Conceptual Archetypes and Testing

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### Conceptual Archetypes and Testing

There are several concept archetypes available:

    #include <boost/concepts/std_real_concept.hpp>

    namespace boost{
    namespace math{
    namespace concepts{

    class std_real_concept;

    }}} // namespaces

`std_real_concept` is an archetype for the built-in Real types.

The main purpose in providing this type is to verify that standard library functions are found via a using declaration - bringing those functions into the current scope - and not just because they happen to be in global scope.

In order to ensure that a call to say `pow` can be found either via argument dependent lookup, or failing that then in the std namespace: all calls to standard library functions are unqualified, with the std:: versions found via a using declaration to make them visible in the current scope. Unfortunately it's all to easy to forget the using declaration, and call the double version of the function that happens to be in the global scope by mistake.

For example if the code calls ::pow rather than std::pow, the code will cleanly compile, but truncation of long doubles to double will cause a significant loss of precision. In contrast a template instantiated with std_real_concept will only compile if the all the standard library functions used have been brought into the current scope with a using declaration.

There is a test program libs/math/test/std_real_concept_check.cpp that instantiates every template in this library with type `std_real_concept` to verify it's usage of standard library functions.

    #include <boost/math/concepts/real_concept.hpp>

    namespace boost{
    namespace math{
    namespace concepts{

    class real_concept;

    }}} // namespaces

`real_concept` is an archetype for user defined real types, it declares it's standard library functions in it's own namespace: these will only be found if they are called unqualified allowing argument dependent lookup to locate them. In addition this type is useable at runtime: this allows code that would not otherwise be exercised by the built-in floating point types to be tested. There is no std::numeric_limits<> support for this type, since this is not a conceptual requirement for RealType's.

NTL RR is an example of a type meeting the requirements that this type models, but note that use of a thin wrapper class is required: refer to "Using With NTL - a High-Precision Floating-Point Library".

There is no specific test case for type `real_concept`, instead, since this type is usable at runtime, each individual test case as well as testing `float`, `double` and `long double`, also tests `real_concept`.

    #include <boost/math/concepts/distribution.hpp>

    namespace boost{
    namespace math{
    namespace concepts{

    template <class RealType>
    class distribution_archetype;

    template <class Distribution>
    struct DistributionConcept;

    }}} // namespaces

The class template `distribution_archetype` is a model of the Distribution concept.

The class template `DistributionConcept` is a concept checking class for distribution types.

The test program distribution_concept_check.cpp is responsible for using `DistributionConcept` to verify that all the distributions in this library conform to the Distribution concept.

The class template `DistributionConcept` verifies the existence (but not proper function) of the non-member accessors required by the Distribution concept. These are checked by calls like

v = pdf(dist, x); // (Result v is ignored).

And in addition, those that accept two arguments do the right thing when the arguments are of different types (the result type is always the same as the distribution's value_type). (This is implemented by some additional forwarding-functions in derived_accessors.hpp, so that there is no need for any code changes. Likewise boilerplate versions of the hazard/chf/coefficient_of_variation functions are implemented in there too.)