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// Copyright (c) 2006-2007 Max-Planck-Institute Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Algebraic_foundations/include/CGAL/extended_euclidean_algorithm.h $ // $Id: include/CGAL/extended_euclidean_algorithm.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Michael Hemmer, Dominik Huelse // // ============================================================================ #ifndef CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H #define CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H 1 #include #include 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::Integral_division idiv; typename Algebraic_structure_traits::Div div; typename Algebraic_structure_traits::Unit_part unit_part; std::vector 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 //