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base_identical

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Base Type Requirements for Identically Equal Comparisons

EqualOpSeq

If function EqualOpSeq is used with arguments of type AD < Base > , the type Base must support the syntax

b = CppAD::EqualOpSeq ( u , v )

This should return true if and only if u is identically equal to v and it makes no different which one is used. The arguments u and v have prototype

      const Base & u

      const Base & v

The return value b has prototype

bool b

The Simple Case

If Base is a relatively simple type, the EqualOpSeq function can be defined by

namespace CppAD {

      inline Base EqualOpSeq ( const Base & u , const Base & v )

      { return u == v ; }

}

For example, see base_alloc .

More Complicated Case

The variables u and v are not identically equal in the following case:

1. The type Base is AD<double> .

2. The following assignment made using type Base : x [0] = x [1] = 1. ,

3. The Independent operations is used to make x the independent variable vector,

4. During the corresponding recording, u = x [0] , v = x [1] .

Note that during a future Forward calculation, u and v could correspond to different values. For example, see adolc EqualOpSeq .

Identical

IdenticalCon

A Base object is a Constant parameter when used in an AD < Base > operation sequence. It is however still possible for a parameter to change its value; e.g., see the more complicated case above.

Prototypes

The argument u has prototype

const Base u

If it is present, the argument v has prototype

const Base v

The result b has prototype

bool b

Identical Functions

The type Base must support the following functions (in the CppAD namespace):

Syntax	Result
b = IdenticalCon ( u )	the Base value will always be the same
b = IdenticalZero ( u )	u equals zero and IdenticalCon ( u )
b = IdenticalOne ( u )	u equals one and IdenticalCon ( u )
b = IdenticalEqualCon ( u , v )	u equals v , IdenticalCon ( u ) and IdenticalCon ( v )

Examples

See base_alloc .