/usr/include/linbox/field/modular.h is in liblinbox-dev 1.3.2-1.1.
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* Copyright (C) 1999-2001 William J Turner,
* 2001 Bradford Hovinen
*
* Written by William J Turner <wjturner@math.ncsu.edu>,
* Bradford Hovinen <hovinen@cis.udel.edu>
*
* ------------------------------------
* 2002-04-10 Bradford Hovinen <hovinen@cis.udel.edu>
*
* LargeModular is now replace by a class Modular parameterized on the element
* type. So, the old LargeModular is equivalent to Modular<integer>. All other
* interface details are exactly the same.
*
* Renamed from large-modular.h to modular.h
* ------------------------------------
*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
/*! @file field/modular.h
* @ingroup field
* @brief A Modular field is a representations of <code>Z/mZ</code>.
* This file groups many implementations/specialisations of modular fields.
* - Modular arithmetic is provided in the <code>ModularXXX<T></code> classes.
* - Specialisations for \ref FieldAXPY, \ref MVProductDomain, \ref DotProductDomain.
* - Random Iterators
* .
*
* @bug move Element& init(const Element&) to FFPACK. use using more..
*/
#ifndef __LINBOX_field_modular_H
#define __LINBOX_field_modular_H
#include <iostream>
#include <climits>
#include <cmath>
#include "linbox/integer.h"
#include "linbox/vector/vector-domain.h"
#include "linbox/matrix/matrix-domain.h"
#include "linbox/field/field-interface.h"
#include "linbox/util/field-axpy.h"
#include "linbox/vector/vector-traits.h"
#include "linbox/linbox-config.h"
#include "linbox/field/field-traits.h"
// Namespace in which all LinBox code resides
namespace LinBox
{
template <class Element>
class Modular;
template <class Ring>
struct ClassifyRing;
template <class Element>
struct ClassifyRing<Modular<Element> >
{
typedef RingCategories::ModularTag categoryTag;
};
template <class Element>
struct ClassifyRing<Modular<Element> const>
{
typedef RingCategories::ModularTag categoryTag;
};
/** * <!-- @name ModularBase-->
* \brief Base for prime fields where the elements are represented by various primitive types (and their operations).
* \ingroup field
* \defgroup Fields Fields <!--for old \ref Fields...-->
*
*
* Normally use it's children. This class is of interest for the
* developer of a new field representation.
*
*
* This parameterized field can be used to construct any prime field.
* Typical use would be Modular<integer> for integers modulo a large
* prime, Modular<long> Modular<long long> for integers modulo a wordsize
* prime, etc. for integers modulo a half-wordsize prime.
*/
template <class _Element>
class ModularBase {
public:
/*- Element type
*/
typedef _Element Element;
/*- Random iterator generator type.
* It must meet the common object interface of random element generators
* as given in the the archetype RandIterArchetype.
*/
class RandIter;
/*- @name Object Management
*/
//@{
/*- Default constructor.
*/
ModularBase (void) {}
/*- Constructor from an element type.
* Sets the modulus of the field throug the static member of the
* element type.
* @param modulus constant reference to integer prime modulus
*/
ModularBase (unsigned long modulus, int e = 1) :
_modulus ((Element)modulus)
{}
/*- Constructor from an integer.
* Sets the modulus of the field throug the static member of the
* element type.
* @param modulus constant reference to integer prime modulus
*/
ModularBase (const integer &modulus) :
_modulus ((Element) modulus)
{}
/*- Copy constructor.
* Constructs Modular object by copying the field.
* This is required to allow field objects to be passed by value
* into functions.
* @param F Modular object.
*/
ModularBase (const ModularBase<Element> &F) :
_modulus (F._modulus)
{}
/*- Conversion of field base element to a template class T.
* This function assumes the output field base element x has already been
* constructed, but that it is not already initialized.
* @return reference to template class T.
* @param x template class T to contain output (reference returned).
* @param y constant field base element.
*/
integer &convert (integer &x, const Element &y) const
{
return x = y;
}
double &convert (double& x, const Element &y) const
{
return x= (double) y;
}
float &convert (float& x, const Element &y) const
{
return x= (float) y;
}
/*- Assignment of one field base element to another.
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &assign (Element &x, const Element &y) const
{
return x = y;
}
/*- Cardinality.
* Return integer representing cardinality of the domain.
* Returns a non-negative integer for all domains with finite
* cardinality, and returns -1 to signify a domain of infinite
* cardinality.
* @return integer representing cardinality of the domain
*/
integer &cardinality (integer &c) const
{
return c = _modulus;
}
integer cardinality () const
{
return _modulus;
}
/*- Characteristic.
* Return integer representing characteristic of the domain.
* Returns a positive integer to all domains with finite characteristic,
* and returns 0 to signify a domain of infinite characteristic.
* @return integer representing characteristic of the domain.
*/
integer &characteristic (integer &c) const
{
return c = _modulus;
}
unsigned long &characteristic (unsigned long &c) const
{
return c = _modulus;
}
integer characteristic () const
{
return _modulus;
}
//@} Object Management
/*- @name Arithmetic Operations
* x <- y op z; x <- op y
* These operations require all elements, including x, to be initialized
* before the operation is called. Uninitialized field base elements will
* give undefined results.
*/
//@{
/*- Equality of two elements.
* This function assumes both field base elements have already been
* constructed and initialized.
* @return boolean true if equal, false if not.
* @param x field base element
* @param y field base element
*/
bool areEqual (const Element &x, const Element &y) const
{
return x == y;
}
/*- Zero equality.
* Test if field base element is equal to zero.
* This function assumes the field base element has already been
* constructed and initialized.
* @return boolean true if equals zero, false if not.
* @param x field base element.
*/
bool isZero (const Element &x) const
{
return x == 0;
}
/*- One equality.
* Test if field base element is equal to one.
* This function assumes the field base element has already been
* constructed and initialized.
* @return boolean true if equals one, false if not.
* @param x field base element.
*/
bool isOne (const Element &x) const
{
return x == 1;
}
//@} Arithmetic Operations
/*- @name Input/Output Operations */
//@{
/*- Print field.
* @return output stream to which field is written.
* @param os output stream to which field is written.
*/
std::ostream &write (std::ostream &os) const
{
return os << "Modular field, mod " << _modulus;
}
/*- Read field.
* @return input stream from which field is read.
* @param is input stream from which field is read.
*/
std::istream &read (std::istream &is) {
return is >> _modulus;
}
/*- Print field base element.
* This function assumes the field base element has already been
* constructed and initialized.
* @return output stream to which field base element is written.
* @param os output stream to which field base element is written.
* @param x field base element.
*/
std::ostream &write (std::ostream &os, const Element &x) const
{
return os << (int) x;
}
/*- Read field base element.
* This function assumes the field base element has already been
* constructed and initialized.
* @return input stream from which field base element is read.
* @param is input stream from which field base element is read.
* @param x field base element.
*/
std::istream &read (std::istream &is, Element &x) const
{
integer tmp;
is >> tmp;
x = abs (tmp) % integer (_modulus);
if (tmp < 0) x = _modulus - x;
return is;
}
//@}
protected:
/// Private (non-static) element for modulus
Element _modulus;
}; // class ModularBase
/* .. such comments as here should be on specialization...
* @param element Element type, e.g. long or integer
* @param Intermediate Type to use for intermediate computations. This
* should be a data type that can support integers
* twice the length of the maximal modulus used.
*
* The primality of the modulus will not be checked, so it is the
* programmer's responsibility to supply a prime modulus. This class
* implements a field of unparameterized integers modulo a prime integer.
* Field has (non-static) member to contain modulus of field.
*/
/** @brief Prime fields of positive characteristic implemented directly in LinBox.
*
* This parameterized field can be used to construct prime fields.
* Typical use would be Modular<integer> for integers modulo a large
* prime, Modular<uint32_t>, Modular<int32_t>, or Modular<double> for
* integers modulo a wordsize prime. Each of those has specialized
* performance features suitable to certain applications.
*/
template <class _Element>
class Modular : public ModularBase<_Element> {
public:
typedef _Element Element;
typedef Modular<_Element> Self_t;
typedef ModularBase<_Element> Father_t;
typedef typename ModularBase<_Element>::RandIter RandIter;
const Element zero,one, mOne;
/*- @name Object Management
* @brief see \ref FieldArchetype for member specs.
*/
//@{
//private:
/*- Default constructor.
*/
Modular () :
zero(0),one(1),mOne(0)
{}
/*- Constructor from an element type
* Sets the modulus of the field throug the static member of the
* element type.
* @param modulus constant reference to integer prime modulus
*/
Modular (unsigned long modulus, unsigned long = 1) :
ModularBase<_Element> (modulus),zero(0),one(1),mOne(modulus-1)
{}
/*- Constructor from an integer
* Sets the modulus of the field throug the static member of the
* element type.
* @param modulus constant reference to integer prime modulus
*/
Modular (const integer &modulus) :
ModularBase<_Element> (modulus),zero(0),one(1),mOne(modulus-1)
{}
/* Assignment operator
* Required by the archetype
*
* @param F constant reference to Modular object
* @return reference to Modular object for self
*/
const Modular &operator=(const Modular &F)
{
ModularBase<Element>::_modulus = F._modulus;
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;
}
public:
static inline Element getMaxModulus()
{
return Element((1ULL<<(sizeof(Element)*8-1))-1);
}
/*- Initialization of field base element from an integer.
* Behaves like C++ allocator construct.
* This function assumes the output field base element x has already been
* constructed, but that it is not already initialized.
* This is not a specialization of the template function because
* such a specialization is not allowed inside the class declaration.
* @return reference to field base element.
* @param x field base element to contain output (reference returned).
* @param y integer.
*/
Element &init (Element &x, const integer &y ) const
{
x = y % ModularBase<Element>::_modulus;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
Element &init (Element &x, const size_t &y ) const
{
x = (Element) y % ModularBase<Element>::_modulus;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
Element &init (Element &x, const int y ) const
{
x = y % ModularBase<Element>::_modulus;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
Element &init (Element &x, const long int y) const
{
x = y % ModularBase<Element>::_modulus;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
/*- Initialization of field base element from a double.
* Behaves like C++ allocator construct.
* This function assumes the output field base element x has already been
* constructed, but that it is not already initialized.
* This is not a specialization of the template function because
* such a specialization is not allowed inside the class declaration.
* @return reference to field base element.
* @param x field base element to contain output (reference returned).
* @param y integer.
*/
Element &init (Element &x, const double &y) const
{
double z = fmod(y, (double)ModularBase<Element>::_modulus);
if (z < 0) z += (double) ModularBase<Element>::_modulus;
return x = (Element) (z+.5);
}
Element &init (Element &x, const float &y) const
{
float z = fmod(y, (float)ModularBase<Element>::_modulus);
if (z < 0) z += (float) ModularBase<Element>::_modulus;
return x = (Element) (z+.5);
}
Element &init(Element &x) const
{
return x = 0 ;
}
//@}
/*- @name Arithmetic Operations
* @brief see \ref FieldArchetype for member specs.
* x <- y op z; x <- op y
* These operations require all elements, including x, to be initialized
* before the operation is called. Uninitialized field base elements will
* give undefined results.
*/
//@{
/*- Addition.
* x = y + z
* This function assumes all the field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
* @param z field base element.
*/
Element &add (Element &x, const Element &y, const Element &z) const
{
x = y + z;
if (x >= ModularBase<Element>::_modulus) x -= ModularBase<Element>::_modulus;
return x;
}
/* Subtraction.
* x = y - z
* This function assumes all the field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
* @param z field base element.
*/
Element &sub (Element &x, const Element &y, const Element &z) const
{
x = y - z;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
/* Multiplication.
* x = y * z
* This function assumes all the field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
* @param z field base element.
*/
Element &mul (Element &x, const Element &y, const Element &z) const
{
return x = (y * z) % ModularBase<Element>::_modulus;
}
/* Division.
* x = y / z
* This function assumes all the field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
* @param z field base element.
*/
Element &div (Element &x, const Element &y, const Element &z) const
{
Element temp;
inv (temp, z);
return mul (x, y, temp);
}
/* Additive Inverse (Negation).
* x = - y
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &neg (Element &x, const Element &y) const
{
if (y == 0)
return x = y;
else
return x = ModularBase<Element>::_modulus - y;
}
/* Multiplicative Inverse.
* x = 1 / y
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &inv (Element &x, const Element &y) const
{
// The extended Euclidean algoritm
Element x_int, y_int, q, tx, ty, temp;
x_int = ModularBase<Element>::_modulus;
y_int = 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
q = x_int / y_int; // integer quotient
temp = y_int; y_int = x_int - q*y_int; x_int = temp;
temp = ty; ty = tx - q*ty; tx = temp;
}
// now x_int = gcd (modulus,residue)
x = tx;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
/* Natural AXPY.
* r = a * x + y
* This function assumes all field elements have already been
* constructed and initialized.
* @return reference to r.
* @param r field element (reference returned).
* @param a field element.
* @param x field element.
* @param y field element.
*/
Element &axpy (Element &r,
const Element &a,
const Element &x,
const Element &y) const
{
r = (a * x + y) % ModularBase<Element>::_modulus;
if (r < 0) r += ModularBase<Element>::_modulus;
return r;
}
//@} Arithmetic Operations
/*- @name Inplace Arithmetic Operations
* @brief see \ref FieldArchetype for member specs.
* x <- x op y; x <- op x
*/
//@{
/*- Inplace Addition.
* x += y
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &addin (Element &x, const Element &y) const
{
x += y;
if (x >= ModularBase<Element>::_modulus) x -= ModularBase<Element>::_modulus;
return x;
}
/* Inplace Subtraction.
* x -= y
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &subin (Element &x, const Element &y) const
{
x -= y;
if (x < 0) x += ModularBase<Element>::_modulus;
return x;
}
/* Inplace Multiplication.
* x *= y
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &mulin (Element &x, const Element &y) const
{
x *= y;
x %= ModularBase<Element>::_modulus;
return x;
}
/* Inplace Division.
* x /= y
* This function assumes both field base elements have already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
* @param y field base element.
*/
Element &divin (Element &x, const Element &y) const
{
Element temp;
inv (temp, y);
return mulin (x, temp);
}
/* Inplace Additive Inverse (Inplace Negation).
* x = - x
* This function assumes the field base element has already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
*/
Element &negin (Element &x) const
{
if (x == 0)
return x;
else
return x = ModularBase<Element>::_modulus - x;
}
/* Inplace Multiplicative Inverse.
* x = 1 / x
* This function assumes the field base elementhas already been
* constructed and initialized.
* @return reference to x.
* @param x field base element (reference returned).
*/
Element &invin (Element &x) const
{
return inv (x, x);
}
/* Inplace AXPY.
* r += a * x
* This function assumes all field elements have already been
* constructed and initialized.
* Purely virtual
* @return reference to r.
* @param r field element (reference returned).
* @param a field element.
* @param x field element.
*/
Element &axpyin (Element &r, const Element &a, const Element &x) const
{
r = (r + a * x) % ModularBase<Element>::_modulus;
if (r < 0) r += ModularBase<Element>::_modulus;
return r;
}
//@} Inplace Arithmetic Operations
private:
friend class FieldAXPY<Modular<Element> >;
}; // class Modular
/*! Specialization of FieldAXPY for parameterized modular field */
template <class _Element>
class FieldAXPY<Modular<_Element> > {
public:
typedef _Element Element;
typedef Modular<_Element> Field;
FieldAXPY (const Field &F) :
_field (F)
{ _y = 0; }
FieldAXPY (const FieldAXPY<Modular<Element> > &faxpy) :
_field (faxpy._field), _y (faxpy._y)
{}
FieldAXPY<Modular <Element> > &operator = (const FieldAXPY &faxpy)
{
_field = faxpy._field;
_y = faxpy._y;
return *this;
}
inline Element& mulacc (const Element &a, const Element &x)
{
return accumulate(a * x);
}
inline Element& accumulate (const Element &t)
{
return _y+=t;
}
inline Element &get (Element &y) { _y %= _field._modulus; y = _y; return y;
}
inline FieldAXPY &assign (const Element y)
{
_y = y;
return *this;
}
inline void reset() {
_field.init(_y, 0);
}
private:
Field _field;
Element _y;
};
template <>
inline std::ostream& ModularBase<Integer>::write (std::ostream &os) const
{
return os << "GMP integers mod " << _modulus;
}
template <>
inline integer& Modular<integer>::init (integer& x, const double& y) const
{
integer tmp = (integer)y % _modulus;
if (tmp<0) tmp += _modulus;
return x = tmp;
}
} // namespace LinBox
#include "linbox/field/Modular/modular-unsigned.h"
#include "linbox/randiter/modular.h"
#include "linbox/field/Modular/modular-int32.h"
#ifdef __LINBOX_HAVE_INT64
#include "linbox/field/Modular/modular-int64.h"
#endif
#include "linbox/field/Modular/modular-short.h"
#include "linbox/field/Modular/modular-byte.h"
#include "linbox/field/Modular/modular-double.h"
#include "linbox/field/Modular/modular-float.h"
#endif // __LINBOX_field_modular_H
// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,:0,t0,+0,=s
// Local Variables:
// mode: C++
// tab-width: 8
// indent-tabs-mode: nil
// c-basic-offset: 8
// End:
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