Polynomial<int> Polynomial<int>::gcd(
const Polynomial<int>& p1, const Polynomial<int>& p2)
{ CGAL_NEF_TRACEN("gcd("<<p1<<" , "<<p2<<")");
if ( p1.is_zero() ) {
if ( p2.is_zero() ) return Polynomial<int>(int(1));
else return p2.abs();
}
if ( p2.is_zero() )
return p1.abs();
Polynomial<int> f1 = p1.abs();
Polynomial<int> f2 = p2.abs();
int f1c = f1.content(), f2c = f2.content();
f1 /= f1c; f2 /= f2c;
int F = CGAL::gcd(f1c,f2c);
Polynomial<int> q,r; int M=1,D;
bool first = true;
while ( ! f2.is_zero() ) {
Polynomial<int>::pseudo_div(f1,f2,q,r,D);
if (!first) M*=D;
CGAL_NEF_TRACEV(f1);CGAL_NEF_TRACEV(f2);CGAL_NEF_TRACEV(q);CGAL_NEF_TRACEV(r);CGAL_NEF_TRACEV(M);
r /= r.content();
f1=f2; f2=r;
first=false;
}
CGAL_NEF_TRACEV(f1.content());
return Polynomial<int>(F)*f1.abs();
}
void Polynomial<int>::pseudo_div(
const Polynomial<int>& f, const Polynomial<int>& g,
Polynomial<int>& q, Polynomial<int>& r, int& D)
{
CGAL_NEF_TRACEN("pseudo_div "<<f<<" , "<< g);
int fd=f.degree(), gd=g.degree();
if ( fd<gd )
{ q = Polynomial<int>(0); r = f; D = 1;
CGAL_postcondition(Polynomial<int>(D)*f==q*g+r); return;
}
// now we know fd >= gd and f>=g
int qd=fd-gd, delta=qd+1, rd=fd;
{ q = Polynomial<int>( std::size_t(delta) ); }; // workaround for SUNPRO
int G = g[gd]; // highest order coeff of g
D = G; while (--delta) D*=G; // D = G^delta
Polynomial<int> res = Polynomial<int>(D)*f;
CGAL_NEF_TRACEN(" pseudo_div start "<<res<<" "<<qd<<" "<<q.degree());
while (qd >= 0) {
int F = res[rd]; // highest order coeff of res
int t = F/G; // ensured to be integer by multiplication of D
q.coeff(qd) = t; // store q coeff
res.minus_offsetmult(g,t,qd);
if (res.is_zero()) break;
rd = res.degree();
qd = rd - gd;
}
r = res;
CGAL_postcondition(Polynomial<int>(D)*f==q*g+r);
CGAL_NEF_TRACEN(" returning "<<q<<", "<<r<<", "<< D);
}
void Polynomial<int>::euclidean_div(
const Polynomial<int>& f, const Polynomial<int>& g,
Polynomial<int>& q, Polynomial<int>& r)
{
r = f; r.copy_on_write();
int rd=r.degree(), gd=g.degree(), qd;
if ( rd < gd ) { q = Polynomial<int>(int(0)); }
else { qd = rd-gd+1; q = Polynomial<int>(std::size_t(qd)); }
while ( rd >= gd && !(r.is_zero())) {
int S = r[rd] / g[gd];
qd = rd-gd;
q.coeff(qd) += S;
r.minus_offsetmult(g,S,qd);
rd = r.degree();
}
CGAL_postcondition( f==q*g+r );
}
