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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 (at) 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 (2*sizeof(void*))
     23 #endif
     24 
     25 #ifdef __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 
     35 template <>
     36 struct is_arithmetic<__m512> {
     37   enum { value = true };
     38 };
     39 template <>
     40 struct is_arithmetic<__m512i> {
     41   enum { value = true };
     42 };
     43 template <>
     44 struct is_arithmetic<__m512d> {
     45   enum { value = true };
     46 };
     47 
     48 template<> struct packet_traits<float>  : default_packet_traits
     49 {
     50   typedef Packet16f type;
     51   typedef Packet8f half;
     52   enum {
     53     Vectorizable = 1,
     54     AlignedOnScalar = 1,
     55     size = 16,
     56     HasHalfPacket = 1,
     57 #if EIGEN_GNUC_AT_LEAST(5, 3)
     58 #ifdef EIGEN_VECTORIZE_AVX512DQ
     59     HasLog = 1,
     60 #endif
     61     HasExp = 1,
     62     HasSqrt = 1,
     63     HasRsqrt = 1,
     64 #endif
     65     HasDiv = 1
     66   };
     67  };
     68 template<> struct packet_traits<double> : default_packet_traits
     69 {
     70   typedef Packet8d type;
     71   typedef Packet4d half;
     72   enum {
     73     Vectorizable = 1,
     74     AlignedOnScalar = 1,
     75     size = 8,
     76     HasHalfPacket = 1,
     77 #if EIGEN_GNUC_AT_LEAST(5, 3)
     78     HasSqrt = 1,
     79     HasRsqrt = EIGEN_FAST_MATH,
     80 #endif
     81     HasDiv = 1
     82   };
     83 };
     84 
     85 /* TODO Implement AVX512 for integers
     86 template<> struct packet_traits<int>    : default_packet_traits
     87 {
     88   typedef Packet16i type;
     89   enum {
     90     Vectorizable = 1,
     91     AlignedOnScalar = 1,
     92     size=8
     93   };
     94 };
     95 */
     96 
     97 template <>
     98 struct unpacket_traits<Packet16f> {
     99   typedef float type;
    100   typedef Packet8f half;
    101   enum { size = 16, alignment=Aligned64 };
    102 };
    103 template <>
    104 struct unpacket_traits<Packet8d> {
    105   typedef double type;
    106   typedef Packet4d half;
    107   enum { size = 8, alignment=Aligned64 };
    108 };
    109 template <>
    110 struct unpacket_traits<Packet16i> {
    111   typedef int type;
    112   typedef Packet8i half;
    113   enum { size = 16, alignment=Aligned64 };
    114 };
    115 
    116 template <>
    117 EIGEN_STRONG_INLINE Packet16f pset1<Packet16f>(const float& from) {
    118   return _mm512_set1_ps(from);
    119 }
    120 template <>
    121 EIGEN_STRONG_INLINE Packet8d pset1<Packet8d>(const double& from) {
    122   return _mm512_set1_pd(from);
    123 }
    124 template <>
    125 EIGEN_STRONG_INLINE Packet16i pset1<Packet16i>(const int& from) {
    126   return _mm512_set1_epi32(from);
    127 }
    128 
    129 template <>
    130 EIGEN_STRONG_INLINE Packet16f pload1<Packet16f>(const float* from) {
    131   return _mm512_broadcastss_ps(_mm_load_ps1(from));
    132 }
    133 template <>
    134 EIGEN_STRONG_INLINE Packet8d pload1<Packet8d>(const double* from) {
    135   return _mm512_broadcastsd_pd(_mm_load_pd1(from));
    136 }
    137 
    138 template <>
    139 EIGEN_STRONG_INLINE Packet16f plset<Packet16f>(const float& a) {
    140   return _mm512_add_ps(
    141       _mm512_set1_ps(a),
    142       _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,
    143                     4.0f, 3.0f, 2.0f, 1.0f, 0.0f));
    144 }
    145 template <>
    146 EIGEN_STRONG_INLINE Packet8d plset<Packet8d>(const double& a) {
    147   return _mm512_add_pd(_mm512_set1_pd(a),
    148                        _mm512_set_pd(7.0, 6.0, 5.0, 4.0, 3.0, 2.0, 1.0, 0.0));
    149 }
    150 
    151 template <>
    152 EIGEN_STRONG_INLINE Packet16f padd<Packet16f>(const Packet16f& a,
    153                                               const Packet16f& b) {
    154   return _mm512_add_ps(a, b);
    155 }
    156 template <>
    157 EIGEN_STRONG_INLINE Packet8d padd<Packet8d>(const Packet8d& a,
    158                                             const Packet8d& b) {
    159   return _mm512_add_pd(a, b);
    160 }
    161 
    162 template <>
    163 EIGEN_STRONG_INLINE Packet16f psub<Packet16f>(const Packet16f& a,
    164                                               const Packet16f& b) {
    165   return _mm512_sub_ps(a, b);
    166 }
    167 template <>
    168 EIGEN_STRONG_INLINE Packet8d psub<Packet8d>(const Packet8d& a,
    169                                             const Packet8d& b) {
    170   return _mm512_sub_pd(a, b);
    171 }
    172 
    173 template <>
    174 EIGEN_STRONG_INLINE Packet16f pnegate(const Packet16f& a) {
    175   return _mm512_sub_ps(_mm512_set1_ps(0.0), a);
    176 }
    177 template <>
    178 EIGEN_STRONG_INLINE Packet8d pnegate(const Packet8d& a) {
    179   return _mm512_sub_pd(_mm512_set1_pd(0.0), a);
    180 }
    181 
    182 template <>
    183 EIGEN_STRONG_INLINE Packet16f pconj(const Packet16f& a) {
    184   return a;
    185 }
    186 template <>
    187 EIGEN_STRONG_INLINE Packet8d pconj(const Packet8d& a) {
    188   return a;
    189 }
    190 template <>
    191 EIGEN_STRONG_INLINE Packet16i pconj(const Packet16i& a) {
    192   return a;
    193 }
    194 
    195 template <>
    196 EIGEN_STRONG_INLINE Packet16f pmul<Packet16f>(const Packet16f& a,
    197                                               const Packet16f& b) {
    198   return _mm512_mul_ps(a, b);
    199 }
    200 template <>
    201 EIGEN_STRONG_INLINE Packet8d pmul<Packet8d>(const Packet8d& a,
    202                                             const Packet8d& b) {
    203   return _mm512_mul_pd(a, b);
    204 }
    205 
    206 template <>
    207 EIGEN_STRONG_INLINE Packet16f pdiv<Packet16f>(const Packet16f& a,
    208                                               const Packet16f& b) {
    209   return _mm512_div_ps(a, b);
    210 }
    211 template <>
    212 EIGEN_STRONG_INLINE Packet8d pdiv<Packet8d>(const Packet8d& a,
    213                                             const Packet8d& b) {
    214   return _mm512_div_pd(a, b);
    215 }
    216 
    217 #ifdef __FMA__
    218 template <>
    219 EIGEN_STRONG_INLINE Packet16f pmadd(const Packet16f& a, const Packet16f& b,
    220                                     const Packet16f& c) {
    221   return _mm512_fmadd_ps(a, b, c);
    222 }
    223 template <>
    224 EIGEN_STRONG_INLINE Packet8d pmadd(const Packet8d& a, const Packet8d& b,
    225                                    const Packet8d& c) {
    226   return _mm512_fmadd_pd(a, b, c);
    227 }
    228 #endif
    229 
    230 template <>
    231 EIGEN_STRONG_INLINE Packet16f pmin<Packet16f>(const Packet16f& a,
    232                                               const Packet16f& b) {
    233   return _mm512_min_ps(a, b);
    234 }
    235 template <>
    236 EIGEN_STRONG_INLINE Packet8d pmin<Packet8d>(const Packet8d& a,
    237                                             const Packet8d& b) {
    238   return _mm512_min_pd(a, b);
    239 }
    240 
    241 template <>
    242 EIGEN_STRONG_INLINE Packet16f pmax<Packet16f>(const Packet16f& a,
    243                                               const Packet16f& b) {
    244   return _mm512_max_ps(a, b);
    245 }
    246 template <>
    247 EIGEN_STRONG_INLINE Packet8d pmax<Packet8d>(const Packet8d& a,
    248                                             const Packet8d& b) {
    249   return _mm512_max_pd(a, b);
    250 }
    251 
    252 template <>
    253 EIGEN_STRONG_INLINE Packet16f pand<Packet16f>(const Packet16f& a,
    254                                               const Packet16f& b) {
    255 #ifdef EIGEN_VECTORIZE_AVX512DQ
    256   return _mm512_and_ps(a, b);
    257 #else
    258   Packet16f res = _mm512_undefined_ps();
    259   Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);
    260   Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);
    261   res = _mm512_insertf32x4(res, _mm_and_ps(lane0_a, lane0_b), 0);
    262 
    263   Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);
    264   Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);
    265   res = _mm512_insertf32x4(res, _mm_and_ps(lane1_a, lane1_b), 1);
    266 
    267   Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);
    268   Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);
    269   res = _mm512_insertf32x4(res, _mm_and_ps(lane2_a, lane2_b), 2);
    270 
    271   Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);
    272   Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);
    273   res = _mm512_insertf32x4(res, _mm_and_ps(lane3_a, lane3_b), 3);
    274 
    275   return res;
    276 #endif
    277 }
    278 template <>
    279 EIGEN_STRONG_INLINE Packet8d pand<Packet8d>(const Packet8d& a,
    280                                             const Packet8d& b) {
    281 #ifdef EIGEN_VECTORIZE_AVX512DQ
    282   return _mm512_and_pd(a, b);
    283 #else
    284   Packet8d res = _mm512_undefined_pd();
    285   Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);
    286   Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);
    287   res = _mm512_insertf64x4(res, _mm256_and_pd(lane0_a, lane0_b), 0);
    288 
    289   Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);
    290   Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);
    291   res = _mm512_insertf64x4(res, _mm256_and_pd(lane1_a, lane1_b), 1);
    292 
    293   return res;
    294 #endif
    295 }
    296 template <>
    297 EIGEN_STRONG_INLINE Packet16f por<Packet16f>(const Packet16f& a,
    298                                              const Packet16f& b) {
    299 #ifdef EIGEN_VECTORIZE_AVX512DQ
    300   return _mm512_or_ps(a, b);
    301 #else
    302   Packet16f res = _mm512_undefined_ps();
    303   Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);
    304   Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);
    305   res = _mm512_insertf32x4(res, _mm_or_ps(lane0_a, lane0_b), 0);
    306 
    307   Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);
    308   Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);
    309   res = _mm512_insertf32x4(res, _mm_or_ps(lane1_a, lane1_b), 1);
    310 
    311   Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);
    312   Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);
    313   res = _mm512_insertf32x4(res, _mm_or_ps(lane2_a, lane2_b), 2);
    314 
    315   Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);
    316   Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);
    317   res = _mm512_insertf32x4(res, _mm_or_ps(lane3_a, lane3_b), 3);
    318 
    319   return res;
    320 #endif
    321 }
    322 
    323 template <>
    324 EIGEN_STRONG_INLINE Packet8d por<Packet8d>(const Packet8d& a,
    325                                            const Packet8d& b) {
    326 #ifdef EIGEN_VECTORIZE_AVX512DQ
    327   return _mm512_or_pd(a, b);
    328 #else
    329   Packet8d res = _mm512_undefined_pd();
    330   Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);
    331   Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);
    332   res = _mm512_insertf64x4(res, _mm256_or_pd(lane0_a, lane0_b), 0);
    333 
    334   Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);
    335   Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);
    336   res = _mm512_insertf64x4(res, _mm256_or_pd(lane1_a, lane1_b), 1);
    337 
    338   return res;
    339 #endif
    340 }
    341 
    342 template <>
    343 EIGEN_STRONG_INLINE Packet16f pxor<Packet16f>(const Packet16f& a,
    344                                               const Packet16f& b) {
    345 #ifdef EIGEN_VECTORIZE_AVX512DQ
    346   return _mm512_xor_ps(a, b);
    347 #else
    348   Packet16f res = _mm512_undefined_ps();
    349   Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);
    350   Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);
    351   res = _mm512_insertf32x4(res, _mm_xor_ps(lane0_a, lane0_b), 0);
    352 
    353   Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);
    354   Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);
    355   res = _mm512_insertf32x4(res, _mm_xor_ps(lane1_a, lane1_b), 1);
    356 
    357   Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);
    358   Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);
    359   res = _mm512_insertf32x4(res, _mm_xor_ps(lane2_a, lane2_b), 2);
    360 
    361   Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);
    362   Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);
    363   res = _mm512_insertf32x4(res, _mm_xor_ps(lane3_a, lane3_b), 3);
    364 
    365   return res;
    366 #endif
    367 }
    368 template <>
    369 EIGEN_STRONG_INLINE Packet8d pxor<Packet8d>(const Packet8d& a,
    370                                             const Packet8d& b) {
    371 #ifdef EIGEN_VECTORIZE_AVX512DQ
    372   return _mm512_xor_pd(a, b);
    373 #else
    374   Packet8d res = _mm512_undefined_pd();
    375   Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);
    376   Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);
    377   res = _mm512_insertf64x4(res, _mm256_xor_pd(lane0_a, lane0_b), 0);
    378 
    379   Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);
    380   Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);
    381   res = _mm512_insertf64x4(res, _mm256_xor_pd(lane1_a, lane1_b), 1);
    382 
    383   return res;
    384 #endif
    385 }
    386 
    387 template <>
    388 EIGEN_STRONG_INLINE Packet16f pandnot<Packet16f>(const Packet16f& a,
    389                                                  const Packet16f& b) {
    390 #ifdef EIGEN_VECTORIZE_AVX512DQ
    391   return _mm512_andnot_ps(a, b);
    392 #else
    393   Packet16f res = _mm512_undefined_ps();
    394   Packet4f lane0_a = _mm512_extractf32x4_ps(a, 0);
    395   Packet4f lane0_b = _mm512_extractf32x4_ps(b, 0);
    396   res = _mm512_insertf32x4(res, _mm_andnot_ps(lane0_a, lane0_b), 0);
    397 
    398   Packet4f lane1_a = _mm512_extractf32x4_ps(a, 1);
    399   Packet4f lane1_b = _mm512_extractf32x4_ps(b, 1);
    400   res = _mm512_insertf32x4(res, _mm_andnot_ps(lane1_a, lane1_b), 1);
    401 
    402   Packet4f lane2_a = _mm512_extractf32x4_ps(a, 2);
    403   Packet4f lane2_b = _mm512_extractf32x4_ps(b, 2);
    404   res = _mm512_insertf32x4(res, _mm_andnot_ps(lane2_a, lane2_b), 2);
    405 
    406   Packet4f lane3_a = _mm512_extractf32x4_ps(a, 3);
    407   Packet4f lane3_b = _mm512_extractf32x4_ps(b, 3);
    408   res = _mm512_insertf32x4(res, _mm_andnot_ps(lane3_a, lane3_b), 3);
    409 
    410   return res;
    411 #endif
    412 }
    413 template <>
    414 EIGEN_STRONG_INLINE Packet8d pandnot<Packet8d>(const Packet8d& a,
    415                                                const Packet8d& b) {
    416 #ifdef EIGEN_VECTORIZE_AVX512DQ
    417   return _mm512_andnot_pd(a, b);
    418 #else
    419   Packet8d res = _mm512_undefined_pd();
    420   Packet4d lane0_a = _mm512_extractf64x4_pd(a, 0);
    421   Packet4d lane0_b = _mm512_extractf64x4_pd(b, 0);
    422   res = _mm512_insertf64x4(res, _mm256_andnot_pd(lane0_a, lane0_b), 0);
    423 
    424   Packet4d lane1_a = _mm512_extractf64x4_pd(a, 1);
    425   Packet4d lane1_b = _mm512_extractf64x4_pd(b, 1);
    426   res = _mm512_insertf64x4(res, _mm256_andnot_pd(lane1_a, lane1_b), 1);
    427 
    428   return res;
    429 #endif
    430 }
    431 
    432 template <>
    433 EIGEN_STRONG_INLINE Packet16f pload<Packet16f>(const float* from) {
    434   EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_ps(from);
    435 }
    436 template <>
    437 EIGEN_STRONG_INLINE Packet8d pload<Packet8d>(const double* from) {
    438   EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_pd(from);
    439 }
    440 template <>
    441 EIGEN_STRONG_INLINE Packet16i pload<Packet16i>(const int* from) {
    442   EIGEN_DEBUG_ALIGNED_LOAD return _mm512_load_si512(
    443       reinterpret_cast<const __m512i*>(from));
    444 }
    445 
    446 template <>
    447 EIGEN_STRONG_INLINE Packet16f ploadu<Packet16f>(const float* from) {
    448   EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_ps(from);
    449 }
    450 template <>
    451 EIGEN_STRONG_INLINE Packet8d ploadu<Packet8d>(const double* from) {
    452   EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_pd(from);
    453 }
    454 template <>
    455 EIGEN_STRONG_INLINE Packet16i ploadu<Packet16i>(const int* from) {
    456   EIGEN_DEBUG_UNALIGNED_LOAD return _mm512_loadu_si512(
    457       reinterpret_cast<const __m512i*>(from));
    458 }
    459 
    460 // Loads 8 floats from memory a returns the packet
    461 // {a0, a0  a1, a1, a2, a2, a3, a3, a4, a4, a5, a5, a6, a6, a7, a7}
    462 template <>
    463 EIGEN_STRONG_INLINE Packet16f ploaddup<Packet16f>(const float* from) {
    464   Packet8f lane0 = _mm256_broadcast_ps((const __m128*)(const void*)from);
    465   // mimic an "inplace" permutation of the lower 128bits using a blend
    466   lane0 = _mm256_blend_ps(
    467       lane0, _mm256_castps128_ps256(_mm_permute_ps(
    468                  _mm256_castps256_ps128(lane0), _MM_SHUFFLE(1, 0, 1, 0))),
    469       15);
    470   // then we can perform a consistent permutation on the global register to get
    471   // everything in shape:
    472   lane0 = _mm256_permute_ps(lane0, _MM_SHUFFLE(3, 3, 2, 2));
    473 
    474   Packet8f lane1 = _mm256_broadcast_ps((const __m128*)(const void*)(from + 4));
    475   // mimic an "inplace" permutation of the lower 128bits using a blend
    476   lane1 = _mm256_blend_ps(
    477       lane1, _mm256_castps128_ps256(_mm_permute_ps(
    478                  _mm256_castps256_ps128(lane1), _MM_SHUFFLE(1, 0, 1, 0))),
    479       15);
    480   // then we can perform a consistent permutation on the global register to get
    481   // everything in shape:
    482   lane1 = _mm256_permute_ps(lane1, _MM_SHUFFLE(3, 3, 2, 2));
    483 
    484 #ifdef EIGEN_VECTORIZE_AVX512DQ
    485   Packet16f res = _mm512_undefined_ps();
    486   return _mm512_insertf32x8(res, lane0, 0);
    487   return _mm512_insertf32x8(res, lane1, 1);
    488   return res;
    489 #else
    490   Packet16f res = _mm512_undefined_ps();
    491   res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane0, 0), 0);
    492   res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane0, 1), 1);
    493   res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane1, 0), 2);
    494   res = _mm512_insertf32x4(res, _mm256_extractf128_ps(lane1, 1), 3);
    495   return res;
    496 #endif
    497 }
    498 // Loads 4 doubles from memory a returns the packet {a0, a0  a1, a1, a2, a2, a3,
    499 // a3}
    500 template <>
    501 EIGEN_STRONG_INLINE Packet8d ploaddup<Packet8d>(const double* from) {
    502   Packet4d lane0 = _mm256_broadcast_pd((const __m128d*)(const void*)from);
    503   lane0 = _mm256_permute_pd(lane0, 3 << 2);
    504 
    505   Packet4d lane1 = _mm256_broadcast_pd((const __m128d*)(const void*)(from + 2));
    506   lane1 = _mm256_permute_pd(lane1, 3 << 2);
    507 
    508   Packet8d res = _mm512_undefined_pd();
    509   res = _mm512_insertf64x4(res, lane0, 0);
    510   return _mm512_insertf64x4(res, lane1, 1);
    511 }
    512 
    513 // Loads 4 floats from memory a returns the packet
    514 // {a0, a0  a0, a0, a1, a1, a1, a1, a2, a2, a2, a2, a3, a3, a3, a3}
    515 template <>
    516 EIGEN_STRONG_INLINE Packet16f ploadquad<Packet16f>(const float* from) {
    517   Packet16f tmp = _mm512_undefined_ps();
    518   tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from), 0);
    519   tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from + 1), 1);
    520   tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from + 2), 2);
    521   tmp = _mm512_insertf32x4(tmp, _mm_load_ps1(from + 3), 3);
    522   return tmp;
    523 }
    524 // Loads 2 doubles from memory a returns the packet
    525 // {a0, a0  a0, a0, a1, a1, a1, a1}
    526 template <>
    527 EIGEN_STRONG_INLINE Packet8d ploadquad<Packet8d>(const double* from) {
    528   Packet8d tmp = _mm512_undefined_pd();
    529   Packet2d tmp0 = _mm_load_pd1(from);
    530   Packet2d tmp1 = _mm_load_pd1(from + 1);
    531   Packet4d lane0 = _mm256_broadcastsd_pd(tmp0);
    532   Packet4d lane1 = _mm256_broadcastsd_pd(tmp1);
    533   tmp = _mm512_insertf64x4(tmp, lane0, 0);
    534   return _mm512_insertf64x4(tmp, lane1, 1);
    535 }
    536 
    537 template <>
    538 EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet16f& from) {
    539   EIGEN_DEBUG_ALIGNED_STORE _mm512_store_ps(to, from);
    540 }
    541 template <>
    542 EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet8d& from) {
    543   EIGEN_DEBUG_ALIGNED_STORE _mm512_store_pd(to, from);
    544 }
    545 template <>
    546 EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet16i& from) {
    547   EIGEN_DEBUG_ALIGNED_STORE _mm512_storeu_si512(reinterpret_cast<__m512i*>(to),
    548                                                 from);
    549 }
    550 
    551 template <>
    552 EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet16f& from) {
    553   EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_ps(to, from);
    554 }
    555 template <>
    556 EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet8d& from) {
    557   EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_pd(to, from);
    558 }
    559 template <>
    560 EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet16i& from) {
    561   EIGEN_DEBUG_UNALIGNED_STORE _mm512_storeu_si512(
    562       reinterpret_cast<__m512i*>(to), from);
    563 }
    564 
    565 template <>
    566 EIGEN_DEVICE_FUNC inline Packet16f pgather<float, Packet16f>(const float* from,
    567                                                              Index stride) {
    568   Packet16i stride_vector = _mm512_set1_epi32(stride);
    569   Packet16i stride_multiplier =
    570       _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
    571   Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
    572 
    573   return _mm512_i32gather_ps(indices, from, 4);
    574 }
    575 template <>
    576 EIGEN_DEVICE_FUNC inline Packet8d pgather<double, Packet8d>(const double* from,
    577                                                             Index stride) {
    578   Packet8i stride_vector = _mm256_set1_epi32(stride);
    579   Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
    580   Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
    581 
    582   return _mm512_i32gather_pd(indices, from, 8);
    583 }
    584 
    585 template <>
    586 EIGEN_DEVICE_FUNC inline void pscatter<float, Packet16f>(float* to,
    587                                                          const Packet16f& from,
    588                                                          Index stride) {
    589   Packet16i stride_vector = _mm512_set1_epi32(stride);
    590   Packet16i stride_multiplier =
    591       _mm512_set_epi32(15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0);
    592   Packet16i indices = _mm512_mullo_epi32(stride_vector, stride_multiplier);
    593   _mm512_i32scatter_ps(to, indices, from, 4);
    594 }
    595 template <>
    596 EIGEN_DEVICE_FUNC inline void pscatter<double, Packet8d>(double* to,
    597                                                          const Packet8d& from,
    598                                                          Index stride) {
    599   Packet8i stride_vector = _mm256_set1_epi32(stride);
    600   Packet8i stride_multiplier = _mm256_set_epi32(7, 6, 5, 4, 3, 2, 1, 0);
    601   Packet8i indices = _mm256_mullo_epi32(stride_vector, stride_multiplier);
    602   _mm512_i32scatter_pd(to, indices, from, 8);
    603 }
    604 
    605 template <>
    606 EIGEN_STRONG_INLINE void pstore1<Packet16f>(float* to, const float& a) {
    607   Packet16f pa = pset1<Packet16f>(a);
    608   pstore(to, pa);
    609 }
    610 template <>
    611 EIGEN_STRONG_INLINE void pstore1<Packet8d>(double* to, const double& a) {
    612   Packet8d pa = pset1<Packet8d>(a);
    613   pstore(to, pa);
    614 }
    615 template <>
    616 EIGEN_STRONG_INLINE void pstore1<Packet16i>(int* to, const int& a) {
    617   Packet16i pa = pset1<Packet16i>(a);
    618   pstore(to, pa);
    619 }
    620 
    621 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
    622 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
    623 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
    624 
    625 template <>
    626 EIGEN_STRONG_INLINE float pfirst<Packet16f>(const Packet16f& a) {
    627   return _mm_cvtss_f32(_mm512_extractf32x4_ps(a, 0));
    628 }
    629 template <>
    630 EIGEN_STRONG_INLINE double pfirst<Packet8d>(const Packet8d& a) {
    631   return _mm_cvtsd_f64(_mm256_extractf128_pd(_mm512_extractf64x4_pd(a, 0), 0));
    632 }
    633 template <>
    634 EIGEN_STRONG_INLINE int pfirst<Packet16i>(const Packet16i& a) {
    635   return _mm_extract_epi32(_mm512_extracti32x4_epi32(a, 0), 0);
    636 }
    637 
    638 template<> EIGEN_STRONG_INLINE Packet16f preverse(const Packet16f& a)
    639 {
    640   return _mm512_permutexvar_ps(_mm512_set_epi32(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15), a);
    641 }
    642 
    643 template<> EIGEN_STRONG_INLINE Packet8d preverse(const Packet8d& a)
    644 {
    645   return _mm512_permutexvar_pd(_mm512_set_epi32(0, 0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7), a);
    646 }
    647 
    648 template<> EIGEN_STRONG_INLINE Packet16f pabs(const Packet16f& a)
    649 {
    650   // _mm512_abs_ps intrinsic not found, so hack around it
    651   return (__m512)_mm512_and_si512((__m512i)a, _mm512_set1_epi32(0x7fffffff));
    652 }
    653 template <>
    654 EIGEN_STRONG_INLINE Packet8d pabs(const Packet8d& a) {
    655   // _mm512_abs_ps intrinsic not found, so hack around it
    656   return (__m512d)_mm512_and_si512((__m512i)a,
    657                                    _mm512_set1_epi64(0x7fffffffffffffff));
    658 }
    659 
    660 #ifdef EIGEN_VECTORIZE_AVX512DQ
    661 // AVX512F does not define _mm512_extractf32x8_ps to extract _m256 from _m512
    662 #define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT)                           \
    663   __m256 OUTPUT##_0 = _mm512_extractf32x8_ps(INPUT, 0) __m256 OUTPUT##_1 = \
    664       _mm512_extractf32x8_ps(INPUT, 1)
    665 #else
    666 #define EIGEN_EXTRACT_8f_FROM_16f(INPUT, OUTPUT)                \
    667   __m256 OUTPUT##_0 = _mm256_insertf128_ps(                     \
    668       _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 0)), \
    669       _mm512_extractf32x4_ps(INPUT, 1), 1);                     \
    670   __m256 OUTPUT##_1 = _mm256_insertf128_ps(                     \
    671       _mm256_castps128_ps256(_mm512_extractf32x4_ps(INPUT, 2)), \
    672       _mm512_extractf32x4_ps(INPUT, 3), 1);
    673 #endif
    674 
    675 #ifdef EIGEN_VECTORIZE_AVX512DQ
    676 #define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB) \
    677   OUTPUT = _mm512_insertf32x8(OUTPUT, INPUTA, 0);        \
    678   OUTPUT = _mm512_insertf32x8(OUTPUT, INPUTB, 1);
    679 #else
    680 #define EIGEN_INSERT_8f_INTO_16f(OUTPUT, INPUTA, INPUTB)                    \
    681   OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 0), 0); \
    682   OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTA, 1), 1); \
    683   OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 0), 2); \
    684   OUTPUT = _mm512_insertf32x4(OUTPUT, _mm256_extractf128_ps(INPUTB, 1), 3);
    685 #endif
    686 template<> EIGEN_STRONG_INLINE Packet16f preduxp<Packet16f>(const Packet16f*
    687 vecs)
    688 {
    689   EIGEN_EXTRACT_8f_FROM_16f(vecs[0], vecs0);
    690   EIGEN_EXTRACT_8f_FROM_16f(vecs[1], vecs1);
    691   EIGEN_EXTRACT_8f_FROM_16f(vecs[2], vecs2);
    692   EIGEN_EXTRACT_8f_FROM_16f(vecs[3], vecs3);
    693   EIGEN_EXTRACT_8f_FROM_16f(vecs[4], vecs4);
    694   EIGEN_EXTRACT_8f_FROM_16f(vecs[5], vecs5);
    695   EIGEN_EXTRACT_8f_FROM_16f(vecs[6], vecs6);
    696   EIGEN_EXTRACT_8f_FROM_16f(vecs[7], vecs7);
    697   EIGEN_EXTRACT_8f_FROM_16f(vecs[8], vecs8);
    698   EIGEN_EXTRACT_8f_FROM_16f(vecs[9], vecs9);
    699   EIGEN_EXTRACT_8f_FROM_16f(vecs[10], vecs10);
    700   EIGEN_EXTRACT_8f_FROM_16f(vecs[11], vecs11);
    701   EIGEN_EXTRACT_8f_FROM_16f(vecs[12], vecs12);
    702   EIGEN_EXTRACT_8f_FROM_16f(vecs[13], vecs13);
    703   EIGEN_EXTRACT_8f_FROM_16f(vecs[14], vecs14);
    704   EIGEN_EXTRACT_8f_FROM_16f(vecs[15], vecs15);
    705 
    706   __m256 hsum1 = _mm256_hadd_ps(vecs0_0, vecs1_0);
    707   __m256 hsum2 = _mm256_hadd_ps(vecs2_0, vecs3_0);
    708   __m256 hsum3 = _mm256_hadd_ps(vecs4_0, vecs5_0);
    709   __m256 hsum4 = _mm256_hadd_ps(vecs6_0, vecs7_0);
    710 
    711   __m256 hsum5 = _mm256_hadd_ps(hsum1, hsum1);
    712   __m256 hsum6 = _mm256_hadd_ps(hsum2, hsum2);
    713   __m256 hsum7 = _mm256_hadd_ps(hsum3, hsum3);
    714   __m256 hsum8 = _mm256_hadd_ps(hsum4, hsum4);
    715 
    716   __m256 perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);
    717   __m256 perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);
    718   __m256 perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);
    719   __m256 perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);
    720 
    721   __m256 sum1 = _mm256_add_ps(perm1, hsum5);
    722   __m256 sum2 = _mm256_add_ps(perm2, hsum6);
    723   __m256 sum3 = _mm256_add_ps(perm3, hsum7);
    724   __m256 sum4 = _mm256_add_ps(perm4, hsum8);
    725 
    726   __m256 blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
    727   __m256 blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
    728 
    729   __m256 final = _mm256_blend_ps(blend1, blend2, 0xf0);
    730 
    731   hsum1 = _mm256_hadd_ps(vecs0_1, vecs1_1);
    732   hsum2 = _mm256_hadd_ps(vecs2_1, vecs3_1);
    733   hsum3 = _mm256_hadd_ps(vecs4_1, vecs5_1);
    734   hsum4 = _mm256_hadd_ps(vecs6_1, vecs7_1);
    735 
    736   hsum5 = _mm256_hadd_ps(hsum1, hsum1);
    737   hsum6 = _mm256_hadd_ps(hsum2, hsum2);
    738   hsum7 = _mm256_hadd_ps(hsum3, hsum3);
    739   hsum8 = _mm256_hadd_ps(hsum4, hsum4);
    740 
    741   perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);
    742   perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);
    743   perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);
    744   perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);
    745 
    746   sum1 = _mm256_add_ps(perm1, hsum5);
    747   sum2 = _mm256_add_ps(perm2, hsum6);
    748   sum3 = _mm256_add_ps(perm3, hsum7);
    749   sum4 = _mm256_add_ps(perm4, hsum8);
    750 
    751   blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
    752   blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
    753 
    754   final = padd(final, _mm256_blend_ps(blend1, blend2, 0xf0));
    755 
    756   hsum1 = _mm256_hadd_ps(vecs8_0, vecs9_0);
    757   hsum2 = _mm256_hadd_ps(vecs10_0, vecs11_0);
    758   hsum3 = _mm256_hadd_ps(vecs12_0, vecs13_0);
    759   hsum4 = _mm256_hadd_ps(vecs14_0, vecs15_0);
    760 
    761   hsum5 = _mm256_hadd_ps(hsum1, hsum1);
    762   hsum6 = _mm256_hadd_ps(hsum2, hsum2);
    763   hsum7 = _mm256_hadd_ps(hsum3, hsum3);
    764   hsum8 = _mm256_hadd_ps(hsum4, hsum4);
    765 
    766   perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);
    767   perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);
    768   perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);
    769   perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);
    770 
    771   sum1 = _mm256_add_ps(perm1, hsum5);
    772   sum2 = _mm256_add_ps(perm2, hsum6);
    773   sum3 = _mm256_add_ps(perm3, hsum7);
    774   sum4 = _mm256_add_ps(perm4, hsum8);
    775 
    776   blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
    777   blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
    778 
    779   __m256 final_1 = _mm256_blend_ps(blend1, blend2, 0xf0);
    780 
    781   hsum1 = _mm256_hadd_ps(vecs8_1, vecs9_1);
    782   hsum2 = _mm256_hadd_ps(vecs10_1, vecs11_1);
    783   hsum3 = _mm256_hadd_ps(vecs12_1, vecs13_1);
    784   hsum4 = _mm256_hadd_ps(vecs14_1, vecs15_1);
    785 
    786   hsum5 = _mm256_hadd_ps(hsum1, hsum1);
    787   hsum6 = _mm256_hadd_ps(hsum2, hsum2);
    788   hsum7 = _mm256_hadd_ps(hsum3, hsum3);
    789   hsum8 = _mm256_hadd_ps(hsum4, hsum4);
    790 
    791   perm1 = _mm256_permute2f128_ps(hsum5, hsum5, 0x23);
    792   perm2 = _mm256_permute2f128_ps(hsum6, hsum6, 0x23);
    793   perm3 = _mm256_permute2f128_ps(hsum7, hsum7, 0x23);
    794   perm4 = _mm256_permute2f128_ps(hsum8, hsum8, 0x23);
    795 
    796   sum1 = _mm256_add_ps(perm1, hsum5);
    797   sum2 = _mm256_add_ps(perm2, hsum6);
    798   sum3 = _mm256_add_ps(perm3, hsum7);
    799   sum4 = _mm256_add_ps(perm4, hsum8);
    800 
    801   blend1 = _mm256_blend_ps(sum1, sum2, 0xcc);
    802   blend2 = _mm256_blend_ps(sum3, sum4, 0xcc);
    803 
    804   final_1 = padd(final_1, _mm256_blend_ps(blend1, blend2, 0xf0));
    805 
    806   __m512 final_output;
    807 
    808   EIGEN_INSERT_8f_INTO_16f(final_output, final, final_1);
    809   return final_output;
    810 }
    811 
    812 template<> EIGEN_STRONG_INLINE Packet8d preduxp<Packet8d>(const Packet8d* vecs)
    813 {
    814   Packet4d vecs0_0 = _mm512_extractf64x4_pd(vecs[0], 0);
    815   Packet4d vecs0_1 = _mm512_extractf64x4_pd(vecs[0], 1);
    816 
    817   Packet4d vecs1_0 = _mm512_extractf64x4_pd(vecs[1], 0);
    818   Packet4d vecs1_1 = _mm512_extractf64x4_pd(vecs[1], 1);
    819 
    820   Packet4d vecs2_0 = _mm512_extractf64x4_pd(vecs[2], 0);
    821   Packet4d vecs2_1 = _mm512_extractf64x4_pd(vecs[2], 1);
    822 
    823   Packet4d vecs3_0 = _mm512_extractf64x4_pd(vecs[3], 0);
    824   Packet4d vecs3_1 = _mm512_extractf64x4_pd(vecs[3], 1);
    825 
    826   Packet4d vecs4_0 = _mm512_extractf64x4_pd(vecs[4], 0);
    827   Packet4d vecs4_1 = _mm512_extractf64x4_pd(vecs[4], 1);
    828 
    829   Packet4d vecs5_0 = _mm512_extractf64x4_pd(vecs[5], 0);
    830   Packet4d vecs5_1 = _mm512_extractf64x4_pd(vecs[5], 1);
    831 
    832   Packet4d vecs6_0 = _mm512_extractf64x4_pd(vecs[6], 0);
    833   Packet4d vecs6_1 = _mm512_extractf64x4_pd(vecs[6], 1);
    834 
    835   Packet4d vecs7_0 = _mm512_extractf64x4_pd(vecs[7], 0);
    836   Packet4d vecs7_1 = _mm512_extractf64x4_pd(vecs[7], 1);
    837 
    838   Packet4d tmp0, tmp1;
    839 
    840   tmp0 = _mm256_hadd_pd(vecs0_0, vecs1_0);
    841   tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));
    842 
    843   tmp1 = _mm256_hadd_pd(vecs2_0, vecs3_0);
    844   tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
    845 
    846   __m256d final_0 = _mm256_blend_pd(tmp0, tmp1, 0xC);
    847 
    848   tmp0 = _mm256_hadd_pd(vecs0_1, vecs1_1);
    849   tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));
    850 
    851   tmp1 = _mm256_hadd_pd(vecs2_1, vecs3_1);
    852   tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
    853 
    854   final_0 = padd(final_0, _mm256_blend_pd(tmp0, tmp1, 0xC));
    855 
    856   tmp0 = _mm256_hadd_pd(vecs4_0, vecs5_0);
    857   tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));
    858 
    859   tmp1 = _mm256_hadd_pd(vecs6_0, vecs7_0);
    860   tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
    861 
    862   __m256d final_1 = _mm256_blend_pd(tmp0, tmp1, 0xC);
    863 
    864   tmp0 = _mm256_hadd_pd(vecs4_1, vecs5_1);
    865   tmp0 = _mm256_add_pd(tmp0, _mm256_permute2f128_pd(tmp0, tmp0, 1));
    866 
    867   tmp1 = _mm256_hadd_pd(vecs6_1, vecs7_1);
    868   tmp1 = _mm256_add_pd(tmp1, _mm256_permute2f128_pd(tmp1, tmp1, 1));
    869 
    870   final_1 = padd(final_1, _mm256_blend_pd(tmp0, tmp1, 0xC));
    871 
    872   __m512d final_output = _mm512_insertf64x4(final_output, final_0, 0);
    873 
    874   return _mm512_insertf64x4(final_output, final_1, 1);
    875 }
    876 
    877 template <>
    878 EIGEN_STRONG_INLINE float predux<Packet16f>(const Packet16f& a) {
    879   //#ifdef EIGEN_VECTORIZE_AVX512DQ
    880 #if 0
    881   Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
    882   Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
    883   Packet8f sum = padd(lane0, lane1);
    884   Packet8f tmp0 = _mm256_hadd_ps(sum, _mm256_permute2f128_ps(a, a, 1));
    885   tmp0 = _mm256_hadd_ps(tmp0, tmp0);
    886   return pfirst(_mm256_hadd_ps(tmp0, tmp0));
    887 #else
    888   Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
    889   Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
    890   Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
    891   Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
    892   Packet4f sum = padd(padd(lane0, lane1), padd(lane2, lane3));
    893   sum = _mm_hadd_ps(sum, sum);
    894   sum = _mm_hadd_ps(sum, _mm_permute_ps(sum, 1));
    895   return pfirst(sum);
    896 #endif
    897 }
    898 template <>
    899 EIGEN_STRONG_INLINE double predux<Packet8d>(const Packet8d& a) {
    900   Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
    901   Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
    902   Packet4d sum = padd(lane0, lane1);
    903   Packet4d tmp0 = _mm256_hadd_pd(sum, _mm256_permute2f128_pd(sum, sum, 1));
    904   return pfirst(_mm256_hadd_pd(tmp0, tmp0));
    905 }
    906 
    907 template <>
    908 EIGEN_STRONG_INLINE Packet8f predux_downto4<Packet16f>(const Packet16f& a) {
    909 #ifdef EIGEN_VECTORIZE_AVX512DQ
    910   Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
    911   Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
    912   return padd(lane0, lane1);
    913 #else
    914   Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
    915   Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
    916   Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
    917   Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
    918   Packet4f sum0 = padd(lane0, lane2);
    919   Packet4f sum1 = padd(lane1, lane3);
    920   return _mm256_insertf128_ps(_mm256_castps128_ps256(sum0), sum1, 1);
    921 #endif
    922 }
    923 template <>
    924 EIGEN_STRONG_INLINE Packet4d predux_downto4<Packet8d>(const Packet8d& a) {
    925   Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
    926   Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
    927   Packet4d res = padd(lane0, lane1);
    928   return res;
    929 }
    930 
    931 template <>
    932 EIGEN_STRONG_INLINE float predux_mul<Packet16f>(const Packet16f& a) {
    933 //#ifdef EIGEN_VECTORIZE_AVX512DQ
    934 #if 0
    935   Packet8f lane0 = _mm512_extractf32x8_ps(a, 0);
    936   Packet8f lane1 = _mm512_extractf32x8_ps(a, 1);
    937   Packet8f res = pmul(lane0, lane1);
    938   res = pmul(res, _mm256_permute2f128_ps(res, res, 1));
    939   res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
    940   return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
    941 #else
    942   Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
    943   Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
    944   Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
    945   Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
    946   Packet4f res = pmul(pmul(lane0, lane1), pmul(lane2, lane3));
    947   res = pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
    948   return pfirst(pmul(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
    949 #endif
    950 }
    951 template <>
    952 EIGEN_STRONG_INLINE double predux_mul<Packet8d>(const Packet8d& a) {
    953   Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
    954   Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
    955   Packet4d res = pmul(lane0, lane1);
    956   res = pmul(res, _mm256_permute2f128_pd(res, res, 1));
    957   return pfirst(pmul(res, _mm256_shuffle_pd(res, res, 1)));
    958 }
    959 
    960 template <>
    961 EIGEN_STRONG_INLINE float predux_min<Packet16f>(const Packet16f& a) {
    962   Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
    963   Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
    964   Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
    965   Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
    966   Packet4f res = _mm_min_ps(_mm_min_ps(lane0, lane1), _mm_min_ps(lane2, lane3));
    967   res = _mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
    968   return pfirst(_mm_min_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
    969 }
    970 template <>
    971 EIGEN_STRONG_INLINE double predux_min<Packet8d>(const Packet8d& a) {
    972   Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
    973   Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
    974   Packet4d res = _mm256_min_pd(lane0, lane1);
    975   res = _mm256_min_pd(res, _mm256_permute2f128_pd(res, res, 1));
    976   return pfirst(_mm256_min_pd(res, _mm256_shuffle_pd(res, res, 1)));
    977 }
    978 
    979 template <>
    980 EIGEN_STRONG_INLINE float predux_max<Packet16f>(const Packet16f& a) {
    981   Packet4f lane0 = _mm512_extractf32x4_ps(a, 0);
    982   Packet4f lane1 = _mm512_extractf32x4_ps(a, 1);
    983   Packet4f lane2 = _mm512_extractf32x4_ps(a, 2);
    984   Packet4f lane3 = _mm512_extractf32x4_ps(a, 3);
    985   Packet4f res = _mm_max_ps(_mm_max_ps(lane0, lane1), _mm_max_ps(lane2, lane3));
    986   res = _mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 3, 2)));
    987   return pfirst(_mm_max_ps(res, _mm_permute_ps(res, _MM_SHUFFLE(0, 0, 0, 1))));
    988 }
    989 template <>
    990 EIGEN_STRONG_INLINE double predux_max<Packet8d>(const Packet8d& a) {
    991   Packet4d lane0 = _mm512_extractf64x4_pd(a, 0);
    992   Packet4d lane1 = _mm512_extractf64x4_pd(a, 1);
    993   Packet4d res = _mm256_max_pd(lane0, lane1);
    994   res = _mm256_max_pd(res, _mm256_permute2f128_pd(res, res, 1));
    995   return pfirst(_mm256_max_pd(res, _mm256_shuffle_pd(res, res, 1)));
    996 }
    997 
    998 template <int Offset>
    999 struct palign_impl<Offset, Packet16f> {
   1000   static EIGEN_STRONG_INLINE void run(Packet16f& first,
   1001                                       const Packet16f& second) {
   1002     if (Offset != 0) {
   1003       __m512i first_idx = _mm512_set_epi32(
   1004           Offset + 15, Offset + 14, Offset + 13, Offset + 12, Offset + 11,
   1005           Offset + 10, Offset + 9, Offset + 8, Offset + 7, Offset + 6,
   1006           Offset + 5, Offset + 4, Offset + 3, Offset + 2, Offset + 1, Offset);
   1007 
   1008       __m512i second_idx =
   1009           _mm512_set_epi32(Offset - 1, Offset - 2, Offset - 3, Offset - 4,
   1010                            Offset - 5, Offset - 6, Offset - 7, Offset - 8,
   1011                            Offset - 9, Offset - 10, Offset - 11, Offset - 12,
   1012                            Offset - 13, Offset - 14, Offset - 15, Offset - 16);
   1013 
   1014       unsigned short mask = 0xFFFF;
   1015       mask <<= (16 - Offset);
   1016 
   1017       first = _mm512_permutexvar_ps(first_idx, first);
   1018       Packet16f tmp = _mm512_permutexvar_ps(second_idx, second);
   1019       first = _mm512_mask_blend_ps(mask, first, tmp);
   1020     }
   1021   }
   1022 };
   1023 template <int Offset>
   1024 struct palign_impl<Offset, Packet8d> {
   1025   static EIGEN_STRONG_INLINE void run(Packet8d& first, const Packet8d& second) {
   1026     if (Offset != 0) {
   1027       __m512i first_idx = _mm512_set_epi32(
   1028           0, Offset + 7, 0, Offset + 6, 0, Offset + 5, 0, Offset + 4, 0,
   1029           Offset + 3, 0, Offset + 2, 0, Offset + 1, 0, Offset);
   1030 
   1031       __m512i second_idx = _mm512_set_epi32(
   1032           0, Offset - 1, 0, Offset - 2, 0, Offset - 3, 0, Offset - 4, 0,
   1033           Offset - 5, 0, Offset - 6, 0, Offset - 7, 0, Offset - 8);
   1034 
   1035       unsigned char mask = 0xFF;
   1036       mask <<= (8 - Offset);
   1037 
   1038       first = _mm512_permutexvar_pd(first_idx, first);
   1039       Packet8d tmp = _mm512_permutexvar_pd(second_idx, second);
   1040       first = _mm512_mask_blend_pd(mask, first, tmp);
   1041     }
   1042   }
   1043 };
   1044 
   1045 
   1046 #define PACK_OUTPUT(OUTPUT, INPUT, INDEX, STRIDE) \
   1047   EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[INDEX], INPUT[INDEX + STRIDE]);
   1048 
   1049 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 16>& kernel) {
   1050   __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
   1051   __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
   1052   __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
   1053   __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
   1054   __m512 T4 = _mm512_unpacklo_ps(kernel.packet[4], kernel.packet[5]);
   1055   __m512 T5 = _mm512_unpackhi_ps(kernel.packet[4], kernel.packet[5]);
   1056   __m512 T6 = _mm512_unpacklo_ps(kernel.packet[6], kernel.packet[7]);
   1057   __m512 T7 = _mm512_unpackhi_ps(kernel.packet[6], kernel.packet[7]);
   1058   __m512 T8 = _mm512_unpacklo_ps(kernel.packet[8], kernel.packet[9]);
   1059   __m512 T9 = _mm512_unpackhi_ps(kernel.packet[8], kernel.packet[9]);
   1060   __m512 T10 = _mm512_unpacklo_ps(kernel.packet[10], kernel.packet[11]);
   1061   __m512 T11 = _mm512_unpackhi_ps(kernel.packet[10], kernel.packet[11]);
   1062   __m512 T12 = _mm512_unpacklo_ps(kernel.packet[12], kernel.packet[13]);
   1063   __m512 T13 = _mm512_unpackhi_ps(kernel.packet[12], kernel.packet[13]);
   1064   __m512 T14 = _mm512_unpacklo_ps(kernel.packet[14], kernel.packet[15]);
   1065   __m512 T15 = _mm512_unpackhi_ps(kernel.packet[14], kernel.packet[15]);
   1066   __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
   1067   __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
   1068   __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
   1069   __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
   1070   __m512 S4 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(1, 0, 1, 0));
   1071   __m512 S5 = _mm512_shuffle_ps(T4, T6, _MM_SHUFFLE(3, 2, 3, 2));
   1072   __m512 S6 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(1, 0, 1, 0));
   1073   __m512 S7 = _mm512_shuffle_ps(T5, T7, _MM_SHUFFLE(3, 2, 3, 2));
   1074   __m512 S8 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(1, 0, 1, 0));
   1075   __m512 S9 = _mm512_shuffle_ps(T8, T10, _MM_SHUFFLE(3, 2, 3, 2));
   1076   __m512 S10 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(1, 0, 1, 0));
   1077   __m512 S11 = _mm512_shuffle_ps(T9, T11, _MM_SHUFFLE(3, 2, 3, 2));
   1078   __m512 S12 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(1, 0, 1, 0));
   1079   __m512 S13 = _mm512_shuffle_ps(T12, T14, _MM_SHUFFLE(3, 2, 3, 2));
   1080   __m512 S14 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(1, 0, 1, 0));
   1081   __m512 S15 = _mm512_shuffle_ps(T13, T15, _MM_SHUFFLE(3, 2, 3, 2));
   1082 
   1083   EIGEN_EXTRACT_8f_FROM_16f(S0, S0);
   1084   EIGEN_EXTRACT_8f_FROM_16f(S1, S1);
   1085   EIGEN_EXTRACT_8f_FROM_16f(S2, S2);
   1086   EIGEN_EXTRACT_8f_FROM_16f(S3, S3);
   1087   EIGEN_EXTRACT_8f_FROM_16f(S4, S4);
   1088   EIGEN_EXTRACT_8f_FROM_16f(S5, S5);
   1089   EIGEN_EXTRACT_8f_FROM_16f(S6, S6);
   1090   EIGEN_EXTRACT_8f_FROM_16f(S7, S7);
   1091   EIGEN_EXTRACT_8f_FROM_16f(S8, S8);
   1092   EIGEN_EXTRACT_8f_FROM_16f(S9, S9);
   1093   EIGEN_EXTRACT_8f_FROM_16f(S10, S10);
   1094   EIGEN_EXTRACT_8f_FROM_16f(S11, S11);
   1095   EIGEN_EXTRACT_8f_FROM_16f(S12, S12);
   1096   EIGEN_EXTRACT_8f_FROM_16f(S13, S13);
   1097   EIGEN_EXTRACT_8f_FROM_16f(S14, S14);
   1098   EIGEN_EXTRACT_8f_FROM_16f(S15, S15);
   1099 
   1100   PacketBlock<Packet8f, 32> tmp;
   1101 
   1102   tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S4_0, 0x20);
   1103   tmp.packet[1] = _mm256_permute2f128_ps(S1_0, S5_0, 0x20);
   1104   tmp.packet[2] = _mm256_permute2f128_ps(S2_0, S6_0, 0x20);
   1105   tmp.packet[3] = _mm256_permute2f128_ps(S3_0, S7_0, 0x20);
   1106   tmp.packet[4] = _mm256_permute2f128_ps(S0_0, S4_0, 0x31);
   1107   tmp.packet[5] = _mm256_permute2f128_ps(S1_0, S5_0, 0x31);
   1108   tmp.packet[6] = _mm256_permute2f128_ps(S2_0, S6_0, 0x31);
   1109   tmp.packet[7] = _mm256_permute2f128_ps(S3_0, S7_0, 0x31);
   1110 
   1111   tmp.packet[8] = _mm256_permute2f128_ps(S0_1, S4_1, 0x20);
   1112   tmp.packet[9] = _mm256_permute2f128_ps(S1_1, S5_1, 0x20);
   1113   tmp.packet[10] = _mm256_permute2f128_ps(S2_1, S6_1, 0x20);
   1114   tmp.packet[11] = _mm256_permute2f128_ps(S3_1, S7_1, 0x20);
   1115   tmp.packet[12] = _mm256_permute2f128_ps(S0_1, S4_1, 0x31);
   1116   tmp.packet[13] = _mm256_permute2f128_ps(S1_1, S5_1, 0x31);
   1117   tmp.packet[14] = _mm256_permute2f128_ps(S2_1, S6_1, 0x31);
   1118   tmp.packet[15] = _mm256_permute2f128_ps(S3_1, S7_1, 0x31);
   1119 
   1120   // Second set of _m256 outputs
   1121   tmp.packet[16] = _mm256_permute2f128_ps(S8_0, S12_0, 0x20);
   1122   tmp.packet[17] = _mm256_permute2f128_ps(S9_0, S13_0, 0x20);
   1123   tmp.packet[18] = _mm256_permute2f128_ps(S10_0, S14_0, 0x20);
   1124   tmp.packet[19] = _mm256_permute2f128_ps(S11_0, S15_0, 0x20);
   1125   tmp.packet[20] = _mm256_permute2f128_ps(S8_0, S12_0, 0x31);
   1126   tmp.packet[21] = _mm256_permute2f128_ps(S9_0, S13_0, 0x31);
   1127   tmp.packet[22] = _mm256_permute2f128_ps(S10_0, S14_0, 0x31);
   1128   tmp.packet[23] = _mm256_permute2f128_ps(S11_0, S15_0, 0x31);
   1129 
   1130   tmp.packet[24] = _mm256_permute2f128_ps(S8_1, S12_1, 0x20);
   1131   tmp.packet[25] = _mm256_permute2f128_ps(S9_1, S13_1, 0x20);
   1132   tmp.packet[26] = _mm256_permute2f128_ps(S10_1, S14_1, 0x20);
   1133   tmp.packet[27] = _mm256_permute2f128_ps(S11_1, S15_1, 0x20);
   1134   tmp.packet[28] = _mm256_permute2f128_ps(S8_1, S12_1, 0x31);
   1135   tmp.packet[29] = _mm256_permute2f128_ps(S9_1, S13_1, 0x31);
   1136   tmp.packet[30] = _mm256_permute2f128_ps(S10_1, S14_1, 0x31);
   1137   tmp.packet[31] = _mm256_permute2f128_ps(S11_1, S15_1, 0x31);
   1138 
   1139   // Pack them into the output
   1140   PACK_OUTPUT(kernel.packet, tmp.packet, 0, 16);
   1141   PACK_OUTPUT(kernel.packet, tmp.packet, 1, 16);
   1142   PACK_OUTPUT(kernel.packet, tmp.packet, 2, 16);
   1143   PACK_OUTPUT(kernel.packet, tmp.packet, 3, 16);
   1144 
   1145   PACK_OUTPUT(kernel.packet, tmp.packet, 4, 16);
   1146   PACK_OUTPUT(kernel.packet, tmp.packet, 5, 16);
   1147   PACK_OUTPUT(kernel.packet, tmp.packet, 6, 16);
   1148   PACK_OUTPUT(kernel.packet, tmp.packet, 7, 16);
   1149 
   1150   PACK_OUTPUT(kernel.packet, tmp.packet, 8, 16);
   1151   PACK_OUTPUT(kernel.packet, tmp.packet, 9, 16);
   1152   PACK_OUTPUT(kernel.packet, tmp.packet, 10, 16);
   1153   PACK_OUTPUT(kernel.packet, tmp.packet, 11, 16);
   1154 
   1155   PACK_OUTPUT(kernel.packet, tmp.packet, 12, 16);
   1156   PACK_OUTPUT(kernel.packet, tmp.packet, 13, 16);
   1157   PACK_OUTPUT(kernel.packet, tmp.packet, 14, 16);
   1158   PACK_OUTPUT(kernel.packet, tmp.packet, 15, 16);
   1159 }
   1160 #define PACK_OUTPUT_2(OUTPUT, INPUT, INDEX, STRIDE)         \
   1161   EIGEN_INSERT_8f_INTO_16f(OUTPUT[INDEX], INPUT[2 * INDEX], \
   1162                            INPUT[2 * INDEX + STRIDE]);
   1163 
   1164 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet16f, 4>& kernel) {
   1165   __m512 T0 = _mm512_unpacklo_ps(kernel.packet[0], kernel.packet[1]);
   1166   __m512 T1 = _mm512_unpackhi_ps(kernel.packet[0], kernel.packet[1]);
   1167   __m512 T2 = _mm512_unpacklo_ps(kernel.packet[2], kernel.packet[3]);
   1168   __m512 T3 = _mm512_unpackhi_ps(kernel.packet[2], kernel.packet[3]);
   1169 
   1170   __m512 S0 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(1, 0, 1, 0));
   1171   __m512 S1 = _mm512_shuffle_ps(T0, T2, _MM_SHUFFLE(3, 2, 3, 2));
   1172   __m512 S2 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(1, 0, 1, 0));
   1173   __m512 S3 = _mm512_shuffle_ps(T1, T3, _MM_SHUFFLE(3, 2, 3, 2));
   1174 
   1175   EIGEN_EXTRACT_8f_FROM_16f(S0, S0);
   1176   EIGEN_EXTRACT_8f_FROM_16f(S1, S1);
   1177   EIGEN_EXTRACT_8f_FROM_16f(S2, S2);
   1178   EIGEN_EXTRACT_8f_FROM_16f(S3, S3);
   1179 
   1180   PacketBlock<Packet8f, 8> tmp;
   1181 
   1182   tmp.packet[0] = _mm256_permute2f128_ps(S0_0, S1_0, 0x20);
   1183   tmp.packet[1] = _mm256_permute2f128_ps(S2_0, S3_0, 0x20);
   1184   tmp.packet[2] = _mm256_permute2f128_ps(S0_0, S1_0, 0x31);
   1185   tmp.packet[3] = _mm256_permute2f128_ps(S2_0, S3_0, 0x31);
   1186 
   1187   tmp.packet[4] = _mm256_permute2f128_ps(S0_1, S1_1, 0x20);
   1188   tmp.packet[5] = _mm256_permute2f128_ps(S2_1, S3_1, 0x20);
   1189   tmp.packet[6] = _mm256_permute2f128_ps(S0_1, S1_1, 0x31);
   1190   tmp.packet[7] = _mm256_permute2f128_ps(S2_1, S3_1, 0x31);
   1191 
   1192   PACK_OUTPUT_2(kernel.packet, tmp.packet, 0, 1);
   1193   PACK_OUTPUT_2(kernel.packet, tmp.packet, 1, 1);
   1194   PACK_OUTPUT_2(kernel.packet, tmp.packet, 2, 1);
   1195   PACK_OUTPUT_2(kernel.packet, tmp.packet, 3, 1);
   1196 }
   1197 
   1198 #define PACK_OUTPUT_SQ_D(OUTPUT, INPUT, INDEX, STRIDE)                \
   1199   OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX], 0); \
   1200   OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[INDEX + STRIDE], 1);
   1201 
   1202 #define PACK_OUTPUT_D(OUTPUT, INPUT, INDEX, STRIDE)                         \
   1203   OUTPUT[INDEX] = _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX)], 0); \
   1204   OUTPUT[INDEX] =                                                           \
   1205       _mm512_insertf64x4(OUTPUT[INDEX], INPUT[(2 * INDEX) + STRIDE], 1);
   1206 
   1207 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 4>& kernel) {
   1208   __m512d T0 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0);
   1209   __m512d T1 = _mm512_shuffle_pd(kernel.packet[0], kernel.packet[1], 0xff);
   1210   __m512d T2 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0);
   1211   __m512d T3 = _mm512_shuffle_pd(kernel.packet[2], kernel.packet[3], 0xff);
   1212 
   1213   PacketBlock<Packet4d, 8> tmp;
   1214 
   1215   tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
   1216                                          _mm512_extractf64x4_pd(T2, 0), 0x20);
   1217   tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
   1218                                          _mm512_extractf64x4_pd(T3, 0), 0x20);
   1219   tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
   1220                                          _mm512_extractf64x4_pd(T2, 0), 0x31);
   1221   tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
   1222                                          _mm512_extractf64x4_pd(T3, 0), 0x31);
   1223 
   1224   tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
   1225                                          _mm512_extractf64x4_pd(T2, 1), 0x20);
   1226   tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
   1227                                          _mm512_extractf64x4_pd(T3, 1), 0x20);
   1228   tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
   1229                                          _mm512_extractf64x4_pd(T2, 1), 0x31);
   1230   tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
   1231                                          _mm512_extractf64x4_pd(T3, 1), 0x31);
   1232 
   1233   PACK_OUTPUT_D(kernel.packet, tmp.packet, 0, 1);
   1234   PACK_OUTPUT_D(kernel.packet, tmp.packet, 1, 1);
   1235   PACK_OUTPUT_D(kernel.packet, tmp.packet, 2, 1);
   1236   PACK_OUTPUT_D(kernel.packet, tmp.packet, 3, 1);
   1237 }
   1238 
   1239 EIGEN_DEVICE_FUNC inline void ptranspose(PacketBlock<Packet8d, 8>& kernel) {
   1240   __m512d T0 = _mm512_unpacklo_pd(kernel.packet[0], kernel.packet[1]);
   1241   __m512d T1 = _mm512_unpackhi_pd(kernel.packet[0], kernel.packet[1]);
   1242   __m512d T2 = _mm512_unpacklo_pd(kernel.packet[2], kernel.packet[3]);
   1243   __m512d T3 = _mm512_unpackhi_pd(kernel.packet[2], kernel.packet[3]);
   1244   __m512d T4 = _mm512_unpacklo_pd(kernel.packet[4], kernel.packet[5]);
   1245   __m512d T5 = _mm512_unpackhi_pd(kernel.packet[4], kernel.packet[5]);
   1246   __m512d T6 = _mm512_unpacklo_pd(kernel.packet[6], kernel.packet[7]);
   1247   __m512d T7 = _mm512_unpackhi_pd(kernel.packet[6], kernel.packet[7]);
   1248 
   1249   PacketBlock<Packet4d, 16> tmp;
   1250 
   1251   tmp.packet[0] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
   1252                                          _mm512_extractf64x4_pd(T2, 0), 0x20);
   1253   tmp.packet[1] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
   1254                                          _mm512_extractf64x4_pd(T3, 0), 0x20);
   1255   tmp.packet[2] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 0),
   1256                                          _mm512_extractf64x4_pd(T2, 0), 0x31);
   1257   tmp.packet[3] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 0),
   1258                                          _mm512_extractf64x4_pd(T3, 0), 0x31);
   1259 
   1260   tmp.packet[4] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
   1261                                          _mm512_extractf64x4_pd(T2, 1), 0x20);
   1262   tmp.packet[5] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
   1263                                          _mm512_extractf64x4_pd(T3, 1), 0x20);
   1264   tmp.packet[6] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T0, 1),
   1265                                          _mm512_extractf64x4_pd(T2, 1), 0x31);
   1266   tmp.packet[7] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T1, 1),
   1267                                          _mm512_extractf64x4_pd(T3, 1), 0x31);
   1268 
   1269   tmp.packet[8] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0),
   1270                                          _mm512_extractf64x4_pd(T6, 0), 0x20);
   1271   tmp.packet[9] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0),
   1272                                          _mm512_extractf64x4_pd(T7, 0), 0x20);
   1273   tmp.packet[10] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 0),
   1274                                           _mm512_extractf64x4_pd(T6, 0), 0x31);
   1275   tmp.packet[11] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 0),
   1276                                           _mm512_extractf64x4_pd(T7, 0), 0x31);
   1277 
   1278   tmp.packet[12] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1),
   1279                                           _mm512_extractf64x4_pd(T6, 1), 0x20);
   1280   tmp.packet[13] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1),
   1281                                           _mm512_extractf64x4_pd(T7, 1), 0x20);
   1282   tmp.packet[14] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T4, 1),
   1283                                           _mm512_extractf64x4_pd(T6, 1), 0x31);
   1284   tmp.packet[15] = _mm256_permute2f128_pd(_mm512_extractf64x4_pd(T5, 1),
   1285                                           _mm512_extractf64x4_pd(T7, 1), 0x31);
   1286 
   1287   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 0, 8);
   1288   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 1, 8);
   1289   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 2, 8);
   1290   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 3, 8);
   1291 
   1292   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 4, 8);
   1293   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 5, 8);
   1294   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 6, 8);
   1295   PACK_OUTPUT_SQ_D(kernel.packet, tmp.packet, 7, 8);
   1296 }
   1297 template <>
   1298 EIGEN_STRONG_INLINE Packet16f pblend(const Selector<16>& /*ifPacket*/,
   1299                                      const Packet16f& /*thenPacket*/,
   1300                                      const Packet16f& /*elsePacket*/) {
   1301   assert(false && "To be implemented");
   1302   return Packet16f();
   1303 }
   1304 template <>
   1305 EIGEN_STRONG_INLINE Packet8d pblend(const Selector<8>& /*ifPacket*/,
   1306                                     const Packet8d& /*thenPacket*/,
   1307                                     const Packet8d& /*elsePacket*/) {
   1308   assert(false && "To be implemented");
   1309   return Packet8d();
   1310 }
   1311 
   1312 } // end namespace internal
   1313 
   1314 } // end namespace Eigen
   1315 
   1316 #endif // EIGEN_PACKET_MATH_AVX512_H
   1317