// ==========================================================================
// Copyright(c)'1994-2015 by The Givaro group
// This file is part of Givaro.
// Givaro is governed by the CeCILL-B license under French law
// and abiding by the rules of distribution of free software.
// see the COPYRIGHT file for more details.
// Authors: JG Dumas
//          A. Breust (adapted)
// ========================================================================

/*! @file givzpzInt.h
 * @ingroup zpz
 *  @brief Arithmetic on Z/pZ, with p a prime number in arbitrary precision.
 */

#ifndef __GIVARO_zpz_gen_H
#define __GIVARO_zpz_gen_H

#include "givaro/givbasictype.h"
#include "givaro/giverror.h"
#include "givaro/givinteger.h"
#include "givaro/givcaster.h"
#include "givaro/givranditer.h"
#include "givaro/modular-general.h"
#include "givaro/ring-interface.h"

namespace Givaro
{

    /*! @brief This class implement the standard arithmetic with Modulo Elements.
     * - The representation of an integer a in Zpz is the value a % p
     * .
     */
    template<typename IntType, typename COMP>
    class Modular : public virtual FiniteFieldInterface<IntType>
    {
    public:
        // ----- Exported Types and constantes
        typedef Modular<IntType> Self_t;
        typedef IntType Residu_t;
        enum { size_rep = sizeof(Residu_t) };
	using Element = typename FiniteFieldInterface<IntType>::Element;

        // ----- Constantes
        const Element zero ;
        const Element one  ;
        const Element mOne;

        // ----- Constructors
        ~Modular() noexcept {}
        Modular()
                : zero(0),
                  one(1),
                  _p(static_cast<Residu_t>(0)) {}

        Modular(const Residu_t p)
            : zero(0)
            , one(1)
            , mOne(p-static_cast<Residu_t>(1)), _p(p)
        {
            assert(_p >= minCardinality());
        }

        template<class IntConvType>
        Modular(const IntConvType& p, const IntConvType& e=1)
            : zero(0)
            , one(1)
            , mOne( Caster<Residu_t>(p-1) )
            , _p( Caster<Residu_t>(p) )
        {
            assert(_p >= minCardinality());
        }

        Modular(const Integer& p, const Integer& e=Integer::one)
            : zero(0)
            , one(1)
            , mOne( Caster<Residu_t>(p-1) )
            , _p( Caster<Residu_t>(p) )
        {
            assert(_p >= minCardinality());
        }

        Modular(const Self_t& F)
                : zero(F.zero),one(F.one),mOne(F.mOne), _p(F._p) {}

        // ----- Accessors
        inline Element minElement() const override { return zero; }
        inline Element maxElement() const override { return mOne; }

        // ----- Access to the modulus
        inline Residu_t residu() const { return _p; }
        inline Residu_t size() const { return _p; }
        inline Residu_t characteristic() const { return _p; }
        inline Residu_t cardinality() const { return _p; }
        template<class T> inline T& characteristic(T& p) const { return p = _p; }
        template<class T> inline T& cardinality(T& p) const { return p = _p; }
        
        static inline Residu_t maxCardinality() { return -1; }
        static inline Residu_t minCardinality() { return 2; }

        // ----- Checkers
        inline bool isZero(const Element& a) const override { return a == zero; }
        inline bool isOne (const Element& a) const override { return a == one; }
        inline bool isMOne(const Element& a) const override { return a == mOne; }
        inline bool areEqual(const Element& a, const Element& b) const override { return a == b; }
        inline size_t length(const Element a) const { return size_rep; }
        
        // ----- Ring-wise operators
        inline bool operator==(const Self_t& F) const { return _p == F._p; }
        inline bool operator!=(const Self_t& F) const { return _p != F._p; }
        inline Self_t& operator=(const Self_t& F)
        {
            F.assign(const_cast<Element&>(one),  F.one);
            F.assign(const_cast<Element&>(zero), F.zero);
            F.assign(const_cast<Element&>(mOne), F.mOne);
            _p = F._p;
            return *this;
        }

        // ----- Initialisation
        Element& init (Element& x) const
	{ return x = 0; }
        Element& init (Element& x, const Integer& y) const
	{ x = y % _p; return reduce(x); }
        template<typename T> Element& init(Element& r, const T& a) const
        { r = Caster<Element>(a); return reduce(r); }

        Element& assign (Element& x, const Element& y) const
	{ return x = y; }
    
        // ----- Convert and reduce
        template<typename T> T& convert(T& r, const Element& a) const
        { return r = static_cast<T>(a); }

        Element& reduce (Element& x, const Element& y) const
	{ x = y % _p; if (x < 0) x += _p; return x; }
        Element& reduce (Element& x) const
	{ x %= _p; if (x < 0) x += _p; return x; }
        
        // ----- Classic arithmetic
        Element& mul(Element& r, const Element& a, const Element& b) const override;
        Element& div(Element& r, const Element& a, const Element& b) const override;
        Element& add(Element& r, const Element& a, const Element& b) const override;
        Element& sub(Element& r, const Element& a, const Element& b) const override;
        Element& neg(Element& r, const Element& a) const override;
        Element& inv(Element& r, const Element& a) const override;

        Element& mulin(Element& r, const Element& a) const override;
        Element& divin(Element& r, const Element& a) const override;
        Element& addin(Element& r, const Element& a) const override;
        Element& subin(Element& r, const Element& a) const override;
        Element& negin(Element& r) const override;
        Element& invin(Element& r) const override;
        
        // -- axpy:   r <- a * x + y
        // -- axpyin: r <- a * x + r
        Element& axpy  (Element& r, const Element& a, const Element& x, const Element& y) const override;
        Element& axpyin(Element& r, const Element& a, const Element& x) const override;

        // -- axmy:   r <- a * x - y
        // -- axmyin: r <- a * x - r
        Element& axmy  (Element& r, const Element& a, const Element& x, const Element& y) const override;
        Element& axmyin(Element& r, const Element& a, const Element& x) const override;

        // -- maxpy:   r <- y - a * x
        // -- maxpyin: r <- r - a * x
        Element& maxpy  (Element& r, const Element& a, const Element& x, const Element& y) const override;
        Element& maxpyin(Element& r, const Element& a, const Element& x) const override;

        // ----- Random generators
        typedef ModularRandIter<Self_t> RandIter;
        typedef GeneralRingNonZeroRandIter<Self_t> NonZeroRandIter;
        template< class Random > Element& random(Random& g, Element& r) const
        { return init(r, g()); }
        template< class Random > Element& nonzerorandom(Random& g, Element& a) const
        { while (isZero(init(a, g())))
                ;
            return a; }
        
        // --- IO methods
        std::ostream& write(std::ostream& s) const;
        std::istream& read (std::istream& s, Element& a) const;
        std::ostream& write(std::ostream& s, const Element& a) const;

    protected:
	
        Residu_t _p;
    };
}

#include "givaro/modular-inttype.inl"

#endif

