PacketMath.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
// Heavily based on Gael's SSE version.
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_PACKET_MATH_NEON_H
#define EIGEN_PACKET_MATH_NEON_H
 
// IWYU pragma: private
#include "../../InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
#endif
 
#ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
#endif
 
#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
#if EIGEN_ARCH_ARM64
#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
#else
#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
#endif
#endif
 
#if EIGEN_COMP_MSVC_STRICT
 
// In MSVC's arm_neon.h header file, all NEON vector types
// are aliases to the same underlying type __n128.
// We thus have to wrap them to make them different C++ types.
// (See also bug 1428)
typedef eigen_packet_wrapper<float32x2_t, 0> Packet2f;
typedef eigen_packet_wrapper<float32x4_t, 1> Packet4f;
typedef eigen_packet_wrapper<int32_t, 2> Packet4c;
typedef eigen_packet_wrapper<int8x8_t, 3> Packet8c;
typedef eigen_packet_wrapper<int8x16_t, 4> Packet16c;
typedef eigen_packet_wrapper<uint32_t, 5> Packet4uc;
typedef eigen_packet_wrapper<uint8x8_t, 6> Packet8uc;
typedef eigen_packet_wrapper<uint8x16_t, 7> Packet16uc;
typedef eigen_packet_wrapper<int16x4_t, 8> Packet4s;
typedef eigen_packet_wrapper<int16x8_t, 9> Packet8s;
typedef eigen_packet_wrapper<uint16x4_t, 10> Packet4us;
typedef eigen_packet_wrapper<uint16x8_t, 11> Packet8us;
typedef eigen_packet_wrapper<int32x2_t, 12> Packet2i;
typedef eigen_packet_wrapper<int32x4_t, 13> Packet4i;
typedef eigen_packet_wrapper<uint32x2_t, 14> Packet2ui;
typedef eigen_packet_wrapper<uint32x4_t, 15> Packet4ui;
typedef eigen_packet_wrapper<int64x2_t, 16> Packet2l;
typedef eigen_packet_wrapper<uint64x2_t, 17> Packet2ul;
 
EIGEN_ALWAYS_INLINE Packet4f make_packet4f(float a, float b, float c, float d) {
  float from[4] = {a, b, c, d};
  return vld1q_f32(from);
}
 
EIGEN_ALWAYS_INLINE Packet2f make_packet2f(float a, float b) {
  float from[2] = {a, b};
  return vld1_f32(from);
}
 
#else
 
typedef float32x2_t Packet2f;
typedef float32x4_t Packet4f;
typedef eigen_packet_wrapper<int32_t, 2> Packet4c;
typedef int8x8_t Packet8c;
typedef int8x16_t Packet16c;
typedef eigen_packet_wrapper<uint32_t, 5> Packet4uc;
typedef uint8x8_t Packet8uc;
typedef uint8x16_t Packet16uc;
typedef int16x4_t Packet4s;
typedef int16x8_t Packet8s;
typedef uint16x4_t Packet4us;
typedef uint16x8_t Packet8us;
typedef int32x2_t Packet2i;
typedef int32x4_t Packet4i;
typedef uint32x2_t Packet2ui;
typedef uint32x4_t Packet4ui;
typedef int64x2_t Packet2l;
typedef uint64x2_t Packet2ul;
 
EIGEN_ALWAYS_INLINE Packet4f make_packet4f(float a, float b, float c, float d) { return Packet4f{a, b, c, d}; }
EIGEN_ALWAYS_INLINE Packet2f make_packet2f(float a, float b) { return Packet2f{a, b}; }
 
#endif  // EIGEN_COMP_MSVC_STRICT
 
EIGEN_STRONG_INLINE Packet4f shuffle1(const Packet4f& m, int mask) {
  const float* a = reinterpret_cast<const float*>(&m);
  Packet4f res =
      make_packet4f(*(a + (mask & 3)), *(a + ((mask >> 2) & 3)), *(a + ((mask >> 4) & 3)), *(a + ((mask >> 6) & 3)));
  return res;
}
 
// functionally equivalent to _mm_shuffle_ps in SSE when interleave
// == false (i.e. shuffle<false>(m, n, mask) equals _mm_shuffle_ps(m, n, mask)),
// interleave m and n when interleave == true. Currently used in LU/arch/InverseSize4.h
// to enable a shared implementation for fast inversion of matrices of size 4.
template <bool interleave>
EIGEN_STRONG_INLINE Packet4f shuffle2(const Packet4f& m, const Packet4f& n, int mask) {
  const float* a = reinterpret_cast<const float*>(&m);
  const float* b = reinterpret_cast<const float*>(&n);
  Packet4f res =
      make_packet4f(*(a + (mask & 3)), *(a + ((mask >> 2) & 3)), *(b + ((mask >> 4) & 3)), *(b + ((mask >> 6) & 3)));
  return res;
}
 
template <>
EIGEN_STRONG_INLINE Packet4f shuffle2<true>(const Packet4f& m, const Packet4f& n, int mask) {
  const float* a = reinterpret_cast<const float*>(&m);
  const float* b = reinterpret_cast<const float*>(&n);
  Packet4f res =
      make_packet4f(*(a + (mask & 3)), *(b + ((mask >> 2) & 3)), *(a + ((mask >> 4) & 3)), *(b + ((mask >> 6) & 3)));
  return res;
}
 
EIGEN_STRONG_INLINE static int eigen_neon_shuffle_mask(int p, int q, int r, int s) {
  return ((s) << 6 | (r) << 4 | (q) << 2 | (p));
}
 
EIGEN_STRONG_INLINE Packet4f vec4f_swizzle1(const Packet4f& a, int p, int q, int r, int s) {
  return shuffle1(a, eigen_neon_shuffle_mask(p, q, r, s));
}
EIGEN_STRONG_INLINE Packet4f vec4f_swizzle2(const Packet4f& a, const Packet4f& b, int p, int q, int r, int s) {
  return shuffle2<false>(a, b, eigen_neon_shuffle_mask(p, q, r, s));
}
EIGEN_STRONG_INLINE Packet4f vec4f_movelh(const Packet4f& a, const Packet4f& b) {
  return shuffle2<false>(a, b, eigen_neon_shuffle_mask(0, 1, 0, 1));
}
EIGEN_STRONG_INLINE Packet4f vec4f_movehl(const Packet4f& a, const Packet4f& b) {
  return shuffle2<false>(b, a, eigen_neon_shuffle_mask(2, 3, 2, 3));
}
EIGEN_STRONG_INLINE Packet4f vec4f_unpacklo(const Packet4f& a, const Packet4f& b) {
  return shuffle2<true>(a, b, eigen_neon_shuffle_mask(0, 0, 1, 1));
}
EIGEN_STRONG_INLINE Packet4f vec4f_unpackhi(const Packet4f& a, const Packet4f& b) {
  return shuffle2<true>(a, b, eigen_neon_shuffle_mask(2, 2, 3, 3));
}
#define vec4f_duplane(a, p) Packet4f(vdupq_lane_f32(vget_low_f32(a), p))
 
#define EIGEN_DECLARE_CONST_Packet4f(NAME, X) const Packet4f p4f_##NAME = pset1<Packet4f>(X)
 
#define EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME, X) \
  const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int32_t>(X))
 
#define EIGEN_DECLARE_CONST_Packet4i(NAME, X) const Packet4i p4i_##NAME = pset1<Packet4i>(X)
 
#if EIGEN_ARCH_ARM64 && EIGEN_COMP_GNUC
// __builtin_prefetch tends to do nothing on ARM64 compilers because the
// prefetch instructions there are too detailed for __builtin_prefetch to map
// meaningfully to them.
#define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__("prfm pldl1keep, [%[addr]]\n" ::[addr] "r"(ADDR) :);
#elif EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
#define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
#elif defined __pld
#define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
#elif EIGEN_ARCH_ARM
#define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__("pld [%[addr]]\n" ::[addr] "r"(ADDR) :);
#else
// by default no explicit prefetching
#define EIGEN_ARM_PREFETCH(ADDR)
#endif
 
template <>
struct packet_traits<float> : default_packet_traits {
  typedef Packet4f type;
  typedef Packet2f half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
    HasDiv = 1,
    HasSin = EIGEN_FAST_MATH,
    HasCos = EIGEN_FAST_MATH,
    HasTan = EIGEN_FAST_MATH,
    HasACos = 1,
    HasASin = 1,
    HasATan = 1,
    HasATanh = 1,
    HasSinh = 1,
    HasCosh = 1,
    HasASinh = 1,
    HasACosh = 1,
    HasLog = 1,
    HasLog10 = 1,
    HasExp = 1,
    HasLog1p = 1,
    HasExpm1 = 1,
    HasPow = 1,
    HasSqrt = 1,
    HasRsqrt = 1,
    HasCbrt = 1,
    HasTanh = EIGEN_FAST_MATH,
    HasErf = EIGEN_FAST_MATH,
    HasErfc = EIGEN_FAST_MATH,
    HasBessel = 0,  // Issues with accuracy.
    HasNdtri = 0
  };
};
 
template <>
struct packet_traits<int8_t> : default_packet_traits {
  typedef Packet16c type;
  typedef Packet8c half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 16,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasAbsDiff = 1,
    HasArg = 0,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
  };
};
 
template <>
struct packet_traits<uint8_t> : default_packet_traits {
  typedef Packet16uc type;
  typedef Packet8uc half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 16,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 0,
    HasAbs = 1,
    HasAbsDiff = 1,
    HasArg = 0,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
 
    HasSqrt = 1
  };
};
 
template <>
struct packet_traits<int16_t> : default_packet_traits {
  typedef Packet8s type;
  typedef Packet4s half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 8,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasAbsDiff = 1,
    HasArg = 0,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
  };
};
 
template <>
struct packet_traits<uint16_t> : default_packet_traits {
  typedef Packet8us type;
  typedef Packet4us half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 8,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 0,
    HasAbs = 1,
    HasAbsDiff = 1,
    HasArg = 0,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
    HasSqrt = 1
  };
};
 
template <>
struct packet_traits<int32_t> : default_packet_traits {
  typedef Packet4i type;
  typedef Packet2i half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
  };
};
 
template <>
struct packet_traits<uint32_t> : default_packet_traits {
  typedef Packet4ui type;
  typedef Packet2ui half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 0,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
 
    HasSqrt = 1
  };
};
 
template <>
struct packet_traits<int64_t> : default_packet_traits {
  typedef Packet2l type;
  typedef Packet2l half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 2,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
  };
};
 
template <>
struct packet_traits<uint64_t> : default_packet_traits {
  typedef Packet2ul type;
  typedef Packet2ul half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 2,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 0,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
  };
};
 
template <typename Packet, typename Scalar>
struct neon_unpacket_default {
  using type = Scalar;
  using half = Packet;
  static constexpr int size = sizeof(Packet) / sizeof(Scalar);
  static constexpr int alignment = sizeof(Packet);
  static constexpr bool vectorizable = true;
  static constexpr bool masked_load_available = false;
  static constexpr bool masked_store_available = false;
};
 
template <>
struct unpacket_traits<Packet2f> : neon_unpacket_default<Packet2f, float> {
  using integer_packet = Packet2i;
};
template <>
struct unpacket_traits<Packet4f> : neon_unpacket_default<Packet4f, float> {
  using half = Packet2f;
  using integer_packet = Packet4i;
};
template <>
struct unpacket_traits<Packet4c> : neon_unpacket_default<Packet4c, int8_t> {};
template <>
struct unpacket_traits<Packet8c> : neon_unpacket_default<Packet8c, int8_t> {
  using half = Packet4c;
};
template <>
struct unpacket_traits<Packet16c> : neon_unpacket_default<Packet16c, int8_t> {
  using half = Packet8c;
};
template <>
struct unpacket_traits<Packet4uc> : neon_unpacket_default<Packet4uc, uint8_t> {};
template <>
struct unpacket_traits<Packet8uc> : neon_unpacket_default<Packet8uc, uint8_t> {
  using half = Packet4uc;
};
template <>
struct unpacket_traits<Packet16uc> : neon_unpacket_default<Packet16uc, uint8_t> {
  using half = Packet8uc;
};
template <>
struct unpacket_traits<Packet4s> : neon_unpacket_default<Packet4s, int16_t> {};
template <>
struct unpacket_traits<Packet8s> : neon_unpacket_default<Packet8s, int16_t> {
  using half = Packet4s;
};
template <>
struct unpacket_traits<Packet4us> : neon_unpacket_default<Packet4us, uint16_t> {};
template <>
struct unpacket_traits<Packet8us> : neon_unpacket_default<Packet8us, uint16_t> {
  using half = Packet4us;
};
template <>
struct unpacket_traits<Packet2i> : neon_unpacket_default<Packet2i, int32_t> {};
template <>
struct unpacket_traits<Packet4i> : neon_unpacket_default<Packet4i, int32_t> {
  using half = Packet2i;
};
template <>
struct unpacket_traits<Packet2ui> : neon_unpacket_default<Packet2ui, uint32_t> {};
template <>
struct unpacket_traits<Packet4ui> : neon_unpacket_default<Packet4ui, uint32_t> {
  using half = Packet2ui;
};
template <>
struct unpacket_traits<Packet2l> : neon_unpacket_default<Packet2l, int64_t> {};
template <>
struct unpacket_traits<Packet2ul> : neon_unpacket_default<Packet2ul, uint64_t> {};
 
template <>
EIGEN_STRONG_INLINE Packet2f pzero(const Packet2f& /*a*/) {
  return vdup_n_f32(0.0f);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f pzero(const Packet4f& /*a*/) {
  return vdupq_n_f32(0.0f);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pset1<Packet2f>(const float& from) {
  return vdup_n_f32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) {
  return vdupq_n_f32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4c pset1<Packet4c>(const int8_t& from) {
  return vget_lane_s32(vreinterpret_s32_s8(vdup_n_s8(from)), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pset1<Packet8c>(const int8_t& from) {
  return vdup_n_s8(from);
}
template <>
EIGEN_STRONG_INLINE Packet16c pset1<Packet16c>(const int8_t& from) {
  return vdupq_n_s8(from);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pset1<Packet4uc>(const uint8_t& from) {
  return vget_lane_u32(vreinterpret_u32_u8(vdup_n_u8(from)), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pset1<Packet8uc>(const uint8_t& from) {
  return vdup_n_u8(from);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pset1<Packet16uc>(const uint8_t& from) {
  return vdupq_n_u8(from);
}
template <>
EIGEN_STRONG_INLINE Packet4s pset1<Packet4s>(const int16_t& from) {
  return vdup_n_s16(from);
}
template <>
EIGEN_STRONG_INLINE Packet8s pset1<Packet8s>(const int16_t& from) {
  return vdupq_n_s16(from);
}
template <>
EIGEN_STRONG_INLINE Packet4us pset1<Packet4us>(const uint16_t& from) {
  return vdup_n_u16(from);
}
template <>
EIGEN_STRONG_INLINE Packet8us pset1<Packet8us>(const uint16_t& from) {
  return vdupq_n_u16(from);
}
template <>
EIGEN_STRONG_INLINE Packet2i pset1<Packet2i>(const int32_t& from) {
  return vdup_n_s32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int32_t& from) {
  return vdupq_n_s32(from);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pset1<Packet2ui>(const uint32_t& from) {
  return vdup_n_u32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pset1<Packet4ui>(const uint32_t& from) {
  return vdupq_n_u32(from);
}
template <>
EIGEN_STRONG_INLINE Packet2l pset1<Packet2l>(const int64_t& from) {
  return vdupq_n_s64(from);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pset1<Packet2ul>(const uint64_t& from) {
  return vdupq_n_u64(from);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pset1frombits<Packet2f>(uint32_t from) {
  return vreinterpret_f32_u32(vdup_n_u32(from));
}
template <>
EIGEN_STRONG_INLINE Packet4f pset1frombits<Packet4f>(uint32_t from) {
  return vreinterpretq_f32_u32(vdupq_n_u32(from));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f plset<Packet2f>(const float& a) {
  const float c[] = {0.0f, 1.0f};
  return vadd_f32(pset1<Packet2f>(a), vld1_f32(c));
}
template <>
EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a) {
  const float c[] = {0.0f, 1.0f, 2.0f, 3.0f};
  return vaddq_f32(pset1<Packet4f>(a), vld1q_f32(c));
}
template <>
EIGEN_STRONG_INLINE Packet4c plset<Packet4c>(const int8_t& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vadd_s8(vreinterpret_s8_u32(vdup_n_u32(0x03020100)), vdup_n_s8(a))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c plset<Packet8c>(const int8_t& a) {
  const int8_t c[] = {0, 1, 2, 3, 4, 5, 6, 7};
  return vadd_s8(pset1<Packet8c>(a), vld1_s8(c));
}
template <>
EIGEN_STRONG_INLINE Packet16c plset<Packet16c>(const int8_t& a) {
  const int8_t c[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
  return vaddq_s8(pset1<Packet16c>(a), vld1q_s8(c));
}
template <>
EIGEN_STRONG_INLINE Packet4uc plset<Packet4uc>(const uint8_t& a) {
  return vget_lane_u32(vreinterpret_u32_u8(vadd_u8(vreinterpret_u8_u32(vdup_n_u32(0x03020100)), vdup_n_u8(a))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc plset<Packet8uc>(const uint8_t& a) {
  const uint8_t c[] = {0, 1, 2, 3, 4, 5, 6, 7};
  return vadd_u8(pset1<Packet8uc>(a), vld1_u8(c));
}
template <>
EIGEN_STRONG_INLINE Packet16uc plset<Packet16uc>(const uint8_t& a) {
  const uint8_t c[] = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15};
  return vaddq_u8(pset1<Packet16uc>(a), vld1q_u8(c));
}
template <>
EIGEN_STRONG_INLINE Packet4s plset<Packet4s>(const int16_t& a) {
  const int16_t c[] = {0, 1, 2, 3};
  return vadd_s16(pset1<Packet4s>(a), vld1_s16(c));
}
template <>
EIGEN_STRONG_INLINE Packet4us plset<Packet4us>(const uint16_t& a) {
  const uint16_t c[] = {0, 1, 2, 3};
  return vadd_u16(pset1<Packet4us>(a), vld1_u16(c));
}
template <>
EIGEN_STRONG_INLINE Packet8s plset<Packet8s>(const int16_t& a) {
  const int16_t c[] = {0, 1, 2, 3, 4, 5, 6, 7};
  return vaddq_s16(pset1<Packet8s>(a), vld1q_s16(c));
}
template <>
EIGEN_STRONG_INLINE Packet8us plset<Packet8us>(const uint16_t& a) {
  const uint16_t c[] = {0, 1, 2, 3, 4, 5, 6, 7};
  return vaddq_u16(pset1<Packet8us>(a), vld1q_u16(c));
}
template <>
EIGEN_STRONG_INLINE Packet2i plset<Packet2i>(const int32_t& a) {
  const int32_t c[] = {0, 1};
  return vadd_s32(pset1<Packet2i>(a), vld1_s32(c));
}
template <>
EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int32_t& a) {
  const int32_t c[] = {0, 1, 2, 3};
  return vaddq_s32(pset1<Packet4i>(a), vld1q_s32(c));
}
template <>
EIGEN_STRONG_INLINE Packet2ui plset<Packet2ui>(const uint32_t& a) {
  const uint32_t c[] = {0, 1};
  return vadd_u32(pset1<Packet2ui>(a), vld1_u32(c));
}
template <>
EIGEN_STRONG_INLINE Packet4ui plset<Packet4ui>(const uint32_t& a) {
  const uint32_t c[] = {0, 1, 2, 3};
  return vaddq_u32(pset1<Packet4ui>(a), vld1q_u32(c));
}
template <>
EIGEN_STRONG_INLINE Packet2l plset<Packet2l>(const int64_t& a) {
  const int64_t c[] = {0, 1};
  return vaddq_s64(pset1<Packet2l>(a), vld1q_s64(c));
}
template <>
EIGEN_STRONG_INLINE Packet2ul plset<Packet2ul>(const uint64_t& a) {
  const uint64_t c[] = {0, 1};
  return vaddq_u64(pset1<Packet2ul>(a), vld1q_u64(c));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f padd<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vadd_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vaddq_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4c padd<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vadd_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c padd<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vadd_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c padd<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vaddq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc padd<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vadd_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc padd<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vadd_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc padd<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vaddq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s padd<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vadd_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s padd<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vaddq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us padd<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vadd_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us padd<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vaddq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i padd<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vadd_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vaddq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui padd<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vadd_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui padd<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vaddq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l padd<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vaddq_s64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul padd<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vaddq_u64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f psub<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vsub_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vsubq_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4c psub<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vsub_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c psub<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vsub_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c psub<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vsubq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc psub<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vsub_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc psub<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vsub_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc psub<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vsubq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s psub<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vsub_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s psub<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vsubq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us psub<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vsub_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us psub<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vsubq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i psub<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vsub_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vsubq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui psub<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vsub_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui psub<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vsubq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l psub<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vsubq_s64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul psub<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vsubq_u64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pxor<Packet2f>(const Packet2f& a, const Packet2f& b);
template <>
EIGEN_STRONG_INLINE Packet2f paddsub<Packet2f>(const Packet2f& a, const Packet2f& b) {
  Packet2f mask = make_packet2f(numext::bit_cast<float>(0x80000000u), 0.0f);
  return padd(a, pxor(mask, b));
}
template <>
EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b);
template <>
EIGEN_STRONG_INLINE Packet4f paddsub<Packet4f>(const Packet4f& a, const Packet4f& b) {
  Packet4f mask = make_packet4f(numext::bit_cast<float>(0x80000000u), 0.0f, numext::bit_cast<float>(0x80000000u), 0.0f);
  return padd(a, pxor(mask, b));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pnegate(const Packet2f& a) {
  return vneg_f32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) {
  return vnegq_f32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4c pnegate(const Packet4c& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vneg_s8(vreinterpret_s8_s32(vdup_n_s32(a)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pnegate(const Packet8c& a) {
  return vneg_s8(a);
}
template <>
EIGEN_STRONG_INLINE Packet16c pnegate(const Packet16c& a) {
  return vnegq_s8(a);
}
template <>
EIGEN_STRONG_INLINE Packet4s pnegate(const Packet4s& a) {
  return vneg_s16(a);
}
template <>
EIGEN_STRONG_INLINE Packet8s pnegate(const Packet8s& a) {
  return vnegq_s16(a);
}
template <>
EIGEN_STRONG_INLINE Packet2i pnegate(const Packet2i& a) {
  return vneg_s32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) {
  return vnegq_s32(a);
}
template <>
EIGEN_STRONG_INLINE Packet2l pnegate(const Packet2l& a) {
#if EIGEN_ARCH_ARM64
  return vnegq_s64(a);
#elif !EIGEN_GNUC_STRICT_AT_LEAST(12, 0, 0)
  return psub(pzero(a), a);
#else
  // NOTE: GCC>=12 refuses to emit `vsub.i64` for `0 - x`: <https://godbolt.org/z/bfaz9ao59>.
  int64x2_t x = a;
  int64x2_t z = vdupq_n_s64(0);
  asm("vsub.i64 %q0, %q1, %q0" : "+w"(x) : "w"(z));
  return x;
#endif
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pmul<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vmul_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vmulq_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4c pmul<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vmul_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pmul<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vmul_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pmul<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vmulq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pmul<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vmul_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pmul<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vmul_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pmul<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vmulq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pmul<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vmul_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pmul<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vmulq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pmul<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vmul_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pmul<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vmulq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pmul<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vmul_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vmulq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pmul<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vmul_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pmul<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vmulq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pmul<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  const uint32x2_t al = vmovn_u64(a);
  const uint32x2_t bl = vmovn_u64(b);
  const uint64x2_t hi = vpaddlq_u32(vmulq_u32(vreinterpretq_u32_u64(a), vrev64q_u32(vreinterpretq_u32_u64(b))));
  return vmlal_u32(vshlq_n_u64(hi, 32), al, bl);
}
template <>
EIGEN_STRONG_INLINE Packet2l pmul<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vreinterpretq_s64_u64(pmul(vreinterpretq_u64_s64(a), vreinterpretq_u64_s64(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4c pdiv<Packet4c>(const Packet4c& /*a*/, const Packet4c& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet4c>(0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pdiv<Packet8c>(const Packet8c& /*a*/, const Packet8c& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet8c>(0);
}
template <>
EIGEN_STRONG_INLINE Packet16c pdiv<Packet16c>(const Packet16c& /*a*/, const Packet16c& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet16c>(0);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pdiv<Packet4uc>(const Packet4uc& /*a*/, const Packet4uc& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet4uc>(0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pdiv<Packet8uc>(const Packet8uc& /*a*/, const Packet8uc& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet8uc>(0);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pdiv<Packet16uc>(const Packet16uc& /*a*/, const Packet16uc& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet16uc>(0);
}
template <>
EIGEN_STRONG_INLINE Packet4s pdiv<Packet4s>(const Packet4s& /*a*/, const Packet4s& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet4s>(0);
}
template <>
EIGEN_STRONG_INLINE Packet8s pdiv<Packet8s>(const Packet8s& /*a*/, const Packet8s& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet8s>(0);
}
template <>
EIGEN_STRONG_INLINE Packet4us pdiv<Packet4us>(const Packet4us& /*a*/, const Packet4us& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet4us>(0);
}
template <>
EIGEN_STRONG_INLINE Packet8us pdiv<Packet8us>(const Packet8us& /*a*/, const Packet8us& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet8us>(0);
}
template <>
EIGEN_STRONG_INLINE Packet2i pdiv<Packet2i>(const Packet2i& /*a*/, const Packet2i& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet2i>(0);
}
template <>
EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet4i>(0);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pdiv<Packet2ui>(const Packet2ui& /*a*/, const Packet2ui& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet2ui>(0);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pdiv<Packet4ui>(const Packet4ui& /*a*/, const Packet4ui& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet4ui>(0);
}
template <>
EIGEN_STRONG_INLINE Packet2l pdiv<Packet2l>(const Packet2l& /*a*/, const Packet2l& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet2l>(0LL);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pdiv<Packet2ul>(const Packet2ul& /*a*/, const Packet2ul& /*b*/) {
  eigen_assert(false && "packet integer division are not supported by NEON");
  return pset1<Packet2ul>(0ULL);
}
 
#ifdef EIGEN_VECTORIZE_FMA
template <>
EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return vfmaq_f32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2f pmadd(const Packet2f& a, const Packet2f& b, const Packet2f& c) {
  return vfma_f32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pnmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return vfmsq_f32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2f pnmadd(const Packet2f& a, const Packet2f& b, const Packet2f& c) {
  return vfms_f32(c, a, b);
}
#else
template <>
EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return vmlaq_f32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2f pmadd(const Packet2f& a, const Packet2f& b, const Packet2f& c) {
  return vmla_f32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pnmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return vmlsq_f32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2f pnmadd(const Packet2f& a, const Packet2f& b, const Packet2f& c) {
  return vmls_f32(c, a, b);
}
#endif
template <>
EIGEN_STRONG_INLINE Packet4f pmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return pnegate(pnmadd(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet2f pmsub(const Packet2f& a, const Packet2f& b, const Packet2f& c) {
  return pnegate(pnmadd(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet4f pnmsub(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
  return pnegate(pmadd(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet2f pnmsub(const Packet2f& a, const Packet2f& b, const Packet2f& c) {
  return pnegate(pmadd(a, b, c));
}
 
// No FMA instruction for int, so use MLA unconditionally.
template <>
EIGEN_STRONG_INLINE Packet4c pmadd(const Packet4c& a, const Packet4c& b, const Packet4c& c) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vmla_s8(vreinterpret_s8_s32(vdup_n_s32(c)), vreinterpret_s8_s32(vdup_n_s32(a)),
                                  vreinterpret_s8_s32(vdup_n_s32(b)))),
      0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pmadd(const Packet8c& a, const Packet8c& b, const Packet8c& c) {
  return vmla_s8(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pmadd(const Packet16c& a, const Packet16c& b, const Packet16c& c) {
  return vmlaq_s8(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pmadd(const Packet4uc& a, const Packet4uc& b, const Packet4uc& c) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vmla_u8(vreinterpret_u8_u32(vdup_n_u32(c)), vreinterpret_u8_u32(vdup_n_u32(a)),
                                  vreinterpret_u8_u32(vdup_n_u32(b)))),
      0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pmadd(const Packet8uc& a, const Packet8uc& b, const Packet8uc& c) {
  return vmla_u8(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pmadd(const Packet16uc& a, const Packet16uc& b, const Packet16uc& c) {
  return vmlaq_u8(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pmadd(const Packet4s& a, const Packet4s& b, const Packet4s& c) {
  return vmla_s16(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pmadd(const Packet8s& a, const Packet8s& b, const Packet8s& c) {
  return vmlaq_s16(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pmadd(const Packet4us& a, const Packet4us& b, const Packet4us& c) {
  return vmla_u16(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pmadd(const Packet8us& a, const Packet8us& b, const Packet8us& c) {
  return vmlaq_u16(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pmadd(const Packet2i& a, const Packet2i& b, const Packet2i& c) {
  return vmla_s32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) {
  return vmlaq_s32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pmadd(const Packet2ui& a, const Packet2ui& b, const Packet2ui& c) {
  return vmla_u32(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pmadd(const Packet4ui& a, const Packet4ui& b, const Packet4ui& c) {
  return vmlaq_u32(c, a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pabsdiff<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vabd_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pabsdiff<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vabdq_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4c pabsdiff<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vabd_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pabsdiff<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vabd_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pabsdiff<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vabdq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pabsdiff<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vabd_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pabsdiff<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vabd_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pabsdiff<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vabdq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pabsdiff<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vabd_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pabsdiff<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vabdq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pabsdiff<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vabd_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pabsdiff<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vabdq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pabsdiff<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vabd_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pabsdiff<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vabdq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pabsdiff<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vabd_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pabsdiff<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vabdq_u32(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pmin<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vmin_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vminq_f32(a, b);
}
 
#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8
// systems).
template <>
EIGEN_STRONG_INLINE Packet4f pmin<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vminnmq_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2f pmin<PropagateNumbers, Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vminnm_f32(a, b);
}
#endif
 
template <>
struct pminmax_propagates_nan<Packet2f> : bool_constant<true> {};
template <>
struct pminmax_propagates_nan<Packet4f> : bool_constant<true> {};
 
template <>
EIGEN_STRONG_INLINE Packet4c pmin<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vmin_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pmin<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vmin_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pmin<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vminq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pmin<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vmin_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pmin<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vmin_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pmin<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vminq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pmin<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vmin_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pmin<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vminq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pmin<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vmin_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pmin<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vminq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pmin<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vmin_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vminq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pmin<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vmin_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pmin<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vminq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pmin<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vsubq_u64(a, vqsubq_u64(a, b));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pmax<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vmax_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vmaxq_f32(a, b);
}
 
#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8
// systems).
template <>
EIGEN_STRONG_INLINE Packet4f pmax<PropagateNumbers, Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vmaxnmq_f32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2f pmax<PropagateNumbers, Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vmaxnm_f32(a, b);
}
#endif
 
template <>
EIGEN_STRONG_INLINE Packet4c pmax<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_s8(vmax_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pmax<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vmax_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pmax<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vmaxq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pmax<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vmax_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pmax<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vmax_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pmax<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vmaxq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pmax<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vmax_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pmax<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vmaxq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pmax<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vmax_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pmax<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vmaxq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pmax<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vmax_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vmaxq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pmax<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vmax_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pmax<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vmaxq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pmax<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vaddq_u64(b, vqsubq_u64(a, b));
}
 
// GCC defines the ARM32 vcge/vcgt float intrinsics as generic vector comparisons and, unless
// -funsafe-math-optimizations is given, expands them one lane at a time through VFP, because Advanced SIMD
// flushes subnormal inputs. Emit the Advanced SIMD comparison directly, as Clang does.
#if EIGEN_COMP_GNUC_STRICT && !EIGEN_ARCH_ARM64
EIGEN_STRONG_INLINE uint32x2_t neon_vcge_f32(float32x2_t a, float32x2_t b) {
  uint32x2_t r;
  __asm__("vcge.f32 %P0, %P1, %P2" : "=w"(r) : "w"(a), "w"(b));
  return r;
}
EIGEN_STRONG_INLINE uint32x4_t neon_vcgeq_f32(float32x4_t a, float32x4_t b) {
  uint32x4_t r;
  __asm__("vcge.f32 %q0, %q1, %q2" : "=w"(r) : "w"(a), "w"(b));
  return r;
}
EIGEN_STRONG_INLINE uint32x2_t neon_vcgt_f32(float32x2_t a, float32x2_t b) {
  uint32x2_t r;
  __asm__("vcgt.f32 %P0, %P1, %P2" : "=w"(r) : "w"(a), "w"(b));
  return r;
}
EIGEN_STRONG_INLINE uint32x4_t neon_vcgtq_f32(float32x4_t a, float32x4_t b) {
  uint32x4_t r;
  __asm__("vcgt.f32 %q0, %q1, %q2" : "=w"(r) : "w"(a), "w"(b));
  return r;
}
#else
EIGEN_STRONG_INLINE uint32x2_t neon_vcge_f32(float32x2_t a, float32x2_t b) { return vcge_f32(a, b); }
EIGEN_STRONG_INLINE uint32x4_t neon_vcgeq_f32(float32x4_t a, float32x4_t b) { return vcgeq_f32(a, b); }
EIGEN_STRONG_INLINE uint32x2_t neon_vcgt_f32(float32x2_t a, float32x2_t b) { return vcgt_f32(a, b); }
EIGEN_STRONG_INLINE uint32x4_t neon_vcgtq_f32(float32x4_t a, float32x4_t b) { return vcgtq_f32(a, b); }
#endif
 
template <>
EIGEN_STRONG_INLINE Packet2f pcmp_le<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(neon_vcge_f32(b, a));
}
template <>
EIGEN_STRONG_INLINE Packet4f pcmp_le<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(neon_vcgeq_f32(b, a));
}
template <>
EIGEN_STRONG_INLINE Packet4c pcmp_le<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_u8(vcle_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pcmp_le<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vreinterpret_s8_u8(vcle_s8(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet16c pcmp_le<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vreinterpretq_s8_u8(vcleq_s8(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4uc pcmp_le<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vcle_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pcmp_le<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vcle_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pcmp_le<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vcleq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pcmp_le<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vreinterpret_s16_u16(vcle_s16(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet8s pcmp_le<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vreinterpretq_s16_u16(vcleq_s16(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4us pcmp_le<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vcle_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pcmp_le<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vcleq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pcmp_le<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vreinterpret_s32_u32(vcle_s32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4i pcmp_le<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vreinterpretq_s32_u32(vcleq_s32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet2ui pcmp_le<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vcle_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pcmp_le<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vcleq_u32(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pcmp_lt<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(neon_vcgt_f32(b, a));
}
template <>
EIGEN_STRONG_INLINE Packet4f pcmp_lt<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(neon_vcgtq_f32(b, a));
}
template <>
EIGEN_STRONG_INLINE Packet4c pcmp_lt<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_u8(vclt_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pcmp_lt<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vreinterpret_s8_u8(vclt_s8(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet16c pcmp_lt<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vreinterpretq_s8_u8(vcltq_s8(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4uc pcmp_lt<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vclt_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pcmp_lt<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vclt_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pcmp_lt<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vcltq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pcmp_lt<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vreinterpret_s16_u16(vclt_s16(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet8s pcmp_lt<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vreinterpretq_s16_u16(vcltq_s16(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4us pcmp_lt<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vclt_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pcmp_lt<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vcltq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pcmp_lt<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vreinterpret_s32_u32(vclt_s32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4i pcmp_lt<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vreinterpretq_s32_u32(vcltq_s32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet2ui pcmp_lt<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vclt_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pcmp_lt<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vcltq_u32(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2l pcmp_lt<Packet2l>(const Packet2l& a, const Packet2l& b) {
#if EIGEN_ARCH_ARM64
  return vreinterpretq_s64_u64(vcltq_s64(a, b));
#else
  return vshrq_n_s64(vqsubq_s64(a, b), 63);
#endif
}
template <>
EIGEN_STRONG_INLINE Packet2ul pcmp_lt<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
#if EIGEN_ARCH_ARM64
  return vcltq_u64(a, b);
#else
  const uint64x2_t flag = vshrq_n_u64(vreinterpretq_u64_u8(vdupq_n_u8(0xFF)), 1);
  return vreinterpretq_u64_s64(vshrq_n_s64(vreinterpretq_s64_u64(vqaddq_u64(vqsubq_u64(b, a), flag)), 63));
#endif
}
template <>
EIGEN_STRONG_INLINE Packet2l pcmp_le<Packet2l>(const Packet2l& a, const Packet2l& b) {
#if EIGEN_ARCH_ARM64
  return vreinterpretq_s64_u64(vcleq_s64(a, b));
#else
  return vreinterpretq_s64_u8(vmvnq_u8(vreinterpretq_u8_s64(pcmp_lt(b, a))));
#endif
}
template <>
EIGEN_STRONG_INLINE Packet2ul pcmp_le<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
#if EIGEN_ARCH_ARM64
  return vcleq_u64(a, b);
#else
  return vreinterpretq_u64_u8(vmvnq_u8(vreinterpretq_u8_u64(pcmp_lt(b, a))));
#endif
}
 
template <>
EIGEN_STRONG_INLINE Packet2l pmin<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vbslq_s64(vreinterpretq_u64_s64(pcmp_lt(a, b)), a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pmax<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vbslq_s64(vreinterpretq_u64_s64(pcmp_lt(b, a)), a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pcmp_eq<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(vceq_f32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4f pcmp_eq<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(vceqq_f32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4c pcmp_eq<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return vget_lane_s32(
      vreinterpret_s32_u8(vceq_s8(vreinterpret_s8_s32(vdup_n_s32(a)), vreinterpret_s8_s32(vdup_n_s32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pcmp_eq<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vreinterpret_s8_u8(vceq_s8(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet16c pcmp_eq<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vreinterpretq_s8_u8(vceqq_s8(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4uc pcmp_eq<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return vget_lane_u32(
      vreinterpret_u32_u8(vceq_u8(vreinterpret_u8_u32(vdup_n_u32(a)), vreinterpret_u8_u32(vdup_n_u32(b)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc pcmp_eq<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vceq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pcmp_eq<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vceqq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pcmp_eq<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vreinterpret_s16_u16(vceq_s16(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet8s pcmp_eq<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vreinterpretq_s16_u16(vceqq_s16(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4us pcmp_eq<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vceq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pcmp_eq<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vceqq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pcmp_eq<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vreinterpret_s32_u32(vceq_s32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet4i pcmp_eq<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vreinterpretq_s32_u32(vceqq_s32(a, b));
}
template <>
EIGEN_STRONG_INLINE Packet2ui pcmp_eq<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vceq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pcmp_eq<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vceqq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pcmp_eq<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
#if EIGEN_ARCH_ARM64
  return vceqq_u64(a, b);
#else
  const uint32x4_t eq = vceqq_u32(vreinterpretq_u32_u64(a), vreinterpretq_u32_u64(b));
  return vreinterpretq_u64_u32(vandq_u32(eq, vrev64q_u32(eq)));
#endif
}
template <>
EIGEN_STRONG_INLINE Packet2l pcmp_eq<Packet2l>(const Packet2l& a, const Packet2l& b) {
#if EIGEN_ARCH_ARM64
  return vreinterpretq_s64_u64(vceqq_s64(a, b));
#else
  return vreinterpretq_s64_u64(pcmp_eq(vreinterpretq_u64_s64(a), vreinterpretq_u64_s64(b)));
#endif
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pcmp_lt_or_nan<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(vmvn_u32(neon_vcge_f32(a, b)));
}
template <>
EIGEN_STRONG_INLINE Packet4f pcmp_lt_or_nan<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(vmvnq_u32(neon_vcgeq_f32(a, b)));
}
 
// Classify with absolute comparisons against infinity: |a| >= inf holds only for +-inf, inf > |a| only for finite
// values, and |a| <= inf fails only for NaN. Each is one instruction (FACGE/FACGT, VACGE/VACGT), is unaffected by
// flushing subnormal inputs, and avoids the self-comparison a != a, which Clang rewrites into two comparisons.
template <>
EIGEN_STRONG_INLINE Packet2f pisinf<Packet2f>(const Packet2f& a) {
  return vreinterpret_f32_u32(vcage_f32(a, pinf<Packet2f>()));
}
template <>
EIGEN_STRONG_INLINE Packet4f pisinf<Packet4f>(const Packet4f& a) {
  return vreinterpretq_f32_u32(vcageq_f32(a, pinf<Packet4f>()));
}
template <>
EIGEN_STRONG_INLINE Packet2f pisfinite<Packet2f>(const Packet2f& a) {
  return vreinterpret_f32_u32(vcagt_f32(pinf<Packet2f>(), a));
}
template <>
EIGEN_STRONG_INLINE Packet4f pisfinite<Packet4f>(const Packet4f& a) {
  return vreinterpretq_f32_u32(vcagtq_f32(pinf<Packet4f>(), a));
}
template <>
EIGEN_STRONG_INLINE Packet2f pisnan<Packet2f>(const Packet2f& a) {
  return vreinterpret_f32_u32(vmvn_u32(vcage_f32(pinf<Packet2f>(), a)));
}
template <>
EIGEN_STRONG_INLINE Packet4f pisnan<Packet4f>(const Packet4f& a) {
  return vreinterpretq_f32_u32(vmvnq_u32(vcageq_f32(pinf<Packet4f>(), a)));
}
 
// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
template <>
EIGEN_STRONG_INLINE Packet2f pand<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(vand_u32(vreinterpret_u32_f32(a), vreinterpret_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a), vreinterpretq_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4c pand<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return a & b;
}
template <>
EIGEN_STRONG_INLINE Packet8c pand<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vand_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pand<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vandq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pand<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return a & b;
}
template <>
EIGEN_STRONG_INLINE Packet8uc pand<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vand_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pand<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vandq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pand<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vand_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pand<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vandq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pand<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vand_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pand<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vandq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pand<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vand_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vandq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pand<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vand_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pand<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vandq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pand<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vandq_s64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pand<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vandq_u64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f por<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(vorr_u32(vreinterpret_u32_f32(a), vreinterpret_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a), vreinterpretq_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4c por<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return a | b;
}
template <>
EIGEN_STRONG_INLINE Packet8c por<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vorr_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c por<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vorrq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc por<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return a | b;
}
template <>
EIGEN_STRONG_INLINE Packet8uc por<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vorr_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc por<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vorrq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s por<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vorr_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s por<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vorrq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us por<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vorr_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us por<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vorrq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i por<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vorr_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vorrq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui por<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vorr_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui por<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vorrq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l por<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vorrq_s64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul por<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vorrq_u64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pxor<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(veor_u32(vreinterpret_u32_f32(a), vreinterpret_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a), vreinterpretq_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4c pxor<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return a ^ b;
}
template <>
EIGEN_STRONG_INLINE Packet8c pxor<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return veor_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pxor<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return veorq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pxor<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return a ^ b;
}
template <>
EIGEN_STRONG_INLINE Packet8uc pxor<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return veor_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pxor<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return veorq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pxor<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return veor_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pxor<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return veorq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pxor<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return veor_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pxor<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return veorq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pxor<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return veor_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return veorq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pxor<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return veor_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pxor<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return veorq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pxor<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return veorq_s64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pxor<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return veorq_u64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pandnot<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return vreinterpret_f32_u32(vbic_u32(vreinterpret_u32_f32(a), vreinterpret_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a), vreinterpretq_u32_f32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4c pandnot<Packet4c>(const Packet4c& a, const Packet4c& b) {
  return a & ~b;
}
template <>
EIGEN_STRONG_INLINE Packet8c pandnot<Packet8c>(const Packet8c& a, const Packet8c& b) {
  return vbic_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16c pandnot<Packet16c>(const Packet16c& a, const Packet16c& b) {
  return vbicq_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc pandnot<Packet4uc>(const Packet4uc& a, const Packet4uc& b) {
  return a & ~b;
}
template <>
EIGEN_STRONG_INLINE Packet8uc pandnot<Packet8uc>(const Packet8uc& a, const Packet8uc& b) {
  return vbic_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet16uc pandnot<Packet16uc>(const Packet16uc& a, const Packet16uc& b) {
  return vbicq_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4s pandnot<Packet4s>(const Packet4s& a, const Packet4s& b) {
  return vbic_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s pandnot<Packet8s>(const Packet8s& a, const Packet8s& b) {
  return vbicq_s16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4us pandnot<Packet4us>(const Packet4us& a, const Packet4us& b) {
  return vbic_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8us pandnot<Packet8us>(const Packet8us& a, const Packet8us& b) {
  return vbicq_u16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2i pandnot<Packet2i>(const Packet2i& a, const Packet2i& b) {
  return vbic_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) {
  return vbicq_s32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ui pandnot<Packet2ui>(const Packet2ui& a, const Packet2ui& b) {
  return vbic_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4ui pandnot<Packet4ui>(const Packet4ui& a, const Packet4ui& b) {
  return vbicq_u32(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2l pandnot<Packet2l>(const Packet2l& a, const Packet2l& b) {
  return vbicq_s64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2ul pandnot<Packet2ul>(const Packet2ul& a, const Packet2ul& b) {
  return vbicq_u64(a, b);
}
 
template <int N>
EIGEN_STRONG_INLINE Packet4c parithmetic_shift_right(const Packet4c& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vshr_n_s8(vreinterpret_s8_s32(vdup_n_s32(a)), N)), 0);
}
template <int N>
EIGEN_STRONG_INLINE Packet8c parithmetic_shift_right(const Packet8c& a) {
  return vshr_n_s8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet16c parithmetic_shift_right(const Packet16c& a) {
  return vshrq_n_s8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4uc parithmetic_shift_right(const Packet4uc& a) {
  return vget_lane_u32(vreinterpret_u32_u8(vshr_n_u8(vreinterpret_u8_u32(vdup_n_u32(a)), N)), 0);
}
template <int N>
EIGEN_STRONG_INLINE Packet8uc parithmetic_shift_right(const Packet8uc& a) {
  return vshr_n_u8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet16uc parithmetic_shift_right(const Packet16uc& a) {
  return vshrq_n_u8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4s parithmetic_shift_right(const Packet4s& a) {
  return vshr_n_s16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet8s parithmetic_shift_right(const Packet8s& a) {
  return vshrq_n_s16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4us parithmetic_shift_right(const Packet4us& a) {
  return vshr_n_u16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet8us parithmetic_shift_right(const Packet8us& a) {
  return vshrq_n_u16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2i parithmetic_shift_right(const Packet2i& a) {
  return vshr_n_s32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4i parithmetic_shift_right(const Packet4i& a) {
  return vshrq_n_s32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2ui parithmetic_shift_right(const Packet2ui& a) {
  return vshr_n_u32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4ui parithmetic_shift_right(const Packet4ui& a) {
  return vshrq_n_u32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2l parithmetic_shift_right(const Packet2l& a) {
  return vshrq_n_s64(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2ul parithmetic_shift_right(const Packet2ul& a) {
  return vshrq_n_u64(a, N);
}
 
template <int N>
EIGEN_STRONG_INLINE Packet4c plogical_shift_right(const Packet4c& a) {
  return vget_lane_s32(vreinterpret_s32_u8(vshr_n_u8(vreinterpret_u8_s32(vdup_n_s32(a)), N)), 0);
}
template <int N>
EIGEN_STRONG_INLINE Packet8c plogical_shift_right(const Packet8c& a) {
  return vreinterpret_s8_u8(vshr_n_u8(vreinterpret_u8_s8(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet16c plogical_shift_right(const Packet16c& a) {
  return vreinterpretq_s8_u8(vshrq_n_u8(vreinterpretq_u8_s8(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet4uc plogical_shift_right(const Packet4uc& a) {
  return vget_lane_u32(vreinterpret_u32_u8(vshr_n_u8(vreinterpret_u8_u32(vdup_n_u32(a)), N)), 0);
}
template <int N>
EIGEN_STRONG_INLINE Packet8uc plogical_shift_right(const Packet8uc& a) {
  return vshr_n_u8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet16uc plogical_shift_right(const Packet16uc& a) {
  return vshrq_n_u8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4s plogical_shift_right(const Packet4s& a) {
  return vreinterpret_s16_u16(vshr_n_u16(vreinterpret_u16_s16(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet8s plogical_shift_right(const Packet8s& a) {
  return vreinterpretq_s16_u16(vshrq_n_u16(vreinterpretq_u16_s16(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet4us plogical_shift_right(const Packet4us& a) {
  return vshr_n_u16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet8us plogical_shift_right(const Packet8us& a) {
  return vshrq_n_u16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2i plogical_shift_right(const Packet2i& a) {
  return vreinterpret_s32_u32(vshr_n_u32(vreinterpret_u32_s32(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet4i plogical_shift_right(const Packet4i& a) {
  return vreinterpretq_s32_u32(vshrq_n_u32(vreinterpretq_u32_s32(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet2ui plogical_shift_right(const Packet2ui& a) {
  return vshr_n_u32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4ui plogical_shift_right(const Packet4ui& a) {
  return vshrq_n_u32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2l plogical_shift_right(const Packet2l& a) {
  return vreinterpretq_s64_u64(vshrq_n_u64(vreinterpretq_u64_s64(a), N));
}
template <int N>
EIGEN_STRONG_INLINE Packet2ul plogical_shift_right(const Packet2ul& a) {
  return vshrq_n_u64(a, N);
}
 
template <int N>
EIGEN_STRONG_INLINE Packet4c plogical_shift_left(const Packet4c& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vshl_n_s8(vreinterpret_s8_s32(vdup_n_s32(a)), N)), 0);
}
template <int N>
EIGEN_STRONG_INLINE Packet8c plogical_shift_left(const Packet8c& a) {
  return vshl_n_s8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet16c plogical_shift_left(const Packet16c& a) {
  return vshlq_n_s8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4uc plogical_shift_left(const Packet4uc& a) {
  return vget_lane_u32(vreinterpret_u32_u8(vshl_n_u8(vreinterpret_u8_u32(vdup_n_u32(a)), N)), 0);
}
template <int N>
EIGEN_STRONG_INLINE Packet8uc plogical_shift_left(const Packet8uc& a) {
  return vshl_n_u8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet16uc plogical_shift_left(const Packet16uc& a) {
  return vshlq_n_u8(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4s plogical_shift_left(const Packet4s& a) {
  return vshl_n_s16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet8s plogical_shift_left(const Packet8s& a) {
  return vshlq_n_s16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4us plogical_shift_left(const Packet4us& a) {
  return vshl_n_u16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet8us plogical_shift_left(const Packet8us& a) {
  return vshlq_n_u16(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2i plogical_shift_left(const Packet2i& a) {
  return vshl_n_s32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4i plogical_shift_left(const Packet4i& a) {
  return vshlq_n_s32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2ui plogical_shift_left(const Packet2ui& a) {
  return vshl_n_u32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet4ui plogical_shift_left(const Packet4ui& a) {
  return vshlq_n_u32(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2l plogical_shift_left(const Packet2l& a) {
  return vshlq_n_s64(a, N);
}
template <int N>
EIGEN_STRONG_INLINE Packet2ul plogical_shift_left(const Packet2ul& a) {
  return vshlq_n_u64(a, N);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pload<Packet2f>(const float* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_f32(assume_aligned<unpacket_traits<Packet2f>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(assume_aligned<unpacket_traits<Packet4f>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4c pload<Packet4c>(const int8_t* from) {
  Packet4c res;
  memcpy(&res, from, sizeof(Packet4c));
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet8c pload<Packet8c>(const int8_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_s8(assume_aligned<unpacket_traits<Packet8c>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet16c pload<Packet16c>(const int8_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s8(assume_aligned<unpacket_traits<Packet16c>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4uc pload<Packet4uc>(const uint8_t* from) {
  Packet4uc res;
  memcpy(&res, from, sizeof(Packet4uc));
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet8uc pload<Packet8uc>(const uint8_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_u8(assume_aligned<unpacket_traits<Packet8uc>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet16uc pload<Packet16uc>(const uint8_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u8(assume_aligned<unpacket_traits<Packet16uc>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4s pload<Packet4s>(const int16_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_s16(assume_aligned<unpacket_traits<Packet4s>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet8s pload<Packet8s>(const int16_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s16(assume_aligned<unpacket_traits<Packet8s>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4us pload<Packet4us>(const uint16_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_u16(assume_aligned<unpacket_traits<Packet4us>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet8us pload<Packet8us>(const uint16_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u16(assume_aligned<unpacket_traits<Packet8us>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet2i pload<Packet2i>(const int32_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_s32(assume_aligned<unpacket_traits<Packet2i>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int32_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(assume_aligned<unpacket_traits<Packet4i>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet2ui pload<Packet2ui>(const uint32_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_u32(assume_aligned<unpacket_traits<Packet2ui>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet4ui pload<Packet4ui>(const uint32_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u32(assume_aligned<unpacket_traits<Packet4ui>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet2l pload<Packet2l>(const int64_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s64(assume_aligned<unpacket_traits<Packet2l>::alignment>(from));
}
template <>
EIGEN_STRONG_INLINE Packet2ul pload<Packet2ul>(const uint64_t* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_u64(assume_aligned<unpacket_traits<Packet2ul>::alignment>(from));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f ploadu<Packet2f>(const float* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_f32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4c ploadu<Packet4c>(const int8_t* from) {
  Packet4c res;
  memcpy(&res, from, sizeof(Packet4c));
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet8c ploadu<Packet8c>(const int8_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_s8(from);
}
template <>
EIGEN_STRONG_INLINE Packet16c ploadu<Packet16c>(const int8_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s8(from);
}
template <>
EIGEN_STRONG_INLINE Packet4uc ploadu<Packet4uc>(const uint8_t* from) {
  Packet4uc res;
  memcpy(&res, from, sizeof(Packet4uc));
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet8uc ploadu<Packet8uc>(const uint8_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_u8(from);
}
template <>
EIGEN_STRONG_INLINE Packet16uc ploadu<Packet16uc>(const uint8_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u8(from);
}
template <>
EIGEN_STRONG_INLINE Packet4s ploadu<Packet4s>(const int16_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_s16(from);
}
template <>
EIGEN_STRONG_INLINE Packet8s ploadu<Packet8s>(const int16_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s16(from);
}
template <>
EIGEN_STRONG_INLINE Packet4us ploadu<Packet4us>(const uint16_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_u16(from);
}
template <>
EIGEN_STRONG_INLINE Packet8us ploadu<Packet8us>(const uint16_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u16(from);
}
template <>
EIGEN_STRONG_INLINE Packet2i ploadu<Packet2i>(const int32_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_s32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int32_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from);
}
template <>
EIGEN_STRONG_INLINE Packet2ui ploadu<Packet2ui>(const uint32_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_u32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4ui ploadu<Packet4ui>(const uint32_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u32(from);
}
template <>
EIGEN_STRONG_INLINE Packet2l ploadu<Packet2l>(const int64_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s64(from);
}
template <>
EIGEN_STRONG_INLINE Packet2ul ploadu<Packet2ul>(const uint64_t* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_u64(from);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f ploaddup<Packet2f>(const float* from) {
  return vld1_dup_f32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from) {
  return vcombine_f32(vld1_dup_f32(from), vld1_dup_f32(from + 1));
}
template <>
EIGEN_STRONG_INLINE Packet4c ploaddup<Packet4c>(const int8_t* from) {
  const int8x8_t a = vreinterpret_s8_s32(vdup_n_s32(pload<Packet4c>(from)));
  return vget_lane_s32(vreinterpret_s32_s8(vzip_s8(a, a).val[0]), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c ploaddup<Packet8c>(const int8_t* from) {
  const int8x8_t a = vld1_s8(from);
  return vzip_s8(a, a).val[0];
}
template <>
EIGEN_STRONG_INLINE Packet16c ploaddup<Packet16c>(const int8_t* from) {
  const int8x8_t a = vld1_s8(from);
  const int8x8x2_t b = vzip_s8(a, a);
  return vcombine_s8(b.val[0], b.val[1]);
}
template <>
EIGEN_STRONG_INLINE Packet4uc ploaddup<Packet4uc>(const uint8_t* from) {
  const uint8x8_t a = vreinterpret_u8_u32(vdup_n_u32(pload<Packet4uc>(from)));
  return vget_lane_u32(vreinterpret_u32_u8(vzip_u8(a, a).val[0]), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc ploaddup<Packet8uc>(const uint8_t* from) {
  const uint8x8_t a = vld1_u8(from);
  return vzip_u8(a, a).val[0];
}
template <>
EIGEN_STRONG_INLINE Packet16uc ploaddup<Packet16uc>(const uint8_t* from) {
  const uint8x8_t a = vld1_u8(from);
  const uint8x8x2_t b = vzip_u8(a, a);
  return vcombine_u8(b.val[0], b.val[1]);
}
template <>
EIGEN_STRONG_INLINE Packet4s ploaddup<Packet4s>(const int16_t* from) {
  return vreinterpret_s16_u32(
      vzip_u32(vreinterpret_u32_s16(vld1_dup_s16(from)), vreinterpret_u32_s16(vld1_dup_s16(from + 1))).val[0]);
}
template <>
EIGEN_STRONG_INLINE Packet8s ploaddup<Packet8s>(const int16_t* from) {
  const int16x4_t a = vld1_s16(from);
  const int16x4x2_t b = vzip_s16(a, a);
  return vcombine_s16(b.val[0], b.val[1]);
}
template <>
EIGEN_STRONG_INLINE Packet4us ploaddup<Packet4us>(const uint16_t* from) {
  return vreinterpret_u16_u32(
      vzip_u32(vreinterpret_u32_u16(vld1_dup_u16(from)), vreinterpret_u32_u16(vld1_dup_u16(from + 1))).val[0]);
}
template <>
EIGEN_STRONG_INLINE Packet8us ploaddup<Packet8us>(const uint16_t* from) {
  const uint16x4_t a = vld1_u16(from);
  const uint16x4x2_t b = vzip_u16(a, a);
  return vcombine_u16(b.val[0], b.val[1]);
}
template <>
EIGEN_STRONG_INLINE Packet2i ploaddup<Packet2i>(const int32_t* from) {
  return vld1_dup_s32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int32_t* from) {
  return vcombine_s32(vld1_dup_s32(from), vld1_dup_s32(from + 1));
}
template <>
EIGEN_STRONG_INLINE Packet2ui ploaddup<Packet2ui>(const uint32_t* from) {
  return vld1_dup_u32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4ui ploaddup<Packet4ui>(const uint32_t* from) {
  return vcombine_u32(vld1_dup_u32(from), vld1_dup_u32(from + 1));
}
template <>
EIGEN_STRONG_INLINE Packet2l ploaddup<Packet2l>(const int64_t* from) {
  return vld1q_dup_s64(from);
}
template <>
EIGEN_STRONG_INLINE Packet2ul ploaddup<Packet2ul>(const uint64_t* from) {
  return vld1q_dup_u64(from);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f ploadquad<Packet4f>(const float* from) {
  return vld1q_dup_f32(from);
}
 
// WORKAROUND: Apple Clang 17.0.0 (and Homebrew Clang 21.1.8) at -O0 optimization
// generate incorrect code for vld1_dup_[su]8, ignoring the pointer offset.
// We use vdup_n_s8(*from) to force a safe scalar load before broadcast.
EIGEN_ALWAYS_INLINE int8x8_t eigen_vld1_dup_s8(const int8_t* ptr) {
#if EIGEN_COMP_CLANGAPPLE && EIGEN_ARCH_ARM64
  return vdup_n_s8(*ptr);
#else
  return vld1_dup_s8(ptr);
#endif
}
 
EIGEN_ALWAYS_INLINE uint8x8_t eigen_vld1_dup_u8(const uint8_t* ptr) {
#if EIGEN_COMP_CLANGAPPLE && EIGEN_ARCH_ARM64
  return vdup_n_u8(*ptr);
#else
  return vld1_dup_u8(ptr);
#endif
}
 
template <>
EIGEN_STRONG_INLINE Packet4c ploadquad<Packet4c>(const int8_t* from) {
  return vget_lane_s32(vreinterpret_s32_s8(eigen_vld1_dup_s8(from)), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c ploadquad<Packet8c>(const int8_t* from) {
  return vreinterpret_s8_u32(
      vzip_u32(vreinterpret_u32_s8(eigen_vld1_dup_s8(from)), vreinterpret_u32_s8(eigen_vld1_dup_s8(from + 1))).val[0]);
}
template <>
EIGEN_STRONG_INLINE Packet16c ploadquad<Packet16c>(const int8_t* from) {
  const int8x8_t a = vreinterpret_s8_u32(
      vzip_u32(vreinterpret_u32_s8(eigen_vld1_dup_s8(from)), vreinterpret_u32_s8(eigen_vld1_dup_s8(from + 1))).val[0]);
  const int8x8_t b = vreinterpret_s8_u32(
      vzip_u32(vreinterpret_u32_s8(eigen_vld1_dup_s8(from + 2)), vreinterpret_u32_s8(eigen_vld1_dup_s8(from + 3)))
          .val[0]);
  return vcombine_s8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet4uc ploadquad<Packet4uc>(const uint8_t* from) {
  return vget_lane_u32(vreinterpret_u32_u8(eigen_vld1_dup_u8(from)), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc ploadquad<Packet8uc>(const uint8_t* from) {
  return vreinterpret_u8_u32(
      vzip_u32(vreinterpret_u32_u8(eigen_vld1_dup_u8(from)), vreinterpret_u32_u8(eigen_vld1_dup_u8(from + 1))).val[0]);
}
template <>
EIGEN_STRONG_INLINE Packet16uc ploadquad<Packet16uc>(const uint8_t* from) {
  const uint8x8_t a = vreinterpret_u8_u32(
      vzip_u32(vreinterpret_u32_u8(eigen_vld1_dup_u8(from)), vreinterpret_u32_u8(eigen_vld1_dup_u8(from + 1))).val[0]);
  const uint8x8_t b = vreinterpret_u8_u32(
      vzip_u32(vreinterpret_u32_u8(eigen_vld1_dup_u8(from + 2)), vreinterpret_u32_u8(eigen_vld1_dup_u8(from + 3)))
          .val[0]);
  return vcombine_u8(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8s ploadquad<Packet8s>(const int16_t* from) {
  return vcombine_s16(vld1_dup_s16(from), vld1_dup_s16(from + 1));
}
template <>
EIGEN_STRONG_INLINE Packet8us ploadquad<Packet8us>(const uint16_t* from) {
  return vcombine_u16(vld1_dup_u16(from), vld1_dup_u16(from + 1));
}
template <>
EIGEN_STRONG_INLINE Packet4i ploadquad<Packet4i>(const int32_t* from) {
  return vld1q_dup_s32(from);
}
template <>
EIGEN_STRONG_INLINE Packet4ui ploadquad<Packet4ui>(const uint32_t* from) {
  return vld1q_dup_u32(from);
}
 
template <>
EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet2f& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_f32(assume_aligned<unpacket_traits<Packet2f>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(assume_aligned<unpacket_traits<Packet4f>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t* to, const Packet4c& from) {
  memcpy(to, &from, sizeof(from));
}
template <>
EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t* to, const Packet8c& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_s8(assume_aligned<unpacket_traits<Packet8c>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int8_t>(int8_t* to, const Packet16c& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_s8(assume_aligned<unpacket_traits<Packet16c>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint8_t>(uint8_t* to, const Packet4uc& from) {
  memcpy(to, &from, sizeof(from));
}
template <>
EIGEN_STRONG_INLINE void pstore<uint8_t>(uint8_t* to, const Packet8uc& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_u8(assume_aligned<unpacket_traits<Packet8uc>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint8_t>(uint8_t* to, const Packet16uc& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_u8(assume_aligned<unpacket_traits<Packet16uc>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int16_t>(int16_t* to, const Packet4s& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_s16(assume_aligned<unpacket_traits<Packet4s>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int16_t>(int16_t* to, const Packet8s& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_s16(assume_aligned<unpacket_traits<Packet8s>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint16_t>(uint16_t* to, const Packet4us& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_u16(assume_aligned<unpacket_traits<Packet4us>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint16_t>(uint16_t* to, const Packet8us& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_u16(assume_aligned<unpacket_traits<Packet8us>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t* to, const Packet2i& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_s32(assume_aligned<unpacket_traits<Packet2i>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t* to, const Packet4i& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(assume_aligned<unpacket_traits<Packet4i>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint32_t>(uint32_t* to, const Packet2ui& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_u32(assume_aligned<unpacket_traits<Packet2ui>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint32_t>(uint32_t* to, const Packet4ui& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_u32(assume_aligned<unpacket_traits<Packet4ui>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<int64_t>(int64_t* to, const Packet2l& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_s64(assume_aligned<unpacket_traits<Packet2l>::alignment>(to), from);
}
template <>
EIGEN_STRONG_INLINE void pstore<uint64_t>(uint64_t* to, const Packet2ul& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_u64(assume_aligned<unpacket_traits<Packet2ul>::alignment>(to), from);
}
 
template <>
EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet2f& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_f32(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t* to, const Packet4c& from) {
  memcpy(to, &from, sizeof(from));
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t* to, const Packet8c& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_s8(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int8_t>(int8_t* to, const Packet16c& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_s8(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint8_t>(uint8_t* to, const Packet4uc& from) {
  memcpy(to, &from, sizeof(from));
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint8_t>(uint8_t* to, const Packet8uc& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_u8(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint8_t>(uint8_t* to, const Packet16uc& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_u8(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int16_t>(int16_t* to, const Packet4s& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_s16(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int16_t>(int16_t* to, const Packet8s& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_s16(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint16_t>(uint16_t* to, const Packet4us& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_u16(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint16_t>(uint16_t* to, const Packet8us& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_u16(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet2i& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_s32(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet4i& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint32_t>(uint32_t* to, const Packet2ui& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_u32(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint32_t>(uint32_t* to, const Packet4ui& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_u32(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<int64_t>(int64_t* to, const Packet2l& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_s64(to, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu<uint64_t>(uint64_t* to, const Packet2ul& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_u64(to, from);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2f pgather<float, Packet2f>(const float* from, Index stride) {
  Packet2f res = vld1_dup_f32(from);
  res = vld1_lane_f32(from + 1 * stride, res, 1);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4f pgather<float, Packet4f>(const float* from, Index stride) {
  if (stride == 2) {
    // Overlap the loads so the second ends at the last gathered coefficient, from[6].
#if EIGEN_ARCH_ARM64
    // lo = [0 1 2 3], hi = [3 4 5 6]. GCC turns the equivalent vuzp2q(vrev64q(lo), hi) into a slower TBL.
    Packet4f lo = vld1q_f32(from);
    Packet4f hi = vld1q_f32(from + 3);
    return vcombine_f32(vget_low_f32(vuzp1q_f32(lo, lo)), vget_high_f32(vuzp2q_f32(hi, hi)));
#else
    return vcombine_f32(vld2_f32(from).val[0], vld2_f32(from + 3).val[1]);
#endif
  }
  Packet4f res = vld1q_dup_f32(from);
  res = vld1q_lane_f32(from + 1 * stride, res, 1);
  res = vld1q_lane_f32(from + 2 * stride, res, 2);
  res = vld1q_lane_f32(from + 3 * stride, res, 3);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4c pgather<int8_t, Packet4c>(const int8_t* from, Index stride) {
  Packet4c res;
  for (int i = 0; i != 4; i++) reinterpret_cast<int8_t*>(&res)[i] = *(from + i * stride);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8c pgather<int8_t, Packet8c>(const int8_t* from, Index stride) {
  Packet8c res = vld1_dup_s8(from);
  res = vld1_lane_s8(from + 1 * stride, res, 1);
  res = vld1_lane_s8(from + 2 * stride, res, 2);
  res = vld1_lane_s8(from + 3 * stride, res, 3);
  res = vld1_lane_s8(from + 4 * stride, res, 4);
  res = vld1_lane_s8(from + 5 * stride, res, 5);
  res = vld1_lane_s8(from + 6 * stride, res, 6);
  res = vld1_lane_s8(from + 7 * stride, res, 7);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16c pgather<int8_t, Packet16c>(const int8_t* from, Index stride) {
  Packet16c res = vld1q_dup_s8(from);
  res = vld1q_lane_s8(from + 1 * stride, res, 1);
  res = vld1q_lane_s8(from + 2 * stride, res, 2);
  res = vld1q_lane_s8(from + 3 * stride, res, 3);
  res = vld1q_lane_s8(from + 4 * stride, res, 4);
  res = vld1q_lane_s8(from + 5 * stride, res, 5);
  res = vld1q_lane_s8(from + 6 * stride, res, 6);
  res = vld1q_lane_s8(from + 7 * stride, res, 7);
  res = vld1q_lane_s8(from + 8 * stride, res, 8);
  res = vld1q_lane_s8(from + 9 * stride, res, 9);
  res = vld1q_lane_s8(from + 10 * stride, res, 10);
  res = vld1q_lane_s8(from + 11 * stride, res, 11);
  res = vld1q_lane_s8(from + 12 * stride, res, 12);
  res = vld1q_lane_s8(from + 13 * stride, res, 13);
  res = vld1q_lane_s8(from + 14 * stride, res, 14);
  res = vld1q_lane_s8(from + 15 * stride, res, 15);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4uc pgather<uint8_t, Packet4uc>(const uint8_t* from, Index stride) {
  Packet4uc res;
  for (int i = 0; i != 4; i++) reinterpret_cast<uint8_t*>(&res)[i] = *(from + i * stride);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8uc pgather<uint8_t, Packet8uc>(const uint8_t* from, Index stride) {
  Packet8uc res = vld1_dup_u8(from);
  res = vld1_lane_u8(from + 1 * stride, res, 1);
  res = vld1_lane_u8(from + 2 * stride, res, 2);
  res = vld1_lane_u8(from + 3 * stride, res, 3);
  res = vld1_lane_u8(from + 4 * stride, res, 4);
  res = vld1_lane_u8(from + 5 * stride, res, 5);
  res = vld1_lane_u8(from + 6 * stride, res, 6);
  res = vld1_lane_u8(from + 7 * stride, res, 7);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16uc pgather<uint8_t, Packet16uc>(const uint8_t* from, Index stride) {
  Packet16uc res = vld1q_dup_u8(from);
  res = vld1q_lane_u8(from + 1 * stride, res, 1);
  res = vld1q_lane_u8(from + 2 * stride, res, 2);
  res = vld1q_lane_u8(from + 3 * stride, res, 3);
  res = vld1q_lane_u8(from + 4 * stride, res, 4);
  res = vld1q_lane_u8(from + 5 * stride, res, 5);
  res = vld1q_lane_u8(from + 6 * stride, res, 6);
  res = vld1q_lane_u8(from + 7 * stride, res, 7);
  res = vld1q_lane_u8(from + 8 * stride, res, 8);
  res = vld1q_lane_u8(from + 9 * stride, res, 9);
  res = vld1q_lane_u8(from + 10 * stride, res, 10);
  res = vld1q_lane_u8(from + 11 * stride, res, 11);
  res = vld1q_lane_u8(from + 12 * stride, res, 12);
  res = vld1q_lane_u8(from + 13 * stride, res, 13);
  res = vld1q_lane_u8(from + 14 * stride, res, 14);
  res = vld1q_lane_u8(from + 15 * stride, res, 15);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4s pgather<int16_t, Packet4s>(const int16_t* from, Index stride) {
  Packet4s res = vld1_dup_s16(from);
  res = vld1_lane_s16(from + 1 * stride, res, 1);
  res = vld1_lane_s16(from + 2 * stride, res, 2);
  res = vld1_lane_s16(from + 3 * stride, res, 3);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8s pgather<int16_t, Packet8s>(const int16_t* from, Index stride) {
  Packet8s res = vld1q_dup_s16(from);
  res = vld1q_lane_s16(from + 1 * stride, res, 1);
  res = vld1q_lane_s16(from + 2 * stride, res, 2);
  res = vld1q_lane_s16(from + 3 * stride, res, 3);
  res = vld1q_lane_s16(from + 4 * stride, res, 4);
  res = vld1q_lane_s16(from + 5 * stride, res, 5);
  res = vld1q_lane_s16(from + 6 * stride, res, 6);
  res = vld1q_lane_s16(from + 7 * stride, res, 7);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4us pgather<uint16_t, Packet4us>(const uint16_t* from, Index stride) {
  Packet4us res = vld1_dup_u16(from);
  res = vld1_lane_u16(from + 1 * stride, res, 1);
  res = vld1_lane_u16(from + 2 * stride, res, 2);
  res = vld1_lane_u16(from + 3 * stride, res, 3);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8us pgather<uint16_t, Packet8us>(const uint16_t* from, Index stride) {
  Packet8us res = vld1q_dup_u16(from);
  res = vld1q_lane_u16(from + 1 * stride, res, 1);
  res = vld1q_lane_u16(from + 2 * stride, res, 2);
  res = vld1q_lane_u16(from + 3 * stride, res, 3);
  res = vld1q_lane_u16(from + 4 * stride, res, 4);
  res = vld1q_lane_u16(from + 5 * stride, res, 5);
  res = vld1q_lane_u16(from + 6 * stride, res, 6);
  res = vld1q_lane_u16(from + 7 * stride, res, 7);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2i pgather<int32_t, Packet2i>(const int32_t* from, Index stride) {
  Packet2i res = vld1_dup_s32(from);
  res = vld1_lane_s32(from + 1 * stride, res, 1);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4i pgather<int32_t, Packet4i>(const int32_t* from, Index stride) {
  Packet4i res = vld1q_dup_s32(from);
  res = vld1q_lane_s32(from + 1 * stride, res, 1);
  res = vld1q_lane_s32(from + 2 * stride, res, 2);
  res = vld1q_lane_s32(from + 3 * stride, res, 3);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ui pgather<uint32_t, Packet2ui>(const uint32_t* from, Index stride) {
  Packet2ui res = vld1_dup_u32(from);
  res = vld1_lane_u32(from + 1 * stride, res, 1);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4ui pgather<uint32_t, Packet4ui>(const uint32_t* from, Index stride) {
  Packet4ui res = vld1q_dup_u32(from);
  res = vld1q_lane_u32(from + 1 * stride, res, 1);
  res = vld1q_lane_u32(from + 2 * stride, res, 2);
  res = vld1q_lane_u32(from + 3 * stride, res, 3);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2l pgather<int64_t, Packet2l>(const int64_t* from, Index stride) {
  Packet2l res = vld1q_dup_s64(from);
  res = vld1q_lane_s64(from + 1 * stride, res, 1);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ul pgather<uint64_t, Packet2ul>(const uint64_t* from, Index stride) {
  Packet2ul res = vld1q_dup_u64(from);
  res = vld1q_lane_u64(from + 1 * stride, res, 1);
  return res;
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<float, Packet2f>(float* to, const Packet2f& from, Index stride) {
  vst1_lane_f32(to + stride * 0, from, 0);
  vst1_lane_f32(to + stride * 1, from, 1);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride) {
  vst1q_lane_f32(to + stride * 0, from, 0);
  vst1q_lane_f32(to + stride * 1, from, 1);
  vst1q_lane_f32(to + stride * 2, from, 2);
  vst1q_lane_f32(to + stride * 3, from, 3);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int8_t, Packet4c>(int8_t* to, const Packet4c& from, Index stride) {
  for (int i = 0; i != 4; i++) *(to + i * stride) = reinterpret_cast<const int8_t*>(&from)[i];
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int8_t, Packet8c>(int8_t* to, const Packet8c& from, Index stride) {
  vst1_lane_s8(to + stride * 0, from, 0);
  vst1_lane_s8(to + stride * 1, from, 1);
  vst1_lane_s8(to + stride * 2, from, 2);
  vst1_lane_s8(to + stride * 3, from, 3);
  vst1_lane_s8(to + stride * 4, from, 4);
  vst1_lane_s8(to + stride * 5, from, 5);
  vst1_lane_s8(to + stride * 6, from, 6);
  vst1_lane_s8(to + stride * 7, from, 7);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int8_t, Packet16c>(int8_t* to, const Packet16c& from,
                                                                       Index stride) {
  vst1q_lane_s8(to + stride * 0, from, 0);
  vst1q_lane_s8(to + stride * 1, from, 1);
  vst1q_lane_s8(to + stride * 2, from, 2);
  vst1q_lane_s8(to + stride * 3, from, 3);
  vst1q_lane_s8(to + stride * 4, from, 4);
  vst1q_lane_s8(to + stride * 5, from, 5);
  vst1q_lane_s8(to + stride * 6, from, 6);
  vst1q_lane_s8(to + stride * 7, from, 7);
  vst1q_lane_s8(to + stride * 8, from, 8);
  vst1q_lane_s8(to + stride * 9, from, 9);
  vst1q_lane_s8(to + stride * 10, from, 10);
  vst1q_lane_s8(to + stride * 11, from, 11);
  vst1q_lane_s8(to + stride * 12, from, 12);
  vst1q_lane_s8(to + stride * 13, from, 13);
  vst1q_lane_s8(to + stride * 14, from, 14);
  vst1q_lane_s8(to + stride * 15, from, 15);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint8_t, Packet4uc>(uint8_t* to, const Packet4uc& from,
                                                                        Index stride) {
  for (int i = 0; i != 4; i++) *(to + i * stride) = reinterpret_cast<const uint8_t*>(&from)[i];
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint8_t, Packet8uc>(uint8_t* to, const Packet8uc& from,
                                                                        Index stride) {
  vst1_lane_u8(to + stride * 0, from, 0);
  vst1_lane_u8(to + stride * 1, from, 1);
  vst1_lane_u8(to + stride * 2, from, 2);
  vst1_lane_u8(to + stride * 3, from, 3);
  vst1_lane_u8(to + stride * 4, from, 4);
  vst1_lane_u8(to + stride * 5, from, 5);
  vst1_lane_u8(to + stride * 6, from, 6);
  vst1_lane_u8(to + stride * 7, from, 7);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint8_t, Packet16uc>(uint8_t* to, const Packet16uc& from,
                                                                         Index stride) {
  vst1q_lane_u8(to + stride * 0, from, 0);
  vst1q_lane_u8(to + stride * 1, from, 1);
  vst1q_lane_u8(to + stride * 2, from, 2);
  vst1q_lane_u8(to + stride * 3, from, 3);
  vst1q_lane_u8(to + stride * 4, from, 4);
  vst1q_lane_u8(to + stride * 5, from, 5);
  vst1q_lane_u8(to + stride * 6, from, 6);
  vst1q_lane_u8(to + stride * 7, from, 7);
  vst1q_lane_u8(to + stride * 8, from, 8);
  vst1q_lane_u8(to + stride * 9, from, 9);
  vst1q_lane_u8(to + stride * 10, from, 10);
  vst1q_lane_u8(to + stride * 11, from, 11);
  vst1q_lane_u8(to + stride * 12, from, 12);
  vst1q_lane_u8(to + stride * 13, from, 13);
  vst1q_lane_u8(to + stride * 14, from, 14);
  vst1q_lane_u8(to + stride * 15, from, 15);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int16_t, Packet4s>(int16_t* to, const Packet4s& from,
                                                                       Index stride) {
  vst1_lane_s16(to + stride * 0, from, 0);
  vst1_lane_s16(to + stride * 1, from, 1);
  vst1_lane_s16(to + stride * 2, from, 2);
  vst1_lane_s16(to + stride * 3, from, 3);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int16_t, Packet8s>(int16_t* to, const Packet8s& from,
                                                                       Index stride) {
  vst1q_lane_s16(to + stride * 0, from, 0);
  vst1q_lane_s16(to + stride * 1, from, 1);
  vst1q_lane_s16(to + stride * 2, from, 2);
  vst1q_lane_s16(to + stride * 3, from, 3);
  vst1q_lane_s16(to + stride * 4, from, 4);
  vst1q_lane_s16(to + stride * 5, from, 5);
  vst1q_lane_s16(to + stride * 6, from, 6);
  vst1q_lane_s16(to + stride * 7, from, 7);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint16_t, Packet4us>(uint16_t* to, const Packet4us& from,
                                                                         Index stride) {
  vst1_lane_u16(to + stride * 0, from, 0);
  vst1_lane_u16(to + stride * 1, from, 1);
  vst1_lane_u16(to + stride * 2, from, 2);
  vst1_lane_u16(to + stride * 3, from, 3);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint16_t, Packet8us>(uint16_t* to, const Packet8us& from,
                                                                         Index stride) {
  vst1q_lane_u16(to + stride * 0, from, 0);
  vst1q_lane_u16(to + stride * 1, from, 1);
  vst1q_lane_u16(to + stride * 2, from, 2);
  vst1q_lane_u16(to + stride * 3, from, 3);
  vst1q_lane_u16(to + stride * 4, from, 4);
  vst1q_lane_u16(to + stride * 5, from, 5);
  vst1q_lane_u16(to + stride * 6, from, 6);
  vst1q_lane_u16(to + stride * 7, from, 7);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int32_t, Packet2i>(int32_t* to, const Packet2i& from,
                                                                       Index stride) {
  vst1_lane_s32(to + stride * 0, from, 0);
  vst1_lane_s32(to + stride * 1, from, 1);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int32_t, Packet4i>(int32_t* to, const Packet4i& from,
                                                                       Index stride) {
  vst1q_lane_s32(to + stride * 0, from, 0);
  vst1q_lane_s32(to + stride * 1, from, 1);
  vst1q_lane_s32(to + stride * 2, from, 2);
  vst1q_lane_s32(to + stride * 3, from, 3);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint32_t, Packet2ui>(uint32_t* to, const Packet2ui& from,
                                                                         Index stride) {
  vst1_lane_u32(to + stride * 0, from, 0);
  vst1_lane_u32(to + stride * 1, from, 1);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint32_t, Packet4ui>(uint32_t* to, const Packet4ui& from,
                                                                         Index stride) {
  vst1q_lane_u32(to + stride * 0, from, 0);
  vst1q_lane_u32(to + stride * 1, from, 1);
  vst1q_lane_u32(to + stride * 2, from, 2);
  vst1q_lane_u32(to + stride * 3, from, 3);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<int64_t, Packet2l>(int64_t* to, const Packet2l& from,
                                                                       Index stride) {
  vst1q_lane_s64(to + stride * 0, from, 0);
  vst1q_lane_s64(to + stride * 1, from, 1);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<uint64_t, Packet2ul>(uint64_t* to, const Packet2ul& from,
                                                                         Index stride) {
  vst1q_lane_u64(to + stride * 0, from, 0);
  vst1q_lane_u64(to + stride * 1, from, 1);
}
 
template <>
EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<int8_t>(const int8_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<uint8_t>(const uint8_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<int16_t>(const int16_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<uint16_t>(const uint16_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<int32_t>(const int32_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<uint32_t>(const uint32_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<int64_t>(const int64_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
template <>
EIGEN_STRONG_INLINE void prefetch<uint64_t>(const uint64_t* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
 
template <>
EIGEN_STRONG_INLINE float pfirst<Packet2f>(const Packet2f& a) {
  return vget_lane_f32(a, 0);
}
template <>
EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) {
  return vgetq_lane_f32(a, 0);
}
template <>
EIGEN_STRONG_INLINE int8_t pfirst<Packet4c>(const Packet4c& a) {
  return static_cast<int8_t>(a & 0xff);
}
template <>
EIGEN_STRONG_INLINE int8_t pfirst<Packet8c>(const Packet8c& a) {
  return vget_lane_s8(a, 0);
}
template <>
EIGEN_STRONG_INLINE int8_t pfirst<Packet16c>(const Packet16c& a) {
  return vgetq_lane_s8(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint8_t pfirst<Packet4uc>(const Packet4uc& a) {
  return static_cast<uint8_t>(a & 0xff);
}
template <>
EIGEN_STRONG_INLINE uint8_t pfirst<Packet8uc>(const Packet8uc& a) {
  return vget_lane_u8(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint8_t pfirst<Packet16uc>(const Packet16uc& a) {
  return vgetq_lane_u8(a, 0);
}
template <>
EIGEN_STRONG_INLINE int16_t pfirst<Packet4s>(const Packet4s& a) {
  return vget_lane_s16(a, 0);
}
template <>
EIGEN_STRONG_INLINE int16_t pfirst<Packet8s>(const Packet8s& a) {
  return vgetq_lane_s16(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t pfirst<Packet4us>(const Packet4us& a) {
  return vget_lane_u16(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t pfirst<Packet8us>(const Packet8us& a) {
  return vgetq_lane_u16(a, 0);
}
template <>
EIGEN_STRONG_INLINE int32_t pfirst<Packet2i>(const Packet2i& a) {
  return vget_lane_s32(a, 0);
}
template <>
EIGEN_STRONG_INLINE int32_t pfirst<Packet4i>(const Packet4i& a) {
  return vgetq_lane_s32(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t pfirst<Packet2ui>(const Packet2ui& a) {
  return vget_lane_u32(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t pfirst<Packet4ui>(const Packet4ui& a) {
  return vgetq_lane_u32(a, 0);
}
template <>
EIGEN_STRONG_INLINE int64_t pfirst<Packet2l>(const Packet2l& a) {
  return vgetq_lane_s64(a, 0);
}
template <>
EIGEN_STRONG_INLINE uint64_t pfirst<Packet2ul>(const Packet2ul& a) {
  return vgetq_lane_u64(a, 0);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f preverse(const Packet2f& a) {
  return vrev64_f32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {
  const float32x4_t a_r64 = vrev64q_f32(a);
  return vcombine_f32(vget_high_f32(a_r64), vget_low_f32(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet4c preverse(const Packet4c& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vrev64_s8(vreinterpret_s8_s32(vdup_n_s32(a)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c preverse(const Packet8c& a) {
  return vrev64_s8(a);
}
template <>
EIGEN_STRONG_INLINE Packet16c preverse(const Packet16c& a) {
  const int8x16_t a_r64 = vrev64q_s8(a);
  return vcombine_s8(vget_high_s8(a_r64), vget_low_s8(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet4uc preverse(const Packet4uc& a) {
  return vget_lane_u32(vreinterpret_u32_u8(vrev64_u8(vreinterpret_u8_u32(vdup_n_u32(a)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc preverse(const Packet8uc& a) {
  return vrev64_u8(a);
}
template <>
EIGEN_STRONG_INLINE Packet16uc preverse(const Packet16uc& a) {
  const uint8x16_t a_r64 = vrev64q_u8(a);
  return vcombine_u8(vget_high_u8(a_r64), vget_low_u8(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet4s preverse(const Packet4s& a) {
  return vrev64_s16(a);
}
template <>
EIGEN_STRONG_INLINE Packet8s preverse(const Packet8s& a) {
  const int16x8_t a_r64 = vrev64q_s16(a);
  return vcombine_s16(vget_high_s16(a_r64), vget_low_s16(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet4us preverse(const Packet4us& a) {
  return vrev64_u16(a);
}
template <>
EIGEN_STRONG_INLINE Packet8us preverse(const Packet8us& a) {
  const uint16x8_t a_r64 = vrev64q_u16(a);
  return vcombine_u16(vget_high_u16(a_r64), vget_low_u16(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet2i preverse(const Packet2i& a) {
  return vrev64_s32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
  const int32x4_t a_r64 = vrev64q_s32(a);
  return vcombine_s32(vget_high_s32(a_r64), vget_low_s32(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet2ui preverse(const Packet2ui& a) {
  return vrev64_u32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4ui preverse(const Packet4ui& a) {
  const uint32x4_t a_r64 = vrev64q_u32(a);
  return vcombine_u32(vget_high_u32(a_r64), vget_low_u32(a_r64));
}
template <>
EIGEN_STRONG_INLINE Packet2l preverse(const Packet2l& a) {
  return vcombine_s64(vget_high_s64(a), vget_low_s64(a));
}
template <>
EIGEN_STRONG_INLINE Packet2ul preverse(const Packet2ul& a) {
  return vcombine_u64(vget_high_u64(a), vget_low_u64(a));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pabs(const Packet2f& a) {
  return vabs_f32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) {
  return vabsq_f32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4c pabs<Packet4c>(const Packet4c& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vabs_s8(vreinterpret_s8_s32(vdup_n_s32(a)))), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8c pabs(const Packet8c& a) {
  return vabs_s8(a);
}
template <>
EIGEN_STRONG_INLINE Packet16c pabs(const Packet16c& a) {
  return vabsq_s8(a);
}
template <>
EIGEN_STRONG_INLINE Packet4s pabs(const Packet4s& a) {
  return vabs_s16(a);
}
template <>
EIGEN_STRONG_INLINE Packet8s pabs(const Packet8s& a) {
  return vabsq_s16(a);
}
template <>
EIGEN_STRONG_INLINE Packet2i pabs(const Packet2i& a) {
  return vabs_s32(a);
}
template <>
EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) {
  return vabsq_s32(a);
}
template <>
EIGEN_STRONG_INLINE Packet2l pabs(const Packet2l& a) {
#if EIGEN_ARCH_ARM64
  return vabsq_s64(a);
#else
  // NOTE: From <https://graphics.stanford.edu/~seander/bithacks.html#IntegerAbs>. The addition is
  // done in the unsigned domain: at `a == INT64_MIN`, `mask == -1`, so the signed `a + mask` is UB
  // (it wraps to INT64_MIN on every real target, which is exactly what's needed here).
  const int64x2_t mask = vshrq_n_s64(a, 63);
  const uint64x2_t sum = vaddq_u64(vreinterpretq_u64_s64(a), vreinterpretq_u64_s64(mask));
  return veorq_s64(vreinterpretq_s64_u64(sum), mask);
#endif
}
template <>
EIGEN_STRONG_INLINE Packet2f psignbit(const Packet2f& a) {
  return vreinterpret_f32_s32(vshr_n_s32(vreinterpret_s32_f32(a), 31));
}
template <>
EIGEN_STRONG_INLINE Packet4f psignbit(const Packet4f& a) {
  return vreinterpretq_f32_s32(vshrq_n_s32(vreinterpretq_s32_f32(a), 31));
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pfrexp<Packet2f>(const Packet2f& a, Packet2f& exponent) {
  return pfrexp_generic(a, exponent);
}
template <>
EIGEN_STRONG_INLINE Packet4f pfrexp<Packet4f>(const Packet4f& a, Packet4f& exponent) {
  return pfrexp_generic(a, exponent);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pldexp<Packet2f>(const Packet2f& a, const Packet2f& exponent) {
  return pldexp_generic(a, exponent);
}
template <>
EIGEN_STRONG_INLINE Packet4f pldexp<Packet4f>(const Packet4f& a, const Packet4f& exponent) {
  return pldexp_generic(a, exponent);
}
 
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE float predux<Packet2f>(const Packet2f& a) {
  return vaddv_f32(a);
}
template <>
EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) {
  return vaddvq_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Index predux_count(const Packet4f& a) {
  const uint32x4_t nonzero = vbicq_u32(vdupq_n_u32(1), vceqq_f32(a, vdupq_n_f32(0.0f)));
  return static_cast<Index>(vaddvq_u32(nonzero));
}
#else
template <>
EIGEN_STRONG_INLINE float predux<Packet2f>(const Packet2f& a) {
  return vget_lane_f32(vpadd_f32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) {
  const float32x2_t sum = vadd_f32(vget_low_f32(a), vget_high_f32(a));
  return vget_lane_f32(vpadd_f32(sum, sum), 0);
}
#endif
template <>
EIGEN_STRONG_INLINE int8_t predux<Packet4c>(const Packet4c& a) {
  const int8x8_t a_dup = vreinterpret_s8_s32(vdup_n_s32(a));
  int8x8_t sum = vpadd_s8(a_dup, a_dup);
  sum = vpadd_s8(sum, sum);
  return vget_lane_s8(sum, 0);
}
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE int8_t predux<Packet8c>(const Packet8c& a) {
  return vaddv_s8(a);
}
template <>
EIGEN_STRONG_INLINE int8_t predux<Packet16c>(const Packet16c& a) {
  return vaddvq_s8(a);
}
#else
template <>
EIGEN_STRONG_INLINE int8_t predux<Packet8c>(const Packet8c& a) {
  int8x8_t sum = vpadd_s8(a, a);
  sum = vpadd_s8(sum, sum);
  sum = vpadd_s8(sum, sum);
  return vget_lane_s8(sum, 0);
}
template <>
EIGEN_STRONG_INLINE int8_t predux<Packet16c>(const Packet16c& a) {
  int8x8_t sum = vadd_s8(vget_low_s8(a), vget_high_s8(a));
  sum = vpadd_s8(sum, sum);
  sum = vpadd_s8(sum, sum);
  sum = vpadd_s8(sum, sum);
  return vget_lane_s8(sum, 0);
}
#endif
template <>
EIGEN_STRONG_INLINE uint8_t predux<Packet4uc>(const Packet4uc& a) {
  const uint8x8_t a_dup = vreinterpret_u8_u32(vdup_n_u32(a));
  uint8x8_t sum = vpadd_u8(a_dup, a_dup);
  sum = vpadd_u8(sum, sum);
  return vget_lane_u8(sum, 0);
}
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE uint8_t predux<Packet8uc>(const Packet8uc& a) {
  return vaddv_u8(a);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux<Packet16uc>(const Packet16uc& a) {
  return vaddvq_u8(a);
}
template <>
EIGEN_STRONG_INLINE int16_t predux<Packet4s>(const Packet4s& a) {
  return vaddv_s16(a);
}
template <>
EIGEN_STRONG_INLINE int16_t predux<Packet8s>(const Packet8s& a) {
  return vaddvq_s16(a);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux<Packet4us>(const Packet4us& a) {
  return vaddv_u16(a);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux<Packet8us>(const Packet8us& a) {
  return vaddvq_u16(a);
}
template <>
EIGEN_STRONG_INLINE int32_t predux<Packet2i>(const Packet2i& a) {
  return vaddv_s32(a);
}
template <>
EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a) {
  return vaddvq_s32(a);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux<Packet2ui>(const Packet2ui& a) {
  return vaddv_u32(a);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux<Packet4ui>(const Packet4ui& a) {
  return vaddvq_u32(a);
}
template <>
EIGEN_STRONG_INLINE int64_t predux<Packet2l>(const Packet2l& a) {
  return vaddvq_s64(a);
}
template <>
EIGEN_STRONG_INLINE uint64_t predux<Packet2ul>(const Packet2ul& a) {
  return vaddvq_u64(a);
}
#else
template <>
EIGEN_STRONG_INLINE uint8_t predux<Packet8uc>(const Packet8uc& a) {
  uint8x8_t sum = vpadd_u8(a, a);
  sum = vpadd_u8(sum, sum);
  sum = vpadd_u8(sum, sum);
  return vget_lane_u8(sum, 0);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux<Packet16uc>(const Packet16uc& a) {
  uint8x8_t sum = vadd_u8(vget_low_u8(a), vget_high_u8(a));
  sum = vpadd_u8(sum, sum);
  sum = vpadd_u8(sum, sum);
  sum = vpadd_u8(sum, sum);
  return vget_lane_u8(sum, 0);
}
template <>
EIGEN_STRONG_INLINE int16_t predux<Packet4s>(const Packet4s& a) {
  const int16x4_t sum = vpadd_s16(a, a);
  return vget_lane_s16(vpadd_s16(sum, sum), 0);
}
template <>
EIGEN_STRONG_INLINE int16_t predux<Packet8s>(const Packet8s& a) {
  int16x4_t sum = vadd_s16(vget_low_s16(a), vget_high_s16(a));
  sum = vpadd_s16(sum, sum);
  sum = vpadd_s16(sum, sum);
  return vget_lane_s16(sum, 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux<Packet4us>(const Packet4us& a) {
  const uint16x4_t sum = vpadd_u16(a, a);
  return vget_lane_u16(vpadd_u16(sum, sum), 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux<Packet8us>(const Packet8us& a) {
  uint16x4_t sum = vadd_u16(vget_low_u16(a), vget_high_u16(a));
  sum = vpadd_u16(sum, sum);
  sum = vpadd_u16(sum, sum);
  return vget_lane_u16(sum, 0);
}
template <>
EIGEN_STRONG_INLINE int32_t predux<Packet2i>(const Packet2i& a) {
  return vget_lane_s32(vpadd_s32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a) {
  const int32x2_t sum = vadd_s32(vget_low_s32(a), vget_high_s32(a));
  return vget_lane_s32(vpadd_s32(sum, sum), 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux<Packet2ui>(const Packet2ui& a) {
  return vget_lane_u32(vpadd_u32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux<Packet4ui>(const Packet4ui& a) {
  const uint32x2_t sum = vadd_u32(vget_low_u32(a), vget_high_u32(a));
  return vget_lane_u32(vpadd_u32(sum, sum), 0);
}
template <>
EIGEN_STRONG_INLINE int64_t predux<Packet2l>(const Packet2l& a) {
  return vgetq_lane_s64(a, 0) + vgetq_lane_s64(a, 1);
}
template <>
EIGEN_STRONG_INLINE uint64_t predux<Packet2ul>(const Packet2ul& a) {
  return vgetq_lane_u64(a, 0) + vgetq_lane_u64(a, 1);
}
#endif
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4c predux_half(const Packet8c& a) {
  return vget_lane_s32(vreinterpret_s32_s8(vadd_s8(a, vreinterpret_s8_s32(vrev64_s32(vreinterpret_s32_s8(a))))), 0);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8c predux_half(const Packet16c& a) {
  return vadd_s8(vget_high_s8(a), vget_low_s8(a));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4uc predux_half(const Packet8uc& a) {
  return vget_lane_u32(vreinterpret_u32_u8(vadd_u8(a, vreinterpret_u8_u32(vrev64_u32(vreinterpret_u32_u8(a))))), 0);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8uc predux_half(const Packet16uc& a) {
  return vadd_u8(vget_high_u8(a), vget_low_u8(a));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4s predux_half(const Packet8s& a) {
  return vadd_s16(vget_high_s16(a), vget_low_s16(a));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4us predux_half(const Packet8us& a) {
  return vadd_u16(vget_high_u16(a), vget_low_u16(a));
}
 
// Other reduction functions:
// mul
template <>
EIGEN_STRONG_INLINE float predux_mul<Packet2f>(const Packet2f& a) {
  return vget_lane_f32(a, 0) * vget_lane_f32(a, 1);
}
template <>
EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a) {
  return predux_mul<Packet2f>(vmul_f32(vget_low_f32(a), vget_high_f32(a)));
}
template <>
EIGEN_STRONG_INLINE int8_t predux_mul<Packet4c>(const Packet4c& a) {
  int8x8_t prod = vreinterpret_s8_s32(vdup_n_s32(a));
  prod = vmul_s8(prod, vrev16_s8(prod));
  return vget_lane_s8(prod, 0) * vget_lane_s8(prod, 2);
}
template <>
EIGEN_STRONG_INLINE int8_t predux_mul<Packet8c>(const Packet8c& a) {
  int8x8_t prod = vmul_s8(a, vrev16_s8(a));
  prod = vmul_s8(prod, vrev32_s8(prod));
  return vget_lane_s8(prod, 0) * vget_lane_s8(prod, 4);
}
template <>
EIGEN_STRONG_INLINE int8_t predux_mul<Packet16c>(const Packet16c& a) {
  return predux_mul<Packet8c>(vmul_s8(vget_low_s8(a), vget_high_s8(a)));
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_mul<Packet4uc>(const Packet4uc& a) {
  uint8x8_t prod = vreinterpret_u8_u32(vdup_n_u32(a));
  prod = vmul_u8(prod, vrev16_u8(prod));
  return vget_lane_u8(prod, 0) * vget_lane_u8(prod, 2);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_mul<Packet8uc>(const Packet8uc& a) {
  uint8x8_t prod = vmul_u8(a, vrev16_u8(a));
  prod = vmul_u8(prod, vrev32_u8(prod));
  return vget_lane_u8(prod, 0) * vget_lane_u8(prod, 4);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_mul<Packet16uc>(const Packet16uc& a) {
  return predux_mul<Packet8uc>(vmul_u8(vget_low_u8(a), vget_high_u8(a)));
}
template <>
EIGEN_STRONG_INLINE int16_t predux_mul<Packet4s>(const Packet4s& a) {
  const int16x4_t prod = vmul_s16(a, vrev32_s16(a));
  return vget_lane_s16(prod, 0) * vget_lane_s16(prod, 2);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_mul<Packet8s>(const Packet8s& a) {
  int16x4_t prod;
 
  // Get the product of a_lo * a_hi -> |a1*a5|a2*a6|a3*a7|a4*a8|
  prod = vmul_s16(vget_low_s16(a), vget_high_s16(a));
  // Swap and multiply |a1*a5*a2*a6|a3*a7*a4*a8|
  prod = vmul_s16(prod, vrev32_s16(prod));
  // Multiply |a1*a5*a2*a6*a3*a7*a4*a8|
  return vget_lane_s16(prod, 0) * vget_lane_s16(prod, 2);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_mul<Packet4us>(const Packet4us& a) {
  const uint16x4_t prod = vmul_u16(a, vrev32_u16(a));
  return vget_lane_u16(prod, 0) * vget_lane_u16(prod, 2);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_mul<Packet8us>(const Packet8us& a) {
  uint16x4_t prod;
 
  // Get the product of a_lo * a_hi -> |a1*a5|a2*a6|a3*a7|a4*a8|
  prod = vmul_u16(vget_low_u16(a), vget_high_u16(a));
  // Swap and multiply |a1*a5*a2*a6|a3*a7*a4*a8|
  prod = vmul_u16(prod, vrev32_u16(prod));
  // Multiply |a1*a5*a2*a6*a3*a7*a4*a8|
  return vget_lane_u16(prod, 0) * vget_lane_u16(prod, 2);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_mul<Packet2i>(const Packet2i& a) {
  return vget_lane_s32(a, 0) * vget_lane_s32(a, 1);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_mul<Packet4i>(const Packet4i& a) {
  return predux_mul<Packet2i>(vmul_s32(vget_low_s32(a), vget_high_s32(a)));
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_mul<Packet2ui>(const Packet2ui& a) {
  return vget_lane_u32(a, 0) * vget_lane_u32(a, 1);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_mul<Packet4ui>(const Packet4ui& a) {
  return predux_mul<Packet2ui>(vmul_u32(vget_low_u32(a), vget_high_u32(a)));
}
template <>
EIGEN_STRONG_INLINE int64_t predux_mul<Packet2l>(const Packet2l& a) {
  return vgetq_lane_s64(a, 0) * vgetq_lane_s64(a, 1);
}
template <>
EIGEN_STRONG_INLINE uint64_t predux_mul<Packet2ul>(const Packet2ul& a) {
  return vgetq_lane_u64(a, 0) * vgetq_lane_u64(a, 1);
}
 
// min
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE float predux_min<Packet2f>(const Packet2f& a) {
  return vminv_f32(a);
}
template <>
EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) {
  return vminvq_f32(a);
}
#else
template <>
EIGEN_STRONG_INLINE float predux_min<Packet2f>(const Packet2f& a) {
  return vget_lane_f32(vpmin_f32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) {
  const float32x2_t min = vmin_f32(vget_low_f32(a), vget_high_f32(a));
  return vget_lane_f32(vpmin_f32(min, min), 0);
}
#endif
template <>
EIGEN_STRONG_INLINE int8_t predux_min<Packet4c>(const Packet4c& a) {
  const int8x8_t a_dup = vreinterpret_s8_s32(vdup_n_s32(a));
  int8x8_t min = vpmin_s8(a_dup, a_dup);
  min = vpmin_s8(min, min);
  return vget_lane_s8(min, 0);
}
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE int8_t predux_min<Packet8c>(const Packet8c& a) {
  return vminv_s8(a);
}
template <>
EIGEN_STRONG_INLINE int8_t predux_min<Packet16c>(const Packet16c& a) {
  return vminvq_s8(a);
}
#else
template <>
EIGEN_STRONG_INLINE int8_t predux_min<Packet8c>(const Packet8c& a) {
  int8x8_t min = vpmin_s8(a, a);
  min = vpmin_s8(min, min);
  min = vpmin_s8(min, min);
  return vget_lane_s8(min, 0);
}
template <>
EIGEN_STRONG_INLINE int8_t predux_min<Packet16c>(const Packet16c& a) {
  int8x8_t min = vmin_s8(vget_low_s8(a), vget_high_s8(a));
  min = vpmin_s8(min, min);
  min = vpmin_s8(min, min);
  min = vpmin_s8(min, min);
  return vget_lane_s8(min, 0);
}
#endif
template <>
EIGEN_STRONG_INLINE uint8_t predux_min<Packet4uc>(const Packet4uc& a) {
  const uint8x8_t a_dup = vreinterpret_u8_u32(vdup_n_u32(a));
  uint8x8_t min = vpmin_u8(a_dup, a_dup);
  min = vpmin_u8(min, min);
  return vget_lane_u8(min, 0);
}
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE uint8_t predux_min<Packet8uc>(const Packet8uc& a) {
  return vminv_u8(a);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_min<Packet16uc>(const Packet16uc& a) {
  return vminvq_u8(a);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_min<Packet4s>(const Packet4s& a) {
  return vminv_s16(a);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_min<Packet8s>(const Packet8s& a) {
  return vminvq_s16(a);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_min<Packet4us>(const Packet4us& a) {
  return vminv_u16(a);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_min<Packet8us>(const Packet8us& a) {
  return vminvq_u16(a);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_min<Packet2i>(const Packet2i& a) {
  return vminv_s32(a);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a) {
  return vminvq_s32(a);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_min<Packet2ui>(const Packet2ui& a) {
  return vminv_u32(a);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_min<Packet4ui>(const Packet4ui& a) {
  return vminvq_u32(a);
}
#else
template <>
EIGEN_STRONG_INLINE uint8_t predux_min<Packet8uc>(const Packet8uc& a) {
  uint8x8_t min = vpmin_u8(a, a);
  min = vpmin_u8(min, min);
  min = vpmin_u8(min, min);
  return vget_lane_u8(min, 0);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_min<Packet16uc>(const Packet16uc& a) {
  uint8x8_t min = vmin_u8(vget_low_u8(a), vget_high_u8(a));
  min = vpmin_u8(min, min);
  min = vpmin_u8(min, min);
  min = vpmin_u8(min, min);
  return vget_lane_u8(min, 0);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_min<Packet4s>(const Packet4s& a) {
  const int16x4_t min = vpmin_s16(a, a);
  return vget_lane_s16(vpmin_s16(min, min), 0);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_min<Packet8s>(const Packet8s& a) {
  int16x4_t min = vmin_s16(vget_low_s16(a), vget_high_s16(a));
  min = vpmin_s16(min, min);
  min = vpmin_s16(min, min);
  return vget_lane_s16(min, 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_min<Packet4us>(const Packet4us& a) {
  const uint16x4_t min = vpmin_u16(a, a);
  return vget_lane_u16(vpmin_u16(min, min), 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_min<Packet8us>(const Packet8us& a) {
  uint16x4_t min = vmin_u16(vget_low_u16(a), vget_high_u16(a));
  min = vpmin_u16(min, min);
  min = vpmin_u16(min, min);
  return vget_lane_u16(min, 0);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_min<Packet2i>(const Packet2i& a) {
  return vget_lane_s32(vpmin_s32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a) {
  const int32x2_t min = vmin_s32(vget_low_s32(a), vget_high_s32(a));
  return vget_lane_s32(vpmin_s32(min, min), 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_min<Packet2ui>(const Packet2ui& a) {
  return vget_lane_u32(vpmin_u32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_min<Packet4ui>(const Packet4ui& a) {
  const uint32x2_t min = vmin_u32(vget_low_u32(a), vget_high_u32(a));
  return vget_lane_u32(vpmin_u32(min, min), 0);
}
#endif
template <>
EIGEN_STRONG_INLINE int64_t predux_min<Packet2l>(const Packet2l& a) {
  return (std::min)(vgetq_lane_s64(a, 0), vgetq_lane_s64(a, 1));
}
template <>
EIGEN_STRONG_INLINE uint64_t predux_min<Packet2ul>(const Packet2ul& a) {
  return (std::min)(vgetq_lane_u64(a, 0), vgetq_lane_u64(a, 1));
}
 
// max
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE float predux_max<Packet2f>(const Packet2f& a) {
  return vmaxv_f32(a);
}
template <>
EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) {
  return vmaxvq_f32(a);
}
#else
template <>
EIGEN_STRONG_INLINE float predux_max<Packet2f>(const Packet2f& a) {
  return vget_lane_f32(vpmax_f32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) {
  const float32x2_t max = vmax_f32(vget_low_f32(a), vget_high_f32(a));
  return vget_lane_f32(vpmax_f32(max, max), 0);
}
#endif
template <>
EIGEN_STRONG_INLINE int8_t predux_max<Packet4c>(const Packet4c& a) {
  const int8x8_t a_dup = vreinterpret_s8_s32(vdup_n_s32(a));
  int8x8_t max = vpmax_s8(a_dup, a_dup);
  max = vpmax_s8(max, max);
  return vget_lane_s8(max, 0);
}
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE int8_t predux_max<Packet8c>(const Packet8c& a) {
  return vmaxv_s8(a);
}
template <>
EIGEN_STRONG_INLINE int8_t predux_max<Packet16c>(const Packet16c& a) {
  return vmaxvq_s8(a);
}
#else
template <>
EIGEN_STRONG_INLINE int8_t predux_max<Packet8c>(const Packet8c& a) {
  int8x8_t max = vpmax_s8(a, a);
  max = vpmax_s8(max, max);
  max = vpmax_s8(max, max);
  return vget_lane_s8(max, 0);
}
template <>
EIGEN_STRONG_INLINE int8_t predux_max<Packet16c>(const Packet16c& a) {
  int8x8_t max = vmax_s8(vget_low_s8(a), vget_high_s8(a));
  max = vpmax_s8(max, max);
  max = vpmax_s8(max, max);
  max = vpmax_s8(max, max);
  return vget_lane_s8(max, 0);
}
#endif
template <>
EIGEN_STRONG_INLINE uint8_t predux_max<Packet4uc>(const Packet4uc& a) {
  const uint8x8_t a_dup = vreinterpret_u8_u32(vdup_n_u32(a));
  uint8x8_t max = vpmax_u8(a_dup, a_dup);
  max = vpmax_u8(max, max);
  return vget_lane_u8(max, 0);
}
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE uint8_t predux_max<Packet8uc>(const Packet8uc& a) {
  return vmaxv_u8(a);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_max<Packet16uc>(const Packet16uc& a) {
  return vmaxvq_u8(a);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_max<Packet4s>(const Packet4s& a) {
  return vmaxv_s16(a);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_max<Packet8s>(const Packet8s& a) {
  return vmaxvq_s16(a);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_max<Packet4us>(const Packet4us& a) {
  return vmaxv_u16(a);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_max<Packet8us>(const Packet8us& a) {
  return vmaxvq_u16(a);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_max<Packet2i>(const Packet2i& a) {
  return vmaxv_s32(a);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a) {
  return vmaxvq_s32(a);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_max<Packet2ui>(const Packet2ui& a) {
  return vmaxv_u32(a);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_max<Packet4ui>(const Packet4ui& a) {
  return vmaxvq_u32(a);
}
#else
template <>
EIGEN_STRONG_INLINE uint8_t predux_max<Packet8uc>(const Packet8uc& a) {
  uint8x8_t max = vpmax_u8(a, a);
  max = vpmax_u8(max, max);
  max = vpmax_u8(max, max);
  return vget_lane_u8(max, 0);
}
template <>
EIGEN_STRONG_INLINE uint8_t predux_max<Packet16uc>(const Packet16uc& a) {
  uint8x8_t max = vmax_u8(vget_low_u8(a), vget_high_u8(a));
  max = vpmax_u8(max, max);
  max = vpmax_u8(max, max);
  max = vpmax_u8(max, max);
  return vget_lane_u8(max, 0);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_max<Packet4s>(const Packet4s& a) {
  const int16x4_t max = vpmax_s16(a, a);
  return vget_lane_s16(vpmax_s16(max, max), 0);
}
template <>
EIGEN_STRONG_INLINE int16_t predux_max<Packet8s>(const Packet8s& a) {
  int16x4_t max = vmax_s16(vget_low_s16(a), vget_high_s16(a));
  max = vpmax_s16(max, max);
  max = vpmax_s16(max, max);
  return vget_lane_s16(max, 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_max<Packet4us>(const Packet4us& a) {
  const uint16x4_t max = vpmax_u16(a, a);
  return vget_lane_u16(vpmax_u16(max, max), 0);
}
template <>
EIGEN_STRONG_INLINE uint16_t predux_max<Packet8us>(const Packet8us& a) {
  uint16x4_t max = vmax_u16(vget_low_u16(a), vget_high_u16(a));
  max = vpmax_u16(max, max);
  max = vpmax_u16(max, max);
  return vget_lane_u16(max, 0);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_max<Packet2i>(const Packet2i& a) {
  return vget_lane_s32(vpmax_s32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a) {
  const int32x2_t max = vmax_s32(vget_low_s32(a), vget_high_s32(a));
  return vget_lane_s32(vpmax_s32(max, max), 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_max<Packet2ui>(const Packet2ui& a) {
  return vget_lane_u32(vpmax_u32(a, a), 0);
}
template <>
EIGEN_STRONG_INLINE uint32_t predux_max<Packet4ui>(const Packet4ui& a) {
  const uint32x2_t max = vmax_u32(vget_low_u32(a), vget_high_u32(a));
  return vget_lane_u32(vpmax_u32(max, max), 0);
}
#endif
template <>
EIGEN_STRONG_INLINE int64_t predux_max<Packet2l>(const Packet2l& a) {
  return (std::max)(vgetq_lane_s64(a, 0), vgetq_lane_s64(a, 1));
}
template <>
EIGEN_STRONG_INLINE uint64_t predux_max<Packet2ul>(const Packet2ul& a) {
  return (std::max)(vgetq_lane_u64(a, 0), vgetq_lane_u64(a, 1));
}
 
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2f& x) {
  return vget_lane_u64(vreinterpret_u64_f32(x), 0) != 0;
}
 
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4f& x) {
  uint32x4_t u = vreinterpretq_u32_f32(x);
#if EIGEN_ARCH_ARM64
  return vget_lane_u64(vreinterpret_u64_u16(vmovn_u32(u)), 0);
#else
  uint32x2_t tmp = vorr_u32(vget_low_u32(u), vget_high_u32(u));
  uint32_t a, b;
  // GCC and Clang refuse to emit this instruction.
  asm("vmov %0, %1, %P2" : "=r"(a), "=r"(b) : "w"(tmp));
  return a | b;
#endif
}
 
namespace detail {
// Whether any bit of a 128-bit register is set. Integer masks reduce through these bits rather than through the
// generic horizontal sum. On ARMv7, the 32-bit lane move after vpmax keeps predux_all's dependency chain as short as
// the sum's; a two-register vmov lengthens it.
EIGEN_STRONG_INLINE bool neon_any_bit(uint32x4_t u) {
#if EIGEN_ARCH_ARM64
  return vmaxvq_u32(u) != 0;
#else
  uint32x2_t tmp = vorr_u32(vget_low_u32(u), vget_high_u32(u));
  return vget_lane_u32(vpmax_u32(tmp, tmp), 0) != 0;
#endif
}
}  // namespace detail
 
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4c& x) {
  return static_cast<int32_t>(x) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4uc& x) {
  return static_cast<uint32_t>(x) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet8c& x) {
  return vget_lane_u64(vreinterpret_u64_s8(x), 0) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet8uc& x) {
  return vget_lane_u64(vreinterpret_u64_u8(x), 0) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet16c& x) {
  return detail::neon_any_bit(vreinterpretq_u32_s8(x));
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet16uc& x) {
  return detail::neon_any_bit(vreinterpretq_u32_u8(x));
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4s& x) {
  return vget_lane_u64(vreinterpret_u64_s16(x), 0) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4us& x) {
  return vget_lane_u64(vreinterpret_u64_u16(x), 0) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet8s& x) {
  return detail::neon_any_bit(vreinterpretq_u32_s16(x));
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet8us& x) {
  return detail::neon_any_bit(vreinterpretq_u32_u16(x));
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2i& x) {
  return vget_lane_u64(vreinterpret_u64_s32(x), 0) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2ui& x) {
  return vget_lane_u64(vreinterpret_u64_u32(x), 0) != 0;
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4i& x) {
  return detail::neon_any_bit(vreinterpretq_u32_s32(x));
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4ui& x) {
  return detail::neon_any_bit(x);
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2l& x) {
  return detail::neon_any_bit(vreinterpretq_u32_s64(x));
}
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2ul& x) {
  return detail::neon_any_bit(vreinterpretq_u32_u64(x));
}
 
// Helpers for ptranspose.
namespace detail {
 
template <typename Packet>
void zip_in_place(Packet& p1, Packet& p2);
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet2f>(Packet2f& p1, Packet2f& p2) {
  const float32x2x2_t tmp = vzip_f32(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet4f>(Packet4f& p1, Packet4f& p2) {
  const float32x4x2_t tmp = vzipq_f32(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet8c>(Packet8c& p1, Packet8c& p2) {
  const int8x8x2_t tmp = vzip_s8(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet16c>(Packet16c& p1, Packet16c& p2) {
  const int8x16x2_t tmp = vzipq_s8(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet8uc>(Packet8uc& p1, Packet8uc& p2) {
  const uint8x8x2_t tmp = vzip_u8(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet16uc>(Packet16uc& p1, Packet16uc& p2) {
  const uint8x16x2_t tmp = vzipq_u8(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet2i>(Packet2i& p1, Packet2i& p2) {
  const int32x2x2_t tmp = vzip_s32(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet4i>(Packet4i& p1, Packet4i& p2) {
  const int32x4x2_t tmp = vzipq_s32(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet2ui>(Packet2ui& p1, Packet2ui& p2) {
  const uint32x2x2_t tmp = vzip_u32(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet4ui>(Packet4ui& p1, Packet4ui& p2) {
  const uint32x4x2_t tmp = vzipq_u32(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet4s>(Packet4s& p1, Packet4s& p2) {
  const int16x4x2_t tmp = vzip_s16(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet8s>(Packet8s& p1, Packet8s& p2) {
  const int16x8x2_t tmp = vzipq_s16(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet4us>(Packet4us& p1, Packet4us& p2) {
  const uint16x4x2_t tmp = vzip_u16(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet8us>(Packet8us& p1, Packet8us& p2) {
  const uint16x8x2_t tmp = vzipq_u16(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
 
template <typename Packet>
EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 2>& kernel) {
  zip_in_place(kernel.packet[0], kernel.packet[1]);
}
 
template <typename Packet>
EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 4>& kernel) {
  zip_in_place(kernel.packet[0], kernel.packet[2]);
  zip_in_place(kernel.packet[1], kernel.packet[3]);
  zip_in_place(kernel.packet[0], kernel.packet[1]);
  zip_in_place(kernel.packet[2], kernel.packet[3]);
}
 
template <typename Packet>
EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 8>& kernel) {
  zip_in_place(kernel.packet[0], kernel.packet[4]);
  zip_in_place(kernel.packet[1], kernel.packet[5]);
  zip_in_place(kernel.packet[2], kernel.packet[6]);
  zip_in_place(kernel.packet[3], kernel.packet[7]);
 
  zip_in_place(kernel.packet[0], kernel.packet[2]);
  zip_in_place(kernel.packet[1], kernel.packet[3]);
  zip_in_place(kernel.packet[4], kernel.packet[6]);
  zip_in_place(kernel.packet[5], kernel.packet[7]);
 
  zip_in_place(kernel.packet[0], kernel.packet[1]);
  zip_in_place(kernel.packet[2], kernel.packet[3]);
  zip_in_place(kernel.packet[4], kernel.packet[5]);
  zip_in_place(kernel.packet[6], kernel.packet[7]);
}
 
template <typename Packet>
EIGEN_ALWAYS_INLINE void ptranspose_impl(PacketBlock<Packet, 16>& kernel) {
  EIGEN_UNROLL_LOOP
  for (int i = 0; i < 4; ++i) {
    const int m = (1 << i);
    EIGEN_UNROLL_LOOP
    for (int j = 0; j < m; ++j) {
      const int n = (1 << (3 - i));
      EIGEN_UNROLL_LOOP
      for (int k = 0; k < n; ++k) {
        const int idx = 2 * j * n + k;
        zip_in_place(kernel.packet[idx], kernel.packet[idx + n]);
      }
    }
  }
}
 
}  // namespace detail
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2f, 2>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4f, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4c, 4>& kernel) {
  const int8x8_t a = vreinterpret_s8_s32(vset_lane_s32(kernel.packet[2], vdup_n_s32(kernel.packet[0]), 1));
  const int8x8_t b = vreinterpret_s8_s32(vset_lane_s32(kernel.packet[3], vdup_n_s32(kernel.packet[1]), 1));
 
  const int8x8x2_t zip8 = vzip_s8(a, b);
  const int16x4x2_t zip16 = vzip_s16(vreinterpret_s16_s8(zip8.val[0]), vreinterpret_s16_s8(zip8.val[1]));
 
  kernel.packet[0] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[0]), 0);
  kernel.packet[1] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[0]), 1);
  kernel.packet[2] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[1]), 0);
  kernel.packet[3] = vget_lane_s32(vreinterpret_s32_s16(zip16.val[1]), 1);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8c, 8>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8c, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16c, 16>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16c, 8>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16c, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4uc, 4>& kernel) {
  const uint8x8_t a = vreinterpret_u8_u32(vset_lane_u32(kernel.packet[2], vdup_n_u32(kernel.packet[0]), 1));
  const uint8x8_t b = vreinterpret_u8_u32(vset_lane_u32(kernel.packet[3], vdup_n_u32(kernel.packet[1]), 1));
 
  const uint8x8x2_t zip8 = vzip_u8(a, b);
  const uint16x4x2_t zip16 = vzip_u16(vreinterpret_u16_u8(zip8.val[0]), vreinterpret_u16_u8(zip8.val[1]));
 
  kernel.packet[0] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[0]), 0);
  kernel.packet[1] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[0]), 1);
  kernel.packet[2] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[1]), 0);
  kernel.packet[3] = vget_lane_u32(vreinterpret_u32_u16(zip16.val[1]), 1);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8uc, 8>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8uc, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16uc, 16>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16uc, 8>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet16uc, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4s, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8s, 8>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8s, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4us, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8us, 8>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8us, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2i, 2>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4i, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2ui, 2>& kernel) {
  detail::zip_in_place(kernel.packet[0], kernel.packet[1]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4ui, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2l, 2>& kernel) {
#if EIGEN_ARCH_ARM64
  const int64x2_t tmp1 = vzip1q_s64(kernel.packet[0], kernel.packet[1]);
  kernel.packet[1] = vzip2q_s64(kernel.packet[0], kernel.packet[1]);
  kernel.packet[0] = tmp1;
#else
  const int64x1_t tmp[2][2] = {{vget_low_s64(kernel.packet[0]), vget_high_s64(kernel.packet[0])},
                               {vget_low_s64(kernel.packet[1]), vget_high_s64(kernel.packet[1])}};
 
  kernel.packet[0] = vcombine_s64(tmp[0][0], tmp[1][0]);
  kernel.packet[1] = vcombine_s64(tmp[0][1], tmp[1][1]);
#endif
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2ul, 2>& kernel) {
#if EIGEN_ARCH_ARM64
  const uint64x2_t tmp1 = vzip1q_u64(kernel.packet[0], kernel.packet[1]);
  kernel.packet[1] = vzip2q_u64(kernel.packet[0], kernel.packet[1]);
  kernel.packet[0] = tmp1;
#else
  const uint64x1_t tmp[2][2] = {{vget_low_u64(kernel.packet[0]), vget_high_u64(kernel.packet[0])},
                                {vget_low_u64(kernel.packet[1]), vget_high_u64(kernel.packet[1])}};
 
  kernel.packet[0] = vcombine_u64(tmp[0][0], tmp[1][0]);
  kernel.packet[1] = vcombine_u64(tmp[0][1], tmp[1][1]);
#endif
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2f pselect(const Packet2f& mask, const Packet2f& a, const Packet2f& b) {
  return vbsl_f32(vreinterpret_u32_f32(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4f pselect(const Packet4f& mask, const Packet4f& a, const Packet4f& b) {
  return vbslq_f32(vreinterpretq_u32_f32(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8c pselect(const Packet8c& mask, const Packet8c& a, const Packet8c& b) {
  return vbsl_s8(vreinterpret_u8_s8(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16c pselect(const Packet16c& mask, const Packet16c& a, const Packet16c& b) {
  return vbslq_s8(vreinterpretq_u8_s8(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8uc pselect(const Packet8uc& mask, const Packet8uc& a, const Packet8uc& b) {
  return vbsl_u8(mask, a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet16uc pselect(const Packet16uc& mask, const Packet16uc& a,
                                                         const Packet16uc& b) {
  return vbslq_u8(mask, a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4s pselect(const Packet4s& mask, const Packet4s& a, const Packet4s& b) {
  return vbsl_s16(vreinterpret_u16_s16(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8s pselect(const Packet8s& mask, const Packet8s& a, const Packet8s& b) {
  return vbslq_s16(vreinterpretq_u16_s16(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4us pselect(const Packet4us& mask, const Packet4us& a, const Packet4us& b) {
  return vbsl_u16(mask, a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8us pselect(const Packet8us& mask, const Packet8us& a, const Packet8us& b) {
  return vbslq_u16(mask, a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2i pselect(const Packet2i& mask, const Packet2i& a, const Packet2i& b) {
  return vbsl_s32(vreinterpret_u32_s32(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4i pselect(const Packet4i& mask, const Packet4i& a, const Packet4i& b) {
  return vbslq_s32(vreinterpretq_u32_s32(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ui pselect(const Packet2ui& mask, const Packet2ui& a, const Packet2ui& b) {
  return vbsl_u32(mask, a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4ui pselect(const Packet4ui& mask, const Packet4ui& a, const Packet4ui& b) {
  return vbslq_u32(mask, a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2l pselect(const Packet2l& mask, const Packet2l& a, const Packet2l& b) {
  return vbslq_s64(vreinterpretq_u64_s64(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2ul pselect(const Packet2ul& mask, const Packet2ul& a, const Packet2ul& b) {
  return vbslq_u64(mask, a, b);
}
 
// Use armv8 rounding intrinsics if available.
#if EIGEN_ARCH_ARMV8
template <>
EIGEN_STRONG_INLINE Packet2f print<Packet2f>(const Packet2f& a) {
  return vrndn_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f print<Packet4f>(const Packet4f& a) {
  return vrndnq_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pfloor<Packet2f>(const Packet2f& a) {
  return vrndm_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f pfloor<Packet4f>(const Packet4f& a) {
  return vrndmq_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pceil<Packet2f>(const Packet2f& a) {
  return vrndp_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f pceil<Packet4f>(const Packet4f& a) {
  return vrndpq_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pround<Packet2f>(const Packet2f& a) {
  return vrnda_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f pround<Packet4f>(const Packet4f& a) {
  return vrndaq_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f ptrunc<Packet2f>(const Packet2f& a) {
  return vrnd_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f ptrunc<Packet4f>(const Packet4f& a) {
  return vrndq_f32(a);
}
#endif

template <>
EIGEN_STRONG_INLINE Packet4uc psqrt(const Packet4uc& a) {
  uint8x8_t x = vreinterpret_u8_u32(vdup_n_u32(a));
  uint8x8_t res = vdup_n_u8(0);
  uint8x8_t add = vdup_n_u8(0x8);
  for (int i = 0; i < 4; i++) {
    const uint8x8_t temp = vorr_u8(res, add);
    res = vbsl_u8(vcge_u8(x, vmul_u8(temp, temp)), temp, res);
    add = vshr_n_u8(add, 1);
  }
  return vget_lane_u32(vreinterpret_u32_u8(res), 0);
}
template <>
EIGEN_STRONG_INLINE Packet8uc psqrt(const Packet8uc& a) {
  uint8x8_t res = vdup_n_u8(0);
  uint8x8_t add = vdup_n_u8(0x8);
  for (int i = 0; i < 4; i++) {
    const uint8x8_t temp = vorr_u8(res, add);
    res = vbsl_u8(vcge_u8(a, vmul_u8(temp, temp)), temp, res);
    add = vshr_n_u8(add, 1);
  }
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet16uc psqrt(const Packet16uc& a) {
  uint8x16_t res = vdupq_n_u8(0);
  uint8x16_t add = vdupq_n_u8(0x8);
  for (int i = 0; i < 4; i++) {
    const uint8x16_t temp = vorrq_u8(res, add);
    res = vbslq_u8(vcgeq_u8(a, vmulq_u8(temp, temp)), temp, res);
    add = vshrq_n_u8(add, 1);
  }
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet4us psqrt(const Packet4us& a) {
  uint16x4_t res = vdup_n_u16(0);
  uint16x4_t add = vdup_n_u16(0x80);
  for (int i = 0; i < 8; i++) {
    const uint16x4_t temp = vorr_u16(res, add);
    res = vbsl_u16(vcge_u16(a, vmul_u16(temp, temp)), temp, res);
    add = vshr_n_u16(add, 1);
  }
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet8us psqrt(const Packet8us& a) {
  uint16x8_t res = vdupq_n_u16(0);
  uint16x8_t add = vdupq_n_u16(0x80);
  for (int i = 0; i < 8; i++) {
    const uint16x8_t temp = vorrq_u16(res, add);
    res = vbslq_u16(vcgeq_u16(a, vmulq_u16(temp, temp)), temp, res);
    add = vshrq_n_u16(add, 1);
  }
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet2ui psqrt(const Packet2ui& a) {
  uint32x2_t res = vdup_n_u32(0);
  uint32x2_t add = vdup_n_u32(0x8000);
  for (int i = 0; i < 16; i++) {
    const uint32x2_t temp = vorr_u32(res, add);
    res = vbsl_u32(vcge_u32(a, vmul_u32(temp, temp)), temp, res);
    add = vshr_n_u32(add, 1);
  }
  return res;
}
template <>
EIGEN_STRONG_INLINE Packet4ui psqrt(const Packet4ui& a) {
  uint32x4_t res = vdupq_n_u32(0);
  uint32x4_t add = vdupq_n_u32(0x8000);
  for (int i = 0; i < 16; i++) {
    const uint32x4_t temp = vorrq_u32(res, add);
    res = vbslq_u32(vcgeq_u32(a, vmulq_u32(temp, temp)), temp, res);
    add = vshrq_n_u32(add, 1);
  }
  return res;
}
 
EIGEN_STRONG_INLINE Packet4f prsqrt_float_unsafe(const Packet4f& a) {
  // Compute approximate reciprocal sqrt.
  // Does not correctly handle +/- 0 or +inf
  float32x4_t result = vrsqrteq_f32(a);
  result = vmulq_f32(vrsqrtsq_f32(vmulq_f32(a, result), result), result);
  result = vmulq_f32(vrsqrtsq_f32(vmulq_f32(a, result), result), result);
  return result;
}
 
EIGEN_STRONG_INLINE Packet2f prsqrt_float_unsafe(const Packet2f& a) {
  // Compute approximate reciprocal sqrt.
  // Does not correctly handle +/- 0 or +inf
  float32x2_t result = vrsqrte_f32(a);
  result = vmul_f32(vrsqrts_f32(vmul_f32(a, result), result), result);
  result = vmul_f32(vrsqrts_f32(vmul_f32(a, result), result), result);
  return result;
}
 
template <typename Packet>
Packet prsqrt_float_common(const Packet& a) {
  const Packet cst_zero = pzero(a);
  const Packet cst_inf = pset1<Packet>(NumTraits<float>::infinity());
  Packet return_zero = pcmp_eq(a, cst_inf);
  Packet return_inf = pcmp_eq(a, cst_zero);
  Packet result = prsqrt_float_unsafe(a);
  result = pselect(return_inf, por(cst_inf, a), result);
  result = pandnot(result, return_zero);
  return result;
}
 
template <>
EIGEN_STRONG_INLINE Packet4f prsqrt(const Packet4f& a) {
  return prsqrt_float_common(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f prsqrt(const Packet2f& a) {
  return prsqrt_float_common(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f preciprocal<Packet4f>(const Packet4f& a) {
  // Compute approximate reciprocal.
  const float32x4_t estimate = vrecpeq_f32(a);
  float32x4_t result = vmulq_f32(vrecpsq_f32(a, estimate), estimate);
  result = vmulq_f32(vrecpsq_f32(a, result), result);
  // 1 / a has the sign of a. The estimate is +-inf for |a| < 2^-128, which the steps turn into -+inf.
  return vbslq_f32(vdupq_n_u32(0x80000000u), a, result);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f preciprocal<Packet2f>(const Packet2f& a) {
  // Compute approximate reciprocal.
  const float32x2_t estimate = vrecpe_f32(a);
  float32x2_t result = vmul_f32(vrecps_f32(a, estimate), estimate);
  result = vmul_f32(vrecps_f32(a, result), result);
  // 1 / a has the sign of a. The estimate is +-inf for |a| < 2^-128, which the steps turn into -+inf.
  return vbsl_f32(vdup_n_u32(0x80000000u), a, result);
}
 
// Unfortunately vsqrt_f32 is only available for A64.
#if EIGEN_ARCH_ARM64
template <>
EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) {
  return vsqrtq_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& a) {
  return vsqrt_f32(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4f pdiv(const Packet4f& a, const Packet4f& b) {
  return vdivq_f32(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pdiv(const Packet2f& a, const Packet2f& b) {
  return vdiv_f32(a, b);
}
#else
template <typename Packet>
EIGEN_STRONG_INLINE Packet psqrt_float_common(const Packet& a) {
  const Packet cst_zero = pzero(a);
  const Packet cst_inf = pset1<Packet>(NumTraits<float>::infinity());
 
  Packet result = pmul(a, prsqrt_float_unsafe(a));
  Packet a_is_zero = pcmp_eq(a, cst_zero);
  Packet a_is_inf = pcmp_eq(a, cst_inf);
  Packet return_a = por(a_is_zero, a_is_inf);
 
  result = pselect(return_a, a, result);
  return result;
}
 
template <>
EIGEN_STRONG_INLINE Packet4f psqrt(const Packet4f& a) {
  return psqrt_float_common(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f psqrt(const Packet2f& a) {
  return psqrt_float_common(a);
}
 
template <typename Packet>
EIGEN_STRONG_INLINE Packet pdiv_float_common(const Packet& a, const Packet& b) {
  // if b is large, NEON intrinsics will flush preciprocal(b) to zero
  // avoid underflow with the following manipulation:
  // a / b = f * (a * reciprocal(f * b))
 
  const Packet cst_one = pset1<Packet>(1.0f);
  const Packet cst_quarter = pset1<Packet>(0.25f);
  const Packet cst_thresh = pset1<Packet>(NumTraits<float>::highest() / 4.0f);
 
  Packet b_will_underflow = pcmp_le(cst_thresh, pabs(b));
  Packet f = pselect(b_will_underflow, cst_quarter, cst_one);
  Packet result = pmul(f, pmul(a, preciprocal(pmul(b, f))));
  return result;
}
 
template <>
EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) {
  return pdiv_float_common(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2f pdiv<Packet2f>(const Packet2f& a, const Packet2f& b) {
  return pdiv_float_common(a, b);
}
#endif
 
//---------- bfloat16 ----------
// TODO: Add support for native armv8.6-a bfloat16_t
 
// TODO: Guard if we have native bfloat16 support
typedef eigen_packet_wrapper<uint16x4_t, 19> Packet4bf;
 
template <>
struct is_arithmetic<Packet4bf> : std::true_type {};
 
template <>
struct packet_traits<bfloat16> : default_packet_traits {
  typedef Packet4bf type;
  typedef Packet4bf half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 4,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
    HasDiv = 1,
    HasSin = EIGEN_FAST_MATH,
    HasCos = EIGEN_FAST_MATH,
    HasLog = 1,
    HasExp = 1,
    HasSqrt = 0,
    HasTanh = EIGEN_FAST_MATH,
    HasErf = EIGEN_FAST_MATH,
    HasBessel = 0,  // Issues with accuracy.
    HasNdtri = 0
  };
};
 
template <>
struct unpacket_traits<Packet4bf> : neon_unpacket_default<Packet4bf, bfloat16> {};
 
namespace detail {
template <>
EIGEN_ALWAYS_INLINE void zip_in_place<Packet4bf>(Packet4bf& p1, Packet4bf& p2) {
  const uint16x4x2_t tmp = vzip_u16(p1, p2);
  p1 = tmp.val[0];
  p2 = tmp.val[1];
}
}  // namespace detail
 
EIGEN_STRONG_INLINE Packet4bf F32ToBf16(const Packet4f& p) {
  // See the scalar implementation in BFloat16.h for a comprehensible explanation
  // of this fast rounding algorithm
  Packet4ui input = Packet4ui(vreinterpretq_u32_f32(p));
 
  // lsb = (input >> 16) & 1
  Packet4ui lsb = vandq_u32(vshrq_n_u32(input, 16), vdupq_n_u32(1));
 
  // rounding_bias = 0x7fff + lsb
  Packet4ui rounding_bias = vaddq_u32(lsb, vdupq_n_u32(0x7fff));
 
  // input += rounding_bias
  input = vaddq_u32(input, rounding_bias);
 
  // input = input >> 16
  input = vshrq_n_u32(input, 16);
 
  // Replace float-nans by bfloat16-nans, that is 0x7fc0
  const Packet4ui bf16_nan = vdupq_n_u32(0x7fc0);
  const Packet4ui mask = vceqq_f32(p, p);
  input = vbslq_u32(mask, input, bf16_nan);
 
  // output = static_cast<uint16_t>(input)
  return vmovn_u32(input);
}
 
// Discard the low 16 bits of each float. Only valid when every lane already holds an exact
// bfloat16 value, in which case this agrees with F32ToBf16 but skips its rounding and NaN
// canonicalization. pmin/pmax qualify: they return one of their operands bit for bit.
EIGEN_STRONG_INLINE Packet4bf F32ToBf16Truncate(const Packet4f& p) { return vshrn_n_u32(vreinterpretq_u32_f32(p), 16); }
 
EIGEN_STRONG_INLINE Packet4f Bf16ToF32(const Packet4bf& p) {
  return Packet4f(vreinterpretq_f32_u32(vshlq_n_u32(vmovl_u16(p), 16)));
}
 
EIGEN_STRONG_INLINE Packet4bf F32MaskToBf16Mask(const Packet4f& p) { return vmovn_u32(vreinterpretq_u32_f32(p)); }
 
template <>
EIGEN_STRONG_INLINE Packet4bf pset1<Packet4bf>(const bfloat16& from) {
  return Packet4bf(pset1<Packet4us>(from.value));
}
 
template <>
EIGEN_STRONG_INLINE bfloat16 pfirst<Packet4bf>(const Packet4bf& from) {
  return bfloat16_impl::raw_uint16_to_bfloat16(static_cast<uint16_t>(pfirst<Packet4us>(Packet4us(from))));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pload<Packet4bf>(const bfloat16* from) {
  return Packet4bf(
      pload<Packet4us>(reinterpret_cast<const uint16_t*>(assume_aligned<unpacket_traits<Packet4bf>::alignment>(from))));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf ploadu<Packet4bf>(const bfloat16* from) {
  return Packet4bf(ploadu<Packet4us>(reinterpret_cast<const uint16_t*>(from)));
}
 
template <>
EIGEN_STRONG_INLINE void pstore<bfloat16>(bfloat16* to, const Packet4bf& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_u16(
      reinterpret_cast<uint16_t*>(assume_aligned<unpacket_traits<Packet4bf>::alignment>(to)), from);
}
 
template <>
EIGEN_STRONG_INLINE void pstoreu<bfloat16>(bfloat16* to, const Packet4bf& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_u16(reinterpret_cast<uint16_t*>(to), from);
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf ploaddup<Packet4bf>(const bfloat16* from) {
  return Packet4bf(ploaddup<Packet4us>(reinterpret_cast<const uint16_t*>(from)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pabs(const Packet4bf& a) {
  return Packet4bf(vand_u16(a, vdup_n_u16(0x7fff)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmin<PropagateNumbers, Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16Truncate(pmin<PropagateNumbers, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4bf pmin<PropagateNaN, Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16Truncate(pmin<PropagateNaN, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmin<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16Truncate(pmin<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmax<PropagateNumbers, Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16Truncate(pmax<PropagateNumbers, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
template <>
EIGEN_STRONG_INLINE Packet4bf pmax<PropagateNaN, Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16Truncate(pmax<PropagateNaN, Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmax<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16Truncate(pmax<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf plset<Packet4bf>(const bfloat16& a) {
  return F32ToBf16(plset<Packet4f>(static_cast<float>(a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf por(const Packet4bf& a, const Packet4bf& b) {
  return Packet4bf(por<Packet4us>(Packet4us(a), Packet4us(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pxor(const Packet4bf& a, const Packet4bf& b) {
  return Packet4bf(pxor<Packet4us>(Packet4us(a), Packet4us(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pand(const Packet4bf& a, const Packet4bf& b) {
  return Packet4bf(pand<Packet4us>(Packet4us(a), Packet4us(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pandnot(const Packet4bf& a, const Packet4bf& b) {
  return Packet4bf(pandnot<Packet4us>(Packet4us(a), Packet4us(b)));
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4bf pselect(const Packet4bf& mask, const Packet4bf& a, const Packet4bf& b) {
  return Packet4bf(pselect<Packet4us>(Packet4us(mask), Packet4us(a), Packet4us(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf print<Packet4bf>(const Packet4bf& a) {
  return F32ToBf16Truncate(print<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pfloor<Packet4bf>(const Packet4bf& a) {
  return F32ToBf16Truncate(pfloor<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pceil<Packet4bf>(const Packet4bf& a) {
  return F32ToBf16Truncate(pceil<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pround<Packet4bf>(const Packet4bf& a) {
  return F32ToBf16Truncate(pround<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf ptrunc<Packet4bf>(const Packet4bf& a) {
  return F32ToBf16Truncate(ptrunc<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf padd<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16(padd<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf psub<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16(psub<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmul<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16(pmul<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmadd<Packet4bf>(const Packet4bf& a, const Packet4bf& b, const Packet4bf& c) {
  return F32ToBf16(pmadd<Packet4f>(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pmsub<Packet4bf>(const Packet4bf& a, const Packet4bf& b, const Packet4bf& c) {
  return F32ToBf16(pmsub<Packet4f>(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pnmadd<Packet4bf>(const Packet4bf& a, const Packet4bf& b, const Packet4bf& c) {
  return F32ToBf16(pnmadd<Packet4f>(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pnmsub<Packet4bf>(const Packet4bf& a, const Packet4bf& b, const Packet4bf& c) {
  return F32ToBf16(pnmsub<Packet4f>(Bf16ToF32(a), Bf16ToF32(b), Bf16ToF32(c)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pdiv<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16(pdiv<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pgather<bfloat16, Packet4bf>(const bfloat16* from, Index stride) {
  return Packet4bf(pgather<uint16_t, Packet4us>(reinterpret_cast<const uint16_t*>(from), stride));
}
 
template <>
EIGEN_STRONG_INLINE void pscatter<bfloat16, Packet4bf>(bfloat16* to, const Packet4bf& from, Index stride) {
  pscatter<uint16_t, Packet4us>(reinterpret_cast<uint16_t*>(to), Packet4us(from), stride);
}
 
template <>
EIGEN_STRONG_INLINE bfloat16 predux<Packet4bf>(const Packet4bf& a) {
  return static_cast<bfloat16>(predux<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE bfloat16 predux_max<Packet4bf>(const Packet4bf& a) {
  return bfloat16_impl::exact_float_to_bfloat16(predux_max<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE bfloat16 predux_min<Packet4bf>(const Packet4bf& a) {
  return bfloat16_impl::exact_float_to_bfloat16(predux_min<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE bfloat16 predux_mul<Packet4bf>(const Packet4bf& a) {
  return static_cast<bfloat16>(predux_mul<Packet4f>(Bf16ToF32(a)));
}
 
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet4bf& a) {
  return vget_lane_u64(vreinterpret_u64_u16(Packet4us(a)), 0) != 0;
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf preverse<Packet4bf>(const Packet4bf& a) {
  return Packet4bf(preverse<Packet4us>(Packet4us(a)));
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4bf, 4>& kernel) {
  detail::ptranspose_impl(kernel);
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pabsdiff<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32ToBf16(pabsdiff<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pcmp_eq<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32MaskToBf16Mask(pcmp_eq<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pcmp_lt<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32MaskToBf16Mask(pcmp_lt<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pcmp_lt_or_nan<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32MaskToBf16Mask(pcmp_lt_or_nan<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
// Classify on the raw bits, as the scalar isinf/isnan/isfinite do: |a| ==, >, < 0x7f80.
template <>
EIGEN_STRONG_INLINE Packet4bf pisinf<Packet4bf>(const Packet4bf& a) {
  constexpr uint16_t kInf = ((1 << 8) - 1) << 7;
  constexpr uint16_t kAbsMask = (1 << 15) - 1;
  return vceq_u16(vand_u16(a, vdup_n_u16(kAbsMask)), vdup_n_u16(kInf));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pisnan<Packet4bf>(const Packet4bf& a) {
  constexpr uint16_t kInf = ((1 << 8) - 1) << 7;
  constexpr uint16_t kAbsMask = (1 << 15) - 1;
  return vcgt_u16(vand_u16(a, vdup_n_u16(kAbsMask)), vdup_n_u16(kInf));
}
 
// Compare encoded lanes: widening bf16 subnormals to float loses them under DAZ/FZ.
template <>
EIGEN_STRONG_INLINE Packet4bf psign<Packet4bf>(const Packet4bf& a) {
  const uint16x4_t abs_mask = vdup_n_u16(0x7fff);
  const uint16x4_t is_nan = vcgt_u16(vand_u16(a, abs_mask), vdup_n_u16(0x7f80));
  const uint16x4_t keep = vorr_u16(is_nan, vdup_n_u16(0x8000));
  return vand_u16(vbsl_u16(keep, a, vdup_n_u16(0x3f80)), vtst_u16(a, abs_mask));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pisfinite<Packet4bf>(const Packet4bf& a) {
  constexpr uint16_t kInf = ((1 << 8) - 1) << 7;
  constexpr uint16_t kAbsMask = (1 << 15) - 1;
  return vclt_u16(vand_u16(a, vdup_n_u16(kAbsMask)), vdup_n_u16(kInf));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pcmp_le<Packet4bf>(const Packet4bf& a, const Packet4bf& b) {
  return F32MaskToBf16Mask(pcmp_le<Packet4f>(Bf16ToF32(a), Bf16ToF32(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4bf pnegate<Packet4bf>(const Packet4bf& a) {
  return Packet4bf(pxor<Packet4us>(Packet4us(a), pset1<Packet4us>(static_cast<uint16_t>(0x8000))));
}
 
//---------- double ----------
 
#if EIGEN_ARCH_ARM64
 
#if EIGEN_COMP_GNUC
// Bug 907: workaround missing declarations of the following two functions in the ADK
// Defining these functions as templates ensures that if these intrinsics are
// already defined in arm_neon.h, then our workaround doesn't cause a conflict
// and has lower priority in overload resolution.
// This doesn't work with MSVC though, since the function names are macros.
template <typename T>
uint64x2_t vreinterpretq_u64_f64(T a) {
  return (uint64x2_t)a;
}
 
template <typename T>
float64x2_t vreinterpretq_f64_u64(T a) {
  return (float64x2_t)a;
}
#endif
 
#if EIGEN_COMP_MSVC_STRICT
typedef eigen_packet_wrapper<float64x2_t, 18> Packet2d;
typedef eigen_packet_wrapper<float64x1_t, 19> Packet1d;
 
EIGEN_ALWAYS_INLINE Packet2d make_packet2d(double a, double b) {
  double from[2] = {a, b};
  return vld1q_f64(from);
}
 
#else
typedef float64x2_t Packet2d;
typedef float64x1_t Packet1d;
 
EIGEN_ALWAYS_INLINE Packet2d make_packet2d(double a, double b) { return Packet2d{a, b}; }
#endif
 
// functionally equivalent to _mm_shuffle_pd in SSE (i.e. shuffle(m, n, mask) equals _mm_shuffle_pd(m,n,mask))
// Currently used in LU/arch/InverseSize4.h to enable a shared implementation
// for fast inversion of matrices of size 4.
EIGEN_STRONG_INLINE Packet2d shuffle(const Packet2d& m, const Packet2d& n, int mask) {
  const double* a = reinterpret_cast<const double*>(&m);
  const double* b = reinterpret_cast<const double*>(&n);
  Packet2d res = make_packet2d(*(a + (mask & 1)), *(b + ((mask >> 1) & 1)));
  return res;
}
 
EIGEN_STRONG_INLINE Packet2d vec2d_swizzle2(const Packet2d& a, const Packet2d& b, int mask) {
  return shuffle(a, b, mask);
}
EIGEN_STRONG_INLINE Packet2d vec2d_unpacklo(const Packet2d& a, const Packet2d& b) { return shuffle(a, b, 0); }
EIGEN_STRONG_INLINE Packet2d vec2d_unpackhi(const Packet2d& a, const Packet2d& b) { return shuffle(a, b, 3); }
#define vec2d_duplane(a, p) Packet2d(vdupq_laneq_f64(a, p))
 
template <>
struct packet_traits<double> : default_packet_traits {
  typedef Packet2d type;
  typedef Packet2d half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 2,
 
    HasCmp = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 1,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
 
    HasDiv = 1,
 
#if EIGEN_ARCH_ARM64
    HasExp = 1,
    HasLog = 1,
    HasLog10 = 1,
    HasLog1p = 1,
    HasExpm1 = 1,
    HasPow = 1,
    HasATan = 1,
    HasATanh = 1,
    HasSinh = 1,
    HasCosh = 1,
    HasASinh = 1,
    HasACosh = 1,
#endif
    HasSin = EIGEN_FAST_MATH,
    HasCos = EIGEN_FAST_MATH,
    HasTan = EIGEN_FAST_MATH,
    HasSqrt = 1,
    HasRsqrt = 1,
    HasCbrt = 1,
    HasTanh = EIGEN_FAST_MATH,
    HasErf = EIGEN_FAST_MATH,
    HasErfc = EIGEN_FAST_MATH
  };
};
 
template <>
struct unpacket_traits<Packet2d> : neon_unpacket_default<Packet2d, double> {
  using integer_packet = Packet2l;
};
 
template <>
EIGEN_STRONG_INLINE Packet2d pzero<Packet2d>(const Packet2d& /*a*/) {
  return vdupq_n_f64(0.0);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) {
  return vdupq_n_f64(from);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a) {
  const double c[] = {0.0, 1.0};
  return vaddq_f64(pset1<Packet2d>(a), vld1q_f64(c));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vaddq_f64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vsubq_f64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d&, const Packet2d&);
template <>
EIGEN_STRONG_INLINE Packet2d paddsub<Packet2d>(const Packet2d& a, const Packet2d& b) {
  const Packet2d mask = make_packet2d(numext::bit_cast<double>(0x8000000000000000ull), 0.0);
  return padd(a, pxor(mask, b));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) {
  return vnegq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vmulq_f64(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vdivq_f64(a, b);
}
 
#ifdef EIGEN_VECTORIZE_FMA
// See bug 936. See above comment about FMA for float.
template <>
EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return vfmaq_f64(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pnmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return vfmsq_f64(c, a, b);
}
#else
template <>
EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return vmlaq_f64(c, a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pnmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return vmlsq_f64(c, a, b);
}
#endif
template <>
EIGEN_STRONG_INLINE Packet2d pmsub(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return pnegate(pnmadd(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet2d pnmsub(const Packet2d& a, const Packet2d& b, const Packet2d& c) {
  return pnegate(pmadd(a, b, c));
}
template <>
EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vminq_f64(a, b);
}
 
#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8
// systems).
template <>
EIGEN_STRONG_INLINE Packet2d pmin<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vminnmq_f64(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet2d pmax<PropagateNumbers, Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vmaxnmq_f64(a, b);
}
 
#endif
 
template <>
struct pminmax_propagates_nan<Packet2d> : bool_constant<true> {};
 
template <>
EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vmaxq_f64(a, b);
}
 
// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
template <>
EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a), vreinterpretq_u64_f64(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a), vreinterpretq_u64_f64(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a), vreinterpretq_u64_f64(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a), vreinterpretq_u64_f64(b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pcmp_le(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(vcleq_f64(a, b));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pcmp_lt(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(vcltq_f64(a, b));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pcmp_lt_or_nan(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u32(vmvnq_u32(vreinterpretq_u32_u64(vcgeq_f64(a, b))));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pcmp_eq(const Packet2d& a, const Packet2d& b) {
  return vreinterpretq_f64_u64(vceqq_f64(a, b));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f64(assume_aligned<unpacket_traits<Packet2d>::alignment>(from));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f64(from);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from) {
  return vld1q_dup_f64(from);
}
template <>
EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_f64(assume_aligned<unpacket_traits<Packet2d>::alignment>(to), from);
}
 
template <>
EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_f64(to, from);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2d pgather<double, Packet2d>(const double* from, Index stride) {
  Packet2d res = pset1<Packet2d>(0.0);
  res = vld1q_lane_f64(from + 0 * stride, res, 0);
  res = vld1q_lane_f64(from + 1 * stride, res, 1);
  return res;
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride) {
  vst1q_lane_f64(to + stride * 0, from, 0);
  vst1q_lane_f64(to + stride * 1, from, 1);
}
 
template <>
EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
 
// FIXME only store the 2 first elements ?
template <>
EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) {
  return vgetq_lane_f64(a, 0);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) {
  return vcombine_f64(vget_high_f64(a), vget_low_f64(a));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) {
  return vabsq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d psignbit(const Packet2d& a) {
  return vreinterpretq_f64_s64(vshrq_n_s64(vreinterpretq_s64_f64(a), 63));
}
 
template <>
EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) {
  return vaddvq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Index predux_count(const Packet2d& a) {
  // Each zero lane contributes UINT64_MAX, so unsigned 2 + sum(mask) is the number of nonzero lanes.
  const uint64_t zeroMaskSum = vaddvq_u64(vceqq_f64(a, vdupq_n_f64(0.0)));
  return static_cast<Index>(zeroMaskSum + 2);
}
 
template <>
EIGEN_STRONG_INLINE bool predux_any(const Packet2d& a) {
  return vmaxvq_u32(vreinterpretq_u32_f64(a)) != 0;
}
 
// Other reduction functions:
// mul
#if EIGEN_COMP_CLANGAPPLE
template <>
EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) {
  return (vget_low_f64(a) * vget_high_f64(a))[0];
}
#else
template <>
EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) {
  return vget_lane_f64(vmul_f64(vget_low_f64(a), vget_high_f64(a)), 0);
}
#endif
 
// min
template <>
EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) {
  return vminvq_f64(a);
}
 
// max
template <>
EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) {
  return vmaxvq_f64(a);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet2d, 2>& kernel) {
  const float64x2_t tmp1 = vzip1q_f64(kernel.packet[0], kernel.packet[1]);
  const float64x2_t tmp2 = vzip2q_f64(kernel.packet[0], kernel.packet[1]);
 
  kernel.packet[0] = tmp1;
  kernel.packet[1] = tmp2;
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet2d pselect(const Packet2d& mask, const Packet2d& a, const Packet2d& b) {
  return vbslq_f64(vreinterpretq_u64_f64(mask), a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d print<Packet2d>(const Packet2d& a) {
  return vrndnq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pfloor<Packet2d>(const Packet2d& a) {
  return vrndmq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pceil<Packet2d>(const Packet2d& a) {
  return vrndpq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pround<Packet2d>(const Packet2d& a) {
  return vrndaq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d ptrunc<Packet2d>(const Packet2d& a) {
  return vrndq_f64(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pldexp<Packet2d>(const Packet2d& a, const Packet2d& exponent) {
  return pldexp_generic(a, exponent);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pfrexp<Packet2d>(const Packet2d& a, Packet2d& exponent) {
  return pfrexp_generic(a, exponent);
}
 
template <>
EIGEN_STRONG_INLINE Packet2d pset1frombits<Packet2d>(uint64_t from) {
  return vreinterpretq_f64_u64(vdupq_n_u64(from));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d prsqrt(const Packet2d& a) {
  // Do Newton iterations for 1/sqrt(x).
  return generic_rsqrt_newton_step<Packet2d, /*Steps=*/3>::run(a, vrsqrteq_f64(a));
}
 
template <>
EIGEN_STRONG_INLINE Packet2d psqrt(const Packet2d& _x) {
  return vsqrtq_f64(_x);
}
 
// Absolute comparisons as for Packet4f.
template <>
EIGEN_STRONG_INLINE Packet2d pisinf<Packet2d>(const Packet2d& a) {
  return vreinterpretq_f64_u64(vcageq_f64(a, pinf<Packet2d>()));
}
template <>
EIGEN_STRONG_INLINE Packet2d pisfinite<Packet2d>(const Packet2d& a) {
  return vreinterpretq_f64_u64(vcagtq_f64(pinf<Packet2d>(), a));
}
// |bits| > inf bits as an unsigned comparison. !vcage(inf, a) is one instruction shorter inside a select, but Clang's
// inliner charges more for the intrinsic, and pexp_complex<Packet1cd> sits within a few units of its threshold.
template <>
EIGEN_STRONG_INLINE Packet2d pisnan<Packet2d>(const Packet2d& a) {
  return vreinterpretq_f64_u64(vcgtq_u64(vreinterpretq_u64_f64(vabsq_f64(a)), vdupq_n_u64(0x7ff0000000000000ull)));
}
 
#endif  // EIGEN_ARCH_ARM64
 
// Do we have fp16 and support Neon intrinsics?
// FIXME: This disables vectorization on ARMv7 even though FP16 vector operations should
// be available with `__ARM_FEATURE_FP16_VECTOR_ARITHMETIC`.  However, since the internal
// feature test macro `EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC` requires `EIGEN_ARCH_ARM64`
// in addition to the ISA feature test, the guard here also only checks for ARM64.
#if EIGEN_ARCH_ARM64 && EIGEN_HAS_ARM64_FP16
typedef float16x4_t Packet4hf;
typedef float16x8_t Packet8hf;
 
// Clang <19.1.0 does not provide `f16` intrinsics for pure data movement instructions.
// Polyfill them with `u16`.
//
// See: <https://github.com/llvm/llvm-project/pull/87467>.
#if EIGEN_CLANG_STRICT_LESS_THAN(19, 1, 0) && !EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
EIGEN_ALWAYS_INLINE float16x4_t vbsl_f16(uint16x4_t a, float16x4_t b, float16x4_t c) {
  return vreinterpret_f16_u16(vbsl_u16(a, vreinterpret_u16_f16(b), vreinterpret_u16_f16(c)));
}
EIGEN_ALWAYS_INLINE float16x8_t vbslq_f16(uint16x8_t a, float16x8_t b, float16x8_t c) {
  return vreinterpretq_f16_u16(vbslq_u16(a, vreinterpretq_u16_f16(b), vreinterpretq_u16_f16(c)));
}
EIGEN_ALWAYS_INLINE float16x4_t vrev64_f16(float16x4_t a) {
  return vreinterpret_f16_u16(vrev64_u16(vreinterpret_u16_f16(a)));
}
EIGEN_ALWAYS_INLINE float16x8_t vrev64q_f16(float16x8_t a) {
  return vreinterpretq_f16_u16(vrev64q_u16(vreinterpretq_u16_f16(a)));
}
EIGEN_ALWAYS_INLINE float16x8x2_t vzipq_f16(float16x8_t a, float16x8_t b) {
  const uint16x8x2_t r = vzipq_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b));
  return {vreinterpretq_f16_u16(r.val[0]), vreinterpretq_f16_u16(r.val[1])};
}
EIGEN_ALWAYS_INLINE float16x8x2_t vuzpq_f16(float16x8_t a, float16x8_t b) {
  const uint16x8x2_t r = vuzpq_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b));
  return {vreinterpretq_f16_u16(r.val[0]), vreinterpretq_f16_u16(r.val[1])};
}
#endif  // EIGEN_CLANG_STRICT_LESS_THAN(19, 1, 0) && !EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
 
template <>
struct packet_traits<half> : default_packet_traits {
  typedef Packet8hf type;
  typedef Packet4hf half;
  enum {
    Vectorizable = 1,
    AlignedOnScalar = 1,
    size = 8,
 
    HasCmp = 1,
    HasCast = 1,
    HasAdd = 1,
    HasSub = 1,
    HasShift = 1,
    HasMul = 1,
    HasNegate = 1,
    HasAbs = 1,
    HasArg = 0,
    HasAbsDiff = 0,
    HasMin = 1,
    HasMax = 1,
    HasConj = 1,
    HasSetLinear = 1,
    HasInsert = 1,
    HasReduxp = 1,
    HasDiv = 1,
    HasSin = 0,
    HasCos = 0,
    HasLog = 0,
    HasExp = 0,
    HasTanh = packet_traits<float>::HasTanh,  // tanh<half> calls tanh<float>
    HasSqrt = 1,
    HasRsqrt = 1,
    HasErf = EIGEN_FAST_MATH,
    HasBessel = 0,  // Issues with accuracy.
    HasNdtri = 0
  };
};
 
template <>
struct unpacket_traits<Packet4hf> : neon_unpacket_default<Packet4hf, half> {};
template <>
struct unpacket_traits<Packet8hf> : neon_unpacket_default<Packet8hf, half> {
  using half = Packet4hf;
};
 
template <>
struct pminmax_propagates_nan<Packet4hf> : bool_constant<true> {};
template <>
struct pminmax_propagates_nan<Packet8hf> : bool_constant<true> {};
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pset1(const half& from) {
  return vdupq_n_f16(from.x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pset1(const half& from) {
  return vdup_n_f16(from.x);
}
 
#define EIGEN_MAKE_HALF_BITWISE_BINOP(name, op)                                                     \
  template <>                                                                                       \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf name(const Packet8hf& a, const Packet8hf& b) {    \
    return vreinterpretq_f16_u16(v##op##q_u16(vreinterpretq_u16_f16(a), vreinterpretq_u16_f16(b))); \
  }                                                                                                 \
  template <>                                                                                       \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf name(const Packet4hf& a, const Packet4hf& b) {    \
    return vreinterpret_f16_u16(v##op##_u16(vreinterpret_u16_f16(a), vreinterpret_u16_f16(b)));     \
  }                                                                                                 \
  static_assert(true, "Trailing semicolon required")
 
EIGEN_MAKE_HALF_BITWISE_BINOP(pand, and);
EIGEN_MAKE_HALF_BITWISE_BINOP(por, orr);
EIGEN_MAKE_HALF_BITWISE_BINOP(pxor, eor);
EIGEN_MAKE_HALF_BITWISE_BINOP(pandnot, bic);
 
#undef EIGEN_MAKE_HALF_BITWISE_BINOP
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pload(const half* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f16(assume_aligned<unpacket_traits<Packet8hf>::alignment>(&from->x));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pload(const half* from) {
  EIGEN_DEBUG_ALIGNED_LOAD return vld1_f16(assume_aligned<unpacket_traits<Packet4hf>::alignment>(&from->x));
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf ploadu(const half* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f16(&from->x);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf ploadu(const half* from) {
  EIGEN_DEBUG_UNALIGNED_LOAD return vld1_f16(&from->x);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf ploaddup(const half* from) {
  Packet8hf packet{};
  packet = vsetq_lane_f16(from[0].x, packet, 0);
  packet = vsetq_lane_f16(from[0].x, packet, 1);
  packet = vsetq_lane_f16(from[1].x, packet, 2);
  packet = vsetq_lane_f16(from[1].x, packet, 3);
  packet = vsetq_lane_f16(from[2].x, packet, 4);
  packet = vsetq_lane_f16(from[2].x, packet, 5);
  packet = vsetq_lane_f16(from[3].x, packet, 6);
  packet = vsetq_lane_f16(from[3].x, packet, 7);
  return packet;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf ploaddup(const half* from) {
  float16x4_t packet{};
  packet = vset_lane_f16(from[0].x, packet, 0);
  packet = vset_lane_f16(from[0].x, packet, 1);
  packet = vset_lane_f16(from[1].x, packet, 2);
  packet = vset_lane_f16(from[1].x, packet, 3);
  return packet;
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf ploadquad(const half* from) {
  Packet4hf lo, hi;
  lo = vld1_dup_f16(&from[0].x);
  hi = vld1_dup_f16(&from[1].x);
  return vcombine_f16(lo, hi);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pinsertfirst(const Packet8hf& a, half b) {
  return vsetq_lane_f16(b.x, a, 0);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pinsertfirst(const Packet4hf& a, half b) {
  return vset_lane_f16(b.x, a, 0);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pselect(const Packet8hf& mask, const Packet8hf& a, const Packet8hf& b) {
  return vbslq_f16(vreinterpretq_u16_f16(mask), a, b);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pselect(const Packet4hf& mask, const Packet4hf& a, const Packet4hf& b) {
  return vbsl_f16(vreinterpret_u16_f16(mask), a, b);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pinsertlast(const Packet8hf& a, half b) {
  return vsetq_lane_f16(b.x, a, 7);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pinsertlast(const Packet4hf& a, half b) {
  return vset_lane_f16(b.x, a, 3);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(half* to, const Packet8hf& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1q_f16(assume_aligned<unpacket_traits<Packet8hf>::alignment>(&to->x), from);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pstore(half* to, const Packet4hf& from) {
  EIGEN_DEBUG_ALIGNED_STORE vst1_f16(assume_aligned<unpacket_traits<Packet4hf>::alignment>(&to->x), from);
}
 
template <>
EIGEN_STRONG_INLINE void pstoreu(half* to, const Packet8hf& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1q_f16(&to->x, from);
}
template <>
EIGEN_STRONG_INLINE void pstoreu(half* to, const Packet4hf& from) {
  EIGEN_DEBUG_UNALIGNED_STORE vst1_f16(&to->x, from);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pgather(const half* from, Index stride) {
  Packet8hf res = pset1<Packet8hf>(half(0.f));
  res = vsetq_lane_f16(from[0 * stride].x, res, 0);
  res = vsetq_lane_f16(from[1 * stride].x, res, 1);
  res = vsetq_lane_f16(from[2 * stride].x, res, 2);
  res = vsetq_lane_f16(from[3 * stride].x, res, 3);
  res = vsetq_lane_f16(from[4 * stride].x, res, 4);
  res = vsetq_lane_f16(from[5 * stride].x, res, 5);
  res = vsetq_lane_f16(from[6 * stride].x, res, 6);
  res = vsetq_lane_f16(from[7 * stride].x, res, 7);
  return res;
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pgather(const half* from, Index stride) {
  Packet4hf res = pset1<Packet4hf>(half(0.f));
  res = vset_lane_f16(from[0 * stride].x, res, 0);
  res = vset_lane_f16(from[1 * stride].x, res, 1);
  res = vset_lane_f16(from[2 * stride].x, res, 2);
  res = vset_lane_f16(from[3 * stride].x, res, 3);
  return res;
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(half* to, const Packet8hf& from, Index stride) {
  to[stride * 0].x = vgetq_lane_f16(from, 0);
  to[stride * 1].x = vgetq_lane_f16(from, 1);
  to[stride * 2].x = vgetq_lane_f16(from, 2);
  to[stride * 3].x = vgetq_lane_f16(from, 3);
  to[stride * 4].x = vgetq_lane_f16(from, 4);
  to[stride * 5].x = vgetq_lane_f16(from, 5);
  to[stride * 6].x = vgetq_lane_f16(from, 6);
  to[stride * 7].x = vgetq_lane_f16(from, 7);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void pscatter(half* to, const Packet4hf& from, Index stride) {
  to[stride * 0].x = vget_lane_f16(from, 0);
  to[stride * 1].x = vget_lane_f16(from, 1);
  to[stride * 2].x = vget_lane_f16(from, 2);
  to[stride * 3].x = vget_lane_f16(from, 3);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void prefetch(const half* addr) {
  EIGEN_ARM_PREFETCH(addr);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half pfirst(const Packet8hf& a) {
  return half(vgetq_lane_f16(a, 0));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half pfirst(const Packet4hf& a) {
  return half(vget_lane_f16(a, 0));
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf preverse(const Packet8hf& a) {
  float16x8_t r = vrev64q_f16(a);
  return vcombine_f16(vget_high_f16(r), vget_low_f16(r));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf preverse(const Packet4hf& a) {
  return vrev64_f16(a);
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf psignbit(const Packet8hf& a) {
  return vreinterpretq_f16_s16(vshrq_n_s16(vreinterpretq_s16_f16(a), 15));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf psignbit(const Packet4hf& a) {
  return vreinterpret_f16_s16(vshr_n_s16(vreinterpret_s16_f16(a), 15));
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool predux_any(const Packet8hf& a) {
  return vget_lane_u64(vreinterpret_u64_u8(vmovn_u16(vreinterpretq_u16_f16(a))), 0);
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool predux_any(const Packet4hf& a) {
  return vget_lane_u64(vreinterpret_u64_f16(a), 0);
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8hf, 4>& kernel) {
  const float16x8x2_t zip16_1 = vzipq_f16(kernel.packet[0], kernel.packet[1]);
  const float16x8x2_t zip16_2 = vzipq_f16(kernel.packet[2], kernel.packet[3]);
 
  const float32x4x2_t zip32_1 = vzipq_f32(vreinterpretq_f32_f16(zip16_1.val[0]), vreinterpretq_f32_f16(zip16_2.val[0]));
  const float32x4x2_t zip32_2 = vzipq_f32(vreinterpretq_f32_f16(zip16_1.val[1]), vreinterpretq_f32_f16(zip16_2.val[1]));
 
  kernel.packet[0] = vreinterpretq_f16_f32(zip32_1.val[0]);
  kernel.packet[1] = vreinterpretq_f16_f32(zip32_1.val[1]);
  kernel.packet[2] = vreinterpretq_f16_f32(zip32_2.val[0]);
  kernel.packet[3] = vreinterpretq_f16_f32(zip32_2.val[1]);
}
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet4hf, 4>& kernel) {
  EIGEN_ALIGN16 float16x4x4_t tmp_x4;
  float16_t* tmp = reinterpret_cast<float16_t*>(&kernel);
  tmp_x4 = vld4_f16(tmp);
 
  kernel.packet[0] = tmp_x4.val[0];
  kernel.packet[1] = tmp_x4.val[1];
  kernel.packet[2] = tmp_x4.val[2];
  kernel.packet[3] = tmp_x4.val[3];
}
 
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void ptranspose(PacketBlock<Packet8hf, 8>& kernel) {
  float16x8x2_t T_1[4];
 
  T_1[0] = vuzpq_f16(kernel.packet[0], kernel.packet[1]);
  T_1[1] = vuzpq_f16(kernel.packet[2], kernel.packet[3]);
  T_1[2] = vuzpq_f16(kernel.packet[4], kernel.packet[5]);
  T_1[3] = vuzpq_f16(kernel.packet[6], kernel.packet[7]);
 
  float16x8x2_t T_2[4];
  T_2[0] = vuzpq_f16(T_1[0].val[0], T_1[1].val[0]);
  T_2[1] = vuzpq_f16(T_1[0].val[1], T_1[1].val[1]);
  T_2[2] = vuzpq_f16(T_1[2].val[0], T_1[3].val[0]);
  T_2[3] = vuzpq_f16(T_1[2].val[1], T_1[3].val[1]);
 
  float16x8x2_t T_3[4];
  T_3[0] = vuzpq_f16(T_2[0].val[0], T_2[2].val[0]);
  T_3[1] = vuzpq_f16(T_2[0].val[1], T_2[2].val[1]);
  T_3[2] = vuzpq_f16(T_2[1].val[0], T_2[3].val[0]);
  T_3[3] = vuzpq_f16(T_2[1].val[1], T_2[3].val[1]);
 
  kernel.packet[0] = T_3[0].val[0];
  kernel.packet[1] = T_3[2].val[0];
  kernel.packet[2] = T_3[1].val[0];
  kernel.packet[3] = T_3[3].val[0];
  kernel.packet[4] = T_3[0].val[1];
  kernel.packet[5] = T_3[2].val[1];
  kernel.packet[6] = T_3[1].val[1];
  kernel.packet[7] = T_3[3].val[1];
}
 
#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf predux_half<Packet8hf>(const Packet8hf& a) {
  return vadd_f16(vget_low_f16(a), vget_high_f16(a));
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf plset<Packet8hf>(const Eigen::half& a) {
  const float16_t f[] = {0, 1, 2, 3, 4, 5, 6, 7};
  Packet8hf countdown = vld1q_f16(f);
  return vaddq_f16(pset1<Packet8hf>(a), countdown);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf plset<Packet4hf>(const Eigen::half& a) {
  const float16_t f[] = {0, 1, 2, 3};
  Packet4hf countdown = vld1_f16(f);
  return vadd_f16(pset1<Packet4hf>(a), countdown);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf padd<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vaddq_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf padd<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vadd_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf psub<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vsubq_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf psub<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vsub_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pnegate(const Packet8hf& a) {
  return vnegq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pnegate(const Packet4hf& a) {
  return vneg_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pmul<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vmulq_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pmul<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vmul_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pdiv<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vdivq_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pdiv<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vdiv_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pmadd(const Packet8hf& a, const Packet8hf& b, const Packet8hf& c) {
  return vfmaq_f16(c, a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pmadd(const Packet4hf& a, const Packet4hf& b, const Packet4hf& c) {
  return vfma_f16(c, a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pnmadd(const Packet8hf& a, const Packet8hf& b, const Packet8hf& c) {
  return vfmsq_f16(c, a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pnmadd(const Packet4hf& a, const Packet4hf& b, const Packet4hf& c) {
  return vfms_f16(c, a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pmin<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vminq_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pmin<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vmin_f16(a, b);
}
 
#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8
// systems).
template <>
EIGEN_STRONG_INLINE Packet4hf pmin<PropagateNumbers, Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vminnm_f16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8hf pmin<PropagateNumbers, Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vminnmq_f16(a, b);
}
#endif
 
template <>
EIGEN_STRONG_INLINE Packet8hf pmax<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vmaxq_f16(a, b);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pmax<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vmax_f16(a, b);
}
 
#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
// numeric max and min are only available if ARM_FEATURE_NUMERIC_MAXMIN is defined (which can only be the case for Armv8
// systems).
template <>
EIGEN_STRONG_INLINE Packet4hf pmax<PropagateNumbers, Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vmaxnm_f16(a, b);
}
template <>
EIGEN_STRONG_INLINE Packet8hf pmax<PropagateNumbers, Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vmaxnmq_f16(a, b);
}
#endif
 
#define EIGEN_MAKE_ARM_FP16_CMP_8(name)                                               \
  template <>                                                                         \
  EIGEN_STRONG_INLINE Packet8hf pcmp_##name(const Packet8hf& a, const Packet8hf& b) { \
    return vreinterpretq_f16_u16(vc##name##q_f16(a, b));                              \
  }
 
#define EIGEN_MAKE_ARM_FP16_CMP_4(name)                                               \
  template <>                                                                         \
  EIGEN_STRONG_INLINE Packet4hf pcmp_##name(const Packet4hf& a, const Packet4hf& b) { \
    return vreinterpret_f16_u16(vc##name##_f16(a, b));                                \
  }
 
EIGEN_MAKE_ARM_FP16_CMP_8(eq)
EIGEN_MAKE_ARM_FP16_CMP_8(lt)
EIGEN_MAKE_ARM_FP16_CMP_8(le)
 
EIGEN_MAKE_ARM_FP16_CMP_4(eq)
EIGEN_MAKE_ARM_FP16_CMP_4(lt)
EIGEN_MAKE_ARM_FP16_CMP_4(le)
 
#undef EIGEN_MAKE_ARM_FP16_CMP_8
#undef EIGEN_MAKE_ARM_FP16_CMP_4
 
template <>
EIGEN_STRONG_INLINE Packet8hf pcmp_lt_or_nan<Packet8hf>(const Packet8hf& a, const Packet8hf& b) {
  return vreinterpretq_f16_u16(vmvnq_u16(vcgeq_f16(a, b)));
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pcmp_lt_or_nan<Packet4hf>(const Packet4hf& a, const Packet4hf& b) {
  return vreinterpret_f16_u16(vmvn_u16(vcge_f16(a, b)));
}
 
// Absolute comparisons as for Packet4f.
template <>
EIGEN_STRONG_INLINE Packet4hf pisinf<Packet4hf>(const Packet4hf& a) {
  return vreinterpret_f16_u16(vcage_f16(a, pinf<Packet4hf>()));
}
template <>
EIGEN_STRONG_INLINE Packet8hf pisinf<Packet8hf>(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vcageq_f16(a, pinf<Packet8hf>()));
}
template <>
EIGEN_STRONG_INLINE Packet4hf pisfinite<Packet4hf>(const Packet4hf& a) {
  return vreinterpret_f16_u16(vcagt_f16(pinf<Packet4hf>(), a));
}
template <>
EIGEN_STRONG_INLINE Packet8hf pisfinite<Packet8hf>(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vcagtq_f16(pinf<Packet8hf>(), a));
}
template <>
EIGEN_STRONG_INLINE Packet4hf pisnan<Packet4hf>(const Packet4hf& a) {
  return vreinterpret_f16_u16(vmvn_u16(vcage_f16(pinf<Packet4hf>(), a)));
}
template <>
EIGEN_STRONG_INLINE Packet8hf pisnan<Packet8hf>(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vmvnq_u16(vcageq_f16(pinf<Packet8hf>(), a)));
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf print<Packet8hf>(const Packet8hf& a) {
  return vrndnq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf print<Packet4hf>(const Packet4hf& a) {
  return vrndn_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pfloor<Packet8hf>(const Packet8hf& a) {
  return vrndmq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pfloor<Packet4hf>(const Packet4hf& a) {
  return vrndm_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pceil<Packet8hf>(const Packet8hf& a) {
  return vrndpq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pceil<Packet4hf>(const Packet4hf& a) {
  return vrndp_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pround<Packet8hf>(const Packet8hf& a) {
  return vrndaq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pround<Packet4hf>(const Packet4hf& a) {
  return vrnda_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf ptrunc<Packet8hf>(const Packet8hf& a) {
  return vrndq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf ptrunc<Packet4hf>(const Packet4hf& a) {
  return vrnd_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf psqrt<Packet8hf>(const Packet8hf& a) {
  return vsqrtq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf psqrt<Packet4hf>(const Packet4hf& a) {
  return vsqrt_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet8hf pabs<Packet8hf>(const Packet8hf& a) {
  return vabsq_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Packet4hf pabs<Packet4hf>(const Packet4hf& a) {
  return vabs_f16(a);
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux<Packet8hf>(const Packet8hf& a) {
  float16x4_t a_lo, a_hi, sum;
 
  a_lo = vget_low_f16(a);
  a_hi = vget_high_f16(a);
  sum = vpadd_f16(a_lo, a_hi);
  sum = vpadd_f16(sum, sum);
  sum = vpadd_f16(sum, sum);
 
  Eigen::half h;
  h.x = vget_lane_f16(sum, 0);
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux<Packet4hf>(const Packet4hf& a) {
  float16x4_t sum;
 
  sum = vpadd_f16(a, a);
  sum = vpadd_f16(sum, sum);
  Eigen::half h;
  h.x = vget_lane_f16(sum, 0);
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet8hf>(const Packet8hf& a) {
  float16x4_t a_lo, a_hi, prod;
 
  a_lo = vget_low_f16(a);
  a_hi = vget_high_f16(a);
  prod = vmul_f16(a_lo, a_hi);
  prod = vmul_f16(prod, vrev64_f16(prod));
 
  Eigen::half h;
  h.x = vmulh_f16(vget_lane_f16(prod, 0), vget_lane_f16(prod, 1));
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux_mul<Packet4hf>(const Packet4hf& a) {
  float16x4_t prod;
  prod = vmul_f16(a, vrev64_f16(a));
  Eigen::half h;
  h.x = vmulh_f16(vget_lane_f16(prod, 0), vget_lane_f16(prod, 1));
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux_min<Packet8hf>(const Packet8hf& a) {
  Eigen::half h;
  h.x = vminvq_f16(a);
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux_min<Packet4hf>(const Packet4hf& a) {
  Eigen::half h;
  h.x = vminv_f16(a);
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux_max<Packet8hf>(const Packet8hf& a) {
  Eigen::half h;
  h.x = vmaxvq_f16(a);
  return h;
}
 
template <>
EIGEN_STRONG_INLINE Eigen::half predux_max<Packet4hf>(const Packet4hf& a) {
  Eigen::half h;
  h.x = vmaxv_f16(a);
  return h;
}
 
#else
 
// Even if we do not have native vector arithmetic on fp16 types, we can still
// assume the presence of conversion instructions to/from fp32 on AArch64
// ([ref]).  As a result, packet arithmetic on AArch64 without `+fp16` is
// implemented through conversion to fp32.  Beware that this comes at the
// expense of additional instructions for casting and potential differences in
// floating-point error accumulation.  The performance is still much better than
// manual fp16, however.
//
// [ref]:
// <https://developer.arm.com/documentation/101028/0012/13--Advanced-SIMD--Neon--intrinsics#availability-of-16-bit-floating-point-vector-interchange-types>
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf predux_half(const Packet8hf& a) {
  return vcvt_f16_f32(vaddq_f32(vcvt_f32_f16(vget_low_f16(a)), vcvt_f32_f16(vget_high_f16(a))));
}
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf plset(const half& a) {
  const float f[] = {0, 1, 2, 3};
  float32x4_t countdown = vld1q_f32(f);
  float32x4_t base = vaddq_f32(vcvt_f32_f16(pset1<Packet4hf>(a)), countdown);
  return vcombine_f16(vcvt_f16_f32(base), vcvt_f16_f32(vaddq_f32(base, vdupq_n_f32(4))));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf plset(const half& a) {
  const float f[] = {0, 1, 2, 3};
  Packet4f countdown = vld1q_f32(f);
  return vcvt_f16_f32(vaddq_f32(pset1<Packet4f>(a), countdown));
}
 
#define EIGEN_MAKE_HALF_UNOP(name, op)                                       \
  template <>                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf name(const Packet4hf& a) { \
    return vcvt_f16_f32(v##op##q_f32(vcvt_f32_f16(a)));                      \
  }                                                                          \
  template <>                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf name(const Packet8hf& a) { \
    return vcombine_f16(name(vget_low_f16(a)), name(vget_high_f16(a)));      \
  }                                                                          \
  static_assert(true, "Trailing semicolon required")
#define EIGEN_MAKE_HALF_BINOP(name, op)                                                                    \
  template <>                                                                                              \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf name(const Packet4hf& a, const Packet4hf& b) {           \
    return vcvt_f16_f32(v##op##q_f32(vcvt_f32_f16(a), vcvt_f32_f16(b)));                                   \
  }                                                                                                        \
  template <>                                                                                              \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf name(const Packet8hf& a, const Packet8hf& b) {           \
    return vcombine_f16(name(vget_low_f16(a), vget_low_f16(b)), name(vget_high_f16(a), vget_high_f16(b))); \
  }                                                                                                        \
  static_assert(true, "Trailing semicolon required")
 
EIGEN_MAKE_HALF_BINOP(padd, add);
EIGEN_MAKE_HALF_BINOP(psub, sub);
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pnegate(const Packet8hf& a) {
  return vreinterpretq_f16_u16(veorq_u16(vreinterpretq_u16_f16(a), vdupq_n_u16(0x8000)));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pnegate(const Packet4hf& a) {
  return vreinterpret_f16_u16(veor_u16(vreinterpret_u16_f16(a), vdup_n_u16(0x8000)));
}
 
EIGEN_MAKE_HALF_BINOP(pmul, mul);
 
#if EIGEN_ARCH_ARM64
EIGEN_MAKE_HALF_BINOP(pdiv, div);
#else
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pdiv(const Packet4hf& a, const Packet4hf& b) {
  return vcvt_f16_f32(pdiv(vcvt_f32_f16(a), vcvt_f32_f16(b)));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pdiv(const Packet8hf& a, const Packet8hf& b) {
  return vcombine_f16(pdiv(vget_low_f16(a), vget_low_f16(b)), pdiv(vget_high_f16(a), vget_high_f16(b)));
}
#endif
 
#define EIGEN_MAKE_HALF_FMA(name, op)                                                                                \
  template <>                                                                                                        \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf name(const Packet4hf& a, const Packet4hf& b, const Packet4hf& c) { \
    return vcvt_f16_f32(v##op##q_f32(vcvt_f32_f16(c), vcvt_f32_f16(a), vcvt_f32_f16(b)));                            \
  }                                                                                                                  \
  template <>                                                                                                        \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf name(const Packet8hf& a, const Packet8hf& b, const Packet8hf& c) { \
    return vcombine_f16(name(vget_low_f16(a), vget_low_f16(b), vget_low_f16(c)),                                     \
                        name(vget_high_f16(a), vget_high_f16(b), vget_high_f16(c)));                                 \
  }                                                                                                                  \
  static_assert(true, "Trailing semicolon required")
 
EIGEN_MAKE_HALF_FMA(pmadd, fma);
EIGEN_MAKE_HALF_FMA(pnmadd, fms);
 
#undef EIGEN_MAKE_HALF_FMA
 
EIGEN_MAKE_HALF_BINOP(pmin, min);
EIGEN_MAKE_HALF_BINOP(pmax, max);
 
#ifdef __ARM_FEATURE_NUMERIC_MAXMIN
 
#define EIGEN_MAKE_HALF_NUMERIC_MAXMIN(name)                                                                 \
  template <>                                                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf p##name<PropagateNumbers, Packet4hf>(const Packet4hf& a,   \
                                                                                       const Packet4hf& b) { \
    return vcvt_f16_f32(v##name##nmq_f32(vcvt_f32_f16(a), vcvt_f32_f16(b)));                                 \
  }                                                                                                          \
  template <>                                                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf p##name<PropagateNumbers, Packet8hf>(const Packet8hf& a,   \
                                                                                       const Packet8hf& b) { \
    return vcombine_f16(p##name<PropagateNumbers, Packet4hf>(vget_low_f16(a), vget_low_f16(b)),              \
                        p##name<PropagateNumbers, Packet4hf>(vget_high_f16(a), vget_high_f16(b)));           \
  }                                                                                                          \
  static_assert(true, "Trailing semicolon required")
 
EIGEN_MAKE_HALF_NUMERIC_MAXMIN(min);
EIGEN_MAKE_HALF_NUMERIC_MAXMIN(max);
 
#undef EIGEN_MAKE_HALF_NUMERIC_MAXMIN
 
#endif
 
#define EIGEN_MAKE_HALF_CMP(name)                                                                       \
  template <>                                                                                           \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pcmp_##name(const Packet4hf& a, const Packet4hf& b) { \
    return vreinterpret_f16_u16(vmovn_u32(vc##name##q_f32(vcvt_f32_f16(a), vcvt_f32_f16(b))));          \
  }                                                                                                     \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pcmp_##name(const Packet8hf& a, const Packet8hf& b) { \
    return vcombine_f16(pcmp_##name(vget_low_f16(a), vget_low_f16(b)),                                  \
                        pcmp_##name(vget_high_f16(a), vget_high_f16(b)));                               \
  }                                                                                                     \
  static_assert(true, "Trailing semicolon required")
 
EIGEN_MAKE_HALF_CMP(eq);
EIGEN_MAKE_HALF_CMP(lt);
EIGEN_MAKE_HALF_CMP(le);
 
#undef EIGEN_MAKE_HALF_CMP
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pcmp_lt_or_nan(const Packet4hf& a, const Packet4hf& b) {
  return vreinterpret_f16_u16(vmovn_u32(vmvnq_u32(vcgeq_f32(vcvt_f32_f16(a), vcvt_f32_f16(b)))));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pcmp_lt_or_nan(const Packet8hf& a, const Packet8hf& b) {
  return vcombine_f16(pcmp_lt_or_nan(vget_low_f16(a), vget_low_f16(b)),
                      pcmp_lt_or_nan(vget_high_f16(a), vget_high_f16(b)));
}
 
EIGEN_MAKE_HALF_UNOP(print, rndn);
EIGEN_MAKE_HALF_UNOP(pfloor, rndm);
EIGEN_MAKE_HALF_UNOP(pceil, rndp);
EIGEN_MAKE_HALF_UNOP(pround, rnda);
EIGEN_MAKE_HALF_UNOP(ptrunc, rnd);
 
#if EIGEN_ARCH_ARM64
EIGEN_MAKE_HALF_UNOP(psqrt, sqrt);
#else
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf psqrt(const Packet4hf& a) {
  return vcvt_f16_f32(psqrt(vcvt_f32_f16(a)));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf psqrt(const Packet8hf& a) {
  return vcombine_f16(psqrt(vget_low_f16(a)), psqrt(vget_high_f16(a)));
}
#endif
 
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet8hf pabs(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vbicq_u16(vreinterpretq_u16_f16(a), vdupq_n_u16(0x8000)));
}
template <>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet4hf pabs(const Packet4hf& a) {
  return vreinterpret_f16_u16(vbic_u16(vreinterpret_u16_f16(a), vdup_n_u16(0x8000)));
}
 
// NOTE: On AArch64, we can use horizontal vector reductions for `add`, `min`, and `max`.
// However, the fallback through `predux<Packet${N}f>` is still necessary for `mul`.
#define EIGEN_HALF_FOLD_REDUX(name, op)                                                      \
  template <>                                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half name(const Packet4hf& a) {                      \
    return half(name(vcvt_f32_f16(a)));                                                      \
  }                                                                                          \
  template <>                                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half name(const Packet8hf& a) {                      \
    return half(name(p##op(vcvt_f32_f16(vget_low_f16(a)), vcvt_f32_f16(vget_high_f16(a))))); \
  }                                                                                          \
  static_assert(true, "Trailing semicolon required")
 
#if EIGEN_ARCH_ARM64
#define EIGEN_HALF_HORIZONTAL_REDUX(name, op)                                                                \
  template <>                                                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half name(const Packet8hf& a) {                                      \
    return half(v##op##vq_f32(v##op##q_f32(vcvt_f32_f16(vget_low_f16(a)), vcvt_f32_f16(vget_high_f16(a))))); \
  }                                                                                                          \
  template <>                                                                                                \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE half name(const Packet4hf& a) {                                      \
    return half(v##op##vq_f32(vcvt_f32_f16(a)));                                                             \
  }                                                                                                          \
  static_assert(true, "Trailing semicolon required")
#else
#define EIGEN_HALF_HORIZONTAL_REDUX(name, op) EIGEN_HALF_FOLD_REDUX(name, op)
#endif
 
EIGEN_HALF_HORIZONTAL_REDUX(predux, add);
EIGEN_HALF_FOLD_REDUX(predux_mul, mul);
EIGEN_HALF_HORIZONTAL_REDUX(predux_min, min);
EIGEN_HALF_HORIZONTAL_REDUX(predux_max, max);
 
#undef EIGEN_HALF_FOLD_REDUX
#undef EIGEN_HALF_HORIZONTAL_REDUX
 
#undef EIGEN_MAKE_HALF_UNOP
#undef EIGEN_MAKE_HALF_BINOP
 
#endif  // end EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
 
#if !EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
// Without FP16 arithmetic, half comparisons convert lane by lane. Classify on the raw bits instead, as for bfloat16:
// |a| ==, >, < 0x7c00.
EIGEN_STRONG_INLINE uint16x4_t neon_half_abs_bits(const Packet4hf& a) {
  return vbic_u16(vreinterpret_u16_f16(a), vdup_n_u16(0x8000));
}
EIGEN_STRONG_INLINE uint16x8_t neon_half_abs_bits(const Packet8hf& a) {
  return vbicq_u16(vreinterpretq_u16_f16(a), vdupq_n_u16(0x8000));
}
template <>
EIGEN_STRONG_INLINE Packet4hf pisinf<Packet4hf>(const Packet4hf& a) {
  return vreinterpret_f16_u16(vceq_u16(neon_half_abs_bits(a), vdup_n_u16(0x7c00)));
}
template <>
EIGEN_STRONG_INLINE Packet8hf pisinf<Packet8hf>(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vceqq_u16(neon_half_abs_bits(a), vdupq_n_u16(0x7c00)));
}
template <>
EIGEN_STRONG_INLINE Packet4hf pisnan<Packet4hf>(const Packet4hf& a) {
  return vreinterpret_f16_u16(vcgt_u16(neon_half_abs_bits(a), vdup_n_u16(0x7c00)));
}
template <>
EIGEN_STRONG_INLINE Packet8hf pisnan<Packet8hf>(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vcgtq_u16(neon_half_abs_bits(a), vdupq_n_u16(0x7c00)));
}
template <>
EIGEN_STRONG_INLINE Packet4hf pisfinite<Packet4hf>(const Packet4hf& a) {
  return vreinterpret_f16_u16(vclt_u16(neon_half_abs_bits(a), vdup_n_u16(0x7c00)));
}
template <>
EIGEN_STRONG_INLINE Packet8hf pisfinite<Packet8hf>(const Packet8hf& a) {
  return vreinterpretq_f16_u16(vcltq_u16(neon_half_abs_bits(a), vdupq_n_u16(0x7c00)));
}
#endif
 
#define EIGEN_MAKE_HALF_NEG_FMA(name, base, packet)                                                      \
  template <>                                                                                            \
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE packet name(const packet& a, const packet& b, const packet& c) { \
    return pnegate(base(a, b, c));                                                                       \
  }                                                                                                      \
  static_assert(true, "Trailing semicolon required")
 
EIGEN_MAKE_HALF_NEG_FMA(pmsub, pnmadd, Packet8hf);
EIGEN_MAKE_HALF_NEG_FMA(pmsub, pnmadd, Packet4hf);
EIGEN_MAKE_HALF_NEG_FMA(pnmsub, pmadd, Packet8hf);
EIGEN_MAKE_HALF_NEG_FMA(pnmsub, pmadd, Packet4hf);
 
#undef EIGEN_MAKE_HALF_NEG_FMA
 
#endif  // end EIGEN_ARCH_ARM64 && EIGEN_HAS_ARM64_FP16
 
}  // end namespace internal
 
}  // end namespace Eigen
 
#endif  // EIGEN_PACKET_MATH_NEON_H