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// 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: A. Breust <alexis.breust@imag.fr>
// ==========================================================================
#ifndef __GIVARO_montgomery_ruint_H
#define __GIVARO_montgomery_ruint_H
#include "recint/ruint.h"
#include "recint/rmgmodule.h"
#include "givaro/givcaster.h"
#include "givaro/givinteger.h"
#include "givaro/givranditer.h"
#include "givaro/ring-interface.h"
namespace Givaro
{
template<class TYPE> class Montgomery;
//! @brief The recint-based Montgomery ring.
//! You can only odd moduli.
//! An integer (a mod p) is stored as (a * r mod 2^{2^K}) with (r = 2^{2^K} mod p).
template<size_t K>
class Montgomery<RecInt::ruint<K>> : public virtual FiniteFieldInterface<RecInt::ruint<K>>
{
public:
// ----- Exported Types and constantes
using Element = RecInt::ruint<K>;
using LargeElement = RecInt::ruint<K+1>;
using Self_t = Montgomery<RecInt::ruint<K>>;
using Residu_t = RecInt::ruint<K>;
enum { size_rep = sizeof(Residu_t) };
// ----- Representation of vector of the Element
typedef Element* Array;
// ----- Constantes
const Element zero;
const Element one;
const Element mOne;
// ----- Constructors
Montgomery()
: zero(0), one(1), mOne(-1)
, _p(0), _p1(0), _r(0), _r2(0), _r3(0)
{}
Montgomery(const Residu_t& p)
: zero(0)
, _p(p)
{
RecInt::arazi_qi(_p1, -_p); // p1 = -inv(p) mod 2^(2^K)
RecInt::mod_n(_r, -_p, _p); // r = 2^(2^K) mod p
LargeElement ltmp;
RecInt::lmul(ltmp, _r, _r);
RecInt::mod_n(_r2, ltmp, _p); // r2 = r^2 mod p
RecInt::lmul(ltmp, _r2, _r);
RecInt::mod_n(_r3, ltmp, _p); // r2 = r^2 mod p
RecInt::copy(const_cast<Element&>(one), _r);
to_mg(const_cast<Element&>(mOne), _p - 1u);
assert( (_p & 1u) != 0u);
assert(_p >= minCardinality());
assert(_p <= maxCardinality());
}
Montgomery(const Self_t& F)
: zero(F.zero), one(F.one), mOne(F.mOne)
, _p(F._p), _p1(F._p1), _r(F._r)
{}
// ----- 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; }
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 to_mg(r);
}
Element& init(Element& r, const Integer& a) const
{
reduce(r, Caster<Element>((a < 0)? -a : a));
if (a < 0) negin(r);
return to_mg(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
{ Element tmp; return r = Caster<T>(mg_reduc(tmp, 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
{ RecInt::rand(r); mod_n(r, _p); return r; }
template< class Random > Element& nonzerorandom(Random& g, Element& a) const
{ while (isZero(random(g, a))) {} 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:
// Internal montgomery-reduction. a <- b * r^{-1}
Element& mg_reduc(Element& a, const Element& b) const;
Element& mg_reduc(Element& a, const LargeElement& b) const;
// a <- b * r
Element& to_mg(Element& a, const Element& b) const;
Element& to_mg(Element& a) const;
protected:
// p is the module (must be odd and > 1)
RecInt::ruint<K> _p;
// p1 = -inv(p) mod 2^(2^K)
RecInt::ruint<K> _p1;
// r = 2^(2^K) mod p
RecInt::ruint<K> _r;
// r2 = r^2 mod p - used to initialize elements
RecInt::ruint<K> _r2;
// r3 = r^3 mod p - used to compute inverse
RecInt::ruint<K> _r3;
};
} // namespace Givaro
#include "givaro/montgomery-ruint.inl"
#endif
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