// @HEADER
// ***********************************************************************
//
//                           Sacado Package
//                 Copyright (2006) Sandia Corporation
//
// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
// the U.S. Government retains certain rights in this software.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
// USA
// Questions? Contact David M. Gay (dmgay@sandia.gov) or Eric T. Phipps
// (etphipp@sandia.gov).
//
// ***********************************************************************
//
// The forward-mode AD classes in Sacado are a derivative work of the
// expression template classes in the Fad package by Nicolas Di Cesare.
// The following banner is included in the original Fad source code:
//
// ************ DO NOT REMOVE THIS BANNER ****************
//
//  Nicolas Di Cesare <Nicolas.Dicesare@ann.jussieu.fr>
//  http://www.ann.jussieu.fr/~dicesare
//
//            CEMRACS 98 : C++ courses,
//         templates : new C++ techniques
//            for scientific computing
//
//********************************************************
//
//  A short implementation ( not all operators and
//  functions are overloaded ) of 1st order Automatic
//  Differentiation in forward mode (FAD) using
//  EXPRESSION TEMPLATES.
//
//********************************************************
// @HEADER

#ifndef SACADO_FAD_OPS_HPP
#define SACADO_FAD_OPS_HPP

#include "Sacado_Fad_Expression.hpp"
#include "Sacado_cmath.hpp"
#include <ostream>      // for std::ostream

#define FAD_UNARYOP_MACRO(OPNAME,OP,VALUE,DX,FASTACCESSDX)              \
namespace Sacado {                                                      \
  namespace Fad {                                                       \
                                                                        \
    template <typename ExprT>                                           \
    class OP {};                                                        \
                                                                        \
    template <typename ExprT>                                           \
    class Expr< OP<ExprT> > {                                           \
    public:                                                             \
                                                                        \
      typedef typename ExprT::value_type value_type;                    \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      Expr(const ExprT& expr_) : expr(expr_)  {}                        \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      int size() const { return expr.size(); }                          \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool hasFastAccess() const { return expr.hasFastAccess(); }       \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool isPassive() const { return expr.isPassive();}                \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool updateValue() const { return expr.updateValue(); }           \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      value_type val() const {                                          \
        return VALUE;                                                   \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      value_type dx(int i) const {                                      \
        return DX;                                                      \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      value_type fastAccessDx(int i) const {                            \
        return FASTACCESSDX;                                            \
      }                                                                 \
                                                                        \
    protected:                                                          \
                                                                        \
      const ExprT& expr;                                                \
    };                                                                  \
                                                                        \
    template <typename T>                                               \
    KOKKOS_INLINE_FUNCTION                                              \
    Expr< OP< Expr<T> > >                                               \
    OPNAME (const Expr<T>& expr)                                        \
    {                                                                   \
      typedef OP< Expr<T> > expr_t;                                     \
                                                                        \
      return Expr<expr_t>(expr);                                        \
    }                                                                   \
  }                                                                     \
}

FAD_UNARYOP_MACRO(operator+,
                  UnaryPlusOp,
                  expr.val(),
                  expr.dx(i),
                  expr.fastAccessDx(i))
FAD_UNARYOP_MACRO(operator-,
                  UnaryMinusOp,
                  -expr.val(),
                  -expr.dx(i),
                  -expr.fastAccessDx(i))
FAD_UNARYOP_MACRO(exp,
                  ExpOp,
                  std::exp(expr.val()),
                  std::exp(expr.val())*expr.dx(i),
                  std::exp(expr.val())*expr.fastAccessDx(i))
FAD_UNARYOP_MACRO(log,
                  LogOp,
                  std::log(expr.val()),
                  expr.dx(i)/expr.val(),
                  expr.fastAccessDx(i)/expr.val())
FAD_UNARYOP_MACRO(log10,
                  Log10Op,
                  std::log10(expr.val()),
                  expr.dx(i)/( std::log(value_type(10))*expr.val()),
                  expr.fastAccessDx(i) / ( std::log(value_type(10))*expr.val()))
FAD_UNARYOP_MACRO(sqrt,
                  SqrtOp,
                  std::sqrt(expr.val()),
                  expr.dx(i)/(value_type(2)* std::sqrt(expr.val())),
                  expr.fastAccessDx(i)/(value_type(2)* std::sqrt(expr.val())))
FAD_UNARYOP_MACRO(cos,
                  CosOp,
                  std::cos(expr.val()),
                  -expr.dx(i)* std::sin(expr.val()),
                  -expr.fastAccessDx(i)* std::sin(expr.val()))
FAD_UNARYOP_MACRO(sin,
                  SinOp,
                  std::sin(expr.val()),
                  expr.dx(i)* std::cos(expr.val()),
                  expr.fastAccessDx(i)* std::cos(expr.val()))
FAD_UNARYOP_MACRO(tan,
                  TanOp,
                  std::tan(expr.val()),
                  expr.dx(i)*
                    (value_type(1)+ std::tan(expr.val())* std::tan(expr.val())),
                  expr.fastAccessDx(i)*
                    (value_type(1)+ std::tan(expr.val())* std::tan(expr.val())))
FAD_UNARYOP_MACRO(acos,
                  ACosOp,
                  std::acos(expr.val()),
                  -expr.dx(i)/ std::sqrt(value_type(1)-expr.val()*expr.val()),
                  -expr.fastAccessDx(i) /
                    std::sqrt(value_type(1)-expr.val()*expr.val()))
FAD_UNARYOP_MACRO(asin,
                  ASinOp,
                  std::asin(expr.val()),
                  expr.dx(i)/ std::sqrt(value_type(1)-expr.val()*expr.val()),
                  expr.fastAccessDx(i) /
                    std::sqrt(value_type(1)-expr.val()*expr.val()))
FAD_UNARYOP_MACRO(atan,
                  ATanOp,
                  std::atan(expr.val()),
                  expr.dx(i)/(value_type(1)+expr.val()*expr.val()),
                  expr.fastAccessDx(i)/(value_type(1)+expr.val()*expr.val()))
FAD_UNARYOP_MACRO(cosh,
                  CoshOp,
                  std::cosh(expr.val()),
                  expr.dx(i)* std::sinh(expr.val()),
                  expr.fastAccessDx(i)* std::sinh(expr.val()))
FAD_UNARYOP_MACRO(sinh,
                  SinhOp,
                  std::sinh(expr.val()),
                  expr.dx(i)* std::cosh(expr.val()),
                  expr.fastAccessDx(i)* std::cosh(expr.val()))
FAD_UNARYOP_MACRO(tanh,
                  TanhOp,
                  std::tanh(expr.val()),
                  expr.dx(i)/( std::cosh(expr.val())* std::cosh(expr.val())),
                  expr.fastAccessDx(i) /
                    ( std::cosh(expr.val())* std::cosh(expr.val())))
FAD_UNARYOP_MACRO(acosh,
                  ACoshOp,
                  std::acosh(expr.val()),
                  expr.dx(i)/ std::sqrt((expr.val()-value_type(1)) *
                                       (expr.val()+value_type(1))),
                  expr.fastAccessDx(i)/ std::sqrt((expr.val()-value_type(1)) *
                                                 (expr.val()+value_type(1))))
FAD_UNARYOP_MACRO(asinh,
                  ASinhOp,
                  std::asinh(expr.val()),
                  expr.dx(i)/ std::sqrt(value_type(1)+expr.val()*expr.val()),
                  expr.fastAccessDx(i)/ std::sqrt(value_type(1)+
                                                 expr.val()*expr.val()))
FAD_UNARYOP_MACRO(atanh,
                  ATanhOp,
                  std::atanh(expr.val()),
                  expr.dx(i)/(value_type(1)-expr.val()*expr.val()),
                  expr.fastAccessDx(i)/(value_type(1)-
                                                 expr.val()*expr.val()))
FAD_UNARYOP_MACRO(abs,
                  AbsOp,
                  std::abs(expr.val()),
                  expr.val() >= 0 ? value_type(+expr.dx(i)) :
                    value_type(-expr.dx(i)),
                  expr.val() >= 0 ? value_type(+expr.fastAccessDx(i)) :
                    value_type(-expr.fastAccessDx(i)))
FAD_UNARYOP_MACRO(fabs,
                  FAbsOp,
                  std::fabs(expr.val()),
                  expr.val() >= 0 ? value_type(+expr.dx(i)) :
                    value_type(-expr.dx(i)),
                  expr.val() >= 0 ? value_type(+expr.fastAccessDx(i)) :
                    value_type(-expr.fastAccessDx(i)))

#undef FAD_UNARYOP_MACRO

#define FAD_BINARYOP_MACRO(OPNAME,OP,VALUE,DX,FASTACCESSDX,VAL_CONST_DX_1,VAL_CONST_DX_2,CONST_DX_1,CONST_DX_2,CONST_FASTACCESSDX_1,CONST_FASTACCESSDX_2) \
namespace Sacado {                                                      \
  namespace Fad {                                                       \
                                                                        \
    template <typename ExprT1, typename ExprT2>                         \
    class OP {};                                                        \
                                                                        \
    template <typename T1, typename T2>                                 \
    class Expr< OP< Expr<T1>, Expr<T2> > > {                            \
                                                                        \
    public:                                                             \
                                                                        \
      typedef Expr<T1> ExprT1;                                          \
      typedef Expr<T2> ExprT2;                                          \
      typedef typename ExprT1::value_type value_type_1;                 \
      typedef typename ExprT2::value_type value_type_2;                 \
      typedef typename Sacado::Promote<value_type_1,                    \
                                       value_type_2>::type value_type;  \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      Expr(const ExprT1& expr1_, const ExprT2& expr2_) :                \
        expr1(expr1_), expr2(expr2_) {}                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      int size() const {                                                \
        int sz1 = expr1.size(), sz2 = expr2.size();                     \
        return sz1 > sz2 ? sz1 : sz2;                                   \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool hasFastAccess() const {                                      \
        return expr1.hasFastAccess() && expr2.hasFastAccess();          \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool isPassive() const {                                          \
        return expr1.isPassive() && expr2.isPassive();                  \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool updateValue() const {                                        \
        return expr1.updateValue() && expr2.updateValue();              \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type val() const {                                    \
        return VALUE;                                                   \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type dx(int i) const {                                \
        return DX;                                                      \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type fastAccessDx(int i) const {                      \
        return FASTACCESSDX;                                            \
      }                                                                 \
                                                                        \
    protected:                                                          \
                                                                        \
      const ExprT1& expr1;                                              \
      const ExprT2& expr2;                                              \
                                                                        \
    };                                                                  \
                                                                        \
    template <typename T1>                                              \
    class Expr< OP< Expr<T1>, typename Expr<T1>::value_type> > {        \
                                                                        \
    public:                                                             \
                                                                        \
      typedef Expr<T1> ExprT1;                                          \
      typedef typename ExprT1::value_type value_type;                   \
      typedef typename ExprT1::value_type ConstT;                       \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      Expr(const ExprT1& expr1_, const ConstT& c_) :                    \
        expr1(expr1_), c(c_) {}                                         \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      int size() const {                                                \
        return expr1.size();                                            \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool hasFastAccess() const {                                      \
        return expr1.hasFastAccess();                                   \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool isPassive() const {                                          \
        return expr1.isPassive();                                       \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool updateValue() const { return expr1.updateValue(); }          \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type val() const {                                    \
        return VAL_CONST_DX_2;                                          \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type dx(int i) const {                                \
        return CONST_DX_2;                                              \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type fastAccessDx(int i) const {                      \
        return CONST_FASTACCESSDX_2;                                    \
      }                                                                 \
                                                                        \
    protected:                                                          \
                                                                        \
      const ExprT1& expr1;                                              \
      const ConstT& c;                                                  \
    };                                                                  \
                                                                        \
    template <typename T2>                                              \
    class Expr< OP< typename Expr<T2>::value_type, Expr<T2> > > {       \
                                                                        \
    public:                                                             \
                                                                        \
      typedef Expr<T2> ExprT2;                                          \
      typedef typename ExprT2::value_type value_type;                   \
      typedef typename ExprT2::value_type ConstT;                       \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      Expr(const ConstT& c_, const ExprT2& expr2_) :                    \
        c(c_), expr2(expr2_) {}                                         \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      int size() const {                                                \
        return expr2.size();                                            \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool hasFastAccess() const {                                      \
        return expr2.hasFastAccess();                                   \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool isPassive() const {                                          \
        return expr2.isPassive();                                       \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      bool updateValue() const { return expr2.updateValue(); }          \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type val() const {                                    \
        return VAL_CONST_DX_1;                                          \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type dx(int i) const {                                \
        return CONST_DX_1;                                              \
      }                                                                 \
                                                                        \
      KOKKOS_INLINE_FUNCTION                                            \
      const value_type fastAccessDx(int i) const {                      \
        return CONST_FASTACCESSDX_1;                                    \
      }                                                                 \
                                                                        \
    protected:                                                          \
                                                                        \
      const ConstT& c;                                                  \
      const ExprT2& expr2;                                              \
    };                                                                  \
                                                                        \
    template <typename T1, typename T2>                                 \
    KOKKOS_INLINE_FUNCTION                                              \
    Expr< OP< Expr<T1>, Expr<T2> > >                                    \
    OPNAME (const Expr<T1>& expr1, const Expr<T2>& expr2)               \
    {                                                                   \
      typedef OP< Expr<T1>, Expr<T2> > expr_t;                          \
                                                                        \
      return Expr<expr_t>(expr1, expr2);                                \
    }                                                                   \
                                                                        \
    template <typename T>                                               \
    KOKKOS_INLINE_FUNCTION                                              \
    Expr< OP< Expr<T>, Expr<T> > >                                      \
    OPNAME (const Expr<T>& expr1, const Expr<T>& expr2)                 \
    {                                                                   \
      typedef OP< Expr<T>, Expr<T> > expr_t;                            \
                                                                        \
      return Expr<expr_t>(expr1, expr2);                                \
    }                                                                   \
                                                                        \
    template <typename T>                                               \
    KOKKOS_INLINE_FUNCTION                                              \
    Expr< OP< typename Expr<T>::value_type, Expr<T> > >                 \
    OPNAME (const typename Expr<T>::value_type& c,                      \
            const Expr<T>& expr)                                        \
    {                                                                   \
      typedef typename Expr<T>::value_type ConstT;                      \
      typedef OP< ConstT, Expr<T> > expr_t;                             \
                                                                        \
      return Expr<expr_t>(c, expr);                                     \
    }                                                                   \
                                                                        \
    template <typename T>                                               \
    KOKKOS_INLINE_FUNCTION                                              \
    Expr< OP< Expr<T>, typename Expr<T>::value_type > >                 \
    OPNAME (const Expr<T>& expr,                                        \
            const typename Expr<T>::value_type& c)                      \
    {                                                                   \
      typedef typename Expr<T>::value_type ConstT;                      \
      typedef OP< Expr<T>, ConstT > expr_t;                             \
                                                                        \
      return Expr<expr_t>(expr, c);                                     \
    }                                                                   \
  }                                                                     \
}


FAD_BINARYOP_MACRO(operator+,
                   AdditionOp,
                   expr1.val() + expr2.val(),
                   expr1.dx(i) + expr2.dx(i),
                   expr1.fastAccessDx(i) + expr2.fastAccessDx(i),
                   c + expr2.val(),
                   expr1.val() + c,
                   expr2.dx(i),
                   expr1.dx(i),
                   expr2.fastAccessDx(i),
                   expr1.fastAccessDx(i))
FAD_BINARYOP_MACRO(operator-,
                   SubtractionOp,
                   expr1.val() - expr2.val(),
                   expr1.dx(i) - expr2.dx(i),
                   expr1.fastAccessDx(i) - expr2.fastAccessDx(i),
                   c - expr2.val(),
                   expr1.val() - c,
                   -expr2.dx(i),
                   expr1.dx(i),
                   -expr2.fastAccessDx(i),
                   expr1.fastAccessDx(i))
// FAD_BINARYOP_MACRO(operator*,
//                 MultiplicationOp,
//                 expr1.val() * expr2.val(),
//                 expr1.val()*expr2.dx(i) + expr1.dx(i)*expr2.val(),
//                 expr1.val()*expr2.fastAccessDx(i) +
//                   expr1.fastAccessDx(i)*expr2.val(),
//                 c * expr2.val(),
//                 expr1.val() * c,
//                 c*expr2.dx(i),
//                 expr1.dx(i)*c,
//                 c*expr2.fastAccessDx(i),
//                 expr1.fastAccessDx(i)*c)
FAD_BINARYOP_MACRO(operator/,
                   DivisionOp,
                   expr1.val() / expr2.val(),
                   (expr1.dx(i)*expr2.val() - expr2.dx(i)*expr1.val()) /
                     (expr2.val()*expr2.val()),
                   (expr1.fastAccessDx(i)*expr2.val() -
                      expr2.fastAccessDx(i)*expr1.val()) /
                      (expr2.val()*expr2.val()),
                   c / expr2.val(),
                   expr1.val() / c,
                   -expr2.dx(i)*c / (expr2.val()*expr2.val()),
                   expr1.dx(i)/c,
                   -expr2.fastAccessDx(i)*c / (expr2.val()*expr2.val()),
                   expr1.fastAccessDx(i)/c)
FAD_BINARYOP_MACRO(atan2,
                   Atan2Op,
                   std::atan2(expr1.val(), expr2.val()),
                   (expr2.val()*expr1.dx(i) - expr1.val()*expr2.dx(i))/
                        (expr1.val()*expr1.val() + expr2.val()*expr2.val()),
                   (expr2.val()*expr1.fastAccessDx(i) - expr1.val()*expr2.fastAccessDx(i))/
                        (expr1.val()*expr1.val() + expr2.val()*expr2.val()),
                   std::atan2(c, expr2.val()),
                   std::atan2(expr1.val(), c),
                   (-c*expr2.dx(i)) / (c*c + expr2.val()*expr2.val()),
                   (c*expr1.dx(i))/ (expr1.val()*expr1.val() + c*c),
                   (-c*expr2.fastAccessDx(i))/ (c*c + expr2.val()*expr2.val()),
                   (c*expr1.fastAccessDx(i))/ (expr1.val()*expr1.val() + c*c))
FAD_BINARYOP_MACRO(pow,
                   PowerOp,
                   std::pow(expr1.val(), expr2.val()),
                   expr1.val() == value_type(0) ? value_type(0) : value_type((expr2.dx(i)*std::log(expr1.val())+expr2.val()*expr1.dx(i)/expr1.val())*std::pow(expr1.val(),expr2.val())),
                   expr1.val() == value_type(0) ? value_type(0.0) : value_type((expr2.fastAccessDx(i)*std::log(expr1.val())+expr2.val()*expr1.fastAccessDx(i)/expr1.val())*std::pow(expr1.val(),expr2.val())),
                   std::pow(c, expr2.val()),
                   std::pow(expr1.val(), c),
                   c == value_type(0) ? value_type(0) : value_type(expr2.dx(i)*std::log(c)*std::pow(c,expr2.val())),
                   expr1.val() == value_type(0) ? value_type(0.0) : value_type(c*expr1.dx(i)/expr1.val()*std::pow(expr1.val(),c)),
                   c == value_type(0) ? value_type(0) : value_type(expr2.fastAccessDx(i)*std::log(c)*std::pow(c,expr2.val())),
                   expr1.val() == value_type(0) ? value_type(0.0) : value_type(c*expr1.fastAccessDx(i)/expr1.val()*std::pow(expr1.val(),c)))
FAD_BINARYOP_MACRO(max,
                   MaxOp,
                   std::max(expr1.val(), expr2.val()),
                   expr1.val() >= expr2.val() ? expr1.dx(i) : expr2.dx(i),
                   expr1.val() >= expr2.val() ? expr1.fastAccessDx(i) :
                                                expr2.fastAccessDx(i),
                   std::max(c, expr2.val()),
                   std::max(expr1.val(), c),
                   c >= expr2.val() ? value_type(0) : expr2.dx(i),
                   expr1.val() >= c ? expr1.dx(i) : value_type(0),
                   c >= expr2.val() ? value_type(0) : expr2.fastAccessDx(i),
                   expr1.val() >= c ? expr1.fastAccessDx(i) : value_type(0))
FAD_BINARYOP_MACRO(min,
                   MinOp,
                   std::min(expr1.val(), expr2.val()),
                   expr1.val() <= expr2.val() ? expr1.dx(i) : expr2.dx(i),
                   expr1.val() <= expr2.val() ? expr1.fastAccessDx(i) :
                                                expr2.fastAccessDx(i),
                   std::min(c, expr2.val()),
                   std::min(expr1.val(), c),
                   c <= expr2.val() ? value_type(0) : expr2.dx(i),
                   expr1.val() <= c ? expr1.dx(i) : value_type(0),
                   c <= expr2.val() ? value_type(0) : expr2.fastAccessDx(i),
                   expr1.val() <= c ? expr1.fastAccessDx(i) : value_type(0))


#undef FAD_BINARYOP_MACRO

namespace Sacado {
  namespace Fad {

    template <typename ExprT1, typename ExprT2>
    class MultiplicationOp {};

    template <typename T1, typename T2>
    class Expr< MultiplicationOp< Expr<T1>, Expr<T2> > > {

    public:

      typedef Expr<T1> ExprT1;
      typedef Expr<T2> ExprT2;
      typedef typename ExprT1::value_type value_type_1;
      typedef typename ExprT2::value_type value_type_2;
      typedef typename Sacado::Promote<value_type_1,
                                       value_type_2>::type value_type;

      KOKKOS_INLINE_FUNCTION
      Expr(const ExprT1& expr1_, const ExprT2& expr2_) :
        expr1(expr1_), expr2(expr2_) {}

      KOKKOS_INLINE_FUNCTION
      int size() const {
        int sz1 = expr1.size(), sz2 = expr2.size();
        return sz1 > sz2 ? sz1 : sz2;
      }

      KOKKOS_INLINE_FUNCTION
      bool hasFastAccess() const {
        return expr1.hasFastAccess() && expr2.hasFastAccess();
      }

      KOKKOS_INLINE_FUNCTION
      bool isPassive() const {
        return expr1.isPassive() && expr2.isPassive();
      }

      KOKKOS_INLINE_FUNCTION
      bool updateValue() const {
        return expr1.updateValue() && expr2.updateValue();
      }

      KOKKOS_INLINE_FUNCTION
      const value_type val() const {
        return expr1.val()*expr2.val();
      }

      KOKKOS_INLINE_FUNCTION
      const value_type dx(int i) const {
        if (expr1.size() > 0 && expr2.size() > 0)
          return expr1.val()*expr2.dx(i) + expr1.dx(i)*expr2.val();
        else if (expr1.size() > 0)
          return expr1.dx(i)*expr2.val();
        else
          return expr1.val()*expr2.dx(i);
      }

      KOKKOS_INLINE_FUNCTION
      const value_type fastAccessDx(int i) const {
        return expr1.val()*expr2.fastAccessDx(i) +
          expr1.fastAccessDx(i)*expr2.val();
      }

    protected:

      const ExprT1& expr1;
      const ExprT2& expr2;

    };

    template <typename T1>
    class Expr< MultiplicationOp< Expr<T1>, typename Expr<T1>::value_type> > {

    public:

      typedef Expr<T1> ExprT1;
      typedef typename ExprT1::value_type value_type;
      typedef typename ExprT1::value_type ConstT;

      KOKKOS_INLINE_FUNCTION
      Expr(const ExprT1& expr1_, const ConstT& c_) :
        expr1(expr1_), c(c_) {}

      KOKKOS_INLINE_FUNCTION
      int size() const {
        return expr1.size();
      }

      KOKKOS_INLINE_FUNCTION
      bool hasFastAccess() const {
        return expr1.hasFastAccess();
      }

      KOKKOS_INLINE_FUNCTION
      bool isPassive() const {
        return expr1.isPassive();
      }

      KOKKOS_INLINE_FUNCTION
      bool updateValue() const { return expr1.updateValue(); }

      KOKKOS_INLINE_FUNCTION
      const value_type val() const {
        return expr1.val()*c;
      }

      KOKKOS_INLINE_FUNCTION
      const value_type dx(int i) const {
        return expr1.dx(i)*c;
      }

      KOKKOS_INLINE_FUNCTION
      const value_type fastAccessDx(int i) const {
        return expr1.fastAccessDx(i)*c;
      }

    protected:

      const ExprT1& expr1;
      const ConstT& c;
    };

    template <typename T2>
    class Expr< MultiplicationOp< typename Expr<T2>::value_type, Expr<T2> > > {

    public:

      typedef Expr<T2> ExprT2;
      typedef typename ExprT2::value_type value_type;
      typedef typename ExprT2::value_type ConstT;

      KOKKOS_INLINE_FUNCTION
      Expr(const ConstT& c_, const ExprT2& expr2_) :
        c(c_), expr2(expr2_) {}

      KOKKOS_INLINE_FUNCTION
      int size() const {
        return expr2.size();
      }

      KOKKOS_INLINE_FUNCTION
      bool hasFastAccess() const {
        return expr2.hasFastAccess();
      }

      KOKKOS_INLINE_FUNCTION
      bool isPassive() const {
        return expr2.isPassive();
      }

      KOKKOS_INLINE_FUNCTION
      bool updateValue() const { return expr2.updateValue(); }

      KOKKOS_INLINE_FUNCTION
      const value_type val() const {
        return c*expr2.val();
      }

      KOKKOS_INLINE_FUNCTION
      const value_type dx(int i) const {
        return c*expr2.dx(i);
      }

      KOKKOS_INLINE_FUNCTION
      const value_type fastAccessDx(int i) const {
        return c*expr2.fastAccessDx(i);
      }

    protected:

      const ConstT& c;
      const ExprT2& expr2;
    };

    template <typename T1, typename T2>
    KOKKOS_INLINE_FUNCTION
    Expr< MultiplicationOp< Expr<T1>, Expr<T2> > >
    operator* (const Expr<T1>& expr1, const Expr<T2>& expr2)
    {
      typedef MultiplicationOp< Expr<T1>, Expr<T2> > expr_t;

      return Expr<expr_t>(expr1, expr2);
    }

    template <typename T>
    KOKKOS_INLINE_FUNCTION
    Expr< MultiplicationOp< Expr<T>, Expr<T> > >
    operator* (const Expr<T>& expr1, const Expr<T>& expr2)
    {
      typedef MultiplicationOp< Expr<T>, Expr<T> > expr_t;

      return Expr<expr_t>(expr1, expr2);
    }

    template <typename T>
    KOKKOS_INLINE_FUNCTION
    Expr< MultiplicationOp< typename Expr<T>::value_type, Expr<T> > >
    operator* (const typename Expr<T>::value_type& c,
            const Expr<T>& expr)
    {
      typedef typename Expr<T>::value_type ConstT;
      typedef MultiplicationOp< ConstT, Expr<T> > expr_t;

      return Expr<expr_t>(c, expr);
    }

    template <typename T>
    KOKKOS_INLINE_FUNCTION
    Expr< MultiplicationOp< Expr<T>, typename Expr<T>::value_type > >
    operator* (const Expr<T>& expr,
            const typename Expr<T>::value_type& c)
    {
      typedef typename Expr<T>::value_type ConstT;
      typedef MultiplicationOp< Expr<T>, ConstT > expr_t;

      return Expr<expr_t>(expr, c);
    }
  }
}

//-------------------------- Relational Operators -----------------------

#define FAD_RELOP_MACRO(OP)                                             \
namespace Sacado {                                                      \
  namespace Fad {                                                       \
    template <typename ExprT1, typename ExprT2>                         \
    KOKKOS_INLINE_FUNCTION                                              \
    bool                                                                \
    operator OP (const Expr<ExprT1>& expr1,                             \
                 const Expr<ExprT2>& expr2)                             \
    {                                                                   \
      return expr1.val() OP expr2.val();                                \
    }                                                                   \
                                                                        \
    template <typename ExprT2>                                          \
    KOKKOS_INLINE_FUNCTION                                              \
    bool                                                                \
    operator OP (const typename Expr<ExprT2>::value_type& a,            \
                 const Expr<ExprT2>& expr2)                             \
    {                                                                   \
      return a OP expr2.val();                                          \
    }                                                                   \
                                                                        \
    template <typename ExprT1>                                          \
    KOKKOS_INLINE_FUNCTION                                              \
    bool                                                                \
    operator OP (const Expr<ExprT1>& expr1,                             \
                 const typename Expr<ExprT1>::value_type& b)            \
    {                                                                   \
      return expr1.val() OP b;                                          \
    }                                                                   \
  }                                                                     \
}

FAD_RELOP_MACRO(==)
FAD_RELOP_MACRO(!=)
FAD_RELOP_MACRO(<)
FAD_RELOP_MACRO(>)
FAD_RELOP_MACRO(<=)
FAD_RELOP_MACRO(>=)
FAD_RELOP_MACRO(<<=)
FAD_RELOP_MACRO(>>=)
FAD_RELOP_MACRO(&)
FAD_RELOP_MACRO(|)

#undef FAD_RELOP_MACRO

namespace Sacado {

  namespace Fad {

    template <typename ExprT>
    KOKKOS_INLINE_FUNCTION
    bool operator ! (const Expr<ExprT>& expr)
    {
      return ! expr.val();
    }

  } // namespace Fad

} // namespace Sacado

//-------------------------- Boolean Operators -----------------------
namespace Sacado {

  namespace Fad {

    template <typename ExprT>
    KOKKOS_INLINE_FUNCTION
    bool toBool(const Expr<ExprT>& x) {
      bool is_zero = (x.val() == 0.0);
      for (int i=0; i<x.size(); i++)
        is_zero = is_zero && (x.dx(i) == 0.0);
      return !is_zero;
    }

  } // namespace Fad

} // namespace Sacado

#define FAD_BOOL_MACRO(OP)                                              \
namespace Sacado {                                                      \
  namespace Fad {                                                       \
    template <typename ExprT1, typename ExprT2>                         \
    KOKKOS_INLINE_FUNCTION                                              \
    bool                                                                \
    operator OP (const Expr<ExprT1>& expr1,                             \
                 const Expr<ExprT2>& expr2)                             \
    {                                                                   \
      return toBool(expr1) OP toBool(expr2);                            \
    }                                                                   \
                                                                        \
    template <typename ExprT2>                                          \
    KOKKOS_INLINE_FUNCTION                                              \
    bool                                                                \
    operator OP (const typename Expr<ExprT2>::value_type& a,            \
                 const Expr<ExprT2>& expr2)                             \
    {                                                                   \
      return a OP toBool(expr2);                                        \
    }                                                                   \
                                                                        \
    template <typename ExprT1>                                          \
    KOKKOS_INLINE_FUNCTION                                              \
    bool                                                                \
    operator OP (const Expr<ExprT1>& expr1,                             \
                 const typename Expr<ExprT1>::value_type& b)            \
    {                                                                   \
      return toBool(expr1) OP b;                                        \
    }                                                                   \
  }                                                                     \
}

FAD_BOOL_MACRO(&&)
FAD_BOOL_MACRO(||)

#undef FAD_BOOL_MACRO

//-------------------------- I/O Operators -----------------------

namespace Sacado {

  namespace Fad {

    template <typename ExprT>
    std::ostream& operator << (std::ostream& os, const Expr<ExprT>& x) {
      os << x.val() << " [";

      for (int i=0; i< x.size(); i++) {
        os << " " << x.dx(i);
      }

      os << " ]";
      return os;
    }

  } // namespace Fad

} // namespace Sacado


#endif // SACADO_FAD_OPS_HPP
