From a0f9754bbe0abd24d01e9a5cbe8bf3f20e7d121e Mon Sep 17 00:00:00 2001
From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
Date: Wed, 22 Aug 2007 15:41:11 +0000
Subject: [PATCH] Add radius(Interval_nt). Replace compare_relative_precision()
 by has_smaller_relative_precision() fixing the case of [-Inf,+Inf].

---
 Number_types/include/CGAL/Interval_nt.h   | 19 +++++++++++++++----
 Number_types/include/CGAL/Lazy_exact_nt.h |  4 ++--
 2 files changed, 17 insertions(+), 6 deletions(-)

diff --git a/Number_types/include/CGAL/Interval_nt.h b/Number_types/include/CGAL/Interval_nt.h
index fc60cb4ed20..5a92a49cf13 100644
--- a/Number_types/include/CGAL/Interval_nt.h
+++ b/Number_types/include/CGAL/Interval_nt.h
@@ -433,10 +433,21 @@ width (const Interval_nt<Protected> & d)
 // Non-documented
 template <bool Protected>
 inline
-Comparison_result
-compare_relative_precision(const Interval_nt<Protected> & d, double prec)
+double
+radius (const Interval_nt<Protected> & d)
 {
-  return CGAL::compare(width(d), prec * magnitude(d));
+  return width(d)/2; // This could be improved to avoid overflow.
+}
+
+// Non-documented
+// This is the relative precision of to_double() (the center of the interval),
+// hence we use radius() instead of width().
+template <bool Protected>
+inline
+bool
+has_smaller_relative_precision(const Interval_nt<Protected> & d, double prec)
+{
+  return magnitude(d) == 0 || radius(d) < prec * magnitude(d);
 }
 
 // Non-documented
@@ -446,7 +457,7 @@ relative_precision(const Interval_nt<Protected> & d)
 {
   if (magnitude(d) == 0.0)
     return 0.0;
-  return width(d) / magnitude(d);
+  return radius(d) / magnitude(d);
 }
 
 
diff --git a/Number_types/include/CGAL/Lazy_exact_nt.h b/Number_types/include/CGAL/Lazy_exact_nt.h
index d59eae0264e..bd244322e45 100644
--- a/Number_types/include/CGAL/Lazy_exact_nt.h
+++ b/Number_types/include/CGAL/Lazy_exact_nt.h
@@ -1078,8 +1078,8 @@ template < typename ET > class Real_embeddable_traits< Lazy_exact_nt<ET> >
                 return r;
 
             // If it's precise enough, then OK.
-            if (compare_relative_precision(app,
-                 Lazy_exact_nt<ET>::get_relative_precision_of_to_double()) <= 0)
+            if (has_smaller_relative_precision(app,
+                 Lazy_exact_nt<ET>::get_relative_precision_of_to_double()))
                 return CGAL_NTS to_double(app);
 
             CGAL_PROFILER(std::string("failures of : ") + std::string(CGAL_PRETTY_FUNCTION));