minimal example for SVD bug

CoreBug.cpp

#include <iostream>
#include <CGAL/leda_real.h>
#include <CGAL/CORE_Expr.h>
#include <CGAL/Lazy_exact_nt.h>


std::ostream& operator<<(std::ostream& os, std::pair<double,double> p)
{
  os << p.first << ", " << p.second;
  return os;
}


template <class FT>
void bug()
{
  FT zero(0);
  FT ipx(0.3080532378), // ipy(0.1282279698)
  iqx(0.3080629044),    // iqy(0.1282376364)
    irx(0.3080725711);  // iry(0.1282473031)

  double d1 = 0.1282376364 - 0.1282279698;// iqy - ipy;
  double d2 = 0.1282473031 - 0.1282376364;// iry - iqy;

  FT a1(d1);
  FT a2(d2);

  FT b1 = ipx - iqx;
  FT b2 = iqx - irx;
  
  FT n1 = a1 * a1 + b1 * b1;
  FT n2 = a2 * a2 + b2 * b2;

  FT D1D2 = n1 * n2;
  FT sqrtD1D2 = CGAL::sqrt(D1D2);
  FT a1a2b1b2 = a1 * a2 + b1 * b2;
  FT uz =  sqrtD1D2 -  a1a2b1b2 ;

  std::cout << "D1D2     " << CGAL::to_interval(D1D2) << std::endl;
  //std::cout << "sqrtD1D2 " <<  CGAL::to_interval(sqrtD1D2) << std::endl;  // uncommented it works
  std::cout << "a1a2b1b2 " <<  CGAL::to_interval(a1a2b1b2) << std::endl;
  std::cout << "uz       " <<  CGAL::to_interval(uz) << std::endl;

 
  CGAL_assertion(uz!=zero);
}

int main()
{
  std::cout.precision(17);
  std::cout << "\nTesting leda::real\n";
  bug<leda::real>();

  std::cout << "\nTesting CGAL::Lazy_exact_nt<CORE::Expr>\n";
  bug<CGAL::Lazy_exact_nt<CORE::Expr> >();
  
  std::cout << "\nTesting CORE::Expr\n";
  bug<CORE::Expr >();
  return 0;
}

sdg-bug.cpp

#include <iostream>

#include <CGAL/Simple_cartesian.h>
#include <CGAL/Segment_Delaunay_graph_2.h>
#include <CGAL/Segment_Delaunay_graph_filtered_traits_2.h>
#include <CGAL/CORE_Expr.h>

typedef  CGAL::Simple_cartesian<double> Rep;

typedef CGAL::Field_with_sqrt_tag MTag;
typedef CGAL::Field_with_sqrt_tag EMTag;
typedef CGAL::Simple_cartesian<CORE::Expr> ERep;
typedef CGAL::Segment_Delaunay_graph_filtered_traits_2<Rep,
							  MTag,
							  ERep,
							  EMTag>  Gt;

typedef CGAL::Segment_Delaunay_graph_2<Gt>          SDG_2;


int main()
{
  SDG_2 svd;

  Gt::Point_2 p(0.3080532378, 0.1282279698),
    q(0.3080629044, 0.1282376364),
    r(0.3080725711, 0.1282473031),
    s(0, 0);

  SDG_2::Vertex_handle vp = svd.insert(p);
  SDG_2::Vertex_handle vq = svd.insert(q);
  svd.insert(vp,vq);
  SDG_2::Vertex_handle vr = svd.insert(r);
  svd.insert(vq,vr);
  
  svd.insert(s);

  return 0;
}

For s we can take any point and it crashes.