text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2008-2010 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_NULLARY_FUNCTORS_H
  #define EIGEN_NULLARY_FUNCTORS_H
  
  namespace Eigen {
  
  namespace internal {
  
  template<typename Scalar>
  struct scalar_constant_op {
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const scalar_constant_op& other) : m_other(other.m_other) { }
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_constant_op(const Scalar& other) : m_other(other) { }
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index, Index = 0) const { return m_other; }
    template<typename Index, typename PacketType>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const PacketType packetOp(Index, Index = 0) const { return internal::pset1<PacketType>(m_other); }
    const Scalar m_other;
  };
  template<typename Scalar>
  struct functor_traits<scalar_constant_op<Scalar> >
  { enum { Cost = 1, PacketAccess = packet_traits<Scalar>::Vectorizable, IsRepeatable = true }; };
  
  template<typename Scalar> struct scalar_identity_op {
    EIGEN_EMPTY_STRUCT_CTOR(scalar_identity_op)
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const { return row==col ? Scalar(1) : Scalar(0); }
  };
  template<typename Scalar>
  struct functor_traits<scalar_identity_op<Scalar> >
  { enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = false, IsRepeatable = true }; };
  
  template <typename Scalar, typename Packet, bool RandomAccess> struct linspaced_op_impl;
  
  // linear access for packet ops:
  // 1) initialization
  //   base = [low, ..., low] + ([step, ..., step] * [-size, ..., 0])
  // 2) each step (where size is 1 for coeff access or PacketSize for packet access)
  //   base += [size*step, ..., size*step]
  //
  // TODO: Perhaps it's better to initialize lazily (so not in the constructor but in packetOp)
  //       in order to avoid the padd() in operator() ?
  template <typename Scalar, typename Packet>
  struct linspaced_op_impl<Scalar,Packet,false>
  {
    linspaced_op_impl(const Scalar& low, const Scalar& step) :
    m_low(low), m_step(step),
    m_packetStep(pset1<Packet>(unpacket_traits<Packet>::size*step)),
    m_base(padd(pset1<Packet>(low), pmul(pset1<Packet>(step),plset<Packet>(-unpacket_traits<Packet>::size)))) {}
  
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index i) const 
    { 
      m_base = padd(m_base, pset1<Packet>(m_step));
      return m_low+Scalar(i)*m_step; 
    }
  
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(Index) const { return m_base = padd(m_base,m_packetStep); }
  
    const Scalar m_low;
    const Scalar m_step;
    const Packet m_packetStep;
    mutable Packet m_base;
  };
  
  // random access for packet ops:
  // 1) each step
  //   [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
  template <typename Scalar, typename Packet>
  struct linspaced_op_impl<Scalar,Packet,true>
  {
    linspaced_op_impl(const Scalar& low, const Scalar& step) :
    m_low(low), m_step(step),
    m_lowPacket(pset1<Packet>(m_low)), m_stepPacket(pset1<Packet>(m_step)), m_interPacket(plset<Packet>(0)) {}
  
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return m_low+i*m_step; }
  
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(Index i) const
    { return internal::padd(m_lowPacket, pmul(m_stepPacket, padd(pset1<Packet>(Scalar(i)),m_interPacket))); }
  
    const Scalar m_low;
    const Scalar m_step;
    const Packet m_lowPacket;
    const Packet m_stepPacket;
    const Packet m_interPacket;
  };
  
  // ----- Linspace functor ----------------------------------------------------------------
  
  // Forward declaration (we default to random access which does not really give
  // us a speed gain when using packet access but it allows to use the functor in
  // nested expressions).
  template <typename Scalar, typename PacketType, bool RandomAccess = true> struct linspaced_op;
  template <typename Scalar, typename PacketType, bool RandomAccess> struct functor_traits< linspaced_op<Scalar,PacketType,RandomAccess> >
  { enum { Cost = 1, PacketAccess = packet_traits<Scalar>::HasSetLinear, IsRepeatable = true }; };
  template <typename Scalar, typename PacketType, bool RandomAccess> struct linspaced_op
  {
    linspaced_op(const Scalar& low, const Scalar& high, Index num_steps) : impl((num_steps==1 ? high : low), (num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1))) {}
  
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index i) const { return impl(i); }
  
    // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
    // there row==0 and col is used for the actual iteration.
    template<typename Index>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (Index row, Index col) const 
    {
      eigen_assert(col==0 || row==0);
      return impl(col + row);
    }
  
    template<typename Index, typename Packet>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(Index i) const { return impl.packetOp(i); }
  
    // We need this function when assigning e.g. a RowVectorXd to a MatrixXd since
    // there row==0 and col is used for the actual iteration.
    template<typename Index, typename Packet>
    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(Index row, Index col) const
    {
      eigen_assert(col==0 || row==0);
      return impl.packetOp(col + row);
    }
  
    // This proxy object handles the actual required temporaries, the different
    // implementations (random vs. sequential access) as well as the
    // correct piping to size 2/4 packet operations.
    const linspaced_op_impl<Scalar,PacketType,RandomAccess> impl;
  };
  
  // all functors allow linear access, except scalar_identity_op. So we fix here a quick meta
  // to indicate whether a functor allows linear access, just always answering 'yes' except for
  // scalar_identity_op.
  template<typename Functor> struct functor_has_linear_access { enum { ret = 1 }; };
  template<typename Scalar> struct functor_has_linear_access<scalar_identity_op<Scalar> > { enum { ret = 0 }; };
  
  } // end namespace internal
  
  } // end namespace Eigen
  
  #endif // EIGEN_NULLARY_FUNCTORS_H
  