/usr/include/givaro/montgomery-int32.h is in libgivaro-dev 4.0.2-5.
This file is owned by root:root, with mode 0o644.
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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: JG Dumas (from P. Zimmermann's Montgomery implementation)
// A. Breust (adapted)
// ==========================================================================
/*! @file givmontg32.h
* @ingroup zpz
* @brief NO DOC
*/
#ifndef __GIVARO_montg32_H
#define __GIVARO_montg32_H
#include "givaro/udl.h"
#include "givaro/givcaster.h"
#include "givaro/givranditer.h"
#include "givaro/modular-general.h" // invext()
#include "givaro/ring-interface.h"
#include <cmath>
#define B32 65536_ui32
#define MASK32 65535_ui32
#define HALF_BITS32 16
namespace Givaro
{
template<class TYPE> class Montgomery;
/*! @brief This class implements the standard arithmetic with Modulo Elements.
* Reduction is made through Montgomery's reduction.
* Representation of a is by storing (aB).
* - We must have gcd(p,2)=1
* - We must have \f$(p-1)^2 + p(B-1) < B^2 \f$, i.e. \f$2<p \leq 40504\f$ for \f$B=2^16\f$.
* - m max is 40503
* - p max is 40499
*/
template<>
class Montgomery<int32_t> : public virtual FiniteFieldInterface<uint32_t>
{
public:
// ----- Exported Types and constantes
using Self_t = Montgomery<int32_t>;
using Residu_t = uint32_t;
enum { size_rep = sizeof(Residu_t) };
// ----- Constantes
const Element zero = 0;
const Element one;
const Element mOne;
// ----- Constructors
Montgomery() : one(1U), mOne(0U), _p(0U), _dp(0.0) {}
Montgomery( Residu_t p, int = 1) :
one(0U), mOne(0U),
_p( (Residu_t) p),
_Bp( (Residu_t) B32%p),
_B2p((Residu_t) (_Bp<<HALF_BITS32) % p),
_B3p((Residu_t) (_B2p<<HALF_BITS32) % p),
_nim((Residu_t) -invext(_p, B32)),
_dp( (double) p)
{
// std::cerr << "_p: " << _p << std::endl;
// std::cerr << "_Bp: " << _Bp << std::endl;
// std::cerr << "_B2p: " << _B2p << std::endl;
// std::cerr << "_B3p: " << _B3p << std::endl;
// std::cerr << "_nim: " << _nim << std::endl;
const_cast<Element&>(one) = _Bp;
const_cast<Element&>(mOne) = _p - one;
}
Montgomery( const Self_t& F)
: one(F.one), mOne(F.mOne)
, _p(F._p), _Bp(F._Bp), _B2p( F._B2p), _B3p( F._B3p)
, _nim(F._nim), _dp(F._dp)
{}
Self_t& operator=(const Self_t& F)
{
_p = (F._p);
_Bp = (F._Bp);
_B2p = ( F._B2p);
_B3p = ( F._B3p);
_nim = (F._nim);
_dp = (F._dp);
F.assign(const_cast<Element&>(one), F.one);
F.assign(const_cast<Element&>(zero), F.zero);
F.assign(const_cast<Element&>(mOne), F.mOne);
return *this;
}
// ----- 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 40503; } // 2^15.3
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; }
// ----- 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
{
// T is supposed to be fit into an Element
Caster<Element>(r, a < 0? -a : a) %= _p;
if (a < 0) negin(r);
return redc(r, r * _B2p);
}
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 c; return r = Caster<T>(redc(c, 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::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:
Element& redc(Element&, const Element) const ;
Element redcal(const Element) const;
Element redcsal(const Element) const;
Element& redcin(Element&) const;
Element& redcs(Element&, const Element) const;
Element& redcsin(Element&) const;
// -- data representation of the domain:
Residu_t _p;
Residu_t _Bp;
Residu_t _B2p;
Residu_t _B3p;
Residu_t _nim;
double _dp;
};
}
#include "givaro/montgomery-int32.inl"
#endif
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