void algebraic_number_test()
{
typedef Coefficient_ Coefficient;
typedef Rational_ Rational;
typedef CGAL::internal::Algebraic_real_d_1<Coefficient,Rational, CGAL::Handle_policy_no_union, RepClass > Algebraic_real_d_1;
typedef typename CGAL::Polynomial_type_generator<Coefficient,1>::Type Poly;
CGAL::test_real_embeddable<Algebraic_real_d_1>();
// general test of comparable functionality
// TODO generates a precondition error in Algebraic_real_rep
//NiX::test_real_comparable<Algebraic_real_d_1>();
// test of constructors
Poly P_00(Coefficient(0)); // zero polynomial
Poly P_01(Coefficient(1)); // constant polynomial
Poly P_1(Coefficient(-1),Coefficient(1)); //(x-1)
Poly P_2(Coefficient(-2),Coefficient(1)); //(x-2)
Poly P_3(Coefficient(-3),Coefficient(1)); //(x-3)
Poly P_4(Coefficient(-4),Coefficient(1)); //(x-4)
Poly P_12=P_1*P_2; //(x-1)(x-2)
Poly P_123=P_1*P_2*P_3; //(x-1)(x-2)(x-3)
Poly P_s2(Coefficient(-2),Coefficient(0),Coefficient(1)); //(x^2-2)
Poly P_s3(Coefficient(-3),Coefficient(0),Coefficient(1)); //(x^2-3)
Poly P_s5(-Coefficient(5),Coefficient(0),Coefficient(1));
Poly P_s10(-Coefficient(10),Coefficient(0),Coefficient(1));
Poly P_s30(-Coefficient(30),Coefficient(0),Coefficient(1));
Poly P_s2510= P_s2*P_s5*P_s10;
Poly P_s530= P_s5 * P_s30;
Algebraic_real_d_1 tmp;
Algebraic_real_d_1 tmp1,tmp2;
Rational m;
// general constructors;
// default
// tmp = IS_Rational_ = 0
tmp = Algebraic_real_d_1();
assert(tmp.is_rational());
assert(tmp.rational()==0);
// from int
tmp = Algebraic_real_d_1(1);
assert(tmp.is_rational());
assert(tmp.rational()==1);
tmp = Algebraic_real_d_1(5);
assert(tmp.is_rational());
assert(tmp.rational()==5);
// from Field
tmp = Algebraic_real_d_1(Rational(0));
assert(tmp.is_rational());
assert(tmp.rational()==0);
tmp = Algebraic_real_d_1(Rational(1));
assert(tmp.is_rational());
assert(tmp.rational()==1);
tmp = Algebraic_real_d_1(Rational(5)/ Rational(2));
assert(tmp.is_rational());
assert(tmp.rational()== Rational(5)/ Rational(2));
// general constructor
// tmp = 1
#if 0
tmp = Algebraic_real_d_1(P_1,-2,+2);
// TODO different behavior with leda and core
assert(!tmp.is_rational());
assert(tmp==Rational(1));
assert(tmp.is_rational());
assert(tmp.rational()==1);
#endif
// special constructors
// from int
tmp = Algebraic_real_d_1(2);
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
//from Rational
tmp = Algebraic_real_d_1(Rational(2));
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
// member functions
// tmp IS_GENERAL == 2;
tmp = Algebraic_real_d_1(P_123,Rational(3)/2,Rational(5)/2);
assert(!tmp.is_rational());
assert(tmp.polynomial()==P_123);
assert(tmp.low()==Rational(3)/2);
assert(tmp.high()==Rational(5)/2);
assert(tmp.sign_at_low()==P_123.sign_at(Rational(3)/2));
// refine
tmp = Algebraic_real_d_1(P_123,Rational(3)/2,Rational(5)/2);
tmp.refine();
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(1),Rational(2));
tmp.refine();
assert(tmp.low() >= Rational(1));
assert(tmp.high() <= Rational(3)/2);
// strong_refine
// tmp IS_GENERAL == 2;
tmp = Algebraic_real_d_1(P_123,Rational(3)/2,Rational(5)/2);
m = Rational(2);
tmp.strong_refine(m);
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(1),Rational(2));
m = Rational(3)/2;
tmp.strong_refine(m);
assert(tmp.low()!=m);
assert(tmp.high()!=m);
// refine_to(a,b)
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_4,Rational(0),Rational(3));
assert(!tmp.is_rational());
tmp.refine_to(Rational(1), Rational(2));
assert(tmp.low() >= Rational(1));
assert(tmp.high() <= Rational(2));
// tmp IS_REAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2,Rational(0),Rational(3));
assert(!tmp.is_rational());
tmp.refine_to(Rational(1), Rational(2));
assert(tmp.low() >= Rational(1));
assert(tmp.high() <= Rational(2));
// compare(rat)
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(1),Rational(2));
m = Rational(1);
assert(tmp.compare(m)==1);
m = Rational(2);
assert(tmp.compare(m)==-1);
// tmp IS_GENERAL = 3
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(2),Rational(4));
m = Rational(3);
assert(tmp.compare(m)==0);
assert(tmp.is_rational());
assert(tmp.rational()==Rational(3));
assert(CGAL::degree(tmp.polynomial()) == 1);
assert(tmp.polynomial().evaluate(Coefficient(3)) == Coefficient(0));
// compare_distinct()
tmp1 = Algebraic_real_d_1(P_s530, Rational(2), Rational(3)); // sqrt(5) = 2.236...
tmp2 = Algebraic_real_d_1(P_s530, Rational(5), Rational(6)); // sqrt(30) = 5.477...
assert(tmp1.compare_distinct(tmp2) == CGAL::SMALLER);
assert(tmp2.compare_distinct(tmp1) == CGAL::LARGER);
//member functions
// is_root_of
tmp1 = Algebraic_real_d_1(P_s2510,Rational(1)/2,Rational(3)/2);
assert(tmp1.is_root_of(P_s530*P_s2));
tmp1 = Algebraic_real_d_1(P_s2510,Rational(1)/2,Rational(3)/2);
assert(!tmp1.is_root_of(P_s530));
//rational_between
{
Rational r;
tmp1 = Algebraic_real_d_1(P_s2,Rational(1),Rational(2)); //sqrt2
tmp2 = Algebraic_real_d_1(P_s3,Rational(1),Rational(3)); //sqrt3
r = tmp1.rational_between(tmp2);
assert(tmp1.compare(r)==CGAL::SMALLER);
assert(tmp2.compare(r)==CGAL::LARGER);
r = tmp2.rational_between(tmp1);
assert(tmp1.compare(r)==CGAL::SMALLER);
assert(tmp2.compare(r)==CGAL::LARGER);
}
// to_double()
tmp = Algebraic_real_d_1(P_1*P_3*P_4, Rational(0), Rational(2));
assert(fabs(tmp.to_double() - 1.0) < 1e-10);
tmp = Algebraic_real_d_1(P_1*P_3, Rational(0), Rational(2));
assert(fabs(tmp.to_double() - 1.0) < 1e-10);
tmp = Algebraic_real_d_1(P_1, Rational(0), Rational(2));
assert(fabs(tmp.to_double() - 1.0) < 1e-10);
//IO tested in _test_algebraic_kernel_1.h
// test for Handle with union
{
typedef
CGAL::internal::Algebraic_real_d_1
<Coefficient,Rational,::CGAL::Handle_policy_union> Int;
Int i(5);
Int j(5);
Int k(6);
assert( ! i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
assert( i == j);
assert( ! (i == k));
assert( i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
// code coverage
assert( i == j);
}
// test for Handle without union
{
typedef
CGAL::internal::Algebraic_real_d_1
<Coefficient,Rational,::CGAL::Handle_policy_no_union> Int;
Int i(5);
Int j(5);
Int k(6);
assert( ! i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
assert( i == j);
assert( ! (i == k));
assert( ! i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
}
// to_interval
// {
// Algebraic_real_d_1 TMP;
// assert(CGAL::in(25.0,CGAL::to_interval(Algebraic_real_d_1(25))));
// assert(CGAL::in(sqrt(2),CGAL::to_interval(Algebraic_real_d_1(P_s2,1,2))));
// assert(CGAL::in(sqrt(2),CGAL::to_interval(Algebraic_real_d_1(P_s2510,1,2))));
// assert(CGAL::in(-sqrt(2),CGAL::to_interval(Algebraic_real_d_1(P_s2510,-2,-1))));
// assert(CGAL::in(sqrt(5),CGAL::to_interval(Algebraic_real_d_1(P_s2510,2,3))));
// assert(CGAL::in(-sqrt(5),CGAL::to_interval(Algebraic_real_d_1(P_s2510,-3,-2))));
// assert(CGAL::in(sqrt(10),CGAL::to_interval(Algebraic_real_d_1(P_s2510,3,4))));
// assert(CGAL::in(-sqrt(10),CGAL::to_interval(Algebraic_real_d_1(P_s2510,-4,-3))));
// }
//simplify
{
// just a synatx check
Algebraic_real_d_1(P_s2510,1,2).simplify();
}
}
template <class Type> void Bench_PackB_IM<Type>::verif()
{
INT def = (INT)(NRrandom3() * 1000);
verif( rectangle(Pt2di(1,0),Pt2di(2,1)));
for (INT k=0; k<10 ; k++)
{
verif( rectangle(Pt2di(k,0),Pt2di(k+1,10) ),def);
verif( rectangle(Pt2di(k,0),Pt2di(k+10,10) ),def);
verif( rectangle(Pt2di(k,0),Pt2di(k+100,10)),def);
verif( rectangle(Pt2di(k,0),Pt2di(k+200,10)),def);
}
verif( im1.all_pts());
verif( rectangle(Pt2di(-10,-20),sz+Pt2di(30,40)),def);
verif( disc(sz/2.0,euclid(sz)/1.8),def);
{
for (INT k=0 ; k<10 ; k++)
{
Pt2dr c = sz/2.0 + Pt2dr(NRrandom3(),NRrandom3())*20;
REAL ray = 1+NRrandom3()*100;
verif(disc(c,ray),def);
}
}
ELISE_COPY(disc(CentreRand(),RayonRand()),1,im1.out()| pck.out());
verif(im1.all_pts());
ELISE_COPY(disc(CentreRand(),RayonRand()),frandr()*8,im1.out()| pck.out());
verif(im1.all_pts());
INT NbPts = (INT)(3 + NRrandom3()*10);
ElList<Pt2di> Lpt;
{
for (INT k=0; k<NbPts ; k++)
Lpt = Lpt+Pt2di(CentreRand());
}
ELISE_COPY(polygone(Lpt),NRrandom3()<0.1,im1.out()| pck.out());
verif(im1.all_pts());
ModifCSte(rectangle(Pt2di(5,0),Pt2di(10,10)),2);
verif(im1.all_pts());
ModifLut(rectangle(Pt2di(0,5),Pt2di(12,12)),FX&3);
verif(im1.all_pts());
//ModifCSte(disc(Pt2di(50,50),20),3);
ModifCSte(disc(Pt2dr(50,50),20),3); // __NEW
verif(im1.all_pts());
for (INT NbC =0 ; NbC < 20 ; NbC++)
{
ElList<Pt2di> lPt;
for (INT iPt =0 ; iPt < 20; iPt ++)
{
lPt = lPt + Pt2di(CentreRand());
}
ModifCSte(polygone(lPt),INT(NRrandom3() * 3));
verif(im1.all_pts());
}
Pt2di P_00 (0,0);
Pt2di P_10 (sz.x,0);
Pt2di P_01 (0,sz.y);
ElList<Pt2di> lP1;
lP1 = lP1 + P_00; lP1 = lP1 + P_01; lP1 = lP1 + P_10;
ModifCSte(polygone(lP1),7);
verif(im1.all_pts());
TiffVerif();
}
