Z_n.hpp

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#pragma once
#include <iostream>
#include <array>
#include <Eigen/Dense>
#include "Types/SFINAE.hpp"
 
 
namespace mackey {
 
    template<int64_t N, typename T = int64_t>
    class Z_mod {
    public:
        constexpr static int64_t order = N; 
        T x; 
        Z_mod() : x(0) {} 
        Z_mod(bool x) : x(x) {} 
        Z_mod(int x); 
        Z_mod(int64_t x); 
        explicit operator char() const;
        explicit operator short() const;
        explicit operator int() const;
        explicit operator int64_t() const;
        explicit operator unsigned char() const;
        explicit operator unsigned short() const;
        explicit operator unsigned int() const;
        explicit operator uint64_t() const;
        Z_mod<N, T> operator +(Z_mod<N, T> b) const;
        Z_mod<N, T> operator -(Z_mod<N, T> b) const;
        Z_mod<N, T>& operator +=(Z_mod<N, T> b);
        Z_mod<N, T>& operator -=(Z_mod<N, T> b);
        Z_mod<N, T>& operator *=(Z_mod<N, T> b);
        Z_mod<N, T>& operator /=(Z_mod<N, T> b);
        bool operator ==(Z_mod<N, T> a) const;
        bool operator !=(Z_mod<N, T> a) const;
        bool operator <=(Z_mod<N, T> a) const; 
    };
 
 
    template<int64_t N, typename T>
    Z_mod<N, T> operator -(Z_mod<N, T> a);
 
    template<int64_t N, typename T>
    Z_mod<N, T> operator *(Z_mod<N, T> a, Z_mod<N, T> b); //Eigen needs this to be non member
 
    template<int64_t N, typename T>
    Z_mod<N, T> operator /(Z_mod<N, T> a, Z_mod<N, T> b);
 
    template<typename T>
    T abs(T a);
 
    template<int64_t N, typename T> //Eigen needs this to be non member
    std::ostream& operator<<(std::ostream& out, const Z_mod<N, T> a);
 
    using Z2 = Z_mod<2, bool>;
}
 
namespace Eigen {
    using namespace mackey;
 
    template<int64_t N, typename T>
    struct NumTraits<Z_mod<N, T>>
    {
        typedef Z_mod<N, T> Real;
        typedef Z_mod<N, T> Nested;
        typedef int Literal;
        enum {
            IsComplex = 0,
            IsInteger = 0,
            IsSigned = 0,
            RequireInitialization = 0,
            ReadCost = 1,
            AddCost = 1,
            MulCost = 1
        };
        static inline Z_mod<N, T> dummy_precision() { return Z_mod<N, T>(0); }
        static inline int digits10() { return 0; }
    };
}
 
#include "impl/Z_n.ipp"