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# ifndef CPPAD_COND_EXP_INCLUDED
# define CPPAD_COND_EXP_INCLUDED

/* --------------------------------------------------------------------------
CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-07 Bradley M. Bell

CppAD is distributed under multiple licenses. This distribution is under
the terms of the 
                    Common Public License Version 1.0.

A copy of this license is included in the COPYING file of this distribution.
Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
-------------------------------------------------------------------------- */

/*
-------------------------------------------------------------------------------
$begin CondExp$$
$spell
        Atan2
        CondExp
        Taylor
        std
        Cpp
        namespace
        inline
        const
        abs
        Op
        bool
        Lt
        Le
        Eq
        Ge
        Gt
$$

$index conditional, expression$$
$index expression, conditional$$
$index assign, conditional$$

$section AD Conditional Expressions$$

$head Syntax$$
$syntax%%result% = CondExp%Op%(%left%, %right%, %trueCase%, %falseCase%)%$$


$head Purpose$$
Record, 
as part of an AD of $italic Base$$
$xref/glossary/Operation/Sequence/operation sequence/1/$$,
a the conditional result of the form 
$syntax%
        if( %left% %op% %right% )
                %result% = %trueCase%
        else    %result% = %falseCase%
%$$
The notation $italic Op$$ and $italic op$$ 
above have the following correspondence: 
$table
$italic Op$$ 
        $pre  $$ $cnext $code Lt$$
        $pre  $$ $cnext $code Le$$
        $pre  $$ $cnext $code Eq$$
        $pre  $$ $cnext $code Ge$$
        $pre  $$ $cnext $code Gt$$
$rnext
$italic op$$ 
        $cnext $code <$$
        $cnext $code <=$$
        $cnext $code ==$$
        $cnext $code >=$$
        $cnext $code >$$
$tend
If $italic f$$ is the $xref/ADFun/$$ object corresponding to the
AD operation sequence,
the choice in an AD conditional expression is made each time
$xref/Forward//f.Forward/$$ is used to evaluate the zero order Taylor
coefficients with new values for the 
$cref/independent variables/glossary/Tape/Independent Variable/$$.
This is in contrast to the $xref/Compare//AD comparison operators/$$
which are boolean valued and not included in the AD operation sequence. 

$head Type$$
We use $italic Type$$ for the type of
$italic left$$, $italic right$$, $italic trueCase$$, and $italic falseCase$$
(which must all have the same type). 
This type must be
$code float$$, $code double$$, or in the 
$cref/AD levels above/glossary/AD Levels Above Base/$$
above $code float$$ or $code double$$.

$head Op$$
In the syntax above, $italic Op$$ represents one of the following
two characters: $code Lt$$, $code Le$$, $code Eq$$, $code Ge$$, $code Gt$$. 
As in the table above,
$italic Op$$ determines the comparison operator $italic op$$.
 
$head left$$
The argument $italic left$$ has prototype
$syntax%
        const %Type% &%left%
%$$
It specifies the value for the left side of the comparison operator.
 
$head right$$
The argument $italic right$$ has prototype
$syntax%
        const %Type% &%right%
%$$
It specifies the value for the right side of the comparison operator.

$head trueCase$$
The argument $italic trueCase$$ has prototype
$syntax%
        const %Type% &%trueCase%
%$$
It specifies the return value if the result of the comparison is true.

$head falseCase$$
The argument $italic falseCase$$ has prototype
$syntax%
        const %Type% &%falseCase%
%$$
It specifies the return value if the result of the comparison is false.

$head result$$
The $italic result$$ has prototype
$syntax%
        %Type% &%falseCase%
%$$


$head CondExp$$
Previous versions of CppAD used 
$syntax%
        CondExp(%flag%, %trueCase%, %falseCase%)
%$$
for the same meaning as 
$syntax%
        CondExpGt(%flag%, %Type%(0), %trueCase%, %falseCase%)
%$$
Use of $code CondExp$$ is deprecated, but continues to be supported.

$head Operation Sequence$$
This is an AD of $italic Base$$
$xref/glossary/Operation/Atomic/atomic operation/1/$$
and hence is part of the current
AD of $italic Base$$
$xref/glossary/Operation/Sequence/operation sequence/1/$$.


$head Example$$

$head Test$$
$children%
        example/cond_exp.cpp
%$$
The file
$xref/CondExp.cpp/$$
contains an example and test of this function.   
It returns true if it succeeds and false otherwise.

$head Atan2$$
The following implementation of the
AD $xref/atan2/$$ function is a more complex
example of using conditional expressions:
$code
$verbatim%cppad/local/atan2.hpp%0%BEGIN CondExp%// END CondExp%$$
$$


$end
-------------------------------------------------------------------------------
*/
//  BEGIN CppAD namespace
namespace CppAD {

// ------------ CondExpOp(cop, left, right, trueCase, falseCase) --------------
// CompareType and ResultType are different for the forward and reverse
// sparese calculations.
template <class CompareType, class ResultType>
inline ResultType CondExpTemplate( 
        enum  CompareOp            cop ,
        const CompareType        &left ,
        const CompareType       &right , 
        const ResultType     &trueCase , 
        const ResultType    &falseCase )
{       ResultType returnValue;
        switch( cop )
        {
                case CompareLt:
                if( left < right )
                        returnValue = trueCase;
                else    returnValue = falseCase;
                break;

                case CompareLe:
                if( left <= right )
                        returnValue = trueCase;
                else    returnValue = falseCase;
                break;

                case CompareEq:
                if( left == right )
                        returnValue = trueCase;
                else    returnValue = falseCase;
                break;

                case CompareGe:
                if( left >= right )
                        returnValue = trueCase;
                else    returnValue = falseCase;
                break;

                case CompareGt:
                if( left > right )
                        returnValue = trueCase;
                else    returnValue = falseCase;
                break;

                default:
                CPPAD_ASSERT_UNKNOWN(0);
                returnValue = trueCase;
        }
        return returnValue;
}

inline float CondExpOp( 
        enum CompareOp     cop ,
        const float      &left ,
        const float     &right , 
        const float  &trueCase , 
        const float &falseCase )
{       return CondExpTemplate(cop, left, right, trueCase, falseCase);
}

inline double CondExpOp( 
        enum CompareOp     cop ,
        const double      &left ,
        const double     &right , 
        const double  &trueCase , 
        const double &falseCase )
{       return CondExpTemplate(cop, left, right, trueCase, falseCase);
}

template <class Base>
inline AD<Base> CondExpOp(
        enum  CompareOp cop       ,
        const AD<Base> &left      , 
        const AD<Base> &right     , 
        const AD<Base> &trueCase  , 
        const AD<Base> &falseCase )
{
        AD<Base> returnValue;
        CPPAD_ASSERT_UNKNOWN( Parameter(returnValue) );

        // check first case where do not need to tape
        if( IdenticalPar(left) & IdenticalPar(right) )
        {       switch( cop )
                {
                        case CompareLt:
                        if( left.value_ < right.value_ )
                                returnValue = trueCase;
                        else    returnValue = falseCase;
                        break;

                        case CompareLe:
                        if( left.value_ <= right.value_ )
                                returnValue = trueCase;
                        else    returnValue = falseCase;
                        break;

                        case CompareEq:
                        if( left.value_ == right.value_ )
                                returnValue = trueCase;
                        else    returnValue = falseCase;
                        break;

                        case CompareGe:
                        if( left.value_ >= right.value_ )
                                returnValue = trueCase;
                        else    returnValue = falseCase;
                        break;

                        case CompareGt:
                        if( left.value_ > right.value_ )
                                returnValue = trueCase;
                        else    returnValue = falseCase;
                        break;

                        default:
                        CPPAD_ASSERT_UNKNOWN(0);
                        returnValue = trueCase;
                }
                return returnValue;
        }

        // must use CondExp incase Base is an AD type and recording
        returnValue.value_ = CondExpOp(cop, 
                left.value_, right.value_, trueCase.value_, falseCase.value_);

        ADTape<Base> *tape = CPPAD_NULL;
        if( Variable(left) )
                tape = left.tape_this();
        if( Variable(right) )
                tape = right.tape_this();
        if( Variable(trueCase) )
                tape = trueCase.tape_this();
        if( Variable(falseCase) )
                tape = falseCase.tape_this();

        // add this operation to the tape
        if( tape != CPPAD_NULL ) 
                tape->RecordCondExp(cop, 
                        returnValue, left, right, trueCase, falseCase);

        return returnValue;
}

// --- RecordCondExp(cop, returnValue, left, right, trueCase, falseCase) -----

template <class Base>
void ADTape<Base>::RecordCondExp(
        enum CompareOp  cop         ,
        AD<Base>       &returnValue ,
        const AD<Base> &left        ,
        const AD<Base> &right       ,
        const AD<Base> &trueCase    ,
        const AD<Base> &falseCase   )
{       size_t   ind0, ind1, ind2, ind3, ind4, ind5;
        size_t   returnValue_taddr;

        // taddr_ of this variable
        returnValue_taddr = Rec.PutOp(CExpOp);

        // ind[0] = cop
        ind0 = size_t( cop );

        // ind[1] = base 2 representaion of the value
        // [Var(left), Var(right), Var(trueCase), Var(falseCase)]
        ind1 = 0;

        // Make sure returnValue is in the list of variables and set its taddr
        if( Parameter(returnValue) )
                returnValue.make_variable(id_, returnValue_taddr );
        else    returnValue.taddr_ = returnValue_taddr;

        // ind[2] = left address
        if( Parameter(left) )
                ind2 = Rec.PutPar(left.value_);
        else
        {       ind1 += 1;
                ind2 = left.taddr_;     
        }

        // ind[3] = right address
        if( Parameter(right) )
                ind3 = Rec.PutPar(right.value_);
        else
        {       ind1 += 2;
                ind3 = right.taddr_;    
        }

        // ind[4] = trueCase address
        if( Parameter(trueCase) )
                ind4 = Rec.PutPar(trueCase.value_);
        else
        {       ind1 += 4;
                ind4 = trueCase.taddr_; 
        }

        // ind[5] =  falseCase address
        if( Parameter(falseCase) )
                ind5 = Rec.PutPar(falseCase.value_);
        else
        {       ind1 += 8;
                ind5 = falseCase.taddr_;        
        }

        CPPAD_ASSERT_UNKNOWN( NumInd(CExpOp) == 6 );
        CPPAD_ASSERT_UNKNOWN( ind1 > 0 );
        Rec.PutInd(ind0, ind1, ind2, ind3, ind4, ind5);

        // check that returnValue is a dependent variable
        CPPAD_ASSERT_UNKNOWN( Variable(returnValue) );
}

// ------------ CondExpOp(left, right, trueCase, falseCase) ----------------

# define CPPAD_COND_EXP(Name)                                              \
        template <class Base>                                              \
        inline AD<Base> CondExp##Name(                                     \
                const AD<Base> &left      ,                                \
                const AD<Base> &right     ,                                \
                const AD<Base> &trueCase  ,                                \
                const AD<Base> &falseCase )                                \
        {                                                                  \
                return CondExpOp(Compare##Name,                            \
                        left, right, trueCase, falseCase);                 \
        }

// AD<Base>
CPPAD_COND_EXP(Lt)
CPPAD_COND_EXP(Le)
CPPAD_COND_EXP(Eq)
CPPAD_COND_EXP(Ge)
CPPAD_COND_EXP(Gt)
template <class Base>
inline AD<Base> CondExp(
        const AD<Base> &flag      , 
        const AD<Base> &trueCase  ,
        const AD<Base> &falseCase )
{       
        return CondExpOp(CompareGt, flag, AD<Base>(0), trueCase, falseCase);
}

# undef CPPAD_COND_EXP
# define CPPAD_COND_EXP(Name, Op, Type)                             \
        inline Type CondExp##Name(                                  \
                const Type &left      ,                             \
                const Type &right     ,                             \
                const Type &trueCase  ,                             \
                const Type &falseCase )                             \
        {       Type returnValue;                                   \
                if( left Op right )                                 \
                        returnValue = trueCase;                     \
                else    returnValue = falseCase;                    \
                return returnValue;                                 \
        }

// float
CPPAD_COND_EXP(Lt,  <, float)
CPPAD_COND_EXP(Le, <=, float)
CPPAD_COND_EXP(Eq, ==, float)
CPPAD_COND_EXP(Ge, >=, float)
CPPAD_COND_EXP(Gt,  >, float)
inline float CondExp(
        const float &flag      , 
        const float &trueCase  ,
        const float &falseCase )
{       
        return CondExpGt(flag, float(0), trueCase, falseCase);
}

// double
CPPAD_COND_EXP(Lt,  <, double)
CPPAD_COND_EXP(Le, <=, double)
CPPAD_COND_EXP(Eq, ==, double)
CPPAD_COND_EXP(Ge, >=, double)
CPPAD_COND_EXP(Gt,  >, double)
inline double CondExp(
        const double &flag      , 
        const double &trueCase  ,
        const double &falseCase )
{       
        return CondExpGt(flag, 0., trueCase, falseCase);
}

# undef CPPAD_COND_EXP

} // END CppAD namespace

# endif 

---