// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2016 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_UNARY_FUNCTORS_H
#define EIGEN_UNARY_FUNCTORS_H

#include "../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

/** \internal
  * \brief Template functor to compute the opposite of a scalar
  *
  * \sa class CwiseUnaryOp, MatrixBase::operator-
  */
template<typename Scalar> struct scalar_opposite_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return -a; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return internal::pnegate(a); }
};
template<typename Scalar>
struct functor_traits<scalar_opposite_op<Scalar> >
{ enum {
    Cost = NumTraits<Scalar>::AddCost,
    PacketAccess = packet_traits<Scalar>::HasNegate };
};

/** \internal
  * \brief Template functor to compute the absolute value of a scalar
  *
  * \sa class CwiseUnaryOp, Cwise::abs
  */
template<typename Scalar> struct scalar_abs_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs(a); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return internal::pabs(a); }
};
template<typename Scalar>
struct functor_traits<scalar_abs_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::AddCost,
    PacketAccess = packet_traits<Scalar>::HasAbs
  };
};

/** \internal
  * \brief Template functor to compute the score of a scalar, to chose a pivot
  *
  * \sa class CwiseUnaryOp
  */
template<typename Scalar> struct scalar_score_coeff_op : scalar_abs_op<Scalar>
{
  typedef void Score_is_abs;
};
template<typename Scalar>
struct functor_traits<scalar_score_coeff_op<Scalar> > : functor_traits<scalar_abs_op<Scalar> > {};

/* Avoid recomputing abs when we know the score and they are the same. Not a true Eigen functor.  */
template<typename Scalar, typename=void> struct abs_knowing_score
{
  typedef typename NumTraits<Scalar>::Real result_type;
  template<typename Score>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a, const Score&) const { return numext::abs(a); }
};
template<typename Scalar> struct abs_knowing_score<Scalar, typename scalar_score_coeff_op<Scalar>::Score_is_abs>
{
  typedef typename NumTraits<Scalar>::Real result_type;
  template<typename Scal>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scal&, const result_type& a) const { return a; }
};

/** \internal
  * \brief Template functor to compute the squared absolute value of a scalar
  *
  * \sa class CwiseUnaryOp, Cwise::abs2
  */
template<typename Scalar> struct scalar_abs2_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::abs2(a); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return internal::pmul(a,a); }
};
template<typename Scalar>
struct functor_traits<scalar_abs2_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasAbs2 }; };

/** \internal
  * \brief Template functor to compute the conjugate of a complex value
  *
  * \sa class CwiseUnaryOp, MatrixBase::conjugate()
  */
template<typename Scalar> struct scalar_conjugate_op {
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::conj(a); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
};
template<typename Scalar>
struct functor_traits<scalar_conjugate_op<Scalar> >
{
  enum {
    Cost = 0,
    // Yes the cost is zero even for complexes because in most cases for which
    // the cost is used, conjugation turns to be a no-op. Some examples:
    //   cost(a*conj(b)) == cost(a*b)
    //   cost(a+conj(b)) == cost(a+b)
    //   <etc.
    // If we don't set it to zero, then:
    //   A.conjugate().lazyProduct(B.conjugate())
    // will bake its operands. We definitely don't want that!
    PacketAccess = packet_traits<Scalar>::HasConj
  };
};

/** \internal
  * \brief Template functor to compute the phase angle of a complex
  *
  * \sa class CwiseUnaryOp, Cwise::arg
  */
template<typename Scalar> struct scalar_arg_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return numext::arg(a); }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return internal::parg(a); }
};
template<typename Scalar>
struct functor_traits<scalar_arg_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::IsComplex ? 5 * NumTraits<Scalar>::MulCost : NumTraits<Scalar>::AddCost,
    PacketAccess = packet_traits<Scalar>::HasArg
  };
};
/** \internal
  * \brief Template functor to cast a scalar to another type
  *
  * \sa class CwiseUnaryOp, MatrixBase::cast()
  */
template<typename Scalar, typename NewType>
struct scalar_cast_op {
  typedef NewType result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const NewType operator() (const Scalar& a) const { return cast<Scalar, NewType>(a); }
};
template<typename Scalar, typename NewType>
struct functor_traits<scalar_cast_op<Scalar,NewType> >
{ enum { Cost = is_same<Scalar, NewType>::value ? 0 : NumTraits<NewType>::AddCost, PacketAccess = false }; };

/** \internal
  * \brief Template functor to arithmetically shift a scalar right by a number of bits
  *
  * \sa class CwiseUnaryOp, MatrixBase::shift_right()
  */
template<typename Scalar, int N>
struct scalar_shift_right_op {

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const
  { return a >> N; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return internal::parithmetic_shift_right<N>(a); }
};
template<typename Scalar, int N>
struct functor_traits<scalar_shift_right_op<Scalar,N> >
{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasShift }; };

/** \internal
  * \brief Template functor to logically shift a scalar left by a number of bits
  *
  * \sa class CwiseUnaryOp, MatrixBase::shift_left()
  */
template<typename Scalar, int N>
struct scalar_shift_left_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const
  { return a << N; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
  { return internal::plogical_shift_left<N>(a); }
};
template<typename Scalar, int N>
struct functor_traits<scalar_shift_left_op<Scalar,N> >
{ enum { Cost = NumTraits<Scalar>::AddCost, PacketAccess = packet_traits<Scalar>::HasShift }; };

/** \internal
  * \brief Template functor to extract the real part of a complex
  *
  * \sa class CwiseUnaryOp, MatrixBase::real()
  */
template<typename Scalar>
struct scalar_real_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::real(a); }
};
template<typename Scalar>
struct functor_traits<scalar_real_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };

/** \internal
  * \brief Template functor to extract the imaginary part of a complex
  *
  * \sa class CwiseUnaryOp, MatrixBase::imag()
  */
template<typename Scalar>
struct scalar_imag_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const { return numext::imag(a); }
};
template<typename Scalar>
struct functor_traits<scalar_imag_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };

/** \internal
  * \brief Template functor to extract the real part of a complex as a reference
  *
  * \sa class CwiseUnaryOp, MatrixBase::real()
  */
template<typename Scalar>
struct scalar_real_ref_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::real_ref(*const_cast<Scalar*>(&a)); }
};
template<typename Scalar>
struct functor_traits<scalar_real_ref_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };

/** \internal
  * \brief Template functor to extract the imaginary part of a complex as a reference
  *
  * \sa class CwiseUnaryOp, MatrixBase::imag()
  */
template<typename Scalar>
struct scalar_imag_ref_op {
  typedef typename NumTraits<Scalar>::Real result_type;
  EIGEN_DEVICE_FUNC
  EIGEN_STRONG_INLINE result_type& operator() (const Scalar& a) const { return numext::imag_ref(*const_cast<Scalar*>(&a)); }
};
template<typename Scalar>
struct functor_traits<scalar_imag_ref_op<Scalar> >
{ enum { Cost = 0, PacketAccess = false }; };

/** \internal
  *
  * \brief Template functor to compute the exponential of a scalar
  *
  * \sa class CwiseUnaryOp, Cwise::exp()
  */
template<typename Scalar> struct scalar_exp_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return internal::pexp(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
};
template <typename Scalar>
struct functor_traits<scalar_exp_op<Scalar> > {
  enum {
    PacketAccess = packet_traits<Scalar>::HasExp,
    // The following numbers are based on the AVX implementation.
#ifdef EIGEN_VECTORIZE_FMA
    // Haswell can issue 2 add/mul/madd per cycle.
    Cost =
    (sizeof(Scalar) == 4
     // float: 8 pmadd, 4 pmul, 2 padd/psub, 6 other
     ? (8 * NumTraits<Scalar>::AddCost + 6 * NumTraits<Scalar>::MulCost)
     // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
     : (14 * NumTraits<Scalar>::AddCost +
        6 * NumTraits<Scalar>::MulCost +
        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
#else
    Cost =
    (sizeof(Scalar) == 4
     // float: 7 pmadd, 6 pmul, 4 padd/psub, 10 other
     ? (21 * NumTraits<Scalar>::AddCost + 13 * NumTraits<Scalar>::MulCost)
     // double: 7 pmadd, 5 pmul, 3 padd/psub, 1 div,  13 other
     : (23 * NumTraits<Scalar>::AddCost +
        12 * NumTraits<Scalar>::MulCost +
        scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value))
#endif
  };
};

/** \internal
  *
  * \brief Template functor to compute the exponential of a scalar - 1.
  *
  * \sa class CwiseUnaryOp, ArrayBase::expm1()
  */
template<typename Scalar> struct scalar_expm1_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::expm1(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pexpm1(a); }
};
template <typename Scalar>
struct functor_traits<scalar_expm1_op<Scalar> > {
  enum {
    PacketAccess = packet_traits<Scalar>::HasExpm1,
    Cost = functor_traits<scalar_exp_op<Scalar> >::Cost // TODO measure cost of expm1
  };
};

/** \internal
  *
  * \brief Template functor to compute the logarithm of a scalar
  *
  * \sa class CwiseUnaryOp, ArrayBase::log()
  */
template<typename Scalar> struct scalar_log_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
};
template <typename Scalar>
struct functor_traits<scalar_log_op<Scalar> > {
  enum {
    PacketAccess = packet_traits<Scalar>::HasLog,
    Cost =
    (PacketAccess
     // The following numbers are based on the AVX implementation.
#ifdef EIGEN_VECTORIZE_FMA
     // 8 pmadd, 6 pmul, 8 padd/psub, 16 other, can issue 2 add/mul/madd per cycle.
     ? (20 * NumTraits<Scalar>::AddCost + 7 * NumTraits<Scalar>::MulCost)
#else
     // 8 pmadd, 6 pmul, 8 padd/psub, 20 other
     ? (36 * NumTraits<Scalar>::AddCost + 14 * NumTraits<Scalar>::MulCost)
#endif
     // Measured cost of std::log.
     : sizeof(Scalar)==4 ? 40 : 85)
  };
};

/** \internal
  *
  * \brief Template functor to compute the logarithm of 1 plus a scalar value
  *
  * \sa class CwiseUnaryOp, ArrayBase::log1p()
  */
template<typename Scalar> struct scalar_log1p_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::log1p(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog1p(a); }
};
template <typename Scalar>
struct functor_traits<scalar_log1p_op<Scalar> > {
  enum {
    PacketAccess = packet_traits<Scalar>::HasLog1p,
    Cost = functor_traits<scalar_log_op<Scalar> >::Cost // TODO measure cost of log1p
  };
};

/** \internal
  *
  * \brief Template functor to compute the base-10 logarithm of a scalar
  *
  * \sa class CwiseUnaryOp, Cwise::log10()
  */
template<typename Scalar> struct scalar_log10_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { EIGEN_USING_STD(log10) return log10(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog10(a); }
};
template<typename Scalar>
struct functor_traits<scalar_log10_op<Scalar> >
{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog10 }; };

/** \internal
  *
  * \brief Template functor to compute the base-2 logarithm of a scalar
  *
  * \sa class CwiseUnaryOp, Cwise::log2()
  */
template<typename Scalar> struct scalar_log2_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return Scalar(EIGEN_LOG2E) * numext::log(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::plog2(a); }
};
template<typename Scalar>
struct functor_traits<scalar_log2_op<Scalar> >
{ enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasLog }; };

/** \internal
  * \brief Template functor to compute the square root of a scalar
  * \sa class CwiseUnaryOp, Cwise::sqrt()
  */
template<typename Scalar> struct scalar_sqrt_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sqrt(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
};
template <typename Scalar>
struct functor_traits<scalar_sqrt_op<Scalar> > {
  enum {
#if EIGEN_FAST_MATH
    // The following numbers are based on the AVX implementation.
    Cost = (sizeof(Scalar) == 8 ? 28
                                // 4 pmul, 1 pmadd, 3 other
                                : (3 * NumTraits<Scalar>::AddCost +
                                   5 * NumTraits<Scalar>::MulCost)),
#else
    // The following numbers are based on min VSQRT throughput on Haswell.
    Cost = (sizeof(Scalar) == 8 ? 28 : 14),
#endif
    PacketAccess = packet_traits<Scalar>::HasSqrt
  };
};

// Boolean specialization to eliminate -Wimplicit-conversion-floating-point-to-bool warnings.
template<> struct scalar_sqrt_op<bool> {
  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
  template <typename Packet>
  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return a; }
};
template <>
struct functor_traits<scalar_sqrt_op<bool> > {
  enum { Cost = 1, PacketAccess = packet_traits<bool>::Vectorizable };
};

/** \internal
  * \brief Template functor to compute the reciprocal square root of a scalar
  * \sa class CwiseUnaryOp, Cwise::rsqrt()
  */
template<typename Scalar> struct scalar_rsqrt_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::rsqrt(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::prsqrt(a); }
};

template<typename Scalar>
struct functor_traits<scalar_rsqrt_op<Scalar> >
{ enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasRsqrt
  };
};

/** \internal
  * \brief Template functor to compute the cosine of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::cos()
  */
template<typename Scalar> struct scalar_cos_op {
  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return numext::cos(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
};
template<typename Scalar>
struct functor_traits<scalar_cos_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasCos
  };
};

/** \internal
  * \brief Template functor to compute the sine of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::sin()
  */
template<typename Scalar> struct scalar_sin_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sin(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
};
template<typename Scalar>
struct functor_traits<scalar_sin_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasSin
  };
};


/** \internal
  * \brief Template functor to compute the tan of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::tan()
  */
template<typename Scalar> struct scalar_tan_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::tan(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
};
template<typename Scalar>
struct functor_traits<scalar_tan_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasTan
  };
};

/** \internal
  * \brief Template functor to compute the arc cosine of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::acos()
  */
template<typename Scalar> struct scalar_acos_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::acos(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
};
template<typename Scalar>
struct functor_traits<scalar_acos_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasACos
  };
};

/** \internal
  * \brief Template functor to compute the arc sine of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::asin()
  */
template<typename Scalar> struct scalar_asin_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::asin(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
};
template<typename Scalar>
struct functor_traits<scalar_asin_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasASin
  };
};


/** \internal
  * \brief Template functor to compute the atan of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::atan()
  */
template<typename Scalar> struct scalar_atan_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::atan(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::patan(a); }
};
template<typename Scalar>
struct functor_traits<scalar_atan_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasATan
  };
};

/** \internal
  * \brief Template functor to compute the tanh of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::tanh()
  */
template <typename Scalar>
struct scalar_tanh_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::tanh(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& x) const { return ptanh(x); }
};

template <typename Scalar>
struct functor_traits<scalar_tanh_op<Scalar> > {
  enum {
    PacketAccess = packet_traits<Scalar>::HasTanh,
    Cost = ( (EIGEN_FAST_MATH && is_same<Scalar,float>::value)
// The following numbers are based on the AVX implementation,
#ifdef EIGEN_VECTORIZE_FMA
                // Haswell can issue 2 add/mul/madd per cycle.
                // 9 pmadd, 2 pmul, 1 div, 2 other
                ? (2 * NumTraits<Scalar>::AddCost +
                   6 * NumTraits<Scalar>::MulCost +
                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
#else
                ? (11 * NumTraits<Scalar>::AddCost +
                   11 * NumTraits<Scalar>::MulCost +
                   scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value)
#endif
                // This number assumes a naive implementation of tanh
                : (6 * NumTraits<Scalar>::AddCost +
                   3 * NumTraits<Scalar>::MulCost +
                   2 * scalar_div_cost<Scalar,packet_traits<Scalar>::HasDiv>::value +
                   functor_traits<scalar_exp_op<Scalar> >::Cost))
  };
};

/** \internal
  * \brief Template functor to compute the atanh of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::atanh()
  */
template <typename Scalar>
struct scalar_atanh_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::atanh(a); }
};

template <typename Scalar>
struct functor_traits<scalar_atanh_op<Scalar> > {
  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
};

/** \internal
  * \brief Template functor to compute the sinh of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::sinh()
  */
template<typename Scalar> struct scalar_sinh_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::sinh(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::psinh(a); }
};
template<typename Scalar>
struct functor_traits<scalar_sinh_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasSinh
  };
};

/** \internal
  * \brief Template functor to compute the asinh of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::asinh()
  */
template <typename Scalar>
struct scalar_asinh_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::asinh(a); }
};

template <typename Scalar>
struct functor_traits<scalar_asinh_op<Scalar> > {
  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
};

/** \internal
  * \brief Template functor to compute the cosh of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::cosh()
  */
template<typename Scalar> struct scalar_cosh_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const { return numext::cosh(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pcosh(a); }
};
template<typename Scalar>
struct functor_traits<scalar_cosh_op<Scalar> >
{
  enum {
    Cost = 5 * NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasCosh
  };
};

/** \internal
  * \brief Template functor to compute the acosh of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::acosh()
  */
template <typename Scalar>
struct scalar_acosh_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator()(const Scalar& a) const { return numext::acosh(a); }
};

template <typename Scalar>
struct functor_traits<scalar_acosh_op<Scalar> > {
  enum { Cost = 5 * NumTraits<Scalar>::MulCost, PacketAccess = false };
};

/** \internal
  * \brief Template functor to compute the inverse of a scalar
  * \sa class CwiseUnaryOp, Cwise::inverse()
  */
template<typename Scalar>
struct scalar_inverse_op {
  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return Scalar(1)/a; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
  { return internal::preciprocal(a); }
};
template <typename Scalar>
struct functor_traits<scalar_inverse_op<Scalar> > {
  enum {
    PacketAccess = packet_traits<Scalar>::HasDiv,
    // If packet_traits<Scalar>::HasReciprocal then the Estimated cost is that
    // of computing an approximation plus a single Newton-Raphson step, which
    // consists of 1 pmul + 1 pmadd.
    Cost = (packet_traits<Scalar>::HasReciprocal
                ? 4 * NumTraits<Scalar>::MulCost
                : scalar_div_cost<Scalar, PacketAccess>::value)
  };
};

/** \internal
  * \brief Template functor to compute the square of a scalar
  * \sa class CwiseUnaryOp, Cwise::square()
  */
template<typename Scalar>
struct scalar_square_op {
  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
  { return internal::pmul(a,a); }
};
template<typename Scalar>
struct functor_traits<scalar_square_op<Scalar> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };

// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
template<>
struct scalar_square_op<bool> {
  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
  template<typename Packet>
  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
  { return a; }
};
template<>
struct functor_traits<scalar_square_op<bool> >
{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };

/** \internal
  * \brief Template functor to compute the cube of a scalar
  * \sa class CwiseUnaryOp, Cwise::cube()
  */
template<typename Scalar>
struct scalar_cube_op {
  EIGEN_DEVICE_FUNC inline Scalar operator() (const Scalar& a) const { return a*a*a; }
  template<typename Packet>
  EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
  { return internal::pmul(a,pmul(a,a)); }
};
template<typename Scalar>
struct functor_traits<scalar_cube_op<Scalar> >
{ enum { Cost = 2*NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };

// Boolean specialization to avoid -Wint-in-bool-context warnings on GCC.
template<>
struct scalar_cube_op<bool> {
  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline bool operator() (const bool& a) const { return a; }
  template<typename Packet>
  EIGEN_DEPRECATED EIGEN_DEVICE_FUNC inline const Packet packetOp(const Packet& a) const
  { return a; }
};
template<>
struct functor_traits<scalar_cube_op<bool> >
{ enum { Cost = 0, PacketAccess = packet_traits<bool>::Vectorizable }; };

/** \internal
  * \brief Template functor to compute the rounded value of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::round()
  */
template<typename Scalar> struct scalar_round_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::round(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pround(a); }
};
template<typename Scalar>
struct functor_traits<scalar_round_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasRound
  };
};

/** \internal
  * \brief Template functor to compute the floor of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::floor()
  */
template<typename Scalar> struct scalar_floor_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::floor(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pfloor(a); }
};
template<typename Scalar>
struct functor_traits<scalar_floor_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasFloor
  };
};

/** \internal
  * \brief Template functor to compute the rounded (with current rounding mode)  value of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::rint()
  */
template<typename Scalar> struct scalar_rint_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::rint(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::print(a); }
};
template<typename Scalar>
struct functor_traits<scalar_rint_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasRint
  };
};

/** \internal
  * \brief Template functor to compute the ceil of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::ceil()
  */
template<typename Scalar> struct scalar_ceil_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return numext::ceil(a); }
  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const { return internal::pceil(a); }
};
template<typename Scalar>
struct functor_traits<scalar_ceil_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = packet_traits<Scalar>::HasCeil
  };
};

/** \internal
  * \brief Template functor to compute whether a scalar is NaN
  * \sa class CwiseUnaryOp, ArrayBase::isnan()
  */
template<typename Scalar> struct scalar_isnan_op {
  typedef bool result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const {
#if defined(SYCL_DEVICE_ONLY)
    return numext::isnan(a);
#else
    return (numext::isnan)(a);
#endif
  }
};
template<typename Scalar>
struct functor_traits<scalar_isnan_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = false
  };
};

/** \internal
  * \brief Template functor to check whether a scalar is +/-inf
  * \sa class CwiseUnaryOp, ArrayBase::isinf()
  */
template<typename Scalar> struct scalar_isinf_op {
  typedef bool result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const {
#if defined(SYCL_DEVICE_ONLY)
    return numext::isinf(a);
#else
    return (numext::isinf)(a);
#endif
  }
};
template<typename Scalar>
struct functor_traits<scalar_isinf_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = false
  };
};

/** \internal
  * \brief Template functor to check whether a scalar has a finite value
  * \sa class CwiseUnaryOp, ArrayBase::isfinite()
  */
template<typename Scalar> struct scalar_isfinite_op {
  typedef bool result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator() (const Scalar& a) const {
#if defined(SYCL_DEVICE_ONLY)
    return numext::isfinite(a);
#else
    return (numext::isfinite)(a);
#endif
  }
};
template<typename Scalar>
struct functor_traits<scalar_isfinite_op<Scalar> >
{
  enum {
    Cost = NumTraits<Scalar>::MulCost,
    PacketAccess = false
  };
};

/** \internal
  * \brief Template functor to compute the logical not of a boolean
  *
  * \sa class CwiseUnaryOp, ArrayBase::operator!
  */
template<typename Scalar> struct scalar_boolean_not_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE bool operator() (const bool& a) const { return !a; }
};
template<typename Scalar>
struct functor_traits<scalar_boolean_not_op<Scalar> > {
  enum {
    Cost = NumTraits<bool>::AddCost,
    PacketAccess = false
  };
};

/** \internal
  * \brief Template functor to compute the signum of a scalar
  * \sa class CwiseUnaryOp, Cwise::sign()
  */
template<typename Scalar>
struct scalar_sign_op {
  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const
  {
    return numext::sign(a);
  }

  template <typename Packet>
  EIGEN_DEVICE_FUNC inline Packet packetOp(const Packet& a) const {
    return internal::psign(a);
  }
};

template<typename Scalar>
struct functor_traits<scalar_sign_op<Scalar> >
{ enum {
    Cost =
        NumTraits<Scalar>::IsComplex
        ? ( 8*NumTraits<Scalar>::MulCost  ) // roughly
        : ( 3*NumTraits<Scalar>::AddCost),
    PacketAccess = packet_traits<Scalar>::HasSign && packet_traits<Scalar>::Vectorizable
  };
};

/** \internal
  * \brief Template functor to compute the logistic function of a scalar
  * \sa class CwiseUnaryOp, ArrayBase::logistic()
  */
template <typename T>
struct scalar_logistic_op {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T operator()(const T& x) const {
    return packetOp(x);
  }

  template <typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
  Packet packetOp(const Packet& x) const {
    const Packet one = pset1<Packet>(T(1));
    const Packet inf = pset1<Packet>(NumTraits<T>::infinity());
    const Packet e = pexp(x);
    const Packet inf_mask = pcmp_eq(e, inf);
    return pselect(inf_mask, one, pdiv(e, padd(one, e)));
  }
};

// TODO(rmlarsen): Enable the following on host when integer_packet is defined
// for the relevant packet types.
#ifdef EIGEN_GPU_CC

/** \internal
  * \brief Template specialization of the logistic function for float.
  * Computes S(x) = exp(x) / (1 + exp(x)), where exp(x) is implemented
  * using an algorithm partly adopted from the implementation of
  * pexp_float. See the individual steps described in the code below.
  * Note that compared to pexp, we use an additional outer multiplicative
  * range reduction step using the identity exp(x) = exp(x/2)^2.
  * This prevert us from having to call ldexp on values that could produce
  * a denormal result, which allows us to call the faster implementation in
  * pldexp_fast_impl<Packet>::run(p, m).
  * The final squaring, however, doubles the error bound on the final
  * approximation. Exhaustive testing shows that we have a worst case error
  * of 4.5 ulps (compared to computing S(x) in double precision), which is
  * acceptable.
  */
template <>
struct scalar_logistic_op<float> {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float operator()(const float& x) const {
    // Truncate at the first point where the interpolant is exactly one.
    const float cst_exp_hi = 16.6355324f;
    const float e = numext::exp(numext::mini(x, cst_exp_hi));
    return e / (1.0f + e);
  }

  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
  packetOp(const Packet& _x) const {
    const Packet cst_zero = pset1<Packet>(0.0f);
    const Packet cst_one = pset1<Packet>(1.0f);
    const Packet cst_half = pset1<Packet>(0.5f);
    // Truncate at the first point where the interpolant is exactly one.
    const Packet cst_exp_hi = pset1<Packet>(16.6355324f);
    const Packet cst_exp_lo = pset1<Packet>(-104.f);

    // Clamp x to the non-trivial range where S(x). Outside this
    // interval the correctly rounded value of S(x) is either zero
    // or one.
    Packet zero_mask = pcmp_lt(_x, cst_exp_lo);
    Packet x = pmin(_x, cst_exp_hi);

    // 1. Multiplicative range reduction:
    // Reduce the range of x by a factor of 2. This avoids having
    // to compute exp(x) accurately where the result is a denormalized
    // value.
    x = pmul(x, cst_half);

    // 2. Subtractive range reduction:
    // Express exp(x) as exp(m*ln(2) + r) = 2^m*exp(r), start by extracting
    // m = floor(x/ln(2) + 0.5), such that x = m*ln(2) + r.
    const Packet cst_cephes_LOG2EF = pset1<Packet>(1.44269504088896341f);
    Packet m = pfloor(pmadd(x, cst_cephes_LOG2EF, cst_half));
    // Get r = x - m*ln(2). We use a trick from Cephes where the term
    // m*ln(2) is subtracted out in two parts, m*C1+m*C2 = m*ln(2),
    // to avoid accumulating truncation errors.
    const Packet cst_cephes_exp_C1 = pset1<Packet>(-0.693359375f);
    const Packet cst_cephes_exp_C2 = pset1<Packet>(2.12194440e-4f);
    Packet r = pmadd(m, cst_cephes_exp_C1, x);
    r = pmadd(m, cst_cephes_exp_C2, r);

    // 3. Compute an approximation to exp(r) using a degree 5 minimax polynomial.
    // We compute even and odd terms separately to increase instruction level
    // parallelism.
    Packet r2 = pmul(r, r);
    const Packet cst_p2 = pset1<Packet>(0.49999141693115234375f);
    const Packet cst_p3 = pset1<Packet>(0.16666877269744873046875f);
    const Packet cst_p4 = pset1<Packet>(4.1898667812347412109375e-2f);
    const Packet cst_p5 = pset1<Packet>(8.33471305668354034423828125e-3f);

    const Packet p_even = pmadd(r2, cst_p4, cst_p2);
    const Packet p_odd = pmadd(r2, cst_p5, cst_p3);
    const Packet p_low = padd(r, cst_one);
    Packet p = pmadd(r, p_odd, p_even);
    p = pmadd(r2, p, p_low);

    // 4. Undo subtractive range reduction exp(m*ln(2) + r) = 2^m * exp(r).
    Packet e = pldexp_fast_impl<Packet>::run(p, m);

    // 5. Undo multiplicative range reduction by using exp(r) = exp(r/2)^2.
    e = pmul(e, e);

    // Return exp(x) / (1 + exp(x))
    return pselect(zero_mask, cst_zero, pdiv(e, padd(cst_one, e)));
  }
};
#endif  // #ifndef EIGEN_GPU_COMPILE_PHASE


template <typename T>
struct functor_traits<scalar_logistic_op<T> > {
  enum {
    // The cost estimate for float here here is for the common(?) case where
    // all arguments are greater than -9.
    Cost = scalar_div_cost<T, packet_traits<T>::HasDiv>::value +
           (internal::is_same<T, float>::value
                ? NumTraits<T>::AddCost * 15 + NumTraits<T>::MulCost * 11
                : NumTraits<T>::AddCost * 2 +
                      functor_traits<scalar_exp_op<T> >::Cost),
    PacketAccess =
        packet_traits<T>::HasAdd && packet_traits<T>::HasDiv &&
        (internal::is_same<T, float>::value
             ? packet_traits<T>::HasMul && packet_traits<T>::HasMax &&
                   packet_traits<T>::HasMin
             : packet_traits<T>::HasNegate && packet_traits<T>::HasExp)
  };
};

template <typename Scalar, typename ExponentScalar, 
          bool IsBaseInteger = NumTraits<Scalar>::IsInteger,
          bool IsExponentInteger = NumTraits<ExponentScalar>::IsInteger,
          bool IsBaseComplex = NumTraits<Scalar>::IsComplex,
          bool IsExponentComplex = NumTraits<ExponentScalar>::IsComplex>
struct scalar_unary_pow_op {
  typedef typename internal::promote_scalar_arg<
      Scalar, ExponentScalar,
      internal::has_ReturnType<ScalarBinaryOpTraits<Scalar,ExponentScalar,scalar_unary_pow_op> >::value>::type PromotedExponent;
  typedef typename ScalarBinaryOpTraits<Scalar, PromotedExponent, scalar_unary_pow_op>::ReturnType result_type;
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_unary_pow_op(const ExponentScalar& exponent) : m_exponent(exponent) {}
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE result_type operator()(const Scalar& a) const {
    EIGEN_USING_STD(pow);
    return static_cast<result_type>(pow(a, m_exponent));
  }

 private:
  const ExponentScalar m_exponent;
  scalar_unary_pow_op() {}
};

template <typename T>
constexpr int exponent_digits() {
  return CHAR_BIT * sizeof(T) - NumTraits<T>::digits() - NumTraits<T>::IsSigned;
}

template<typename From, typename To>
struct is_floating_exactly_representable {
  // TODO(rmlarsen): Add radix to NumTraits and enable this check.
  // (NumTraits<To>::radix == NumTraits<From>::radix) &&
  static constexpr bool value = (exponent_digits<To>() >= exponent_digits<From>() &&
                                  NumTraits<To>::digits() >= NumTraits<From>::digits());
};


// Specialization for real, non-integer types, non-complex types.
template <typename Scalar, typename ExponentScalar>
struct scalar_unary_pow_op<Scalar, ExponentScalar, false, false, false, false> {
  template <bool IsExactlyRepresentable = is_floating_exactly_representable<ExponentScalar, Scalar>::value>
  std::enable_if_t<IsExactlyRepresentable, void> check_is_representable() const {}

  // Issue a deprecation warning if we do a narrowing conversion on the exponent.
  template <bool IsExactlyRepresentable = is_floating_exactly_representable<ExponentScalar, Scalar>::value>
  EIGEN_DEPRECATED std::enable_if_t<!IsExactlyRepresentable, void> check_is_representable() const {}

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
      scalar_unary_pow_op(const ExponentScalar& exponent) : m_exponent(static_cast<Scalar>(exponent)) {
    check_is_representable();
  }

  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a) const {
    EIGEN_USING_STD(pow);
    return static_cast<Scalar>(pow(a, m_exponent));
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const {
    return unary_pow_impl<Packet, Scalar>::run(a, m_exponent);
  }

 private:
  const Scalar m_exponent;
  scalar_unary_pow_op() {}
};

template <typename Scalar, typename ExponentScalar, bool BaseIsInteger>
struct scalar_unary_pow_op<Scalar, ExponentScalar, BaseIsInteger, true, false, false> {
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE scalar_unary_pow_op(const ExponentScalar& exponent) : m_exponent(exponent) {}
  // TODO: error handling logic for complex^real_integer
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Scalar operator()(const Scalar& a) const {
    return unary_pow_impl<Scalar, ExponentScalar>::run(a, m_exponent);
  }
  template <typename Packet>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const {
    return unary_pow_impl<Packet, ExponentScalar>::run(a, m_exponent);
  }

 private:
  const ExponentScalar m_exponent;
  scalar_unary_pow_op() {}
};

template <typename Scalar, typename ExponentScalar>
struct functor_traits<scalar_unary_pow_op<Scalar, ExponentScalar>> {
  enum {
    GenPacketAccess = functor_traits<scalar_pow_op<Scalar, ExponentScalar>>::PacketAccess,
    IntPacketAccess = !NumTraits<Scalar>::IsComplex && packet_traits<Scalar>::HasMul && (packet_traits<Scalar>::HasDiv || NumTraits<Scalar>::IsInteger) && packet_traits<Scalar>::HasCmp,
    PacketAccess = NumTraits<ExponentScalar>::IsInteger ? IntPacketAccess : (IntPacketAccess && GenPacketAccess),
    Cost = functor_traits<scalar_pow_op<Scalar, ExponentScalar>>::Cost
  };
};

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_FUNCTORS_H