// Copyright 2019 Google LLC
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// 512-bit AVX512 vectors and operations.
// External include guard in highway.h - see comment there.

// WARNING: most operations do not cross 128-bit block boundaries. In
// particular, "Broadcast", pack and zip behavior may be surprising.

#include <immintrin.h>  // AVX2+

#include "hwy/base.h"

#if defined(_MSC_VER) && defined(__clang__)
// Including <immintrin.h> should be enough, but Clang's headers helpfully skip
// including these headers when _MSC_VER is defined, like when using clang-cl.
// Include these directly here.
// clang-format off
#include <smmintrin.h>

#include <avxintrin.h>
#include <avx2intrin.h>
#include <f16cintrin.h>
#include <fmaintrin.h>

#include <avx512fintrin.h>
#include <avx512vlintrin.h>
#include <avx512bwintrin.h>
#include <avx512dqintrin.h>
#include <avx512vlbwintrin.h>
#include <avx512vldqintrin.h>
#include <avx512bitalgintrin.h>
#include <avx512vlbitalgintrin.h>
#include <avx512vpopcntdqintrin.h>
#include <avx512vpopcntdqvlintrin.h>
// clang-format on
#endif

#include <stddef.h>
#include <stdint.h>

// For half-width vectors. Already includes base.h and shared-inl.h.
#include "hwy/ops/x86_256-inl.h"

HWY_BEFORE_NAMESPACE();
namespace hwy {
namespace HWY_NAMESPACE {

namespace detail {

template <typename T>
struct Raw512 {
  using type = __m512i;
};
template <>
struct Raw512<float> {
  using type = __m512;
};
template <>
struct Raw512<double> {
  using type = __m512d;
};

// Template arg: sizeof(lane type)
template <size_t size>
struct RawMask512 {};
template <>
struct RawMask512<1> {
  using type = __mmask64;
};
template <>
struct RawMask512<2> {
  using type = __mmask32;
};
template <>
struct RawMask512<4> {
  using type = __mmask16;
};
template <>
struct RawMask512<8> {
  using type = __mmask8;
};

}  // namespace detail

template <typename T>
class Vec512 {
  using Raw = typename detail::Raw512<T>::type;

 public:
  // Compound assignment. Only usable if there is a corresponding non-member
  // binary operator overload. For example, only f32 and f64 support division.
  HWY_INLINE Vec512& operator*=(const Vec512 other) {
    return *this = (*this * other);
  }
  HWY_INLINE Vec512& operator/=(const Vec512 other) {
    return *this = (*this / other);
  }
  HWY_INLINE Vec512& operator+=(const Vec512 other) {
    return *this = (*this + other);
  }
  HWY_INLINE Vec512& operator-=(const Vec512 other) {
    return *this = (*this - other);
  }
  HWY_INLINE Vec512& operator&=(const Vec512 other) {
    return *this = (*this & other);
  }
  HWY_INLINE Vec512& operator|=(const Vec512 other) {
    return *this = (*this | other);
  }
  HWY_INLINE Vec512& operator^=(const Vec512 other) {
    return *this = (*this ^ other);
  }

  Raw raw;
};

// Mask register: one bit per lane.
template <typename T>
struct Mask512 {
  typename detail::RawMask512<sizeof(T)>::type raw;
};

// ------------------------------ BitCast

namespace detail {

HWY_INLINE __m512i BitCastToInteger(__m512i v) { return v; }
HWY_INLINE __m512i BitCastToInteger(__m512 v) { return _mm512_castps_si512(v); }
HWY_INLINE __m512i BitCastToInteger(__m512d v) {
  return _mm512_castpd_si512(v);
}

template <typename T>
HWY_INLINE Vec512<uint8_t> BitCastToByte(Vec512<T> v) {
  return Vec512<uint8_t>{BitCastToInteger(v.raw)};
}

// Cannot rely on function overloading because return types differ.
template <typename T>
struct BitCastFromInteger512 {
  HWY_INLINE __m512i operator()(__m512i v) { return v; }
};
template <>
struct BitCastFromInteger512<float> {
  HWY_INLINE __m512 operator()(__m512i v) { return _mm512_castsi512_ps(v); }
};
template <>
struct BitCastFromInteger512<double> {
  HWY_INLINE __m512d operator()(__m512i v) { return _mm512_castsi512_pd(v); }
};

template <typename T>
HWY_INLINE Vec512<T> BitCastFromByte(Full512<T> /* tag */, Vec512<uint8_t> v) {
  return Vec512<T>{BitCastFromInteger512<T>()(v.raw)};
}

}  // namespace detail

template <typename T, typename FromT>
HWY_API Vec512<T> BitCast(Full512<T> d, Vec512<FromT> v) {
  return detail::BitCastFromByte(d, detail::BitCastToByte(v));
}

// ------------------------------ Set

// Returns an all-zero vector.
template <typename T>
HWY_API Vec512<T> Zero(Full512<T> /* tag */) {
  return Vec512<T>{_mm512_setzero_si512()};
}
HWY_API Vec512<float> Zero(Full512<float> /* tag */) {
  return Vec512<float>{_mm512_setzero_ps()};
}
HWY_API Vec512<double> Zero(Full512<double> /* tag */) {
  return Vec512<double>{_mm512_setzero_pd()};
}

// Returns a vector with all lanes set to "t".
HWY_API Vec512<uint8_t> Set(Full512<uint8_t> /* tag */, const uint8_t t) {
  return Vec512<uint8_t>{_mm512_set1_epi8(static_cast<char>(t))};  // NOLINT
}
HWY_API Vec512<uint16_t> Set(Full512<uint16_t> /* tag */, const uint16_t t) {
  return Vec512<uint16_t>{_mm512_set1_epi16(static_cast<short>(t))};  // NOLINT
}
HWY_API Vec512<uint32_t> Set(Full512<uint32_t> /* tag */, const uint32_t t) {
  return Vec512<uint32_t>{_mm512_set1_epi32(static_cast<int>(t))};
}
HWY_API Vec512<uint64_t> Set(Full512<uint64_t> /* tag */, const uint64_t t) {
  return Vec512<uint64_t>{
      _mm512_set1_epi64(static_cast<long long>(t))};  // NOLINT
}
HWY_API Vec512<int8_t> Set(Full512<int8_t> /* tag */, const int8_t t) {
  return Vec512<int8_t>{_mm512_set1_epi8(static_cast<char>(t))};  // NOLINT
}
HWY_API Vec512<int16_t> Set(Full512<int16_t> /* tag */, const int16_t t) {
  return Vec512<int16_t>{_mm512_set1_epi16(static_cast<short>(t))};  // NOLINT
}
HWY_API Vec512<int32_t> Set(Full512<int32_t> /* tag */, const int32_t t) {
  return Vec512<int32_t>{_mm512_set1_epi32(t)};
}
HWY_API Vec512<int64_t> Set(Full512<int64_t> /* tag */, const int64_t t) {
  return Vec512<int64_t>{
      _mm512_set1_epi64(static_cast<long long>(t))};  // NOLINT
}
HWY_API Vec512<float> Set(Full512<float> /* tag */, const float t) {
  return Vec512<float>{_mm512_set1_ps(t)};
}
HWY_API Vec512<double> Set(Full512<double> /* tag */, const double t) {
  return Vec512<double>{_mm512_set1_pd(t)};
}

HWY_DIAGNOSTICS(push)
HWY_DIAGNOSTICS_OFF(disable : 4700, ignored "-Wuninitialized")

// Returns a vector with uninitialized elements.
template <typename T>
HWY_API Vec512<T> Undefined(Full512<T> /* tag */) {
  // Available on Clang 6.0, GCC 6.2, ICC 16.03, MSVC 19.14. All but ICC
  // generate an XOR instruction.
  return Vec512<T>{_mm512_undefined_epi32()};
}
HWY_API Vec512<float> Undefined(Full512<float> /* tag */) {
  return Vec512<float>{_mm512_undefined_ps()};
}
HWY_API Vec512<double> Undefined(Full512<double> /* tag */) {
  return Vec512<double>{_mm512_undefined_pd()};
}

HWY_DIAGNOSTICS(pop)

// ================================================== LOGICAL

// ------------------------------ Not

template <typename T>
HWY_API Vec512<T> Not(const Vec512<T> v) {
  using TU = MakeUnsigned<T>;
  const __m512i vu = BitCast(Full512<TU>(), v).raw;
  return BitCast(Full512<T>(),
                 Vec512<TU>{_mm512_ternarylogic_epi32(vu, vu, vu, 0x55)});
}

// ------------------------------ And

template <typename T>
HWY_API Vec512<T> And(const Vec512<T> a, const Vec512<T> b) {
  return Vec512<T>{_mm512_and_si512(a.raw, b.raw)};
}

HWY_API Vec512<float> And(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_and_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> And(const Vec512<double> a, const Vec512<double> b) {
  return Vec512<double>{_mm512_and_pd(a.raw, b.raw)};
}

// ------------------------------ AndNot

// Returns ~not_mask & mask.
template <typename T>
HWY_API Vec512<T> AndNot(const Vec512<T> not_mask, const Vec512<T> mask) {
  return Vec512<T>{_mm512_andnot_si512(not_mask.raw, mask.raw)};
}
HWY_API Vec512<float> AndNot(const Vec512<float> not_mask,
                             const Vec512<float> mask) {
  return Vec512<float>{_mm512_andnot_ps(not_mask.raw, mask.raw)};
}
HWY_API Vec512<double> AndNot(const Vec512<double> not_mask,
                              const Vec512<double> mask) {
  return Vec512<double>{_mm512_andnot_pd(not_mask.raw, mask.raw)};
}

// ------------------------------ Or

template <typename T>
HWY_API Vec512<T> Or(const Vec512<T> a, const Vec512<T> b) {
  return Vec512<T>{_mm512_or_si512(a.raw, b.raw)};
}

HWY_API Vec512<float> Or(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_or_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> Or(const Vec512<double> a, const Vec512<double> b) {
  return Vec512<double>{_mm512_or_pd(a.raw, b.raw)};
}

// ------------------------------ Xor

template <typename T>
HWY_API Vec512<T> Xor(const Vec512<T> a, const Vec512<T> b) {
  return Vec512<T>{_mm512_xor_si512(a.raw, b.raw)};
}

HWY_API Vec512<float> Xor(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_xor_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> Xor(const Vec512<double> a, const Vec512<double> b) {
  return Vec512<double>{_mm512_xor_pd(a.raw, b.raw)};
}

// ------------------------------ OrAnd

template <typename T>
HWY_API Vec512<T> OrAnd(Vec512<T> o, Vec512<T> a1, Vec512<T> a2) {
  const Full512<T> d;
  const RebindToUnsigned<decltype(d)> du;
  using VU = VFromD<decltype(du)>;
  const __m512i ret = _mm512_ternarylogic_epi64(
      BitCast(du, o).raw, BitCast(du, a1).raw, BitCast(du, a2).raw, 0xF8);
  return BitCast(d, VU{ret});
}

// ------------------------------ IfVecThenElse

template <typename T>
HWY_API Vec512<T> IfVecThenElse(Vec512<T> mask, Vec512<T> yes, Vec512<T> no) {
  const Full512<T> d;
  const RebindToUnsigned<decltype(d)> du;
  using VU = VFromD<decltype(du)>;
  return BitCast(d, VU{_mm512_ternarylogic_epi64(BitCast(du, mask).raw,
                                                 BitCast(du, yes).raw,
                                                 BitCast(du, no).raw, 0xCA)});
}

// ------------------------------ Operator overloads (internal-only if float)

template <typename T>
HWY_API Vec512<T> operator&(const Vec512<T> a, const Vec512<T> b) {
  return And(a, b);
}

template <typename T>
HWY_API Vec512<T> operator|(const Vec512<T> a, const Vec512<T> b) {
  return Or(a, b);
}

template <typename T>
HWY_API Vec512<T> operator^(const Vec512<T> a, const Vec512<T> b) {
  return Xor(a, b);
}

// ------------------------------ PopulationCount

// 8/16 require BITALG, 32/64 require VPOPCNTDQ.
#if HWY_TARGET == HWY_AVX3_DL

#ifdef HWY_NATIVE_POPCNT
#undef HWY_NATIVE_POPCNT
#else
#define HWY_NATIVE_POPCNT
#endif

namespace detail {

template <typename T>
HWY_INLINE Vec512<T> PopulationCount(hwy::SizeTag<1> /* tag */, Vec512<T> v) {
  return Vec512<T>{_mm512_popcnt_epi8(v.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> PopulationCount(hwy::SizeTag<2> /* tag */, Vec512<T> v) {
  return Vec512<T>{_mm512_popcnt_epi16(v.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> PopulationCount(hwy::SizeTag<4> /* tag */, Vec512<T> v) {
  return Vec512<T>{_mm512_popcnt_epi32(v.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> PopulationCount(hwy::SizeTag<8> /* tag */, Vec512<T> v) {
  return Vec512<T>{_mm512_popcnt_epi64(v.raw)};
}

}  // namespace detail

template <typename T>
HWY_API Vec512<T> PopulationCount(Vec512<T> v) {
  return detail::PopulationCount(hwy::SizeTag<sizeof(T)>(), v);
}

#endif  // HWY_TARGET == HWY_AVX3_DL

// ================================================== SIGN

// ------------------------------ CopySign

template <typename T>
HWY_API Vec512<T> CopySign(const Vec512<T> magn, const Vec512<T> sign) {
  static_assert(IsFloat<T>(), "Only makes sense for floating-point");

  const Full512<T> d;
  const auto msb = SignBit(d);

  const Rebind<MakeUnsigned<T>, decltype(d)> du;
  // Truth table for msb, magn, sign | bitwise msb ? sign : mag
  //                  0    0     0   |  0
  //                  0    0     1   |  0
  //                  0    1     0   |  1
  //                  0    1     1   |  1
  //                  1    0     0   |  0
  //                  1    0     1   |  1
  //                  1    1     0   |  0
  //                  1    1     1   |  1
  // The lane size does not matter because we are not using predication.
  const __m512i out = _mm512_ternarylogic_epi32(
      BitCast(du, msb).raw, BitCast(du, magn).raw, BitCast(du, sign).raw, 0xAC);
  return BitCast(d, decltype(Zero(du)){out});
}

template <typename T>
HWY_API Vec512<T> CopySignToAbs(const Vec512<T> abs, const Vec512<T> sign) {
  // AVX3 can also handle abs < 0, so no extra action needed.
  return CopySign(abs, sign);
}

// ================================================== MASK

// ------------------------------ FirstN

// Possibilities for constructing a bitmask of N ones:
// - kshift* only consider the lowest byte of the shift count, so they would
//   not correctly handle large n.
// - Scalar shifts >= 64 are UB.
// - BZHI has the desired semantics; we assume AVX-512 implies BMI2. However,
//   we need 64-bit masks for sizeof(T) == 1, so special-case 32-bit builds.

#if HWY_ARCH_X86_32
namespace detail {

// 32 bit mask is sufficient for lane size >= 2.
template <typename T, HWY_IF_NOT_LANE_SIZE(T, 1)>
HWY_INLINE Mask512<T> FirstN(size_t n) {
  Mask512<T> m;
  const uint32_t all = ~uint32_t(0);
  // BZHI only looks at the lower 8 bits of n!
  m.raw = static_cast<decltype(m.raw)>((n > 255) ? all : _bzhi_u32(all, n));
  return m;
}

template <typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_INLINE Mask512<T> FirstN(size_t n) {
  const uint64_t bits = n < 64 ? ((1ULL << n) - 1) : ~uint64_t(0);
  return Mask512<T>{static_cast<__mmask64>(bits)};
}

}  // namespace detail
#endif  // HWY_ARCH_X86_32

template <typename T>
HWY_API Mask512<T> FirstN(const Full512<T> /*tag*/, size_t n) {
#if HWY_ARCH_X86_64
  Mask512<T> m;
  const uint64_t all = ~uint64_t(0);
  // BZHI only looks at the lower 8 bits of n!
  m.raw = static_cast<decltype(m.raw)>((n > 255) ? all : _bzhi_u64(all, n));
  return m;
#else
  return detail::FirstN<T>(n);
#endif  // HWY_ARCH_X86_64
}

// ------------------------------ IfThenElse

// Returns mask ? b : a.

namespace detail {

// Templates for signed/unsigned integer of a particular size.
template <typename T>
HWY_INLINE Vec512<T> IfThenElse(hwy::SizeTag<1> /* tag */,
                                const Mask512<T> mask, const Vec512<T> yes,
                                const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_mov_epi8(no.raw, mask.raw, yes.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenElse(hwy::SizeTag<2> /* tag */,
                                const Mask512<T> mask, const Vec512<T> yes,
                                const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_mov_epi16(no.raw, mask.raw, yes.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenElse(hwy::SizeTag<4> /* tag */,
                                const Mask512<T> mask, const Vec512<T> yes,
                                const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_mov_epi32(no.raw, mask.raw, yes.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenElse(hwy::SizeTag<8> /* tag */,
                                const Mask512<T> mask, const Vec512<T> yes,
                                const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_mov_epi64(no.raw, mask.raw, yes.raw)};
}

}  // namespace detail

template <typename T>
HWY_API Vec512<T> IfThenElse(const Mask512<T> mask, const Vec512<T> yes,
                             const Vec512<T> no) {
  return detail::IfThenElse(hwy::SizeTag<sizeof(T)>(), mask, yes, no);
}
HWY_API Vec512<float> IfThenElse(const Mask512<float> mask,
                                 const Vec512<float> yes,
                                 const Vec512<float> no) {
  return Vec512<float>{_mm512_mask_mov_ps(no.raw, mask.raw, yes.raw)};
}
HWY_API Vec512<double> IfThenElse(const Mask512<double> mask,
                                  const Vec512<double> yes,
                                  const Vec512<double> no) {
  return Vec512<double>{_mm512_mask_mov_pd(no.raw, mask.raw, yes.raw)};
}

namespace detail {

template <typename T>
HWY_INLINE Vec512<T> IfThenElseZero(hwy::SizeTag<1> /* tag */,
                                    const Mask512<T> mask,
                                    const Vec512<T> yes) {
  return Vec512<T>{_mm512_maskz_mov_epi8(mask.raw, yes.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenElseZero(hwy::SizeTag<2> /* tag */,
                                    const Mask512<T> mask,
                                    const Vec512<T> yes) {
  return Vec512<T>{_mm512_maskz_mov_epi16(mask.raw, yes.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenElseZero(hwy::SizeTag<4> /* tag */,
                                    const Mask512<T> mask,
                                    const Vec512<T> yes) {
  return Vec512<T>{_mm512_maskz_mov_epi32(mask.raw, yes.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenElseZero(hwy::SizeTag<8> /* tag */,
                                    const Mask512<T> mask,
                                    const Vec512<T> yes) {
  return Vec512<T>{_mm512_maskz_mov_epi64(mask.raw, yes.raw)};
}

}  // namespace detail

template <typename T>
HWY_API Vec512<T> IfThenElseZero(const Mask512<T> mask, const Vec512<T> yes) {
  return detail::IfThenElseZero(hwy::SizeTag<sizeof(T)>(), mask, yes);
}
HWY_API Vec512<float> IfThenElseZero(const Mask512<float> mask,
                                     const Vec512<float> yes) {
  return Vec512<float>{_mm512_maskz_mov_ps(mask.raw, yes.raw)};
}
HWY_API Vec512<double> IfThenElseZero(const Mask512<double> mask,
                                      const Vec512<double> yes) {
  return Vec512<double>{_mm512_maskz_mov_pd(mask.raw, yes.raw)};
}

namespace detail {

template <typename T>
HWY_INLINE Vec512<T> IfThenZeroElse(hwy::SizeTag<1> /* tag */,
                                    const Mask512<T> mask, const Vec512<T> no) {
  // xor_epi8/16 are missing, but we have sub, which is just as fast for u8/16.
  return Vec512<T>{_mm512_mask_sub_epi8(no.raw, mask.raw, no.raw, no.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenZeroElse(hwy::SizeTag<2> /* tag */,
                                    const Mask512<T> mask, const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_sub_epi16(no.raw, mask.raw, no.raw, no.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenZeroElse(hwy::SizeTag<4> /* tag */,
                                    const Mask512<T> mask, const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_xor_epi32(no.raw, mask.raw, no.raw, no.raw)};
}
template <typename T>
HWY_INLINE Vec512<T> IfThenZeroElse(hwy::SizeTag<8> /* tag */,
                                    const Mask512<T> mask, const Vec512<T> no) {
  return Vec512<T>{_mm512_mask_xor_epi64(no.raw, mask.raw, no.raw, no.raw)};
}

}  // namespace detail

template <typename T>
HWY_API Vec512<T> IfThenZeroElse(const Mask512<T> mask, const Vec512<T> no) {
  return detail::IfThenZeroElse(hwy::SizeTag<sizeof(T)>(), mask, no);
}
HWY_API Vec512<float> IfThenZeroElse(const Mask512<float> mask,
                                     const Vec512<float> no) {
  return Vec512<float>{_mm512_mask_xor_ps(no.raw, mask.raw, no.raw, no.raw)};
}
HWY_API Vec512<double> IfThenZeroElse(const Mask512<double> mask,
                                      const Vec512<double> no) {
  return Vec512<double>{_mm512_mask_xor_pd(no.raw, mask.raw, no.raw, no.raw)};
}

template <typename T>
HWY_API Vec512<T> IfNegativeThenElse(Vec512<T> v, Vec512<T> yes, Vec512<T> no) {
  static_assert(IsSigned<T>(), "Only works for signed/float");
  // AVX3 MaskFromVec only looks at the MSB
  return IfThenElse(MaskFromVec(v), yes, no);
}

template <typename T, HWY_IF_FLOAT(T)>
HWY_API Vec512<T> ZeroIfNegative(const Vec512<T> v) {
  // AVX3 MaskFromVec only looks at the MSB
  return IfThenZeroElse(MaskFromVec(v), v);
}

// ================================================== ARITHMETIC

// ------------------------------ Addition

// Unsigned
HWY_API Vec512<uint8_t> operator+(const Vec512<uint8_t> a,
                                  const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_add_epi8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> operator+(const Vec512<uint16_t> a,
                                   const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_add_epi16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> operator+(const Vec512<uint32_t> a,
                                   const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_add_epi32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> operator+(const Vec512<uint64_t> a,
                                   const Vec512<uint64_t> b) {
  return Vec512<uint64_t>{_mm512_add_epi64(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int8_t> operator+(const Vec512<int8_t> a,
                                 const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_add_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> operator+(const Vec512<int16_t> a,
                                  const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_add_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> operator+(const Vec512<int32_t> a,
                                  const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_add_epi32(a.raw, b.raw)};
}
HWY_API Vec512<int64_t> operator+(const Vec512<int64_t> a,
                                  const Vec512<int64_t> b) {
  return Vec512<int64_t>{_mm512_add_epi64(a.raw, b.raw)};
}

// Float
HWY_API Vec512<float> operator+(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_add_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> operator+(const Vec512<double> a,
                                 const Vec512<double> b) {
  return Vec512<double>{_mm512_add_pd(a.raw, b.raw)};
}

// ------------------------------ Subtraction

// Unsigned
HWY_API Vec512<uint8_t> operator-(const Vec512<uint8_t> a,
                                  const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_sub_epi8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> operator-(const Vec512<uint16_t> a,
                                   const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_sub_epi16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> operator-(const Vec512<uint32_t> a,
                                   const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_sub_epi32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> operator-(const Vec512<uint64_t> a,
                                   const Vec512<uint64_t> b) {
  return Vec512<uint64_t>{_mm512_sub_epi64(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int8_t> operator-(const Vec512<int8_t> a,
                                 const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_sub_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> operator-(const Vec512<int16_t> a,
                                  const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_sub_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> operator-(const Vec512<int32_t> a,
                                  const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_sub_epi32(a.raw, b.raw)};
}
HWY_API Vec512<int64_t> operator-(const Vec512<int64_t> a,
                                  const Vec512<int64_t> b) {
  return Vec512<int64_t>{_mm512_sub_epi64(a.raw, b.raw)};
}

// Float
HWY_API Vec512<float> operator-(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_sub_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> operator-(const Vec512<double> a,
                                 const Vec512<double> b) {
  return Vec512<double>{_mm512_sub_pd(a.raw, b.raw)};
}

// ------------------------------ SumsOf8
HWY_API Vec512<uint64_t> SumsOf8(const Vec512<uint8_t> v) {
  return Vec512<uint64_t>{_mm512_sad_epu8(v.raw, _mm512_setzero_si512())};
}

// ------------------------------ SaturatedAdd

// Returns a + b clamped to the destination range.

// Unsigned
HWY_API Vec512<uint8_t> SaturatedAdd(const Vec512<uint8_t> a,
                                     const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_adds_epu8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> SaturatedAdd(const Vec512<uint16_t> a,
                                      const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_adds_epu16(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int8_t> SaturatedAdd(const Vec512<int8_t> a,
                                    const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_adds_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> SaturatedAdd(const Vec512<int16_t> a,
                                     const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_adds_epi16(a.raw, b.raw)};
}

// ------------------------------ SaturatedSub

// Returns a - b clamped to the destination range.

// Unsigned
HWY_API Vec512<uint8_t> SaturatedSub(const Vec512<uint8_t> a,
                                     const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_subs_epu8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> SaturatedSub(const Vec512<uint16_t> a,
                                      const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_subs_epu16(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int8_t> SaturatedSub(const Vec512<int8_t> a,
                                    const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_subs_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> SaturatedSub(const Vec512<int16_t> a,
                                     const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_subs_epi16(a.raw, b.raw)};
}

// ------------------------------ Average

// Returns (a + b + 1) / 2

// Unsigned
HWY_API Vec512<uint8_t> AverageRound(const Vec512<uint8_t> a,
                                     const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_avg_epu8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> AverageRound(const Vec512<uint16_t> a,
                                      const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_avg_epu16(a.raw, b.raw)};
}

// ------------------------------ Abs (Sub)

// Returns absolute value, except that LimitsMin() maps to LimitsMax() + 1.
HWY_API Vec512<int8_t> Abs(const Vec512<int8_t> v) {
#if HWY_COMPILER_MSVC
  // Workaround for incorrect codegen? (untested due to internal compiler error)
  const auto zero = Zero(Full512<int8_t>());
  return Vec512<int8_t>{_mm512_max_epi8(v.raw, (zero - v).raw)};
#else
  return Vec512<int8_t>{_mm512_abs_epi8(v.raw)};
#endif
}
HWY_API Vec512<int16_t> Abs(const Vec512<int16_t> v) {
  return Vec512<int16_t>{_mm512_abs_epi16(v.raw)};
}
HWY_API Vec512<int32_t> Abs(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_abs_epi32(v.raw)};
}
HWY_API Vec512<int64_t> Abs(const Vec512<int64_t> v) {
  return Vec512<int64_t>{_mm512_abs_epi64(v.raw)};
}

// These aren't native instructions, they also involve AND with constant.
HWY_API Vec512<float> Abs(const Vec512<float> v) {
  return Vec512<float>{_mm512_abs_ps(v.raw)};
}
HWY_API Vec512<double> Abs(const Vec512<double> v) {
  return Vec512<double>{_mm512_abs_pd(v.raw)};
}
// ------------------------------ ShiftLeft

template <int kBits>
HWY_API Vec512<uint16_t> ShiftLeft(const Vec512<uint16_t> v) {
  return Vec512<uint16_t>{_mm512_slli_epi16(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<uint32_t> ShiftLeft(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_slli_epi32(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<uint64_t> ShiftLeft(const Vec512<uint64_t> v) {
  return Vec512<uint64_t>{_mm512_slli_epi64(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<int16_t> ShiftLeft(const Vec512<int16_t> v) {
  return Vec512<int16_t>{_mm512_slli_epi16(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<int32_t> ShiftLeft(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_slli_epi32(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<int64_t> ShiftLeft(const Vec512<int64_t> v) {
  return Vec512<int64_t>{_mm512_slli_epi64(v.raw, kBits)};
}

template <int kBits, typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_API Vec512<T> ShiftLeft(const Vec512<T> v) {
  const Full512<T> d8;
  const RepartitionToWide<decltype(d8)> d16;
  const auto shifted = BitCast(d8, ShiftLeft<kBits>(BitCast(d16, v)));
  return kBits == 1
             ? (v + v)
             : (shifted & Set(d8, static_cast<T>((0xFF << kBits) & 0xFF)));
}

// ------------------------------ ShiftRight

template <int kBits>
HWY_API Vec512<uint16_t> ShiftRight(const Vec512<uint16_t> v) {
  return Vec512<uint16_t>{_mm512_srli_epi16(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<uint32_t> ShiftRight(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_srli_epi32(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<uint64_t> ShiftRight(const Vec512<uint64_t> v) {
  return Vec512<uint64_t>{_mm512_srli_epi64(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<uint8_t> ShiftRight(const Vec512<uint8_t> v) {
  const Full512<uint8_t> d8;
  // Use raw instead of BitCast to support N=1.
  const Vec512<uint8_t> shifted{ShiftRight<kBits>(Vec512<uint16_t>{v.raw}).raw};
  return shifted & Set(d8, 0xFF >> kBits);
}

template <int kBits>
HWY_API Vec512<int16_t> ShiftRight(const Vec512<int16_t> v) {
  return Vec512<int16_t>{_mm512_srai_epi16(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<int32_t> ShiftRight(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_srai_epi32(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<int64_t> ShiftRight(const Vec512<int64_t> v) {
  return Vec512<int64_t>{_mm512_srai_epi64(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<int8_t> ShiftRight(const Vec512<int8_t> v) {
  const Full512<int8_t> di;
  const Full512<uint8_t> du;
  const auto shifted = BitCast(di, ShiftRight<kBits>(BitCast(du, v)));
  const auto shifted_sign = BitCast(di, Set(du, 0x80 >> kBits));
  return (shifted ^ shifted_sign) - shifted_sign;
}

// ------------------------------ RotateRight

template <int kBits>
HWY_API Vec512<uint32_t> RotateRight(const Vec512<uint32_t> v) {
  static_assert(0 <= kBits && kBits < 32, "Invalid shift count");
  return Vec512<uint32_t>{_mm512_ror_epi32(v.raw, kBits)};
}

template <int kBits>
HWY_API Vec512<uint64_t> RotateRight(const Vec512<uint64_t> v) {
  static_assert(0 <= kBits && kBits < 64, "Invalid shift count");
  return Vec512<uint64_t>{_mm512_ror_epi64(v.raw, kBits)};
}

// ------------------------------ ShiftLeftSame

HWY_API Vec512<uint16_t> ShiftLeftSame(const Vec512<uint16_t> v,
                                       const int bits) {
  return Vec512<uint16_t>{_mm512_sll_epi16(v.raw, _mm_cvtsi32_si128(bits))};
}
HWY_API Vec512<uint32_t> ShiftLeftSame(const Vec512<uint32_t> v,
                                       const int bits) {
  return Vec512<uint32_t>{_mm512_sll_epi32(v.raw, _mm_cvtsi32_si128(bits))};
}
HWY_API Vec512<uint64_t> ShiftLeftSame(const Vec512<uint64_t> v,
                                       const int bits) {
  return Vec512<uint64_t>{_mm512_sll_epi64(v.raw, _mm_cvtsi32_si128(bits))};
}

HWY_API Vec512<int16_t> ShiftLeftSame(const Vec512<int16_t> v, const int bits) {
  return Vec512<int16_t>{_mm512_sll_epi16(v.raw, _mm_cvtsi32_si128(bits))};
}

HWY_API Vec512<int32_t> ShiftLeftSame(const Vec512<int32_t> v, const int bits) {
  return Vec512<int32_t>{_mm512_sll_epi32(v.raw, _mm_cvtsi32_si128(bits))};
}

HWY_API Vec512<int64_t> ShiftLeftSame(const Vec512<int64_t> v, const int bits) {
  return Vec512<int64_t>{_mm512_sll_epi64(v.raw, _mm_cvtsi32_si128(bits))};
}

template <typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_API Vec512<T> ShiftLeftSame(const Vec512<T> v, const int bits) {
  const Full512<T> d8;
  const RepartitionToWide<decltype(d8)> d16;
  const auto shifted = BitCast(d8, ShiftLeftSame(BitCast(d16, v), bits));
  return shifted & Set(d8, static_cast<T>((0xFF << bits) & 0xFF));
}

// ------------------------------ ShiftRightSame

HWY_API Vec512<uint16_t> ShiftRightSame(const Vec512<uint16_t> v,
                                        const int bits) {
  return Vec512<uint16_t>{_mm512_srl_epi16(v.raw, _mm_cvtsi32_si128(bits))};
}
HWY_API Vec512<uint32_t> ShiftRightSame(const Vec512<uint32_t> v,
                                        const int bits) {
  return Vec512<uint32_t>{_mm512_srl_epi32(v.raw, _mm_cvtsi32_si128(bits))};
}
HWY_API Vec512<uint64_t> ShiftRightSame(const Vec512<uint64_t> v,
                                        const int bits) {
  return Vec512<uint64_t>{_mm512_srl_epi64(v.raw, _mm_cvtsi32_si128(bits))};
}

HWY_API Vec512<uint8_t> ShiftRightSame(Vec512<uint8_t> v, const int bits) {
  const Full512<uint8_t> d8;
  const RepartitionToWide<decltype(d8)> d16;
  const auto shifted = BitCast(d8, ShiftRightSame(BitCast(d16, v), bits));
  return shifted & Set(d8, static_cast<uint8_t>(0xFF >> bits));
}

HWY_API Vec512<int16_t> ShiftRightSame(const Vec512<int16_t> v,
                                       const int bits) {
  return Vec512<int16_t>{_mm512_sra_epi16(v.raw, _mm_cvtsi32_si128(bits))};
}

HWY_API Vec512<int32_t> ShiftRightSame(const Vec512<int32_t> v,
                                       const int bits) {
  return Vec512<int32_t>{_mm512_sra_epi32(v.raw, _mm_cvtsi32_si128(bits))};
}
HWY_API Vec512<int64_t> ShiftRightSame(const Vec512<int64_t> v,
                                       const int bits) {
  return Vec512<int64_t>{_mm512_sra_epi64(v.raw, _mm_cvtsi32_si128(bits))};
}

HWY_API Vec512<int8_t> ShiftRightSame(Vec512<int8_t> v, const int bits) {
  const Full512<int8_t> di;
  const Full512<uint8_t> du;
  const auto shifted = BitCast(di, ShiftRightSame(BitCast(du, v), bits));
  const auto shifted_sign =
      BitCast(di, Set(du, static_cast<uint8_t>(0x80 >> bits)));
  return (shifted ^ shifted_sign) - shifted_sign;
}

// ------------------------------ Shl

HWY_API Vec512<uint16_t> operator<<(const Vec512<uint16_t> v,
                                    const Vec512<uint16_t> bits) {
  return Vec512<uint16_t>{_mm512_sllv_epi16(v.raw, bits.raw)};
}

HWY_API Vec512<uint32_t> operator<<(const Vec512<uint32_t> v,
                                    const Vec512<uint32_t> bits) {
  return Vec512<uint32_t>{_mm512_sllv_epi32(v.raw, bits.raw)};
}

HWY_API Vec512<uint64_t> operator<<(const Vec512<uint64_t> v,
                                    const Vec512<uint64_t> bits) {
  return Vec512<uint64_t>{_mm512_sllv_epi64(v.raw, bits.raw)};
}

// Signed left shift is the same as unsigned.
template <typename T, HWY_IF_SIGNED(T)>
HWY_API Vec512<T> operator<<(const Vec512<T> v, const Vec512<T> bits) {
  const Full512<T> di;
  const Full512<MakeUnsigned<T>> du;
  return BitCast(di, BitCast(du, v) << BitCast(du, bits));
}

// ------------------------------ Shr

HWY_API Vec512<uint16_t> operator>>(const Vec512<uint16_t> v,
                                    const Vec512<uint16_t> bits) {
  return Vec512<uint16_t>{_mm512_srlv_epi16(v.raw, bits.raw)};
}

HWY_API Vec512<uint32_t> operator>>(const Vec512<uint32_t> v,
                                    const Vec512<uint32_t> bits) {
  return Vec512<uint32_t>{_mm512_srlv_epi32(v.raw, bits.raw)};
}

HWY_API Vec512<uint64_t> operator>>(const Vec512<uint64_t> v,
                                    const Vec512<uint64_t> bits) {
  return Vec512<uint64_t>{_mm512_srlv_epi64(v.raw, bits.raw)};
}

HWY_API Vec512<int16_t> operator>>(const Vec512<int16_t> v,
                                   const Vec512<int16_t> bits) {
  return Vec512<int16_t>{_mm512_srav_epi16(v.raw, bits.raw)};
}

HWY_API Vec512<int32_t> operator>>(const Vec512<int32_t> v,
                                   const Vec512<int32_t> bits) {
  return Vec512<int32_t>{_mm512_srav_epi32(v.raw, bits.raw)};
}

HWY_API Vec512<int64_t> operator>>(const Vec512<int64_t> v,
                                   const Vec512<int64_t> bits) {
  return Vec512<int64_t>{_mm512_srav_epi64(v.raw, bits.raw)};
}

// ------------------------------ Minimum

// Unsigned
HWY_API Vec512<uint8_t> Min(const Vec512<uint8_t> a, const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_min_epu8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> Min(const Vec512<uint16_t> a,
                             const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_min_epu16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> Min(const Vec512<uint32_t> a,
                             const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_min_epu32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> Min(const Vec512<uint64_t> a,
                             const Vec512<uint64_t> b) {
  return Vec512<uint64_t>{_mm512_min_epu64(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int8_t> Min(const Vec512<int8_t> a, const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_min_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> Min(const Vec512<int16_t> a, const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_min_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> Min(const Vec512<int32_t> a, const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_min_epi32(a.raw, b.raw)};
}
HWY_API Vec512<int64_t> Min(const Vec512<int64_t> a, const Vec512<int64_t> b) {
  return Vec512<int64_t>{_mm512_min_epi64(a.raw, b.raw)};
}

// Float
HWY_API Vec512<float> Min(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_min_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> Min(const Vec512<double> a, const Vec512<double> b) {
  return Vec512<double>{_mm512_min_pd(a.raw, b.raw)};
}

// ------------------------------ Maximum

// Unsigned
HWY_API Vec512<uint8_t> Max(const Vec512<uint8_t> a, const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_max_epu8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> Max(const Vec512<uint16_t> a,
                             const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_max_epu16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> Max(const Vec512<uint32_t> a,
                             const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_max_epu32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> Max(const Vec512<uint64_t> a,
                             const Vec512<uint64_t> b) {
  return Vec512<uint64_t>{_mm512_max_epu64(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int8_t> Max(const Vec512<int8_t> a, const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_max_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> Max(const Vec512<int16_t> a, const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_max_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> Max(const Vec512<int32_t> a, const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_max_epi32(a.raw, b.raw)};
}
HWY_API Vec512<int64_t> Max(const Vec512<int64_t> a, const Vec512<int64_t> b) {
  return Vec512<int64_t>{_mm512_max_epi64(a.raw, b.raw)};
}

// Float
HWY_API Vec512<float> Max(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_max_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> Max(const Vec512<double> a, const Vec512<double> b) {
  return Vec512<double>{_mm512_max_pd(a.raw, b.raw)};
}

// ------------------------------ Integer multiplication

// Unsigned
HWY_API Vec512<uint16_t> operator*(const Vec512<uint16_t> a,
                                   const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_mullo_epi16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> operator*(const Vec512<uint32_t> a,
                                   const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_mullo_epi32(a.raw, b.raw)};
}

// Signed
HWY_API Vec512<int16_t> operator*(const Vec512<int16_t> a,
                                  const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_mullo_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> operator*(const Vec512<int32_t> a,
                                  const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_mullo_epi32(a.raw, b.raw)};
}

// Returns the upper 16 bits of a * b in each lane.
HWY_API Vec512<uint16_t> MulHigh(const Vec512<uint16_t> a,
                                 const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_mulhi_epu16(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> MulHigh(const Vec512<int16_t> a,
                                const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_mulhi_epi16(a.raw, b.raw)};
}

// Multiplies even lanes (0, 2 ..) and places the double-wide result into
// even and the upper half into its odd neighbor lane.
HWY_API Vec512<int64_t> MulEven(const Vec512<int32_t> a,
                                const Vec512<int32_t> b) {
  return Vec512<int64_t>{_mm512_mul_epi32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> MulEven(const Vec512<uint32_t> a,
                                 const Vec512<uint32_t> b) {
  return Vec512<uint64_t>{_mm512_mul_epu32(a.raw, b.raw)};
}

// ------------------------------ Neg (Sub)

template <typename T, HWY_IF_FLOAT(T)>
HWY_API Vec512<T> Neg(const Vec512<T> v) {
  return Xor(v, SignBit(Full512<T>()));
}

template <typename T, HWY_IF_NOT_FLOAT(T)>
HWY_API Vec512<T> Neg(const Vec512<T> v) {
  return Zero(Full512<T>()) - v;
}

// ------------------------------ Floating-point mul / div

HWY_API Vec512<float> operator*(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_mul_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> operator*(const Vec512<double> a,
                                 const Vec512<double> b) {
  return Vec512<double>{_mm512_mul_pd(a.raw, b.raw)};
}

HWY_API Vec512<float> operator/(const Vec512<float> a, const Vec512<float> b) {
  return Vec512<float>{_mm512_div_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> operator/(const Vec512<double> a,
                                 const Vec512<double> b) {
  return Vec512<double>{_mm512_div_pd(a.raw, b.raw)};
}

// Approximate reciprocal
HWY_API Vec512<float> ApproximateReciprocal(const Vec512<float> v) {
  return Vec512<float>{_mm512_rcp14_ps(v.raw)};
}

// Absolute value of difference.
HWY_API Vec512<float> AbsDiff(const Vec512<float> a, const Vec512<float> b) {
  return Abs(a - b);
}

// ------------------------------ Floating-point multiply-add variants

// Returns mul * x + add
HWY_API Vec512<float> MulAdd(const Vec512<float> mul, const Vec512<float> x,
                             const Vec512<float> add) {
  return Vec512<float>{_mm512_fmadd_ps(mul.raw, x.raw, add.raw)};
}
HWY_API Vec512<double> MulAdd(const Vec512<double> mul, const Vec512<double> x,
                              const Vec512<double> add) {
  return Vec512<double>{_mm512_fmadd_pd(mul.raw, x.raw, add.raw)};
}

// Returns add - mul * x
HWY_API Vec512<float> NegMulAdd(const Vec512<float> mul, const Vec512<float> x,
                                const Vec512<float> add) {
  return Vec512<float>{_mm512_fnmadd_ps(mul.raw, x.raw, add.raw)};
}
HWY_API Vec512<double> NegMulAdd(const Vec512<double> mul,
                                 const Vec512<double> x,
                                 const Vec512<double> add) {
  return Vec512<double>{_mm512_fnmadd_pd(mul.raw, x.raw, add.raw)};
}

// Returns mul * x - sub
HWY_API Vec512<float> MulSub(const Vec512<float> mul, const Vec512<float> x,
                             const Vec512<float> sub) {
  return Vec512<float>{_mm512_fmsub_ps(mul.raw, x.raw, sub.raw)};
}
HWY_API Vec512<double> MulSub(const Vec512<double> mul, const Vec512<double> x,
                              const Vec512<double> sub) {
  return Vec512<double>{_mm512_fmsub_pd(mul.raw, x.raw, sub.raw)};
}

// Returns -mul * x - sub
HWY_API Vec512<float> NegMulSub(const Vec512<float> mul, const Vec512<float> x,
                                const Vec512<float> sub) {
  return Vec512<float>{_mm512_fnmsub_ps(mul.raw, x.raw, sub.raw)};
}
HWY_API Vec512<double> NegMulSub(const Vec512<double> mul,
                                 const Vec512<double> x,
                                 const Vec512<double> sub) {
  return Vec512<double>{_mm512_fnmsub_pd(mul.raw, x.raw, sub.raw)};
}

// ------------------------------ Floating-point square root

// Full precision square root
HWY_API Vec512<float> Sqrt(const Vec512<float> v) {
  return Vec512<float>{_mm512_sqrt_ps(v.raw)};
}
HWY_API Vec512<double> Sqrt(const Vec512<double> v) {
  return Vec512<double>{_mm512_sqrt_pd(v.raw)};
}

// Approximate reciprocal square root
HWY_API Vec512<float> ApproximateReciprocalSqrt(const Vec512<float> v) {
  return Vec512<float>{_mm512_rsqrt14_ps(v.raw)};
}

// ------------------------------ Floating-point rounding

// Work around warnings in the intrinsic definitions (passing -1 as a mask).
HWY_DIAGNOSTICS(push)
HWY_DIAGNOSTICS_OFF(disable : 4245 4365, ignored "-Wsign-conversion")

// Toward nearest integer, tie to even
HWY_API Vec512<float> Round(const Vec512<float> v) {
  return Vec512<float>{_mm512_roundscale_ps(
      v.raw, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC)};
}
HWY_API Vec512<double> Round(const Vec512<double> v) {
  return Vec512<double>{_mm512_roundscale_pd(
      v.raw, _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC)};
}

// Toward zero, aka truncate
HWY_API Vec512<float> Trunc(const Vec512<float> v) {
  return Vec512<float>{
      _mm512_roundscale_ps(v.raw, _MM_FROUND_TO_ZERO | _MM_FROUND_NO_EXC)};
}
HWY_API Vec512<double> Trunc(const Vec512<double> v) {
  return Vec512<double>{
      _mm512_roundscale_pd(v.raw, _MM_FROUND_TO_ZERO | _MM_FROUND_NO_EXC)};
}

// Toward +infinity, aka ceiling
HWY_API Vec512<float> Ceil(const Vec512<float> v) {
  return Vec512<float>{
      _mm512_roundscale_ps(v.raw, _MM_FROUND_TO_POS_INF | _MM_FROUND_NO_EXC)};
}
HWY_API Vec512<double> Ceil(const Vec512<double> v) {
  return Vec512<double>{
      _mm512_roundscale_pd(v.raw, _MM_FROUND_TO_POS_INF | _MM_FROUND_NO_EXC)};
}

// Toward -infinity, aka floor
HWY_API Vec512<float> Floor(const Vec512<float> v) {
  return Vec512<float>{
      _mm512_roundscale_ps(v.raw, _MM_FROUND_TO_NEG_INF | _MM_FROUND_NO_EXC)};
}
HWY_API Vec512<double> Floor(const Vec512<double> v) {
  return Vec512<double>{
      _mm512_roundscale_pd(v.raw, _MM_FROUND_TO_NEG_INF | _MM_FROUND_NO_EXC)};
}

HWY_DIAGNOSTICS(pop)

// ================================================== COMPARE

// Comparisons set a mask bit to 1 if the condition is true, else 0.

template <typename TFrom, typename TTo>
HWY_API Mask512<TTo> RebindMask(Full512<TTo> /*tag*/, Mask512<TFrom> m) {
  static_assert(sizeof(TFrom) == sizeof(TTo), "Must have same size");
  return Mask512<TTo>{m.raw};
}

namespace detail {

template <typename T>
HWY_INLINE Mask512<T> TestBit(hwy::SizeTag<1> /*tag*/, const Vec512<T> v,
                              const Vec512<T> bit) {
  return Mask512<T>{_mm512_test_epi8_mask(v.raw, bit.raw)};
}
template <typename T>
HWY_INLINE Mask512<T> TestBit(hwy::SizeTag<2> /*tag*/, const Vec512<T> v,
                              const Vec512<T> bit) {
  return Mask512<T>{_mm512_test_epi16_mask(v.raw, bit.raw)};
}
template <typename T>
HWY_INLINE Mask512<T> TestBit(hwy::SizeTag<4> /*tag*/, const Vec512<T> v,
                              const Vec512<T> bit) {
  return Mask512<T>{_mm512_test_epi32_mask(v.raw, bit.raw)};
}
template <typename T>
HWY_INLINE Mask512<T> TestBit(hwy::SizeTag<8> /*tag*/, const Vec512<T> v,
                              const Vec512<T> bit) {
  return Mask512<T>{_mm512_test_epi64_mask(v.raw, bit.raw)};
}

}  // namespace detail

template <typename T>
HWY_API Mask512<T> TestBit(const Vec512<T> v, const Vec512<T> bit) {
  static_assert(!hwy::IsFloat<T>(), "Only integer vectors supported");
  return detail::TestBit(hwy::SizeTag<sizeof(T)>(), v, bit);
}

// ------------------------------ Equality

template <typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_API Mask512<T> operator==(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpeq_epi8_mask(a.raw, b.raw)};
}
template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Mask512<T> operator==(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpeq_epi16_mask(a.raw, b.raw)};
}
template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Mask512<T> operator==(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpeq_epi32_mask(a.raw, b.raw)};
}
template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Mask512<T> operator==(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpeq_epi64_mask(a.raw, b.raw)};
}

HWY_API Mask512<float> operator==(Vec512<float> a, Vec512<float> b) {
  return Mask512<float>{_mm512_cmp_ps_mask(a.raw, b.raw, _CMP_EQ_OQ)};
}

HWY_API Mask512<double> operator==(Vec512<double> a, Vec512<double> b) {
  return Mask512<double>{_mm512_cmp_pd_mask(a.raw, b.raw, _CMP_EQ_OQ)};
}

// ------------------------------ Inequality

template <typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_API Mask512<T> operator!=(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpneq_epi8_mask(a.raw, b.raw)};
}
template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Mask512<T> operator!=(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpneq_epi16_mask(a.raw, b.raw)};
}
template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Mask512<T> operator!=(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpneq_epi32_mask(a.raw, b.raw)};
}
template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Mask512<T> operator!=(Vec512<T> a, Vec512<T> b) {
  return Mask512<T>{_mm512_cmpneq_epi64_mask(a.raw, b.raw)};
}

HWY_API Mask512<float> operator!=(Vec512<float> a, Vec512<float> b) {
  return Mask512<float>{_mm512_cmp_ps_mask(a.raw, b.raw, _CMP_NEQ_OQ)};
}

HWY_API Mask512<double> operator!=(Vec512<double> a, Vec512<double> b) {
  return Mask512<double>{_mm512_cmp_pd_mask(a.raw, b.raw, _CMP_NEQ_OQ)};
}

// ------------------------------ Strict inequality

HWY_API Mask512<uint8_t> operator>(Vec512<uint8_t> a, Vec512<uint8_t> b) {
  return Mask512<uint8_t>{_mm512_cmpgt_epu8_mask(a.raw, b.raw)};
}
HWY_API Mask512<uint16_t> operator>(Vec512<uint16_t> a, Vec512<uint16_t> b) {
  return Mask512<uint16_t>{_mm512_cmpgt_epu16_mask(a.raw, b.raw)};
}
HWY_API Mask512<uint32_t> operator>(Vec512<uint32_t> a, Vec512<uint32_t> b) {
  return Mask512<uint32_t>{_mm512_cmpgt_epu32_mask(a.raw, b.raw)};
}
HWY_API Mask512<uint64_t> operator>(Vec512<uint64_t> a, Vec512<uint64_t> b) {
  return Mask512<uint64_t>{_mm512_cmpgt_epu64_mask(a.raw, b.raw)};
}

HWY_API Mask512<int8_t> operator>(Vec512<int8_t> a, Vec512<int8_t> b) {
  return Mask512<int8_t>{_mm512_cmpgt_epi8_mask(a.raw, b.raw)};
}
HWY_API Mask512<int16_t> operator>(Vec512<int16_t> a, Vec512<int16_t> b) {
  return Mask512<int16_t>{_mm512_cmpgt_epi16_mask(a.raw, b.raw)};
}
HWY_API Mask512<int32_t> operator>(Vec512<int32_t> a, Vec512<int32_t> b) {
  return Mask512<int32_t>{_mm512_cmpgt_epi32_mask(a.raw, b.raw)};
}
HWY_API Mask512<int64_t> operator>(Vec512<int64_t> a, Vec512<int64_t> b) {
  return Mask512<int64_t>{_mm512_cmpgt_epi64_mask(a.raw, b.raw)};
}

HWY_API Mask512<float> operator>(Vec512<float> a, Vec512<float> b) {
  return Mask512<float>{_mm512_cmp_ps_mask(a.raw, b.raw, _CMP_GT_OQ)};
}
HWY_API Mask512<double> operator>(Vec512<double> a, Vec512<double> b) {
  return Mask512<double>{_mm512_cmp_pd_mask(a.raw, b.raw, _CMP_GT_OQ)};
}

// ------------------------------ Weak inequality

HWY_API Mask512<float> operator>=(Vec512<float> a, Vec512<float> b) {
  return Mask512<float>{_mm512_cmp_ps_mask(a.raw, b.raw, _CMP_GE_OQ)};
}
HWY_API Mask512<double> operator>=(Vec512<double> a, Vec512<double> b) {
  return Mask512<double>{_mm512_cmp_pd_mask(a.raw, b.raw, _CMP_GE_OQ)};
}

// ------------------------------ Reversed comparisons

template <typename T>
HWY_API Mask512<T> operator<(Vec512<T> a, Vec512<T> b) {
  return b > a;
}

template <typename T>
HWY_API Mask512<T> operator<=(Vec512<T> a, Vec512<T> b) {
  return b >= a;
}

// ------------------------------ Mask

namespace detail {

template <typename T>
HWY_INLINE Mask512<T> MaskFromVec(hwy::SizeTag<1> /*tag*/, const Vec512<T> v) {
  return Mask512<T>{_mm512_movepi8_mask(v.raw)};
}
template <typename T>
HWY_INLINE Mask512<T> MaskFromVec(hwy::SizeTag<2> /*tag*/, const Vec512<T> v) {
  return Mask512<T>{_mm512_movepi16_mask(v.raw)};
}
template <typename T>
HWY_INLINE Mask512<T> MaskFromVec(hwy::SizeTag<4> /*tag*/, const Vec512<T> v) {
  return Mask512<T>{_mm512_movepi32_mask(v.raw)};
}
template <typename T>
HWY_INLINE Mask512<T> MaskFromVec(hwy::SizeTag<8> /*tag*/, const Vec512<T> v) {
  return Mask512<T>{_mm512_movepi64_mask(v.raw)};
}

}  // namespace detail

template <typename T>
HWY_API Mask512<T> MaskFromVec(const Vec512<T> v) {
  return detail::MaskFromVec(hwy::SizeTag<sizeof(T)>(), v);
}
// There do not seem to be native floating-point versions of these instructions.
HWY_API Mask512<float> MaskFromVec(const Vec512<float> v) {
  return Mask512<float>{MaskFromVec(BitCast(Full512<int32_t>(), v)).raw};
}
HWY_API Mask512<double> MaskFromVec(const Vec512<double> v) {
  return Mask512<double>{MaskFromVec(BitCast(Full512<int64_t>(), v)).raw};
}

HWY_API Vec512<uint8_t> VecFromMask(const Mask512<uint8_t> v) {
  return Vec512<uint8_t>{_mm512_movm_epi8(v.raw)};
}
HWY_API Vec512<int8_t> VecFromMask(const Mask512<int8_t> v) {
  return Vec512<int8_t>{_mm512_movm_epi8(v.raw)};
}

HWY_API Vec512<uint16_t> VecFromMask(const Mask512<uint16_t> v) {
  return Vec512<uint16_t>{_mm512_movm_epi16(v.raw)};
}
HWY_API Vec512<int16_t> VecFromMask(const Mask512<int16_t> v) {
  return Vec512<int16_t>{_mm512_movm_epi16(v.raw)};
}

HWY_API Vec512<uint32_t> VecFromMask(const Mask512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_movm_epi32(v.raw)};
}
HWY_API Vec512<int32_t> VecFromMask(const Mask512<int32_t> v) {
  return Vec512<int32_t>{_mm512_movm_epi32(v.raw)};
}
HWY_API Vec512<float> VecFromMask(const Mask512<float> v) {
  return Vec512<float>{_mm512_castsi512_ps(_mm512_movm_epi32(v.raw))};
}

HWY_API Vec512<uint64_t> VecFromMask(const Mask512<uint64_t> v) {
  return Vec512<uint64_t>{_mm512_movm_epi64(v.raw)};
}
HWY_API Vec512<int64_t> VecFromMask(const Mask512<int64_t> v) {
  return Vec512<int64_t>{_mm512_movm_epi64(v.raw)};
}
HWY_API Vec512<double> VecFromMask(const Mask512<double> v) {
  return Vec512<double>{_mm512_castsi512_pd(_mm512_movm_epi64(v.raw))};
}

template <typename T>
HWY_API Vec512<T> VecFromMask(Full512<T> /* tag */, const Mask512<T> v) {
  return VecFromMask(v);
}

// ------------------------------ Mask logical

namespace detail {

template <typename T>
HWY_INLINE Mask512<T> Not(hwy::SizeTag<1> /*tag*/, const Mask512<T> m) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_knot_mask64(m.raw)};
#else
  return Mask512<T>{~m.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Not(hwy::SizeTag<2> /*tag*/, const Mask512<T> m) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_knot_mask32(m.raw)};
#else
  return Mask512<T>{~m.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Not(hwy::SizeTag<4> /*tag*/, const Mask512<T> m) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_knot_mask16(m.raw)};
#else
  return Mask512<T>{static_cast<uint16_t>(~m.raw & 0xFFFF)};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Not(hwy::SizeTag<8> /*tag*/, const Mask512<T> m) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_knot_mask8(m.raw)};
#else
  return Mask512<T>{static_cast<uint8_t>(~m.raw & 0xFF)};
#endif
}

template <typename T>
HWY_INLINE Mask512<T> And(hwy::SizeTag<1> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kand_mask64(a.raw, b.raw)};
#else
  return Mask512<T>{a.raw & b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> And(hwy::SizeTag<2> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kand_mask32(a.raw, b.raw)};
#else
  return Mask512<T>{a.raw & b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> And(hwy::SizeTag<4> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kand_mask16(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint16_t>(a.raw & b.raw)};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> And(hwy::SizeTag<8> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kand_mask8(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint8_t>(a.raw & b.raw)};
#endif
}

template <typename T>
HWY_INLINE Mask512<T> AndNot(hwy::SizeTag<1> /*tag*/, const Mask512<T> a,
                             const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kandn_mask64(a.raw, b.raw)};
#else
  return Mask512<T>{~a.raw & b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> AndNot(hwy::SizeTag<2> /*tag*/, const Mask512<T> a,
                             const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kandn_mask32(a.raw, b.raw)};
#else
  return Mask512<T>{~a.raw & b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> AndNot(hwy::SizeTag<4> /*tag*/, const Mask512<T> a,
                             const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kandn_mask16(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint16_t>(~a.raw & b.raw)};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> AndNot(hwy::SizeTag<8> /*tag*/, const Mask512<T> a,
                             const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kandn_mask8(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint8_t>(~a.raw & b.raw)};
#endif
}

template <typename T>
HWY_INLINE Mask512<T> Or(hwy::SizeTag<1> /*tag*/, const Mask512<T> a,
                         const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kor_mask64(a.raw, b.raw)};
#else
  return Mask512<T>{a.raw | b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Or(hwy::SizeTag<2> /*tag*/, const Mask512<T> a,
                         const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kor_mask32(a.raw, b.raw)};
#else
  return Mask512<T>{a.raw | b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Or(hwy::SizeTag<4> /*tag*/, const Mask512<T> a,
                         const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kor_mask16(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint16_t>(a.raw | b.raw)};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Or(hwy::SizeTag<8> /*tag*/, const Mask512<T> a,
                         const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kor_mask8(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint8_t>(a.raw | b.raw)};
#endif
}

template <typename T>
HWY_INLINE Mask512<T> Xor(hwy::SizeTag<1> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kxor_mask64(a.raw, b.raw)};
#else
  return Mask512<T>{a.raw ^ b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Xor(hwy::SizeTag<2> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kxor_mask32(a.raw, b.raw)};
#else
  return Mask512<T>{a.raw ^ b.raw};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Xor(hwy::SizeTag<4> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kxor_mask16(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint16_t>(a.raw ^ b.raw)};
#endif
}
template <typename T>
HWY_INLINE Mask512<T> Xor(hwy::SizeTag<8> /*tag*/, const Mask512<T> a,
                          const Mask512<T> b) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return Mask512<T>{_kxor_mask8(a.raw, b.raw)};
#else
  return Mask512<T>{static_cast<uint8_t>(a.raw ^ b.raw)};
#endif
}

}  // namespace detail

template <typename T>
HWY_API Mask512<T> Not(const Mask512<T> m) {
  return detail::Not(hwy::SizeTag<sizeof(T)>(), m);
}

template <typename T>
HWY_API Mask512<T> And(const Mask512<T> a, Mask512<T> b) {
  return detail::And(hwy::SizeTag<sizeof(T)>(), a, b);
}

template <typename T>
HWY_API Mask512<T> AndNot(const Mask512<T> a, Mask512<T> b) {
  return detail::AndNot(hwy::SizeTag<sizeof(T)>(), a, b);
}

template <typename T>
HWY_API Mask512<T> Or(const Mask512<T> a, Mask512<T> b) {
  return detail::Or(hwy::SizeTag<sizeof(T)>(), a, b);
}

template <typename T>
HWY_API Mask512<T> Xor(const Mask512<T> a, Mask512<T> b) {
  return detail::Xor(hwy::SizeTag<sizeof(T)>(), a, b);
}

// ------------------------------ BroadcastSignBit (ShiftRight, compare, mask)

HWY_API Vec512<int8_t> BroadcastSignBit(const Vec512<int8_t> v) {
  return VecFromMask(v < Zero(Full512<int8_t>()));
}

HWY_API Vec512<int16_t> BroadcastSignBit(const Vec512<int16_t> v) {
  return ShiftRight<15>(v);
}

HWY_API Vec512<int32_t> BroadcastSignBit(const Vec512<int32_t> v) {
  return ShiftRight<31>(v);
}

HWY_API Vec512<int64_t> BroadcastSignBit(const Vec512<int64_t> v) {
  return Vec512<int64_t>{_mm512_srai_epi64(v.raw, 63)};
}

// ================================================== MEMORY

// ------------------------------ Load

template <typename T>
HWY_API Vec512<T> Load(Full512<T> /* tag */, const T* HWY_RESTRICT aligned) {
  return Vec512<T>{_mm512_load_si512(aligned)};
}
HWY_API Vec512<float> Load(Full512<float> /* tag */,
                           const float* HWY_RESTRICT aligned) {
  return Vec512<float>{_mm512_load_ps(aligned)};
}
HWY_API Vec512<double> Load(Full512<double> /* tag */,
                            const double* HWY_RESTRICT aligned) {
  return Vec512<double>{_mm512_load_pd(aligned)};
}

template <typename T>
HWY_API Vec512<T> LoadU(Full512<T> /* tag */, const T* HWY_RESTRICT p) {
  return Vec512<T>{_mm512_loadu_si512(p)};
}
HWY_API Vec512<float> LoadU(Full512<float> /* tag */,
                            const float* HWY_RESTRICT p) {
  return Vec512<float>{_mm512_loadu_ps(p)};
}
HWY_API Vec512<double> LoadU(Full512<double> /* tag */,
                             const double* HWY_RESTRICT p) {
  return Vec512<double>{_mm512_loadu_pd(p)};
}

// ------------------------------ MaskedLoad

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> MaskedLoad(Mask512<T> m, Full512<T> /* tag */,
                             const T* HWY_RESTRICT aligned) {
  return Vec512<T>{_mm512_maskz_load_epi32(m.raw, aligned)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> MaskedLoad(Mask512<T> m, Full512<T> /* tag */,
                             const T* HWY_RESTRICT aligned) {
  return Vec512<T>{_mm512_maskz_load_epi64(m.raw, aligned)};
}

HWY_API Vec512<float> MaskedLoad(Mask512<float> m, Full512<float> /* tag */,
                                 const float* HWY_RESTRICT aligned) {
  return Vec512<float>{_mm512_maskz_load_ps(m.raw, aligned)};
}

HWY_API Vec512<double> MaskedLoad(Mask512<double> m, Full512<double> /* tag */,
                                  const double* HWY_RESTRICT aligned) {
  return Vec512<double>{_mm512_maskz_load_pd(m.raw, aligned)};
}

// There is no load_epi8/16, so use loadu instead.
template <typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_API Vec512<T> MaskedLoad(Mask512<T> m, Full512<T> /* tag */,
                             const T* HWY_RESTRICT aligned) {
  return Vec512<T>{_mm512_maskz_loadu_epi8(m.raw, aligned)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> MaskedLoad(Mask512<T> m, Full512<T> /* tag */,
                             const T* HWY_RESTRICT aligned) {
  return Vec512<T>{_mm512_maskz_loadu_epi16(m.raw, aligned)};
}

// ------------------------------ LoadDup128

// Loads 128 bit and duplicates into both 128-bit halves. This avoids the
// 3-cycle cost of moving data between 128-bit halves and avoids port 5.
template <typename T>
HWY_API Vec512<T> LoadDup128(Full512<T> /* tag */,
                             const T* const HWY_RESTRICT p) {
  // Clang 3.9 generates VINSERTF128 which is slower, but inline assembly leads
  // to "invalid output size for constraint" without -mavx512:
  // https://gcc.godbolt.org/z/-Jt_-F
#if HWY_LOADDUP_ASM
  __m512i out;
  asm("vbroadcasti128 %1, %[reg]" : [reg] "=x"(out) : "m"(p[0]));
  return Vec512<T>{out};
#else
  const auto x4 = LoadU(Full128<T>(), p);
  return Vec512<T>{_mm512_broadcast_i32x4(x4.raw)};
#endif
}
HWY_API Vec512<float> LoadDup128(Full512<float> /* tag */,
                                 const float* const HWY_RESTRICT p) {
#if HWY_LOADDUP_ASM
  __m512 out;
  asm("vbroadcastf128 %1, %[reg]" : [reg] "=x"(out) : "m"(p[0]));
  return Vec512<float>{out};
#else
  const __m128 x4 = _mm_loadu_ps(p);
  return Vec512<float>{_mm512_broadcast_f32x4(x4)};
#endif
}

HWY_API Vec512<double> LoadDup128(Full512<double> /* tag */,
                                  const double* const HWY_RESTRICT p) {
#if HWY_LOADDUP_ASM
  __m512d out;
  asm("vbroadcastf128 %1, %[reg]" : [reg] "=x"(out) : "m"(p[0]));
  return Vec512<double>{out};
#else
  const __m128d x2 = _mm_loadu_pd(p);
  return Vec512<double>{_mm512_broadcast_f64x2(x2)};
#endif
}

// ------------------------------ Store

template <typename T>
HWY_API void Store(const Vec512<T> v, Full512<T> /* tag */,
                   T* HWY_RESTRICT aligned) {
  _mm512_store_si512(reinterpret_cast<__m512i*>(aligned), v.raw);
}
HWY_API void Store(const Vec512<float> v, Full512<float> /* tag */,
                   float* HWY_RESTRICT aligned) {
  _mm512_store_ps(aligned, v.raw);
}
HWY_API void Store(const Vec512<double> v, Full512<double> /* tag */,
                   double* HWY_RESTRICT aligned) {
  _mm512_store_pd(aligned, v.raw);
}

template <typename T>
HWY_API void StoreU(const Vec512<T> v, Full512<T> /* tag */,
                    T* HWY_RESTRICT p) {
  _mm512_storeu_si512(reinterpret_cast<__m512i*>(p), v.raw);
}
HWY_API void StoreU(const Vec512<float> v, Full512<float> /* tag */,
                    float* HWY_RESTRICT p) {
  _mm512_storeu_ps(p, v.raw);
}
HWY_API void StoreU(const Vec512<double> v, Full512<double>,
                    double* HWY_RESTRICT p) {
  _mm512_storeu_pd(p, v.raw);
}

// ------------------------------ Non-temporal stores

template <typename T>
HWY_API void Stream(const Vec512<T> v, Full512<T> /* tag */,
                    T* HWY_RESTRICT aligned) {
  _mm512_stream_si512(reinterpret_cast<__m512i*>(aligned), v.raw);
}
HWY_API void Stream(const Vec512<float> v, Full512<float> /* tag */,
                    float* HWY_RESTRICT aligned) {
  _mm512_stream_ps(aligned, v.raw);
}
HWY_API void Stream(const Vec512<double> v, Full512<double>,
                    double* HWY_RESTRICT aligned) {
  _mm512_stream_pd(aligned, v.raw);
}

// ------------------------------ Scatter

// Work around warnings in the intrinsic definitions (passing -1 as a mask).
HWY_DIAGNOSTICS(push)
HWY_DIAGNOSTICS_OFF(disable : 4245 4365, ignored "-Wsign-conversion")

namespace detail {

template <typename T>
HWY_INLINE void ScatterOffset(hwy::SizeTag<4> /* tag */, Vec512<T> v,
                              Full512<T> /* tag */, T* HWY_RESTRICT base,
                              const Vec512<int32_t> offset) {
  _mm512_i32scatter_epi32(base, offset.raw, v.raw, 1);
}
template <typename T>
HWY_INLINE void ScatterIndex(hwy::SizeTag<4> /* tag */, Vec512<T> v,
                             Full512<T> /* tag */, T* HWY_RESTRICT base,
                             const Vec512<int32_t> index) {
  _mm512_i32scatter_epi32(base, index.raw, v.raw, 4);
}

template <typename T>
HWY_INLINE void ScatterOffset(hwy::SizeTag<8> /* tag */, Vec512<T> v,
                              Full512<T> /* tag */, T* HWY_RESTRICT base,
                              const Vec512<int64_t> offset) {
  _mm512_i64scatter_epi64(base, offset.raw, v.raw, 1);
}
template <typename T>
HWY_INLINE void ScatterIndex(hwy::SizeTag<8> /* tag */, Vec512<T> v,
                             Full512<T> /* tag */, T* HWY_RESTRICT base,
                             const Vec512<int64_t> index) {
  _mm512_i64scatter_epi64(base, index.raw, v.raw, 8);
}

}  // namespace detail

template <typename T, typename Offset>
HWY_API void ScatterOffset(Vec512<T> v, Full512<T> d, T* HWY_RESTRICT base,
                           const Vec512<Offset> offset) {
  static_assert(sizeof(T) == sizeof(Offset), "Must match for portability");
  return detail::ScatterOffset(hwy::SizeTag<sizeof(T)>(), v, d, base, offset);
}
template <typename T, typename Index>
HWY_API void ScatterIndex(Vec512<T> v, Full512<T> d, T* HWY_RESTRICT base,
                          const Vec512<Index> index) {
  static_assert(sizeof(T) == sizeof(Index), "Must match for portability");
  return detail::ScatterIndex(hwy::SizeTag<sizeof(T)>(), v, d, base, index);
}

HWY_API void ScatterOffset(Vec512<float> v, Full512<float> /* tag */,
                           float* HWY_RESTRICT base,
                           const Vec512<int32_t> offset) {
  _mm512_i32scatter_ps(base, offset.raw, v.raw, 1);
}
HWY_API void ScatterIndex(Vec512<float> v, Full512<float> /* tag */,
                          float* HWY_RESTRICT base,
                          const Vec512<int32_t> index) {
  _mm512_i32scatter_ps(base, index.raw, v.raw, 4);
}

HWY_API void ScatterOffset(Vec512<double> v, Full512<double> /* tag */,
                           double* HWY_RESTRICT base,
                           const Vec512<int64_t> offset) {
  _mm512_i64scatter_pd(base, offset.raw, v.raw, 1);
}
HWY_API void ScatterIndex(Vec512<double> v, Full512<double> /* tag */,
                          double* HWY_RESTRICT base,
                          const Vec512<int64_t> index) {
  _mm512_i64scatter_pd(base, index.raw, v.raw, 8);
}

// ------------------------------ Gather

namespace detail {

template <typename T>
HWY_INLINE Vec512<T> GatherOffset(hwy::SizeTag<4> /* tag */,
                                  Full512<T> /* tag */,
                                  const T* HWY_RESTRICT base,
                                  const Vec512<int32_t> offset) {
  return Vec512<T>{_mm512_i32gather_epi32(offset.raw, base, 1)};
}
template <typename T>
HWY_INLINE Vec512<T> GatherIndex(hwy::SizeTag<4> /* tag */,
                                 Full512<T> /* tag */,
                                 const T* HWY_RESTRICT base,
                                 const Vec512<int32_t> index) {
  return Vec512<T>{_mm512_i32gather_epi32(index.raw, base, 4)};
}

template <typename T>
HWY_INLINE Vec512<T> GatherOffset(hwy::SizeTag<8> /* tag */,
                                  Full512<T> /* tag */,
                                  const T* HWY_RESTRICT base,
                                  const Vec512<int64_t> offset) {
  return Vec512<T>{_mm512_i64gather_epi64(offset.raw, base, 1)};
}
template <typename T>
HWY_INLINE Vec512<T> GatherIndex(hwy::SizeTag<8> /* tag */,
                                 Full512<T> /* tag */,
                                 const T* HWY_RESTRICT base,
                                 const Vec512<int64_t> index) {
  return Vec512<T>{_mm512_i64gather_epi64(index.raw, base, 8)};
}

}  // namespace detail

template <typename T, typename Offset>
HWY_API Vec512<T> GatherOffset(Full512<T> d, const T* HWY_RESTRICT base,
                               const Vec512<Offset> offset) {
  static_assert(sizeof(T) == sizeof(Offset), "Must match for portability");
  return detail::GatherOffset(hwy::SizeTag<sizeof(T)>(), d, base, offset);
}
template <typename T, typename Index>
HWY_API Vec512<T> GatherIndex(Full512<T> d, const T* HWY_RESTRICT base,
                              const Vec512<Index> index) {
  static_assert(sizeof(T) == sizeof(Index), "Must match for portability");
  return detail::GatherIndex(hwy::SizeTag<sizeof(T)>(), d, base, index);
}

HWY_API Vec512<float> GatherOffset(Full512<float> /* tag */,
                                   const float* HWY_RESTRICT base,
                                   const Vec512<int32_t> offset) {
  return Vec512<float>{_mm512_i32gather_ps(offset.raw, base, 1)};
}
HWY_API Vec512<float> GatherIndex(Full512<float> /* tag */,
                                  const float* HWY_RESTRICT base,
                                  const Vec512<int32_t> index) {
  return Vec512<float>{_mm512_i32gather_ps(index.raw, base, 4)};
}

HWY_API Vec512<double> GatherOffset(Full512<double> /* tag */,
                                    const double* HWY_RESTRICT base,
                                    const Vec512<int64_t> offset) {
  return Vec512<double>{_mm512_i64gather_pd(offset.raw, base, 1)};
}
HWY_API Vec512<double> GatherIndex(Full512<double> /* tag */,
                                   const double* HWY_RESTRICT base,
                                   const Vec512<int64_t> index) {
  return Vec512<double>{_mm512_i64gather_pd(index.raw, base, 8)};
}

HWY_DIAGNOSTICS(pop)

// ================================================== SWIZZLE

// ------------------------------ LowerHalf

template <typename T>
HWY_API Vec256<T> LowerHalf(Full256<T> /* tag */, Vec512<T> v) {
  return Vec256<T>{_mm512_castsi512_si256(v.raw)};
}
HWY_API Vec256<float> LowerHalf(Full256<float> /* tag */, Vec512<float> v) {
  return Vec256<float>{_mm512_castps512_ps256(v.raw)};
}
HWY_API Vec256<double> LowerHalf(Full256<double> /* tag */, Vec512<double> v) {
  return Vec256<double>{_mm512_castpd512_pd256(v.raw)};
}

template <typename T>
HWY_API Vec256<T> LowerHalf(Vec512<T> v) {
  return LowerHalf(Full256<T>(), v);
}

// ------------------------------ UpperHalf

template <typename T>
HWY_API Vec256<T> UpperHalf(Full256<T> /* tag */, Vec512<T> v) {
  return Vec256<T>{_mm512_extracti32x8_epi32(v.raw, 1)};
}
HWY_API Vec256<float> UpperHalf(Full256<float> /* tag */, Vec512<float> v) {
  return Vec256<float>{_mm512_extractf32x8_ps(v.raw, 1)};
}
HWY_API Vec256<double> UpperHalf(Full256<double> /* tag */, Vec512<double> v) {
  return Vec256<double>{_mm512_extractf64x4_pd(v.raw, 1)};
}

// ------------------------------ GetLane (LowerHalf)
template <typename T>
HWY_API T GetLane(const Vec512<T> v) {
  return GetLane(LowerHalf(v));
}

// ------------------------------ ZeroExtendVector

// Unfortunately the initial _mm512_castsi256_si512 intrinsic leaves the upper
// bits undefined. Although it makes sense for them to be zero (EVEX encoded
// instructions have that effect), a compiler could decide to optimize out code
// that relies on this.
//
// The newer _mm512_zextsi256_si512 intrinsic fixes this by specifying the
// zeroing, but it is not available on GCC until 10.1. For older GCC, we can
// still obtain the desired code thanks to pattern recognition; note that the
// expensive insert instruction is not actually generated, see
// https://gcc.godbolt.org/z/1MKGaP.

template <typename T>
HWY_API Vec512<T> ZeroExtendVector(Full512<T> /* tag */, Vec256<T> lo) {
#if !HWY_COMPILER_CLANG && HWY_COMPILER_GCC && (HWY_COMPILER_GCC < 1000)
  return Vec512<T>{_mm512_inserti32x8(_mm512_setzero_si512(), lo.raw, 0)};
#else
  return Vec512<T>{_mm512_zextsi256_si512(lo.raw)};
#endif
}
HWY_API Vec512<float> ZeroExtendVector(Full512<float> /* tag */,
                                       Vec256<float> lo) {
#if !HWY_COMPILER_CLANG && HWY_COMPILER_GCC && (HWY_COMPILER_GCC < 1000)
  return Vec512<float>{_mm512_insertf32x8(_mm512_setzero_ps(), lo.raw, 0)};
#else
  return Vec512<float>{_mm512_zextps256_ps512(lo.raw)};
#endif
}
HWY_API Vec512<double> ZeroExtendVector(Full512<double> /* tag */,
                                        Vec256<double> lo) {
#if !HWY_COMPILER_CLANG && HWY_COMPILER_GCC && (HWY_COMPILER_GCC < 1000)
  return Vec512<double>{_mm512_insertf64x4(_mm512_setzero_pd(), lo.raw, 0)};
#else
  return Vec512<double>{_mm512_zextpd256_pd512(lo.raw)};
#endif
}

// ------------------------------ Combine

template <typename T>
HWY_API Vec512<T> Combine(Full512<T> d, Vec256<T> hi, Vec256<T> lo) {
  const auto lo512 = ZeroExtendVector(d, lo);
  return Vec512<T>{_mm512_inserti32x8(lo512.raw, hi.raw, 1)};
}
HWY_API Vec512<float> Combine(Full512<float> d, Vec256<float> hi,
                              Vec256<float> lo) {
  const auto lo512 = ZeroExtendVector(d, lo);
  return Vec512<float>{_mm512_insertf32x8(lo512.raw, hi.raw, 1)};
}
HWY_API Vec512<double> Combine(Full512<double> d, Vec256<double> hi,
                               Vec256<double> lo) {
  const auto lo512 = ZeroExtendVector(d, lo);
  return Vec512<double>{_mm512_insertf64x4(lo512.raw, hi.raw, 1)};
}

// ------------------------------ ShiftLeftBytes

template <int kBytes, typename T>
HWY_API Vec512<T> ShiftLeftBytes(Full512<T> /* tag */, const Vec512<T> v) {
  static_assert(0 <= kBytes && kBytes <= 16, "Invalid kBytes");
  return Vec512<T>{_mm512_bslli_epi128(v.raw, kBytes)};
}

template <int kBytes, typename T>
HWY_API Vec512<T> ShiftLeftBytes(const Vec512<T> v) {
  return ShiftLeftBytes<kBytes>(Full512<T>(), v);
}

// ------------------------------ ShiftLeftLanes

template <int kLanes, typename T>
HWY_API Vec512<T> ShiftLeftLanes(Full512<T> d, const Vec512<T> v) {
  const Repartition<uint8_t, decltype(d)> d8;
  return BitCast(d, ShiftLeftBytes<kLanes * sizeof(T)>(BitCast(d8, v)));
}

template <int kLanes, typename T>
HWY_API Vec512<T> ShiftLeftLanes(const Vec512<T> v) {
  return ShiftLeftLanes<kLanes>(Full512<T>(), v);
}

// ------------------------------ ShiftRightBytes
template <int kBytes, typename T>
HWY_API Vec512<T> ShiftRightBytes(Full512<T> /* tag */, const Vec512<T> v) {
  static_assert(0 <= kBytes && kBytes <= 16, "Invalid kBytes");
  return Vec512<T>{_mm512_bsrli_epi128(v.raw, kBytes)};
}

// ------------------------------ ShiftRightLanes
template <int kLanes, typename T>
HWY_API Vec512<T> ShiftRightLanes(Full512<T> d, const Vec512<T> v) {
  const Repartition<uint8_t, decltype(d)> d8;
  return BitCast(d, ShiftRightBytes<kLanes * sizeof(T)>(d8, BitCast(d8, v)));
}

// ------------------------------ CombineShiftRightBytes

template <int kBytes, typename T, class V = Vec512<T>>
HWY_API V CombineShiftRightBytes(Full512<T> d, V hi, V lo) {
  const Repartition<uint8_t, decltype(d)> d8;
  return BitCast(d, Vec512<uint8_t>{_mm512_alignr_epi8(
                        BitCast(d8, hi).raw, BitCast(d8, lo).raw, kBytes)});
}

// ------------------------------ Broadcast/splat any lane

// Unsigned
template <int kLane>
HWY_API Vec512<uint16_t> Broadcast(const Vec512<uint16_t> v) {
  static_assert(0 <= kLane && kLane < 8, "Invalid lane");
  if (kLane < 4) {
    const __m512i lo = _mm512_shufflelo_epi16(v.raw, (0x55 * kLane) & 0xFF);
    return Vec512<uint16_t>{_mm512_unpacklo_epi64(lo, lo)};
  } else {
    const __m512i hi =
        _mm512_shufflehi_epi16(v.raw, (0x55 * (kLane - 4)) & 0xFF);
    return Vec512<uint16_t>{_mm512_unpackhi_epi64(hi, hi)};
  }
}
template <int kLane>
HWY_API Vec512<uint32_t> Broadcast(const Vec512<uint32_t> v) {
  static_assert(0 <= kLane && kLane < 4, "Invalid lane");
  constexpr _MM_PERM_ENUM perm = static_cast<_MM_PERM_ENUM>(0x55 * kLane);
  return Vec512<uint32_t>{_mm512_shuffle_epi32(v.raw, perm)};
}
template <int kLane>
HWY_API Vec512<uint64_t> Broadcast(const Vec512<uint64_t> v) {
  static_assert(0 <= kLane && kLane < 2, "Invalid lane");
  constexpr _MM_PERM_ENUM perm = kLane ? _MM_PERM_DCDC : _MM_PERM_BABA;
  return Vec512<uint64_t>{_mm512_shuffle_epi32(v.raw, perm)};
}

// Signed
template <int kLane>
HWY_API Vec512<int16_t> Broadcast(const Vec512<int16_t> v) {
  static_assert(0 <= kLane && kLane < 8, "Invalid lane");
  if (kLane < 4) {
    const __m512i lo = _mm512_shufflelo_epi16(v.raw, (0x55 * kLane) & 0xFF);
    return Vec512<int16_t>{_mm512_unpacklo_epi64(lo, lo)};
  } else {
    const __m512i hi =
        _mm512_shufflehi_epi16(v.raw, (0x55 * (kLane - 4)) & 0xFF);
    return Vec512<int16_t>{_mm512_unpackhi_epi64(hi, hi)};
  }
}
template <int kLane>
HWY_API Vec512<int32_t> Broadcast(const Vec512<int32_t> v) {
  static_assert(0 <= kLane && kLane < 4, "Invalid lane");
  constexpr _MM_PERM_ENUM perm = static_cast<_MM_PERM_ENUM>(0x55 * kLane);
  return Vec512<int32_t>{_mm512_shuffle_epi32(v.raw, perm)};
}
template <int kLane>
HWY_API Vec512<int64_t> Broadcast(const Vec512<int64_t> v) {
  static_assert(0 <= kLane && kLane < 2, "Invalid lane");
  constexpr _MM_PERM_ENUM perm = kLane ? _MM_PERM_DCDC : _MM_PERM_BABA;
  return Vec512<int64_t>{_mm512_shuffle_epi32(v.raw, perm)};
}

// Float
template <int kLane>
HWY_API Vec512<float> Broadcast(const Vec512<float> v) {
  static_assert(0 <= kLane && kLane < 4, "Invalid lane");
  constexpr _MM_PERM_ENUM perm = static_cast<_MM_PERM_ENUM>(0x55 * kLane);
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, perm)};
}
template <int kLane>
HWY_API Vec512<double> Broadcast(const Vec512<double> v) {
  static_assert(0 <= kLane && kLane < 2, "Invalid lane");
  constexpr _MM_PERM_ENUM perm = static_cast<_MM_PERM_ENUM>(0xFF * kLane);
  return Vec512<double>{_mm512_shuffle_pd(v.raw, v.raw, perm)};
}

// ------------------------------ Hard-coded shuffles

// Notation: let Vec512<int32_t> have lanes 7,6,5,4,3,2,1,0 (0 is
// least-significant). Shuffle0321 rotates four-lane blocks one lane to the
// right (the previous least-significant lane is now most-significant =>
// 47650321). These could also be implemented via CombineShiftRightBytes but
// the shuffle_abcd notation is more convenient.

// Swap 32-bit halves in 64-bit halves.
HWY_API Vec512<uint32_t> Shuffle2301(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_CDAB)};
}
HWY_API Vec512<int32_t> Shuffle2301(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_CDAB)};
}
HWY_API Vec512<float> Shuffle2301(const Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_CDAB)};
}

// Swap 64-bit halves
HWY_API Vec512<uint32_t> Shuffle1032(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<int32_t> Shuffle1032(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<float> Shuffle1032(const Vec512<float> v) {
  // Shorter encoding than _mm512_permute_ps.
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<uint64_t> Shuffle01(const Vec512<uint64_t> v) {
  return Vec512<uint64_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<int64_t> Shuffle01(const Vec512<int64_t> v) {
  return Vec512<int64_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<double> Shuffle01(const Vec512<double> v) {
  // Shorter encoding than _mm512_permute_pd.
  return Vec512<double>{_mm512_shuffle_pd(v.raw, v.raw, _MM_PERM_BBBB)};
}

// Rotate right 32 bits
HWY_API Vec512<uint32_t> Shuffle0321(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_ADCB)};
}
HWY_API Vec512<int32_t> Shuffle0321(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_ADCB)};
}
HWY_API Vec512<float> Shuffle0321(const Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_ADCB)};
}
// Rotate left 32 bits
HWY_API Vec512<uint32_t> Shuffle2103(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_CBAD)};
}
HWY_API Vec512<int32_t> Shuffle2103(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_CBAD)};
}
HWY_API Vec512<float> Shuffle2103(const Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_CBAD)};
}

// Reverse
HWY_API Vec512<uint32_t> Shuffle0123(const Vec512<uint32_t> v) {
  return Vec512<uint32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_ABCD)};
}
HWY_API Vec512<int32_t> Shuffle0123(const Vec512<int32_t> v) {
  return Vec512<int32_t>{_mm512_shuffle_epi32(v.raw, _MM_PERM_ABCD)};
}
HWY_API Vec512<float> Shuffle0123(const Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_ABCD)};
}

// ------------------------------ TableLookupLanes

// Returned by SetTableIndices/IndicesFromVec for use by TableLookupLanes.
template <typename T>
struct Indices512 {
  __m512i raw;
};

template <typename T, typename TI>
HWY_API Indices512<T> IndicesFromVec(Full512<T> /* tag */, Vec512<TI> vec) {
  static_assert(sizeof(T) == sizeof(TI), "Index size must match lane");
#if HWY_IS_DEBUG_BUILD
  const Full512<TI> di;
  HWY_DASSERT(AllFalse(di, Lt(vec, Zero(di))) &&
              AllTrue(di, Lt(vec, Set(di, static_cast<TI>(64 / sizeof(T))))));
#endif
  return Indices512<T>{vec.raw};
}

template <typename T, typename TI>
HWY_API Indices512<T> SetTableIndices(const Full512<T> d, const TI* idx) {
  const Rebind<TI, decltype(d)> di;
  return IndicesFromVec(d, LoadU(di, idx));
}

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> TableLookupLanes(Vec512<T> v, Indices512<T> idx) {
  return Vec512<T>{_mm512_permutexvar_epi32(idx.raw, v.raw)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> TableLookupLanes(Vec512<T> v, Indices512<T> idx) {
  return Vec512<T>{_mm512_permutexvar_epi64(idx.raw, v.raw)};
}

HWY_API Vec512<float> TableLookupLanes(Vec512<float> v, Indices512<float> idx) {
  return Vec512<float>{_mm512_permutexvar_ps(idx.raw, v.raw)};
}

HWY_API Vec512<double> TableLookupLanes(Vec512<double> v,
                                        Indices512<double> idx) {
  return Vec512<double>{_mm512_permutexvar_pd(idx.raw, v.raw)};
}

// ------------------------------ Reverse

template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> Reverse(Full512<T> d, const Vec512<T> v) {
  const RebindToSigned<decltype(d)> di;
  alignas(64) constexpr int16_t kReverse[32] = {
      31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16,
      15, 14, 13, 12, 11, 10, 9,  8,  7,  6,  5,  4,  3,  2,  1,  0};
  const Vec512<int16_t> idx = Load(di, kReverse);
  return BitCast(d, Vec512<int16_t>{
                        _mm512_permutexvar_epi16(idx.raw, BitCast(di, v).raw)});
}

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> Reverse(Full512<T> d, const Vec512<T> v) {
  alignas(64) constexpr int32_t kReverse[16] = {15, 14, 13, 12, 11, 10, 9, 8,
                                                7,  6,  5,  4,  3,  2,  1, 0};
  return TableLookupLanes(v, SetTableIndices(d, kReverse));
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> Reverse(Full512<T> d, const Vec512<T> v) {
  alignas(64) constexpr int64_t kReverse[8] = {7, 6, 5, 4, 3, 2, 1, 0};
  return TableLookupLanes(v, SetTableIndices(d, kReverse));
}

// ------------------------------ Reverse2

template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> Reverse2(Full512<T> d, const Vec512<T> v) {
  const Full512<uint32_t> du32;
  return BitCast(d, RotateRight<16>(BitCast(du32, v)));
}

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> Reverse2(Full512<T> /* tag */, const Vec512<T> v) {
  return Shuffle2301(v);
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> Reverse2(Full512<T> /* tag */, const Vec512<T> v) {
  return Shuffle01(v);
}

// ------------------------------ Reverse4

template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> Reverse4(Full512<T> d, const Vec512<T> v) {
  const RebindToSigned<decltype(d)> di;
  alignas(64) constexpr int16_t kReverse4[32] = {
      3,  2,  1,  0,  7,  6,  5,  4,  11, 10, 9,  8,  15, 14, 13, 12,
      19, 18, 17, 16, 23, 22, 21, 20, 27, 26, 25, 24, 31, 30, 29, 28};
  const Vec512<int16_t> idx = Load(di, kReverse4);
  return BitCast(d, Vec512<int16_t>{
                        _mm512_permutexvar_epi16(idx.raw, BitCast(di, v).raw)});
}

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> Reverse4(Full512<T> /* tag */, const Vec512<T> v) {
  return Shuffle0123(v);
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> Reverse4(Full512<T> /* tag */, const Vec512<T> v) {
  return Vec512<T>{_mm512_permutex_epi64(v.raw, _MM_SHUFFLE(0, 1, 2, 3))};
}
HWY_API Vec512<double> Reverse4(Full512<double> /* tag */, Vec512<double> v) {
  return Vec512<double>{_mm512_permutex_pd(v.raw, _MM_SHUFFLE(0, 1, 2, 3))};
}

// ------------------------------ Reverse8

template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> Reverse8(Full512<T> d, const Vec512<T> v) {
  const RebindToSigned<decltype(d)> di;
  alignas(64) constexpr int16_t kReverse8[32] = {
      7,  6,  5,  4,  3,  2,  1,  0,  15, 14, 13, 12, 11, 10, 9,  8,
      23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24};
  const Vec512<int16_t> idx = Load(di, kReverse8);
  return BitCast(d, Vec512<int16_t>{
                        _mm512_permutexvar_epi16(idx.raw, BitCast(di, v).raw)});
}

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> Reverse8(Full512<T> d, const Vec512<T> v) {
  const RebindToSigned<decltype(d)> di;
  alignas(64) constexpr int32_t kReverse8[16] = {7,  6,  5,  4,  3,  2,  1, 0,
                                                 15, 14, 13, 12, 11, 10, 9, 8};
  const Vec512<int32_t> idx = Load(di, kReverse8);
  return BitCast(d, Vec512<int32_t>{
                        _mm512_permutexvar_epi32(idx.raw, BitCast(di, v).raw)});
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> Reverse8(Full512<T> d, const Vec512<T> v) {
  return Reverse(d, v);
}

// ------------------------------ InterleaveLower

// Interleaves lanes from halves of the 128-bit blocks of "a" (which provides
// the least-significant lane) and "b". To concatenate two half-width integers
// into one, use ZipLower/Upper instead (also works with scalar).

HWY_API Vec512<uint8_t> InterleaveLower(const Vec512<uint8_t> a,
                                        const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_unpacklo_epi8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> InterleaveLower(const Vec512<uint16_t> a,
                                         const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_unpacklo_epi16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> InterleaveLower(const Vec512<uint32_t> a,
                                         const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_unpacklo_epi32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> InterleaveLower(const Vec512<uint64_t> a,
                                         const Vec512<uint64_t> b) {
  return Vec512<uint64_t>{_mm512_unpacklo_epi64(a.raw, b.raw)};
}

HWY_API Vec512<int8_t> InterleaveLower(const Vec512<int8_t> a,
                                       const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_unpacklo_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> InterleaveLower(const Vec512<int16_t> a,
                                        const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_unpacklo_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> InterleaveLower(const Vec512<int32_t> a,
                                        const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_unpacklo_epi32(a.raw, b.raw)};
}
HWY_API Vec512<int64_t> InterleaveLower(const Vec512<int64_t> a,
                                        const Vec512<int64_t> b) {
  return Vec512<int64_t>{_mm512_unpacklo_epi64(a.raw, b.raw)};
}

HWY_API Vec512<float> InterleaveLower(const Vec512<float> a,
                                      const Vec512<float> b) {
  return Vec512<float>{_mm512_unpacklo_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> InterleaveLower(const Vec512<double> a,
                                       const Vec512<double> b) {
  return Vec512<double>{_mm512_unpacklo_pd(a.raw, b.raw)};
}

// ------------------------------ InterleaveUpper

// All functions inside detail lack the required D parameter.
namespace detail {

HWY_API Vec512<uint8_t> InterleaveUpper(const Vec512<uint8_t> a,
                                        const Vec512<uint8_t> b) {
  return Vec512<uint8_t>{_mm512_unpackhi_epi8(a.raw, b.raw)};
}
HWY_API Vec512<uint16_t> InterleaveUpper(const Vec512<uint16_t> a,
                                         const Vec512<uint16_t> b) {
  return Vec512<uint16_t>{_mm512_unpackhi_epi16(a.raw, b.raw)};
}
HWY_API Vec512<uint32_t> InterleaveUpper(const Vec512<uint32_t> a,
                                         const Vec512<uint32_t> b) {
  return Vec512<uint32_t>{_mm512_unpackhi_epi32(a.raw, b.raw)};
}
HWY_API Vec512<uint64_t> InterleaveUpper(const Vec512<uint64_t> a,
                                         const Vec512<uint64_t> b) {
  return Vec512<uint64_t>{_mm512_unpackhi_epi64(a.raw, b.raw)};
}

HWY_API Vec512<int8_t> InterleaveUpper(const Vec512<int8_t> a,
                                       const Vec512<int8_t> b) {
  return Vec512<int8_t>{_mm512_unpackhi_epi8(a.raw, b.raw)};
}
HWY_API Vec512<int16_t> InterleaveUpper(const Vec512<int16_t> a,
                                        const Vec512<int16_t> b) {
  return Vec512<int16_t>{_mm512_unpackhi_epi16(a.raw, b.raw)};
}
HWY_API Vec512<int32_t> InterleaveUpper(const Vec512<int32_t> a,
                                        const Vec512<int32_t> b) {
  return Vec512<int32_t>{_mm512_unpackhi_epi32(a.raw, b.raw)};
}
HWY_API Vec512<int64_t> InterleaveUpper(const Vec512<int64_t> a,
                                        const Vec512<int64_t> b) {
  return Vec512<int64_t>{_mm512_unpackhi_epi64(a.raw, b.raw)};
}

HWY_API Vec512<float> InterleaveUpper(const Vec512<float> a,
                                      const Vec512<float> b) {
  return Vec512<float>{_mm512_unpackhi_ps(a.raw, b.raw)};
}
HWY_API Vec512<double> InterleaveUpper(const Vec512<double> a,
                                       const Vec512<double> b) {
  return Vec512<double>{_mm512_unpackhi_pd(a.raw, b.raw)};
}

}  // namespace detail

template <typename T, class V = Vec512<T>>
HWY_API V InterleaveUpper(Full512<T> /* tag */, V a, V b) {
  return detail::InterleaveUpper(a, b);
}

// ------------------------------ ZipLower/ZipUpper (InterleaveLower)

// Same as Interleave*, except that the return lanes are double-width integers;
// this is necessary because the single-lane scalar cannot return two values.
template <typename T, typename TW = MakeWide<T>>
HWY_API Vec512<TW> ZipLower(Vec512<T> a, Vec512<T> b) {
  return BitCast(Full512<TW>(), InterleaveLower(a, b));
}
template <typename T, typename TW = MakeWide<T>>
HWY_API Vec512<TW> ZipLower(Full512<TW> /* d */, Vec512<T> a, Vec512<T> b) {
  return BitCast(Full512<TW>(), InterleaveLower(a, b));
}

template <typename T, typename TW = MakeWide<T>>
HWY_API Vec512<TW> ZipUpper(Full512<TW> d, Vec512<T> a, Vec512<T> b) {
  return BitCast(Full512<TW>(), InterleaveUpper(d, a, b));
}

// ------------------------------ Concat* halves

// hiH,hiL loH,loL |-> hiL,loL (= lower halves)
template <typename T>
HWY_API Vec512<T> ConcatLowerLower(Full512<T> /* tag */, const Vec512<T> hi,
                                   const Vec512<T> lo) {
  return Vec512<T>{_mm512_shuffle_i32x4(lo.raw, hi.raw, _MM_PERM_BABA)};
}
HWY_API Vec512<float> ConcatLowerLower(Full512<float> /* tag */,
                                       const Vec512<float> hi,
                                       const Vec512<float> lo) {
  return Vec512<float>{_mm512_shuffle_f32x4(lo.raw, hi.raw, _MM_PERM_BABA)};
}
HWY_API Vec512<double> ConcatLowerLower(Full512<double> /* tag */,
                                        const Vec512<double> hi,
                                        const Vec512<double> lo) {
  return Vec512<double>{_mm512_shuffle_f64x2(lo.raw, hi.raw, _MM_PERM_BABA)};
}

// hiH,hiL loH,loL |-> hiH,loH (= upper halves)
template <typename T>
HWY_API Vec512<T> ConcatUpperUpper(Full512<T> /* tag */, const Vec512<T> hi,
                                   const Vec512<T> lo) {
  return Vec512<T>{_mm512_shuffle_i32x4(lo.raw, hi.raw, _MM_PERM_DCDC)};
}
HWY_API Vec512<float> ConcatUpperUpper(Full512<float> /* tag */,
                                       const Vec512<float> hi,
                                       const Vec512<float> lo) {
  return Vec512<float>{_mm512_shuffle_f32x4(lo.raw, hi.raw, _MM_PERM_DCDC)};
}
HWY_API Vec512<double> ConcatUpperUpper(Full512<double> /* tag */,
                                        const Vec512<double> hi,
                                        const Vec512<double> lo) {
  return Vec512<double>{_mm512_shuffle_f64x2(lo.raw, hi.raw, _MM_PERM_DCDC)};
}

// hiH,hiL loH,loL |-> hiL,loH (= inner halves / swap blocks)
template <typename T>
HWY_API Vec512<T> ConcatLowerUpper(Full512<T> /* tag */, const Vec512<T> hi,
                                   const Vec512<T> lo) {
  return Vec512<T>{_mm512_shuffle_i32x4(lo.raw, hi.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<float> ConcatLowerUpper(Full512<float> /* tag */,
                                       const Vec512<float> hi,
                                       const Vec512<float> lo) {
  return Vec512<float>{_mm512_shuffle_f32x4(lo.raw, hi.raw, _MM_PERM_BADC)};
}
HWY_API Vec512<double> ConcatLowerUpper(Full512<double> /* tag */,
                                        const Vec512<double> hi,
                                        const Vec512<double> lo) {
  return Vec512<double>{_mm512_shuffle_f64x2(lo.raw, hi.raw, _MM_PERM_BADC)};
}

// hiH,hiL loH,loL |-> hiH,loL (= outer halves)
template <typename T>
HWY_API Vec512<T> ConcatUpperLower(Full512<T> /* tag */, const Vec512<T> hi,
                                   const Vec512<T> lo) {
  // There are no imm8 blend in AVX512. Use blend16 because 32-bit masks
  // are efficiently loaded from 32-bit regs.
  const __mmask32 mask = /*_cvtu32_mask32 */ (0x0000FFFF);
  return Vec512<T>{_mm512_mask_blend_epi16(mask, hi.raw, lo.raw)};
}
HWY_API Vec512<float> ConcatUpperLower(Full512<float> /* tag */,
                                       const Vec512<float> hi,
                                       const Vec512<float> lo) {
  const __mmask16 mask = /*_cvtu32_mask16 */ (0x00FF);
  return Vec512<float>{_mm512_mask_blend_ps(mask, hi.raw, lo.raw)};
}
HWY_API Vec512<double> ConcatUpperLower(Full512<double> /* tag */,
                                        const Vec512<double> hi,
                                        const Vec512<double> lo) {
  const __mmask8 mask = /*_cvtu32_mask8 */ (0x0F);
  return Vec512<double>{_mm512_mask_blend_pd(mask, hi.raw, lo.raw)};
}

// ------------------------------ ConcatOdd

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> ConcatOdd(Full512<T> d, Vec512<T> hi, Vec512<T> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint32_t kIdx[16] = {1,  3,  5,  7,  9,  11, 13, 15,
                                             17, 19, 21, 23, 25, 27, 29, 31};
  return BitCast(d, Vec512<uint32_t>{_mm512_mask2_permutex2var_epi32(
                        BitCast(du, lo).raw, Load(du, kIdx).raw,
                        __mmask16{0xFFFF}, BitCast(du, hi).raw)});
}

HWY_API Vec512<float> ConcatOdd(Full512<float> d, Vec512<float> hi,
                                Vec512<float> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint32_t kIdx[16] = {1,  3,  5,  7,  9,  11, 13, 15,
                                             17, 19, 21, 23, 25, 27, 29, 31};
  return Vec512<float>{_mm512_mask2_permutex2var_ps(lo.raw, Load(du, kIdx).raw,
                                                    __mmask16{0xFFFF}, hi.raw)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> ConcatOdd(Full512<T> d, Vec512<T> hi, Vec512<T> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint64_t kIdx[8] = {1, 3, 5, 7, 9, 11, 13, 15};
  return BitCast(d, Vec512<uint64_t>{_mm512_mask2_permutex2var_epi64(
                        BitCast(du, lo).raw, Load(du, kIdx).raw, __mmask8{0xFF},
                        BitCast(du, hi).raw)});
}

HWY_API Vec512<double> ConcatOdd(Full512<double> d, Vec512<double> hi,
                                 Vec512<double> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint64_t kIdx[8] = {1, 3, 5, 7, 9, 11, 13, 15};
  return Vec512<double>{_mm512_mask2_permutex2var_pd(lo.raw, Load(du, kIdx).raw,
                                                     __mmask8{0xFF}, hi.raw)};
}

// ------------------------------ ConcatEven

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> ConcatEven(Full512<T> d, Vec512<T> hi, Vec512<T> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint32_t kIdx[16] = {0,  2,  4,  6,  8,  10, 12, 14,
                                             16, 18, 20, 22, 24, 26, 28, 30};
  return BitCast(d, Vec512<uint32_t>{_mm512_mask2_permutex2var_epi32(
                        BitCast(du, lo).raw, Load(du, kIdx).raw,
                        __mmask16{0xFFFF}, BitCast(du, hi).raw)});
}

HWY_API Vec512<float> ConcatEven(Full512<float> d, Vec512<float> hi,
                                 Vec512<float> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint32_t kIdx[16] = {0,  2,  4,  6,  8,  10, 12, 14,
                                             16, 18, 20, 22, 24, 26, 28, 30};
  return Vec512<float>{_mm512_mask2_permutex2var_ps(lo.raw, Load(du, kIdx).raw,
                                                    __mmask16{0xFFFF}, hi.raw)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> ConcatEven(Full512<T> d, Vec512<T> hi, Vec512<T> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint64_t kIdx[8] = {0, 2, 4, 6, 8, 10, 12, 14};
  return BitCast(d, Vec512<uint64_t>{_mm512_mask2_permutex2var_epi64(
                        BitCast(du, lo).raw, Load(du, kIdx).raw, __mmask8{0xFF},
                        BitCast(du, hi).raw)});
}

HWY_API Vec512<double> ConcatEven(Full512<double> d, Vec512<double> hi,
                                  Vec512<double> lo) {
  const RebindToUnsigned<decltype(d)> du;
  alignas(64) constexpr uint64_t kIdx[8] = {0, 2, 4, 6, 8, 10, 12, 14};
  return Vec512<double>{_mm512_mask2_permutex2var_pd(lo.raw, Load(du, kIdx).raw,
                                                     __mmask8{0xFF}, hi.raw)};
}

// ------------------------------ DupEven (InterleaveLower)

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> DupEven(Vec512<T> v) {
  return Vec512<T>{_mm512_shuffle_epi32(v.raw, _MM_PERM_CCAA)};
}
HWY_API Vec512<float> DupEven(Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_CCAA)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> DupEven(const Vec512<T> v) {
  return InterleaveLower(Full512<T>(), v, v);
}

// ------------------------------ DupOdd (InterleaveUpper)

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> DupOdd(Vec512<T> v) {
  return Vec512<T>{_mm512_shuffle_epi32(v.raw, _MM_PERM_DDBB)};
}
HWY_API Vec512<float> DupOdd(Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_ps(v.raw, v.raw, _MM_PERM_DDBB)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> DupOdd(const Vec512<T> v) {
  return InterleaveUpper(Full512<T>(), v, v);
}

// ------------------------------ OddEven

template <typename T>
HWY_API Vec512<T> OddEven(const Vec512<T> a, const Vec512<T> b) {
  constexpr size_t s = sizeof(T);
  constexpr int shift = s == 1 ? 0 : s == 2 ? 32 : s == 4 ? 48 : 56;
  return IfThenElse(Mask512<T>{0x5555555555555555ull >> shift}, b, a);
}

// ------------------------------ OddEvenBlocks

template <typename T>
HWY_API Vec512<T> OddEvenBlocks(Vec512<T> odd, Vec512<T> even) {
  return Vec512<T>{_mm512_mask_blend_epi64(__mmask8{0x33u}, odd.raw, even.raw)};
}

HWY_API Vec512<float> OddEvenBlocks(Vec512<float> odd, Vec512<float> even) {
  return Vec512<float>{
      _mm512_mask_blend_ps(__mmask16{0x0F0Fu}, odd.raw, even.raw)};
}

HWY_API Vec512<double> OddEvenBlocks(Vec512<double> odd, Vec512<double> even) {
  return Vec512<double>{
      _mm512_mask_blend_pd(__mmask8{0x33u}, odd.raw, even.raw)};
}

// ------------------------------ SwapAdjacentBlocks

template <typename T>
HWY_API Vec512<T> SwapAdjacentBlocks(Vec512<T> v) {
  return Vec512<T>{_mm512_shuffle_i32x4(v.raw, v.raw, _MM_PERM_CDAB)};
}

HWY_API Vec512<float> SwapAdjacentBlocks(Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_f32x4(v.raw, v.raw, _MM_PERM_CDAB)};
}

HWY_API Vec512<double> SwapAdjacentBlocks(Vec512<double> v) {
  return Vec512<double>{_mm512_shuffle_f64x2(v.raw, v.raw, _MM_PERM_CDAB)};
}

// ------------------------------ ReverseBlocks

template <typename T>
HWY_API Vec512<T> ReverseBlocks(Full512<T> /* tag */, Vec512<T> v) {
  return Vec512<T>{_mm512_shuffle_i32x4(v.raw, v.raw, _MM_PERM_ABCD)};
}
HWY_API Vec512<float> ReverseBlocks(Full512<float> /* tag */, Vec512<float> v) {
  return Vec512<float>{_mm512_shuffle_f32x4(v.raw, v.raw, _MM_PERM_ABCD)};
}
HWY_API Vec512<double> ReverseBlocks(Full512<double> /* tag */,
                                     Vec512<double> v) {
  return Vec512<double>{_mm512_shuffle_f64x2(v.raw, v.raw, _MM_PERM_ABCD)};
}

// ------------------------------ TableLookupBytes (ZeroExtendVector)

// Both full
template <typename T, typename TI>
HWY_API Vec512<TI> TableLookupBytes(Vec512<T> bytes, Vec512<TI> indices) {
  return Vec512<TI>{_mm512_shuffle_epi8(bytes.raw, indices.raw)};
}

// Partial index vector
template <typename T, typename TI, size_t NI>
HWY_API Vec128<TI, NI> TableLookupBytes(Vec512<T> bytes, Vec128<TI, NI> from) {
  const Full512<TI> d512;
  const Half<decltype(d512)> d256;
  const Half<decltype(d256)> d128;
  // First expand to full 128, then 256, then 512.
  const Vec128<TI> from_full{from.raw};
  const auto from_512 =
      ZeroExtendVector(d512, ZeroExtendVector(d256, from_full));
  const auto tbl_full = TableLookupBytes(bytes, from_512);
  // Shrink to 256, then 128, then partial.
  return Vec128<TI, NI>{LowerHalf(d128, LowerHalf(d256, tbl_full)).raw};
}
template <typename T, typename TI>
HWY_API Vec256<TI> TableLookupBytes(Vec512<T> bytes, Vec256<TI> from) {
  const auto from_512 = ZeroExtendVector(Full512<TI>(), from);
  return LowerHalf(Full256<TI>(), TableLookupBytes(bytes, from_512));
}

// Partial table vector
template <typename T, size_t N, typename TI>
HWY_API Vec512<TI> TableLookupBytes(Vec128<T, N> bytes, Vec512<TI> from) {
  const Full512<TI> d512;
  const Half<decltype(d512)> d256;
  const Half<decltype(d256)> d128;
  // First expand to full 128, then 256, then 512.
  const Vec128<T> bytes_full{bytes.raw};
  const auto bytes_512 =
      ZeroExtendVector(d512, ZeroExtendVector(d256, bytes_full));
  return TableLookupBytes(bytes_512, from);
}
template <typename T, typename TI>
HWY_API Vec512<TI> TableLookupBytes(Vec256<T> bytes, Vec512<TI> from) {
  const auto bytes_512 = ZeroExtendVector(Full512<T>(), bytes);
  return TableLookupBytes(bytes_512, from);
}

// Partial both are handled by x86_128/256.

// ================================================== CONVERT

// ------------------------------ Promotions (part w/ narrow lanes -> full)

// Unsigned: zero-extend.
// Note: these have 3 cycle latency; if inputs are already split across the
// 128 bit blocks (in their upper/lower halves), then Zip* would be faster.
HWY_API Vec512<uint16_t> PromoteTo(Full512<uint16_t> /* tag */,
                                   Vec256<uint8_t> v) {
  return Vec512<uint16_t>{_mm512_cvtepu8_epi16(v.raw)};
}
HWY_API Vec512<uint32_t> PromoteTo(Full512<uint32_t> /* tag */,
                                   Vec128<uint8_t> v) {
  return Vec512<uint32_t>{_mm512_cvtepu8_epi32(v.raw)};
}
HWY_API Vec512<int16_t> PromoteTo(Full512<int16_t> /* tag */,
                                  Vec256<uint8_t> v) {
  return Vec512<int16_t>{_mm512_cvtepu8_epi16(v.raw)};
}
HWY_API Vec512<int32_t> PromoteTo(Full512<int32_t> /* tag */,
                                  Vec128<uint8_t> v) {
  return Vec512<int32_t>{_mm512_cvtepu8_epi32(v.raw)};
}
HWY_API Vec512<uint32_t> PromoteTo(Full512<uint32_t> /* tag */,
                                   Vec256<uint16_t> v) {
  return Vec512<uint32_t>{_mm512_cvtepu16_epi32(v.raw)};
}
HWY_API Vec512<int32_t> PromoteTo(Full512<int32_t> /* tag */,
                                  Vec256<uint16_t> v) {
  return Vec512<int32_t>{_mm512_cvtepu16_epi32(v.raw)};
}
HWY_API Vec512<uint64_t> PromoteTo(Full512<uint64_t> /* tag */,
                                   Vec256<uint32_t> v) {
  return Vec512<uint64_t>{_mm512_cvtepu32_epi64(v.raw)};
}

// Signed: replicate sign bit.
// Note: these have 3 cycle latency; if inputs are already split across the
// 128 bit blocks (in their upper/lower halves), then ZipUpper/lo followed by
// signed shift would be faster.
HWY_API Vec512<int16_t> PromoteTo(Full512<int16_t> /* tag */,
                                  Vec256<int8_t> v) {
  return Vec512<int16_t>{_mm512_cvtepi8_epi16(v.raw)};
}
HWY_API Vec512<int32_t> PromoteTo(Full512<int32_t> /* tag */,
                                  Vec128<int8_t> v) {
  return Vec512<int32_t>{_mm512_cvtepi8_epi32(v.raw)};
}
HWY_API Vec512<int32_t> PromoteTo(Full512<int32_t> /* tag */,
                                  Vec256<int16_t> v) {
  return Vec512<int32_t>{_mm512_cvtepi16_epi32(v.raw)};
}
HWY_API Vec512<int64_t> PromoteTo(Full512<int64_t> /* tag */,
                                  Vec256<int32_t> v) {
  return Vec512<int64_t>{_mm512_cvtepi32_epi64(v.raw)};
}

// Float
HWY_API Vec512<float> PromoteTo(Full512<float> /* tag */,
                                const Vec256<float16_t> v) {
  return Vec512<float>{_mm512_cvtph_ps(v.raw)};
}

HWY_API Vec512<float> PromoteTo(Full512<float> df32,
                                const Vec256<bfloat16_t> v) {
  const Rebind<uint16_t, decltype(df32)> du16;
  const RebindToSigned<decltype(df32)> di32;
  return BitCast(df32, ShiftLeft<16>(PromoteTo(di32, BitCast(du16, v))));
}

HWY_API Vec512<double> PromoteTo(Full512<double> /* tag */, Vec256<float> v) {
  return Vec512<double>{_mm512_cvtps_pd(v.raw)};
}

HWY_API Vec512<double> PromoteTo(Full512<double> /* tag */, Vec256<int32_t> v) {
  return Vec512<double>{_mm512_cvtepi32_pd(v.raw)};
}

// ------------------------------ Demotions (full -> part w/ narrow lanes)

HWY_API Vec256<uint16_t> DemoteTo(Full256<uint16_t> /* tag */,
                                  const Vec512<int32_t> v) {
  const Vec512<uint16_t> u16{_mm512_packus_epi32(v.raw, v.raw)};

  // Compress even u64 lanes into 256 bit.
  alignas(64) static constexpr uint64_t kLanes[8] = {0, 2, 4, 6, 0, 2, 4, 6};
  const auto idx64 = Load(Full512<uint64_t>(), kLanes);
  const Vec512<uint16_t> even{_mm512_permutexvar_epi64(idx64.raw, u16.raw)};
  return LowerHalf(even);
}

HWY_API Vec256<int16_t> DemoteTo(Full256<int16_t> /* tag */,
                                 const Vec512<int32_t> v) {
  const Vec512<int16_t> i16{_mm512_packs_epi32(v.raw, v.raw)};

  // Compress even u64 lanes into 256 bit.
  alignas(64) static constexpr uint64_t kLanes[8] = {0, 2, 4, 6, 0, 2, 4, 6};
  const auto idx64 = Load(Full512<uint64_t>(), kLanes);
  const Vec512<int16_t> even{_mm512_permutexvar_epi64(idx64.raw, i16.raw)};
  return LowerHalf(even);
}

HWY_API Vec128<uint8_t, 16> DemoteTo(Full128<uint8_t> /* tag */,
                                     const Vec512<int32_t> v) {
  const Vec512<uint16_t> u16{_mm512_packus_epi32(v.raw, v.raw)};
  // packus treats the input as signed; we want unsigned. Clear the MSB to get
  // unsigned saturation to u8.
  const Vec512<int16_t> i16{
      _mm512_and_si512(u16.raw, _mm512_set1_epi16(0x7FFF))};
  const Vec512<uint8_t> u8{_mm512_packus_epi16(i16.raw, i16.raw)};

  alignas(16) static constexpr uint32_t kLanes[4] = {0, 4, 8, 12};
  const auto idx32 = LoadDup128(Full512<uint32_t>(), kLanes);
  const Vec512<uint8_t> fixed{_mm512_permutexvar_epi32(idx32.raw, u8.raw)};
  return LowerHalf(LowerHalf(fixed));
}

HWY_API Vec256<uint8_t> DemoteTo(Full256<uint8_t> /* tag */,
                                 const Vec512<int16_t> v) {
  const Vec512<uint8_t> u8{_mm512_packus_epi16(v.raw, v.raw)};

  // Compress even u64 lanes into 256 bit.
  alignas(64) static constexpr uint64_t kLanes[8] = {0, 2, 4, 6, 0, 2, 4, 6};
  const auto idx64 = Load(Full512<uint64_t>(), kLanes);
  const Vec512<uint8_t> even{_mm512_permutexvar_epi64(idx64.raw, u8.raw)};
  return LowerHalf(even);
}

HWY_API Vec128<int8_t, 16> DemoteTo(Full128<int8_t> /* tag */,
                                    const Vec512<int32_t> v) {
  const Vec512<int16_t> i16{_mm512_packs_epi32(v.raw, v.raw)};
  const Vec512<int8_t> i8{_mm512_packs_epi16(i16.raw, i16.raw)};

  alignas(16) static constexpr uint32_t kLanes[16] = {0, 4, 8, 12, 0, 4, 8, 12,
                                                      0, 4, 8, 12, 0, 4, 8, 12};
  const auto idx32 = LoadDup128(Full512<uint32_t>(), kLanes);
  const Vec512<int8_t> fixed{_mm512_permutexvar_epi32(idx32.raw, i8.raw)};
  return LowerHalf(LowerHalf(fixed));
}

HWY_API Vec256<int8_t> DemoteTo(Full256<int8_t> /* tag */,
                                const Vec512<int16_t> v) {
  const Vec512<int8_t> u8{_mm512_packs_epi16(v.raw, v.raw)};

  // Compress even u64 lanes into 256 bit.
  alignas(64) static constexpr uint64_t kLanes[8] = {0, 2, 4, 6, 0, 2, 4, 6};
  const auto idx64 = Load(Full512<uint64_t>(), kLanes);
  const Vec512<int8_t> even{_mm512_permutexvar_epi64(idx64.raw, u8.raw)};
  return LowerHalf(even);
}

HWY_API Vec256<float16_t> DemoteTo(Full256<float16_t> /* tag */,
                                   const Vec512<float> v) {
  // Work around warnings in the intrinsic definitions (passing -1 as a mask).
  HWY_DIAGNOSTICS(push)
  HWY_DIAGNOSTICS_OFF(disable : 4245 4365, ignored "-Wsign-conversion")
  return Vec256<float16_t>{_mm512_cvtps_ph(v.raw, _MM_FROUND_NO_EXC)};
  HWY_DIAGNOSTICS(pop)
}

HWY_API Vec256<bfloat16_t> DemoteTo(Full256<bfloat16_t> dbf16,
                                    const Vec512<float> v) {
  // TODO(janwas): _mm512_cvtneps_pbh once we have avx512bf16.
  const Rebind<int32_t, decltype(dbf16)> di32;
  const Rebind<uint32_t, decltype(dbf16)> du32;  // for logical shift right
  const Rebind<uint16_t, decltype(dbf16)> du16;
  const auto bits_in_32 = BitCast(di32, ShiftRight<16>(BitCast(du32, v)));
  return BitCast(dbf16, DemoteTo(du16, bits_in_32));
}

HWY_API Vec512<bfloat16_t> ReorderDemote2To(Full512<bfloat16_t> dbf16,
                                            Vec512<float> a, Vec512<float> b) {
  // TODO(janwas): _mm512_cvtne2ps_pbh once we have avx512bf16.
  const RebindToUnsigned<decltype(dbf16)> du16;
  const Repartition<uint32_t, decltype(dbf16)> du32;
  const Vec512<uint32_t> b_in_even = ShiftRight<16>(BitCast(du32, b));
  return BitCast(dbf16, OddEven(BitCast(du16, a), BitCast(du16, b_in_even)));
}

HWY_API Vec256<float> DemoteTo(Full256<float> /* tag */,
                               const Vec512<double> v) {
  return Vec256<float>{_mm512_cvtpd_ps(v.raw)};
}

HWY_API Vec256<int32_t> DemoteTo(Full256<int32_t> /* tag */,
                                 const Vec512<double> v) {
  const auto clamped = detail::ClampF64ToI32Max(Full512<double>(), v);
  return Vec256<int32_t>{_mm512_cvttpd_epi32(clamped.raw)};
}

// For already range-limited input [0, 255].
HWY_API Vec128<uint8_t, 16> U8FromU32(const Vec512<uint32_t> v) {
  const Full512<uint32_t> d32;
  // In each 128 bit block, gather the lower byte of 4 uint32_t lanes into the
  // lowest 4 bytes.
  alignas(16) static constexpr uint32_t k8From32[4] = {0x0C080400u, ~0u, ~0u,
                                                       ~0u};
  const auto quads = TableLookupBytes(v, LoadDup128(d32, k8From32));
  // Gather the lowest 4 bytes of 4 128-bit blocks.
  alignas(16) static constexpr uint32_t kIndex32[4] = {0, 4, 8, 12};
  const Vec512<uint8_t> bytes{
      _mm512_permutexvar_epi32(LoadDup128(d32, kIndex32).raw, quads.raw)};
  return LowerHalf(LowerHalf(bytes));
}

// ------------------------------ Convert integer <=> floating point

HWY_API Vec512<float> ConvertTo(Full512<float> /* tag */,
                                const Vec512<int32_t> v) {
  return Vec512<float>{_mm512_cvtepi32_ps(v.raw)};
}

HWY_API Vec512<double> ConvertTo(Full512<double> /* tag */,
                                 const Vec512<int64_t> v) {
  return Vec512<double>{_mm512_cvtepi64_pd(v.raw)};
}

// Truncates (rounds toward zero).
HWY_API Vec512<int32_t> ConvertTo(Full512<int32_t> d, const Vec512<float> v) {
  return detail::FixConversionOverflow(d, v, _mm512_cvttps_epi32(v.raw));
}
HWY_API Vec512<int64_t> ConvertTo(Full512<int64_t> di, const Vec512<double> v) {
  return detail::FixConversionOverflow(di, v, _mm512_cvttpd_epi64(v.raw));
}

HWY_API Vec512<int32_t> NearestInt(const Vec512<float> v) {
  const Full512<int32_t> di;
  return detail::FixConversionOverflow(di, v, _mm512_cvtps_epi32(v.raw));
}

// ================================================== CRYPTO

#if !defined(HWY_DISABLE_PCLMUL_AES)

// Per-target flag to prevent generic_ops-inl.h from defining AESRound.
#ifdef HWY_NATIVE_AES
#undef HWY_NATIVE_AES
#else
#define HWY_NATIVE_AES
#endif

HWY_API Vec512<uint8_t> AESRound(Vec512<uint8_t> state,
                                 Vec512<uint8_t> round_key) {
#if HWY_TARGET == HWY_AVX3_DL
  return Vec512<uint8_t>{_mm512_aesenc_epi128(state.raw, round_key.raw)};
#else
  const Full512<uint8_t> d;
  const Half<decltype(d)> d2;
  return Combine(d, AESRound(UpperHalf(d2, state), UpperHalf(d2, round_key)),
                 AESRound(LowerHalf(state), LowerHalf(round_key)));
#endif
}

HWY_API Vec512<uint8_t> AESLastRound(Vec512<uint8_t> state,
                                     Vec512<uint8_t> round_key) {
#if HWY_TARGET == HWY_AVX3_DL
  return Vec512<uint8_t>{_mm512_aesenclast_epi128(state.raw, round_key.raw)};
#else
  const Full512<uint8_t> d;
  const Half<decltype(d)> d2;
  return Combine(d,
                 AESLastRound(UpperHalf(d2, state), UpperHalf(d2, round_key)),
                 AESLastRound(LowerHalf(state), LowerHalf(round_key)));
#endif
}

HWY_API Vec512<uint64_t> CLMulLower(Vec512<uint64_t> va, Vec512<uint64_t> vb) {
#if HWY_TARGET == HWY_AVX3_DL
  return Vec512<uint64_t>{_mm512_clmulepi64_epi128(va.raw, vb.raw, 0x00)};
#else
  alignas(64) uint64_t a[8];
  alignas(64) uint64_t b[8];
  const Full512<uint64_t> d;
  const Full128<uint64_t> d128;
  Store(va, d, a);
  Store(vb, d, b);
  for (size_t i = 0; i < 8; i += 2) {
    const auto mul = CLMulLower(Load(d128, a + i), Load(d128, b + i));
    Store(mul, d128, a + i);
  }
  return Load(d, a);
#endif
}

HWY_API Vec512<uint64_t> CLMulUpper(Vec512<uint64_t> va, Vec512<uint64_t> vb) {
#if HWY_TARGET == HWY_AVX3_DL
  return Vec512<uint64_t>{_mm512_clmulepi64_epi128(va.raw, vb.raw, 0x11)};
#else
  alignas(64) uint64_t a[8];
  alignas(64) uint64_t b[8];
  const Full512<uint64_t> d;
  const Full128<uint64_t> d128;
  Store(va, d, a);
  Store(vb, d, b);
  for (size_t i = 0; i < 8; i += 2) {
    const auto mul = CLMulUpper(Load(d128, a + i), Load(d128, b + i));
    Store(mul, d128, a + i);
  }
  return Load(d, a);
#endif
}

#endif  // HWY_DISABLE_PCLMUL_AES

// ================================================== MISC

// Returns a vector with lane i=[0, N) set to "first" + i.
template <typename T, typename T2>
Vec512<T> Iota(const Full512<T> d, const T2 first) {
  HWY_ALIGN T lanes[64 / sizeof(T)];
  for (size_t i = 0; i < 64 / sizeof(T); ++i) {
    lanes[i] = static_cast<T>(first + static_cast<T2>(i));
  }
  return Load(d, lanes);
}

// ------------------------------ Mask testing

// Beware: the suffix indicates the number of mask bits, not lane size!

namespace detail {

template <typename T>
HWY_INLINE bool AllFalse(hwy::SizeTag<1> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestz_mask64_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0;
#endif
}
template <typename T>
HWY_INLINE bool AllFalse(hwy::SizeTag<2> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestz_mask32_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0;
#endif
}
template <typename T>
HWY_INLINE bool AllFalse(hwy::SizeTag<4> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestz_mask16_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0;
#endif
}
template <typename T>
HWY_INLINE bool AllFalse(hwy::SizeTag<8> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestz_mask8_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0;
#endif
}

}  // namespace detail

template <typename T>
HWY_API bool AllFalse(const Full512<T> /* tag */, const Mask512<T> mask) {
  return detail::AllFalse(hwy::SizeTag<sizeof(T)>(), mask);
}

namespace detail {

template <typename T>
HWY_INLINE bool AllTrue(hwy::SizeTag<1> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestc_mask64_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0xFFFFFFFFFFFFFFFFull;
#endif
}
template <typename T>
HWY_INLINE bool AllTrue(hwy::SizeTag<2> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestc_mask32_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0xFFFFFFFFull;
#endif
}
template <typename T>
HWY_INLINE bool AllTrue(hwy::SizeTag<4> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestc_mask16_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0xFFFFull;
#endif
}
template <typename T>
HWY_INLINE bool AllTrue(hwy::SizeTag<8> /*tag*/, const Mask512<T> mask) {
#if HWY_COMPILER_HAS_MASK_INTRINSICS
  return _kortestc_mask8_u8(mask.raw, mask.raw);
#else
  return mask.raw == 0xFFull;
#endif
}

}  // namespace detail

template <typename T>
HWY_API bool AllTrue(const Full512<T> /* tag */, const Mask512<T> mask) {
  return detail::AllTrue(hwy::SizeTag<sizeof(T)>(), mask);
}

// `p` points to at least 8 readable bytes, not all of which need be valid.
template <typename T>
HWY_API Mask512<T> LoadMaskBits(const Full512<T> /* tag */,
                                const uint8_t* HWY_RESTRICT bits) {
  Mask512<T> mask;
  CopyBytes<8 / sizeof(T)>(bits, &mask.raw);
  // N >= 8 (= 512 / 64), so no need to mask invalid bits.
  return mask;
}

// `p` points to at least 8 writable bytes.
template <typename T>
HWY_API size_t StoreMaskBits(const Full512<T> /* tag */, const Mask512<T> mask,
                             uint8_t* bits) {
  const size_t kNumBytes = 8 / sizeof(T);
  CopyBytes<kNumBytes>(&mask.raw, bits);
  // N >= 8 (= 512 / 64), so no need to mask invalid bits.
  return kNumBytes;
}

template <typename T>
HWY_API size_t CountTrue(const Full512<T> /* tag */, const Mask512<T> mask) {
  return PopCount(static_cast<uint64_t>(mask.raw));
}

template <typename T, HWY_IF_NOT_LANE_SIZE(T, 1)>
HWY_API intptr_t FindFirstTrue(const Full512<T> /* tag */,
                               const Mask512<T> mask) {
  return mask.raw ? intptr_t(Num0BitsBelowLS1Bit_Nonzero32(mask.raw)) : -1;
}

template <typename T, HWY_IF_LANE_SIZE(T, 1)>
HWY_API intptr_t FindFirstTrue(const Full512<T> /* tag */,
                               const Mask512<T> mask) {
  return mask.raw ? intptr_t(Num0BitsBelowLS1Bit_Nonzero64(mask.raw)) : -1;
}

// ------------------------------ Compress

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API Vec512<T> Compress(Vec512<T> v, Mask512<T> mask) {
  return Vec512<T>{_mm512_maskz_compress_epi32(mask.raw, v.raw)};
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API Vec512<T> Compress(Vec512<T> v, Mask512<T> mask) {
  return Vec512<T>{_mm512_maskz_compress_epi64(mask.raw, v.raw)};
}

HWY_API Vec512<float> Compress(Vec512<float> v, Mask512<float> mask) {
  return Vec512<float>{_mm512_maskz_compress_ps(mask.raw, v.raw)};
}

HWY_API Vec512<double> Compress(Vec512<double> v, Mask512<double> mask) {
  return Vec512<double>{_mm512_maskz_compress_pd(mask.raw, v.raw)};
}

// 16-bit may use the 32-bit Compress and must be defined after it.
//
// Ignore IDE redefinition error - this is not actually defined in x86_256 if
// we are including x86_512-inl.h.
template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec256<T> Compress(Vec256<T> v, Mask256<T> mask) {
  const Full256<T> d;
  const Rebind<uint16_t, decltype(d)> du;
  const auto vu = BitCast(du, v);  // (required for float16_t inputs)

#if HWY_TARGET == HWY_AVX3_DL  // VBMI2
  const Vec256<uint16_t> cu{_mm256_maskz_compress_epi16(mask.raw, vu.raw)};
#else
  // Promote to i32 (512-bit vector!) so we can use the native Compress.
  const auto vw = PromoteTo(Rebind<int32_t, decltype(d)>(), vu);
  const Mask512<int32_t> mask32{static_cast<__mmask16>(mask.raw)};
  const auto cu = DemoteTo(du, Compress(vw, mask32));
#endif  // HWY_TARGET == HWY_AVX3_DL

  return BitCast(d, cu);
}

// Expands to 32-bit, compresses, concatenate demoted halves.
template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> Compress(Vec512<T> v, const Mask512<T> mask) {
  const Full512<T> d;
  const Rebind<uint16_t, decltype(d)> du;
  const auto vu = BitCast(du, v);  // (required for float16_t inputs)

#if HWY_TARGET == HWY_AVX3_DL  // VBMI2
  const Vec512<uint16_t> cu{_mm512_maskz_compress_epi16(mask.raw, v.raw)};
#else
  const Repartition<int32_t, decltype(d)> dw;
  const Half<decltype(du)> duh;
  const auto promoted0 = PromoteTo(dw, LowerHalf(duh, vu));
  const auto promoted1 = PromoteTo(dw, UpperHalf(duh, vu));

  const uint32_t mask_bits{mask.raw};
  const Mask512<int32_t> mask0{static_cast<__mmask16>(mask_bits & 0xFFFF)};
  const Mask512<int32_t> mask1{static_cast<__mmask16>(mask_bits >> 16)};
  const auto compressed0 = Compress(promoted0, mask0);
  const auto compressed1 = Compress(promoted1, mask1);

  const auto demoted0 = ZeroExtendVector(du, DemoteTo(duh, compressed0));
  const auto demoted1 = ZeroExtendVector(du, DemoteTo(duh, compressed1));

  // Concatenate into single vector by shifting upper with writemask.
  const size_t num0 = CountTrue(dw, mask0);
  const __mmask32 m_upper = ~((1u << num0) - 1);
  alignas(64) uint16_t iota[64] = {
      0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
      0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,
      0,  1,  2,  3,  4,  5,  6,  7,  8,  9,  10, 11, 12, 13, 14, 15,
      16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31};
  const auto idx = LoadU(du, iota + 32 - num0);
  const Vec512<uint16_t> cu{_mm512_mask_permutexvar_epi16(
      demoted0.raw, m_upper, idx.raw, demoted1.raw)};
#endif  // HWY_TARGET == HWY_AVX3_DL

  return BitCast(d, cu);
}

// ------------------------------ CompressBits
template <typename T>
HWY_API Vec512<T> CompressBits(Vec512<T> v, const uint8_t* HWY_RESTRICT bits) {
  return Compress(v, LoadMaskBits(Full512<T>(), bits));
}

// ------------------------------ CompressStore

template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API size_t CompressStore(Vec512<T> v, Mask512<T> mask, Full512<T> d,
                             T* HWY_RESTRICT unaligned) {
  const Rebind<uint16_t, decltype(d)> du;
  const auto vu = BitCast(du, v);  // (required for float16_t inputs)

  const uint64_t mask_bits{mask.raw};

#if HWY_TARGET == HWY_AVX3_DL  // VBMI2
  _mm512_mask_compressstoreu_epi16(unaligned, mask.raw, v.raw);
#else
  const Repartition<int32_t, decltype(d)> dw;
  const Half<decltype(du)> duh;
  const auto promoted0 = PromoteTo(dw, LowerHalf(duh, vu));
  const auto promoted1 = PromoteTo(dw, UpperHalf(duh, vu));

  const uint64_t maskL = mask_bits & 0xFFFF;
  const uint64_t maskH = mask_bits >> 16;
  const Mask512<int32_t> mask0{static_cast<__mmask16>(maskL)};
  const Mask512<int32_t> mask1{static_cast<__mmask16>(maskH)};
  const auto compressed0 = Compress(promoted0, mask0);
  const auto compressed1 = Compress(promoted1, mask1);

  const Half<decltype(d)> dh;
  const auto demoted0 = BitCast(dh, DemoteTo(duh, compressed0));
  const auto demoted1 = BitCast(dh, DemoteTo(duh, compressed1));

  // Store 256-bit halves
  StoreU(demoted0, dh, unaligned);
  StoreU(demoted1, dh, unaligned + PopCount(maskL));
#endif

  return PopCount(mask_bits);
}

template <typename T, HWY_IF_LANE_SIZE(T, 4)>
HWY_API size_t CompressStore(Vec512<T> v, Mask512<T> mask, Full512<T> /* tag */,
                             T* HWY_RESTRICT unaligned) {
  _mm512_mask_compressstoreu_epi32(unaligned, mask.raw, v.raw);
  return PopCount(uint64_t{mask.raw});
}

template <typename T, HWY_IF_LANE_SIZE(T, 8)>
HWY_API size_t CompressStore(Vec512<T> v, Mask512<T> mask, Full512<T> /* tag */,
                             T* HWY_RESTRICT unaligned) {
  _mm512_mask_compressstoreu_epi64(unaligned, mask.raw, v.raw);
  return PopCount(uint64_t{mask.raw});
}

HWY_API size_t CompressStore(Vec512<float> v, Mask512<float> mask,
                             Full512<float> /* tag */,
                             float* HWY_RESTRICT unaligned) {
  _mm512_mask_compressstoreu_ps(unaligned, mask.raw, v.raw);
  return PopCount(uint64_t{mask.raw});
}

HWY_API size_t CompressStore(Vec512<double> v, Mask512<double> mask,
                             Full512<double> /* tag */,
                             double* HWY_RESTRICT unaligned) {
  _mm512_mask_compressstoreu_pd(unaligned, mask.raw, v.raw);
  return PopCount(uint64_t{mask.raw});
}

// ------------------------------ CompressBlendedStore
template <typename T>
HWY_API size_t CompressBlendedStore(Vec512<T> v, Mask512<T> m, Full512<T> d,
                                    T* HWY_RESTRICT unaligned) {
  // AVX-512 already does the blending at no extra cost (latency 11,
  // rthroughput 2 - same as compress plus store).
  if (HWY_TARGET == HWY_AVX3_DL || sizeof(T) != 2) {
    return CompressStore(v, m, d, unaligned);
  } else {
    const size_t count = CountTrue(d, m);
    const Vec512<T> compressed = Compress(v, m);
    const Vec512<T> prev = LoadU(d, unaligned);
    StoreU(IfThenElse(FirstN(d, count), compressed, prev), d, unaligned);
    return count;
  }
}

// ------------------------------ CompressBitsStore
template <typename T>
HWY_API size_t CompressBitsStore(Vec512<T> v, const uint8_t* HWY_RESTRICT bits,
                                 Full512<T> d, T* HWY_RESTRICT unaligned) {
  return CompressStore(v, LoadMaskBits(d, bits), d, unaligned);
}

// ------------------------------ StoreInterleaved3 (CombineShiftRightBytes,
// TableLookupBytes)

HWY_API void StoreInterleaved3(const Vec512<uint8_t> a, const Vec512<uint8_t> b,
                               const Vec512<uint8_t> c, Full512<uint8_t> d,
                               uint8_t* HWY_RESTRICT unaligned) {
  const auto k5 = Set(d, 5);
  const auto k6 = Set(d, 6);

  // Shuffle (a,b,c) vector bytes to (MSB on left): r5, bgr[4:0].
  // 0x80 so lanes to be filled from other vectors are 0 for blending.
  alignas(16) static constexpr uint8_t tbl_r0[16] = {
      0, 0x80, 0x80, 1, 0x80, 0x80, 2, 0x80, 0x80,  //
      3, 0x80, 0x80, 4, 0x80, 0x80, 5};
  alignas(16) static constexpr uint8_t tbl_g0[16] = {
      0x80, 0, 0x80, 0x80, 1, 0x80,  //
      0x80, 2, 0x80, 0x80, 3, 0x80, 0x80, 4, 0x80, 0x80};
  const auto shuf_r0 = LoadDup128(d, tbl_r0);
  const auto shuf_g0 = LoadDup128(d, tbl_g0);  // cannot reuse r0 due to 5
  const auto shuf_b0 = CombineShiftRightBytes<15>(d, shuf_g0, shuf_g0);
  const auto r0 = TableLookupBytes(a, shuf_r0);  // 5..4..3..2..1..0
  const auto g0 = TableLookupBytes(b, shuf_g0);  // ..4..3..2..1..0.
  const auto b0 = TableLookupBytes(c, shuf_b0);  // .4..3..2..1..0..
  const auto i = (r0 | g0 | b0).raw;  // low byte in each 128bit: 30 20 10 00

  // Second vector: g10,r10, bgr[9:6], b5,g5
  const auto shuf_r1 = shuf_b0 + k6;  // .A..9..8..7..6..
  const auto shuf_g1 = shuf_r0 + k5;  // A..9..8..7..6..5
  const auto shuf_b1 = shuf_g0 + k5;  // ..9..8..7..6..5.
  const auto r1 = TableLookupBytes(a, shuf_r1);
  const auto g1 = TableLookupBytes(b, shuf_g1);
  const auto b1 = TableLookupBytes(c, shuf_b1);
  const auto j = (r1 | g1 | b1).raw;  // low byte in each 128bit: 35 25 15 05

  // Third vector: bgr[15:11], b10
  const auto shuf_r2 = shuf_b1 + k6;  // ..F..E..D..C..B.
  const auto shuf_g2 = shuf_r1 + k5;  // .F..E..D..C..B..
  const auto shuf_b2 = shuf_g1 + k5;  // F..E..D..C..B..A
  const auto r2 = TableLookupBytes(a, shuf_r2);
  const auto g2 = TableLookupBytes(b, shuf_g2);
  const auto b2 = TableLookupBytes(c, shuf_b2);
  const auto k = (r2 | g2 | b2).raw;  // low byte in each 128bit: 3A 2A 1A 0A

  // To obtain 10 0A 05 00 in one vector, transpose "rows" into "columns".
  const auto k3_k0_i3_i0 = _mm512_shuffle_i64x2(i, k, _MM_PERM_DADA);
  const auto i1_i2_j0_j1 = _mm512_shuffle_i64x2(j, i, _MM_PERM_BCAB);
  const auto j2_j3_k1_k2 = _mm512_shuffle_i64x2(k, j, _MM_PERM_CDBC);

  // Alternating order, most-significant 128 bits from the second arg.
  const __mmask8 m = 0xCC;
  const auto i1_k0_j0_i0 = _mm512_mask_blend_epi64(m, k3_k0_i3_i0, i1_i2_j0_j1);
  const auto j2_i2_k1_j1 = _mm512_mask_blend_epi64(m, i1_i2_j0_j1, j2_j3_k1_k2);
  const auto k3_j3_i3_k2 = _mm512_mask_blend_epi64(m, j2_j3_k1_k2, k3_k0_i3_i0);

  StoreU(Vec512<uint8_t>{i1_k0_j0_i0}, d, unaligned + 0 * 64);  //  10 0A 05 00
  StoreU(Vec512<uint8_t>{j2_i2_k1_j1}, d, unaligned + 1 * 64);  //  25 20 1A 15
  StoreU(Vec512<uint8_t>{k3_j3_i3_k2}, d, unaligned + 2 * 64);  //  3A 35 30 2A
}

// ------------------------------ StoreInterleaved4

HWY_API void StoreInterleaved4(const Vec512<uint8_t> v0,
                               const Vec512<uint8_t> v1,
                               const Vec512<uint8_t> v2,
                               const Vec512<uint8_t> v3, Full512<uint8_t> d8,
                               uint8_t* HWY_RESTRICT unaligned) {
  const RepartitionToWide<decltype(d8)> d16;
  const RepartitionToWide<decltype(d16)> d32;
  // let a,b,c,d denote v0..3.
  const auto ba0 = ZipLower(d16, v0, v1);  // b7 a7 .. b0 a0
  const auto dc0 = ZipLower(d16, v2, v3);  // d7 c7 .. d0 c0
  const auto ba8 = ZipUpper(d16, v0, v1);
  const auto dc8 = ZipUpper(d16, v2, v3);
  const auto i = ZipLower(d32, ba0, dc0).raw;  // 4x128bit: d..a3 d..a0
  const auto j = ZipUpper(d32, ba0, dc0).raw;  // 4x128bit: d..a7 d..a4
  const auto k = ZipLower(d32, ba8, dc8).raw;  // 4x128bit: d..aB d..a8
  const auto l = ZipUpper(d32, ba8, dc8).raw;  // 4x128bit: d..aF d..aC
  // 128-bit blocks were independent until now; transpose 4x4.
  const auto j1_j0_i1_i0 = _mm512_shuffle_i64x2(i, j, _MM_PERM_BABA);
  const auto l1_l0_k1_k0 = _mm512_shuffle_i64x2(k, l, _MM_PERM_BABA);
  const auto j3_j2_i3_i2 = _mm512_shuffle_i64x2(i, j, _MM_PERM_DCDC);
  const auto l3_l2_k3_k2 = _mm512_shuffle_i64x2(k, l, _MM_PERM_DCDC);
  constexpr _MM_PERM_ENUM k20 = _MM_PERM_CACA;
  constexpr _MM_PERM_ENUM k31 = _MM_PERM_DBDB;
  const auto l0_k0_j0_i0 = _mm512_shuffle_i64x2(j1_j0_i1_i0, l1_l0_k1_k0, k20);
  const auto l1_k1_j1_i1 = _mm512_shuffle_i64x2(j1_j0_i1_i0, l1_l0_k1_k0, k31);
  const auto l2_k2_j2_i2 = _mm512_shuffle_i64x2(j3_j2_i3_i2, l3_l2_k3_k2, k20);
  const auto l3_k3_j3_i3 = _mm512_shuffle_i64x2(j3_j2_i3_i2, l3_l2_k3_k2, k31);
  StoreU(Vec512<uint8_t>{l0_k0_j0_i0}, d8, unaligned + 0 * 64);
  StoreU(Vec512<uint8_t>{l1_k1_j1_i1}, d8, unaligned + 1 * 64);
  StoreU(Vec512<uint8_t>{l2_k2_j2_i2}, d8, unaligned + 2 * 64);
  StoreU(Vec512<uint8_t>{l3_k3_j3_i3}, d8, unaligned + 3 * 64);
}

// ------------------------------ MulEven/Odd (Shuffle2301, InterleaveLower)

HWY_INLINE Vec512<uint64_t> MulEven(const Vec512<uint64_t> a,
                                    const Vec512<uint64_t> b) {
  const DFromV<decltype(a)> du64;
  const RepartitionToNarrow<decltype(du64)> du32;
  const auto maskL = Set(du64, 0xFFFFFFFFULL);
  const auto a32 = BitCast(du32, a);
  const auto b32 = BitCast(du32, b);
  // Inputs for MulEven: we only need the lower 32 bits
  const auto aH = Shuffle2301(a32);
  const auto bH = Shuffle2301(b32);

  // Knuth double-word multiplication. We use 32x32 = 64 MulEven and only need
  // the even (lower 64 bits of every 128-bit block) results. See
  // https://github.com/hcs0/Hackers-Delight/blob/master/muldwu.c.tat
  const auto aLbL = MulEven(a32, b32);
  const auto w3 = aLbL & maskL;

  const auto t2 = MulEven(aH, b32) + ShiftRight<32>(aLbL);
  const auto w2 = t2 & maskL;
  const auto w1 = ShiftRight<32>(t2);

  const auto t = MulEven(a32, bH) + w2;
  const auto k = ShiftRight<32>(t);

  const auto mulH = MulEven(aH, bH) + w1 + k;
  const auto mulL = ShiftLeft<32>(t) + w3;
  return InterleaveLower(mulL, mulH);
}

HWY_INLINE Vec512<uint64_t> MulOdd(const Vec512<uint64_t> a,
                                   const Vec512<uint64_t> b) {
  const DFromV<decltype(a)> du64;
  const RepartitionToNarrow<decltype(du64)> du32;
  const auto maskL = Set(du64, 0xFFFFFFFFULL);
  const auto a32 = BitCast(du32, a);
  const auto b32 = BitCast(du32, b);
  // Inputs for MulEven: we only need bits [95:64] (= upper half of input)
  const auto aH = Shuffle2301(a32);
  const auto bH = Shuffle2301(b32);

  // Same as above, but we're using the odd results (upper 64 bits per block).
  const auto aLbL = MulEven(a32, b32);
  const auto w3 = aLbL & maskL;

  const auto t2 = MulEven(aH, b32) + ShiftRight<32>(aLbL);
  const auto w2 = t2 & maskL;
  const auto w1 = ShiftRight<32>(t2);

  const auto t = MulEven(a32, bH) + w2;
  const auto k = ShiftRight<32>(t);

  const auto mulH = MulEven(aH, bH) + w1 + k;
  const auto mulL = ShiftLeft<32>(t) + w3;
  return InterleaveUpper(du64, mulL, mulH);
}

// ------------------------------ ReorderWidenMulAccumulate (MulAdd, ZipLower)

HWY_API Vec512<float> ReorderWidenMulAccumulate(Full512<float> df32,
                                                Vec512<bfloat16_t> a,
                                                Vec512<bfloat16_t> b,
                                                const Vec512<float> sum0,
                                                Vec512<float>& sum1) {
  // TODO(janwas): _mm512_dpbf16_ps when available
  const Repartition<uint16_t, decltype(df32)> du16;
  const RebindToUnsigned<decltype(df32)> du32;
  const Vec512<uint16_t> zero = Zero(du16);
  // Lane order within sum0/1 is undefined, hence we can avoid the
  // longer-latency lane-crossing PromoteTo.
  const Vec512<uint32_t> a0 = ZipLower(du32, zero, BitCast(du16, a));
  const Vec512<uint32_t> a1 = ZipUpper(du32, zero, BitCast(du16, a));
  const Vec512<uint32_t> b0 = ZipLower(du32, zero, BitCast(du16, b));
  const Vec512<uint32_t> b1 = ZipUpper(du32, zero, BitCast(du16, b));
  sum1 = MulAdd(BitCast(df32, a1), BitCast(df32, b1), sum1);
  return MulAdd(BitCast(df32, a0), BitCast(df32, b0), sum0);
}

// ------------------------------ Reductions

// Returns the sum in each lane.
HWY_API Vec512<int32_t> SumOfLanes(Full512<int32_t> d, Vec512<int32_t> v) {
  return Set(d, _mm512_reduce_add_epi32(v.raw));
}
HWY_API Vec512<int64_t> SumOfLanes(Full512<int64_t> d, Vec512<int64_t> v) {
  return Set(d, _mm512_reduce_add_epi64(v.raw));
}
HWY_API Vec512<uint32_t> SumOfLanes(Full512<uint32_t> d, Vec512<uint32_t> v) {
  return Set(d, static_cast<uint32_t>(_mm512_reduce_add_epi32(v.raw)));
}
HWY_API Vec512<uint64_t> SumOfLanes(Full512<uint64_t> d, Vec512<uint64_t> v) {
  return Set(d, static_cast<uint64_t>(_mm512_reduce_add_epi64(v.raw)));
}
HWY_API Vec512<float> SumOfLanes(Full512<float> d, Vec512<float> v) {
  return Set(d, _mm512_reduce_add_ps(v.raw));
}
HWY_API Vec512<double> SumOfLanes(Full512<double> d, Vec512<double> v) {
  return Set(d, _mm512_reduce_add_pd(v.raw));
}

// Returns the minimum in each lane.
HWY_API Vec512<int32_t> MinOfLanes(Full512<int32_t> d, Vec512<int32_t> v) {
  return Set(d, _mm512_reduce_min_epi32(v.raw));
}
HWY_API Vec512<int64_t> MinOfLanes(Full512<int64_t> d, Vec512<int64_t> v) {
  return Set(d, _mm512_reduce_min_epi64(v.raw));
}
HWY_API Vec512<uint32_t> MinOfLanes(Full512<uint32_t> d, Vec512<uint32_t> v) {
  return Set(d, _mm512_reduce_min_epu32(v.raw));
}
HWY_API Vec512<uint64_t> MinOfLanes(Full512<uint64_t> d, Vec512<uint64_t> v) {
  return Set(d, _mm512_reduce_min_epu64(v.raw));
}
HWY_API Vec512<float> MinOfLanes(Full512<float> d, Vec512<float> v) {
  return Set(d, _mm512_reduce_min_ps(v.raw));
}
HWY_API Vec512<double> MinOfLanes(Full512<double> d, Vec512<double> v) {
  return Set(d, _mm512_reduce_min_pd(v.raw));
}
template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> MinOfLanes(Full512<T> d, Vec512<T> v) {
  const Repartition<int32_t, decltype(d)> d32;
  const auto even = And(BitCast(d32, v), Set(d32, 0xFFFF));
  const auto odd = ShiftRight<16>(BitCast(d32, v));
  const auto min = MinOfLanes(d32, Min(even, odd));
  // Also broadcast into odd lanes.
  return BitCast(d, Or(min, ShiftLeft<16>(min)));
}

// Returns the maximum in each lane.
HWY_API Vec512<int32_t> MaxOfLanes(Full512<int32_t> d, Vec512<int32_t> v) {
  return Set(d, _mm512_reduce_max_epi32(v.raw));
}
HWY_API Vec512<int64_t> MaxOfLanes(Full512<int64_t> d, Vec512<int64_t> v) {
  return Set(d, _mm512_reduce_max_epi64(v.raw));
}
HWY_API Vec512<uint32_t> MaxOfLanes(Full512<uint32_t> d, Vec512<uint32_t> v) {
  return Set(d, _mm512_reduce_max_epu32(v.raw));
}
HWY_API Vec512<uint64_t> MaxOfLanes(Full512<uint64_t> d, Vec512<uint64_t> v) {
  return Set(d, _mm512_reduce_max_epu64(v.raw));
}
HWY_API Vec512<float> MaxOfLanes(Full512<float> d, Vec512<float> v) {
  return Set(d, _mm512_reduce_max_ps(v.raw));
}
HWY_API Vec512<double> MaxOfLanes(Full512<double> d, Vec512<double> v) {
  return Set(d, _mm512_reduce_max_pd(v.raw));
}
template <typename T, HWY_IF_LANE_SIZE(T, 2)>
HWY_API Vec512<T> MaxOfLanes(Full512<T> d, Vec512<T> v) {
  const Repartition<int32_t, decltype(d)> d32;
  const auto even = And(BitCast(d32, v), Set(d32, 0xFFFF));
  const auto odd = ShiftRight<16>(BitCast(d32, v));
  const auto min = MaxOfLanes(d32, Max(even, odd));
  // Also broadcast into odd lanes.
  return BitCast(d, Or(min, ShiftLeft<16>(min)));
}

// NOLINTNEXTLINE(google-readability-namespace-comments)
}  // namespace HWY_NAMESPACE
}  // namespace hwy
HWY_AFTER_NAMESPACE();