IndexedViewHelper.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2017 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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_INDEXED_VIEW_HELPER_H
#define EIGEN_INDEXED_VIEW_HELPER_H

// IWYU pragma: private
#include "../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {
struct symbolic_last_tag {};

struct all_t {};

}  // namespace internal

namespace placeholders {

typedef symbolic::SymbolExpr<internal::symbolic_last_tag> last_t;

static constexpr const last_t last;

typedef symbolic::AddExpr<symbolic::SymbolExpr<internal::symbolic_last_tag>,
                          symbolic::ValueExpr<Eigen::internal::FixedInt<1>>>
    lastp1_t;
typedef Eigen::internal::all_t all_t;

#ifdef EIGEN_PARSED_BY_DOXYGEN
static constexpr auto lastp1 = last + fix<1>;
#else
// Using a FixedExpr<1> expression is important here to make sure the compiler
// can fully optimize the computation starting indices with zero overhead.
static constexpr lastp1_t lastp1 = lastp1_t{};
#endif

static constexpr lastp1_t end = lastp1;

static constexpr Eigen::internal::all_t all;

}  // namespace placeholders

namespace internal {

// Evaluate a symbolic expression or constant given the "size" of an object, allowing
// any symbols like `last` to be evaluated.  The default here assumes a dynamic constant.
template <typename Expr, int SizeAtCompileTime, typename EnableIf = void>
struct SymbolicExpressionEvaluator {
  static constexpr Index ValueAtCompileTime = Undefined;
  static Index eval(const Expr& expr, Index /*size*/) { return static_cast<Index>(expr); }
};

// Symbolic expression with size known at compile-time.
template <typename Expr, int SizeAtCompileTime>
struct SymbolicExpressionEvaluator<Expr, SizeAtCompileTime, std::enable_if_t<symbolic::is_symbolic<Expr>::value>> {
  static constexpr Index ValueAtCompileTime =
      Expr::Derived::eval_at_compile_time(Eigen::placeholders::last = fix<SizeAtCompileTime - 1>);
  static Index eval(const Expr& expr, Index /*size*/) {
    return expr.eval(Eigen::placeholders::last = fix<SizeAtCompileTime - 1>);
  }
};

// Symbolic expression with dynamic size.
template <typename Expr>
struct SymbolicExpressionEvaluator<Expr, Dynamic, std::enable_if_t<symbolic::is_symbolic<Expr>::value>> {
  static constexpr Index ValueAtCompileTime = Undefined;
  static Index eval(const Expr& expr, Index size) { return expr.eval(Eigen::placeholders::last = size - 1); }
};

// Fixed int.
template <int N, int SizeAtCompileTime>
struct SymbolicExpressionEvaluator<FixedInt<N>, SizeAtCompileTime, void> {
  static constexpr Index ValueAtCompileTime = static_cast<Index>(N);
  static Index eval(const FixedInt<N>& /*expr*/, Index /*size*/) { return ValueAtCompileTime; }
};

//--------------------------------------------------------------------------------
// Handling of generic indices (e.g. array)
//--------------------------------------------------------------------------------

// Potentially wrap indices in a type that is better-suited for IndexedView evaluation.
template <typename Indices, int NestedSizeAtCompileTime, typename EnableIf = void>
struct IndexedViewHelperIndicesWrapper {
  using type = Indices;
  static const type& CreateIndexSequence(const Indices& indices, Index /*nested_size*/) { return indices; }
};

// Extract compile-time and runtime first, size, increments.
template <typename Indices, typename EnableIf = void>
struct IndexedViewHelper {
  static constexpr Index FirstAtCompileTime = Undefined;
  static constexpr Index SizeAtCompileTime = array_size<Indices>::value;
  static constexpr Index IncrAtCompileTime = Undefined;

  static constexpr Index first(const Indices& indices) { return static_cast<Index>(indices[0]); }
  static constexpr Index size(const Indices& indices) { return index_list_size(indices); }
  static constexpr Index incr(const Indices& /*indices*/) { return Undefined; }
};

//--------------------------------------------------------------------------------
// Handling of ArithmeticSequence
//--------------------------------------------------------------------------------

template <Index FirstAtCompileTime_, Index SizeAtCompileTime_, Index IncrAtCompileTime_>
class ArithmeticSequenceRange {
 public:
  static constexpr Index FirstAtCompileTime = FirstAtCompileTime_;
  static constexpr Index SizeAtCompileTime = SizeAtCompileTime_;
  static constexpr Index IncrAtCompileTime = IncrAtCompileTime_;

  constexpr ArithmeticSequenceRange(Index first, Index size, Index incr) : first_{first}, size_{size}, incr_{incr} {}
  constexpr Index operator[](Index i) const { return first() + i * incr(); }
  constexpr Index first() const noexcept { return first_.value(); }
  constexpr Index size() const noexcept { return size_.value(); }
  constexpr Index incr() const noexcept { return incr_.value(); }

 private:
  variable_if_dynamicindex<Index, int(FirstAtCompileTime)> first_;
  variable_if_dynamic<Index, int(SizeAtCompileTime)> size_;
  variable_if_dynamicindex<Index, int(IncrAtCompileTime)> incr_;
};

template <typename FirstType, typename SizeType, typename IncrType, int NestedSizeAtCompileTime>
struct IndexedViewHelperIndicesWrapper<ArithmeticSequence<FirstType, SizeType, IncrType>, NestedSizeAtCompileTime,
                                       void> {
  static constexpr Index EvalFirstAtCompileTime =
      SymbolicExpressionEvaluator<FirstType, NestedSizeAtCompileTime>::ValueAtCompileTime;
  static constexpr Index EvalSizeAtCompileTime =
      SymbolicExpressionEvaluator<SizeType, NestedSizeAtCompileTime>::ValueAtCompileTime;
  static constexpr Index EvalIncrAtCompileTime =
      SymbolicExpressionEvaluator<IncrType, NestedSizeAtCompileTime>::ValueAtCompileTime;

  static constexpr Index FirstAtCompileTime =
      (int(EvalFirstAtCompileTime) == Undefined) ? Index(DynamicIndex) : EvalFirstAtCompileTime;
  static constexpr Index SizeAtCompileTime =
      (int(EvalSizeAtCompileTime) == Undefined) ? Index(Dynamic) : EvalSizeAtCompileTime;
  static constexpr Index IncrAtCompileTime =
      (int(EvalIncrAtCompileTime) == Undefined) ? Index(DynamicIndex) : EvalIncrAtCompileTime;

  using Indices = ArithmeticSequence<FirstType, SizeType, IncrType>;
  using type = ArithmeticSequenceRange<FirstAtCompileTime, SizeAtCompileTime, IncrAtCompileTime>;

  static type CreateIndexSequence(const Indices& indices, Index nested_size) {
    Index first =
        SymbolicExpressionEvaluator<FirstType, NestedSizeAtCompileTime>::eval(indices.firstObject(), nested_size);
    Index size =
        SymbolicExpressionEvaluator<SizeType, NestedSizeAtCompileTime>::eval(indices.sizeObject(), nested_size);
    Index incr =
        SymbolicExpressionEvaluator<IncrType, NestedSizeAtCompileTime>::eval(indices.incrObject(), nested_size);
    return type(first, size, incr);
  }
};

template <Index FirstAtCompileTime_, Index SizeAtCompileTime_, Index IncrAtCompileTime_>
struct IndexedViewHelper<ArithmeticSequenceRange<FirstAtCompileTime_, SizeAtCompileTime_, IncrAtCompileTime_>, void> {
 public:
  using Indices = ArithmeticSequenceRange<FirstAtCompileTime_, SizeAtCompileTime_, IncrAtCompileTime_>;
  static constexpr Index FirstAtCompileTime = Indices::FirstAtCompileTime;
  static constexpr Index SizeAtCompileTime = Indices::SizeAtCompileTime;
  static constexpr Index IncrAtCompileTime = Indices::IncrAtCompileTime;
  static Index first(const Indices& indices) { return indices.first(); }
  static Index size(const Indices& indices) { return indices.size(); }
  static Index incr(const Indices& indices) { return indices.incr(); }
};

//--------------------------------------------------------------------------------
// Handling of a single index.
//--------------------------------------------------------------------------------

template <Index ValueAtCompileTime>
class SingleRange {
 public:
  static constexpr Index FirstAtCompileTime = ValueAtCompileTime;
  static constexpr Index SizeAtCompileTime = Index(1);
  static constexpr Index IncrAtCompileTime = Index(1);  // Needs to be 1 to be treated as block-like.

  constexpr SingleRange(Index v) noexcept : value_(v) {}
  constexpr Index operator[](Index) const noexcept { return first(); }
  constexpr Index first() const noexcept { return value_.value(); }
  constexpr Index size() const noexcept { return SizeAtCompileTime; }
  constexpr Index incr() const noexcept { return IncrAtCompileTime; }

 private:
  variable_if_dynamicindex<Index, int(ValueAtCompileTime)> value_;
};

template <typename T>
struct is_single_range : public std::false_type {};

template <Index ValueAtCompileTime>
struct is_single_range<SingleRange<ValueAtCompileTime>> : public std::true_type {};

template <typename SingleIndex, int NestedSizeAtCompileTime>
struct IndexedViewHelperIndicesWrapper<
    SingleIndex, NestedSizeAtCompileTime,
    std::enable_if_t<std::is_integral<SingleIndex>::value || symbolic::is_symbolic<SingleIndex>::value>> {
  static constexpr Index EvalValueAtCompileTime =
      SymbolicExpressionEvaluator<SingleIndex, NestedSizeAtCompileTime>::ValueAtCompileTime;
  static constexpr Index ValueAtCompileTime =
      (int(EvalValueAtCompileTime) == Undefined) ? Index(DynamicIndex) : EvalValueAtCompileTime;
  using type = SingleRange<ValueAtCompileTime>;
  static type CreateIndexSequence(const SingleIndex& index, Index nested_size) {
    return type(SymbolicExpressionEvaluator<SingleIndex, NestedSizeAtCompileTime>::eval(index, nested_size));
  }
};

template <int N, int NestedSizeAtCompileTime>
struct IndexedViewHelperIndicesWrapper<FixedInt<N>, NestedSizeAtCompileTime, void> {
  using type = SingleRange<Index(N)>;
  static type CreateIndexSequence(const FixedInt<N>& /*index*/) { return type(Index(N)); }
};

template <Index ValueAtCompileTime>
struct IndexedViewHelper<SingleRange<ValueAtCompileTime>, void> {
  using Indices = SingleRange<ValueAtCompileTime>;
  static constexpr Index FirstAtCompileTime = Indices::FirstAtCompileTime;
  static constexpr Index SizeAtCompileTime = Indices::SizeAtCompileTime;
  static constexpr Index IncrAtCompileTime = Indices::IncrAtCompileTime;

  static constexpr Index first(const Indices& indices) { return indices.first(); }
  static constexpr Index size(const Indices& /*indices*/) { return SizeAtCompileTime; }
  static constexpr Index incr(const Indices& /*indices*/) { return IncrAtCompileTime; }
};

//--------------------------------------------------------------------------------
// Handling of all
//--------------------------------------------------------------------------------

// Convert a symbolic 'all' into a usable range type
template <Index SizeAtCompileTime_>
class AllRange {
 public:
  static constexpr Index FirstAtCompileTime = Index(0);
  static constexpr Index SizeAtCompileTime = SizeAtCompileTime_;
  static constexpr Index IncrAtCompileTime = Index(1);
  constexpr AllRange(Index size) : size_(size) {}
  constexpr Index operator[](Index i) const noexcept { return i; }
  constexpr Index first() const noexcept { return FirstAtCompileTime; }
  constexpr Index size() const noexcept { return size_.value(); }
  constexpr Index incr() const noexcept { return IncrAtCompileTime; }

 private:
  variable_if_dynamic<Index, int(SizeAtCompileTime)> size_;
};

template <int NestedSizeAtCompileTime>
struct IndexedViewHelperIndicesWrapper<all_t, NestedSizeAtCompileTime, void> {
  using type = AllRange<Index(NestedSizeAtCompileTime)>;
  static type CreateIndexSequence(const all_t& /*indices*/, Index nested_size) { return type(nested_size); }
};

template <Index SizeAtCompileTime_>
struct IndexedViewHelper<AllRange<SizeAtCompileTime_>, void> {
  using Indices = AllRange<SizeAtCompileTime_>;
  static constexpr Index FirstAtCompileTime = Indices::FirstAtCompileTime;
  static constexpr Index SizeAtCompileTime = Indices::SizeAtCompileTime;
  static constexpr Index IncrAtCompileTime = Indices::IncrAtCompileTime;

  static Index first(const Indices& indices) { return indices.first(); }
  static Index size(const Indices& indices) { return indices.size(); }
  static Index incr(const Indices& indices) { return indices.incr(); }
};

// this helper class assumes internal::valid_indexed_view_overload<RowIndices, ColIndices>::value == true
template <typename Derived, typename RowIndices, typename ColIndices, typename EnableIf = void>
struct IndexedViewSelector;

template <typename Indices, int SizeAtCompileTime>
using IvcType = typename internal::IndexedViewHelperIndicesWrapper<Indices, SizeAtCompileTime>::type;

template <int SizeAtCompileTime, typename Indices>
inline IvcType<Indices, SizeAtCompileTime> CreateIndexSequence(size_t size, const Indices& indices) {
  return internal::IndexedViewHelperIndicesWrapper<Indices, SizeAtCompileTime>::CreateIndexSequence(indices, size);
}

// Generic
template <typename Derived, typename RowIndices, typename ColIndices>
struct IndexedViewSelector<Derived, RowIndices, ColIndices,
                           std::enable_if_t<internal::traits<
                               IndexedView<Derived, IvcType<RowIndices, Derived::RowsAtCompileTime>,
                                           IvcType<ColIndices, Derived::ColsAtCompileTime>>>::ReturnAsIndexedView>> {
  using ReturnType = IndexedView<Derived, IvcType<RowIndices, Derived::RowsAtCompileTime>,
                                 IvcType<ColIndices, Derived::ColsAtCompileTime>>;
  using ConstReturnType = IndexedView<const Derived, IvcType<RowIndices, Derived::RowsAtCompileTime>,
                                      IvcType<ColIndices, Derived::ColsAtCompileTime>>;

  static inline ReturnType run(Derived& derived, const RowIndices& rowIndices, const ColIndices& colIndices) {
    return ReturnType(derived, CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), rowIndices),
                      CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), colIndices));
  }
  static inline ConstReturnType run(const Derived& derived, const RowIndices& rowIndices,
                                    const ColIndices& colIndices) {
    return ConstReturnType(derived, CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), rowIndices),
                           CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), colIndices));
  }
};

// Block
template <typename Derived, typename RowIndices, typename ColIndices>
struct IndexedViewSelector<
    Derived, RowIndices, ColIndices,
    std::enable_if_t<internal::traits<IndexedView<Derived, IvcType<RowIndices, Derived::RowsAtCompileTime>,
                                                  IvcType<ColIndices, Derived::ColsAtCompileTime>>>::ReturnAsBlock>> {
  using ActualRowIndices = IvcType<RowIndices, Derived::RowsAtCompileTime>;
  using ActualColIndices = IvcType<ColIndices, Derived::ColsAtCompileTime>;
  using IndexedViewType = IndexedView<Derived, ActualRowIndices, ActualColIndices>;
  using ConstIndexedViewType = IndexedView<const Derived, ActualRowIndices, ActualColIndices>;
  using ReturnType = typename internal::traits<IndexedViewType>::BlockType;
  using ConstReturnType = typename internal::traits<ConstIndexedViewType>::BlockType;
  using RowHelper = internal::IndexedViewHelper<ActualRowIndices>;
  using ColHelper = internal::IndexedViewHelper<ActualColIndices>;

  static inline ReturnType run(Derived& derived, const RowIndices& rowIndices, const ColIndices& colIndices) {
    auto actualRowIndices = CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), rowIndices);
    auto actualColIndices = CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), colIndices);
    return ReturnType(derived, RowHelper::first(actualRowIndices), ColHelper::first(actualColIndices),
                      RowHelper::size(actualRowIndices), ColHelper::size(actualColIndices));
  }
  static inline ConstReturnType run(const Derived& derived, const RowIndices& rowIndices,
                                    const ColIndices& colIndices) {
    auto actualRowIndices = CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), rowIndices);
    auto actualColIndices = CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), colIndices);
    return ConstReturnType(derived, RowHelper::first(actualRowIndices), ColHelper::first(actualColIndices),
                           RowHelper::size(actualRowIndices), ColHelper::size(actualColIndices));
  }
};

// Scalar
template <typename Derived, typename RowIndices, typename ColIndices>
struct IndexedViewSelector<
    Derived, RowIndices, ColIndices,
    std::enable_if_t<internal::traits<IndexedView<Derived, IvcType<RowIndices, Derived::RowsAtCompileTime>,
                                                  IvcType<ColIndices, Derived::ColsAtCompileTime>>>::ReturnAsScalar>> {
  using ReturnType = typename DenseBase<Derived>::Scalar&;
  using ConstReturnType = typename DenseBase<Derived>::CoeffReturnType;
  using ActualRowIndices = IvcType<RowIndices, Derived::RowsAtCompileTime>;
  using ActualColIndices = IvcType<ColIndices, Derived::ColsAtCompileTime>;
  using RowHelper = internal::IndexedViewHelper<ActualRowIndices>;
  using ColHelper = internal::IndexedViewHelper<ActualColIndices>;
  static inline ReturnType run(Derived& derived, const RowIndices& rowIndices, const ColIndices& colIndices) {
    auto actualRowIndices = CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), rowIndices);
    auto actualColIndices = CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), colIndices);
    return derived(RowHelper::first(actualRowIndices), ColHelper::first(actualColIndices));
  }
  static inline ConstReturnType run(const Derived& derived, const RowIndices& rowIndices,
                                    const ColIndices& colIndices) {
    auto actualRowIndices = CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), rowIndices);
    auto actualColIndices = CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), colIndices);
    return derived(RowHelper::first(actualRowIndices), ColHelper::first(actualColIndices));
  }
};

// this helper class assumes internal::is_valid_index_type<Indices>::value == false
template <typename Derived, typename Indices, typename EnableIf = void>
struct VectorIndexedViewSelector;

// Generic
template <typename Derived, typename Indices>
struct VectorIndexedViewSelector<
    Derived, Indices,
    std::enable_if_t<!internal::is_single_range<IvcType<Indices, Derived::SizeAtCompileTime>>::value &&
                     internal::IndexedViewHelper<IvcType<Indices, Derived::SizeAtCompileTime>>::IncrAtCompileTime !=
                         1>> {
  static constexpr bool IsRowMajor = DenseBase<Derived>::IsRowMajor;
  using ZeroIndex = internal::SingleRange<Index(0)>;
  using RowMajorReturnType = IndexedView<Derived, ZeroIndex, IvcType<Indices, Derived::SizeAtCompileTime>>;
  using ConstRowMajorReturnType = IndexedView<const Derived, ZeroIndex, IvcType<Indices, Derived::SizeAtCompileTime>>;

  using ColMajorReturnType = IndexedView<Derived, IvcType<Indices, Derived::SizeAtCompileTime>, ZeroIndex>;
  using ConstColMajorReturnType = IndexedView<const Derived, IvcType<Indices, Derived::SizeAtCompileTime>, ZeroIndex>;

  using ReturnType = typename internal::conditional<IsRowMajor, RowMajorReturnType, ColMajorReturnType>::type;
  using ConstReturnType =
      typename internal::conditional<IsRowMajor, ConstRowMajorReturnType, ConstColMajorReturnType>::type;

  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<UseRowMajor, bool> = true>
  static inline RowMajorReturnType run(Derived& derived, const Indices& indices) {
    return RowMajorReturnType(derived, ZeroIndex(0),
                              CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), indices));
  }
  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<UseRowMajor, bool> = true>
  static inline ConstRowMajorReturnType run(const Derived& derived, const Indices& indices) {
    return ConstRowMajorReturnType(derived, ZeroIndex(0),
                                   CreateIndexSequence<Derived::ColsAtCompileTime>(derived.cols(), indices));
  }
  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<!UseRowMajor, bool> = true>
  static inline ColMajorReturnType run(Derived& derived, const Indices& indices) {
    return ColMajorReturnType(derived, CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), indices),
                              ZeroIndex(0));
  }
  template <bool UseRowMajor = IsRowMajor, std::enable_if_t<!UseRowMajor, bool> = true>
  static inline ConstColMajorReturnType run(const Derived& derived, const Indices& indices) {
    return ConstColMajorReturnType(derived, CreateIndexSequence<Derived::RowsAtCompileTime>(derived.rows(), indices),
                                   ZeroIndex(0));
  }
};

// Block
template <typename Derived, typename Indices>
struct VectorIndexedViewSelector<
    Derived, Indices,
    std::enable_if_t<!internal::is_single_range<IvcType<Indices, Derived::SizeAtCompileTime>>::value &&
                     internal::IndexedViewHelper<IvcType<Indices, Derived::SizeAtCompileTime>>::IncrAtCompileTime ==
                         1>> {
  using Helper = internal::IndexedViewHelper<IvcType<Indices, Derived::SizeAtCompileTime>>;
  using ReturnType = VectorBlock<Derived, Helper::SizeAtCompileTime>;
  using ConstReturnType = VectorBlock<const Derived, Helper::SizeAtCompileTime>;
  static inline ReturnType run(Derived& derived, const Indices& indices) {
    auto actualIndices = CreateIndexSequence<Derived::SizeAtCompileTime>(derived.size(), indices);
    return ReturnType(derived, Helper::first(actualIndices), Helper::size(actualIndices));
  }
  static inline ConstReturnType run(const Derived& derived, const Indices& indices) {
    auto actualIndices = CreateIndexSequence<Derived::SizeAtCompileTime>(derived.size(), indices);
    return ConstReturnType(derived, Helper::first(actualIndices), Helper::size(actualIndices));
  }
};

// Symbolic
template <typename Derived, typename Indices>
struct VectorIndexedViewSelector<
    Derived, Indices,
    std::enable_if_t<internal::is_single_range<IvcType<Indices, Derived::SizeAtCompileTime>>::value>> {
  using ReturnType = typename DenseBase<Derived>::Scalar&;
  using ConstReturnType = typename DenseBase<Derived>::CoeffReturnType;
  using Helper = internal::IndexedViewHelper<IvcType<Indices, Derived::SizeAtCompileTime>>;
  static inline ReturnType run(Derived& derived, const Indices& indices) {
    auto actualIndices = CreateIndexSequence<Derived::SizeAtCompileTime>(derived.size(), indices);
    return derived(Helper::first(actualIndices));
  }
  static inline ConstReturnType run(const Derived& derived, const Indices& indices) {
    auto actualIndices = CreateIndexSequence<Derived::SizeAtCompileTime>(derived.size(), indices);
    return derived(Helper::first(actualIndices));
  }
};

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_INDEXED_VIEW_HELPER_H