cgal/Modular_arithmetic/include/CGAL/extended_euclidean_algorithm.h

60 lines
1.5 KiB
C++

//Author(s) : Michael Hemmer <mhemmer@uni-mainz.de>
#ifndef CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H
#define CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H 1
#include <CGAL/basic.h>
namespace CGAL {
template< class NT >
NT extended_euclidean_algorithm(const NT& a_, const NT& b_, NT& u, NT& v){
typedef Algebraic_structure_traits<NT> AST;
typename AST::Div_mod div_mod;
typename AST::Unit_part unit_part;
typename AST::Integral_division idiv;
NT unit_part_a(unit_part(a_));
NT unit_part_b(unit_part(b_));
NT a(idiv(a_,unit_part_a));
NT b(idiv(b_,unit_part_b));
NT x(0),y(1),last_x(1),last_y(0);
NT temp, quotient;
// typename AST::Div div;
// typename AST::Mod mod;
//TODO: unroll to avoid swapping
while (b != 0){
temp = b;
div_mod(a,b,quotient,b);
a = temp;
temp = x;
x = last_x-quotient*x;
last_x = temp;
temp = y;
y = last_y-quotient*y;
last_y = temp;
}
u = last_x * unit_part_a;
v = last_y * unit_part_b;
// std::cout <<"a_: "<<a_ <<std::endl;
// std::cout <<"b_: "<<b_ <<std::endl;
// std::cout <<"gcd: "<<a <<std::endl;
// std::cout <<"u: "<<u <<std::endl;
// std::cout <<"v: "<<v <<std::endl;
// std::cout <<std::endl;
CGAL_precondition(unit_part(a) == NT(1));
CGAL_precondition(a == a_*u + b_*v);
return a;
}
} // namespace CGAL
#endif // CGAL_EXTENDED_EUCLIDEAN_ALGORITHM_H //