TensorReduction.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
// Copyright (C) 2016 Mehdi Goli, Codeplay Software Ltd <eigen@codeplay.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
#ifndef EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H
#define EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H
 
// clang is incompatible with the CUDA syntax wrt making a kernel a class friend,
// so we'll use a macro to make clang happy.
#ifndef KERNEL_FRIEND
#if defined(__clang__) && (defined(__CUDA__) || defined(__HIP__))
#define KERNEL_FRIEND friend __global__ EIGEN_HIP_LAUNCH_BOUNDS_1024
#else
#define KERNEL_FRIEND friend
#endif
#endif
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
template <typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
struct traits<TensorReductionOp<Op, Dims, XprType, MakePointer_> > : traits<XprType> {
  typedef traits<XprType> XprTraits;
  typedef typename XprTraits::Scalar Scalar;
  typedef typename XprTraits::StorageKind StorageKind;
  typedef typename XprTraits::Index Index;
  typedef typename XprType::Nested Nested;
  static constexpr int NumDimensions = XprTraits::NumDimensions - array_size<Dims>::value;
  static constexpr int Layout = XprTraits::Layout;
  typedef typename XprTraits::PointerType PointerType;
 
  template <class T>
  struct MakePointer {
    // Intermediate typedef to workaround MSVC issue.
    typedef MakePointer_<T> MakePointerT;
    typedef typename MakePointerT::Type Type;
  };
};
 
template <typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
struct eval<TensorReductionOp<Op, Dims, XprType, MakePointer_>, Eigen::Dense> {
  typedef const TensorReductionOp<Op, Dims, XprType, MakePointer_>& type;
};
 
template <typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
struct nested<TensorReductionOp<Op, Dims, XprType, MakePointer_>, 1,
              typename eval<TensorReductionOp<Op, Dims, XprType, MakePointer_> >::type> {
  typedef TensorReductionOp<Op, Dims, XprType, MakePointer_> type;
};
 
template <typename OutputDims>
struct DimInitializer {
  template <typename InputDims, typename ReducedDims>
  EIGEN_DEVICE_FUNC static void run(const InputDims& input_dims,
                                    const array<bool, internal::array_size<InputDims>::value>& reduced,
                                    OutputDims* output_dims, ReducedDims* reduced_dims) {
    const int NumInputDims = internal::array_size<InputDims>::value;
    int outputIndex = 0;
    int reduceIndex = 0;
    for (int i = 0; i < NumInputDims; ++i) {
      if (reduced[i]) {
        (*reduced_dims)[reduceIndex] = input_dims[i];
        ++reduceIndex;
      } else {
        (*output_dims)[outputIndex] = input_dims[i];
        ++outputIndex;
      }
    }
  }
};
 
template <>
struct DimInitializer<Sizes<> > {
  template <typename InputDims, typename Index, size_t Rank>
  EIGEN_DEVICE_FUNC static void run(const InputDims& input_dims, const array<bool, Rank>&, Sizes<>*,
                                    array<Index, Rank>* reduced_dims) {
    const int NumInputDims = internal::array_size<InputDims>::value;
    for (int i = 0; i < NumInputDims; ++i) {
      (*reduced_dims)[i] = input_dims[i];
    }
  }
};
 
template <typename ReducedDims, int NumTensorDims, int Layout>
struct are_inner_most_dims {
  static const bool value = false;
};
template <typename ReducedDims, int NumTensorDims, int Layout>
struct preserve_inner_most_dims {
  static const bool value = false;
};
 
template <typename ReducedDims, int NumTensorDims>
struct are_inner_most_dims<ReducedDims, NumTensorDims, ColMajor> {
  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
  static const bool tmp2 = index_statically_eq<ReducedDims>(0, 0);
  static const bool tmp3 =
      index_statically_eq<ReducedDims>(array_size<ReducedDims>::value - 1, array_size<ReducedDims>::value - 1);
  static const bool value = tmp1 & tmp2 & tmp3;
};
template <typename ReducedDims, int NumTensorDims>
struct are_inner_most_dims<ReducedDims, NumTensorDims, RowMajor> {
  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
  static const bool tmp2 = index_statically_eq<ReducedDims>(0, NumTensorDims - array_size<ReducedDims>::value);
  static const bool tmp3 = index_statically_eq<ReducedDims>(array_size<ReducedDims>::value - 1, NumTensorDims - 1);
  static const bool value = tmp1 & tmp2 & tmp3;
};
template <typename ReducedDims, int NumTensorDims>
struct preserve_inner_most_dims<ReducedDims, NumTensorDims, ColMajor> {
  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
  static const bool tmp2 = index_statically_gt<ReducedDims>(0, 0);
  static const bool value = tmp1 & tmp2;
};
template <typename ReducedDims, int NumTensorDims>
struct preserve_inner_most_dims<ReducedDims, NumTensorDims, RowMajor> {
  static const bool tmp1 = indices_statically_known_to_increase<ReducedDims>();
  static const bool tmp2 = index_statically_lt<ReducedDims>(array_size<ReducedDims>::value - 1, NumTensorDims - 1);
  static const bool value = tmp1 & tmp2;
};
 
template <int DimIndex, typename Self, typename Op>
struct GenericDimReducer {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex,
                                                           Op& reducer, typename Self::CoeffReturnType* accum) {
    EIGEN_STATIC_ASSERT((DimIndex > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
    for (int j = 0; j < self.m_reducedDims[DimIndex]; ++j) {
      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[DimIndex];
      GenericDimReducer<DimIndex - 1, Self, Op>::reduce(self, input, reducer, accum);
    }
  }
};
template <typename Self, typename Op>
struct GenericDimReducer<0, Self, Op> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex,
                                                           Op& reducer, typename Self::CoeffReturnType* accum) {
    for (int j = 0; j < self.m_reducedDims[0]; ++j) {
      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[0];
      reducer.reduce(self.m_impl.coeff(input), accum);
    }
  }
};
template <typename Self, typename Op>
struct GenericDimReducer<-1, Self, Op> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index index, Op& reducer,
                                                           typename Self::CoeffReturnType* accum) {
    reducer.reduce(self.m_impl.coeff(index), accum);
  }
};
 
template <typename Self, typename Op,
          bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess),
          bool UseTreeReduction = (!Self::ReducerTraits::IsStateful && !Self::ReducerTraits::IsExactlyAssociative &&
                                   // GPU threads can quickly run out of stack space
                                   // for moderately sized inputs.
                                   !Self::RunningOnGPU)>
struct InnerMostDimReducer {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(
      const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {
    typename Self::CoeffReturnType accum = reducer.initialize();
    for (typename Self::Index j = 0; j < numValuesToReduce; ++j) {
      reducer.reduce(self.m_impl.coeff(firstIndex + j), &accum);
    }
    return reducer.finalize(accum);
  }
};
 
template <typename Self, typename Op>
struct InnerMostDimReducer<Self, Op, true, false> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(
      const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer0) {
    using Index = typename Self::Index;
    constexpr Index packetSize = internal::unpacket_traits<typename Self::PacketReturnType>::size;
    Index start = 0;
    typename Self::PacketReturnType paccum0 = reducer0.template initializePacket<typename Self::PacketReturnType>();
    if (!Self::ReducerTraits::IsStateful && numValuesToReduce >= 4 * packetSize) {
      const Index VectorizedSize4 = (numValuesToReduce / (4 * packetSize)) * (4 * packetSize);
      typename Self::PacketReturnType paccum1 = reducer0.template initializePacket<typename Self::PacketReturnType>();
      typename Self::PacketReturnType paccum2 = reducer0.template initializePacket<typename Self::PacketReturnType>();
      typename Self::PacketReturnType paccum3 = reducer0.template initializePacket<typename Self::PacketReturnType>();
      const Index offset0 = firstIndex;
      const Index offset1 = firstIndex + packetSize;
      const Index offset2 = firstIndex + 2 * packetSize;
      const Index offset3 = firstIndex + 3 * packetSize;
      for (Index j = 0; j < VectorizedSize4; j += 4 * packetSize) {
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset0 + j), &paccum0);
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset1 + j), &paccum1);
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset2 + j), &paccum2);
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(offset3 + j), &paccum3);
      }
      reducer0.reducePacket(paccum1, &paccum0);
      reducer0.reducePacket(paccum2, &paccum0);
      reducer0.reducePacket(paccum3, &paccum0);
      start = VectorizedSize4;
    }
    if (start <= (numValuesToReduce - packetSize)) {
      const Index VectorizedSize = (numValuesToReduce / packetSize) * packetSize;
      for (Index j = start; j < VectorizedSize; j += packetSize) {
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(firstIndex + j), &paccum0);
      }
      start = VectorizedSize;
    }
    typename Self::CoeffReturnType accum = reducer0.initialize();
    for (Index j = start; j < numValuesToReduce; ++j) {
      reducer0.reduce(self.m_impl.coeff(firstIndex + j), &accum);
    }
    return reducer0.finalizeBoth(accum, paccum0);
  }
};
 
#if !defined(EIGEN_HIPCC)
 
// The following implements tree-based reduction, which improves the accuracy
// of sum and mean reductions, since each of the n inputs only participates in
// O(log n) additions.
template <typename T>
EIGEN_DEVICE_FUNC inline Index LeafSize() {
  return 1024;
}
template <>
EIGEN_DEVICE_FUNC inline Index LeafSize<half>() {
  return 200;
}
template <>
EIGEN_DEVICE_FUNC inline Index LeafSize<bfloat16>() {
  return 128;
}
 
template <typename Self, typename Op>
struct InnerMostDimReducer<Self, Op, false, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(
      const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {
    const Index kLeafSize = LeafSize<typename Self::CoeffReturnType>();
    typename Self::CoeffReturnType accum = reducer.initialize();
    if (numValuesToReduce > kLeafSize) {
      const typename Self::Index half = numValuesToReduce / 2;
      // Recursively reduce the two halves.
      reducer.reduce(reduce(self, firstIndex, half, reducer), &accum);
      reducer.reduce(reduce(self, firstIndex + half, numValuesToReduce - half, reducer), &accum);
      return reducer.finalize(accum);
    } else {
      return InnerMostDimReducer<Self, Op, false, false>::reduce(self, firstIndex, numValuesToReduce, reducer);
    }
  }
};
 
template <typename Self, typename Op>
struct InnerMostDimReducer<Self, Op, true, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Self::CoeffReturnType reduce(
      const Self& self, typename Self::Index firstIndex, typename Self::Index numValuesToReduce, Op& reducer) {
    const Index kLeafSize = LeafSize<typename Self::CoeffReturnType>();
    const typename Self::Index packetSize = internal::unpacket_traits<typename Self::PacketReturnType>::size;
    typename Self::CoeffReturnType accum = reducer.initialize();
    if (numValuesToReduce > packetSize * kLeafSize) {
      // Make sure the split point is aligned on a packet boundary.
      const typename Self::Index split =
          packetSize *
          numext::div_ceil(firstIndex + numext::div_ceil(numValuesToReduce, typename Self::Index(2)), packetSize);
      const typename Self::Index num_left = numext::mini(split - firstIndex, numValuesToReduce);
      reducer.reduce(reduce(self, firstIndex, num_left, reducer), &accum);
      if (num_left < numValuesToReduce) {
        reducer.reduce(reduce(self, split, numValuesToReduce - num_left, reducer), &accum);
      }
      return reducer.finalize(accum);
    } else {
      return InnerMostDimReducer<Self, Op, true, false>::reduce(self, firstIndex, numValuesToReduce, reducer);
    }
  }
};
#endif
 
template <int DimIndex, typename Self, typename Op,
          bool vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
struct InnerMostDimPreserver {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&,
                                                           typename Self::PacketReturnType*) {
    eigen_assert(false && "should never be called");
  }
};
 
template <int DimIndex, typename Self, typename Op>
struct InnerMostDimPreserver<DimIndex, Self, Op, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex,
                                                           Op& reducer, typename Self::PacketReturnType* accum) {
    EIGEN_STATIC_ASSERT((DimIndex > 0), YOU_MADE_A_PROGRAMMING_MISTAKE);
    for (typename Self::Index j = 0; j < self.m_reducedDims[DimIndex]; ++j) {
      const typename Self::Index input = firstIndex + j * self.m_reducedStrides[DimIndex];
      InnerMostDimPreserver<DimIndex - 1, Self, Op>::reduce(self, input, reducer, accum);
    }
  }
};
 
template <typename Self, typename Op>
struct InnerMostDimPreserver<0, Self, Op, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self& self, typename Self::Index firstIndex,
                                                           Op& reducer0, typename Self::PacketReturnType* accum0) {
    using Index = typename Self::Index;
    const Index stride = self.m_reducedStrides[0];
    const Index size = self.m_reducedDims[0];
    if (!Self::ReducerTraits::IsStateful && size >= 16) {
      const Index unrolled_size4 = (size / 4) * 4;
      typename Self::PacketReturnType accum1 = reducer0.template initializePacket<typename Self::PacketReturnType>();
      typename Self::PacketReturnType accum2 = reducer0.template initializePacket<typename Self::PacketReturnType>();
      typename Self::PacketReturnType accum3 = reducer0.template initializePacket<typename Self::PacketReturnType>();
      for (Index j = 0; j < unrolled_size4; j += 4) {
        const Index input0 = firstIndex + j * stride;
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input0), accum0);
        const Index input1 = firstIndex + (j + 1) * stride;
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input1), &accum1);
        const Index input2 = firstIndex + (j + 2) * stride;
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input2), &accum2);
        const Index input3 = firstIndex + (j + 3) * stride;
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input3), &accum3);
      }
      reducer0.reducePacket(accum1, accum0);
      reducer0.reducePacket(accum2, accum0);
      reducer0.reducePacket(accum3, accum0);
      for (Index j = unrolled_size4; j < size; ++j) {
        Index input = firstIndex + j * stride;
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input), accum0);
      }
    } else {
      for (Index j = 0; j < size; ++j) {
        Index input = firstIndex + j * stride;
        reducer0.reducePacket(self.m_impl.template packet<Unaligned>(input), accum0);
      }
    }
  }
};
template <typename Self, typename Op>
struct InnerMostDimPreserver<-1, Self, Op, true> {
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void reduce(const Self&, typename Self::Index, Op&,
                                                           typename Self::PacketReturnType*) {
    eigen_assert(false && "should never be called");
  }
};
 
// Default full reducer
template <typename Self, typename Op, typename Device,
          bool Vectorizable = (Self::InputPacketAccess && Self::ReducerTraits::PacketAccess)>
struct FullReducer {
  static constexpr bool HasOptimizedImplementation = false;
 
  static EIGEN_DEVICE_FUNC void run(const Self& self, Op& reducer, const Device&,
                                    typename Self::EvaluatorPointerType output) {
    const typename Self::Index num_coeffs = array_prod(self.m_impl.dimensions());
    *output = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, 0, num_coeffs, reducer);
  }
};
 
#ifdef EIGEN_USE_THREADS
// Multithreaded full reducer
template <typename Self, typename Op, bool Vectorizable>
struct FullReducer<Self, Op, ThreadPoolDevice, Vectorizable> {
  static constexpr bool HasOptimizedImplementation = !Self::ReducerTraits::IsStateful;
  static constexpr Index PacketSize = unpacket_traits<typename Self::PacketReturnType>::size;
 
  // launch one reducer per thread and accumulate the result.
  static void run(const Self& self, Op& reducer, const ThreadPoolDevice& device,
                  typename Self::CoeffReturnType* output) {
    typedef typename Self::Index Index;
    const Index num_coeffs = array_prod(self.m_impl.dimensions());
    if (num_coeffs == 0) {
      *output = reducer.finalize(reducer.initialize());
      return;
    }
    const TensorOpCost cost = self.m_impl.costPerCoeff(Vectorizable) +
                              TensorOpCost(0, 0, internal::functor_traits<Op>::Cost, Vectorizable, PacketSize);
    const Index num_threads = TensorCostModel<ThreadPoolDevice>::numThreads(num_coeffs, cost, device.numThreads());
    if (num_threads == 1) {
      *output = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, 0, num_coeffs, reducer);
      return;
    }
    const Index blocksize = num_coeffs / num_threads;
    const Index numblocks = blocksize > 0 ? num_coeffs / blocksize : 0;
    eigen_assert(num_coeffs >= numblocks * blocksize);
 
    Barrier barrier(internal::convert_index<unsigned int>(numblocks));
    MaxSizeVector<typename Self::CoeffReturnType> shards(numblocks, reducer.initialize());
    for (Index i = 0; i < numblocks; ++i) {
      auto run_shard = [i, blocksize, &self, &barrier, &shards, &reducer](){
        shards[i] = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, i * blocksize, blocksize, reducer);
        barrier.Notify();
      };
      device.enqueue(std::move(run_shard));
    }
    typename Self::CoeffReturnType finalShard;
    if (numblocks * blocksize < num_coeffs) {
      finalShard = InnerMostDimReducer<Self, Op, Vectorizable>::reduce(self, numblocks * blocksize,
                                                                       num_coeffs - numblocks * blocksize, reducer);
    } else {
      finalShard = reducer.initialize();
    }
    barrier.Wait();
 
    for (Index i = 0; i < numblocks; ++i) {
      reducer.reduce(shards[i], &finalShard);
    }
    *output = reducer.finalize(finalShard);
  }
};
 
#endif
 
// Default inner reducer
template <typename Self, typename Op, typename Device>
struct InnerReducer {
  static constexpr bool HasOptimizedImplementation = false;
 
  EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*,
                                    typename Self::Index, typename Self::Index) {
    eigen_assert(false && "Not implemented");
    return true;
  }
};
 
// Default outer reducer
template <typename Self, typename Op, typename Device>
struct OuterReducer {
  static constexpr bool HasOptimizedImplementation = false;
 
  EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*,
                                    typename Self::Index, typename Self::Index) {
    eigen_assert(false && "Not implemented");
    return true;
  }
};
 
#ifdef EIGEN_USE_SYCL
// Default Generic reducer
template <typename Self, typename Op, typename Device>
struct GenericReducer {
  static constexpr bool HasOptimizedImplementation = false;
 
  EIGEN_DEVICE_FUNC static bool run(const Self&, Op&, const Device&, typename Self::CoeffReturnType*,
                                    typename Self::Index, typename Self::Index) {
    eigen_assert(false && "Not implemented");
    return true;
  }
};
#endif
 
#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
template <int B, int N, typename S, typename R, typename I_>
__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernel(R, const S, I_, typename S::CoeffReturnType*,
                                                                 unsigned int*);
 
#if defined(EIGEN_HAS_GPU_FP16)
template <typename S, typename R, typename I_>
__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void ReductionInitFullReduxKernelHalfFloat(
    R, const S, I_, internal::packet_traits<half>::type*);
template <int B, int N, typename S, typename R, typename I_>
__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void FullReductionKernelHalfFloat(R, const S, I_, half*,
                                                                          internal::packet_traits<half>::type*);
template <int NPT, typename S, typename R, typename I_>
__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void InnerReductionKernelHalfFloat(R, const S, I_, I_, half*);
 
#endif
 
template <int NPT, typename S, typename R, typename I_>
__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void InnerReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
 
template <int NPT, typename S, typename R, typename I_>
__global__ EIGEN_HIP_LAUNCH_BOUNDS_1024 void OuterReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
#endif

template <typename Op, typename CoeffReturnType>
struct ReductionReturnType {
#if defined(EIGEN_USE_SYCL)
  typedef std::remove_const_t<decltype(std::declval<Op>().initialize())> type;
#else
  typedef std::remove_const_t<CoeffReturnType> type;
#endif
};
 
}  // end namespace internal

template <typename Op, typename Dims, typename XprType, template <class> class MakePointer_>
class TensorReductionOp : public TensorBase<TensorReductionOp<Op, Dims, XprType, MakePointer_>, ReadOnlyAccessors> {
 public:
  typedef typename Eigen::internal::traits<TensorReductionOp>::Scalar Scalar;
  typedef typename Eigen::NumTraits<Scalar>::Real RealScalar;
  typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
  typedef typename Eigen::internal::nested<TensorReductionOp>::type Nested;
  typedef typename Eigen::internal::traits<TensorReductionOp>::StorageKind StorageKind;
  typedef typename Eigen::internal::traits<TensorReductionOp>::Index Index;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReductionOp(const XprType& expr, const Dims& dims)
      : m_expr(expr), m_dims(dims) {}
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorReductionOp(const XprType& expr, const Dims& dims, const Op& reducer)
      : m_expr(expr), m_dims(dims), m_reducer(reducer) {}
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const XprType& expression() const { return m_expr; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dims& dims() const { return m_dims; }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Op& reducer() const { return m_reducer; }
 
 protected:
  typename XprType::Nested m_expr;
  const Dims m_dims;
  const Op m_reducer;
};
 
template <typename ArgType, typename Device>
struct TensorReductionEvaluatorBase;
 
// Eval as rvalue
template <typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>
struct TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> {
  typedef internal::reducer_traits<Op, Device> ReducerTraits;
  typedef Dims ReducedDims;
  typedef TensorReductionOp<Op, Dims, ArgType, MakePointer_> XprType;
  typedef typename XprType::Index Index;
  typedef ArgType ChildType;
  typedef typename TensorEvaluator<ArgType, Device>::Dimensions InputDimensions;
  static constexpr int NumInputDims = internal::array_size<InputDimensions>::value;
  static constexpr int NumReducedDims = internal::array_size<Dims>::value;
  static constexpr int NumOutputDims = NumInputDims - NumReducedDims;
  typedef std::conditional_t<NumOutputDims == 0, Sizes<>, DSizes<Index, NumOutputDims> > Dimensions;
  typedef typename XprType::Scalar Scalar;
  typedef TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> Self;
  static constexpr bool InputPacketAccess = TensorEvaluator<ArgType, Device>::PacketAccess;
  typedef typename internal::ReductionReturnType<Op, typename XprType::CoeffReturnType>::type CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, Device>::type PacketReturnType;
  static constexpr Index PacketSize = PacketType<CoeffReturnType, Device>::size;
 
  typedef typename Eigen::internal::traits<XprType>::PointerType TensorPointerType;
  typedef StorageMemory<CoeffReturnType, Device> Storage;
  typedef typename Storage::Type EvaluatorPointerType;
 
  // Subset of strides of the input tensor for the non-reduced dimensions.
  // Indexed by output dimensions.
  static constexpr int NumPreservedStrides = max_n_1<NumOutputDims>::size;
 
  // For full reductions
#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
  static constexpr bool RunningOnGPU = internal::is_same<Device, Eigen::GpuDevice>::value;
  static constexpr bool RunningOnSycl = false;
#elif defined(EIGEN_USE_SYCL)
  static constexpr bool RunningOnSycl = internal::is_same<internal::remove_all_t<Device>, Eigen::SyclDevice>::value;
  static constexpr bool RunningOnGPU = false;
#else
  static constexpr bool RunningOnGPU = false;
  static constexpr bool RunningOnSycl = false;
#endif
 
  static constexpr int Layout = TensorEvaluator<ArgType, Device>::Layout;
  enum {
    IsAligned = false,
    PacketAccess = Self::InputPacketAccess && ReducerTraits::PacketAccess,
    BlockAccess = false,
    PreferBlockAccess = true,
    CoordAccess = false,  // to be implemented
    RawAccess = false
  };
 
  typedef std::remove_const_t<Scalar> ScalarNoConst;
 
  //===- Tensor block evaluation strategy (see TensorBlock.h) -------------===//
  typedef internal::TensorBlockNotImplemented TensorBlock;
  //===--------------------------------------------------------------------===//
 
  static constexpr bool ReducingInnerMostDims = internal::are_inner_most_dims<Dims, NumInputDims, Layout>::value;
  static constexpr bool PreservingInnerMostDims = internal::preserve_inner_most_dims<Dims, NumInputDims, Layout>::value;
  static constexpr bool RunningFullReduction = (NumOutputDims == 0);
 
  EIGEN_STRONG_INLINE TensorReductionEvaluatorBase(const XprType& op, const Device& device)
      : m_impl(op.expression(), device), m_reducer(op.reducer()), m_result(NULL), m_device(device) {
    EIGEN_STATIC_ASSERT((NumInputDims >= NumReducedDims), YOU_MADE_A_PROGRAMMING_MISTAKE);
    EIGEN_STATIC_ASSERT((!ReducingInnerMostDims | !PreservingInnerMostDims | (NumReducedDims == NumInputDims)),
                        YOU_MADE_A_PROGRAMMING_MISTAKE);
 
    // Build the bitmap indicating if an input dimension is reduced or not.
    for (int i = 0; i < NumInputDims; ++i) {
      m_reduced[i] = false;
    }
    for (int i = 0; i < NumReducedDims; ++i) {
      eigen_assert(op.dims()[i] >= 0);
      eigen_assert(op.dims()[i] < NumInputDims);
      m_reduced[op.dims()[i]] = true;
    }
 
    const typename TensorEvaluator<ArgType, Device>::Dimensions& input_dims = m_impl.dimensions();
    internal::DimInitializer<Dimensions>::run(input_dims, m_reduced, &m_dimensions, &m_reducedDims);
 
    // Precompute output strides.
    if (NumOutputDims > 0) {
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        m_outputStrides[0] = 1;
        for (int i = 1; i < NumOutputDims; ++i) {
          m_outputStrides[i] = m_outputStrides[i - 1] * m_dimensions[i - 1];
          m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);
        }
      } else {
        m_outputStrides[static_cast<size_t>(NumOutputDims - 1)] = 1;
        for (int i = NumOutputDims - 2; i >= 0; --i) {
          m_outputStrides[i] = m_outputStrides[i + 1] * m_dimensions[i + 1];
          m_fastOutputStrides[i] = internal::TensorIntDivisor<Index>(m_outputStrides[i]);
        }
      }
    }
 
    // Precompute input strides.
    if (NumInputDims > 0) {
      array<Index, NumInputDims> input_strides;
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        input_strides[0] = 1;
        for (int i = 1; i < NumInputDims; ++i) {
          input_strides[i] = input_strides[i - 1] * input_dims[i - 1];
        }
      } else {
        input_strides.back() = 1;
        for (int i = NumInputDims - 2; i >= 0; --i) {
          input_strides[i] = input_strides[i + 1] * input_dims[i + 1];
        }
      }
 
      int outputIndex = 0;
      int reduceIndex = 0;
      for (int i = 0; i < NumInputDims; ++i) {
        if (m_reduced[i]) {
          m_reducedStrides[reduceIndex] = input_strides[i];
          ++reduceIndex;
        } else {
          m_preservedStrides[outputIndex] = input_strides[i];
          m_output_to_input_dim_map[outputIndex] = i;
          ++outputIndex;
        }
      }
    }
 
    // Special case for full reductions
    if (NumOutputDims == 0) {
      m_preservedStrides[0] = internal::array_prod(input_dims);
    }
 
    m_numValuesToReduce = NumOutputDims == 0 ? internal::array_prod(input_dims)
                          : (static_cast<int>(Layout) == static_cast<int>(ColMajor))
                              ? m_preservedStrides[0]
                              : m_preservedStrides[static_cast<size_t>(NumOutputDims - 1)];
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Dimensions& dimensions() const { return m_dimensions; }
 
  EIGEN_STRONG_INLINE bool evalSubExprsIfNeededCommon(EvaluatorPointerType data) {
    // Use the FullReducer if possible.
    if ((RunningFullReduction && RunningOnSycl) ||
        (RunningFullReduction && internal::FullReducer<Self, Op, Device>::HasOptimizedImplementation &&
         ((RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) || !RunningOnGPU))) {
      bool need_assign = false;
      if (!data) {
        m_result = static_cast<EvaluatorPointerType>(
            m_device.get((CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType))));
        data = m_result;
        need_assign = true;
      }
      Op reducer(m_reducer);
      internal::FullReducer<Self, Op, Device>::run(*this, reducer, m_device, data);
      return need_assign;
    }
 
    // Attempt to use an optimized reduction.
    else if ((RunningOnGPU && (m_device.majorDeviceVersion() >= 3)) || (RunningOnSycl)) {
      bool reducing_inner_dims = true;
      for (int i = 0; i < NumReducedDims; ++i) {
        if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
          reducing_inner_dims &= m_reduced[i];
        } else {
          reducing_inner_dims &= m_reduced[NumInputDims - 1 - i];
        }
      }
      if (internal::InnerReducer<Self, Op, Device>::HasOptimizedImplementation &&
          (reducing_inner_dims || ReducingInnerMostDims)) {
        const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
        const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);
        if (!data) {
          if ((num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve &&
               num_values_to_reduce > 128) ||
              (RunningOnSycl)) {
            data = static_cast<EvaluatorPointerType>(m_device.get(
                (CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType) * num_coeffs_to_preserve)));
            m_result = data;
          } else {
            return true;
          }
        }
        Op reducer(m_reducer);
        // For SYCL this if always return false
        if (internal::InnerReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce,
                                                          num_coeffs_to_preserve)) {
          if (m_result) {
            m_device.deallocate_temp(m_result);
            m_result = NULL;
          }
          return true;
        } else {
          return (m_result != NULL);
        }
      }
 
      bool preserving_inner_dims = true;
      for (int i = 0; i < NumReducedDims; ++i) {
        if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
          preserving_inner_dims &= m_reduced[NumInputDims - 1 - i];
        } else {
          preserving_inner_dims &= m_reduced[i];
        }
      }
      if (internal::OuterReducer<Self, Op, Device>::HasOptimizedImplementation && preserving_inner_dims) {
        const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
        const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);
        if (!data) {
          if ((num_coeffs_to_preserve < 1024 && num_values_to_reduce > num_coeffs_to_preserve &&
               num_values_to_reduce > 32) ||
              (RunningOnSycl)) {
            data = static_cast<EvaluatorPointerType>(m_device.get(
                (CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType) * num_coeffs_to_preserve)));
            m_result = data;
          } else {
            return true;
          }
        }
        Op reducer(m_reducer);
        // For SYCL this if always return false
        if (internal::OuterReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce,
                                                          num_coeffs_to_preserve)) {
          if (m_result) {
            m_device.deallocate_temp(m_result);
            m_result = NULL;
          }
          return true;
        } else {
          return (m_result != NULL);
        }
      }
#if defined(EIGEN_USE_SYCL)
      // If there is no Optimised version for SYCL, the reduction expression
      // must break into two subexpression and use the SYCL generic Reducer on the device.
      if (RunningOnSycl) {
        const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
        const Index num_coeffs_to_preserve = internal::array_prod(m_dimensions);
        if (!data) {
          data = static_cast<EvaluatorPointerType>(
              m_device.get((CoeffReturnType*)m_device.allocate_temp(sizeof(CoeffReturnType) * num_coeffs_to_preserve)));
          m_result = data;
        }
        Op reducer(m_reducer);
        internal::GenericReducer<Self, Op, Device>::run(*this, reducer, m_device, data, num_values_to_reduce,
                                                        num_coeffs_to_preserve);
        return (m_result != NULL);
      }
#endif
    }
    return true;
  }
 
#ifdef EIGEN_USE_THREADS
  template <typename EvalSubExprsCallback>
  EIGEN_STRONG_INLINE void evalSubExprsIfNeededAsync(EvaluatorPointerType data, EvalSubExprsCallback done) {
    m_impl.evalSubExprsIfNeededAsync(NULL, [this, data, done](bool) { done(evalSubExprsIfNeededCommon(data)); });
  }
#endif
 
  EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(EvaluatorPointerType data) {
    m_impl.evalSubExprsIfNeeded(NULL);
    return evalSubExprsIfNeededCommon(data);
  }
 
  EIGEN_STRONG_INLINE void cleanup() {
    m_impl.cleanup();
    if (m_result) {
      m_device.deallocate_temp(m_result);
      m_result = NULL;
    }
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    if ((RunningFullReduction || RunningOnGPU) && m_result) {
      return *(m_result + index);
    }
    Op reducer(m_reducer);
    if (ReducingInnerMostDims || RunningFullReduction) {
      const Index num_values_to_reduce = (static_cast<int>(Layout) == static_cast<int>(ColMajor))
                                             ? m_preservedStrides[0]
                                             : m_preservedStrides[NumPreservedStrides - 1];
      return internal::InnerMostDimReducer<Self, Op>::reduce(*this, firstInput(index), num_values_to_reduce, reducer);
    } else {
      typename Self::CoeffReturnType accum = reducer.initialize();
      internal::GenericDimReducer<NumReducedDims - 1, Self, Op>::reduce(*this, firstInput(index), reducer, &accum);
      return reducer.finalize(accum);
    }
  }
 
  // TODO(bsteiner): provide a more efficient implementation.
  template <int LoadMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketReturnType packet(Index index) const {
    eigen_assert(index + PacketSize - 1 < Index(internal::array_prod(dimensions())));
 
    if (RunningOnGPU && m_result) {
      return internal::pload<PacketReturnType>(m_result + index);
    }
 
    EIGEN_ALIGN_MAX std::remove_const_t<CoeffReturnType> values[PacketSize];
    if (ReducingInnerMostDims) {
      const Index num_values_to_reduce = (static_cast<int>(Layout) == static_cast<int>(ColMajor))
                                             ? m_preservedStrides[0]
                                             : m_preservedStrides[NumPreservedStrides - 1];
      const Index firstIndex = firstInput(index);
      for (Index i = 0; i < PacketSize; ++i) {
        Op reducer(m_reducer);
        values[i] = internal::InnerMostDimReducer<Self, Op>::reduce(*this, firstIndex + i * num_values_to_reduce,
                                                                    num_values_to_reduce, reducer);
      }
    } else if (PreservingInnerMostDims) {
      const Index firstIndex = firstInput(index);
      const int innermost_dim = (static_cast<int>(Layout) == static_cast<int>(ColMajor)) ? 0 : NumOutputDims - 1;
      // TBD: extend this the the n innermost dimensions that we preserve.
      if (((firstIndex % m_dimensions[innermost_dim]) + PacketSize - 1) < m_dimensions[innermost_dim]) {
        Op reducer(m_reducer);
        typename Self::PacketReturnType accum = reducer.template initializePacket<typename Self::PacketReturnType>();
        internal::InnerMostDimPreserver<NumReducedDims - 1, Self, Op>::reduce(*this, firstIndex, reducer, &accum);
        return reducer.finalizePacket(accum);
      } else {
        for (int i = 0; i < PacketSize; ++i) {
          values[i] = coeff(index + i);
        }
      }
    } else {
      for (int i = 0; i < PacketSize; ++i) {
        values[i] = coeff(index + i);
      }
    }
    PacketReturnType rslt = internal::pload<PacketReturnType>(values);
    return rslt;
  }
 
  // Must be called after evalSubExprsIfNeeded().
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE TensorOpCost costPerCoeff(bool vectorized) const {
    if (RunningFullReduction && m_result) {
      return TensorOpCost(sizeof(CoeffReturnType), 0, 0, vectorized, PacketSize);
    } else {
      const Index num_values_to_reduce = internal::array_prod(m_reducedDims);
      const double compute_cost = num_values_to_reduce * internal::functor_traits<Op>::Cost;
      return m_impl.costPerCoeff(vectorized) * num_values_to_reduce +
             TensorOpCost(0, 0, compute_cost, vectorized, PacketSize);
    }
  }
 
  EIGEN_DEVICE_FUNC EvaluatorPointerType data() const { return m_result; }
  EIGEN_DEVICE_FUNC const TensorEvaluator<ArgType, Device>& impl() const { return m_impl; }
  EIGEN_DEVICE_FUNC const Device& device() const { return m_device; }
 
 private:
  template <int, typename, typename>
  friend struct internal::GenericDimReducer;
  template <typename, typename, bool, bool>
  friend struct internal::InnerMostDimReducer;
  template <int, typename, typename, bool>
  friend struct internal::InnerMostDimPreserver;
  template <typename S, typename O, typename D, bool V>
  friend struct internal::FullReducer;
#if defined(EIGEN_USE_GPU) && (defined(EIGEN_GPUCC))
  template <int B, int N, typename S, typename R, typename I_>
  KERNEL_FRIEND void internal::FullReductionKernel(R, const S, I_, typename S::CoeffReturnType*, unsigned int*);
#if defined(EIGEN_HAS_GPU_FP16)
  template <typename S, typename R, typename I_>
  KERNEL_FRIEND void internal::ReductionInitFullReduxKernelHalfFloat(R, const S, I_,
                                                                     internal::packet_traits<Eigen::half>::type*);
  template <int B, int N, typename S, typename R, typename I_>
  KERNEL_FRIEND void internal::FullReductionKernelHalfFloat(R, const S, I_, half*,
                                                            internal::packet_traits<Eigen::half>::type*);
  template <int NPT, typename S, typename R, typename I_>
  KERNEL_FRIEND void internal::InnerReductionKernelHalfFloat(R, const S, I_, I_, half*);
#endif
  template <int NPT, typename S, typename R, typename I_>
  KERNEL_FRIEND void internal::InnerReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
 
  template <int NPT, typename S, typename R, typename I_>
  KERNEL_FRIEND void internal::OuterReductionKernel(R, const S, I_, I_, typename S::CoeffReturnType*);
#endif
 
#if defined(EIGEN_USE_SYCL)
  template <typename Evaluator_, typename Op__>
  friend class TensorSycl::internal::GenericNondeterministicReducer;
  // SYCL need the Generic reducer for the case the recution algorithm is neither inner, outer, and full reducer
  template <typename, typename, typename>
  friend struct internal::GenericReducer;
#endif
 
  template <typename S, typename O, typename D>
  friend struct internal::InnerReducer;
 
  struct BlockIteratorState {
    Index input_dim;
    Index output_size;
    Index output_count;
  };
 
  // Returns the Index in the input tensor of the first value that needs to be
  // used to compute the reduction at output index "index".
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index firstInput(Index index) const {
    if (ReducingInnerMostDims) {
      if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
        return index * m_preservedStrides[0];
      } else {
        return index * m_preservedStrides[NumPreservedStrides - 1];
      }
    }
    // TBD: optimize the case where we preserve the innermost dimensions.
    Index startInput = 0;
    if (static_cast<int>(Layout) == static_cast<int>(ColMajor)) {
      for (int i = NumOutputDims - 1; i > 0; --i) {
        // This is index_i in the output tensor.
        const Index idx = index / m_outputStrides[i];
        startInput += idx * m_preservedStrides[i];
        index -= idx * m_outputStrides[i];
      }
      if (PreservingInnerMostDims) {
        eigen_assert(m_preservedStrides[0] == 1);
        startInput += index;
      } else {
        startInput += index * m_preservedStrides[0];
      }
    } else {
      for (int i = 0; i < NumOutputDims - 1; ++i) {
        // This is index_i in the output tensor.
        const Index idx = index / m_outputStrides[i];
        startInput += idx * m_preservedStrides[i];
        index -= idx * m_outputStrides[i];
      }
      if (PreservingInnerMostDims) {
        eigen_assert(m_preservedStrides[NumPreservedStrides - 1] == 1);
        startInput += index;
      } else {
        startInput += index * m_preservedStrides[NumPreservedStrides - 1];
      }
    }
    return startInput;
  }
 
  // Bitmap indicating if an input dimension is reduced or not.
  array<bool, NumInputDims> m_reduced;
  // Dimensions of the output of the operation.
  Dimensions m_dimensions;
  // Precomputed strides for the output tensor.
  // Avoid zero-sized arrays, since element access fails to compile on GPU.
  array<Index, (std::max)(NumOutputDims, 1)> m_outputStrides;
  array<internal::TensorIntDivisor<Index>, (std::max)(NumOutputDims, 1)> m_fastOutputStrides;
  array<Index, (std::max)(NumPreservedStrides, 1)> m_preservedStrides;
  // Map from output to input dimension index.
  array<Index, (std::max)(NumOutputDims, 1)> m_output_to_input_dim_map;
  // How many values go into each reduction
  Index m_numValuesToReduce;
 
  // Subset of strides of the input tensor for the reduced dimensions.
  // Indexed by reduced dimensions.
  array<Index, NumReducedDims> m_reducedStrides;
  // Size of the input dimensions that are reduced.
  // Indexed by reduced dimensions.
  array<Index, NumReducedDims> m_reducedDims;
 
  // Evaluator for the input expression.
  TensorEvaluator<ArgType, Device> m_impl;
 
  // Operation to apply for computing the reduction.
  Op m_reducer;
 
  EvaluatorPointerType m_result;
 
  const Device EIGEN_DEVICE_REF m_device;
};
 
template <typename Op, typename Dims, typename ArgType, template <class> class MakePointer_, typename Device>
struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device>
    : public TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> {
  typedef TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Device> Base;
  EIGEN_STRONG_INLINE TensorEvaluator(const typename Base::XprType& op, const Device& device) : Base(op, device) {}
};
 
template <typename Op, typename Dims, typename ArgType, template <class> class MakePointer_>
struct TensorEvaluator<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Eigen::SyclDevice>
    : public TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Eigen::SyclDevice> {
  typedef TensorReductionEvaluatorBase<const TensorReductionOp<Op, Dims, ArgType, MakePointer_>, Eigen::SyclDevice>
      Base;
  EIGEN_STRONG_INLINE TensorEvaluator(const typename Base::XprType& op, const Eigen::SyclDevice& device)
      : Base(op, device) {}
  // The coeff function in the base the recursive method which is not an standard layout and cannot be used in the SYCL
  // kernel
  // Therefore the coeff function should be overridden by for SYCL kernel
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Base::CoeffReturnType coeff(typename Base::Index index) const {
    return *(this->data() + index);
  }
  // The packet function in the base the recursive method which is not an standard layout and cannot be used in the SYCL
  // kernel
  // Therefore the packet function should be overridden by for SYCL kernel
  template <int LoadMode>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename Base::PacketReturnType packet(typename Base::Index index) const {
    return internal::pload<typename Base::PacketReturnType>(this->data() + index);
  }
};
 
}  // end namespace Eigen
 
#endif  // EIGEN_CXX11_TENSOR_TENSOR_REDUCTION_H