diff --git a/Number_types/include/CGAL/NT_converter.h b/Number_types/include/CGAL/NT_converter.h
index 1d7c4a8d639..ac225f1e0cb 100644
--- a/Number_types/include/CGAL/NT_converter.h
+++ b/Number_types/include/CGAL/NT_converter.h
@@ -61,6 +61,17 @@ struct NT_converter < NT1, double >
     }
 };
 
+template < class NT1 >
+struct NT_converter < NT1, float >
+  : public CGAL::cpp98::unary_function< NT1, float >
+{
+    float
+    operator()(const NT1 &a) const
+    {
+        return static_cast<float>(to_double(a));
+    }
+};
+
 template <>
 struct NT_converter < double, double >
   : public CGAL::cpp98::unary_function< double, double >
@@ -72,6 +83,17 @@ struct NT_converter < double, double >
     }
 };
 
+template <>
+struct NT_converter < float, float >
+  : public CGAL::cpp98::unary_function< float, float >
+{
+    const float &
+    operator()(const float &a) const
+    {
+        return a;
+    }
+};
+
 template < class NT1, bool b >
 struct NT_converter < NT1, Interval_nt<b> >
   : public CGAL::cpp98::unary_function< NT1, Interval_nt<b> >
diff --git a/Point_set_processing_3/include/CGAL/compute_average_spacing.h b/Point_set_processing_3/include/CGAL/compute_average_spacing.h
index bb66e4b5ef9..fe6840810be 100644
--- a/Point_set_processing_3/include/CGAL/compute_average_spacing.h
+++ b/Point_set_processing_3/include/CGAL/compute_average_spacing.h
@@ -81,7 +81,7 @@ compute_average_spacing(const typename NeighborQuery::Kernel::Point_3& query, //
      boost::make_function_output_iterator
      ([&](const Point& p)
       {
-        sum_distances += std::sqrt(CGAL::squared_distance (query,p));
+        sum_distances += CGAL::approximate_sqrt(CGAL::squared_distance (query,p));
         ++ i;
       }));
 
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_cell_criteria_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_cell_criteria_3.h
index 74d507927ea..4c78d772ce5 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_cell_criteria_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_cell_criteria_3.h
@@ -27,15 +27,16 @@ namespace Poisson {
 
 template <class Tr>
 class Constant_sizing_field {
-  double sq_radius_bound;
+  typedef typename Tr::FT FT;
+  FT sq_radius_bound;
 public:
-  double cell_radius_bound() const { return CGAL::sqrt(sq_radius_bound); }
+  FT cell_radius_bound() const { return CGAL::approximate_sqrt(sq_radius_bound); }
 
-  Constant_sizing_field(double sq_radius_bound = 0.)
+  Constant_sizing_field(FT sq_radius_bound = 0.)
     : sq_radius_bound(sq_radius_bound) {}
 
   template <typename Point>
-  double operator()(const Point&) const { return sq_radius_bound; }
+  FT operator()(const Point&) const { return sq_radius_bound; }
 }; // end class Constant_sizing_field
 
 } // end namespace Poisson
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
index 80e3a9d10ff..7fb5c3e68f3 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
@@ -110,18 +110,19 @@ struct Poisson_visitor {
 // The wrapper stores only pointers to the two functors.
 template <typename F1, typename F2>
 struct Special_wrapper_of_two_functions_keep_pointers {
+  typedef typename F2::FT FT;
   F1 *f1;
   F2 *f2;
   Special_wrapper_of_two_functions_keep_pointers(F1* f1, F2* f2)
     : f1(f1), f2(f2) {}
 
   template <typename X>
-  double operator()(const X& x) const {
+  FT operator()(const X& x) const {
     return (std::max)((*f1)(x), CGAL::square((*f2)(x)));
   }
 
   template <typename X>
-  double operator()(const X& x) {
+  FT operator()(const X& x) {
     return (std::max)((*f1)(x), CGAL::square((*f2)(x)));
   }
 }; // end struct Special_wrapper_of_two_functions_keep_pointers<F1, F2>
@@ -211,7 +212,7 @@ private:
   {
   private:
     std::atomic<Cache_state> m_state;
-    std::array<double, 9> m_bary;
+    std::array<FT, 9> m_bary;
   public:
     Cached_bary_coord() : m_state (UNINITIALIZED) { }
 
@@ -242,8 +243,8 @@ private:
 
     void set_initialized() { m_state = INITIALIZED; }
 
-    const double& operator[] (const std::size_t& idx) const { return m_bary[idx]; }
-    double& operator[] (const std::size_t& idx) { return m_bary[idx]; }
+    const FT& operator[] (const std::size_t& idx) const { return m_bary[idx]; }
+    FT& operator[] (const std::size_t& idx) { return m_bary[idx]; }
   };
 
   // Wrapper for thread safety of maintained cell hint for fast
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h b/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
index dddb6759fe7..3a79d458803 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
@@ -94,9 +94,10 @@ namespace CGAL {
     typedef typename boost::property_traits<PointMap>::value_type Point;
     typedef typename Kernel_traits<Point>::Kernel Kernel;
     typedef typename Kernel::Sphere_3 Sphere;
+    typedef typename Kernel::FT FT;
 
     typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
-    typedef CGAL::Surface_mesh_default_triangulation_3 STr;
+    typedef typename CGAL::Surface_mesher::Surface_mesh_default_triangulation_3_generator<Kernel>::Type STr;
     typedef CGAL::Surface_mesh_complex_2_in_triangulation_3<STr> C2t3;
     typedef CGAL::Implicit_surface_3<Kernel, Poisson_reconstruction_function> Surface_3;
 
@@ -106,10 +107,10 @@ namespace CGAL {
 
     Point inner_point = function.get_inner_point();
     Sphere bsphere = function.bounding_sphere();
-    double radius = std::sqrt(bsphere.squared_radius());
+    FT radius = CGAL::approximate_sqrt(bsphere.squared_radius());
 
-    double sm_sphere_radius = 5.0 * radius;
-    double sm_dichotomy_error = sm_distance * spacing / 1000.0;
+    FT sm_sphere_radius = 5.0 * radius;
+    FT sm_dichotomy_error = sm_distance * spacing / 1000.0;
 
     Surface_3 surface(function,
                       Sphere (inner_point, sm_sphere_radius * sm_sphere_radius),