Visitor.h

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 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_VISITOR_H
#define EIGEN_VISITOR_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {
 
namespace internal {
 
template <typename Visitor, typename Derived, int UnrollCount,
          bool Vectorize = (Derived::PacketAccess && functor_traits<Visitor>::PacketAccess), bool LinearAccess = false,
          bool ShortCircuitEvaluation = false>
struct visitor_impl;
 
template <typename Visitor, bool ShortCircuitEvaluation = false>
struct short_circuit_eval_impl {
  // if short circuit evaluation is not used, do nothing
  static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Visitor&) { return false; }
};
template <typename Visitor>
struct short_circuit_eval_impl<Visitor, true> {
  // if short circuit evaluation is used, check the visitor
  static EIGEN_CONSTEXPR EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool run(const Visitor& visitor) {
    return visitor.done();
  }
};
 
// unrolled inner-outer traversal
template <typename Visitor, typename Derived, int UnrollCount, bool Vectorize, bool ShortCircuitEvaluation>
struct visitor_impl<Visitor, Derived, UnrollCount, Vectorize, false, ShortCircuitEvaluation> {
  // don't use short circuit evaluation for unrolled version
  using Scalar = typename Derived::Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  static constexpr bool RowMajor = Derived::IsRowMajor;
  static constexpr int RowsAtCompileTime = Derived::RowsAtCompileTime;
  static constexpr int ColsAtCompileTime = Derived::ColsAtCompileTime;
  static constexpr int PacketSize = packet_traits<Scalar>::size;
 
  static constexpr bool CanVectorize(int K) {
    constexpr int InnerSizeAtCompileTime = RowMajor ? ColsAtCompileTime : RowsAtCompileTime;
    if (InnerSizeAtCompileTime < PacketSize) return false;
    return Vectorize && (InnerSizeAtCompileTime - (K % InnerSizeAtCompileTime) >= PacketSize);
  }
 
  template <int K = 0, bool Empty = (K == UnrollCount), std::enable_if_t<Empty, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived&, Visitor&) {}
 
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && Initialize && !DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    visitor.init(mat.coeff(0, 0), 0, 0);
    run<1>(mat, visitor);
  }
 
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && !Initialize && !DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    static constexpr int R = RowMajor ? (K / ColsAtCompileTime) : (K % RowsAtCompileTime);
    static constexpr int C = RowMajor ? (K % ColsAtCompileTime) : (K / RowsAtCompileTime);
    visitor(mat.coeff(R, C), R, C);
    run<K + 1>(mat, visitor);
  }
 
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && Initialize && DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    Packet P = mat.template packet<Packet>(0, 0);
    visitor.initpacket(P, 0, 0);
    run<PacketSize>(mat, visitor);
  }
 
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && !Initialize && DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    static constexpr int R = RowMajor ? (K / ColsAtCompileTime) : (K % RowsAtCompileTime);
    static constexpr int C = RowMajor ? (K % ColsAtCompileTime) : (K / RowsAtCompileTime);
    Packet P = mat.template packet<Packet>(R, C);
    visitor.packet(P, R, C);
    run<K + PacketSize>(mat, visitor);
  }
};
 
// unrolled linear traversal
template <typename Visitor, typename Derived, int UnrollCount, bool Vectorize, bool ShortCircuitEvaluation>
struct visitor_impl<Visitor, Derived, UnrollCount, Vectorize, true, ShortCircuitEvaluation> {
  // don't use short circuit evaluation for unrolled version
  using Scalar = typename Derived::Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  static constexpr int PacketSize = packet_traits<Scalar>::size;
 
  static constexpr bool CanVectorize(int K) { return Vectorize && ((UnrollCount - K) >= PacketSize); }
 
  // empty
  template <int K = 0, bool Empty = (K == UnrollCount), std::enable_if_t<Empty, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived&, Visitor&) {}
 
  // scalar initialization
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && Initialize && !DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    visitor.init(mat.coeff(0), 0);
    run<1>(mat, visitor);
  }
 
  // scalar iteration
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && !Initialize && !DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    visitor(mat.coeff(K), K);
    run<K + 1>(mat, visitor);
  }
 
  // vector initialization
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && Initialize && DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    Packet P = mat.template packet<Packet>(0);
    visitor.initpacket(P, 0);
    run<PacketSize>(mat, visitor);
  }
 
  // vector iteration
  template <int K = 0, bool Empty = (K == UnrollCount), bool Initialize = (K == 0), bool DoVectorOp = CanVectorize(K),
            std::enable_if_t<!Empty && !Initialize && DoVectorOp, bool> = true>
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    Packet P = mat.template packet<Packet>(K);
    visitor.packet(P, K);
    run<K + PacketSize>(mat, visitor);
  }
};
 
// dynamic scalar outer-inner traversal
template <typename Visitor, typename Derived, bool ShortCircuitEvaluation>
struct visitor_impl<Visitor, Derived, Dynamic, /*Vectorize=*/false, /*LinearAccess=*/false, ShortCircuitEvaluation> {
  using short_circuit = short_circuit_eval_impl<Visitor, ShortCircuitEvaluation>;
  static constexpr bool RowMajor = Derived::IsRowMajor;
 
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    const Index innerSize = RowMajor ? mat.cols() : mat.rows();
    const Index outerSize = RowMajor ? mat.rows() : mat.cols();
    if (innerSize == 0 || outerSize == 0) return;
    {
      visitor.init(mat.coeff(0, 0), 0, 0);
      if (short_circuit::run(visitor)) return;
      for (Index i = 1; i < innerSize; ++i) {
        Index r = RowMajor ? 0 : i;
        Index c = RowMajor ? i : 0;
        visitor(mat.coeff(r, c), r, c);
        if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      }
    }
    for (Index j = 1; j < outerSize; j++) {
      for (Index i = 0; i < innerSize; ++i) {
        Index r = RowMajor ? j : i;
        Index c = RowMajor ? i : j;
        visitor(mat.coeff(r, c), r, c);
        if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      }
    }
  }
};
 
// dynamic vectorized outer-inner traversal
template <typename Visitor, typename Derived, bool ShortCircuitEvaluation>
struct visitor_impl<Visitor, Derived, Dynamic, /*Vectorize=*/true, /*LinearAccess=*/false, ShortCircuitEvaluation> {
  using Scalar = typename Derived::Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  static constexpr int PacketSize = packet_traits<Scalar>::size;
  using short_circuit = short_circuit_eval_impl<Visitor, ShortCircuitEvaluation>;
  static constexpr bool RowMajor = Derived::IsRowMajor;
 
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    const Index innerSize = RowMajor ? mat.cols() : mat.rows();
    const Index outerSize = RowMajor ? mat.rows() : mat.cols();
    if (innerSize == 0 || outerSize == 0) return;
    {
      Index i = 0;
      if (innerSize < PacketSize) {
        visitor.init(mat.coeff(0, 0), 0, 0);
        i = 1;
      } else {
        Packet p = mat.template packet<Packet>(0, 0);
        visitor.initpacket(p, 0, 0);
        i = PacketSize;
      }
      if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      for (; i + PacketSize - 1 < innerSize; i += PacketSize) {
        Index r = RowMajor ? 0 : i;
        Index c = RowMajor ? i : 0;
        Packet p = mat.template packet<Packet>(r, c);
        visitor.packet(p, r, c);
        if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      }
      for (; i < innerSize; ++i) {
        Index r = RowMajor ? 0 : i;
        Index c = RowMajor ? i : 0;
        visitor(mat.coeff(r, c), r, c);
        if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      }
    }
    for (Index j = 1; j < outerSize; j++) {
      Index i = 0;
      for (; i + PacketSize - 1 < innerSize; i += PacketSize) {
        Index r = RowMajor ? j : i;
        Index c = RowMajor ? i : j;
        Packet p = mat.template packet<Packet>(r, c);
        visitor.packet(p, r, c);
        if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      }
      for (; i < innerSize; ++i) {
        Index r = RowMajor ? j : i;
        Index c = RowMajor ? i : j;
        visitor(mat.coeff(r, c), r, c);
        if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
      }
    }
  }
};
 
// dynamic scalar linear traversal
template <typename Visitor, typename Derived, bool ShortCircuitEvaluation>
struct visitor_impl<Visitor, Derived, Dynamic, /*Vectorize=*/false, /*LinearAccess=*/true, ShortCircuitEvaluation> {
  using short_circuit = short_circuit_eval_impl<Visitor, ShortCircuitEvaluation>;
 
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    const Index size = mat.size();
    if (size == 0) return;
    visitor.init(mat.coeff(0), 0);
    if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
    for (Index k = 1; k < size; k++) {
      visitor(mat.coeff(k), k);
      if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
    }
  }
};
 
// dynamic vectorized linear traversal
template <typename Visitor, typename Derived, bool ShortCircuitEvaluation>
struct visitor_impl<Visitor, Derived, Dynamic, /*Vectorize=*/true, /*LinearAccess=*/true, ShortCircuitEvaluation> {
  using Scalar = typename Derived::Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  static constexpr int PacketSize = packet_traits<Scalar>::size;
  using short_circuit = short_circuit_eval_impl<Visitor, ShortCircuitEvaluation>;
 
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const Derived& mat, Visitor& visitor) {
    const Index size = mat.size();
    if (size == 0) return;
    Index k = 0;
    if (size < PacketSize) {
      visitor.init(mat.coeff(0), 0);
      k = 1;
    } else {
      Packet p = mat.template packet<Packet>(k);
      visitor.initpacket(p, k);
      k = PacketSize;
    }
    if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
    for (; k + PacketSize - 1 < size; k += PacketSize) {
      Packet p = mat.template packet<Packet>(k);
      visitor.packet(p, k);
      if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
    }
    for (; k < size; k++) {
      visitor(mat.coeff(k), k);
      if EIGEN_PREDICT_FALSE (short_circuit::run(visitor)) return;
    }
  }
};
 
// evaluator adaptor
template <typename XprType>
class visitor_evaluator {
 public:
  typedef evaluator<XprType> Evaluator;
  typedef typename XprType::Scalar Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  typedef std::remove_const_t<typename XprType::CoeffReturnType> CoeffReturnType;
 
  static constexpr bool PacketAccess = static_cast<bool>(Evaluator::Flags & PacketAccessBit);
  static constexpr bool LinearAccess = static_cast<bool>(Evaluator::Flags & LinearAccessBit);
  static constexpr bool IsRowMajor = static_cast<bool>(XprType::IsRowMajor);
  static constexpr int RowsAtCompileTime = XprType::RowsAtCompileTime;
  static constexpr int ColsAtCompileTime = XprType::ColsAtCompileTime;
  static constexpr int XprAlignment = Evaluator::Alignment;
  static constexpr int CoeffReadCost = Evaluator::CoeffReadCost;
 
  EIGEN_DEVICE_FUNC explicit visitor_evaluator(const XprType& xpr) : m_evaluator(xpr), m_xpr(xpr) {}
 
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT { return m_xpr.rows(); }
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT { return m_xpr.cols(); }
  EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT { return m_xpr.size(); }
  // outer-inner access
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
    return m_evaluator.coeff(row, col);
  }
  template <typename Packet, int Alignment = Unaligned>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(Index row, Index col) const {
    return m_evaluator.template packet<Alignment, Packet>(row, col);
  }
  // linear access
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const { return m_evaluator.coeff(index); }
  template <typename Packet, int Alignment = XprAlignment>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packet(Index index) const {
    return m_evaluator.template packet<Alignment, Packet>(index);
  }
 
 protected:
  Evaluator m_evaluator;
  const XprType& m_xpr;
};
 
template <typename Derived, typename Visitor, bool ShortCircuitEvaulation>
struct visit_impl {
  using Evaluator = visitor_evaluator<Derived>;
  using Scalar = typename DenseBase<Derived>::Scalar;
 
  static constexpr bool IsRowMajor = DenseBase<Derived>::IsRowMajor;
  static constexpr int SizeAtCompileTime = DenseBase<Derived>::SizeAtCompileTime;
  static constexpr int RowsAtCompileTime = DenseBase<Derived>::RowsAtCompileTime;
  static constexpr int ColsAtCompileTime = DenseBase<Derived>::ColsAtCompileTime;
  static constexpr int InnerSizeAtCompileTime = IsRowMajor ? ColsAtCompileTime : RowsAtCompileTime;
  static constexpr int OuterSizeAtCompileTime = IsRowMajor ? RowsAtCompileTime : ColsAtCompileTime;
 
  static constexpr bool LinearAccess =
      Evaluator::LinearAccess && static_cast<bool>(functor_traits<Visitor>::LinearAccess);
  static constexpr bool Vectorize = Evaluator::PacketAccess && static_cast<bool>(functor_traits<Visitor>::PacketAccess);
 
  static constexpr int PacketSize = packet_traits<Scalar>::size;
  static constexpr int VectorOps =
      Vectorize ? (LinearAccess ? (SizeAtCompileTime / PacketSize)
                                : (OuterSizeAtCompileTime * (InnerSizeAtCompileTime / PacketSize)))
                : 0;
  static constexpr int ScalarOps = SizeAtCompileTime - (VectorOps * PacketSize);
  // treat vector op and scalar op as same cost for unroll logic
  static constexpr int TotalOps = VectorOps + ScalarOps;
 
  static constexpr int UnrollCost = int(Evaluator::CoeffReadCost) + int(functor_traits<Visitor>::Cost);
  static constexpr bool Unroll = (SizeAtCompileTime != Dynamic) && ((TotalOps * UnrollCost) <= EIGEN_UNROLLING_LIMIT);
  static constexpr int UnrollCount = Unroll ? int(SizeAtCompileTime) : Dynamic;
 
  using impl = visitor_impl<Visitor, Evaluator, UnrollCount, Vectorize, LinearAccess, ShortCircuitEvaulation>;
 
  static EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE void run(const DenseBase<Derived>& mat, Visitor& visitor) {
    Evaluator evaluator(mat.derived());
    impl::run(evaluator, visitor);
  }
};
 
}  // end namespace internal
 
template <typename Derived>
template <typename Visitor>
EIGEN_DEVICE_FUNC void DenseBase<Derived>::visit(Visitor& visitor) const {
  using impl = internal::visit_impl<Derived, Visitor, /*ShortCircuitEvaulation*/ false>;
  impl::run(derived(), visitor);
}
 
namespace internal {
 
template <typename Derived>
struct coeff_visitor {
  // default initialization to avoid countless invalid maybe-uninitialized warnings by gcc
  EIGEN_DEVICE_FUNC coeff_visitor() : row(-1), col(-1), res(0) {}
  typedef typename Derived::Scalar Scalar;
  Index row, col;
  Scalar res;
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index i, Index j) {
    res = value;
    row = i;
    col = j;
  }
};
 
template <typename Scalar, int NaNPropagation, bool is_min = true>
struct minmax_compare {
  typedef typename packet_traits<Scalar>::type Packet;
  static EIGEN_DEVICE_FUNC inline bool compare(Scalar a, Scalar b) { return a < b; }
  static EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& p) { return predux_min<NaNPropagation>(p); }
};
 
template <typename Scalar, int NaNPropagation>
struct minmax_compare<Scalar, NaNPropagation, false> {
  typedef typename packet_traits<Scalar>::type Packet;
  static EIGEN_DEVICE_FUNC inline bool compare(Scalar a, Scalar b) { return a > b; }
  static EIGEN_DEVICE_FUNC inline Scalar predux(const Packet& p) { return predux_max<NaNPropagation>(p); }
};
 
// Default implementation used by non-floating types, where we do not
// need special logic for NaN handling.
template <typename Derived, bool is_min, int NaNPropagation,
          bool isInt = NumTraits<typename Derived::Scalar>::IsInteger>
struct minmax_coeff_visitor : coeff_visitor<Derived> {
  using Scalar = typename Derived::Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  using Comparator = minmax_compare<Scalar, NaNPropagation, is_min>;
  static constexpr Index PacketSize = packet_traits<Scalar>::size;
 
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index i, Index j) {
    if (Comparator::compare(value, this->res)) {
      this->res = value;
      this->row = i;
      this->col = j;
    }
  }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index i, Index j) {
    Scalar value = Comparator::predux(p);
    if (Comparator::compare(value, this->res)) {
      const Packet range = preverse(plset<Packet>(Scalar(1)));
      Packet mask = pcmp_eq(pset1<Packet>(value), p);
      Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
      this->res = value;
      this->row = Derived::IsRowMajor ? i : i + max_idx;
      this->col = Derived::IsRowMajor ? j + max_idx : j;
    }
  }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index i, Index j) {
    Scalar value = Comparator::predux(p);
    const Packet range = preverse(plset<Packet>(Scalar(1)));
    Packet mask = pcmp_eq(pset1<Packet>(value), p);
    Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
    this->res = value;
    this->row = Derived::IsRowMajor ? i : i + max_idx;
    this->col = Derived::IsRowMajor ? j + max_idx : j;
  }
};
 
// Suppress NaN. The only case in which we return NaN is if the matrix is all NaN,
// in which case, row=0, col=0 is returned for the location.
template <typename Derived, bool is_min>
struct minmax_coeff_visitor<Derived, is_min, PropagateNumbers, false> : coeff_visitor<Derived> {
  typedef typename Derived::Scalar Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  using Comparator = minmax_compare<Scalar, PropagateNumbers, is_min>;
 
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index i, Index j) {
    if ((!(numext::isnan)(value) && (numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
      this->res = value;
      this->row = i;
      this->col = j;
    }
  }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index i, Index j) {
    const Index PacketSize = packet_traits<Scalar>::size;
    Scalar value = Comparator::predux(p);
    if ((!(numext::isnan)(value) && (numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
      const Packet range = preverse(plset<Packet>(Scalar(1)));
      /* mask will be zero for NaNs, so they will be ignored. */
      Packet mask = pcmp_eq(pset1<Packet>(value), p);
      Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
      this->res = value;
      this->row = Derived::IsRowMajor ? i : i + max_idx;
      this->col = Derived::IsRowMajor ? j + max_idx : j;
    }
  }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index i, Index j) {
    const Index PacketSize = packet_traits<Scalar>::size;
    Scalar value = Comparator::predux(p);
    if ((numext::isnan)(value)) {
      this->res = value;
      this->row = 0;
      this->col = 0;
      return;
    }
    const Packet range = preverse(plset<Packet>(Scalar(1)));
    /* mask will be zero for NaNs, so they will be ignored. */
    Packet mask = pcmp_eq(pset1<Packet>(value), p);
    Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
    this->res = value;
    this->row = Derived::IsRowMajor ? i : i + max_idx;
    this->col = Derived::IsRowMajor ? j + max_idx : j;
  }
};
 
// Propagate NaNs. If the matrix contains NaN, the location of the first NaN
// will be returned in row and col.
template <typename Derived, bool is_min, int NaNPropagation>
struct minmax_coeff_visitor<Derived, is_min, NaNPropagation, false> : coeff_visitor<Derived> {
  typedef typename Derived::Scalar Scalar;
  using Packet = typename packet_traits<Scalar>::type;
  using Comparator = minmax_compare<Scalar, PropagateNaN, is_min>;
 
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index i, Index j) {
    const bool value_is_nan = (numext::isnan)(value);
    if ((value_is_nan && !(numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
      this->res = value;
      this->row = i;
      this->col = j;
    }
  }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index i, Index j) {
    const Index PacketSize = packet_traits<Scalar>::size;
    Scalar value = Comparator::predux(p);
    const bool value_is_nan = (numext::isnan)(value);
    if ((value_is_nan && !(numext::isnan)(this->res)) || Comparator::compare(value, this->res)) {
      const Packet range = preverse(plset<Packet>(Scalar(1)));
      // If the value is NaN, pick the first position of a NaN, otherwise pick the first extremal value.
      Packet mask = value_is_nan ? pnot(pcmp_eq(p, p)) : pcmp_eq(pset1<Packet>(value), p);
      Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
      this->res = value;
      this->row = Derived::IsRowMajor ? i : i + max_idx;
      this->col = Derived::IsRowMajor ? j + max_idx : j;
    }
  }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index i, Index j) {
    const Index PacketSize = packet_traits<Scalar>::size;
    Scalar value = Comparator::predux(p);
    const bool value_is_nan = (numext::isnan)(value);
    const Packet range = preverse(plset<Packet>(Scalar(1)));
    // If the value is NaN, pick the first position of a NaN, otherwise pick the first extremal value.
    Packet mask = value_is_nan ? pnot(pcmp_eq(p, p)) : pcmp_eq(pset1<Packet>(value), p);
    Index max_idx = PacketSize - static_cast<Index>(predux_max(pand(range, mask)));
    this->res = value;
    this->row = Derived::IsRowMajor ? i : i + max_idx;
    this->col = Derived::IsRowMajor ? j + max_idx : j;
  }
};
 
template <typename Derived, bool is_min, int NaNPropagation>
struct functor_traits<minmax_coeff_visitor<Derived, is_min, NaNPropagation>> {
  using Scalar = typename Derived::Scalar;
  enum { Cost = NumTraits<Scalar>::AddCost, LinearAccess = false, PacketAccess = packet_traits<Scalar>::HasCmp };
};
 
template <typename Scalar>
struct all_visitor {
  using result_type = bool;
  using Packet = typename packet_traits<Scalar>::type;
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index, Index) { res = (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index) { res = (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline bool all_predux(const Packet& p) const { return !predux_any(pcmp_eq(p, pzero(p))); }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index, Index) { res = all_predux(p); }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index) { res = all_predux(p); }
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index, Index) { res = res && (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index) { res = res && (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index, Index) { res = res && all_predux(p); }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index) { res = res && all_predux(p); }
  EIGEN_DEVICE_FUNC inline bool done() const { return !res; }
  bool res = true;
};
template <typename Scalar>
struct functor_traits<all_visitor<Scalar>> {
  enum { Cost = NumTraits<Scalar>::ReadCost, LinearAccess = true, PacketAccess = packet_traits<Scalar>::HasCmp };
};
 
template <typename Scalar>
struct any_visitor {
  using result_type = bool;
  using Packet = typename packet_traits<Scalar>::type;
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index, Index) { res = (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index) { res = (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline bool any_predux(const Packet& p) const {
    return predux_any(pandnot(ptrue(p), pcmp_eq(p, pzero(p))));
  }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index, Index) { res = any_predux(p); }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index) { res = any_predux(p); }
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index, Index) { res = res || (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index) { res = res || (value != Scalar(0)); }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index, Index) { res = res || any_predux(p); }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index) { res = res || any_predux(p); }
  EIGEN_DEVICE_FUNC inline bool done() const { return res; }
  bool res = false;
};
template <typename Scalar>
struct functor_traits<any_visitor<Scalar>> {
  enum { Cost = NumTraits<Scalar>::ReadCost, LinearAccess = true, PacketAccess = packet_traits<Scalar>::HasCmp };
};
 
template <typename Scalar>
struct count_visitor {
  using result_type = Index;
  using Packet = typename packet_traits<Scalar>::type;
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index, Index) { res = value != Scalar(0) ? 1 : 0; }
  EIGEN_DEVICE_FUNC inline void init(const Scalar& value, Index) { res = value != Scalar(0) ? 1 : 0; }
  EIGEN_DEVICE_FUNC inline Index count_redux(const Packet& p) const {
    const Packet cst_one = pset1<Packet>(Scalar(1));
    Packet true_vals = pandnot(cst_one, pcmp_eq(p, pzero(p)));
    Scalar num_true = predux(true_vals);
    return static_cast<Index>(num_true);
  }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index, Index) { res = count_redux(p); }
  EIGEN_DEVICE_FUNC inline void initpacket(const Packet& p, Index) { res = count_redux(p); }
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index, Index) {
    if (value != Scalar(0)) res++;
  }
  EIGEN_DEVICE_FUNC inline void operator()(const Scalar& value, Index) {
    if (value != Scalar(0)) res++;
  }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index, Index) { res += count_redux(p); }
  EIGEN_DEVICE_FUNC inline void packet(const Packet& p, Index) { res += count_redux(p); }
  Index res = 0;
};
 
template <typename Scalar>
struct functor_traits<count_visitor<Scalar>> {
  enum {
    Cost = NumTraits<Scalar>::AddCost,
    LinearAccess = true,
    // predux is problematic for bool
    PacketAccess = packet_traits<Scalar>::HasCmp && packet_traits<Scalar>::HasAdd && !is_same<Scalar, bool>::value
  };
};
 
}  // end namespace internal
 
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* rowId,
                                                                                          IndexType* colId) const {
  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
 
  internal::minmax_coeff_visitor<Derived, true, NaNPropagation> minVisitor;
  this->visit(minVisitor);
  *rowId = minVisitor.row;
  if (colId) *colId = minVisitor.col;
  return minVisitor.res;
}
 
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::minCoeff(IndexType* index) const {
  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
 
  internal::minmax_coeff_visitor<Derived, true, NaNPropagation> minVisitor;
  this->visit(minVisitor);
  *index = IndexType((RowsAtCompileTime == 1) ? minVisitor.col : minVisitor.row);
  return minVisitor.res;
}
 
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* rowPtr,
                                                                                          IndexType* colPtr) const {
  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
 
  internal::minmax_coeff_visitor<Derived, false, NaNPropagation> maxVisitor;
  this->visit(maxVisitor);
  *rowPtr = maxVisitor.row;
  if (colPtr) *colPtr = maxVisitor.col;
  return maxVisitor.res;
}
 
template <typename Derived>
template <int NaNPropagation, typename IndexType>
EIGEN_DEVICE_FUNC typename internal::traits<Derived>::Scalar DenseBase<Derived>::maxCoeff(IndexType* index) const {
  eigen_assert(this->rows() > 0 && this->cols() > 0 && "you are using an empty matrix");
 
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  internal::minmax_coeff_visitor<Derived, false, NaNPropagation> maxVisitor;
  this->visit(maxVisitor);
  *index = (RowsAtCompileTime == 1) ? maxVisitor.col : maxVisitor.row;
  return maxVisitor.res;
}
 
template <typename Derived>
EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::all() const {
  using Visitor = internal::all_visitor<Scalar>;
  using impl = internal::visit_impl<Derived, Visitor, /*ShortCircuitEvaulation*/ true>;
  Visitor visitor;
  impl::run(derived(), visitor);
  return visitor.res;
}
 
template <typename Derived>
EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::any() const {
  using Visitor = internal::any_visitor<Scalar>;
  using impl = internal::visit_impl<Derived, Visitor, /*ShortCircuitEvaulation*/ true>;
  Visitor visitor;
  impl::run(derived(), visitor);
  return visitor.res;
}
 
template <typename Derived>
EIGEN_DEVICE_FUNC Index DenseBase<Derived>::count() const {
  using Visitor = internal::count_visitor<Scalar>;
  using impl = internal::visit_impl<Derived, Visitor, /*ShortCircuitEvaulation*/ false>;
  Visitor visitor;
  impl::run(derived(), visitor);
  return visitor.res;
}
 
template <typename Derived>
EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::hasNaN() const {
  return derived().cwiseTypedNotEqual(derived()).any();
}
 
template <typename Derived>
EIGEN_DEVICE_FUNC inline bool DenseBase<Derived>::allFinite() const {
  return derived().array().isFiniteTyped().all();
}
 
}  // end namespace Eigen
 
#endif  // EIGEN_VISITOR_H