base_cond_exp

Base Type Requirements for Conditional Expressions

Purpose

These definitions are required by the user’s code to support the AD < Base > type for CondExp operations:

CompareOp

The following enum type is used in the specifications below:

namespace CppAD {
// The conditional expression operator enum type
enum CompareOp
{  CompareLt, // less than
CompareLe, // less than or equal
CompareEq, // equal
CompareGe, // greater than or equal
CompareGt, // greater than
CompareNe  // not equal
};
}

CondExpTemplate

The type Base must support the syntax

      result = CppAD::CondExpOp (
            cop , left , right , exp_if_true , exp_if_false
      )

which computes implements the corresponding CondExp function when the result has prototype

Base result

The argument cop has prototype

enum CppAD::CompareOp cop

The other arguments have the prototype

      const Base & left
      const Base & right
      const Base & exp_if_true
      const Base & exp_if_false

Ordered Type

If Base is a relatively simple type that supports < , <= , == , >= , and > operators its CondExpOp function can be defined by

namespace CppAD {
      inline Base CondExpOp (
      enum CppAD::CompareOp cop ,
      const Base & left ,
      const Base & right ,
      const Base & exp_if_true ,
      const Base & exp_if_false )
      { return CondExpTemplate (
                  cop , left , right , trueCase , falseCase );
      }
}

For example, see double CondExpOp . For an example of and implementation of CondExpOp with a more involved Base type see adolc CondExpOp .

Not Ordered

If the type Base does not support ordering, the CondExpOp function does not make sense. In this case one might (but need not) define CondExpOp as follows:

namespace CppAD {
      inline Base CondExpOp (
      enum CompareOp cop ,
      const Base & left ,
      const Base & right ,
      const Base & exp_if_true ,
      const Base & exp_if_false )
      { // attempt to use CondExp with a Base argument
            assert (0);
            return Base (0);
      }
}

For example, see complex CondExpOp .

CondExpRel

The macro invocation

CPPAD_COND_EXP_REL ( Base )

uses CondExpOp above to define the following functions

      CondExpLt ( left , right , exp_if_true , exp_if_false )
      CondExpLe ( left , right , exp_if_true , exp_if_false )
      CondExpEq ( left , right , exp_if_true , exp_if_false )
      CondExpGe ( left , right , exp_if_true , exp_if_false )
      CondExpGt ( left , right , exp_if_true , exp_if_false )

where the arguments have type Base . This should be done inside of the CppAD namespace. For example, see base_alloc .