\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

base_ordered

Base Type Requirements for Ordered Comparisons

Purpose

The following operations (in the CppAD namespace) are required to use the type AD < Base > :

Syntax	Result
b = GreaterThanZero ( x )	\(x > 0\)
b = GreaterThanOrZero ( x )	\(x \geq 0\)
b = LessThanZero ( x )	\(x < 0\)
b = LessThanOrZero ( x )	\(x \leq 0\)
b = abs_geq ( x , y )	\(|x| \geq |y|\).

where the arguments and return value have the prototypes

      const Base & x

      const Base & y

      bool b

Ordered Type

If the type Base supports ordered operations, these functions should have their corresponding definitions. For example,

namespace CppAD {

      inline bool GreaterThanZero ( const Base & x )

      { return ( x > 0 );

      }

}

The other functions would replace > by the corresponding operator. For example, see base_alloc .

Not Ordered

If the type Base does not support ordering, one might (but need not) define GreaterThanZero as follows:

namespace CppAD {

      inline bool GreaterThanZero ( const Base & x )

      { // attempt to use GreaterThanZero with a Base argument

            assert (0);

            return x ;

      }

}

The other functions would have the corresponding definition. For example, see complex Ordered .

Special Requirements

The following are special requirements when there is no ordered comparison for the base type:

Independent

record_compare must be false in the call to Independent .

Optimize

The no_conditional_skip option must be present when optimize is used.

PrintFor

The PrintFor operator cannot be used.