Add some useful functions for Interval_nt:

- width()
- magnitude()
- compare_relative_precision(Interval, double)
And use the last one in to_double(Lazy_exact_nt).

Number_types/include/CGAL/Interval_nt.h

@@ -280,6 +280,7 @@ Uncertain<bool>
 operator!=(const Interval_nt<Protected> &a, int b)
 { return ! (a == b); }
 
+// Non-documented
 // Returns true if the interval is a unique representable double.
 template <bool Protected>
 inline
@@ -292,6 +293,7 @@ fit_in_double (const Interval_nt<Protected> & d, double &r)
   return b;
 }
 
+// Non-documented
 template <bool Protected>
 inline
 bool
@@ -300,6 +302,34 @@ is_singleton (const Interval_nt<Protected> & d)
   return d.is_point();
 }
 
+// Non-documented
+template <bool Protected>
+inline
+double
+magnitude (const Interval_nt<Protected> & d)
+{
+  return (std::max)(std::fabs(d.inf()), std::fabs(d.sup()));
+}
+
+// Non-documented
+template <bool Protected>
+inline
+double
+width (const Interval_nt<Protected> & d)
+{
+  return d.sup() - d.inf();
+}
+
+// Non-documented
+template <bool Protected>
+inline
+Comparison_result
+compare_relative_precision(const Interval_nt<Protected> & d, double prec)
+{
+  return CGAL::compare(width(d), prec * magnitude(d));
+}
+
+
 template< bool Protected >
 class Is_valid< Interval_nt<Protected> >
   : public Unary_function< Interval_nt<Protected>, bool > {

Number_types/include/CGAL/Lazy_exact_nt.h

@@ -1039,9 +1039,8 @@ template < typename ET > class Real_embeddable_traits< Lazy_exact_nt<ET> >
                 return r;
 
             // If it's precise enough, then OK.
-            if ((app.sup() - app.inf())
-                    < Lazy_exact_nt<ET>::get_relative_precision_of_to_double()
-                    * (std::max)(std::fabs(app.inf()), std::fabs(app.sup())) )
+            if (compare_relative_precision(app,
+                 Lazy_exact_nt<ET>::get_relative_precision_of_to_double()) <= 0)
                 return CGAL_NTS to_double(app);
 
             CGAL_PROFILER(std::string("failures of : ") + std::string(CGAL_PRETTY_FUNCTION));