CoreEvaluators.h

Go to the documentation of this file.

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2011-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2011-2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// 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_COREEVALUATORS_H
#define EIGEN_COREEVALUATORS_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
// This class returns the evaluator kind from the expression storage kind.
// Default assumes index based accessors
template <typename StorageKind>
struct storage_kind_to_evaluator_kind {
  typedef IndexBased Kind;
};
 
// This class returns the evaluator shape from the expression storage kind.
// It can be Dense, Sparse, Triangular, Diagonal, SelfAdjoint, Band, etc.
template <typename StorageKind>
struct storage_kind_to_shape;
 
template <>
struct storage_kind_to_shape<Dense> {
  typedef DenseShape Shape;
};
template <>
struct storage_kind_to_shape<SolverStorage> {
  typedef SolverShape Shape;
};
template <>
struct storage_kind_to_shape<PermutationStorage> {
  typedef PermutationShape Shape;
};
template <>
struct storage_kind_to_shape<TranspositionsStorage> {
  typedef TranspositionsShape Shape;
};
 
// Evaluators have to be specialized with respect to various criteria such as:
//  - storage/structure/shape
//  - scalar type
//  - etc.
// Therefore, we need specialization of evaluator providing additional template arguments for each kind of evaluators.
// We currently distinguish the following kind of evaluators:
// - unary_evaluator    for expressions taking only one arguments (CwiseUnaryOp, CwiseUnaryView, Transpose,
// MatrixWrapper, ArrayWrapper, Reverse, Replicate)
// - binary_evaluator   for expression taking two arguments (CwiseBinaryOp)
// - ternary_evaluator   for expression taking three arguments (CwiseTernaryOp)
// - product_evaluator  for linear algebra products (Product); special case of binary_evaluator because it requires
// additional tags for dispatching.
// - mapbase_evaluator  for Map, Block, Ref
// - block_evaluator    for Block (special dispatching to a mapbase_evaluator or unary_evaluator)
 
template <typename T, typename Arg1Kind = typename evaluator_traits<typename T::Arg1>::Kind,
          typename Arg2Kind = typename evaluator_traits<typename T::Arg2>::Kind,
          typename Arg3Kind = typename evaluator_traits<typename T::Arg3>::Kind,
          typename Arg1Scalar = typename traits<typename T::Arg1>::Scalar,
          typename Arg2Scalar = typename traits<typename T::Arg2>::Scalar,
          typename Arg3Scalar = typename traits<typename T::Arg3>::Scalar>
struct ternary_evaluator;
 
template <typename T, typename LhsKind = typename evaluator_traits<typename T::Lhs>::Kind,
          typename RhsKind = typename evaluator_traits<typename T::Rhs>::Kind,
          typename LhsScalar = typename traits<typename T::Lhs>::Scalar,
          typename RhsScalar = typename traits<typename T::Rhs>::Scalar>
struct binary_evaluator;
 
template <typename T, typename Kind = typename evaluator_traits<typename T::NestedExpression>::Kind,
          typename Scalar = typename T::Scalar>
struct unary_evaluator;
 
// evaluator_traits<T> contains traits for evaluator<T>
 
template <typename T>
struct evaluator_traits_base {
  // by default, get evaluator kind and shape from storage
  typedef typename storage_kind_to_evaluator_kind<typename traits<T>::StorageKind>::Kind Kind;
  typedef typename storage_kind_to_shape<typename traits<T>::StorageKind>::Shape Shape;
};
 
// Default evaluator traits
template <typename T>
struct evaluator_traits : public evaluator_traits_base<T> {};
 
template <typename T, typename Shape = typename evaluator_traits<T>::Shape>
struct evaluator_assume_aliasing {
  static const bool value = false;
};
 
// By default, we assume a unary expression:
template <typename T>
struct evaluator : public unary_evaluator<T> {
  typedef unary_evaluator<T> Base;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const T& xpr) : Base(xpr) {}
};
 
// TODO: Think about const-correctness
template <typename T>
struct evaluator<const T> : evaluator<T> {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const T& xpr) : evaluator<T>(xpr) {}
};
 
// ---------- base class for all evaluators ----------
 
template <typename ExpressionType>
struct evaluator_base {
  // TODO that's not very nice to have to propagate all these traits. They are currently only needed to handle
  // outer,inner indices.
  typedef traits<ExpressionType> ExpressionTraits;
 
  enum { Alignment = 0 };
  // noncopyable:
  // Don't make this class inherit noncopyable as this kills EBO (Empty Base Optimization)
  // and make complex evaluator much larger than then should do.
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr evaluator_base() = default;
 
 private:
  EIGEN_DEVICE_FUNC evaluator_base(const evaluator_base&);
  EIGEN_DEVICE_FUNC const evaluator_base& operator=(const evaluator_base&);
};
 
// -------------------- Matrix and Array --------------------
//
// evaluator<PlainObjectBase> is a common base class for the
// Matrix and Array evaluators.
// Here we directly specialize evaluator. This is not really a unary expression, and it is, by definition, dense,
// so no need for more sophisticated dispatching.
 
// this helper permits to completely eliminate m_outerStride if it is known at compiletime.
template <typename Scalar, int OuterStride>
class plainobjectbase_evaluator_data {
 public:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plainobjectbase_evaluator_data(const Scalar* ptr, Index outerStride)
      : data(ptr) {
#ifndef EIGEN_INTERNAL_DEBUGGING
    EIGEN_UNUSED_VARIABLE(outerStride);
#endif
    eigen_internal_assert(outerStride == OuterStride);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index outerStride() const EIGEN_NOEXCEPT { return OuterStride; }
  const Scalar* data;
};
 
template <typename Scalar>
class plainobjectbase_evaluator_data<Scalar, Dynamic> {
 public:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr plainobjectbase_evaluator_data(const Scalar* ptr, Index outerStride)
      : data(ptr), m_outerStride(outerStride) {}
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Index outerStride() const { return m_outerStride; }
  const Scalar* data;
 
 protected:
  Index m_outerStride;
};
 
template <typename Derived>
struct evaluator<PlainObjectBase<Derived>> : evaluator_base<Derived> {
  typedef PlainObjectBase<Derived> PlainObjectType;
  typedef typename PlainObjectType::Scalar Scalar;
  typedef typename PlainObjectType::CoeffReturnType CoeffReturnType;
 
  enum {
    IsRowMajor = PlainObjectType::IsRowMajor,
    IsVectorAtCompileTime = PlainObjectType::IsVectorAtCompileTime,
    RowsAtCompileTime = PlainObjectType::RowsAtCompileTime,
    ColsAtCompileTime = PlainObjectType::ColsAtCompileTime,
 
    CoeffReadCost = NumTraits<Scalar>::ReadCost,
    Flags = traits<Derived>::EvaluatorFlags,
    Alignment = traits<Derived>::Alignment
  };
  enum {
    // We do not need to know the outer stride for vectors
    OuterStrideAtCompileTime = IsVectorAtCompileTime ? 0
                               : int(IsRowMajor)     ? ColsAtCompileTime
                                                     : RowsAtCompileTime
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr evaluator() : m_d(0, OuterStrideAtCompileTime) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr explicit evaluator(const PlainObjectType& m)
      : m_d(m.data(), IsVectorAtCompileTime ? 0 : m.outerStride()) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index row, Index col) const {
    if (IsRowMajor)
      return m_d.data[row * m_d.outerStride() + col];
    else
      return m_d.data[row + col * m_d.outerStride()];
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr CoeffReturnType coeff(Index index) const { return m_d.data[index]; }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index row, Index col) {
    if (IsRowMajor)
      return const_cast<Scalar*>(m_d.data)[row * m_d.outerStride() + col];
    else
      return const_cast<Scalar*>(m_d.data)[row + col * m_d.outerStride()];
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr Scalar& coeffRef(Index index) {
    return const_cast<Scalar*>(m_d.data)[index];
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    if (IsRowMajor)
      return ploadt<PacketType, LoadMode>(m_d.data + row * m_d.outerStride() + col);
    else
      return ploadt<PacketType, LoadMode>(m_d.data + row + col * m_d.outerStride());
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return ploadt<PacketType, LoadMode>(m_d.data + index);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketType& x) {
    if (IsRowMajor)
      return pstoret<Scalar, PacketType, StoreMode>(const_cast<Scalar*>(m_d.data) + row * m_d.outerStride() + col, x);
    else
      return pstoret<Scalar, PacketType, StoreMode>(const_cast<Scalar*>(m_d.data) + row + col * m_d.outerStride(), x);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index index, const PacketType& x) {
    return pstoret<Scalar, PacketType, StoreMode>(const_cast<Scalar*>(m_d.data) + index, x);
  }
 
 protected:
  plainobjectbase_evaluator_data<Scalar, OuterStrideAtCompileTime> m_d;
};
 
template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct evaluator<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols>>
    : evaluator<PlainObjectBase<Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols>>> {
  typedef Matrix<Scalar, Rows, Cols, Options, MaxRows, MaxCols> XprType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr evaluator() = default;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr explicit evaluator(const XprType& m)
      : evaluator<PlainObjectBase<XprType>>(m) {}
};
 
template <typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct evaluator<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols>>
    : evaluator<PlainObjectBase<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols>>> {
  typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> XprType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr evaluator() = default;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE constexpr explicit evaluator(const XprType& m)
      : evaluator<PlainObjectBase<XprType>>(m) {}
};
 
// -------------------- Transpose --------------------
 
template <typename ArgType>
struct unary_evaluator<Transpose<ArgType>, IndexBased> : evaluator_base<Transpose<ArgType>> {
  typedef Transpose<ArgType> XprType;
 
  enum {
    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
    Flags = evaluator<ArgType>::Flags ^ RowMajorBit,
    Alignment = evaluator<ArgType>::Alignment
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& t) : m_argImpl(t.nestedExpression()) {}
 
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_argImpl.coeff(col, row);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const { return m_argImpl.coeff(index); }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) { return m_argImpl.coeffRef(col, row); }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename XprType::Scalar& coeffRef(Index index) {
    return m_argImpl.coeffRef(index);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    return m_argImpl.template packet<LoadMode, PacketType>(col, row);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return m_argImpl.template packet<LoadMode, PacketType>(index);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketType& x) {
    m_argImpl.template writePacket<StoreMode, PacketType>(col, row, x);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index index, const PacketType& x) {
    m_argImpl.template writePacket<StoreMode, PacketType>(index, x);
  }
 
 protected:
  evaluator<ArgType> m_argImpl;
};
 
// -------------------- CwiseNullaryOp --------------------
// Like Matrix and Array, this is not really a unary expression, so we directly specialize evaluator.
// Likewise, there is not need to more sophisticated dispatching here.
 
template <typename Scalar, typename NullaryOp, bool has_nullary = has_nullary_operator<NullaryOp>::value,
          bool has_unary = has_unary_operator<NullaryOp>::value,
          bool has_binary = has_binary_operator<NullaryOp>::value>
struct nullary_wrapper {
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {
    return op(i, j);
  }
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const {
    return op(i);
  }
 
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {
    return op.template packetOp<T>(i, j);
  }
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const {
    return op.template packetOp<T>(i);
  }
};
 
template <typename Scalar, typename NullaryOp>
struct nullary_wrapper<Scalar, NullaryOp, true, false, false> {
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType = 0, IndexType = 0) const {
    return op();
  }
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType = 0, IndexType = 0) const {
    return op.template packetOp<T>();
  }
};
 
template <typename Scalar, typename NullaryOp>
struct nullary_wrapper<Scalar, NullaryOp, false, false, true> {
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j = 0) const {
    return op(i, j);
  }
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j = 0) const {
    return op.template packetOp<T>(i, j);
  }
};
 
// We need the following specialization for vector-only functors assigned to a runtime vector,
// for instance, using linspace and assigning a RowVectorXd to a MatrixXd or even a row of a MatrixXd.
// In this case, i==0 and j is used for the actual iteration.
template <typename Scalar, typename NullaryOp>
struct nullary_wrapper<Scalar, NullaryOp, false, true, false> {
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {
    eigen_assert(i == 0 || j == 0);
    return op(i + j);
  }
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {
    eigen_assert(i == 0 || j == 0);
    return op.template packetOp<T>(i + j);
  }
 
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const {
    return op(i);
  }
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const {
    return op.template packetOp<T>(i);
  }
};
 
template <typename Scalar, typename NullaryOp>
struct nullary_wrapper<Scalar, NullaryOp, false, false, false> {};
 
#if 0 && EIGEN_COMP_MSVC > 0
// Disable this ugly workaround. This is now handled in traits<Ref>::match,
// but this piece of code might still become handly if some other weird compilation
// errors pop up again.
 
// MSVC exhibits a weird compilation error when
// compiling:
//    Eigen::MatrixXf A = MatrixXf::Random(3,3);
//    Ref<const MatrixXf> R = 2.f*A;
// and that has_*ary_operator<scalar_constant_op<float>> have not been instantiated yet.
// The "problem" is that evaluator<2.f*A> is instantiated by traits<Ref>::match<2.f*A>
// and at that time has_*ary_operator<T> returns true regardless of T.
// Then nullary_wrapper is badly instantiated as nullary_wrapper<.,.,true,true,true>.
// The trick is thus to defer the proper instantiation of nullary_wrapper when coeff(),
// and packet() are really instantiated as implemented below:
 
// This is a simple wrapper around Index to enforce the re-instantiation of
// has_*ary_operator when needed.
template<typename T> struct nullary_wrapper_workaround_msvc {
  nullary_wrapper_workaround_msvc(const T&);
  operator T()const;
};
 
template<typename Scalar,typename NullaryOp>
struct nullary_wrapper<Scalar,NullaryOp,true,true,true>
{
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i, IndexType j) const {
    return nullary_wrapper<Scalar,NullaryOp,
    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().operator()(op,i,j);
  }
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const NullaryOp& op, IndexType i) const {
    return nullary_wrapper<Scalar,NullaryOp,
    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().operator()(op,i);
  }
 
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i, IndexType j) const {
    return nullary_wrapper<Scalar,NullaryOp,
    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().template packetOp<T>(op,i,j);
  }
  template <typename T, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T packetOp(const NullaryOp& op, IndexType i) const {
    return nullary_wrapper<Scalar,NullaryOp,
    has_nullary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_unary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value,
    has_binary_operator<NullaryOp,nullary_wrapper_workaround_msvc<IndexType> >::value>().template packetOp<T>(op,i);
  }
};
#endif  // MSVC workaround
 
template <typename NullaryOp, typename PlainObjectType>
struct evaluator<CwiseNullaryOp<NullaryOp, PlainObjectType>>
    : evaluator_base<CwiseNullaryOp<NullaryOp, PlainObjectType>> {
  typedef CwiseNullaryOp<NullaryOp, PlainObjectType> XprType;
  typedef internal::remove_all_t<PlainObjectType> PlainObjectTypeCleaned;
 
  enum {
    CoeffReadCost = internal::functor_traits<NullaryOp>::Cost,
 
    Flags = (evaluator<PlainObjectTypeCleaned>::Flags &
             (HereditaryBits | (functor_has_linear_access<NullaryOp>::ret ? LinearAccessBit : 0) |
              (functor_traits<NullaryOp>::PacketAccess ? PacketAccessBit : 0))) |
            (functor_traits<NullaryOp>::IsRepeatable ? 0 : EvalBeforeNestingBit),
    Alignment = AlignedMax
  };
 
  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& n) : m_functor(n.functor()), m_wrapper() {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(IndexType row, IndexType col) const {
    return m_wrapper(m_functor, row, col);
  }
 
  template <typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(IndexType index) const {
    return m_wrapper(m_functor, index);
  }
 
  template <int LoadMode, typename PacketType, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(IndexType row, IndexType col) const {
    return m_wrapper.template packetOp<PacketType>(m_functor, row, col);
  }
 
  template <int LoadMode, typename PacketType, typename IndexType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(IndexType index) const {
    return m_wrapper.template packetOp<PacketType>(m_functor, index);
  }
 
 protected:
  const NullaryOp m_functor;
  const internal::nullary_wrapper<CoeffReturnType, NullaryOp> m_wrapper;
};
 
// -------------------- CwiseUnaryOp --------------------
 
template <typename UnaryOp, typename ArgType>
struct unary_evaluator<CwiseUnaryOp<UnaryOp, ArgType>, IndexBased> : evaluator_base<CwiseUnaryOp<UnaryOp, ArgType>> {
  typedef CwiseUnaryOp<UnaryOp, ArgType> XprType;
 
  enum {
    CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<UnaryOp>::Cost),
 
    Flags = evaluator<ArgType>::Flags &
            (HereditaryBits | LinearAccessBit | (functor_traits<UnaryOp>::PacketAccess ? PacketAccessBit : 0)),
    Alignment = evaluator<ArgType>::Alignment
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& op) : m_d(op) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_d.func()(m_d.argImpl.coeff(row, col));
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_d.func()(m_d.argImpl.coeff(index));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    return m_d.func().packetOp(m_d.argImpl.template packet<LoadMode, PacketType>(row, col));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return m_d.func().packetOp(m_d.argImpl.template packet<LoadMode, PacketType>(index));
  }
 
 protected:
  // this helper permits to completely eliminate the functor if it is empty
  struct Data {
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Data(const XprType& xpr)
        : op(xpr.functor()), argImpl(xpr.nestedExpression()) {}
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryOp& func() const { return op; }
    UnaryOp op;
    evaluator<ArgType> argImpl;
  };
 
  Data m_d;
};
 
// ----------------------- Casting ---------------------
 
template <typename SrcType, typename DstType, typename ArgType>
struct unary_evaluator<CwiseUnaryOp<core_cast_op<SrcType, DstType>, ArgType>, IndexBased> {
  using CastOp = core_cast_op<SrcType, DstType>;
  using XprType = CwiseUnaryOp<CastOp, ArgType>;
 
  // Use the largest packet type by default
  using SrcPacketType = typename packet_traits<SrcType>::type;
  static constexpr int SrcPacketSize = unpacket_traits<SrcPacketType>::size;
  static constexpr int SrcPacketBytes = SrcPacketSize * sizeof(SrcType);
 
  enum {
    CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<CastOp>::Cost),
    PacketAccess = functor_traits<CastOp>::PacketAccess,
    ActualPacketAccessBit = PacketAccess ? PacketAccessBit : 0,
    Flags = evaluator<ArgType>::Flags & (HereditaryBits | LinearAccessBit | ActualPacketAccessBit),
    IsRowMajor = (evaluator<ArgType>::Flags & RowMajorBit),
    Alignment = evaluator<ArgType>::Alignment
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& xpr)
      : m_argImpl(xpr.nestedExpression()), m_rows(xpr.rows()), m_cols(xpr.cols()) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<CastOp>::Cost);
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  template <typename DstPacketType>
  using AltSrcScalarOp = std::enable_if_t<(unpacket_traits<DstPacketType>::size < SrcPacketSize &&
                                           !find_packet_by_size<SrcType, unpacket_traits<DstPacketType>::size>::value),
                                          bool>;
  template <typename DstPacketType>
  using SrcPacketArgs1 =
      std::enable_if_t<(find_packet_by_size<SrcType, unpacket_traits<DstPacketType>::size>::value), bool>;
  template <typename DstPacketType>
  using SrcPacketArgs2 = std::enable_if_t<(unpacket_traits<DstPacketType>::size) == (2 * SrcPacketSize), bool>;
  template <typename DstPacketType>
  using SrcPacketArgs4 = std::enable_if_t<(unpacket_traits<DstPacketType>::size) == (4 * SrcPacketSize), bool>;
  template <typename DstPacketType>
  using SrcPacketArgs8 = std::enable_if_t<(unpacket_traits<DstPacketType>::size) == (8 * SrcPacketSize), bool>;
 
  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<UseRowMajor, bool> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_array_bounds(Index, Index col, Index packetSize) const {
    return col + packetSize <= cols();
  }
  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<!UseRowMajor, bool> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_array_bounds(Index row, Index, Index packetSize) const {
    return row + packetSize <= rows();
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool check_array_bounds(Index index, Index packetSize) const {
    return index + packetSize <= size();
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE SrcType srcCoeff(Index row, Index col, Index offset) const {
    Index actualRow = IsRowMajor ? row : row + offset;
    Index actualCol = IsRowMajor ? col + offset : col;
    return m_argImpl.coeff(actualRow, actualCol);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE SrcType srcCoeff(Index index, Index offset) const {
    Index actualIndex = index + offset;
    return m_argImpl.coeff(actualIndex);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstType coeff(Index row, Index col) const {
    return cast<SrcType, DstType>(srcCoeff(row, col, 0));
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstType coeff(Index index) const {
    return cast<SrcType, DstType>(srcCoeff(index, 0));
  }
 
  template <int LoadMode, typename PacketType = SrcPacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType srcPacket(Index row, Index col, Index offset) const {
    constexpr int PacketSize = unpacket_traits<PacketType>::size;
    Index actualRow = IsRowMajor ? row : row + (offset * PacketSize);
    Index actualCol = IsRowMajor ? col + (offset * PacketSize) : col;
    eigen_assert(check_array_bounds(actualRow, actualCol, PacketSize) && "Array index out of bounds");
    return m_argImpl.template packet<LoadMode, PacketType>(actualRow, actualCol);
  }
  template <int LoadMode, typename PacketType = SrcPacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType srcPacket(Index index, Index offset) const {
    constexpr int PacketSize = unpacket_traits<PacketType>::size;
    Index actualIndex = index + (offset * PacketSize);
    eigen_assert(check_array_bounds(actualIndex, PacketSize) && "Array index out of bounds");
    return m_argImpl.template packet<LoadMode, PacketType>(actualIndex);
  }
 
  // There is no source packet type with equal or fewer elements than DstPacketType.
  // This is problematic as the evaluation loop may attempt to access data outside the bounds of the array.
  // For example, consider the cast utilizing pcast<Packet4f,Packet2d> with an array of size 4: {0.0f,1.0f,2.0f,3.0f}.
  // The first iteration of the evaluation loop will load 16 bytes: {0.0f,1.0f,2.0f,3.0f} and cast to {0.0,1.0}, which
  // is acceptable. The second iteration will load 16 bytes: {2.0f,3.0f,?,?}, which is outside the bounds of the array.
 
  // Instead, perform runtime check to determine if the load would access data outside the bounds of the array.
  // If not, perform full load. Otherwise, revert to a scalar loop to perform a partial load.
  // In either case, perform a vectorized cast of the source packet.
  template <int LoadMode, typename DstPacketType, AltSrcScalarOp<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
    SrcPacketType src;
    if (EIGEN_PREDICT_TRUE(check_array_bounds(row, col, SrcPacketSize))) {
      src = srcPacket<SrcLoadMode>(row, col, 0);
    } else {
      Array<SrcType, SrcPacketSize, 1> srcArray;
      for (size_t k = 0; k < DstPacketSize; k++) srcArray[k] = srcCoeff(row, col, k);
      for (size_t k = DstPacketSize; k < SrcPacketSize; k++) srcArray[k] = SrcType(0);
      src = pload<SrcPacketType>(srcArray.data());
    }
    return pcast<SrcPacketType, DstPacketType>(src);
  }
  // Use the source packet type with the same size as DstPacketType, if it exists
  template <int LoadMode, typename DstPacketType, SrcPacketArgs1<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
    using SizedSrcPacketType = typename find_packet_by_size<SrcType, DstPacketSize>::type;
    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
    return pcast<SizedSrcPacketType, DstPacketType>(srcPacket<SrcLoadMode, SizedSrcPacketType>(row, col, 0));
  }
  // unpacket_traits<DstPacketType>::size == 2 * SrcPacketSize
  template <int LoadMode, typename DstPacketType, SrcPacketArgs2<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
    return pcast<SrcPacketType, DstPacketType>(srcPacket<SrcLoadMode>(row, col, 0),
                                               srcPacket<SrcLoadMode>(row, col, 1));
  }
  // unpacket_traits<DstPacketType>::size == 4 * SrcPacketSize
  template <int LoadMode, typename DstPacketType, SrcPacketArgs4<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
    return pcast<SrcPacketType, DstPacketType>(srcPacket<SrcLoadMode>(row, col, 0), srcPacket<SrcLoadMode>(row, col, 1),
                                               srcPacket<SrcLoadMode>(row, col, 2),
                                               srcPacket<SrcLoadMode>(row, col, 3));
  }
  // unpacket_traits<DstPacketType>::size == 8 * SrcPacketSize
  template <int LoadMode, typename DstPacketType, SrcPacketArgs8<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index row, Index col) const {
    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
    return pcast<SrcPacketType, DstPacketType>(
        srcPacket<SrcLoadMode>(row, col, 0), srcPacket<SrcLoadMode>(row, col, 1), srcPacket<SrcLoadMode>(row, col, 2),
        srcPacket<SrcLoadMode>(row, col, 3), srcPacket<SrcLoadMode>(row, col, 4), srcPacket<SrcLoadMode>(row, col, 5),
        srcPacket<SrcLoadMode>(row, col, 6), srcPacket<SrcLoadMode>(row, col, 7));
  }
 
  // Analogous routines for linear access.
  template <int LoadMode, typename DstPacketType, AltSrcScalarOp<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
    SrcPacketType src;
    if (EIGEN_PREDICT_TRUE(check_array_bounds(index, SrcPacketSize))) {
      src = srcPacket<SrcLoadMode>(index, 0);
    } else {
      Array<SrcType, SrcPacketSize, 1> srcArray;
      for (size_t k = 0; k < DstPacketSize; k++) srcArray[k] = srcCoeff(index, k);
      for (size_t k = DstPacketSize; k < SrcPacketSize; k++) srcArray[k] = SrcType(0);
      src = pload<SrcPacketType>(srcArray.data());
    }
    return pcast<SrcPacketType, DstPacketType>(src);
  }
  template <int LoadMode, typename DstPacketType, SrcPacketArgs1<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
    constexpr int DstPacketSize = unpacket_traits<DstPacketType>::size;
    using SizedSrcPacketType = typename find_packet_by_size<SrcType, DstPacketSize>::type;
    constexpr int SrcBytesIncrement = DstPacketSize * sizeof(SrcType);
    constexpr int SrcLoadMode = plain_enum_min(SrcBytesIncrement, LoadMode);
    return pcast<SizedSrcPacketType, DstPacketType>(srcPacket<SrcLoadMode, SizedSrcPacketType>(index, 0));
  }
  template <int LoadMode, typename DstPacketType, SrcPacketArgs2<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
    return pcast<SrcPacketType, DstPacketType>(srcPacket<SrcLoadMode>(index, 0), srcPacket<SrcLoadMode>(index, 1));
  }
  template <int LoadMode, typename DstPacketType, SrcPacketArgs4<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
    return pcast<SrcPacketType, DstPacketType>(srcPacket<SrcLoadMode>(index, 0), srcPacket<SrcLoadMode>(index, 1),
                                               srcPacket<SrcLoadMode>(index, 2), srcPacket<SrcLoadMode>(index, 3));
  }
  template <int LoadMode, typename DstPacketType, SrcPacketArgs8<DstPacketType> = true>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DstPacketType packet(Index index) const {
    constexpr int SrcLoadMode = plain_enum_min(SrcPacketBytes, LoadMode);
    return pcast<SrcPacketType, DstPacketType>(srcPacket<SrcLoadMode>(index, 0), srcPacket<SrcLoadMode>(index, 1),
                                               srcPacket<SrcLoadMode>(index, 2), srcPacket<SrcLoadMode>(index, 3),
                                               srcPacket<SrcLoadMode>(index, 4), srcPacket<SrcLoadMode>(index, 5),
                                               srcPacket<SrcLoadMode>(index, 6), srcPacket<SrcLoadMode>(index, 7));
  }
 
  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index rows() const { return m_rows; }
  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index cols() const { return m_cols; }
  constexpr EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Index size() const { return m_rows * m_cols; }
 
 protected:
  const evaluator<ArgType> m_argImpl;
  const variable_if_dynamic<Index, XprType::RowsAtCompileTime> m_rows;
  const variable_if_dynamic<Index, XprType::ColsAtCompileTime> m_cols;
};
 
// -------------------- CwiseTernaryOp --------------------
 
// this is a ternary expression
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
struct evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>>
    : public ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>> {
  typedef CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> XprType;
  typedef ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>> Base;
 
  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : Base(xpr) {}
};
 
template <typename TernaryOp, typename Arg1, typename Arg2, typename Arg3>
struct ternary_evaluator<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>, IndexBased, IndexBased>
    : evaluator_base<CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>> {
  typedef CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3> XprType;
 
  enum {
    CoeffReadCost = int(evaluator<Arg1>::CoeffReadCost) + int(evaluator<Arg2>::CoeffReadCost) +
                    int(evaluator<Arg3>::CoeffReadCost) + int(functor_traits<TernaryOp>::Cost),
 
    Arg1Flags = evaluator<Arg1>::Flags,
    Arg2Flags = evaluator<Arg2>::Flags,
    Arg3Flags = evaluator<Arg3>::Flags,
    SameType = is_same<typename Arg1::Scalar, typename Arg2::Scalar>::value &&
               is_same<typename Arg1::Scalar, typename Arg3::Scalar>::value,
    StorageOrdersAgree = (int(Arg1Flags) & RowMajorBit) == (int(Arg2Flags) & RowMajorBit) &&
                         (int(Arg1Flags) & RowMajorBit) == (int(Arg3Flags) & RowMajorBit),
    Flags0 = (int(Arg1Flags) | int(Arg2Flags) | int(Arg3Flags)) &
             (HereditaryBits |
              (int(Arg1Flags) & int(Arg2Flags) & int(Arg3Flags) &
               ((StorageOrdersAgree ? LinearAccessBit : 0) |
                (functor_traits<TernaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)))),
    Flags = (Flags0 & ~RowMajorBit) | (Arg1Flags & RowMajorBit),
    Alignment = plain_enum_min(plain_enum_min(evaluator<Arg1>::Alignment, evaluator<Arg2>::Alignment),
                               evaluator<Arg3>::Alignment)
  };
 
  EIGEN_DEVICE_FUNC explicit ternary_evaluator(const XprType& xpr) : m_d(xpr) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<TernaryOp>::Cost);
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_d.func()(m_d.arg1Impl.coeff(row, col), m_d.arg2Impl.coeff(row, col), m_d.arg3Impl.coeff(row, col));
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_d.func()(m_d.arg1Impl.coeff(index), m_d.arg2Impl.coeff(index), m_d.arg3Impl.coeff(index));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    return m_d.func().packetOp(m_d.arg1Impl.template packet<LoadMode, PacketType>(row, col),
                               m_d.arg2Impl.template packet<LoadMode, PacketType>(row, col),
                               m_d.arg3Impl.template packet<LoadMode, PacketType>(row, col));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return m_d.func().packetOp(m_d.arg1Impl.template packet<LoadMode, PacketType>(index),
                               m_d.arg2Impl.template packet<LoadMode, PacketType>(index),
                               m_d.arg3Impl.template packet<LoadMode, PacketType>(index));
  }
 
 protected:
  // this helper permits to completely eliminate the functor if it is empty
  struct Data {
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Data(const XprType& xpr)
        : op(xpr.functor()), arg1Impl(xpr.arg1()), arg2Impl(xpr.arg2()), arg3Impl(xpr.arg3()) {}
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const TernaryOp& func() const { return op; }
    TernaryOp op;
    evaluator<Arg1> arg1Impl;
    evaluator<Arg2> arg2Impl;
    evaluator<Arg3> arg3Impl;
  };
 
  Data m_d;
};
 
// specialization for expressions like (a < b).select(c, d) to enable full vectorization
template <typename Arg1, typename Arg2, typename Scalar, typename CmpLhsType, typename CmpRhsType, ComparisonName cmp>
struct evaluator<CwiseTernaryOp<scalar_boolean_select_op<Scalar, Scalar, bool>, Arg1, Arg2,
                                CwiseBinaryOp<scalar_cmp_op<Scalar, Scalar, cmp, false>, CmpLhsType, CmpRhsType>>>
    : public ternary_evaluator<
          CwiseTernaryOp<scalar_boolean_select_op<Scalar, Scalar, Scalar>, Arg1, Arg2,
                         CwiseBinaryOp<scalar_cmp_op<Scalar, Scalar, cmp, true>, CmpLhsType, CmpRhsType>>> {
  using DummyTernaryOp = scalar_boolean_select_op<Scalar, Scalar, bool>;
  using DummyArg3 = CwiseBinaryOp<scalar_cmp_op<Scalar, Scalar, cmp, false>, CmpLhsType, CmpRhsType>;
  using DummyXprType = CwiseTernaryOp<DummyTernaryOp, Arg1, Arg2, DummyArg3>;
 
  using TernaryOp = scalar_boolean_select_op<Scalar, Scalar, Scalar>;
  using Arg3 = CwiseBinaryOp<scalar_cmp_op<Scalar, Scalar, cmp, true>, CmpLhsType, CmpRhsType>;
  using XprType = CwiseTernaryOp<TernaryOp, Arg1, Arg2, Arg3>;
 
  using Base = ternary_evaluator<XprType>;
 
  EIGEN_DEVICE_FUNC explicit evaluator(const DummyXprType& xpr)
      : Base(XprType(xpr.arg1(), xpr.arg2(), Arg3(xpr.arg3().lhs(), xpr.arg3().rhs()))) {}
};
 
// -------------------- CwiseBinaryOp --------------------
 
// this is a binary expression
template <typename BinaryOp, typename Lhs, typename Rhs>
struct evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>> : public binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>> {
  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
  typedef binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>> Base;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& xpr) : Base(xpr) {}
};
 
template <typename BinaryOp, typename Lhs, typename Rhs>
struct binary_evaluator<CwiseBinaryOp<BinaryOp, Lhs, Rhs>, IndexBased, IndexBased>
    : evaluator_base<CwiseBinaryOp<BinaryOp, Lhs, Rhs>> {
  typedef CwiseBinaryOp<BinaryOp, Lhs, Rhs> XprType;
 
  enum {
    CoeffReadCost =
        int(evaluator<Lhs>::CoeffReadCost) + int(evaluator<Rhs>::CoeffReadCost) + int(functor_traits<BinaryOp>::Cost),
 
    LhsFlags = evaluator<Lhs>::Flags,
    RhsFlags = evaluator<Rhs>::Flags,
    SameType = is_same<typename Lhs::Scalar, typename Rhs::Scalar>::value,
    StorageOrdersAgree = (int(LhsFlags) & RowMajorBit) == (int(RhsFlags) & RowMajorBit),
    Flags0 = (int(LhsFlags) | int(RhsFlags)) &
             (HereditaryBits |
              (int(LhsFlags) & int(RhsFlags) &
               ((StorageOrdersAgree ? LinearAccessBit : 0) |
                (functor_traits<BinaryOp>::PacketAccess && StorageOrdersAgree && SameType ? PacketAccessBit : 0)))),
    Flags = (Flags0 & ~RowMajorBit) | (LhsFlags & RowMajorBit),
    Alignment = plain_enum_min(evaluator<Lhs>::Alignment, evaluator<Rhs>::Alignment)
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit binary_evaluator(const XprType& xpr) : m_d(xpr) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<BinaryOp>::Cost);
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_d.func()(m_d.lhsImpl.coeff(row, col), m_d.rhsImpl.coeff(row, col));
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_d.func()(m_d.lhsImpl.coeff(index), m_d.rhsImpl.coeff(index));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    return m_d.func().packetOp(m_d.lhsImpl.template packet<LoadMode, PacketType>(row, col),
                               m_d.rhsImpl.template packet<LoadMode, PacketType>(row, col));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return m_d.func().packetOp(m_d.lhsImpl.template packet<LoadMode, PacketType>(index),
                               m_d.rhsImpl.template packet<LoadMode, PacketType>(index));
  }
 
 protected:
  // this helper permits to completely eliminate the functor if it is empty
  struct Data {
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Data(const XprType& xpr)
        : op(xpr.functor()), lhsImpl(xpr.lhs()), rhsImpl(xpr.rhs()) {}
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const BinaryOp& func() const { return op; }
    BinaryOp op;
    evaluator<Lhs> lhsImpl;
    evaluator<Rhs> rhsImpl;
  };
 
  Data m_d;
};
 
// -------------------- CwiseUnaryView --------------------
 
template <typename UnaryOp, typename ArgType, typename StrideType>
struct unary_evaluator<CwiseUnaryView<UnaryOp, ArgType, StrideType>, IndexBased>
    : evaluator_base<CwiseUnaryView<UnaryOp, ArgType, StrideType>> {
  typedef CwiseUnaryView<UnaryOp, ArgType, StrideType> XprType;
 
  enum {
    CoeffReadCost = int(evaluator<ArgType>::CoeffReadCost) + int(functor_traits<UnaryOp>::Cost),
 
    Flags = (evaluator<ArgType>::Flags & (HereditaryBits | LinearAccessBit | DirectAccessBit)),
 
    Alignment = 0  // FIXME it is not very clear why alignment is necessarily lost...
  };
 
  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op) : m_d(op) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(functor_traits<UnaryOp>::Cost);
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_d.func()(m_d.argImpl.coeff(row, col));
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_d.func()(m_d.argImpl.coeff(index));
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
    return m_d.func()(m_d.argImpl.coeffRef(row, col));
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
    return m_d.func()(m_d.argImpl.coeffRef(index));
  }
 
 protected:
  // this helper permits to completely eliminate the functor if it is empty
  struct Data {
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Data(const XprType& xpr)
        : op(xpr.functor()), argImpl(xpr.nestedExpression()) {}
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const UnaryOp& func() const { return op; }
    UnaryOp op;
    evaluator<ArgType> argImpl;
  };
 
  Data m_d;
};
 
// -------------------- Map --------------------
 
// FIXME perhaps the PlainObjectType could be provided by Derived::PlainObject ?
// but that might complicate template specialization
template <typename Derived, typename PlainObjectType>
struct mapbase_evaluator;
 
template <typename Derived, typename PlainObjectType>
struct mapbase_evaluator : evaluator_base<Derived> {
  typedef Derived XprType;
  typedef typename XprType::PointerType PointerType;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  enum {
    IsRowMajor = XprType::RowsAtCompileTime,
    ColsAtCompileTime = XprType::ColsAtCompileTime,
    CoeffReadCost = NumTraits<Scalar>::ReadCost
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit mapbase_evaluator(const XprType& map)
      : m_data(const_cast<PointerType>(map.data())),
        m_innerStride(map.innerStride()),
        m_outerStride(map.outerStride()) {
    EIGEN_STATIC_ASSERT(check_implication((evaluator<Derived>::Flags & PacketAccessBit) != 0,
                                          internal::inner_stride_at_compile_time<Derived>::ret == 1),
                        PACKET_ACCESS_REQUIRES_TO_HAVE_INNER_STRIDE_FIXED_TO_1);
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_data[col * colStride() + row * rowStride()];
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_data[index * m_innerStride.value()];
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
    return m_data[col * colStride() + row * rowStride()];
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) { return m_data[index * m_innerStride.value()]; }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    PointerType ptr = m_data + row * rowStride() + col * colStride();
    return internal::ploadt<PacketType, LoadMode>(ptr);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return internal::ploadt<PacketType, LoadMode>(m_data + index * m_innerStride.value());
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketType& x) {
    PointerType ptr = m_data + row * rowStride() + col * colStride();
    return internal::pstoret<Scalar, PacketType, StoreMode>(ptr, x);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index index, const PacketType& x) {
    internal::pstoret<Scalar, PacketType, StoreMode>(m_data + index * m_innerStride.value(), x);
  }
 
 protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rowStride() const EIGEN_NOEXCEPT {
    return XprType::IsRowMajor ? m_outerStride.value() : m_innerStride.value();
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index colStride() const EIGEN_NOEXCEPT {
    return XprType::IsRowMajor ? m_innerStride.value() : m_outerStride.value();
  }
 
  PointerType m_data;
  const internal::variable_if_dynamic<Index, XprType::InnerStrideAtCompileTime> m_innerStride;
  const internal::variable_if_dynamic<Index, XprType::OuterStrideAtCompileTime> m_outerStride;
};
 
template <typename PlainObjectType, int MapOptions, typename StrideType>
struct evaluator<Map<PlainObjectType, MapOptions, StrideType>>
    : public mapbase_evaluator<Map<PlainObjectType, MapOptions, StrideType>, PlainObjectType> {
  typedef Map<PlainObjectType, MapOptions, StrideType> XprType;
  typedef typename XprType::Scalar Scalar;
  // TODO: should check for smaller packet types once we can handle multi-sized packet types
  typedef typename packet_traits<Scalar>::type PacketScalar;
 
  enum {
    InnerStrideAtCompileTime = StrideType::InnerStrideAtCompileTime == 0
                                   ? int(PlainObjectType::InnerStrideAtCompileTime)
                                   : int(StrideType::InnerStrideAtCompileTime),
    OuterStrideAtCompileTime = StrideType::OuterStrideAtCompileTime == 0
                                   ? int(PlainObjectType::OuterStrideAtCompileTime)
                                   : int(StrideType::OuterStrideAtCompileTime),
    HasNoInnerStride = InnerStrideAtCompileTime == 1,
    HasNoOuterStride = StrideType::OuterStrideAtCompileTime == 0,
    HasNoStride = HasNoInnerStride && HasNoOuterStride,
    IsDynamicSize = PlainObjectType::SizeAtCompileTime == Dynamic,
 
    PacketAccessMask = bool(HasNoInnerStride) ? ~int(0) : ~int(PacketAccessBit),
    LinearAccessMask =
        bool(HasNoStride) || bool(PlainObjectType::IsVectorAtCompileTime) ? ~int(0) : ~int(LinearAccessBit),
    Flags = int(evaluator<PlainObjectType>::Flags) & (LinearAccessMask & PacketAccessMask),
 
    Alignment = int(MapOptions) & int(AlignedMask)
  };
 
  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& map) : mapbase_evaluator<XprType, PlainObjectType>(map) {}
};
 
// -------------------- Ref --------------------
 
template <typename PlainObjectType, int RefOptions, typename StrideType>
struct evaluator<Ref<PlainObjectType, RefOptions, StrideType>>
    : public mapbase_evaluator<Ref<PlainObjectType, RefOptions, StrideType>, PlainObjectType> {
  typedef Ref<PlainObjectType, RefOptions, StrideType> XprType;
 
  enum {
    Flags = evaluator<Map<PlainObjectType, RefOptions, StrideType>>::Flags,
    Alignment = evaluator<Map<PlainObjectType, RefOptions, StrideType>>::Alignment
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& ref)
      : mapbase_evaluator<XprType, PlainObjectType>(ref) {}
};
 
// -------------------- Block --------------------
 
template <typename ArgType, int BlockRows, int BlockCols, bool InnerPanel,
          bool HasDirectAccess = internal::has_direct_access<ArgType>::ret>
struct block_evaluator;
 
template <typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
struct evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>>
    : block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel> {
  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
  typedef typename XprType::Scalar Scalar;
  // TODO: should check for smaller packet types once we can handle multi-sized packet types
  typedef typename packet_traits<Scalar>::type PacketScalar;
 
  enum {
    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
 
    RowsAtCompileTime = traits<XprType>::RowsAtCompileTime,
    ColsAtCompileTime = traits<XprType>::ColsAtCompileTime,
    MaxRowsAtCompileTime = traits<XprType>::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = traits<XprType>::MaxColsAtCompileTime,
 
    ArgTypeIsRowMajor = (int(evaluator<ArgType>::Flags) & RowMajorBit) != 0,
    IsRowMajor = (MaxRowsAtCompileTime == 1 && MaxColsAtCompileTime != 1)   ? 1
                 : (MaxColsAtCompileTime == 1 && MaxRowsAtCompileTime != 1) ? 0
                                                                            : ArgTypeIsRowMajor,
    HasSameStorageOrderAsArgType = (IsRowMajor == ArgTypeIsRowMajor),
    InnerSize = IsRowMajor ? int(ColsAtCompileTime) : int(RowsAtCompileTime),
    InnerStrideAtCompileTime = HasSameStorageOrderAsArgType ? int(inner_stride_at_compile_time<ArgType>::ret)
                                                            : int(outer_stride_at_compile_time<ArgType>::ret),
    OuterStrideAtCompileTime = HasSameStorageOrderAsArgType ? int(outer_stride_at_compile_time<ArgType>::ret)
                                                            : int(inner_stride_at_compile_time<ArgType>::ret),
    MaskPacketAccessBit = (InnerStrideAtCompileTime == 1 || HasSameStorageOrderAsArgType) ? PacketAccessBit : 0,
 
    FlagsLinearAccessBit = (RowsAtCompileTime == 1 || ColsAtCompileTime == 1 ||
                            (InnerPanel && (evaluator<ArgType>::Flags & LinearAccessBit)))
                               ? LinearAccessBit
                               : 0,
    FlagsRowMajorBit = XprType::Flags & RowMajorBit,
    Flags0 = evaluator<ArgType>::Flags & ((HereditaryBits & ~RowMajorBit) | DirectAccessBit | MaskPacketAccessBit),
    Flags = Flags0 | FlagsLinearAccessBit | FlagsRowMajorBit,
 
    PacketAlignment = unpacket_traits<PacketScalar>::alignment,
    Alignment0 = (InnerPanel && (OuterStrideAtCompileTime != Dynamic) && (OuterStrideAtCompileTime != 0) &&
                  (((OuterStrideAtCompileTime * int(sizeof(Scalar))) % int(PacketAlignment)) == 0))
                     ? int(PacketAlignment)
                     : 0,
    Alignment = plain_enum_min(evaluator<ArgType>::Alignment, Alignment0)
  };
  typedef block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel> block_evaluator_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& block) : block_evaluator_type(block) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
};
 
// no direct-access => dispatch to a unary evaluator
template <typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
struct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /*HasDirectAccess*/ false>
    : unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>> {
  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit block_evaluator(const XprType& block)
      : unary_evaluator<XprType>(block) {}
};
 
template <typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
struct unary_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>, IndexBased>
    : evaluator_base<Block<ArgType, BlockRows, BlockCols, InnerPanel>> {
  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& block)
      : m_argImpl(block.nestedExpression()),
        m_startRow(block.startRow()),
        m_startCol(block.startCol()),
        m_linear_offset(ForwardLinearAccess
                            ? (ArgType::IsRowMajor
                                   ? block.startRow() * block.nestedExpression().cols() + block.startCol()
                                   : block.startCol() * block.nestedExpression().rows() + block.startRow())
                            : 0) {}
 
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  enum {
    RowsAtCompileTime = XprType::RowsAtCompileTime,
    ForwardLinearAccess = (InnerPanel || int(XprType::IsRowMajor) == int(ArgType::IsRowMajor)) &&
                          bool(evaluator<ArgType>::Flags & LinearAccessBit)
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_argImpl.coeff(m_startRow.value() + row, m_startCol.value() + col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return linear_coeff_impl(index, bool_constant<ForwardLinearAccess>());
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
    return m_argImpl.coeffRef(m_startRow.value() + row, m_startCol.value() + col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
    return linear_coeffRef_impl(index, bool_constant<ForwardLinearAccess>());
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    return m_argImpl.template packet<LoadMode, PacketType>(m_startRow.value() + row, m_startCol.value() + col);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    if (ForwardLinearAccess)
      return m_argImpl.template packet<LoadMode, PacketType>(m_linear_offset.value() + index);
    else
      return packet<LoadMode, PacketType>(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketType& x) {
    return m_argImpl.template writePacket<StoreMode, PacketType>(m_startRow.value() + row, m_startCol.value() + col, x);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index index, const PacketType& x) {
    if (ForwardLinearAccess)
      return m_argImpl.template writePacket<StoreMode, PacketType>(m_linear_offset.value() + index, x);
    else
      return writePacket<StoreMode, PacketType>(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0,
                                                x);
  }
 
 protected:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType
  linear_coeff_impl(Index index, internal::true_type /* ForwardLinearAccess */) const {
    return m_argImpl.coeff(m_linear_offset.value() + index);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType
  linear_coeff_impl(Index index, internal::false_type /* not ForwardLinearAccess */) const {
    return coeff(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& linear_coeffRef_impl(Index index,
                                                                     internal::true_type /* ForwardLinearAccess */) {
    return m_argImpl.coeffRef(m_linear_offset.value() + index);
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& linear_coeffRef_impl(
      Index index, internal::false_type /* not ForwardLinearAccess */) {
    return coeffRef(RowsAtCompileTime == 1 ? 0 : index, RowsAtCompileTime == 1 ? index : 0);
  }
 
  evaluator<ArgType> m_argImpl;
  const variable_if_dynamic<Index, (ArgType::RowsAtCompileTime == 1 && BlockRows == 1) ? 0 : Dynamic> m_startRow;
  const variable_if_dynamic<Index, (ArgType::ColsAtCompileTime == 1 && BlockCols == 1) ? 0 : Dynamic> m_startCol;
  const variable_if_dynamic<Index, ForwardLinearAccess ? Dynamic : 0> m_linear_offset;
};
 
// TODO: This evaluator does not actually use the child evaluator;
// all action is via the data() as returned by the Block expression.
 
template <typename ArgType, int BlockRows, int BlockCols, bool InnerPanel>
struct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /* HasDirectAccess */ true>
    : mapbase_evaluator<Block<ArgType, BlockRows, BlockCols, InnerPanel>,
                        typename Block<ArgType, BlockRows, BlockCols, InnerPanel>::PlainObject> {
  typedef Block<ArgType, BlockRows, BlockCols, InnerPanel> XprType;
  typedef typename XprType::Scalar Scalar;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit block_evaluator(const XprType& block)
      : mapbase_evaluator<XprType, typename XprType::PlainObject>(block) {
    eigen_internal_assert((internal::is_constant_evaluated() ||
                           (std::uintptr_t(block.data()) % plain_enum_max(1, evaluator<XprType>::Alignment)) == 0) &&
                          "data is not aligned");
  }
};
 
// -------------------- Select --------------------
// NOTE shall we introduce a ternary_evaluator?
 
// TODO enable vectorization for Select
template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
struct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType>>
    : evaluator_base<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType>> {
  typedef Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> XprType;
  enum {
    CoeffReadCost = evaluator<ConditionMatrixType>::CoeffReadCost +
                    plain_enum_max(evaluator<ThenMatrixType>::CoeffReadCost, evaluator<ElseMatrixType>::CoeffReadCost),
 
    Flags = (unsigned int)evaluator<ThenMatrixType>::Flags & evaluator<ElseMatrixType>::Flags & HereditaryBits,
 
    Alignment = plain_enum_min(evaluator<ThenMatrixType>::Alignment, evaluator<ElseMatrixType>::Alignment)
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& select)
      : m_conditionImpl(select.conditionMatrix()), m_thenImpl(select.thenMatrix()), m_elseImpl(select.elseMatrix()) {
    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
  }
 
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    if (m_conditionImpl.coeff(row, col))
      return m_thenImpl.coeff(row, col);
    else
      return m_elseImpl.coeff(row, col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    if (m_conditionImpl.coeff(index))
      return m_thenImpl.coeff(index);
    else
      return m_elseImpl.coeff(index);
  }
 
 protected:
  evaluator<ConditionMatrixType> m_conditionImpl;
  evaluator<ThenMatrixType> m_thenImpl;
  evaluator<ElseMatrixType> m_elseImpl;
};
 
// -------------------- Replicate --------------------
 
template <typename ArgType, int RowFactor, int ColFactor>
struct unary_evaluator<Replicate<ArgType, RowFactor, ColFactor>>
    : evaluator_base<Replicate<ArgType, RowFactor, ColFactor>> {
  typedef Replicate<ArgType, RowFactor, ColFactor> XprType;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  enum { Factor = (RowFactor == Dynamic || ColFactor == Dynamic) ? Dynamic : RowFactor * ColFactor };
  typedef typename internal::nested_eval<ArgType, Factor>::type ArgTypeNested;
  typedef internal::remove_all_t<ArgTypeNested> ArgTypeNestedCleaned;
 
  enum {
    CoeffReadCost = evaluator<ArgTypeNestedCleaned>::CoeffReadCost,
    LinearAccessMask = XprType::IsVectorAtCompileTime ? LinearAccessBit : 0,
    Flags = (evaluator<ArgTypeNestedCleaned>::Flags & (HereditaryBits | LinearAccessMask) & ~RowMajorBit) |
            (traits<XprType>::Flags & RowMajorBit),
 
    Alignment = evaluator<ArgTypeNestedCleaned>::Alignment
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& replicate)
      : m_arg(replicate.nestedExpression()),
        m_argImpl(m_arg),
        m_rows(replicate.nestedExpression().rows()),
        m_cols(replicate.nestedExpression().cols()) {}
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    // try to avoid using modulo; this is a pure optimization strategy
    const Index actual_row = internal::traits<XprType>::RowsAtCompileTime == 1 ? 0
                             : RowFactor == 1                                  ? row
                                                                               : row % m_rows.value();
    const Index actual_col = internal::traits<XprType>::ColsAtCompileTime == 1 ? 0
                             : ColFactor == 1                                  ? col
                                                                               : col % m_cols.value();
 
    return m_argImpl.coeff(actual_row, actual_col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    // try to avoid using modulo; this is a pure optimization strategy
    const Index actual_index = internal::traits<XprType>::RowsAtCompileTime == 1
                                   ? (ColFactor == 1 ? index : index % m_cols.value())
                                   : (RowFactor == 1 ? index : index % m_rows.value());
 
    return m_argImpl.coeff(actual_index);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    const Index actual_row = internal::traits<XprType>::RowsAtCompileTime == 1 ? 0
                             : RowFactor == 1                                  ? row
                                                                               : row % m_rows.value();
    const Index actual_col = internal::traits<XprType>::ColsAtCompileTime == 1 ? 0
                             : ColFactor == 1                                  ? col
                                                                               : col % m_cols.value();
 
    return m_argImpl.template packet<LoadMode, PacketType>(actual_row, actual_col);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    const Index actual_index = internal::traits<XprType>::RowsAtCompileTime == 1
                                   ? (ColFactor == 1 ? index : index % m_cols.value())
                                   : (RowFactor == 1 ? index : index % m_rows.value());
 
    return m_argImpl.template packet<LoadMode, PacketType>(actual_index);
  }
 
 protected:
  const ArgTypeNested m_arg;
  evaluator<ArgTypeNestedCleaned> m_argImpl;
  const variable_if_dynamic<Index, ArgType::RowsAtCompileTime> m_rows;
  const variable_if_dynamic<Index, ArgType::ColsAtCompileTime> m_cols;
};
 
// -------------------- MatrixWrapper and ArrayWrapper --------------------
//
// evaluator_wrapper_base<T> is a common base class for the
// MatrixWrapper and ArrayWrapper evaluators.
 
template <typename XprType>
struct evaluator_wrapper_base : evaluator_base<XprType> {
  typedef remove_all_t<typename XprType::NestedExpressionType> ArgType;
  enum {
    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
    Flags = evaluator<ArgType>::Flags,
    Alignment = evaluator<ArgType>::Alignment
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator_wrapper_base(const ArgType& arg) : m_argImpl(arg) {}
 
  typedef typename ArgType::Scalar Scalar;
  typedef typename ArgType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_argImpl.coeff(row, col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const { return m_argImpl.coeff(index); }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) { return m_argImpl.coeffRef(row, col); }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) { return m_argImpl.coeffRef(index); }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    return m_argImpl.template packet<LoadMode, PacketType>(row, col);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    return m_argImpl.template packet<LoadMode, PacketType>(index);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketType& x) {
    m_argImpl.template writePacket<StoreMode>(row, col, x);
  }
 
  template <int StoreMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index index, const PacketType& x) {
    m_argImpl.template writePacket<StoreMode>(index, x);
  }
 
 protected:
  evaluator<ArgType> m_argImpl;
};
 
template <typename TArgType>
struct unary_evaluator<MatrixWrapper<TArgType>> : evaluator_wrapper_base<MatrixWrapper<TArgType>> {
  typedef MatrixWrapper<TArgType> XprType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& wrapper)
      : evaluator_wrapper_base<MatrixWrapper<TArgType>>(wrapper.nestedExpression()) {}
};
 
template <typename TArgType>
struct unary_evaluator<ArrayWrapper<TArgType>> : evaluator_wrapper_base<ArrayWrapper<TArgType>> {
  typedef ArrayWrapper<TArgType> XprType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& wrapper)
      : evaluator_wrapper_base<ArrayWrapper<TArgType>>(wrapper.nestedExpression()) {}
};
 
// -------------------- Reverse --------------------
 
// defined in Reverse.h:
template <typename PacketType, bool ReversePacket>
struct reverse_packet_cond;
 
template <typename ArgType, int Direction>
struct unary_evaluator<Reverse<ArgType, Direction>> : evaluator_base<Reverse<ArgType, Direction>> {
  typedef Reverse<ArgType, Direction> XprType;
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  enum {
    IsRowMajor = XprType::IsRowMajor,
    IsColMajor = !IsRowMajor,
    ReverseRow = (Direction == Vertical) || (Direction == BothDirections),
    ReverseCol = (Direction == Horizontal) || (Direction == BothDirections),
    ReversePacket = (Direction == BothDirections) || ((Direction == Vertical) && IsColMajor) ||
                    ((Direction == Horizontal) && IsRowMajor),
 
    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
 
    // let's enable LinearAccess only with vectorization because of the product overhead
    // FIXME enable DirectAccess with negative strides?
    Flags0 = evaluator<ArgType>::Flags,
    LinearAccess =
        ((Direction == BothDirections) && (int(Flags0) & PacketAccessBit)) ||
                ((ReverseRow && XprType::ColsAtCompileTime == 1) || (ReverseCol && XprType::RowsAtCompileTime == 1))
            ? LinearAccessBit
            : 0,
 
    Flags = int(Flags0) & (HereditaryBits | PacketAccessBit | LinearAccess),
 
    Alignment = 0  // FIXME in some rare cases, Alignment could be preserved, like a Vector4f.
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit unary_evaluator(const XprType& reverse)
      : m_argImpl(reverse.nestedExpression()),
        m_rows(ReverseRow ? reverse.nestedExpression().rows() : 1),
        m_cols(ReverseCol ? reverse.nestedExpression().cols() : 1) {}
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_argImpl.coeff(ReverseRow ? m_rows.value() - row - 1 : row, ReverseCol ? m_cols.value() - col - 1 : col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_argImpl.coeff(m_rows.value() * m_cols.value() - index - 1);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index col) {
    return m_argImpl.coeffRef(ReverseRow ? m_rows.value() - row - 1 : row, ReverseCol ? m_cols.value() - col - 1 : col);
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
    return m_argImpl.coeffRef(m_rows.value() * m_cols.value() - index - 1);
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index row, Index col) const {
    enum {
      PacketSize = unpacket_traits<PacketType>::size,
      OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
      OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1
    };
    typedef internal::reverse_packet_cond<PacketType, ReversePacket> reverse_packet;
    return reverse_packet::run(m_argImpl.template packet<LoadMode, PacketType>(
        ReverseRow ? m_rows.value() - row - OffsetRow : row, ReverseCol ? m_cols.value() - col - OffsetCol : col));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE PacketType packet(Index index) const {
    enum { PacketSize = unpacket_traits<PacketType>::size };
    return preverse(
        m_argImpl.template packet<LoadMode, PacketType>(m_rows.value() * m_cols.value() - index - PacketSize));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index row, Index col, const PacketType& x) {
    // FIXME we could factorize some code with packet(i,j)
    enum {
      PacketSize = unpacket_traits<PacketType>::size,
      OffsetRow = ReverseRow && IsColMajor ? PacketSize : 1,
      OffsetCol = ReverseCol && IsRowMajor ? PacketSize : 1
    };
    typedef internal::reverse_packet_cond<PacketType, ReversePacket> reverse_packet;
    m_argImpl.template writePacket<LoadMode>(ReverseRow ? m_rows.value() - row - OffsetRow : row,
                                             ReverseCol ? m_cols.value() - col - OffsetCol : col,
                                             reverse_packet::run(x));
  }
 
  template <int LoadMode, typename PacketType>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void writePacket(Index index, const PacketType& x) {
    enum { PacketSize = unpacket_traits<PacketType>::size };
    m_argImpl.template writePacket<LoadMode>(m_rows.value() * m_cols.value() - index - PacketSize, preverse(x));
  }
 
 protected:
  evaluator<ArgType> m_argImpl;
 
  // If we do not reverse rows, then we do not need to know the number of rows; same for columns
  // Nonetheless, in this case it is important to set to 1 such that the coeff(index) method works fine for vectors.
  const variable_if_dynamic<Index, ReverseRow ? ArgType::RowsAtCompileTime : 1> m_rows;
  const variable_if_dynamic<Index, ReverseCol ? ArgType::ColsAtCompileTime : 1> m_cols;
};
 
// -------------------- Diagonal --------------------
 
template <typename ArgType, int DiagIndex>
struct evaluator<Diagonal<ArgType, DiagIndex>> : evaluator_base<Diagonal<ArgType, DiagIndex>> {
  typedef Diagonal<ArgType, DiagIndex> XprType;
 
  enum {
    CoeffReadCost = evaluator<ArgType>::CoeffReadCost,
 
    Flags =
        (unsigned int)(evaluator<ArgType>::Flags & (HereditaryBits | DirectAccessBit) & ~RowMajorBit) | LinearAccessBit,
 
    Alignment = 0
  };
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& diagonal)
      : m_argImpl(diagonal.nestedExpression()), m_index(diagonal.index()) {}
 
  typedef typename XprType::Scalar Scalar;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index) const {
    return m_argImpl.coeff(row + rowOffset(), row + colOffset());
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
    return m_argImpl.coeff(index + rowOffset(), index + colOffset());
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index row, Index) {
    return m_argImpl.coeffRef(row + rowOffset(), row + colOffset());
  }
 
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar& coeffRef(Index index) {
    return m_argImpl.coeffRef(index + rowOffset(), index + colOffset());
  }
 
 protected:
  evaluator<ArgType> m_argImpl;
  const internal::variable_if_dynamicindex<Index, XprType::DiagIndex> m_index;
 
 private:
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index rowOffset() const {
    return m_index.value() > 0 ? 0 : -m_index.value();
  }
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR Index colOffset() const {
    return m_index.value() > 0 ? m_index.value() : 0;
  }
};
 
//----------------------------------------------------------------------
// deprecated code
//----------------------------------------------------------------------
 
// -------------------- EvalToTemp --------------------
 
// expression class for evaluating nested expression to a temporary
 
template <typename ArgType>
class EvalToTemp;
 
template <typename ArgType>
struct traits<EvalToTemp<ArgType>> : public traits<ArgType> {};
 
template <typename ArgType>
class EvalToTemp : public dense_xpr_base<EvalToTemp<ArgType>>::type {
 public:
  typedef typename dense_xpr_base<EvalToTemp>::type Base;
  EIGEN_GENERIC_PUBLIC_INTERFACE(EvalToTemp)
 
  explicit EvalToTemp(const ArgType& arg) : m_arg(arg) {}
 
  const ArgType& arg() const { return m_arg; }
 
  EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_arg.rows(); }
 
  EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_arg.cols(); }
 
 private:
  const ArgType& m_arg;
};
 
template <typename ArgType>
struct evaluator<EvalToTemp<ArgType>> : public evaluator<typename ArgType::PlainObject> {
  typedef EvalToTemp<ArgType> XprType;
  typedef typename ArgType::PlainObject PlainObject;
  typedef evaluator<PlainObject> Base;
 
  EIGEN_DEVICE_FUNC explicit evaluator(const XprType& xpr) : m_result(xpr.arg()) {
    internal::construct_at<Base>(this, m_result);
  }
 
  // This constructor is used when nesting an EvalTo evaluator in another evaluator
  EIGEN_DEVICE_FUNC evaluator(const ArgType& arg) : m_result(arg) { internal::construct_at<Base>(this, m_result); }
 
 protected:
  PlainObject m_result;
};
 
}  // namespace internal
 
}  // end namespace Eigen
 
#endif  // EIGEN_COREEVALUATORS_H