/usr/include/givaro/modular-uint64.inl is in libgivaro-dev 4.0.2-8ubuntu1.
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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: Brice Boyer (briceboyer) <boyer.brice@gmail.com>
// A. Breust (taken from FFLAS-FFPACK)
// ==========================================================================
#ifndef __GIVARO_modular_uint64_INL
#define __GIVARO_modular_uint64_INL
#include "givaro/modular-defines.h"
namespace Givaro
{
// -------------
// ----- Modular
template<>
inline Modular<uint64_t, uint64_t>::Residu_t
Modular<uint64_t, uint64_t>::maxCardinality() { return 4294967295_ui64; } // 2^32 - 1
template<>
inline Modular<uint64_t, int64_t>::Residu_t
Modular<uint64_t, int64_t>::maxCardinality() { return 4294967295_ui64; }
#ifdef __GIVARO_HAVE_INT128
template<>
inline Modular<uint64_t, uint128_t>::Residu_t
Modular<uint64_t, uint128_t>::maxCardinality() { return 9223372036854775807_ui64; } // 2^63 - 1
template<>
inline Modular<uint64_t, int128_t>::Residu_t
Modular<uint64_t, int128_t>::maxCardinality() { return 9223372036854775807_ui64; }
#endif
// ------------------------
// ----- Classic arithmetic
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::add
(Element &x, const Element &y, const Element &z) const
{
__GIVARO_MODULAR_INTEGER_ADD(x,_p,y,z);
return x;
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::sub
(Element &x, const Element &y, const Element &z) const
{
return __GIVARO_MODULAR_INTEGER_SUB(x,_p,y,z);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::mul
(Element &x, const Element &y, const Element &z) const
{
return __GIVARO_MODULAR_INTEGER_MUL(x,_p,y,z);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::div
(Element &x, const Element &y, const Element &z) const
{
return mulin(inv(x, z), y);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::neg
(Element &x, const Element &y) const
{
return __GIVARO_MODULAR_INTEGER_NEG(x,_p,y);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::inv
(Element &x, const Element &y) const
{
// The extended Euclidean algorithm
int64_t x_int, y_int, tx, ty;
x_int = int64_t(_p);
y_int = int64_t(y);
tx = 0;
ty = 1;
while (y_int != 0) {
// always: gcd (modulus,residue) = gcd (x_int,y_int)
// sx*modulus + tx*residue = x_int
// sy*modulus + ty*residue = y_int
int64_t q = x_int / y_int; // integer quotient
int64_t temp = y_int; y_int = x_int - q * y_int;
x_int = temp;
temp = ty; ty = tx - q * ty;
tx = temp;
}
if (tx < 0) tx += _p;
// now x_int = gcd (modulus,residue)
return x = Element(tx);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::addin
(Element &x, const Element &y) const
{
__GIVARO_MODULAR_INTEGER_ADDIN(x,_p,y);
return x;
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::subin
(Element &x, const Element &y) const
{
__GIVARO_MODULAR_INTEGER_SUBIN(x,_p,y);
return x;
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::mulin
(Element &x, const Element &y) const
{
return __GIVARO_MODULAR_INTEGER_MULIN(x,_p,y);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::divin
(Element &x, const Element &y) const
{
typename Modular<uint64_t, COMP>::Element iy;
return mulin(x, inv(iy, y));
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::negin
(Element &x) const
{
return __GIVARO_MODULAR_INTEGER_NEGIN(x,_p);
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::invin
(Element &x) const
{
return inv(x, x);
}
// -- axpy: r <- a * x + y
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::axpy
(Element &r, const Element &a, const Element &x, const Element &y) const
{
__GIVARO_MODULAR_INTEGER_MULADD(r, _p, a, x, y);
return r;
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::axpyin
(Element &r, const Element &a, const Element &x) const
{
__GIVARO_MODULAR_INTEGER_MULADDIN(r, _p, a, x);
return r;
}
// -- axmy: r <- a * x - y
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::axmy
(Element& r, const Element &a, const Element &x, const Element &y) const
{
__GIVARO_MODULAR_INTEGER_MULSUB(r, _p, a, x, y);
return r;
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element &Modular<uint64_t, COMP>::axmyin
(Element& r, const Element &a, const Element &x) const
{
maxpyin(r,a,x);
return negin(r);
}
// -- maxpy: r <- y - a * x
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element& Modular<uint64_t, COMP>::maxpy
(Element& r, const Element& a, const Element& x, const Element& y) const
{
r = y;
__GIVARO_MODULAR_INTEGER_SUBMULIN(r, _p, a, x);
return r;
}
template<typename COMP>
inline typename Modular<uint64_t, COMP>::Element& Modular<uint64_t, COMP>::maxpyin
(Element& r, const Element& a, const Element& x) const
{
__GIVARO_MODULAR_INTEGER_SUBMULIN(r, _p, a, x);
return r;
}
// --------------------
// ----- Initialisation
template<typename COMP> inline typename Modular<uint64_t, COMP>::Element&
Modular<uint64_t, COMP>::init (Element& r, const Integer& a) const
{
r = static_cast<Element>(((a < 0)? -a : a) % _p);
if (a < 0) negin(r);
return r;
}
// ----------------
// ----- IO methods
template<>
inline std::ostream &Modular<uint64_t, int64_t>::write (std::ostream &os) const
{
return os << "Modular<uint64_t, uint64_t> modulo " << _p;
}
template<>
inline std::ostream &Modular<uint64_t, uint64_t>::write (std::ostream &os) const
{
return os << "Modular<uint64_t, uint64_t> modulo " << _p;
}
#ifdef __GIVARO_HAVE_INT128
template<>
inline std::ostream& Modular<uint64_t, int128_t>::write (std::ostream& s ) const
{
return s << "Modular<uint64_t, int128_t> modulo " << residu();
}
template<>
inline std::ostream& Modular<uint64_t, uint128_t>::write (std::ostream& s ) const
{
return s << "Modular<uint64_t, uint128_t> modulo " << residu();
}
#endif
template<typename COMP>
inline std::istream &Modular<uint64_t, COMP>::read (std::istream &is)
{
is >> _p;
return is;
}
template<typename COMP>
inline std::ostream &Modular<uint64_t, COMP>::write (std::ostream &os, const Element &x) const
{
return os << x;
}
template<typename COMP>
inline std::istream &Modular<uint64_t, COMP>::read (std::istream &is, Element &x) const
{
int64_t tmp;
is >> tmp;
init(x,tmp);
return is;
}
} // namespace Givaro
#endif // __GIVARO_modular_uint64_INL
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