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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 (adapted)
// ==========================================================================
#ifndef __GIVARO_montgomery_ruint_INL
#define __GIVARO_montgomery_ruint_INL
#include "modular-defines.h"
namespace Givaro
{
// ------------------------
// ----- Internal reduction
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element&
Montgomery<RecInt::ruint<K>>::mg_reduc(Element& a, const Element& b) const
{
bool r;
Element b0;
RecInt::mul(b0, b, _p1); // m = b * p1 mod r
RecInt::laddmul(r, a, b0, b0, _p, b); // a|b0 = b * (p1 * p + 1)
if (r || a >= _p) RecInt::sub(a, _p);
return a;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element&
Montgomery<RecInt::ruint<K>>::mg_reduc(Element& a, const LargeElement& b) const
{
bool r;
Element b0;
RecInt::mul(b0, b.Low, _p1); // m = b * p1 mod r
RecInt::laddmul(r, a, b0, b0, _p, b); // a|b0 = b * (p1 * p + 1)
if (r || a >= _p) RecInt::sub(a, _p);
return a;
}
template <size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element&
Montgomery<RecInt::ruint<K>>::to_mg(Element& a, const Element& b) const
{
mul(a, b, _r2);
return a;
}
template <size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element&
Montgomery<RecInt::ruint<K>>::to_mg(Element& a) const
{
return to_mg(a, a);
}
// ------------------------
// ----- Classic arithmetic
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::mul
(Element& r, const Element& a, const Element& b) const
{
LargeElement res;
RecInt::lmul(res, a, b);
mg_reduc(r, res);
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::sub
(Element& r, const Element& a, const Element& b) const
{
if (a < b) { // b > 0 and (a - b) < p
RecInt::sub(r, _p, b);
RecInt::add(r, a);
} else {
RecInt::sub(r, a, b);
}
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::add
(Element& r, const Element& a, const Element& b) const
{
bool ret;
RecInt::add(ret, r, a, b);
if (ret || r >= _p) RecInt::sub(r, _p);
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::neg
(Element& r, const Element& a) const
{
__GIVARO_MODULAR_RECINT_NEG(r,_p,a);
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::inv
(Element& r, const Element& a) const
{
RecInt::inv_mod(r, a, _p); // r = (aR)^-1 mod p
return mulin(r, _r3); // r = a^-1 * R mod p
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::div
(Element& r, const Element& a, const Element& b) const
{
return mulin(inv(r, b), a);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::mulin
(Element& r, const Element& a) const
{
LargeElement res;
RecInt::lmul(res, r, a);
return mg_reduc(r, res);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::divin
(Element& r, const Element& a) const
{
Element ia;
return mulin(r, inv(ia, a));
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::addin
(Element& r, const Element& a) const
{
bool ret;
RecInt::add(ret, r, a);
if (ret || r >= _p) RecInt::sub(r, _p);
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::subin
(Element& r, const Element& a) const
{
if (r < a) {
RecInt::add(r, _p - a);
} else {
RecInt::sub(r, a);
}
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::negin
(Element& r) const
{
__GIVARO_MODULAR_RECINT_NEGIN(r,_p);
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::invin
(Element& r) const
{
return inv(r, r);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::axpy
(Element& r, const Element& a, const Element& b, const Element& c) const
{
mul(r, a, b);
return addin(r, c);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::axpyin
(Element& r, const Element& a, const Element& b) const
{
Element res;
mul(res, a, b);
return addin(r, res);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::maxpy
(Element& r, const Element& a, const Element& b, const Element& c) const
{
mul(r, a, b);
return sub(r, c, r);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::maxpyin
(Element& r, const Element& a, const Element& b) const
{
Element res;
mul(res, a, b);
return subin(r, res);
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::axmy
(Element& r, const Element& a, const Element& b, const Element& c) const
{
mul(r, a, b);
subin(r, c);
return r;
}
template<size_t K>
inline typename Montgomery<RecInt::ruint<K>>::Element& Montgomery<RecInt::ruint<K>>::axmyin
(Element& r, const Element& a, const Element& b) const
{
Element res;
mul(res, a, b);
return sub(r, res, r);
}
//----- IO
template<size_t K>
inline std::ostream& Montgomery<RecInt::ruint<K>>::write (std::ostream& s) const
{
return s << "Montgomery<RecInt::ruint<" << K << ">> modulo " << residu();
}
template<size_t K>
inline std::istream& Montgomery<RecInt::ruint<K>>::read (std::istream& s, Element& a) const
{
Integer tmp;
s >> tmp;
init(a, tmp);
return s;
}
template<size_t K>
inline std::ostream& Montgomery<RecInt::ruint<K>>::write (std::ostream& s, const Element& a) const
{
Element ar;
return s << mg_reduc(ar, a);
}
}
#endif
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