79 lines
2.3 KiB
C++
Executable File
79 lines
2.3 KiB
C++
Executable File
// Copyright (c) 2006-2007 Max-Planck-Institute Saarbruecken (Germany).
|
|
// All rights reserved.
|
|
//
|
|
// This file is part of CGAL (www.cgal.org); 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 3 of the License,
|
|
// or (at your option) any later version.
|
|
//
|
|
// Licensees holding a valid commercial license may use this file in
|
|
// accordance with the commercial license agreement provided with the software.
|
|
//
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
|
//
|
|
// $URL$
|
|
// $Id$
|
|
// SPDX-License-Identifier: LGPL-3.0+
|
|
//
|
|
// Author(s) : Michael Hemmer, Dominik Huelse
|
|
//
|
|
// ============================================================================
|
|
|
|
#ifndef CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H
|
|
#define CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H 1
|
|
|
|
#include <CGAL/basic.h>
|
|
#include <vector>
|
|
|
|
namespace CGAL {
|
|
|
|
// EEA computing the normalized gcd
|
|
// Modern Computer Algebra (Hardcover)
|
|
// by Joachim von zur Gathen (Author), Juergen Gerhard (Author)
|
|
// Publisher: Cambridge University Press; 2 edition (September 1, 2003)
|
|
// Language: English
|
|
// ISBN-10: 0521826462
|
|
// ISBN-13: 978-0521826464
|
|
// pp.: 55
|
|
|
|
template< class AS >
|
|
AS extended_euclidean_algorithm(const AS& f, const AS& g, AS& s_, AS& t_){
|
|
typename Algebraic_structure_traits<AS>::Integral_division idiv;
|
|
typename Algebraic_structure_traits<AS>::Div div;
|
|
typename Algebraic_structure_traits<AS>::Unit_part unit_part;
|
|
|
|
std::vector<AS> p,r,s,t,q;
|
|
p.push_back(unit_part(f));
|
|
r.push_back(idiv(f,p[0]));
|
|
s.push_back(idiv(AS(1),p[0]));
|
|
t.push_back(AS(0));
|
|
q.push_back(AS(0));
|
|
|
|
p.push_back(unit_part(g));
|
|
r.push_back(idiv(g,p[1]));
|
|
s.push_back(AS(0));
|
|
t.push_back(idiv(AS(1),p[1]));
|
|
|
|
int i = 1;
|
|
while(!is_zero(r[i])){
|
|
q.push_back(div(r[i-1],r[i]));
|
|
r.push_back(r[i-1]-q[i]*r[i]);
|
|
p.push_back(unit_part(r[i+1]));
|
|
r[i+1] = idiv(r[i+1],p[i+1]);
|
|
s.push_back(idiv(s[i-1]-q[i]*s[i],p[i+1]));
|
|
t.push_back(idiv(t[i-1]-q[i]*t[i],p[i+1]));
|
|
i++;
|
|
}
|
|
|
|
s_=s[i-1];
|
|
t_=t[i-1];
|
|
AS h = r[i-1];
|
|
CGAL_precondition( h == f*s_ + g*t_);
|
|
return h;
|
|
}
|
|
|
|
} //namespace CGAL
|
|
|
|
#endif // NiX_EXTENDED_EUCLIDEAN_ALGORITHM_H //
|