native_ordered_monoid.h

// Description: Native types as an ordered monoid concept
// DocumentationOf: ordered_monoid_concept.h

#ifndef PASTELSYS_NATIVE_ORDERED_MONOID_H
#define PASTELSYS_NATIVE_ORDERED_MONOID_H

#include "pastel/sys/sfinae.h"

#include <cstdlib>

#define PASTEL_DEFINE_ABS(T) inline const T abs(T that) {return that;}

namespace Pastel
{

    // Ordered additive monoid

    // The abs-functions for unsigned integers
    // need to be defined as normal functions;
    // a single function template constrained
    // to unsigned integers will not do. The
    // reason is that otherwise abs((uchar)1)
    // is ambiguous between std::abs(int) and
    // the template.
    PASTEL_DEFINE_ABS(uchar)
    PASTEL_DEFINE_ABS(uint)
    PASTEL_DEFINE_ABS(ulong)
    PASTEL_DEFINE_ABS(ulonglong)

}

#undef PASTEL_DEFINE_ABS

namespace Pastel
{

    // Support abs() for floating-point and signed integers.
    using std::abs;

    template <typename Type>
    requires 
        std::is_floating_point_v<Type> ||
        std::is_signed_v<Type>
    bool negative(const Type& that)
    {
        return that < 0;
    }

    template <typename Type>
    requires std::is_unsigned_v<Type>
    bool negative(const Type& that)
    {
        // An unsigned integer is never negative.
        return false;
    }

    template <Arithmetic_Concept Type>
    bool positive(const Type& that)
    {
        return that > 0;
    }

}

#endif