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 dreal numbers.
    template <typename T>
    concept Real_Ring_Concept_ = 
        Ordered_Ring_Concept<T> &&
        Ring_Concept<T> &&
        Additive_SemiGroup_Concept<T> &&
        requires(T t) {
        //! Constructs with value 0.
        T();
        //! Constructs from an int8.
        T((int8)0);
        //! Constructs from an uint8.
        T((uint8)0);
        //! Constructs from an int16.
        T((int16)0);
        //! Constructs from an uint16.
        T((uint16)0);
        //! Constructs from an int32.
        T((int32)0);
        //! Constructs from an uint32.
        T((uint32)0);
        //! Constructs from a float.
        T((float)0);
        //! Constructs from a double.
        T((double)0);
        //! Constructs from a NaN.
        T(Nan());
        //! Constructs from an Infinity.
        T(Infinity());
        //! Constructs from -Infinity.
        T(-Infinity());
        //! Returns the greatest integer <= that.
        {floor(addConst(t))} -> std::convertible_to<T>;
        //! Returns the least integer >= that.
        {ceil(addConst(t))} -> std::convertible_to<T>;
        // //! Returns the number in scientific notation.
        // {asScientific(addConst(t))} -> std::convertible_to<ScientificNotation>;
    };

    template <typename T>
    concept Real_Ring_Concept = 
        Real_Ring_Concept_<RemoveCvRef<T>>;

    using Real_Ring_Archetype = integer;

}

#endif