// ==========================================================================
// $Source: /var/lib/cvs/Givaro/src/kernel/zpz/givzpz32uns.h,v $
// Copyright(c)'1994-2009 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: T. Gautier
// $Id: givzpz32uns.h,v 1.13 2011-02-02 17:16:43 briceboyer Exp $
// ==========================================================================
//
//  Modified by Pascal Giorgi on 2002/02/13  (pascal.giorgi@ens-lyon.fr)

/*! @file givzpz32uns.h
 * @ingroup zpz
 * @brief    Arithmetic on Z/pZ, with p a prime number less than 2^32.
 *   Modulo typedef is a signed long number. In case it was modified
 *   then Bézout algorithm must be changed (coefficient can be negative).
 */
#ifndef __GIVARO_zpz32unsigned_H
#define __GIVARO_zpz32unsigned_H

#include "givaro/givinteger.h"
#include "givaro/ring-interface.h"
#include "givaro/givranditer.h"
#include "givaro/modular-general.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
     * - m max is 65536
     * - p max is 65521
     * .
     */
    template<typename COMP>
    class Modular<uint32_t, COMP> : public virtual FiniteFieldInterface<uint32_t>
    {
    public:
        // ----- Exported Types and constantes
        using Self_t = Modular<uint32_t, COMP>;
        using Compute_t = typename std::make_unsigned<COMP>::type;
        using Residu_t = uint32_t;
        enum { size_rep = sizeof(Residu_t) };

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

        // ----- Constructors
        Modular() : zero(0), one(1), mOne(0), _p(0), _dp(0.0) {}

        Modular(Residu_t p)
            : zero(0), one(1), mOne((Element)p-1), _p(p), _dp((double)p)
        {
            assert(_p >= minCardinality());
            assert(_p <= maxCardinality());
        }

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

        // ----- 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();
        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
        bool operator==(const Self_t& F) const { return _p == F._p; }
        bool operator!=(const Self_t& F) const { return _p != F._p; }
        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;
            _dp = F._dp;
            return *this;
        }

        // ----- Initialisation
        Element& init (Element& x) const
        { return x = 0; }
        Element& init (Element& x, const double a) const;
        Element& init (Element& x, const int64_t a) const;
        Element& init (Element& x, const uint64_t a) const;
        Element& init (Element& x, const Integer& a) const;
        template<typename T> Element& init(Element& r, const T& a) const
        {
            reduce( Caster<Element,T>(r, (a < 0)? -a : a) );
            return (a<0 ? negin(r) : 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 Caster<T,Element>(r,a); }

        Element& reduce (Element& x, const Element& y) const
        { return x = y % _p;}
        Element& reduce (Element& x) const
        { return x %= _p; }
        
        // ----- 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;
        double _dp;

    };
}

#include "givaro/modular-uint32.inl"

#endif

