real_ring_concept.h

// Description: Real ring concept
// Documentation: reals.txt

#ifndef PASTELSYS_REAL_RING_CONCEPT_H
#define PASTELSYS_REAL_RING_CONCEPT_H

#include "pastel/sys/algebra/ordered_ring_concept.h"
#include "pastel/sys/real/scientific_notation_fwd.h"

// See concept.txt for why native types must be 
// defined _before_ the concept.
#include "pastel/sys/real/native_real.h"
#include "pastel/sys/integer/native_integer.h"

namespace Pastel
{

    //! A sub-ring of real numbers.
    struct Real_Ring_Concept
    : Refines<Ordered_Ring_Concept>
    {
        template <typename Type>
        auto requires_(Type&& t) -> decltype(
            conceptCheck(
                //! Constructs with value 0.
                Type(),
                //! Constructs from an int8.
                Type((int8)0),
                //! Constructs from an uint8.
                Type((uint8)0),
                //! Constructs from an int16.
                Type((int16)0),
                //! Constructs from an uint16.
                Type((uint16)0),
                //! Constructs from an int32.
                Type((int32)0),
                //! Constructs from an uint32.
                Type((uint32)0),
                //! Constructs from a float.
                Type((float)0),
                //! Constructs from a double.
                Type((double)0),
                //! Constructs from a NaN.
                Type(Nan()),
                //! Constructs from an Infinity.
                Type(Infinity()),
                //! Constructs from -Infinity.
                Type(-Infinity()),
                //! Returns the greatest integer <= that.
                Concept::convertsTo<Type>(floor(t)),
                //! Returns the least integer >= that.
                Concept::convertsTo<Type>(ceil(t))
                //! Returns the number in scientific notation.
                //Concept::convertsTo<ScientificNotation>(asScientific(t))
            )
        );
    };

    using Real_Ring_Archetype = integer;

}

#endif