// ==========================================================================
// 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: Brice Boyer (briceboyer) <boyer.brice@gmail.com>
//          A. Breust (taken from FFLAS-FFPACK)
// ==========================================================================

/*! @file field/modular-uint64.h
 * @ingroup field
 * @brief  representation of <code>Z/mZ</code> over \c uint64_t .
 */

#ifndef __GIVARO_modular_uint8_H
#define __GIVARO_modular_uint8_H

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

namespace Givaro {

    template <typename COMP>
    class Modular<uint8_t, COMP> : public virtual FiniteFieldInterface<uint8_t>
    {
    public:
	// ----- Exported Types and constantes
	using Self_t = Modular<uint8_t, COMP>;
	using Compute_t = typename std::make_unsigned<COMP>::type;
	using Residu_t = uint8_t;

	enum { size_rep = sizeof(Residu_t) };

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

	// ----- Constructors
	Modular()
	    : _p(static_cast<Residu_t>(0)) {}

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

	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();
	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;
            return *this;
	}

        // ----- Initialisation
        Element& init (Element& x) const
        { return x = 0; }
        Element& init (Element& x, const float a) const;
        Element& init (Element& x, const double a) const;
        Element& init (Element& x, const int16_t a) const;
        Element& init (Element& x, const uint16_t a) const;
        Element& init (Element& x, const int32_t a) const;
        Element& init (Element& x, const uint32_t 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(r, Caster<Element>((a < 0)? -a : a));
	    if (a < 0) negin(r);
            return 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 = Caster<T>(a); }

        Element& reduce (Element& x, const Element& y) const
        { x = y % _p; return x; }
        Element& reduce (Element& x) const
        { 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::istream& read (std::istream& s);
	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-uint8.inl"

#endif

