBessel
@ HasBessel
Definition: GenericPacketMath.h:91
Eigen::internal::ploadu< Packet16f >
EIGEN_STRONG_INLINE Packet16f ploadu< Packet16f >(const float *from)
Definition: AVX512/PacketMath.h:693
Eigen::internal::pmax< PropagateNumbers, Packet16f >
EIGEN_STRONG_INLINE Packet16f pmax< PropagateNumbers, Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:406
PACK_OUTPUT_D
#define PACK_OUTPUT_D(OUTPUT, INPUT, INDEX, STRIDE)
Definition: AVX512/PacketMath.h:1260
Eigen::internal::unpacket_traits
Definition: GenericPacketMath.h:132
Eigen::internal::ptranspose
EIGEN_STRONG_INLINE void ptranspose(PacketBlock< Packet2cf, 2 > &kernel)
Definition: AltiVec/Complex.h:224
Eigen::internal::pceil< Packet16f >
EIGEN_STRONG_INLINE Packet16f pceil< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:529
Eigen::internal::F32ToBf16
EIGEN_STRONG_INLINE Packet8bf F32ToBf16(Packet4f p4f)
Definition: AltiVec/PacketMath.h:1252
Eigen::internal::por< Packet16f >
EIGEN_STRONG_INLINE Packet16f por< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:588
l
static const Line3 l(Rot3(), 1, 1)
Eigen::internal::pselect
EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f &mask, const Packet4f &a, const Packet4f &b)
Definition: AltiVec/PacketMath.h:917
Eigen::internal::unpacket_traits< Packet16h >::half
Packet8h half
Definition: AVX512/PacketMath.h:192
Eigen::internal::ptrue< Packet16i >
EIGEN_STRONG_INLINE Packet16i ptrue< Packet16i >(const Packet16i &)
Definition: AVX512/PacketMath.h:536
EIGEN_DEBUG_ALIGNED_LOAD
#define EIGEN_DEBUG_ALIGNED_LOAD
Definition: GenericPacketMath.h:27
Eigen::internal::pround< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pround< Packet16bf >(const Packet16bf &a)
Definition: AVX512/PacketMath.h:2014
EIGEN_STRONG_INLINE
#define EIGEN_STRONG_INLINE
Definition: Macros.h:917
Eigen::internal::predux_min< Packet16f >
EIGEN_STRONG_INLINE float predux_min< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:1057
Eigen::internal::padd< Packet8h >
EIGEN_STRONG_INLINE Packet8h padd< Packet8h >(const Packet8h &a, const Packet8h &b)
Definition: AVX/PacketMath.h:1100
Eigen::internal::predux< Packet8f >
EIGEN_STRONG_INLINE float predux< Packet8f >(const Packet8f &a)
Definition: AVX/PacketMath.h:798
Eigen::internal::pmax
EIGEN_DEVICE_FUNC Packet pmax(const Packet &a, const Packet &b)
Definition: GenericPacketMath.h:524
Eigen::internal::pfloor< Packet16f >
EIGEN_STRONG_INLINE Packet16f pfloor< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:532
Eigen::internal::ploadquad< Packet16f >
EIGEN_STRONG_INLINE Packet16f ploadquad< Packet16f >(const float *from)
Definition: AVX512/PacketMath.h:752
Eigen::internal::predux< Packet16bf >
EIGEN_STRONG_INLINE bfloat16 predux< Packet16bf >(const Packet16bf &p)
Definition: AVX512/PacketMath.h:2121
Eigen::internal::ploaddup< Packet8d >
EIGEN_STRONG_INLINE Packet8d ploaddup< Packet8d >(const double *from)
Definition: AVX512/PacketMath.h:739
Eigen::internal::default_packet_traits::HasErf
@ HasErf
Definition: GenericPacketMath.h:88
Eigen::internal::pblend
EIGEN_STRONG_INLINE Packet4i pblend(const Selector< 4 > &ifPacket, const Packet4i &thenPacket, const Packet4i &elsePacket)
Definition: AltiVec/PacketMath.h:2107
Eigen::internal::pmul< Packet16h >
EIGEN_STRONG_INLINE Packet16h pmul< Packet16h >(const Packet16h &a, const Packet16h &b)
Definition: AVX512/PacketMath.h:1586
Eigen::internal::pcmp_lt_or_nan
EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan(const Packet4f &a, const Packet4f &b)
Definition: AltiVec/PacketMath.h:870
T5
static const Similarity3 T5(R, P, 10)
Eigen::internal::default_packet_traits::HasSqrt
@ HasSqrt
Definition: GenericPacketMath.h:66
Eigen::internal::pload< Packet16f >
EIGEN_STRONG_INLINE Packet16f pload< Packet16f >(const float *from)
Definition: AVX512/PacketMath.h:679
Eigen::internal::pand
EIGEN_STRONG_INLINE Packet8h pand(const Packet8h &a, const Packet8h &b)
Definition: AVX/PacketMath.h:1050
Eigen::internal::Packet8i
__m256i Packet8i
Definition: AVX/PacketMath.h:32
Eigen::internal::psub
EIGEN_DEVICE_FUNC Packet psub(const Packet &a, const Packet &b)
Definition: GenericPacketMath.h:222
Eigen::internal::pload1< Packet8d >
EIGEN_STRONG_INLINE Packet8d pload1< Packet8d >(const double *from)
Definition: AVX512/PacketMath.h:241
Eigen::internal::ploadu< Packet16i >
EIGEN_STRONG_INLINE Packet16i ploadu< Packet16i >(const int *from)
Definition: AVX512/PacketMath.h:701
m
Matrix3f m
Definition: AngleAxis_mimic_euler.cpp:1
Eigen::internal::pgather< float, Packet16f >
EIGEN_DEVICE_FUNC Packet16f pgather< float, Packet16f >(const float *from, Index stride)
Definition: AVX512/PacketMath.h:803
T2
static const Pose3 T2(Rot3::Rodrigues(0.3, 0.2, 0.1), P2)
Eigen::internal::pfirst< Packet16bf >
EIGEN_STRONG_INLINE bfloat16 pfirst< Packet16bf >(const Packet16bf &from)
Definition: AVX512/PacketMath.h:1888
Eigen::internal::Packet16h
eigen_packet_wrapper< __m256i, 1 > Packet16h
Definition: AVX512/PacketMath.h:34
Eigen::internal::extract128
EIGEN_STRONG_INLINE Packet2d extract128(Packet8d x)
Definition: AVX512/PacketMath.h:442
Eigen::internal::pset1< Packet8d >
EIGEN_STRONG_INLINE Packet8d pset1< Packet8d >(const double &from)
Definition: AVX512/PacketMath.h:201
Eigen::internal::pscatter< half, Packet16h >
EIGEN_STRONG_INLINE void pscatter< half, Packet16h >(half *to, const Packet16h &from, Index stride)
Definition: AVX512/PacketMath.h:1646
Eigen::internal::default_packet_traits::HasCeil
@ HasCeil
Definition: GenericPacketMath.h:101
Eigen::internal::plset< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf plset< Packet16bf >(const bfloat16 &a)
Definition: AVX512/PacketMath.h:2109
Eigen::internal::pand< Packet16i >
EIGEN_STRONG_INLINE Packet16i pand< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:551
Eigen::internal::pmin< PropagateNumbers, Packet8d >
EIGEN_STRONG_INLINE Packet8d pmin< PropagateNumbers, Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:402
Eigen::internal::default_packet_traits::HasFloor
@ HasFloor
Definition: GenericPacketMath.h:100
Eigen::internal::print< Packet16f >
EIGEN_STRONG_INLINE Packet16f print< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:526
Eigen::internal::pstore
EIGEN_DEVICE_FUNC void pstore(Scalar *to, const Packet &from)
Definition: GenericPacketMath.h:696
out
std::ofstream out("Result.txt")
g
void g(const string &key, int i)
Definition: testBTree.cpp:41
Eigen::internal::packet_traits< float >::type
Packet16f type
Definition: AVX512/PacketMath.h:97
Eigen::internal::pandnot< Packet16f >
EIGEN_STRONG_INLINE Packet16f pandnot< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:635
Eigen::internal::default_packet_traits::HasTanh
@ HasTanh
Definition: GenericPacketMath.h:83
Eigen::internal::pceil< Packet8d >
EIGEN_STRONG_INLINE Packet8d pceil< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:530
Eigen::internal::pfloor< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pfloor< Packet16bf >(const Packet16bf &a)
Definition: AVX512/PacketMath.h:2027
Eigen::internal::pmin< PropagateNumbers, Packet16f >
EIGEN_STRONG_INLINE Packet16f pmin< PropagateNumbers, Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:398
Eigen::internal::pand< Packet16f >
EIGEN_STRONG_INLINE Packet16f pand< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:557
Eigen::internal::unpacket_traits::masked_load_available
@ masked_load_available
Definition: GenericPacketMath.h:141
Eigen::internal::predux_any
EIGEN_STRONG_INLINE bool predux_any(const Packet4f &x)
Definition: AltiVec/PacketMath.h:1765
tree::f
Point2(* f)(const Point3 &, OptionalJacobian< 2, 3 >)
Definition: testExpression.cpp:218
Eigen::internal::print< Packet16h >
EIGEN_STRONG_INLINE Packet16h print< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1535
Eigen::internal::pmax< PropagateNumbers, Packet8d >
EIGEN_STRONG_INLINE Packet8d pmax< PropagateNumbers, Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:410
Eigen::internal::pmax< PropagateNaN, Packet8d >
EIGEN_STRONG_INLINE Packet8d pmax< PropagateNaN, Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:426
Eigen::internal::pzero
EIGEN_STRONG_INLINE Packet8f pzero(const Packet8f &)
Definition: AVX/PacketMath.h:247
Eigen::internal::plset< Packet8d >
EIGEN_STRONG_INLINE Packet8d plset< Packet8d >(const double &a)
Definition: AVX512/PacketMath.h:253
Eigen::internal::ptrue< Packet16f >
EIGEN_STRONG_INLINE Packet16f ptrue< Packet16f >(const Packet16f &a)
Definition: AVX512/PacketMath.h:541
Eigen::internal::packet_traits< double >::type
Packet8d type
Definition: AVX512/PacketMath.h:134
PACK_OUTPUT_SQ_D
#define PACK_OUTPUT_SQ_D(OUTPUT, INPUT, INDEX, STRIDE)
Definition: AVX512/PacketMath.h:1256
Eigen::internal::pstoreu< bfloat16 >
EIGEN_STRONG_INLINE void pstoreu< bfloat16 >(bfloat16 *to, const Packet8bf &from)
Definition: AltiVec/PacketMath.h:1104
Eigen::internal::cat256
EIGEN_STRONG_INLINE Packet16f cat256(Packet8f a, Packet8f b)
Definition: AVX512/PacketMath.h:446
Eigen::internal::pscatter< float, Packet16f >
EIGEN_DEVICE_FUNC void pscatter< float, Packet16f >(float *to, const Packet16f &from, Index stride)
Definition: AVX512/PacketMath.h:823
Eigen::internal::Bf16ToF32
EIGEN_STRONG_INLINE Packet8f Bf16ToF32(const Packet8bf &a)
Definition: AVX/PacketMath.h:1260
a
ArrayXXi a
Definition: Array_initializer_list_23_cxx11.cpp:1
Eigen::internal::por< Packet8i >
EIGEN_STRONG_INLINE Packet8i por< Packet8i >(const Packet8i &a, const Packet8i &b)
Definition: AVX/PacketMath.h:501
Eigen::internal::pstore1< Packet16f >
EIGEN_STRONG_INLINE void pstore1< Packet16f >(float *to, const float &a)
Definition: AVX512/PacketMath.h:843
Eigen::internal::packet_traits::HasAbs2
@ HasAbs2
Definition: GenericPacketMath.h:122
Eigen::internal::default_packet_traits::HasExp
@ HasExp
Definition: GenericPacketMath.h:68
Eigen::internal::unpacket_traits< Packet16f >::half
Packet8f half
Definition: AVX512/PacketMath.h:171
Eigen::internal::pfrexp< Packet16f >
EIGEN_STRONG_INLINE Packet16f pfrexp< Packet16f >(const Packet16f &a, Packet16f &exponent)
Definition: AVX512/PacketMath.h:898
Eigen::internal::unpacket_traits< Packet16f >::integer_packet
Packet16i integer_packet
Definition: AVX512/PacketMath.h:172
Eigen::internal::packet_traits< half >::type
Packet16h type
Definition: AVX512/PacketMath.h:54
Eigen::internal::predux
EIGEN_DEVICE_FUNC unpacket_traits< Packet >::type predux(const Packet &a)
Definition: GenericPacketMath.h:875
Eigen::internal::psub< Packet16f >
EIGEN_STRONG_INLINE Packet16f psub< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:275
Eigen::internal::pmax< Packet8d >
EIGEN_STRONG_INLINE Packet8d pmax< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:390
Eigen::internal::pminmax_propagate_nan
EIGEN_STRONG_INLINE Packet pminmax_propagate_nan(const Packet &a, const Packet &b, Op op)
Definition: SSE/PacketMath.h:555
PACK_OUTPUT_2
#define PACK_OUTPUT_2(OUTPUT, INPUT, INDEX, STRIDE)
Definition: AVX512/PacketMath.h:1218
Eigen::internal::pmul
EIGEN_DEVICE_FUNC Packet pmul(const Packet &a, const Packet &b)
Definition: GenericPacketMath.h:237
Eigen::internal::pfirst< Packet16h >
EIGEN_STRONG_INLINE Eigen::half pfirst< Packet16h >(const Packet16h &from)
Definition: AVX512/PacketMath.h:1382
Eigen::internal::padd< Packet8bf >
EIGEN_STRONG_INLINE Packet8bf padd< Packet8bf >(const Packet8bf &a, const Packet8bf &b)
Definition: AltiVec/PacketMath.h:1324
Eigen::internal::pmin< PropagateNaN, Packet8d >
EIGEN_STRONG_INLINE Packet8d pmin< PropagateNaN, Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:418
Eigen::internal::ploadu< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf ploadu< Packet16bf >(const bfloat16 *from)
Definition: AVX512/PacketMath.h:1900
Eigen::internal::ptrue< Packet8i >
EIGEN_STRONG_INLINE Packet8i ptrue< Packet8i >(const Packet8i &a)
Definition: AVX/PacketMath.h:459
Eigen::internal::Packet2d
v2f64 Packet2d
Definition: MSA/PacketMath.h:820
EIGEN_DEBUG_UNALIGNED_LOAD
#define EIGEN_DEBUG_UNALIGNED_LOAD
Definition: GenericPacketMath.h:31
Eigen::internal::padd< Packet16bf >
EIGEN_STRONG_INLINE Packet16bf padd< Packet16bf >(const Packet16bf &a, const Packet16bf &b)
Definition: AVX512/PacketMath.h:2073
S3
Symmetric< 3 > S3
Definition: testGroup.cpp:88
Eigen::internal::pxor< Packet8i >
EIGEN_STRONG_INLINE Packet8i pxor< Packet8i >(const Packet8i &a, const Packet8i &b)
Definition: AVX/PacketMath.h:511
Eigen::internal::padd< Packet16i >
EIGEN_STRONG_INLINE Packet16i padd< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:269
f3
double f3(double x1, double x2)
Definition: testNumericalDerivative.cpp:76
Eigen::internal::default_packet_traits::HasRsqrt
@ HasRsqrt
Definition: GenericPacketMath.h:67
hd
HessenbergDecomposition< MatrixXcf > hd(4)
Eigen::internal::SsePrefetchPtrType
const typedef char * SsePrefetchPtrType
Definition: SSE/PacketMath.h:864
Eigen::internal::unpacket_traits< Packet16f >::mask_t
uint16_t mask_t
Definition: AVX512/PacketMath.h:173
Eigen::internal::default_packet_traits::HasExpm1
@ HasExpm1
Definition: GenericPacketMath.h:69
Eigen::internal::predux_half_dowto4< Packet16bf >
EIGEN_STRONG_INLINE Packet8bf predux_half_dowto4< Packet16bf >(const Packet16bf &a)
Definition: AVX512/PacketMath.h:2114
Eigen::internal::plogical_shift_right
EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i &a)
Definition: AltiVec/PacketMath.h:1189
Eigen::internal::pstore< int >
EIGEN_STRONG_INLINE void pstore< int >(int *to, const Packet4i &from)
Definition: AltiVec/PacketMath.h:496
Eigen::internal::pmadd
EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f &a, const Packet4f &b, const Packet4f &c)
Definition: AltiVec/PacketMath.h:827
p
float * p
Definition: Tutorial_Map_using.cpp:9
Eigen::internal::pldexp< Packet16f >
EIGEN_STRONG_INLINE Packet16f pldexp< Packet16f >(const Packet16f &a, const Packet16f &exponent)
Definition: AVX512/PacketMath.h:919
Eigen::internal::pstoreu< double >
EIGEN_STRONG_INLINE void pstoreu< double >(double *to, const Packet4d &from)
Definition: AVX/PacketMath.h:627
Eigen::internal::pdiv< Packet16f >
EIGEN_STRONG_INLINE Packet16f pdiv< Packet16f >(const Packet16f &a, const Packet16f &b)
Definition: AVX512/PacketMath.h:329
uint16_t
unsigned short uint16_t
Definition: ms_stdint.h:84
Eigen::internal::prefetch< int >
EIGEN_STRONG_INLINE void prefetch< int >(const int *addr)
Definition: AltiVec/PacketMath.h:1118
Eigen::half_impl::raw_uint16_to_half
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR __half_raw raw_uint16_to_half(numext::uint16_t x)
Definition: Half.h:495
Eigen::internal::pstore1< Packet16i >
EIGEN_STRONG_INLINE void pstore1< Packet16i >(int *to, const int &a)
Definition: AVX512/PacketMath.h:853
Eigen::internal::packet_traits::HasAdd
@ HasAdd
Definition: GenericPacketMath.h:117
Eigen::internal::pabs
EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f &a)
Definition: AltiVec/PacketMath.h:1176
Eigen::internal::pgather< bfloat16, Packet16bf >
EIGEN_STRONG_INLINE Packet16bf pgather< bfloat16, Packet16bf >(const bfloat16 *from, Index stride)
Definition: AVX512/PacketMath.h:2153
Eigen::internal::unpacket_traits< Packet16bf >::half
Packet8bf half
Definition: AVX512/PacketMath.h:1879
Eigen::internal::default_packet_traits::HasRint
@ HasRint
Definition: GenericPacketMath.h:99
Eigen::half_impl::__half_raw::x
numext::uint16_t x
Definition: Half.h:104
f4
double f4(double x, double y, double z)
Definition: testNumericalDerivative.cpp:105
Eigen::internal::padd< Packet8d >
EIGEN_STRONG_INLINE Packet8d padd< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:264
Eigen::internal::pmin< Packet8d >
EIGEN_STRONG_INLINE Packet8d pmin< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:377
Eigen::internal::packet_traits::HasMax
@ HasMax
Definition: GenericPacketMath.h:124
Eigen::internal::packet_traits< bfloat16 >::half
Packet8bf half
Definition: AVX512/PacketMath.h:1845
Eigen::internal::half2float
EIGEN_STRONG_INLINE Packet8f half2float(const Packet8h &a)
Definition: AVX/PacketMath.h:988
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EIGEN_STRONG_INLINE Packet16i pmul< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:323
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EIGEN_DEVICE_FUNC Packet padd(const Packet &a, const Packet &b)
Definition: GenericPacketMath.h:215
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EIGEN_STRONG_INLINE Packet8d pmul< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:318
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EIGEN_DEVICE_FUNC Packet pmin(const Packet &a, const Packet &b)
Definition: GenericPacketMath.h:512
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Definition: AVX512/PacketMath.h:170
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Definition: DogLegOptimizerExample.py:113
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@ HasNegate
Definition: GenericPacketMath.h:120
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EIGEN_STRONG_INLINE Packet8h por(const Packet8h &a, const Packet8h &b)
Definition: AVX/PacketMath.h:1042
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@ HasDiv
Definition: GenericPacketMath.h:65
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EIGEN_STRONG_INLINE int pfirst< Packet16i >(const Packet16i &a)
Definition: AVX512/PacketMath.h:871
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EIGEN_STRONG_INLINE Packet16i por< Packet16i >(const Packet16i &a, const Packet16i &b)
Definition: AVX512/PacketMath.h:583
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EIGEN_STRONG_INLINE Packet8i pandnot< Packet8i >(const Packet8i &a, const Packet8i &b)
Definition: AVX/PacketMath.h:521
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Definition: igam.h:9
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EIGEN_STRONG_INLINE double predux_mul< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:1048
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Definition: BandTriangularSolver.h:13
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EIGEN_STRONG_INLINE void pstoreu< float >(float *to, const Packet4f &from)
Definition: AltiVec/PacketMath.h:1088
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EIGEN_STRONG_INLINE Packet16h ploadu< Packet16h >(const Eigen::half *from)
Definition: AVX512/PacketMath.h:1390
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EIGEN_STRONG_INLINE Packet16h pset1< Packet16h >(const Eigen::half &from)
Definition: AVX512/PacketMath.h:1378
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EIGEN_STRONG_INLINE __m256i Pack32To16(Packet16f rf)
Definition: AVX512/PacketMath.h:454
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EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Packet pldexp_generic(const Packet &a, const Packet &exponent)
Definition: GenericPacketMathFunctions.h:85
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EIGEN_STRONG_INLINE Packet8d pround< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:658
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Definition: AVX512/PacketMath.h:437
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EIGEN_STRONG_INLINE Packet16bf pceil< Packet16bf >(const Packet16bf &a)
Definition: AVX512/PacketMath.h:2023
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EIGEN_STRONG_INLINE Packet16bf pload< Packet16bf >(const bfloat16 *from)
Definition: AVX512/PacketMath.h:1895
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Definition: Half.h:142
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@ HasCmp
Definition: GenericPacketMath.h:63
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Definition: AVX512/PacketMath.h:1386
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EIGEN_STRONG_INLINE Packet8h pandnot(const Packet8h &a, const Packet8h &b)
Definition: AVX/PacketMath.h:1053
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Definition: AVX/PacketMath.h:743
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EIGEN_STRONG_INLINE bfloat16 predux_mul< Packet16bf >(const Packet16bf &from)
Definition: AVX512/PacketMath.h:2126
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Definition: Constants.h:236
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EIGEN_STRONG_INLINE Packet8h float2half(const Packet8f &a)
Definition: AVX/PacketMath.h:1007
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EIGEN_STRONG_INLINE Packet8i pset1< Packet8i >(const int &from)
Definition: AVX/PacketMath.h:242
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EIGEN_STRONG_INLINE Packet16h ploaddup< Packet16h >(const Eigen::half *from)
Definition: AVX512/PacketMath.h:1407
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EIGEN_STRONG_INLINE Eigen::half predux_max< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1612
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EIGEN_STRONG_INLINE Packet16h padd< Packet16h >(const Packet16h &a, const Packet16h &b)
Definition: AVX512/PacketMath.h:1572
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EIGEN_STRONG_INLINE void prefetch< double >(const double *addr)
Definition: AVX/PacketMath.h:692
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@ HasMul
Definition: GenericPacketMath.h:119
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EIGEN_STRONG_INLINE Packet4f pcmp_le(const Packet4f &a, const Packet4f &b)
Definition: AltiVec/PacketMath.h:867
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@ Aligned64
Definition: Constants.h:237
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@ Vectorizable
Definition: GenericPacketMath.h:111
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Definition: test_callbacks.py:158
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Definition: BiCGSTAB_step_by_step.cpp:9
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EIGEN_STRONG_INLINE Packet8d pandnot< Packet8d >(const Packet8d &a, const Packet8d &b)
Definition: AVX512/PacketMath.h:643
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EIGEN_STRONG_INLINE double predux_max< Packet8d >(const Packet8d &a)
Definition: AVX512/PacketMath.h:1087
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EIGEN_STRONG_INLINE bfloat16 predux_min< Packet16bf >(const Packet16bf &from)
Definition: AVX512/PacketMath.h:2131
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#define EIGEN_DEBUG_ALIGNED_STORE
Definition: GenericPacketMath.h:35
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Definition: AVX512/PacketMath.h:1877
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EIGEN_STRONG_INLINE void pstore< float >(float *to, const Packet4f &from)
Definition: AltiVec/PacketMath.h:491
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Definition: AVX512/PacketMath.h:185
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EIGEN_STRONG_INLINE Packet8h ptrue(const Packet8h &a)
Definition: AVX/PacketMath.h:978
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__m256 Packet8f
Definition: AVX/PacketMath.h:31
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EIGEN_DEVICE_FUNC void pscatter< double, Packet8d >(double *to, const Packet8d &from, Index stride)
Definition: AVX512/PacketMath.h:833
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@ HasSetLinear
Definition: GenericPacketMath.h:126
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Definition: Meta.h:133
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EIGEN_STRONG_INLINE Packet16h pround< Packet16h >(const Packet16h &a)
Definition: AVX512/PacketMath.h:1531
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EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
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#define EIGEN_FAST_MATH
Definition: Macros.h:49
Eigen::internal::pfrexp_generic
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Packet pfrexp_generic(const Packet &a, Packet &exponent)
Definition: GenericPacketMathFunctions.h:40
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@ HasRound
Definition: GenericPacketMath.h:98
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EIGEN_STRONG_INLINE void pstoreu< half >(Eigen::half *to, const Packet16h &from)
Definition: AVX512/PacketMath.h:1400

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autogenerated on Sat Jun 1 2024 03:02:28