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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 Cases
The variables u and v are not identically equal in the following case (which CppAD automatically defines EqualOpSeq for): The type Base is AD<double> , x[0] = x[1] = 1. , then independent is used to make x the independent variable vector, and then 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

IdenticalPar
A Base is a parameter when used in an AD<Base> operation sequence. It is however still possible for a parameter to change its value. For example, the Base value u is not identically a parameter equal in the following case (which CppAD automatically defines IdenticalPar for): The type Base is AD<double> , x[0] = 1. , then independent is used to make x the independent variable vector, and then u = x[0] , Note that during a future Forward calculation, u could correspond to different values.

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 = IdenticalPar(u)    the Base value will always be the same b = IdenticalZero(u)    u equals zero and IdenticalPar(u) b = IdenticalOne(u)    u equals one and IdenticalPar(u) b = IdenticalEqualPar(u, v)    u equals v , IdenticalPar(u) and IdenticalPar(v)

Examples
See base_alloc .
Input File: omh/base_require/base_identical.omh