Merge remote-tracking branch 'cgal/master' into HEAD

.github/test.sh

@@ -9,4 +9,5 @@ PLUGINS_ARRAY=(${LIST_OF_PLUGINS});
 NB_OF_PLUGINS=${#PLUGINS_ARRAY[@]}
 DEL=$(($NB_OF_PLUGINS / 4))
 cd build
-make -j2 ${PLUGINS_ARRAY[@]:$(($FACTOR * $DEL)):$((($FACTOR + 1) * $DEL))}
+NUM_PROCS=$(nproc)
+make -j${NUM_PROCS} ${PLUGINS_ARRAY[@]:$(($FACTOR * $DEL)):$((($FACTOR + 1) * $DEL))}

.github/workflows/build_doc.yml

@@ -104,8 +104,8 @@ jobs:
               echo "DoxygenError=No package affected." >> $GITHUB_OUTPUT
               exit 1
             fi
-            cd build_doc && make -j2 doc
+            cd build_doc && make -j$(nproc) doc
-            make -j2 doc_with_postprocessing 2>tmp.log
+            make -j$(nproc) doc_with_postprocessing 2>tmp.log
             if [ -s tmp.log ]; then
               content=`cat ./tmp.log`
               delimiter="$(openssl rand -hex 8)"

.github/workflows/reuse.yml

@@ -12,24 +12,24 @@ jobs:
     steps:
     - uses: actions/checkout@v4
     - name: REUSE version
-      uses: fsfe/reuse-action@v2
+      uses: fsfe/reuse-action@v3
       with:
         args: --version
     - name: REUSE lint
-      uses: fsfe/reuse-action@v2
+      uses: fsfe/reuse-action@v3
       with:
         args: --include-submodules lint
     - name: REUSE SPDX SBOM
-      uses: fsfe/reuse-action@v2
+      uses: fsfe/reuse-action@v3
       with:
         args: spdx
     - name: install dependencies
-      run: sudo apt-get install -y cmake
+      run: sudo apt-get update && sudo apt-get install -y cmake
     - name: Create CGAL internal release
       run: |
         mkdir -p ./release
         cmake -DDESTINATION=./release -DCGAL_VERSION=9.9 -P ./Scripts/developer_scripts/cgal_create_release_with_cmake.cmake
     - name: REUSE lint release tarball
-      uses: fsfe/reuse-action@v2
+      uses: fsfe/reuse-action@v3
       with:
         args: --root ./release/CGAL-9.9 --include-submodules lint

AABB_tree/include/CGAL/AABB_tree/internal/AABB_traversal_traits.h

@@ -73,7 +73,7 @@ public:
   Result;
 public:
   First_intersection_traits(const AABBTraits& traits)
-    : m_result(), m_traits(traits)
+    : m_result(std::nullopt), m_traits(traits)
   {}
 
   bool go_further() const {
@@ -202,7 +202,7 @@ class First_primitive_traits
 public:
   First_primitive_traits(const AABBTraits& traits)
     : m_is_found(false)
-    , m_result()
+    , m_result(std::nullopt)
     , m_traits(traits) {}
 
   bool go_further() const { return !m_is_found; }

Advancing_front_surface_reconstruction/package_info/Advancing_front_surface_reconstruction/dependencies

@@ -2,6 +2,7 @@ Advancing_front_surface_reconstruction
 Algebraic_foundations
 Arithmetic_kernel
 BGL
+CGAL_Core
 Cartesian_kernel
 Circulator
 Distance_2

Algebraic_foundations/include/CGAL/Rational_traits.h

@@ -53,7 +53,7 @@ struct Rational_traits_base<Rational, true>
 {
 private:
     typedef Fraction_traits<Rational> FT;
-    typedef typename FT::Decompose Decomose;
+    typedef typename FT::Decompose Decompose;
     typedef typename FT::Compose Compose;
 
 public:
@@ -61,13 +61,13 @@ public:
 
     RT numerator (const Rational& r) const {
         RT num,den;
-        Decomose()(r,num,den);
+        Decompose()(r,num,den);
         return num;
     }
 
     RT denominator (const Rational& r) const {
         RT num,den;
-        Decomose()(r,num,den);
+        Decompose()(r,num,den);
         return den;
     }
 

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes_E08_tree.h

@@ -303,7 +303,7 @@ public:
             Integer alpha_num = Integer(1), int log_denom = 1
     ) : alpha_num_(alpha_num),
         beta_num_((Integer(1) << log_denom) - alpha_num),
-        half_((log_denom > 0) ? (Integer(1) << log_denom-1) : 0),
+        half_((log_denom > 0) ? Integer(Integer(1) << log_denom-1) : 0),
         log_denom_(log_denom)
     {
         CGAL_precondition(log_denom_ >= 0);

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes_rndl_tree.h

@@ -206,7 +206,7 @@ polynomial_power_to_bernstein_approx(
     std::vector<Integer> f(n+1);
     polynomial_affine_transform_approx_log_denom(
             first, beyond, f.begin(),
-            upper_num - lower_num, lower_num, log_denom,
+            Integer(upper_num - lower_num), lower_num, log_denom,
             p+q,
             approx, log, logl
     );

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Bitstream_descartes_rndl_tree_traits.h

@@ -27,31 +27,10 @@
 
 #include <vector>
 
-#if CGAL_USE_CORE
-namespace CORE { class BigInt; }
-#endif
-
 namespace CGAL {
 
 namespace internal {
 
-#if CGAL_USE_CORE
-// bugfix for CORE by Michael Kerber
-// why is there a specialized function for CORE?
-inline CORE::BigInt shift_integer_by(CORE::BigInt x, long shift){
-  if( shift > 0 ){
-    while(shift>63) {
-      x = (x >> 63);
-      shift-=63;
-    }
-    x = (x >> shift);
-  }else{
-    // add 0 bits
-    x = (x << -shift);
-  }
-  return x;
-}
-#endif
 
 template <class Shiftable>
 Shiftable shift_integer_by(Shiftable x, long shift){

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Real_embeddable_extension.h

@@ -327,7 +327,7 @@ public:
     long operator()( CORE::BigFloat x ) const {
       CGAL_precondition(!CGAL::zero_in(x));
       x = CGAL::abs(x);
-      return CORE::floorLg(x.m()-x.err())+x.exp()*CORE::CHUNK_BIT;
+      return CORE::floorLg(CORE::BigInt(x.m()-x.err()))+x.exp()*CORE::CHUNK_BIT;
     }
   };
 
@@ -337,7 +337,7 @@ public:
       // (already commented out in EXACUS)...
       //   NiX_precond(!(NiX::in_zero(x) && NiX::singleton(x)));
       x = CGAL::abs(x);
-      return CORE::ceilLg(x.m()+x.err())+x.exp()*CORE::CHUNK_BIT;
+      return CORE::ceilLg(CORE::BigInt(x.m()+x.err()))+x.exp()*CORE::CHUNK_BIT;
     }
   };
 

Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/bound_between_1.h

@@ -220,7 +220,7 @@ simple_bound_between(const Algebraic_real& a,
             final_mantissa = final_mantissa << 1;
             final_mantissa++;
             y_log--;
-            x_m = x_m==0 ? 0 : x_m & ((Integer(1) << x_log) - 1); //x_m - CGAL::ipower(Integer(2),x_log);
+            x_m = x_m==0 ? 0 : Integer(x_m & ((Integer(1) << x_log) - 1)); //x_m - CGAL::ipower(Integer(2),x_log);
             x_log = x_m==0 ? -1 : CGAL::internal::floor_log2_abs(x_m);
         }
         final_mantissa = final_mantissa << 1;

Algebraic_kernel_for_circles/package_info/Algebraic_kernel_for_circles/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Algebraic_kernel_for_circles
 Arithmetic_kernel
+CGAL_Core
 Filtered_kernel
 Installation
 Interval_support

Algebraic_kernel_for_spheres/package_info/Algebraic_kernel_for_spheres/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Algebraic_kernel_for_spheres
 Arithmetic_kernel
+CGAL_Core
 Filtered_kernel
 Installation
 Interval_support

Alpha_shapes_2/package_info/Alpha_shapes_2/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Alpha_shapes_2
 Arithmetic_kernel
+CGAL_Core
 Cartesian_kernel
 Hash_map
 Homogeneous_kernel

Alpha_shapes_3/package_info/Alpha_shapes_3/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Alpha_shapes_3
 Arithmetic_kernel
+CGAL_Core
 Cartesian_kernel
 Circulator
 Filtered_kernel

Alpha_wrap_3/package_info/Alpha_wrap_3/dependencies

@@ -4,6 +4,7 @@ Alpha_wrap_3
 Arithmetic_kernel
 BGL
 Box_intersection_d
+CGAL_Core
 Cartesian_kernel
 Circulator
 Distance_2

Arithmetic_kernel/include/CGAL/BOOST_MP_arithmetic_kernel.h

@@ -19,6 +19,10 @@
 
 #ifdef CGAL_USE_BOOST_MP
 
+#ifdef CGAL_USE_CORE
+#include <CGAL/CORE_arithmetic_kernel.h>
+#endif
+
 //Currently already included in boost_mp.h
 //#include <boost/multiprecision/cpp_int.hpp>
 //#ifdef CGAL_USE_GMP
@@ -26,20 +30,29 @@
 //#endif
 
 // FIXME: the could be several kernels based on Boost.Multiprecision.
-
 namespace CGAL {
 /** \ingroup CGAL_Arithmetic_kernel
  *  \brief The Boost.Multiprecision set of exact number types
  */
+
+#if !defined(CGAL_USE_CORE) || defined(CGAL_CORE_USE_GMP_BACKEND)
 struct BOOST_cpp_arithmetic_kernel : internal::Arithmetic_kernel_base {
   typedef boost::multiprecision::cpp_int Integer;
   typedef boost::multiprecision::cpp_rational Rational;
 };
+#else
+typedef CORE_arithmetic_kernel BOOST_cpp_arithmetic_kernel;
+#endif
+
 #ifdef CGAL_USE_GMP
+#if !defined(CGAL_USE_CORE) || !defined(CGAL_CORE_USE_GMP_BACKEND)
 struct BOOST_gmp_arithmetic_kernel : internal::Arithmetic_kernel_base {
   typedef boost::multiprecision::mpz_int Integer;
   typedef boost::multiprecision::mpq_rational Rational;
 };
+#else
+typedef CORE_arithmetic_kernel BOOST_gmp_arithmetic_kernel;
+#endif
 #endif
 
 template <class T1, class T2, class T3, class T4, class T5>

Arithmetic_kernel/include/CGAL/CORE_arithmetic_kernel.h

@@ -55,14 +55,6 @@ public:
 };
 
 
-template <>
-struct Get_arithmetic_kernel<CORE::BigInt>{
-  typedef CORE_arithmetic_kernel Arithmetic_kernel;
-};
-template <>
-struct Get_arithmetic_kernel<CORE::BigRat>{
-  typedef CORE_arithmetic_kernel Arithmetic_kernel;
-};
 template <>
 struct Get_arithmetic_kernel<CORE::Expr>{
   typedef CORE_arithmetic_kernel Arithmetic_kernel;
@@ -74,6 +66,8 @@ struct Get_arithmetic_kernel<CORE::BigFloat>{
 
 } //namespace CGAL
 
+#include <CGAL/BOOST_MP_arithmetic_kernel.h>
+
 #endif // CGAL_USE_CORE
 
 #endif //  CGAL_CORE_ARITHMETIC_KERNEL_H

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/ArrangementTypes.h

@@ -15,7 +15,6 @@
 
 #include <CGAL/Arrangement_with_history_2.h>
 #include <CGAL/Cartesian.h>
-#include <CGAL/Arr_default_dcel.h>
 #include <CGAL/Arr_segment_traits_2.h>
 #include <CGAL/Arr_linear_traits_2.h>
 #include <CGAL/Arr_polyline_traits_2.h>

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils/IntersectCurves.cpp

@@ -11,7 +11,7 @@
 
 #include "IntersectCurves.h"
 #include "ArrangementTypes.h"
-#include <boost/function_output_iterator.hpp>
+#include <boost/iterator/function_output_iterator.hpp>
 
 
 template <typename Traits_>

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/Utils/Utils.cpp

@@ -202,7 +202,7 @@ operator()(const Point_2& p, const X_monotone_curve_2& curve) const {
   auto points = painterOstream.getPointsList(curve);
 
   QPoint p_viewport =
-    view->mapFromScene(QPointF{p.x().doubleValue(), p.y().doubleValue()});
+    view->mapFromScene(QPointF{CGAL::to_double(p.x()), CGAL::to_double(p.y())});
 
   double min_dist = (std::numeric_limits<double>::max)();
   for (auto& vec : points) {

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt

@@ -69,10 +69,10 @@ class Arrangement_2 { ... };
 
 An instance of this template represents an arrangement embedded in the
 plane. When the template is instantiated, the `GeometryTraits`
-parameter must be substituted with a type that defines a set of
+parameter must be substituted by a type that defines a set of
 geometric-object types, such as point and curve, and a set of
 operations on objects of these types (see Section \ref
-aos_sec-geom_traits); the `Dcel` parameter must be substituted with a
+aos_sec-geom_traits); the `Dcel` parameter must be substituted by a
 type that represents a doubly-connected edge list (\dcel) data
 structure. It defines types of topological objects, such as vertices,
 edges, and faces, and the operations required to maintain the
@@ -91,7 +91,7 @@ An instance of this template represents a two-dimensional arrangement
 embedded in a surface in three dimensional space. When the template is
 instantiated, the `GeometryTraits` parameter must be substituted as
 described above; the `TopologyTraits` parameter must be substituted
-with a type that deals with the topology of the surface (see Section
+by a type that deals with the topology of the surface (see Section
 \ref aos_sec-topol_traits). In particular, it maintains a
 representation of the arrangement graph embedded in the surface using
 a doubly-connected edge list (\dcel) data-structure suitable for
@@ -390,7 +390,7 @@ the `Arrangement_2` class template; their description follows.
 
 <UL>
 
-<LI>The `Traits` template-parameter should be instantiated with a
+<LI>The `Traits` template-parameter should be substituted by a
   model of the `ArrangementBasicTraits_2` concept and optionally
   additional geometry traits concepts. A model of the
   `ArrangementBasicTraits_2` concept defines the types of
@@ -415,14 +415,15 @@ the `Arrangement_2` class template; their description follows.
   rational functions. We exemplify the usage of these traits classes
   in Section \ref aos_sec-geom_traits.
 
-<LI>The `Dcel` template-parameter should be instantiated with a class
+<LI>The `Dcel` template-parameter should be substituted by a class
   that models the `ArrangementDcel` concept, which is used to represent
   the topological layout of the arrangement. This parameter is
-  substituted with `Arr_default_dcel<Traits>` by default, and
+  substituted by `Arr_default_dcel<Traits>` by default, and
   we use this default value in this and in the following three
-  sections. However, in many applications it is necessary to
+  sections. However, in many applications it is necessary to extend the
-  extend the \dcel features. This is done by substituting the
+  \dcel features. This is done by substituting the `Dcel` parameter with
-  `Dcel` parameter with a different type; see Section \ref arr_ssecex_dcel
+  a different type (typically, a different instance of the
+  `Arr_dcel<>` class template); see Section \ref arr_ssecex_dcel
   for further explanations and examples.
 </UL>
 
@@ -1001,7 +1002,7 @@ segments common to all examples that do not construct new geometric
 objects. They are kept in the header file
 `arr_inexact_construction_segments.h`.  In these examples the `Traits`
 parameter of the `Arrangement_2<Traits, Dcel>` class template is
-substituted with an instance of the
+substituted by an instance of the
 `Arr_non_caching_segment_traits_2<Kernel>` class template. The
 `Arr_non_caching_segment_traits_2` class template is instantiated with
 the predefined kernel that evaluates predicates in an exact manner,
@@ -1438,7 +1439,7 @@ vary according to the user choice.} for answering queries:
 
   The landmark strategy requires that the type of the attached
   arrangement be an instance of the `Arrangement_2<Traits,Dcel>` class
-  template, where the `Traits` parameter is substituted with a
+  template, where the `Traits` parameter is substituted by a
   geometry-traits class that models the `ArrangementLandmarkTraits_2`
   concept, which refines the basic `ArrangementBasicTraits_2` concept;
   see Section \ref aos_sssec-tr_landmarks_concept for details. Most
@@ -1742,7 +1743,7 @@ query results, and insert \f$c\f$ at its proper
 location.\cgalFootnote{The \cgalFootnoteCode{CGAL::insert_non_intersecting_curve<>()}
 function template, as all other functions reviewed in this section, is
 parameterized by an arrangement type and a point-location type (The
-latter must be substituted with a model of the
+latter must be substituted by a model of the
 `ArrangementPointLocation_2` concept).} The insertion operation thus
 hardly requires any geometric operations on top of the ones needed to
 answer the point-location queries. Moreover, it is sufficient that the
@@ -1846,7 +1847,7 @@ condition. Consider the call \link CGAL::insert<>() `insert(arr, c,
 pl)`\endlink, where \f$c\f$ is not necessarily \f$x\f$-monotone. In
 this case the type of `arr` must be an instance of the
 `Arrangement_2<Traits, Dcel>` class template, where the `Traits`
-template parameter is substituted with a traits class that models the
+template parameter is substituted by a traits class that models the
 concept `ArrangementTraits_2`, which refines the
 `ArrangementXMonotoneTraits_2` concept. It has to define an additional
 \link ArrangementTraits_2::Curve_2 `Curve_2`\endlink type, which may
@@ -2267,7 +2268,7 @@ accepts the name of an input file that contains the plain-text
 description of the geometric objects and an output iterator for
 storing the newly constructed objects.  When the function is
 instantiated, the first template parameter, namely `Type`, must be
-substituted with the type of objects to read. It is assumed that an
+substituted by the type of objects to read. It is assumed that an
 extractor operator (`>>`) that extracts objects of the given type from
 the input stream is available. The listing of the function template,
 which is defined in the file `read_objects.h`, is omitted here
@@ -2704,7 +2705,7 @@ All the free functions that operate on arrangements of bounded curves
 of unbounded curves. For example, consider a container of linear
 curves that has to be inserted into an arrangement object, the type of
 which is an instance of the `Arrangement_2<Traits,Dcel>` class
-template, where the `Traits` parameter is substituted with the traits
+template, where the `Traits` parameter is substituted by the traits
 class that handles linear curves; see Section \ref
 arr_sssectr_linear. You can do it incrementally; namely, insert the
 curves one by one as follows:
@@ -3485,7 +3486,7 @@ point-location strategy.
 The type of an arrangement associated with the landmark point-location
 strategy (see Section \ref arr_ssecpl) must be an instance of the
 `Arrangement_on_surface_2<GeomTraits, TopolTraits>` class template,
-where the `GeomTraits` parameter is substituted with a model of the
+where the `GeomTraits` parameter is substituted by a model of the
 concept `ArrangementLandmarkTraits_2`. (Naturally, it can also model
 either the `ArrangementXMonotoneTraits_2` concept or the
 `ArrangementTraits_2` concept.) The `ArrangementLandmarkTraits_2`
@@ -4541,7 +4542,7 @@ PkgBooleanSetOperations2Ref. Note that it is not a model of the
 computations with square root numbers, which makes it attractive for
 arrangements induced by line segments, circular arcs, and whole
 circles.  When the traits class-template is instantiated, the `Kernel`
-template parameter must be substituted with a geometric kernel that
+template parameter must be substituted by a geometric kernel that
 models the `Kernel` concept. Always plug in a kernel that uses a
 rational number type, such as
 `Exact_predicates_exact_constructions_kernel`. Observe that the nested
@@ -4722,20 +4723,20 @@ follows:
 
 <UL>
 
-<LI>The `RatKernel` template parameter must be substituted with a
+<LI>The `RatKernel` template parameter must be substituted by a
 geometric kernel whose field type is an exact rational type. It is
 used to define basic geometric entities (e.g., a line segment or a
 circle) with rational coefficients. Typically we use one of the
 standard \cgal kernels, instantiated with the number type
 `NtTraits::Rational` (see below).
 
-<LI>The `AlgKernel` template parameter must be substituted with a
+<LI>The `AlgKernel` template parameter must be substituted by a
 geometric kernel whose field type is an exact algebraic type. It is
 used to define points with algebraic coordinates. Typically, we use
 one of the standard \cgal kernels, instantiated with the number type
 `NtTraits::Algebraic` (see below).
 
-<LI>The `NtTraits` template parameter must be substituted with a type
+<LI>The `NtTraits` template parameter must be substituted by a type
 that encapsulates all the numeric operations needed for performing
 geometric computation carried out by the geometric traits class.  It
 defines the `Integer`, `Rational`, and `Algebraic` number-types, and
@@ -4916,7 +4917,7 @@ provided by the traits in form of functors.
 
 When the `Arr_rational_function_traits_2<AlgebraicKernel_d_1>` class
 template is instantiated, the template parameter must be substituted
-with a model of the `AlgebraicKernel_d_1` concept. Models of this
+by a model of the `AlgebraicKernel_d_1` concept. Models of this
 concept, such as the `Algebraic_kernel_d_1<Coefficient>` class
 template provided by the package \ref PkgAlgebraicFoundations are
 meant to support algebraic functionalities on univariate polynomials
@@ -5176,11 +5177,11 @@ polynomial.  Currently supported integral number types are `Gmpz`,
 statements included in the header file `integer_type.h`, the listings
 of which are omitted here. This header file is used by the two example
 programs listed in this section. The template parameter `Coefficient`
-can be substituted in addition with an instance of the
+can be substituted in addition by an instance of the
 `Sqrt_extension<A,B>` class template, where the template parameters
-`NT` and `Root` are substituted in turn with one of the integral
+`NT` and `Root` are substituted in turn by one of the integral
 number types above. Finally, the template parameter `Coefficient` can
-be substituted also with a rational number type, where the type of the
+be substituted also by a rational number type, where the type of the
 numerator and denominator is one of the types above.
 
 The type \link Arr_algebraic_segment_traits_2::Curve_2
@@ -5487,7 +5488,7 @@ decorator used to attach a data field to curves and to
 \f$x\f$-monotone curves. It is a class template named
 `Arr_curve_data_traits_2<BaseTraits, XMonotoneCurveData, Merge,
 CurveData, Convert>` parameterized by a base-traits class, which must
-be substituted with one of the geometric traits models described in
+be substituted by one of the geometric traits models described in
 the previous subsections or with a user-defined traits model, when the
 decorator is instantiated. The curve-data decorator derives from the
 base-traits class, and in particular inherits its \link
@@ -5882,12 +5883,12 @@ applications.
 
 All examples presented so far use the default \dcel; namely, they
 employ the `Arr_default_dcel<Traits>` instance. This is done
-implicitly, as an instance of this class template serves as the
+implicitly, as this instance of the `Arr_default_dcel` class template
-default parameter for the `Arrangement_2` class template; see Section
+serves as the default parameter for the `Arrangement_2` class
-\ref aos_ssec-basic-arr_class. The default \dcel class associates
+template; see Section \ref aos_ssec-basic-arr_class. The default \dcel
-points with vertices and \f$x\f$-monotone curves with halfedges, but
+class associates points with vertices and \f$x\f$-monotone curves with
-nothing more.  In this section we show how to use alternative
+halfedges, but nothing more.  In this section we show how to use
-\dcel types to extend the desired \dcel records.
+alternative \dcel types to extend the desired \dcel records.
 
 <!-- ------------------------------------------------------------------------- -->
 \subsubsection arr_sssecex_dcel_face Extending the DCEL Faces
@@ -6107,7 +6108,7 @@ ovl_traits)`\endlink constructs the arrangement `arr_o`, which is the
 overlay of two input arrangement `arr_r` and `arr_b`. All three
 arrangements must use the same geometric primitives. In other words,
 their types are instances of the `Arrangement_2<Traits,Dcel>` class
-template, where the `Traits` parameter is substituted with three
+template, where the `Traits` parameter is substituted by three
 geometry-traits classes, respectively. The geometry-traits classes of
 the input arrangements must be convertible to the geometry-traits
 class of the resulting arrangement.\cgalFootnote{It is sufficient that
@@ -6116,17 +6117,17 @@ of arrangements derive from a common ancestor that models the
 geometry-traits concept.} Typically, all three arrangements use the
 same geometry-traits class.
 
-The `overlay()` function template is suitable for
+The `overlay()` function template is suitable for arrangements that do
-arrangements that do not store any additional data with their
+not store any additional data with their \dcel records; namely,
-\dcel records; namely, arrangements defined using an instance of
+arrangements defined using the default \dcel, which is the instance
-the default \dcel class-template `Arr_default_dcel`. Typically,
+`Arr_default_dcel<Traits>`. Typically, the overlay arrangement in this
-the overlay arrangement in this case does not store extra data with
+case does not store extra data with its \dcel records as well. (If it
-its \dcel records as well (or if it does, the additional
+does, the additional data-fields cannot be computed by the overlay
-data-fields cannot be computed by the overlay operation). The overlay
+operation in this case.) The overlay arrangement is equivalent to the
-arrangement is equivalent to the arrangement induced by all curves of
+arrangement induced by all curves of `arr_r` and `arr_b`. Indeed, it
-`arr_r` and `arr_b`. Indeed, it is possible to obtain the same result
+is possible to obtain the same result using the standard
-using the standard insertion-operations instead, but, as mentioned
+insertion-operations instead, but, as mentioned above, this is less
-above, this is less efficient.
+efficient.
 
 <!-- ------------------------------------------------------------------------- -->
 \cgalFigureBegin{aos_figex_overlay,overlay.png}
@@ -6168,7 +6169,7 @@ arrangement that results from overlaying two face-extended
 arrangements typically also stores additional data-fields with its
 faces. The types of such arrangements, for example, could be instances
 of the `Arrangement_2<Traits,Dcel>` class template, where the `Dcel`
-parameters are substituted with instances of the
+parameters are substituted by instances of the
 `Arr_face_extended_dcel` class template (see Section \ref
 arr_sssecex_dcel_face). The data field that is attached to an overlay
 face can be computed from the data fields of the two faces (in `arr_r`
@@ -6178,7 +6179,7 @@ data fields with all their \dcel records typically also stores
 additional data-fields with all its \dcel records. The types of
 such arrangements, for example, could be instances of the
 `Arrangement_2<Traits,Dcel>` class template, where the `Dcel`
-parameters are substituted with instances of the `Arr_extended_dcel`
+parameters are substituted by instances of the `Arr_extended_dcel`
 class template (see Section \ref arr_sssecex_dcel_all). The data field
 attached to an overlay feature can be computed from the data fields of
 the two features (in `arr_r` and `arr_b`) that induce the overlay
@@ -6193,7 +6194,7 @@ of the overlay traits can be an instance of the class template
 `Arr_face_overlay_traits<ArrangementR,ArrangementB,ArrangementO,OverlayFaceData>`,
 which models the concept `OverlayTraits`. An object of this type
 operates on face-extended arrangements. When instantiated, the
-`OverlayFaceData` parameter must be substituted with a functor that is
+`OverlayFaceData` parameter must be substituted by a functor that is
 capable of combining two face-data fields of types
 `ArrangementR::Dcel::Face_data` and `ArrangementB::Dcel::Face_data`
 and computing the output `ArrangementO::Dcel::Face_data` object. The
@@ -6208,7 +6209,7 @@ flag. A polygon is represented as a <em>marked</em> arrangement face
 (whose flag is set). The example uses an instance of the
 `Arr_face_overlay_traits<ArrR,ArrB,ArrO,OverlayFaceData>` class
 template as the face-overlay traits class where the `OverlayFaceData`
-template parameter is substituted with a functor that simply performs
+template parameter is substituted by a functor that simply performs
 a logical <em>and</em> operation on Boolean flags. As a result, a face
 in the overlay arrangement is marked only when it corresponds to an
 overlapping region of two marked faces in the input
@@ -6406,12 +6407,12 @@ between these curves and the arrangement edges they induce. Similarly,
 the `Arrangement_with_history_2<GeometryTraits,Dcel>` class-template
 extends the `Arrangement_2<GeometryTraits,Dcel>` class template. The
 `GeometryTraits` template parameter, of either class templates, must
-be substituted with a model of the `ArrangementTraits_2` concept; see
+be substituted by a model of the `ArrangementTraits_2` concept; see
 Section \ref aos_ssec-insert_gen. It should define the \link
 ArrangementTraits_2::Curve_2 `Curve_2`\endlink type and support its
 subdivision into \link ArrangementBasicTraits_2::X_monotone_curve_2
 `X_monotone_curve_2`\endlink objects, among the others.  The `Dcel`
-parameter must be substituted with a model of the `ArrangementDcel`
+parameter must be substituted by a model of the `ArrangementDcel`
 concept. You can use either the default \dcel class or an extended
 \dcel class (see Section \ref arr_ssecex_dcel) based on your needs. An
 arrangement that support the cross-mapping mentioned above is referred
@@ -6488,7 +6489,7 @@ iterators is \link Arrangement_with_history_2::Curve_2
 Overlaying two arrangement-with-history objects is possible only if
 their types are instances of the
 `Arrangement_with_history_2<Traits,Dcel>` class template, where the
-respective `Traits` parameters are substituted with two traits classes
+respective `Traits` parameters are substituted by two traits classes
 that are convertible to one another. In this case, the resulting
 arrangement stores a consolidated container of input curves, and
 automatically preserves the cross-mapping between the arrangement
@@ -6668,15 +6669,15 @@ a file.
 \subsection arr_ssecarr_io_aux_data Arrangements with Auxiliary Data
 <!-- ------------------------------------------------------------------------- -->
 
-\cgalAdvancedBegin
+\cgalAdvancedBegin The inserter and extractor both ignore any
-The inserter and extractor both ignore any auxiliary data stored with
+auxiliary data stored with the arrangement features. Thus, they are
-the arrangement features. Thus, they are ideal for arrangements
+ideal for arrangements instantiated using the default \dcel, which is
-instantiated using the `Arr_default_dcel` class.
+the instance `Arr_default_dcel<Traits>`.  However, as explained in
-However, as explained in Section \ref arr_ssecex_dcel, one can easily
+Section \ref arr_ssecex_dcel, one can easily extend the arrangement
-extend the arrangement faces by using the `Arr_face_extended_dcel`
+faces by using the `Arr_face_extended_dcel` template, extend all \dcel
-template, or extend all \dcel records by using the `Arr_extended_dcel`
+records by using the `Arr_extended_dcel` template, or use the
-template. In such cases, it might be crucial that the auxiliary data fields
+`Arr_dcel` template. In such cases, it might be crucial that the
-are written to the file and read from there.
+auxiliary data fields are written to the file and read from there.
 
 The arrangement package includes the free functions
 `write(arr, os, formatter)`, which writes the arrangement `arr`
@@ -6973,7 +6974,7 @@ algorithm on a dual arrangement. It uses the functor template
 information stored inside the faces. The functor implements a property
 map that utilizes the `data()` and `set_data()` member functions of the
 extended face to update or obtain the property. When the property map
-is instantiated, the `Type` parameter must be substituted with the
+is instantiated, the `Type` parameter must be substituted by the
 same type that is used to extend the arrangement face; see Section
 \ref arr_sssecex_dcel_face. The functor template is defined in the
 header file `Extended_face_property_map.h` listed below.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_bounded_planar_topology_traits_2.h

@@ -9,13 +9,13 @@ namespace CGAL {
  *
  * The `Arr_bounded_planar_topology_traits_2` template has two parameters:
  * <UL>
- * <LI>The `GeometryTraits_2` template-parameter should be instantiated with
+ * <LI>The `GeometryTraits_2` template-parameter should be substituted by
  * a model of the `ArrangementBasicTraits_2` concept. The traits
  * class defines the types of \f$x\f$-monotone curves and two-dimensional
  * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
  * `ArrangementBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
- * <LI>The `Dcel` template-parameter should be instantiated with
+ * <LI>The `Dcel` template-parameter should be substituted by
  * a class that is a model of the `ArrangementDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_conic_traits_2.h

@@ -57,17 +57,17 @@ namespace CGAL {
  * algebraic number of degree \f$d\f$ if there exist a polynomial \f$ p\f$ with
  * <I>integer</I> coefficient of degree \f$d\f$ such that \f$p(\alpha) = 0\f$).
  * We therefore require separate representations of the curve
- * coefficients and the point coordinates. The `NtTraits` should be instantiated
+ * coefficients and the point coordinates. The `NtTraits` should be substituted
- * with a class that defines nested `Integer`, `Rational`, and `Algebraic` number
+ * by a class that defines nested `Integer`, `Rational`, and `Algebraic` number
  * types and supports various operations on them, yielding certified computation
  * results (for example, it can convert rational numbers to algebraic numbers
  * and can compute roots of polynomials with integer coefficients).  The other
  * template parameters, `RatKernel` and `AlgKernel` should be geometric kernels
  * instantiated with the `NtTraits::Rational` and `NtTraits::Algebraic` number
- * types, respectively.  It is recommended instantiating the
+ * types, respectively.  It is recommended substituting the
- * `CORE_algebraic_number_traits` class as the `NtTraits` parameter, with
+ * `CORE_algebraic_number_traits` class for the `NtTraits` parameter, and
- * `Cartesian<NtTraits::Rational>` and `Cartesian<NtTraits::Algebraic>`
+ * the `Cartesian<NtTraits::Rational>` and `Cartesian<NtTraits::Algebraic>`
- * instantiating the two kernel types, respectively.  The number types in this
+ * instances for two kernel types, respectively.  The number types in this
  * case are provided by the \core library, with its ability to exactly represent
  * simple algebraic numbers.
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_dcel.h

@@ -0,0 +1,39 @@
+namespace CGAL {
+
+/*! \ingroup PkgArrangementOnSurface2DCEL
+ *
+ * The \dcel class used by the `Arrangement_2`,
+ * `Arr_bounded_planar_topology_traits_2`, `Arr_unb_planar_topology_traits_2`
+ * class templates and other templates.  It is parameterized by a geometry
+ * traits type and optionaly by a vertex, halfedge, or face types. By default,
+ * the `Arr_dcel` class template uses the \link
+ * ArrangementBasicTraits_2::Point_2 `Point_2`\endlink and \link
+ * ArrangementBasicTraits_2::X_monotone_curve_2 `X_monotone_curve_2`\endlink
+ * types nested in the traits type to instantiate the vertex and base halfedge
+ * types, respectively. Thus, by default the \dcel only stores the topological
+ * incidence relations and the geometric data attached to vertices and
+ * edges. Any one of the vertex, halfedge, or face types can be
+ * overriden. Notice that if the vertex and halfedge types are overriden, the
+ * traits type is ignored.
+ *
+ * \cgalModels{ArrangementDcelWithRebind}
+ *
+ * \tparam Traits a geometry traits type, which is a model of the
+ *                `ArrangementBasicTraits_2` concept.
+ * \tparam V the vertex type, which is a model of the `ArrangementDcelVertex`
+ *           concept.
+ * \tparam H the halfedge type, which is a model of the
+ *            `ArrangementDcelHalfedge` concept.
+ * \tparam F the face type, which is a model of the `ArrangementDcelFace`
+ *           concept.
+ *
+ * \sa `Arr_dcel_base<V, H, F>`
+ */
+template <typename Traits,
+          typename V = Arr_vertex_base<typename Traits::Point_2>,
+          typename H = Arr_halfedge_base<typename Traits::X_monotone_curve_2>,
+          typename F = Arr_face_base>
+class Arr_dcel : public Arr_dcel_base<V, H, F> {
+};
+
+} /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_default_dcel.h

@@ -1,26 +1,25 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2DCEL
-\ingroup PkgArrangementOnSurface2DCEL
+ *
+ * The default \dcel class used by the `Arrangement_2`,
+ * `Arr_bounded_planar_topology_traits_2`, `Arr_unb_planar_topology_traits_2`
+ * class templates and other templates.  It is parameterized by a geometry
+ * traits type. It uses the \link ArrangementBasicTraits_2::Point_2
+ * `Point_2`\endlink and \link ArrangementBasicTraits_2::X_monotone_curve_2
+ * `X_monotone_curve_2`\endlink types nested in the traits type to instantiate
+ * the vertex and base halfedge types, respectively. Thus, by default the \dcel
+ * only stores the topological incidence relations and the geometric data
+ * attached to vertices and edges.
+ *
+ * \cgalModels{ArrangementDcelWithRebind}
+ *
+ * \tparam Traits a geometry traits type, which is a model of the
+ *                `ArrangementBasicTraits_2` concept.
+ *
+ * \sa `Arr_dcel<Traits, V, H, F>`
+ * \sa `Arr_dcel_base<V, H, F>`
+ */
+template <typename Traits> using Arr_default_dcel = Arr_dcel<Traits>;
 
-The default \dcel class used by the `Arrangement_2` class-template
-is parameterized by a traits class, which is a model of the
-`ArrangementBasicTraits_2` concept. It simply uses the nested
-`Traits::Point_2` and `Traits::X_monotone_curve_2` to instantiate
-the base vertex and halfedge types, respectively. Thus, the default
-\dcel records store no other information, except for the topological
-incidence relations and the geometric data attached to vertices and edges.
-
-\cgalModels{ArrangementDcelWithRebind}
-
-\sa `Arr_dcel_base<V,H,F>`
-*/
-template< typename Traits >
-class Arr_default_dcel :
-    public Arr_dcel_base< Arr_vertex_base<typename Traits_::Point_2>,
-                          Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
-                          Arr_face_base>
-{
-}; /* end Arr_default_dcel */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_non_caching_segment_basic_traits_2.h

@@ -16,7 +16,7 @@ that are not provided by the kernel. The kernel is parameterized with a
 number type, which should support the arithmetic operations \f$ +\f$, \f$ -\f$ and
 \f$ \times\f$ in an exact manner in order to avoid robustness problems.
 Using `Cartesian<MP_Float>` or `Cartesian<Gmpz>` are possible
-instantiations for the kernel. Using other (inexact) number types
+substitutions for the kernel. Using other (inexact) number types
 (for example, instantiating the template with
 `Simple_cartesian<double>`) is also possible, at the user's own
 risk.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h

@@ -4,10 +4,10 @@ namespace CGAL {
  *
  * The traits class `Arr_segment_traits_2` is a model of the
  * `ArrangementTraits_2` concept, which allows the construction and maintenance
- * of arrangements of line segments. It should be parameterized with a
+ * of arrangements of line segments. It is parameterized with a
  * \cgal-kernel model that is templated in turn with a number type. To avoid
  * numerical errors and robustness problems, the number type should support
- * exact rational arithmetic - that is, the number type should support the
+ * exact rational arithmetic; that is, the number type should support the
  * arithmetic operations \f$ +\f$, \f$ -\f$, \f$ \times\f$ and \f$ \div\f$
  * carried out without loss of precision.
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h

@@ -9,13 +9,13 @@ namespace CGAL {
  *
  * The `Arr_spherical_topology_traits_2` template has two parameters:
  * <UL>
- * <LI>The `GeometryTraits_2` template-parameter should be instantiated with
+ * <LI>The `GeometryTraits_2` template-parameter should be substituted by
  * a model of the `ArrangementBasicTraits_2` concept. The traits
  * class defines the types of \f$x\f$-monotone curves and two-dimensional
  * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
  * `ArrangementBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
- * <LI>The `Dcel` template-parameter should be instantiated with
+ * <LI>The `Dcel` template-parameter should be substituted by
  * a class that is a model of the `ArrangementDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_unb_planar_topology_traits_2.h

@@ -9,13 +9,13 @@ namespace CGAL {
  *
  * The `Arr_unb_planar_topology_traits_2` template has two parameters:
  * <UL>
- * <LI>The `GeometryTraits_2` template-parameter should be instantiated with
+ * <LI>The `GeometryTraits_2` template-parameter should be substituted by
  * a model of the `ArrangementBasicTraits_2` concept. The traits
  * class defines the types of \f$x\f$-monotone curves and two-dimensional
  * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
  * `ArrangementBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
- * <LI>The `Dcel` template-parameter should be instantiated with
+ * <LI>The `Dcel` template-parameter should be substituted by
  * a class that is a model of the `ArrangementDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h

@@ -16,14 +16,14 @@ namespace CGAL {
 
  * The `Arrangement_on_surface_2` template has two parameters:
  * <UL>
- * <LI>The `GeometryTraits` template-parameter should be instantiated with
+ * <LI>The `GeometryTraits` template-parameter should be substituted by
  * a model of a geometry traits. The minimal requirements are defined by the
  * `ArrangementBasicTraits_2` concept. A model of this concept defines
  * the types of \f$ x\f$-monotone curves and two-dimensional points, namely
  * `ArrangementBasicTraits_2::X_monotone_curve_2` and
  * `ArrangementBasicTraits_2::Point_2`, respectively, and supports basic
  * geometric predicates on them.
- * <LI>The `TopologyTraits` template-parameter should be instantiated with a
+ * <LI>The `TopologyTraits` template-parameter should be substituted by a
  * class that is a model of the `ArrangementTopologyTraits` concept.
  * </UL>
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_with_history_2.h

@@ -25,16 +25,15 @@ namespace CGAL {
  * The `Arrangement_on_surface_with_history_2` template has two parameters:
  *
  * <UL>
- * <LI>The `GeometryTraits` template-parameter should be instantiated with a
+ * <LI>The `GeometryTraits` template-parameter should be substituted by a
  * model of the `ArrangementTraits_2` concept. The traits class defines the
  * `Curve_2` type, which represents an input curve.  It also defines the types
  * of \f$ x\f$-monotone curves and two-dimensional points, namely
  * `ArrangementTraits_2::X_monotone_curve_2` and
  * `ArrangementTraits_2::Point_2`, respectively, and supports basic
  * geometric predicates on them.
- * <LI>The `Dcel` template-parameter should be instantiated with a class that is
+ * <LI>The `TopologyTraits` template-parameter should be substituted by a
- * a model of the `ArrangementDcelWithRebind` concept. The value of this
+ * class that is a model of the `ArrangementTopologyTraits` concept.
- * parameter is by default `Arr_default_dcel<Traits>`.
  * </UL>
  *
  * \sa `Arrangement_with_history_2<GeometryTraits,Dcel>`

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_with_history_2.h

@@ -23,13 +23,13 @@ namespace CGAL {
  *
  * The `Arrangement_with_history_2` template has two parameters:
  * <UL>
- * <LI>The `Traits` template-parameter should be instantiated with a model of
+ * <LI>The `Traits` template-parameter should be substituted by a model of
  * the `ArrangementTraits_2` concept. The traits class defines the `Curve_2`
  * type, which represents an input curve.  It also defines the types of \f$
  * x\f$-monotone curves and two-dimensional points, namely
  * `ArrangementTraits_2::X_monotone_curve_2` and `ArrangementTraits_2::Point_2`,
  * respectively, and supports basic geometric predicates on them.
- * <LI>The `Dcel` template-parameter should be instantiated with a class that is
+ * <LI>The `Dcel` template-parameter should be substituted by a class that is
  * a model of the `ArrangementDcelWithRebind` concept. The value of this
  * parameter is by default `Arr_default_dcel<Traits>`.
  * </UL>

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementDcelWithRebind.h

@@ -12,6 +12,7 @@ Instantiate a dcel class with many different possible types without ad-hoc limit
 
 \cgalHasModelsBegin
 \cgalHasModels{CGAL::Arr_default_dcel<Traits>}
+\cgalHasModels{CGAL::Arr_dcel<Traits,V,H,F>}
 \cgalHasModels{CGAL::Arr_face_extended_dcel<Traits,FData,V,H,F>}
 \cgalHasModels{CGAL::Arr_extended_dcel<Traits,VData,HData,FData,V,H,F>}
 \cgalHasModelsEnd
@@ -48,4 +49,3 @@ Arr_dcel();
 /// @}
 
 }; /* end ArrangementDcelWithRebind */
-

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/ArrangementLandmarkTraits_2.h

@@ -7,7 +7,7 @@
  * associated with the landmark point-location strategy (see
  * `CGAL::Arr_landmarks_point_location`) must be an instance of the
  * `CGAL::Arrangement_2<Traits,Dcel>` class template, where the Traits parameter
- * is substituted with a model of this concept.
+ * is substituted by a model of this concept.
  *
  * \cgalRefines{ArrangementApproximateTraits_2,ArrangementConstructXMonotoneCurveTraits_2}
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt

@@ -205,6 +205,7 @@ implemented as peripheral classes or as free (global) functions.
 - `CGAL::Arrangement_2::Halfedge`
 - `CGAL::Arrangement_2::Face`
 - `CGAL::Arr_dcel_base<V,H,F>`
+- `CGAL::Arr_dcel<Traits,V,H,F>`
 - `CGAL::Arr_default_dcel<Traits>`
 - `CGAL::Arr_face_extended_dcel<Traits,FData,V,H,F>`
 - `CGAL::Arr_extended_dcel<Traits,VData,HData,FData,V,H,F>`

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/curve_history.tex

@@ -2,56 +2,62 @@
 \input{header}
 \pagestyle{empty}
 \begin{document}
-\psscalebox{1.8}{\arrset{1}%
+  \begin{tikzpicture}[scale=1]
-  \pspicture[](-1,-1)(8,7)
+    \myAxes{-1}{-1}{8}{7}
-  \arraxes(0,0)(-1,-1)(8,7)
+    \coordinate (a) at (0,0);
-  \arrMainVertex(0,0){1}
+    \coordinate (b) at (0,3);
-  \arrMainVertex(0,3){2}
+    \coordinate (d) at (2,3);
-  \arrEmptyVertex(1,3){3}
+    \coordinate (j) at (4,3);
-  \arrMainVertex(2,3){4}
+    \coordinate (l) at (5,3);
-  \arrMainVertex(2,6){5}
+    %
-  \arrMainVertex(3,1){6}
+    \arrMainVertexZ(a){1}
-  \arrEmptyVertex(3,3){7}
+    \arrMainVertexZ(b){2}
-  \arrMainVertex(3,4){8}
+    \arrIntersectionVertexZ(1,3){3}
-  \arrMainVertex(3,5){9}
+    \arrMainVertexZ(d){4}
-  \arrMainVertex(4,3){10}
+    \arrMainVertexZ(2,6){5}
-  \arrEmptyVertex(4,4){11}
+    \arrMainVertexZ(3,1){6}
-  \arrMainVertex(5,3){12}
+    \arrIntersectionVertexZ(3,3){7}
-  \arrMainVertex(6,4){13}
+    \arrMainVertexZ(3,4){8}
-  \arrMainVertex(7,1){14}
+    \arrMainVertexZ(3,5){9}
-  \arrCrossVertex(4,6){x1}\uput[-45]{0}(4,6){$q_1$}
+    \arrMainVertexZ(j){10}
-  \arrCrossVertex(6,2){x2}\uput[45]{0}(6,2){$q_2$}
+    \arrIntersectionVertexZ(4,4){11}
-  \arrCrossVertex(2,4){x3}\uput[45]{0}(2,4){$q_3$}
+    \arrMainVertexZ(l){12}
-  %
+    \arrMainVertexZ(6,4){13}
-  \ncline[linewidth=1pt,linecolor=blue]{1}{3}
+    \arrMainVertexZ(7,1){14}
-  \ncline[linewidth=1pt,linecolor=blue]{3}{5}
+    %
-  \ncline[linewidth=1pt,linecolor=blue]{5}{9}
+    \draw[edge](1)--(3);
-  \ncline[linewidth=1pt,linecolor=blue]{9}{11}
+    \draw[edge](3)--(5);
-  \ncline[linewidth=1pt,linecolor=blue]{11}{12}
+    \draw[edge](5)--(9);
-  \ncline[linewidth=1pt,linecolor=blue]{12}{14}
+    \draw[edge](9)--(11);
-  %
+    \draw[edge](11)--(12);
-  \ncline[linewidth=1pt,linecolor=blue]{6}{7}
+    \draw[edge](12)--(14);
-  \ncline[linewidth=1pt,linecolor=blue]{7}{8}\Bput[1pt]{\textcolor{blue}{$s_2$}}
+    %
-  \ncline[linewidth=1pt,linecolor=blue]{8}{9}
+    \draw[edge](6)--node[sloped,below,pos=0.4] {\textcolor{blue}{$s_2$}} (7);
-  %
+    \draw[edge](7)--(8);
-  \ncline[linewidth=1pt,linecolor=blue]{8}{11}
+    \draw[edge](8)--(9);
-  \ncline[linewidth=1pt,linecolor=blue]{11}{13}
+    %
-  %
+    \draw[edge](8)--(11);
-  \ncline[linewidth=1pt,linecolor=blue]{4}{7}
+    \draw[edge](11)--(13);
-  \ncline[linewidth=1pt,linecolor=blue]{7}{10}
+    %
-  \ncline[linewidth=1pt,linecolor=blue]{10}{12}
+    \draw[edge](4)--(7);
-  %
+    \draw[edge](7)--(10);
-  \ncline[linestyle=dashed,dash=2pt 2pt,linewidth=1pt,linecolor=red]{2}{3}
+    \draw[edge](10)--(12);
-  \ncline[linestyle=dashed,dash=2pt 2pt,linewidth=1pt,linecolor=red]{3}{4}
+    %
-  \ncline[linestyle=dashed,dash=2pt 2pt,linewidth=1pt,linecolor=red]{4}{7}
+    \draw[edge=red,dashed](2)--(3);
-  \ncline[linestyle=dashed,dash=2pt 2pt,linewidth=1pt,linecolor=red]{7}{10}
+    \draw[edge=red,dashed](3)--(4);
-  %
+    \draw[edge=red,dashed](4)--(7);
-  \pnode(2,2){a}\uput{2pt}[-90]{0}(2,2){\textcolor{red}{$s_1$}}
+    \draw[edge=red,dashed](7)--(10);
-  \nccurve[linewidth=0.25pt,angleA=-90,angleB=90]{2}{a}
+    %
-  \nccurve[linewidth=0.25pt,angleA=-90,angleB=90]{10}{a}
+    \arrQueryLabeledVertexZ[-45](4,6){x1}{$q_1$}
-  \pnode(3.5,2){b}\uput{2pt}[-90]{0}(3.5,2){\textcolor{blue}{$s_3$}}
+    \arrQueryLabeledVertexZ[45](6,2){x2}{$q_2$}
-  \nccurve[linewidth=0.25pt,angleA=-90,angleB=90]{4}{b}
+    \arrQueryLabeledVertexZ[45](2,4){x3}{$q_3$}
-  \nccurve[linewidth=0.25pt,angleA=-90,angleB=90]{12}{b}
+    %
-  \endpspicture
+    \draw [decoration={calligraphic brace,
-}
+        raise=2pt,
+        amplitude=10pt,aspect=0.5},decorate,line width=0.2pt] (j)--(b)
+    node[midway,below=10pt,red]{$s_1$};
+    \draw [decoration={calligraphic brace,raise=2pt,
+        amplitude=10pt,aspect=0.5},decorate,line width=0.2pt] (d)--(l)
+    node[midway,above=10pt,blue]{$s_3$};
+  \end{tikzpicture}
 \end{document}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/header.tex

@@ -11,7 +11,7 @@
 % ======== Math ===============================================================
 \usepackage{amsmath,amscd,amsthm}
 \usepackage{empheq}
-
+\usepackage{bm}
 % ======== pdf, url and hyperlink =============================================
 % \usepackage{url}
 \usepackage{hyperref}
@@ -42,24 +42,33 @@
 % graphicx.
 \usepackage{tikz}
 \usepackage{pgfplots}
+% \pgfplotsset{compat=1.16}
+\pgfplotsset{compat=newest}
+\usepgfplotslibrary{fillbetween}
+\usepackage{tikz-3dplot}
 \usepackage{mathptmx}
-\usetikzlibrary{calc}
+\usetikzlibrary{arrows,arrows.meta}
+\usetikzlibrary{automata}
 \usetikzlibrary{backgrounds}
+\usetikzlibrary{calligraphy}
+\usetikzlibrary{calc}
+\usetikzlibrary{chains}
+\usetikzlibrary{cd}
 \usetikzlibrary{decorations.pathmorphing}
 \usetikzlibrary{decorations.markings}
 \usetikzlibrary{decorations.pathreplacing}
-\usetikzlibrary{patterns}
-\usetikzlibrary{matrix}
 \usetikzlibrary{fit}
-\usetikzlibrary{arrows,arrows.meta}
+\usetikzlibrary{intersections}
-\usetikzlibrary{automata}
+\usetikzlibrary{math}
+\usetikzlibrary{matrix}
+\usetikzlibrary{patterns}
 \usetikzlibrary{positioning}
 \usetikzlibrary{shapes}
-\usetikzlibrary{chains}
+\usetikzlibrary{shapes.geometric}
+\usetikzlibrary{shapes.misc}
+\usetikzlibrary{shadows.blur}
 \usetikzlibrary{spy}
-\usetikzlibrary{intersections}
 \usetikzlibrary{through}
-\usetikzlibrary{cd}
 \usepackage{tikz-3dplot}
 %\usetikzlibrary{quotes,angles,graph}
 \tikzset{%
@@ -72,6 +81,23 @@
   point/.default=red,
   halfedge/.style={-{Stealth[left,scale=1.5]},commutative diagrams/shift left=#1},
   halfedge/.default=3pt
+  edge/.style={line width=0.8pt,draw=#1},
+  edge/.default=blue,
+  halfedge/.style={-{Stealth[left,scale=1.5]},
+    commutative diagrams/shift left=#1},
+  halfedge/.default=3pt,
+  cross/.style={#1,cross out,draw,very thick,rotate=0,
+    minimum size=2*(4pt-\pgflinewidth),inner sep=0pt,outer sep=0pt},
+  cross/.default=red
+}
+\pgfplotsset{%
+  axisLimits/.style={enlarge x limits={abs value=\axisLimitsAbsValue,auto},
+    enlarge y limits={abs value=\axisLimitsAbsValue,auto}}}
+\newlength{\axisLimitsAbsValue}\setlength{\axisLimitsAbsValue}{0.08cm}
+% ------------------------------------------------------------------------------
+\newcommand{\mySimpleAxes}[4]{%
+  \draw[-{Stealth[scale=1.5]}] (#1,0)--(#3,0) node[right]{$x$};
+  \draw[-{Stealth[scale=1.5]}] (0,#2)--(0,#4) node[above]{$y$};
 }
 % ------------------------------------------------------------------------------
 % #1 half length of tick

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/simple_arr.tex

@@ -2,33 +2,38 @@
 \input{header}
 \pagestyle{empty}
 \begin{document}
-\psscalebox{1.8}{\arrset{1}%
+\begin{tikzpicture}[scale=1.0,smooth]
-  \pspicture[](-3.1,-0.725)(3.1,1.709)
+  \begin{axis}[ticks=none,axis line style={draw=none},unit vector ratio*=1 1 1,
-  %
+      enlarge x limits={abs value=0.08,auto},
-  \pscustom[linecolor=blue,linewidth=0pt,fillstyle=hlines,hatchcolor=orange,hatchsep=2pt,hatchwidth=1pt]{%
+      enlarge y limits={abs value=0.08,auto},
-    \psplot{-2}{0}{0 x x mul x mul add x x mul add x 4 mul sub 1 add 8 div}
+      % The following miraculously solves the wierd shift in the intersection
-    \psplot{0}{-2}{0 x x mul x mul sub x x mul add x 4 mul add 1 add 8 div}
+      % computation
-  }
+      anchor=left of west
-  %
+    ]
-  \pscustom[linecolor=blue,linewidth=0pt,fillstyle=vlines,hatchcolor=orange,hatchsep=2pt,hatchwidth=1pt]{
+    % x^3+x^2-4x-8y=-1
-    \psplot{0}{2}{0 x x mul x mul add x x mul add x 4 mul sub 1 add 8 div}
+    % -x^3+x^2+4x-8y=-1
-    \psplot{2}{0}{0 x x mul x mul sub x x mul add x 4 mul add 1 add 8 div}
+    \addplot [draw=none,name path=f11,domain=-2:0]{(1-x^3+x^2+4*x)*0.125};
-  }
+    \addplot [draw=none,name path=f12,domain=0:-2]{(1+x^3+x^2-4*x)*0.125};
-  %
+    \addplot [draw=none,name path=f21,domain=0:2]{(1-x^3+x^2+4*x)/8.0};
-  \psplot[linecolor=blue]{-2.5}{3}{0 x x mul x mul sub x x mul add x 4 mul add 1 add 8 div}
+    \addplot [draw=none,name path=f22,domain=2:0]{(1+x^3+x^2-4*x)/8.0};
-  \psplot[linecolor=blue]{-3}{2.5}{0 x x mul x mul add x x mul add x 4 mul sub 1 add 8 div}
+    %
-  %
+    \addplot [name path global=A,color=blue,thick,domain=-2.5:3]
-  \arrMainVertex(-3,-0.625){1}
+             {(1-x^3+x^2+4*x)*0.125} coordinate[point,pos=0] coordinate[point];
-  \arrMainVertex( 3,-0.625){2}
+    \addplot [name path global=B,color=blue,thick,domain=-3:2.5]
-  \arrMainVertex(-2.5,1.609){3}
+             {(1+x^3+x^2-4*x)*0.125} coordinate[point,pos=0] coordinate[point];
-  \arrMainVertex( 2.5,1.609){4}
+    \coordinate [name intersections={of=A and B,name=x}];
-  \arrEmptyVertex(-2,0.625){x1}
+    %
-  \arrEmptyVertex( 2,0.625){x2}
+    \node[point=white] at (x-1) {};
-  \arrEmptyVertex(0,0.125){x3}
+    \node[point=white] at (x-2) {};
-  \rput(-2.5,1){\textcolor{blue}{$c_1$}}
+    \node[point=white] at (x-3) {};
-  \rput(-2.9,0.15){\textcolor{blue}{$c_2$}}
+    %
-  \rput(-1,0.3){\boldmath{$f_1$}}
+    \addplot[pattern={north east lines},pattern color=orange] fill between[of=f11 and f12];
-  \rput(1,0.3){\boldmath{$f_2$}}
+    \addplot[pattern={north west lines},pattern color=orange] fill between[of=f21 and f22];
-  \endpspicture
+    %
-}
+    \node at (-2.5,1){\textcolor{blue}{$c_1$}};
+    \node at (-2.9,0.15){\textcolor{blue}{$c_2$}};
+    \node at (-1,0.3){$\bm{f_1}$};
+    \node at (1,0.3){$\bm{f_2}$};
+  \end{axis}
+\end{tikzpicture}
 \end{document}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/unb_asymptote.tex

@@ -2,7 +2,7 @@
 \input{header}
 \pagestyle{empty}
 \begin{document}
-\psscalebox{1.8}{\arrset{0.9}%
+\psscalebox{1.0}{\arrset{0.75}%
   \begin{pspicture}(-3.5,-3.5)(2.1,2.1)
     \newpsstyle{SimpleHandle}{fillstyle=solid,fillcolor=white,framearc=0.5}
     \psframe[linewidth=0.25pt](-2,-2)(2,2)

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/fig_src/unb_dcel.tex

@@ -2,143 +2,134 @@
 \input{header}
 \pagestyle{empty}
 \begin{document}
-\psscalebox{1.8}{\arrset{1}%
+  \begin{tikzpicture}[scale=0.93]
-  \begin{pspicture}(0,0)(10,7)
+    \fill[lightyellow](0,0)rectangle(1,7);
-    \psframe*[linecolor=lightyellow](0,0)(1,7)
+    \fill[lightyellow](9,0)rectangle(10,7);
-    \psframe*[linecolor=lightyellow](9,0)(10,7)
+    \fill[lightyellow](1,0)rectangle(9,1);
-    \psframe*[linecolor=lightyellow](1,0)(9,1)
+    \fill[lightyellow](1,6)rectangle(9,7);
-    \psframe*[linecolor=lightyellow](1,6)(9,7)
+    \draw[line width=0.25pt](0,0)rectangle(10,7);
-    \psframe[linewidth=0.25pt](0,0)(10,7)
     %
-    \arrlvertex[225](1,1){bl}{$v_{\mathrm{bl}}$}
+    \arrMainLabeledVertexZ[225](1,1){bl}{$v_{\mathrm{bl}}$}
-    \arrlvertex[135](1,6){tl}{$v_{\mathrm{tl}}$}
+    \arrMainLabeledVertexZ[135](1,6){tl}{$v_{\mathrm{tl}}$}
-    \arrlvertex[315](9,1){br}{$v_{\mathrm{br}}$}
+    \arrMainLabeledVertexZ[315](9,1){br}{$v_{\mathrm{br}}$}
-    \arrlvertex[45](9,6){tr}{$v_{\mathrm{tr}}$}
+    \arrMainLabeledVertexZ[45](9,6){tr}{$v_{\mathrm{tr}}$}
-    \arrv[180](1,2.5){1}
+    \arrvZ[180](1,2.5){1}
-    \arrv[180](1,4){2}
+    \arrvZ[180](1,4){2}
-    \arrv[180](1,5){3}
+    \arrvZ[180](1,5){3}
-    \arrv[270](5,1){4}
+    \arrvZ[270](5,1){4}
-    \arrv[90](5,6){5}
+    \arrvZ[90](5,6){5}
-    \arrv[0](9,1.5){6}
+    \arrvZ[0](9,1.5){6}
-    \arrv[0](9,4){7}
+    \arrvZ[0](9,4){7}
-    \arrv[0](9,5.5){8}
+    \arrvZ[0](9,5.5){8}
     %
-    \arrEmptyIntersectionVertex(1,4)(9,4)(5,1)(5,6){9}
+    \node[point=white] (9) at (intersection of 2--7 and 4--5) {};
-    \arrEmptyIntersectionVertex(1,4)(9,4)(1,5)(9,1.5){10}
+    \node[point=white] (10) at (intersection of 2--7 and 3--6) {};
-    \arrEmptyIntersectionVertex(1,5)(9,1.5)(5,1)(5,6){11}
+    \node[point=white] (11) at (intersection of 3--6 and 4--5) {};
-    \arrEmptyIntersectionVertex(1,5)(9,1.5)(1,2.5)(9,5.5){12}
+    \node[point=white] (12) at (intersection of 3--6 and 1--8) {};
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{bl}{1}
+    \draw[dashed,line width=0.5pt](bl)--(1);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{bl}{1}
+    \draw[halfedge](bl)to(1);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepB=1pt]{->}{1}{bl}
+    \draw[halfedge](1)to(bl);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{1}{2}
+    \draw[dashed,line width=0.5pt](1)--(2);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{1}{2}
+    \draw[halfedge](1)to(2);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt,nodesepB=2pt]{->}{2}{1}
+    \draw[halfedge,shorten >=1pt](2)to(1);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{2}{3}
+    \draw[dashed,line width=0.5pt](2)--(3);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{2}{3}
+    \draw[halfedge](2)to(3);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=3pt,nodesepB=1pt]{->}{3}{2}
+    \draw[halfedge,shorten <=2pt](3)to(2);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{3}{tl}
+    \draw[dashed,line width=0.5pt](3)--(tl);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{3}{tl}
+    \draw[halfedge](3)to(tl);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt]{->}{tl}{3}
+    \draw[halfedge](tl)to(3);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{tl}{5}
+    \draw[dashed,line width=0.5pt](tl)--(5);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{tl}{5}
+    \draw[halfedge](tl)to(5);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt,nodesepB=1pt]{->}{5}{tl}
+    \draw[halfedge](5)to(tl);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{5}{tr}
+    \draw[dashed,line width=0.5pt](5)--(tr);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{5}{tr}
+    \draw[halfedge](5)to(tr);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt,nodesepB=1pt]{->}{tr}{5}
+    \draw[halfedge](tr)to(5);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{tr}{8}
+    \draw[dashed,line width=0.5pt](tr)--(8);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{tr}{8}
+    \draw[halfedge](tr)to(8);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepB=1pt]{->}{8}{tr}
+    \draw[halfedge](8)to(tr);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{8}{7}
+    \draw[dashed,line width=0.5pt](8)--(7);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{8}{7}
+    \draw[halfedge](8)to(7);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt,nodesepB=2pt]{->}{7}{8}
+    \draw[halfedge,shorten >=1pt](7)to(8);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{7}{6}
+    \draw[dashed,line width=0.5pt](7)--(6);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{7}{6}
+    \draw[halfedge](7)to(6);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=3pt,nodesepB=1pt]{->}{6}{7}
+    \draw[halfedge,shorten <=1.8pt](6)to(7);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{6}{br}
+    \draw[dashed,line width=0.5pt](6)--(br);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{6}{br}
+    \draw[halfedge](6)to(br);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt]{->}{br}{6}
+    \draw[halfedge](br)to(6);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{br}{4}
+    \draw[dashed,line width=0.5pt](br)--(4);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{br}{4}
+    \draw[halfedge](br)to(4);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt,nodesepB=1pt]{->}{4}{br}
+    \draw[halfedge](4)to(br);
     %
-    \ncline[linestyle=dashed,linewidth=0.5pt]{4}{bl}
+    \draw[dashed,line width=0.5pt](4)--(bl);
-    \ncline[linewidth=0.5pt,offset=3pt]{->}{4}{bl}
+    \draw[halfedge](4)to(bl);
-    \ncline[linewidth=0.5pt,offset=3pt,nodesepA=1pt,nodesepB=1pt]{->}{bl}{4}
+    \draw[halfedge](bl)to(4);
     %
-    %\arredge{3}{10}
+    \draw[edge](3)--(10);
-    \ncline[linewidth=0.5pt,linecolor=blue]{3}{10}
+    \draw[halfedge](3)to(10);
-    \ncline[linewidth=0.25pt,offset=3pt]{->}{3}{10}
+    \draw[halfedge,shorten <=11pt,shorten >=1.6pt](10)to(3);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=12pt,nodesepB=2pt]{->}{10}{3}
+    \draw[edge](10)--(12);
-    %\arredge{10}{12}
+    \draw[halfedge,shorten <=4pt](12)to(10);
-    \ncline[linewidth=0.5pt,linecolor=blue]{10}{12}
+    \draw[halfedge,shorten <=10pt,shorten >=-1.8pt](10)to(12);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=6pt]{->}{12}{10}
+    \draw[edge](12)--(11);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=16pt,nodesepB=-2pt]{->}{10}{12}
+    \draw[halfedge](11)to(12);
-    %\arredge{12}{11}
+    \draw[halfedge,shorten <=4.2pt,shorten >=1.2pt](12)to(11);
-    \ncline[linewidth=0.5pt,linecolor=blue]{12}{11}
+    \draw[edge](11)--(6);
-    \ncline[linewidth=0.25pt,offset=3pt]{->}{11}{12}
+    \draw[halfedge,shorten >=1.6pt](11)to(6);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=6pt,nodesepB=2pt]{->}{12}{11}
+    \draw[halfedge,shorten >=1.6pt](6)to(11);
-    %\arredge{11}{6}
-    \ncline[linewidth=0.5pt,linecolor=blue]{11}{6}
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepB=2pt]{->}{11}{6}
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepB=2pt]{->}{6}{11}
 
-    %\arredge{1}{12}
+    \draw[edge](1)--(12);
-    \ncline[linewidth=0.5pt,linecolor=blue]{1}{12}
+    \draw[halfedge,shorten <=1.4pt,shorten >=4pt](1)to(12);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=2pt,nodesepB=5pt]{->}{1}{12}
+    \draw[halfedge](12)to(1);
-    \ncline[linewidth=0.25pt,offset=3pt]{->}{12}{1}
+    \draw[edge](12)--(9);
-    %\arredge{12}{9}
+    \draw[halfedge,shorten >=11.6pt](12)to(9);
-    \ncline[linewidth=0.5pt,linecolor=blue]{12}{9}
+    \draw[halfedge,shorten <=2pt,shorten >=3.6pt](9)to(12);
-    \ncline[linewidth=0.25pt,,offset=3pt,nodesepB=12pt]{->}{12}{9}
+    \draw[edge](9)--(8);
-    \ncline[linewidth=0.25pt,,offset=3pt,nodesepA=2pt,nodesepB=5pt]{->}{9}{12}
+    \draw[halfedge,shorten <=1.4pt](9)to(8);
-    %\arredge{9}{8}
+    \draw[halfedge,shorten <=1.8pt,shorten >=11.8pt](8)to(9);
-    \ncline[linewidth=0.5pt,linecolor=blue]{9}{8}
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=2pt]{->}{9}{8}
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=2pt,nodesepB=12pt]{->}{8}{9}
 
-    \ncline[linewidth=0.5pt,linecolor=blue]{2}{10}
+    \draw[edge](2)--(10);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=1pt,nodesepB=10pt]{->}{2}{10}
+    \draw[halfedge,shorten >=10pt](2)to(10);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepB=1pt]{->}{10}{2}
+    \draw[halfedge](10)to(2);
 
-    \ncline[linewidth=0.5pt,linecolor=blue]{10}{9}
+    \draw[edge](10)--(9);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepB=1pt]{->}{10}{9}
+    \draw[halfedge](10)to(9);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=16pt,nodesepB=10pt]{->}{9}{10}
+    \draw[halfedge,shorten <=13pt,shorten >=9.4pt](9)to(10);
 
-    \ncline[linewidth=0.5pt,linecolor=blue]{9}{7}
+    \draw[edge](9)--(7);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=16pt,nodesepB=1pt]{->}{9}{7}
+    \draw[halfedge,shorten <=13pt](9)to(7);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=1pt,nodesepB=1pt]{->}{7}{9}
+    \draw[halfedge](7)to(9);
 
-    \ncline[linewidth=0.5pt,linecolor=blue]{4}{11}
+    \draw[edge](4)--(11);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=1pt]{->}{4}{11}
+    \draw[halfedge](4)to(11);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=2pt,nodesepB=1pt]{->}{11}{4}
+    \draw[halfedge,shorten <=2pt](11)to(4);
 
-    \ncline[linewidth=0.5pt,linecolor=blue]{11}{9}
+    \draw[edge](11)--(9);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=1pt]{->}{9}{11}
+    \draw[halfedge](9)to(11);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=2pt,nodesepB=2pt]{->}{11}{9}
+    \draw[halfedge,shorten <=2pt,shorten >=1pt](11)to(9);
 
-    \ncline[linewidth=0.5pt,linecolor=blue]{9}{5}
+    \draw[edge](9)--(5);
-    \ncline[linewidth=0.25pt,offset=3pt,nodesepA=1pt,nodesepB=1pt]{->}{9}{5}
+    \draw[halfedge](9)to(5);
-    \ncline[linewidth=0.25pt,offset=3pt,,nodesepA=1pt,nodesepB=2pt]{->}{5}{9}
+    \draw[halfedge,shorten >=1.2pt](5)to(9);
     %
-    \rput(2,6.5){$\tilde{f}$}
+    \node at(2,6.5){$\tilde{f}$};
-    \rput(6.2,5.2){$f_1$}
+    \node at(6.2,5.2){$f_1$};
-    \rput(8.5,4.4){$f_2$}
+    \node at(8.5,4.4){$f_2$};
-    \rput(8.3,3.4){$f_3$}
+    \node at(8.3,3.4){$f_3$};
-    \rput(6.2,2){$f_4$}
+    \node at(6.2,2){$f_4$};
-    \rput(3.8,2){$f_5$}
+    \node at(3.8,2){$f_5$};
-    \rput(1.7,3.4){$f_6$}
+    \node at(1.7,3.4){$f_6$};
-    \rput(1.5,4.4){$f_7$}
+    \node at(1.5,4.4){$f_7$};
-    \rput(3.8,5.2){$f_8$}
+    \node at (3.8,5.2){$f_8$};
-  \end{pspicture}
+  \end{tikzpicture}
-}
 \end{document}

Arrangement_on_surface_2/include/CGAL/Arr_bounded_planar_topology_traits_2.h

@@ -26,6 +26,7 @@
  */
 
 #include <CGAL/Arr_tags.h>
+#include <CGAL/Arr_default_dcel.h>
 #include <CGAL/Arr_topology_traits/Arr_planar_topology_traits_base_2.h>
 #include <CGAL/Arr_topology_traits/Arr_bounded_planar_construction_helper.h>
 #include <CGAL/Arr_topology_traits/Arr_bounded_planar_insertion_helper.h>

Arrangement_on_surface_2/include/CGAL/Arr_conic_traits_2.h

@@ -3316,9 +3316,9 @@ public:
     //                sqrt((r - s)^2 + t^2)
     //
     const int or_fact = (cv.orientation() == CLOCKWISE) ? -1 : 1;
-    const Algebraic r = m_nt_traits->convert(or_fact * cv.r());
+    const Algebraic r = m_nt_traits->convert(Integer(or_fact * cv.r()));
-    const Algebraic s = m_nt_traits->convert(or_fact * cv.s());
+    const Algebraic s = m_nt_traits->convert(Integer(or_fact * cv.s()));
-    const Algebraic t = m_nt_traits->convert(or_fact * cv.t());
+    const Algebraic t = m_nt_traits->convert(Integer(or_fact * cv.t()));
     const Algebraic cos_2phi = (r - s) / m_nt_traits->sqrt((r-s)*(r-s) + t*t);
     const Algebraic zero = 0;
     const Algebraic one = 1;
@@ -3363,8 +3363,8 @@ public:
     //        4*r*s - t^2                4*r*s - t^2
     //
     // The denominator (4*r*s - t^2) must be negative for hyperbolas.
-    const Algebraic u = m_nt_traits->convert(or_fact * cv.u());
+    const Algebraic u = m_nt_traits->convert(Integer(or_fact * cv.u()));
-    const Algebraic v = m_nt_traits->convert(or_fact * cv.v());
+    const Algebraic v = m_nt_traits->convert(Integer(or_fact * cv.v()));
     const Algebraic det = 4*r*s - t*t;
     Algebraic x0, y0;
 
@@ -3803,9 +3803,9 @@ public:
     auto u = cv.u();
     auto v = cv.v();
     auto w = cv.w();
-    Algebraic* xs_end = m_nt_traits->solve_quadratic_equation(t*t - four*r*s,
+    Algebraic* xs_end = m_nt_traits->solve_quadratic_equation(Integer(t*t - four*r*s),
-                                                              two*t*v - four*s*u,
+                                                              Integer(two*t*v - four*s*u),
-                                                              v*v - four*s*w,
+                                                              Integer(v*v - four*s*w),
                                                               xs);
     auto n_xs = static_cast<int>(xs_end - xs);
 
@@ -3816,15 +3816,15 @@ public:
 
     if (CGAL::sign(cv.t()) == ZERO) {
       // The two vertical tangency points have the same y coordinate:
-      ys[0] = m_nt_traits->convert(-v) / m_nt_traits->convert(two*s);
+      ys[0] = m_nt_traits->convert(Integer(- v)) / m_nt_traits->convert(Integer(two * s));
       n_ys = 1;
     }
     else {
-      ys_end = m_nt_traits->solve_quadratic_equation(four*r*s*s - s*t*t,
+      ys_end = m_nt_traits->solve_quadratic_equation(Integer(four*r*s*s - s*t*t),
-                                                     four*r*s*v - two*s*t*u,
+                                                     Integer(four*r*s*v - two*s*t*u),
-                                                     r*v*v - t*u*v +
+                                                     Integer((r*v*v - t*u*v) + (t*t*w)),
-                                                     t*t*w,
                                                      ys);
+
       n_ys = static_cast<int>(ys_end - ys);
     }
 
@@ -3837,7 +3837,7 @@ public:
       }
       else {
         for (int j = 0; j < n_ys; ++j) {
-          if (CGAL::compare(m_nt_traits->convert(two*s) * ys[j],
+          if (CGAL::compare(m_nt_traits->convert(Integer(two*s)) * ys[j],
                             -(m_nt_traits->convert(t) * xs[i] +
                               m_nt_traits->convert(v))) == EQUAL)
           {
@@ -3904,10 +3904,11 @@ public:
     auto u = cv.u();
     auto v = cv.v();
     auto w = cv.w();
-    Algebraic* ys_end = m_nt_traits->solve_quadratic_equation(t*t - four*r*s,
+    Algebraic* ys_end = m_nt_traits->template
-                                                              two*t*u - four*r*v,
+      solve_quadratic_equation<Integer>(t*t - four*r*s,
-                                                              u*u - four*r*w,
+                                        two*t*u - four*r*v,
-                                                              ys);
+                                        u*u - four*r*w,
+                                        ys);
     auto n = static_cast<int>(ys_end - ys);
 
     // Compute the x coordinates and construct the horizontal tangency points.
@@ -3915,7 +3916,7 @@ public:
       // Having computed y, x is the single solution to the quadratic equation
       // above, and since its discriminant is 0, x is simply given by:
       Algebraic x = -(m_nt_traits->convert(t)*ys[i] + m_nt_traits->convert(u)) /
-        m_nt_traits->convert(two*r);
+        m_nt_traits->convert(Integer(two*r));
       ps[i] = Point_2(x, ys[i]);
     }
 

Arrangement_on_surface_2/include/CGAL/Arr_dcel.h

@@ -0,0 +1,69 @@
+// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s): Ron Wein        <wein@post.tau.ac.il>
+//            Baruch Zukerman <baruchzu@post.tau.ac.il>
+//            Efi Fogel       <efifogel@gmail.com>
+
+#ifndef CGAL_ARR_DCEL_H
+#define CGAL_ARR_DCEL_H
+
+#include <CGAL/license/Arrangement_on_surface_2.h>
+
+#include <CGAL/disable_warnings.h>
+
+/*! \file
+ * The definition of the Arr_dcel<Traits> class.
+ */
+
+#include <CGAL/Arr_dcel_base.h>
+
+namespace CGAL {
+
+/*! \class
+ * The arrangement DCEL class.
+ * The Traits parameters corresponds to a geometric traits class, which
+ * defines the Point_2 and X_monotone_curve_2 types.
+ */
+template <typename Traits,
+          typename V = Arr_vertex_base<typename Traits::Point_2>,
+          typename H = Arr_halfedge_base<typename Traits::X_monotone_curve_2>,
+          typename F = Arr_face_base>
+class Arr_dcel : public Arr_dcel_base<V, H, F> {
+public:
+  /*! \struct
+   * An auxiliary structure for rebinding the DCEL with a new traits class.
+   */
+  template <typename T>
+  struct rebind {
+  private:
+    using Pnt = typename T::Point_2;
+    using Xcv = typename T::X_monotone_curve_2;
+    using Rebind_v = typename V::template rebind<Pnt>;
+    using V_other = typename Rebind_v::other;
+    using Rebind_h = typename H::template rebind<Xcv>;
+    using H_other = typename Rebind_h::other;
+
+  public:
+    using other = Arr_dcel<T, V_other, H_other, F>;
+  };
+
+  /*! Default constructor. */
+  Arr_dcel() {}
+
+  /*! Destructor. */
+  virtual ~Arr_dcel() {}
+};
+
+} //namespace CGAL
+
+#include <CGAL/enable_warnings.h>
+
+#endif

Arrangement_on_surface_2/include/CGAL/Arr_dcel_base.h

@@ -8,8 +8,9 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Ron Wein <wein@post.tau.ac.il>
+// Author(s): Ron Wein          <wein@post.tau.ac.il>
-//                 (based on old version by: Iddo Hanniel and Oren Nechushtan)
+//            Efi Fogel         <efif@post.tau.ac.il>
+//            (based on old version by: Iddo Hanniel and Oren Nechushtan)
 
 #ifndef CGAL_ARR_DCEL_BASE_H
 #define CGAL_ARR_DCEL_BASE_H
@@ -23,11 +24,12 @@
  * peripheral records.
  */
 
-#include <CGAL/basic.h>
-#include <CGAL/Arr_enums.h>
 #include <list>
 #include <map>
-#include <CGAL/N_step_adaptor_derived.h>
+
+#include <CGAL/basic.h>
+#include <CGAL/Arr_enums.h>
+#include <CGAL/iterator.h>
 #include <CGAL/In_place_list.h>
 #include <CGAL/function_objects.h>
 #include <CGAL/Iterator_project.h>

Arrangement_on_surface_2/include/CGAL/Arr_default_dcel.h

@@ -1,4 +1,4 @@
-// Copyright (c) 2005,2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
+// Copyright (c) 2023 Tel-Aviv University (Israel).
 // All rights reserved.
 //
 // This file is part of CGAL (www.cgal.org).
@@ -8,8 +8,7 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Ron Wein        <wein@post.tau.ac.il>
+// Author(s): Efi Fogel       <efifogel@gmail.com>
-//                 Baruch Zukerman <baruchzu@post.tau.ac.il>
 
 #ifndef CGAL_ARR_DEFAULT_DCEL_H
 #define CGAL_ARR_DEFAULT_DCEL_H
@@ -19,46 +18,19 @@
 #include <CGAL/disable_warnings.h>
 
 /*! \file
- * The definition of the Arr_default_dcel<Traits> class.
+ * The definition of the Arr_default_dcel<Traits> type.
  */
 
-#include <CGAL/Arr_dcel_base.h>
+#include <CGAL/Arr_dcel.h>
 
 namespace CGAL {
 
-/*! \class
+/*! The default arrangement DCEL type.
- * The default arrangement DCEL class.
  * The Traits parameters corresponds to a geometric traits class, which
  * defines the Point_2 and X_monotone_curve_2 types.
  */
-template <class Traits_>
+template <typename Traits> using Arr_default_dcel = Arr_dcel<Traits>;
-class Arr_default_dcel :
-  public Arr_dcel_base<Arr_vertex_base<typename Traits_::Point_2>,
-                       Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
-                       Arr_face_base>
-{
-public:
-
-  /*! \struct
-   * An auxiliary structure for rebinding the DCEL with a new traits class.
-   */
-  template<typename T>
-  struct rebind
-  {
-    typedef Arr_default_dcel<T> other;
-  };
-
-  /*! Default constructor. */
-  Arr_default_dcel()
-  {}
-
-  /*! Destructor. */
-  virtual ~Arr_default_dcel()
-  {}
-};
 
 } //namespace CGAL
 
-#include <CGAL/enable_warnings.h>
-
 #endif

Arrangement_on_surface_2/include/CGAL/Arr_default_overlay_traits.h

@@ -8,8 +8,9 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Ron Wein <wein@post.tau.ac.il>
+// Author(s): Ron Wein          <wein@post.tau.ac.il>
-//                 Baruch Zukerman <baruchzu@post.tau.ac.il>
+//            Baruch Zukerman   <baruchzu@post.tau.ac.il>
+//            Efi Fogel         <efif@post.tau.ac.il>
 
 #ifndef CGAL_ARR_DEFAULT_OVERLAY_TRAITS_H
 #define CGAL_ARR_DEFAULT_OVERLAY_TRAITS_H
@@ -23,7 +24,6 @@
  * Definition of default overlay-traits classes.
  */
 
-#include <CGAL/Arr_default_dcel.h>
 #include <CGAL/Arr_extended_dcel.h>
 #include <CGAL/Surface_sweep_2/Arr_default_overlay_traits_base.h>
 

Arrangement_on_surface_2/include/CGAL/Arr_extended_dcel.h

@@ -8,8 +8,8 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 //
-// Author(s)     : Ron Wein    <wein@post.tau.ac.il>
+// Author(s): Ron Wein    <wein@post.tau.ac.il>
-//                 Efi Fogel   <efif@post.tau.ac.il>
+//            Efi Fogel   <efif@post.tau.ac.il>
 
 #ifndef CGAL_ARR_EXTENDED_DCEL_H
 #define CGAL_ARR_EXTENDED_DCEL_H
@@ -26,142 +26,115 @@
 
 namespace CGAL {
 
-/*!
+/*! \class
- * \class
  * An extended DCEL vertex with auxiliary data field.
  */
-template <class VertexBase_, typename VertexData_>
+template <typename VertexBase, typename VertexData>
-class Arr_extended_vertex : public VertexBase_
+class Arr_extended_vertex : public VertexBase {
-{
+  using Vertex_base = VertexBase;
-  typedef Arr_extended_vertex<VertexBase_, VertexData_>  Self;
+  using Vertex_data = VertexData;
-  typedef VertexBase_                                    Base;
+
+  using Self = Arr_extended_vertex<Vertex_base, Vertex_data>;
 
 public:
-  typedef VertexData_                                     Data;
+  typedef Vertex_data                                    Data;
 
 private:
-
+  Data m_data;       // The auxiliary data field.
-  Data       m_data;       // The auxiliary data field.
 
 public:
-
   /*! Get the auxiliary data (const version). */
-  const Data& data () const
+  const Data& data() const { return m_data; }
-  {
-    return (m_data);
-  }
 
   /*! Get the auxiliary data (non-const version). */
-  Data& data ()
+  Data& data() { return m_data; }
-  {
-    return (m_data);
-  }
 
   /*! Set the auxiliary data. */
-  void set_data (const Data& data)
+  void set_data(const Data& data) { m_data = data; }
-  {
-    m_data = data;
-  }
 
   /*! Assign from another vertex. */
-  virtual void assign (const Base& v)
+  virtual void assign(const Vertex_base& v) {
-  {
+    Vertex_base::assign(v);
-    Base::assign (v);
+    const Self& ex_v = static_cast<const Self&>(v);
-
-    const Self&  ex_v = static_cast<const Self&>(v);
     m_data = ex_v.m_data;
   }
+
+  template <typename Point_>
+  struct rebind {
+    using Point_2 = Point_;
+    using other = typename Vertex_base::template rebind<Point_2>;
+  };
 };
 
-/*!
+/*! \class
- * \class
  * An extended DCEL halfedge with auxiliary data field.
  */
-template <class HalfedgeBase_, typename HalfedgeData_>
+template <typename HalfedgeBase, typename HalfedgeData>
-class Arr_extended_halfedge : public HalfedgeBase_
+class Arr_extended_halfedge : public HalfedgeBase {
-{
+  using Halfedge_base = HalfedgeBase;
-  typedef Arr_extended_halfedge<HalfedgeBase_, HalfedgeData_>  Self;
+  using Halfedge_data = HalfedgeData;
-  typedef HalfedgeBase_                                        Base;
+
+  using Self = Arr_extended_halfedge<Halfedge_base, Halfedge_data>;
 
 public:
-  typedef HalfedgeData_                                        Data;
+  typedef Halfedge_data                                       Data;
 
 private:
-
+  Data m_data;       // The auxiliary data field.
-  Data       m_data;       // The auxiliary data field.
 
 public:
-
   /*! Get the auxiliary data (const version). */
-  const Data& data () const
+  const Data& data() const { return m_data; }
-  {
-    return (m_data);
-  }
 
   /*! Get the auxiliary data (non-const version). */
-  Data& data ()
+  Data& data() { return m_data; }
-  {
-    return (m_data);
-  }
 
   /*! Set the auxiliary data. */
-  void set_data (const Data& data)
+  void set_data(const Data& data) { m_data = data; }
-  {
-    m_data = data;
-  }
 
-  /*! Assign from another vertex. */
+  /*! Assign from another halfedge. */
-  virtual void assign (const Base& he)
+  virtual void assign(const Halfedge_base& he) {
-  {
+    Halfedge_base::assign(he);
-    Base::assign (he);
+    const Self& ex_he = static_cast<const Self&>(he);
-
-    const Self&  ex_he = static_cast<const Self&>(he);
     m_data = ex_he.m_data;
   }
+
+  template <typename XMonotoneCurve>
+  struct rebind {
+    using X_monotonote_curve_2 = XMonotoneCurve;
+    using other = typename Halfedge_base::template rebind<X_monotonote_curve_2>;
+  };
 };
 
-/*!
+/*! \class
- * \class
  * An extended DCEL face with auxiliary data field.
  */
-template <class FaceBase_, typename FaceData_>
+template <typename FaceBase, typename FaceData>
-class Arr_extended_face : public FaceBase_
+class Arr_extended_face : public FaceBase {
-{
+  using Face_base = FaceBase;
-  typedef Arr_extended_face<FaceBase_, FaceData_>  Self;
+  using Face_data = FaceData;
-  typedef FaceBase_                                Base;
+
+  using Self = Arr_extended_face<Face_base, Face_data>;
 
 public:
-  typedef FaceData_                                Data;
+  typedef Face_data                               Data;
 
 private:
-
+  Data m_data;       // The auxiliary data field.
-  Data       m_data;       // The auxiliary data field.
 
 public:
-
   /*! Get the auxiliary data (const version). */
-  const Data& data () const
+  const Data& data() const { return m_data; }
-  {
-    return (m_data);
-  }
 
   /*! Get the auxiliary data (non-const version). */
-  Data& data ()
+  Data& data() { return m_data; }
-  {
-    return (m_data);
-  }
 
   /*! Set the auxiliary data. */
-  void set_data (const Data& data)
+  void set_data(const Data& data) { m_data = data; }
-  {
-    m_data = data;
-  }
-
-  /*! Assign from another vertex. */
-  virtual void assign (const Base& f)
-  {
-    Base::assign (f);
 
+  /*! Assign from another face. */
+  virtual void assign(const Face_base& f) {
+    Face_base::assign(f);
     const Self&  ex_f = static_cast<const Self&>(f);
     m_data = ex_f.m_data;
   }
@@ -173,49 +146,41 @@ public:
  * defines the Point_2 and X_monotone_curve_2 types.
  * The FaceData parameter specifies the object type stored with each face.
  */
-template <class Traits_, typename FaceData_,
+template <typename Traits_, typename FaceData,
-          class VertexBase_ = Arr_vertex_base<typename Traits_::Point_2>,
+          typename VertexBase = Arr_vertex_base<typename Traits_::Point_2>,
-          class HalfedgeBase_ =
+          typename HalfedgeBase =
-                        Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
+            Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
-          class FaceBase_ = Arr_face_base>
+          typename FaceBase = Arr_face_base>
 class Arr_face_extended_dcel :
-  public Arr_dcel_base<VertexBase_,
+  public Arr_dcel_base<VertexBase, HalfedgeBase,
-                       HalfedgeBase_,
+                       Arr_extended_face<FaceBase, FaceData>> {
-                       Arr_extended_face<FaceBase_, FaceData_> >
-{
 public:
-
+  using Face_base = FaceBase;
-  typedef FaceData_                    Face_data;
+  using Face_data = FaceData;
 
   /*! \struct
    * An auxiliary structure for rebinding the DCEL with a new traits class.
    */
-  template<typename T>
+  template <typename T>
-  class rebind
+  class rebind {
-  {
+  private:
-    typedef typename VertexBase_::template rebind
+    using Pnt = typename T::Point_2;
-                        <typename T::Point_2>              Rebind_vertex;
+    using Xcv = typename T::X_monotone_curve_2;
-    typedef typename Rebind_vertex::other                  Vertex_base;
+    using Rebind_vertex = typename VertexBase::template rebind<Pnt>;
-    typedef typename HalfedgeBase_::template rebind
+    using Vertex_other = typename Rebind_vertex::other;
-                        <typename T::X_monotone_curve_2>   Rebind_halfedge;
+    using Rebind_halfedge = typename HalfedgeBase::template rebind<Xcv>;
-    typedef typename Rebind_halfedge::other                Halfedge_base;
+    using Halfedge_other = typename Rebind_halfedge::other;
 
   public:
-
+    using other = Arr_face_extended_dcel<T, Face_data, Vertex_other,
-    typedef Arr_face_extended_dcel<T,
+                                         Halfedge_other, Face_base>;
-                                   Face_data,
-                                   Vertex_base,
-                                   Halfedge_base,
-                                   FaceBase_>              other;
   };
 
   /*! Default constructor. */
-  Arr_face_extended_dcel ()
+  Arr_face_extended_dcel() {}
-  {}
 
   /*! Destructor. */
-  virtual ~Arr_face_extended_dcel ()
+  virtual ~Arr_face_extended_dcel() {}
-  {}
 };
 
 /*! \class
@@ -225,54 +190,48 @@ public:
  * The VertexData, HalfedgeData and FaceData parameter specify the object types
  * stored with each vertex, halfedge and face, respectively.
  */
-template <class Traits_,
+template <typename Traits_,
-          typename VertexData_, typename HalfedgeData_, typename FaceData_,
+          typename VertexData, typename HalfedgeData, typename FaceData,
-          class VertexBase_ = Arr_vertex_base<typename Traits_::Point_2>,
+          typename VertexBase = Arr_vertex_base<typename Traits_::Point_2>,
-          class HalfedgeBase_ =
+          typename HalfedgeBase =
-                        Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
+            Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
-          class FaceBase_ = Arr_face_base>
+          typename FaceBase = Arr_face_base>
 class Arr_extended_dcel :
-  public Arr_dcel_base<Arr_extended_vertex<VertexBase_, VertexData_>,
+  public Arr_dcel_base<Arr_extended_vertex<VertexBase, VertexData>,
-                       Arr_extended_halfedge<HalfedgeBase_, HalfedgeData_>,
+                       Arr_extended_halfedge<HalfedgeBase, HalfedgeData>,
-                       Arr_extended_face<FaceBase_, FaceData_> >
+                       Arr_extended_face<FaceBase, FaceData>> {
-{
 public:
-
+  using Vertex_data = VertexData;
-  typedef VertexData_                  Vertex_data;
+  using Halfedge_data = HalfedgeData;
-  typedef HalfedgeData_                Halfedge_data;
+  using Face_data = FaceData;
-  typedef FaceData_                    Face_data;
+  using Vertex_base = VertexBase;
+  using Halfedge_base = HalfedgeBase;
+  using Face_base = FaceBase;
 
   /*! \struct
    * An auxiliary structure for rebinding the DCEL with a new traits class.
    */
-  template<typename T>
+  template <typename T>
-  class rebind
+  struct rebind {
-  {
+  private:
-    typedef typename VertexBase_::template rebind
+    using Pnt = typename T::Point_2;
-                        <typename T::Point_2>              Rebind_vertex;
+    using Xcv = typename T::X_monotone_curve_2;
-    typedef typename Rebind_vertex::other                  Vertex_base;
+    using Rebind_vertex = typename VertexBase::template rebind<Pnt>;
-    typedef typename HalfedgeBase_::template rebind
+    using Vertex_other = typename Rebind_vertex::other;
-                        <typename T::X_monotone_curve_2>   Rebind_halfedge;
+    using Rebind_halfedge = typename HalfedgeBase::template rebind<Xcv>;
-    typedef typename Rebind_halfedge::other                Halfedge_base;
+    using Halfedge_other = typename Rebind_halfedge::other;
 
   public:
-
+    using other = Arr_extended_dcel<T,
-    typedef Arr_extended_dcel<T,
+                                    Vertex_data, Halfedge_data, Face_data,
-                              Vertex_data,
+                                    Vertex_other, Halfedge_other, Face_base>;
-                              Halfedge_data,
-                              Face_data,
-                              Vertex_base,
-                              Halfedge_base,
-                              FaceBase_>                   other;
   };
 
   /*! Default constructor. */
-  Arr_extended_dcel ()
+  Arr_extended_dcel() {}
-  {}
 
   /*! Destructor. */
-  virtual ~Arr_extended_dcel ()
+  virtual ~Arr_extended_dcel() {}
-  {}
 };
 
 } //namespace CGAL

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Circle_segment_2.h

@@ -1430,8 +1430,8 @@ protected:
     {
       // Actually compare the slopes.
       const bool swap_res = (sign_denom1 != sign_denom2);
-      const CoordNT A = (cv.y0() - y0())*p.x() + (y0()*cv.x0() - cv.y0()*x0());
+      const CoordNT A = NT(cv.y0() - y0())*p.x() + (y0()*cv.x0() - cv.y0()*x0());
-      const CoordNT B = (cv.x0() - x0())*p.y();
+      const CoordNT B = NT(cv.x0() - x0())*p.y();
 
       slope_res = CGAL::compare (A, B);
 

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Conic_arc_2.h

@@ -1110,9 +1110,9 @@ protected:
     //
     Nt_traits nt_traits;
     const int or_fact = (m_orient == CLOCKWISE) ? -1 : 1;
-    const Algebraic r = nt_traits.convert(or_fact * m_r);
+    const Algebraic r = nt_traits.convert(Integer(or_fact * m_r));
-    const Algebraic s = nt_traits.convert(or_fact * m_s);
+    const Algebraic s = nt_traits.convert(Integer(or_fact * m_s));
-    const Algebraic t = nt_traits.convert(or_fact * m_t);
+    const Algebraic t = nt_traits.convert(Integer(or_fact * m_t));
     const Algebraic cos_2phi = (r - s) / nt_traits.sqrt((r-s)*(r-s) + t*t);
     const Algebraic zero = 0;
     const Algebraic one = 1;
@@ -1158,8 +1158,8 @@ protected:
     //        4*r*s - t^2                4*r*s - t^2
     //
     // The denominator (4*r*s - t^2) must be negative for hyperbolas.
-    const Algebraic u = nt_traits.convert(or_fact * m_u);
+    const Algebraic u = nt_traits.convert(Integer(or_fact * m_u));
-    const Algebraic v = nt_traits.convert(or_fact * m_v);
+    const Algebraic v = nt_traits.convert(Integer(or_fact * m_v));
     const Algebraic det = 4*r*s - t*t;
     Algebraic x0, y0;
 

Arrangement_on_surface_2/include/CGAL/Arr_geometry_traits/Conic_intersections_2.h

@@ -64,8 +64,9 @@ int compute_resultant_roots(const Nt_traits& nt_traits,
   }
 
   // Act according to the degree of the first conic curve.
-  const typename Nt_traits::Integer two = 2;
+  typedef typename Nt_traits::Integer Integer;
-  typename Nt_traits::Integer c[5];
+  const Integer two = 2;
+  Integer c[5];
   unsigned int degree = 4;
   typename Nt_traits::Algebraic* xs_end;
 
@@ -73,7 +74,7 @@ int compute_resultant_roots(const Nt_traits& nt_traits,
     // The first curve has no quadratic coefficients, and represents a line.
     if (CGAL::sign (v1) == ZERO) {
       // The first line is u1*x + w1 = 0, therefore:
-      xs[0] = nt_traits.convert(-w1) / nt_traits.convert(u1);
+      xs[0] = nt_traits.convert(Integer(- w1)) / nt_traits.convert(u1);
       return 1;
     }
 
@@ -87,7 +88,7 @@ int compute_resultant_roots(const Nt_traits& nt_traits,
       // Return if the two lines are parallel
       if (CGAL::sign (c[1]) == ZERO) return 0;
 
-      xs[0] =  nt_traits.convert(-c[0]) / nt_traits.convert(c[1]);
+      xs[0] =  nt_traits.convert(Integer(- c[0])) / nt_traits.convert(c[1]);
       return 1;
     }
 

Arrangement_on_surface_2/include/CGAL/Arr_rat_arc/Algebraic_point_2.h

@@ -225,10 +225,11 @@ public:
         if (CGAL::compare(
                 CGAL::width(y_bfi),
                 CGAL::lower(CGAL::abs(y_bfi)) * eps)
-            == SMALLER)
+            == SMALLER){
           return std::make_pair(
               Bound(CGAL::lower(y_bfi)),
               Bound(CGAL::upper(y_bfi)));
+        }
       }
       else precision*=2;
     }
@@ -287,10 +288,11 @@ private:
       if (CGAL::zero_in(y_denom_bfi) == false)
       {
         BFI y_bfi(y_numer_bfi/y_denom_bfi);
-        if (CGAL::width(y_bfi) < eps )
+        if (CGAL::width(y_bfi) < eps ){
           return std::make_pair(
               Bound(CGAL::lower(y_bfi)),
               Bound(CGAL::upper(y_bfi)));
+        }
 
       }
       else precision*=2;

Arrangement_on_surface_2/include/CGAL/Arr_unb_planar_topology_traits_2.h

@@ -23,6 +23,7 @@
  */
 
 #include <CGAL/Arr_tags.h>
+#include <CGAL/Arr_default_dcel.h>
 #include <CGAL/Arr_topology_traits/Arr_planar_topology_traits_base_2.h>
 #include <CGAL/Arr_topology_traits/Arr_unb_planar_construction_helper.h>
 #include <CGAL/Arr_topology_traits/Arr_unb_planar_insertion_helper.h>

Arrangement_on_surface_2/include/CGAL/Arrangement_2.h

@@ -25,6 +25,7 @@
 #include <CGAL/Arr_tags.h>
 #include <CGAL/Arrangement_on_surface_2.h>
 #include <CGAL/Arrangement_2/Arr_default_planar_topology.h>
+#include <CGAL/Arr_default_dcel.h>
 
 namespace CGAL {
 

Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arr_traits_adaptor_2.h

@@ -577,7 +577,7 @@ public:
           return (m_self->compare_y_at_x_right_2_object()(xcv1, xcv2, left1));
       }
 
-      // We now that the curves do not share a common endpoint, and we can
+      // We know that the curves do not share a common endpoint, and we can
       // compare their relative y-position (which does not change to the left
       // of the given point p).
       return (m_self->compare_y_position_2_object()(xcv1, xcv2));

Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_2.h

@@ -39,11 +39,11 @@
 #include <CGAL/HalfedgeDS_iterator.h>
 #include <CGAL/Arrangement_2/Arrangement_2_iterators.h>
 #include <CGAL/In_place_list.h>
-#include <CGAL/Arr_default_dcel.h>
 #include <CGAL/Aos_observer.h>
 #include <CGAL/Arr_accessor.h>
 #include <CGAL/Arrangement_2/Arr_traits_adaptor_2.h>
 #include <CGAL/function_objects.h>
+#include <CGAL/iterator.h>
 #include <CGAL/Iterator_project.h>
 #include <CGAL/Iterator_transform.h>
 #include <CGAL/Arr_point_location_result.h>

Arrangement_on_surface_2/include/CGAL/Arrangement_on_surface_with_history_2.h

@@ -166,104 +166,75 @@ protected:
   // Forward declaration:
   class Curve_halfedges_observer;
 
+public:
   /*! \class
    * Extension of a curve with the set of edges that it induces.
    * Each edge is represented by one of the halfedges.
    */
   class Curve_halfedges : public Curve_2,
-                          public In_place_list_base<Curve_halfedges>
+                          public In_place_list_base<Curve_halfedges> {
-  {
+    using Gt = Geometry_traits_2;
+    using Btt = Base_topology_traits;
+    using Aos_wh = Arrangement_on_surface_with_history_2<Gt, Btt>;
+
     friend class Curve_halfedges_observer;
-    friend class Arrangement_on_surface_with_history_2<Geometry_traits_2,
+    friend class Arrangement_on_surface_with_history_2<Gt, Btt>;
-                                                       Base_topology_traits>;
+    friend class Arr_with_history_accessor<Aos_wh>;
-    friend class Arr_with_history_accessor<
-      Arrangement_on_surface_with_history_2<Geometry_traits_2,
-                                            Base_topology_traits> >;
 
   private:
-    typedef std::set<Halfedge_handle, Less_halfedge_handle>  Halfedges_set;
+    using Halfedges_set = std::set<Halfedge_handle, Less_halfedge_handle>;
 
     // Data members:
     Halfedges_set m_halfedges;
 
   public:
     /*! Default constructor. */
-    Curve_halfedges ()
+    Curve_halfedges() {}
-    {}
 
     /*! Constructor from a given curve. */
-    Curve_halfedges (const Curve_2& curve) :
+    Curve_halfedges(const Curve_2& curve) : Curve_2(curve) {}
-      Curve_2(curve)
-    {}
 
-    typedef typename Halfedges_set::iterator             iterator;
+    using iterator = typename Halfedges_set::iterator;
-    typedef typename Halfedges_set::const_iterator       const_iterator;
+    using const_iterator = typename Halfedges_set::const_iterator;
 
   private:
-
     /*! Get the number of edges induced by the curve. */
-    Size _size () const
+    Size size() const { return m_halfedges.size(); }
-    {
-      return (m_halfedges.size());
-    }
 
     /*! Get an iterator for the first edge in the set (const version). */
-    const_iterator _begin () const
+    const_iterator begin() const { return m_halfedges.begin(); }
-    {
-      return m_halfedges.begin();
-    }
 
     /*! Get an iterator for the first edge in the set (non-const version). */
-    iterator _begin ()
+    iterator begin() { return m_halfedges.begin(); }
-    {
-      return m_halfedges.begin();
-    }
 
     /*! Get a past-the-end iterator for the set edges (const version). */
-    const_iterator _end () const
+    const_iterator end() const { return m_halfedges.end(); }
-    {
-      return m_halfedges.end();
-    }
 
     /*! Get a past-the-end iterator for the set edges (non-const version). */
-    iterator _end ()
+    iterator end() { return m_halfedges.end(); }
-    {
-      return m_halfedges.end();
-    }
 
     /*! Insert an edge to the set. */
-    iterator _insert (Halfedge_handle he)
+    iterator _insert(Halfedge_handle he) {
-    {
       std::pair<iterator, bool> res = m_halfedges.insert(he);
       CGAL_assertion(res.second);
-      return (res.first);
+      return res.first;
     }
 
     /*! Erase an edge, given by its position, from the set. */
-    void _erase(iterator pos)
+    void erase(iterator pos) { m_halfedges.erase(pos); }
-    {
-      m_halfedges.erase(pos);
-      return;
-    }
 
     /*! Erase an edge from the set. */
-    void _erase (Halfedge_handle he)
+    void _erase(Halfedge_handle he) {
-    {
       size_t res = m_halfedges.erase(he);
-      if (res == 0)
+      if (res == 0) res = m_halfedges.erase(he->twin());
-        res = m_halfedges.erase(he->twin());
       CGAL_assertion(res != 0);
-      return;
     }
 
     /*! Cleat the edges set. */
-    void _clear ()
+    void clear() { m_halfedges.clear(); }
-    {
-      m_halfedges.clear();
-      return;
-    }
   };
 
+protected:
   typedef CGAL_ALLOCATOR(Curve_halfedges)               Curves_alloc;
   typedef In_place_list<Curve_halfedges, false>         Curve_halfedges_list;
 
@@ -505,16 +476,13 @@ public:
 
   /// \name Traversal of the edges induced by a curve.
   //@{
-  Size number_of_induced_edges (Curve_const_handle c) const
+  Size number_of_induced_edges (Curve_const_handle c) const { return c->size(); }
-  {
-    return (c->_size());
-  }
 
   Induced_edge_iterator
-  induced_edges_begin (Curve_const_handle c) const { return (c->_begin()); }
+  induced_edges_begin (Curve_const_handle c) const { return (c->begin()); }
 
   Induced_edge_iterator
-  induced_edges_end (Curve_const_handle c) const { return (c->_end()); }
+  induced_edges_end (Curve_const_handle c) const { return (c->end()); }
   //@}
 
   /// \name Manipulating edges.
@@ -646,12 +614,12 @@ protected:
   Size _remove_curve (Curve_handle ch)
   {
     // Go over all edges the given curve induces.
-    Curve_halfedges                           *p_cv = &(*ch);
+    Curve_halfedges* p_cv = &(*ch);
-    typename Curve_halfedges::const_iterator   it = ch->_begin();
+    Halfedge_handle he;
-    Halfedge_handle                            he;
+    Size n_removed = 0;
-    Size                                       n_removed = 0;
 
-    while (it != ch->_end()) {
+    typename Curve_halfedges::const_iterator it = ch->begin();
+    while (it != ch->end()) {
       // Check how many curves have originated the current edge.
       // Note we increment the iterator now, as the edge may be removed.
       he = *it;

Arrangement_on_surface_2/include/CGAL/Arrangement_with_history_2.h

@@ -9,6 +9,7 @@
 //
 //
 // Author(s): Ron Wein          <wein@post.tau.ac.il>
+//            Efi Fogel         <efif@post.tau.ac.il>
 
 #ifndef CGAL_ARRANGEMENT_WITH_HISTORY_2_H
 #define CGAL_ARRANGEMENT_WITH_HISTORY_2_H
@@ -23,6 +24,7 @@
 
 #include <CGAL/Arrangement_on_surface_with_history_2.h>
 #include <CGAL/Arrangement_2/Arr_default_planar_topology.h>
+#include <CGAL/Arr_default_dcel.h>
 
 namespace CGAL {
 

Arrangement_on_surface_2/include/CGAL/CORE_algebraic_number_traits.h

@@ -106,7 +106,7 @@ public:
       ix1 = scaled_x1.BigIntValue();
       ix2 = scaled_x2.BigIntValue();
 
-      if (CORE::abs (ix2 - ix1) > one)
+      if (CGAL::abs (ix2 - ix1) > one)
         break;
 
       // Scale the values by a factor of 2.
@@ -179,9 +179,9 @@ public:
         temp_gcd = numer_gcd;
 
         denom_lcm *= denom;
-        denom_lcm /= CORE::gcd (temp_lcm, denom);
+        denom_lcm /= CGAL::gcd (temp_lcm, denom);
 
-        numer_gcd = CORE::gcd (temp_gcd, numer);
+        numer_gcd = CGAL::gcd (temp_gcd, numer);
       }
 
       ++q_iter;
@@ -246,8 +246,8 @@ public:
 
     if (sign_disc == ZERO)
     {
-      // We have one real root with mutliplicity 2.
+      // We have one real root with multiplicity 2.
-      *oi = -Algebraic (b) / Algebraic (2*a);
+      *oi = -Algebraic (b) / Algebraic (NT(2*a));
       ++oi;
     }
     else if (sign_disc == POSITIVE)
@@ -255,7 +255,7 @@ public:
       // We have two distinct real roots. We return them in ascending order.
       const Algebraic      sqrt_disc = CGAL::sqrt (Algebraic (disc));
       const Algebraic      alg_b = b;
-      const Algebraic      alg_2a = 2*a;
+      const Algebraic      alg_2a = NT(2*a);
 
       if (sign_a == POSITIVE)
       {
@@ -334,7 +334,7 @@ public:
         temp_lcm = denom_lcm;
 
         denom_lcm *= denom;
-        denom_lcm /= CORE::gcd (temp_lcm, denom);
+        denom_lcm /= CGAL::gcd (temp_lcm, denom);
       }
 
       index--;

Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_2.h

@@ -865,7 +865,7 @@ void draw(const Arc_2& arc,
             get_pixel_coords(l, y_clip, pix_beg);
             get_pixel_coords(ptmp->left, it->second ? engine.y_max_r :
                 engine.y_min_r, pix_end);
-            if(CGAL_ABS(ptmp->left - l) <= engine.pixel_w_r*2) {
+            if(CGAL_ABS(Rational(ptmp->left - l)) <= engine.pixel_w_r*2) {
 
                 Coordinate_2 xy(Coordinate_1(pt), *support, arc.arcno());
                 Rational _;

Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_internals.h

@@ -91,8 +91,6 @@ struct Pixel_2_
     Integer sub_x, sub_y; // subpixel coordinates relative to pixel's boundary
                           // (always 0 for pixels)
 
-    Pixel_2_& operator =(const Pixel_2_& pix) = default;
-
     bool operator ==(const Pixel_2_& pix) const {
         return (
           x == pix.x && y == pix.y && level == pix.level &&
@@ -697,7 +695,7 @@ bool get_range_QF_1(int var, const NT& l_, const NT& r_, const NT& key,
             while(der_it != der_begin) {
                 --der_it;
 
-                e1 = xsum_abs * e1 + CGAL_ABS(x1 * z1);
+                e1 = xsum_abs * e1 + CGAL_ABS(NT(x1 * z1));
                 z1 = x0*z1 + x1*y1;
                 y1 = y1*x0 + x1*y0;
                 y0 = x0*y0 + extract(*cache_it)*(*der_it);
@@ -728,7 +726,7 @@ bool get_range_QF_1(int var, const NT& l_, const NT& r_, const NT& key,
         NT y0 = extract(*cache_it), y1(0), z1(0), e1(0);
         while(cache_it != begin) {
             --cache_it;
-            e1 = xsum_abs * e1 + CGAL_ABS(x1*z1);
+            e1 = xsum_abs * e1 + CGAL_ABS(NT(x1*z1));
             z1 = x0*z1 + x1*y1;
             y1 = y1*x0 + x1*y0;
             y0 = x0*y0 + extract(*cache_it);

Arrangement_on_surface_2/include/CGAL/Curved_kernel_via_analysis_2/gfx/Curve_renderer_traits.h

@@ -336,7 +336,7 @@ struct Curve_renderer_traits<CGAL::Interval_nt<true>, CORE::BigRat > :
 
 //! Specialization for \c CORE::BigFloat
 template <>
-struct Curve_renderer_traits<CORE::BigFloat, class CORE::BigRat>
+struct Curve_renderer_traits<CORE::BigFloat, CORE::BigRat>
          : public Curve_renderer_traits_base<CORE::BigFloat, CORE::BigInt,
                 CORE::BigRat> {
 
@@ -347,7 +347,7 @@ struct Curve_renderer_traits<CORE::BigFloat, class CORE::BigRat>
         typedef Integer result_type;
 
         Integer operator()(const Rational& x) const {
-            return x.BigIntValue();
+            return numerator(x)/denominator(x);
         }
     };
 
@@ -400,7 +400,7 @@ struct Curve_renderer_traits<CORE::BigRat, CORE::BigRat> :
         typedef Integer result_type;
 
         Integer operator()(const Rational& x) const {
-            return x.BigIntValue();
+            return numerator(x)/denominator(x);
         }
     };
 
@@ -409,9 +409,7 @@ struct Curve_renderer_traits<CORE::BigRat, CORE::BigRat> :
         typedef std::size_t result_type;
 
         inline result_type operator()(const Float& key) const {
-            const CORE::BigRatRep& rep = key.getRep();
+            return std::hash<Float>()(key);
-            std::size_t ret = reinterpret_cast<std::size_t>(&rep);
-            return ret;
         }
     };
 };

Arrangement_on_surface_2/test/Arrangement_on_surface_2/cgal_test.cmake

@@ -877,7 +877,7 @@ endfunction()
 #---------------------------------------------------------------------#
 function(test_polycurve_conic_traits)
 #  echo polycurve test starting
-  if(CGAL_DISABLE_GMP)
+  if(NOT CGAL_Core_FOUND)
     MESSAGE(STATUS "test_polycurve_conic_traits requires CORE and will not be executed")
     return()
   endif()
@@ -948,7 +948,7 @@ endfunction()
 # polycurve bezier traits
 #---------------------------------------------------------------------#
 function(test_polycurve_bezier_traits)
-  if(CGAL_DISABLE_GMP)
+  if(NOT CGAL_Core_FOUND)
     MESSAGE(STATUS "test_polycurve_bezier_traits requires CORE and will not be executed")
     return()
   endif()
@@ -1057,7 +1057,7 @@ endfunction()
 # conic traits
 #---------------------------------------------------------------------#
 function(test_conic_traits)
-  if(CGAL_DISABLE_GMP)
+  if(NOT CGAL_Core_FOUND)
     MESSAGE(STATUS "test_conic_traits requires CORE and will not be executed")
     return()
   endif()
@@ -1188,7 +1188,7 @@ endfunction()
 # bezier traits
 #---------------------------------------------------------------------#
 function(test_bezier_traits)
-  if(CGAL_DISABLE_GMP)
+  if(NOT CGAL_Core_FOUND)
     MESSAGE(STATUS "test_bezier_traits requires CORE and will not be executed")
     return()
   endif()
@@ -1235,7 +1235,7 @@ endfunction()
 # rational arc traits
 #---------------------------------------------------------------------#
 function(test_rational_arc_traits)
-  if(CGAL_DISABLE_GMP)
+  if(NOT CGAL_Core_FOUND)
     MESSAGE(STATUS "test_rational_arc_traits requires CORE and will not be executed")
     return()
   endif()
@@ -1302,7 +1302,7 @@ endfunction()
 #---------------------------------------------------------------------#
 function(test_algebraic_traits_core)
   #TODO: Adapt
-  if(CGAL_DISABLE_GMP)
+  if(NOT CGAL_Core_FOUND)
     MESSAGE(STATUS "test_algebraic_traits_core requires CORE and will not be executed")
     return()
   endif()

Arrangement_on_surface_2/test/Arrangement_on_surface_2/data/polycurves_bezier/points

@@ -7,18 +7,18 @@
 # We need the bezier curve (not polycurve) to contruct a bezier point.
 #
 # Point ID: 0
-r c 4 0 0 500 200 100 200 900 0 0.5
+r c 4 0 0 500 200 100 200 900 0 1/2
 # Point ID: 1
-r c 4 900 0 1200 600 1500 400 900 600 0.3
+r c 4 900 0 1200 600 1500 400 900 600 3/10
 # Point id: 2
-r c 4 0 0 100 200 500 200 900 0 0.0
+r c 4 0 0 100 200 500 200 900 0 0
 # Point id: 3
-r c 4 900 0 1200 300 1500 400 2000 450 1.0
+r c 4 900 0 1200 300 1500 400 2000 450 1
 # Point id: 4
-r c 4 2000 450 2100 300 2200 200 2300 450 0.0
+r c 4 2000 450 2100 300 2200 200 2300 450 0
 # Point id: 5
-r c 4 2300 450 2500 500 2800 600 3000 450 1.0
+r c 4 2300 450 2500 500 2800 600 3000 450 1
 # Point id: 6
-r c 4 0 0 100 200 500 200 900 0 0.0
+r c 4 0 0 100 200 500 200 900 0 0
 # Point id: 7
-r c 4 2300 450 2500 500 2800 600 3000 450 1.0
+r c 4 2300 450 2500 500 2800 600 3000 450 1

Barycentric_coordinates_2/package_info/Barycentric_coordinates_2/dependencies

@@ -2,6 +2,7 @@ Algebraic_foundations
 Arithmetic_kernel
 BGL
 Barycentric_coordinates_2
+CGAL_Core
 Cartesian_kernel
 Circulator
 Distance_2

Boolean_set_operations_2/package_info/Boolean_set_operations_2/dependencies

@@ -2,6 +2,7 @@ Algebraic_foundations
 Arithmetic_kernel
 Arrangement_on_surface_2
 Boolean_set_operations_2
+CGAL_Core
 Cartesian_kernel
 Circular_kernel_2
 Circulator

CGAL_Core/examples/Core/CMakeLists.txt

@@ -9,4 +9,5 @@ if(NOT CGAL_Core_FOUND)
   return()
 endif()
 
+create_single_source_cgal_program("zero-one.cpp")
 create_single_source_cgal_program("delaunay.cpp")

CGAL_Core/examples/Core/zero-one.cpp

@@ -0,0 +1,32 @@
+
+#include <CGAL/CORE_Expr.h>
+
+typedef CORE::Expr Real;
+
+int main()
+{
+  Real r(3.14);
+
+  CGAL::is_zero(r);
+
+  CGAL::is_one(r);
+
+  r = CGAL::sqrt(r);
+
+
+  CGAL::is_zero(r);
+
+  CGAL::is_one(r);
+
+  r = r * r;
+
+  CGAL::is_zero(r);
+
+  CGAL::is_one(r);
+
+  r = r - r;
+
+  CGAL::is_zero(r);
+
+  return 0;
+}

CGAL_Core/include/CGAL/CORE/BigFloat.h

@@ -59,7 +59,7 @@ public:
   /// constructor for <tt>const char* </tt>(default base = 10)
   BigFloat(const char* s) : RCBigFloat(new BigFloatRep(s)) {}
   /// constructor for <tt>std::string</tt>(default base = 10)
-  BigFloat(const std::string& s) : RCBigFloat(new BigFloatRep(s)) {}
+  BigFloat(const std::string& s) : RCBigFloat(new BigFloatRep(s.c_str())) {}
 
   /// constructor for <tt>int</tt> and <tt>long</tt>
   //     This is a hack because in Sturm, we need to approximate any
@@ -106,6 +106,9 @@ public:
   explicit BigFloat(BigFloatRep* r, bool) : RCBigFloat(r) {
   }
 
+  operator BigRat() const {
+    return this->BigRatValue();
+  }
 
   //@}
 
@@ -510,32 +513,6 @@ inline long minStar(long m, long n) {
 }
 /// \name Functions for Compatibility with BigInt (needed by Poly, Curves)
 //@{
-/// isDivisible(a,b) = "is a divisible by b"
-/**         Assuming that a and  b are in coanonized forms.
-        Defined to be true if mantissa(b) | mantissa(a) &&
-        exp(b) = min*(exp(b), exp(a)).
- *      This concepts assume a and b are exact BigFloats.
- */
-inline bool isDivisible(const BigFloat& a, const BigFloat& b) {
-  // assert: a and b are exact BigFloats.
-  if (sign(a.m()) == 0) return true;
-  if (sign(b.m()) == 0) return false;
-  unsigned long bin_a = getBinExpo(a.m());
-  unsigned long bin_b = getBinExpo(b.m());
-
-  BigInt m_a = a.m() >> bin_a;
-  BigInt m_b = b.m() >> bin_b;
-  long e_a = bin_a + BigFloatRep::bits(a.exp());
-  long e_b = bin_b + BigFloatRep::bits(b.exp());
-  long dx = minStar(e_a, e_b);
-
-  return isDivisible(m_a, m_b) && (dx == e_b);
-}
-
-inline bool isDivisible(double x, double y) {
-  //Are these exact?
-  return isDivisible(BigFloat(x), BigFloat(y));
-}
 
 /// div_exact(x,y) returns the BigFloat quotient of x divided by y
 /**        This is defined only if isDivisible(x,y).
@@ -548,7 +525,6 @@ inline bool isDivisible(double x, double y) {
 // normalizing it then we get zero.
 inline BigFloat div_exact(const BigFloat& x, const BigFloat& y) {
   BigInt z;
-  CGAL_assertion (isDivisible(x,y));
   unsigned long bin_x = getBinExpo(x.m());
   unsigned long bin_y = getBinExpo(y.m());
 
@@ -615,15 +591,20 @@ inline BigFloat gcd(const BigFloat& a, const BigFloat& b) {
 //}//
 
 
-// constructor BigRat from BigFloat
+inline double doubleValue(const BigFloat& bf)
-inline BigRat::BigRat(const BigFloat& f) : RCBigRat(new BigRatRep()){
+{
-  *this = f.BigRatValue();
+  return bf.doubleValue();
 }
+
+inline long longValue(const BigFloat& bf)
+{
+  return bf.longValue();
+}
+
 } //namespace CORE
 
 #ifdef CGAL_HEADER_ONLY
 #include <CGAL/CORE/BigFloat_impl.h>
-#include <CGAL/CORE/CoreIO_impl.h>
 #endif // CGAL_HEADER_ONLY
 
 #include <CGAL/enable_warnings.h>

CGAL_Core/include/CGAL/CORE/BigFloatRep.h

@@ -317,7 +317,7 @@ inline void BigFloatRep::eliminateTrailingZeroes() {
 //  builtin functions
 inline extLong BigFloatRep::lMSB() const {
   if (!isZeroIn())
-    return extLong(floorLg(abs(m) - err)) + bits(exp);
+    return extLong(floorLg(BigInt(abs(m) - err))) + bits(exp);
   else
     return extLong(CORE_negInfty);
 }
@@ -327,7 +327,7 @@ inline extLong BigFloatRep::lMSB() const {
  * Not well-defined if zero is in the interval.
  */
 inline extLong BigFloatRep::uMSB() const {
-  return extLong(floorLg(abs(m) + err)) + bits(exp);
+  return extLong(floorLg(BigInt(abs(m) + err))) + bits(exp);
 }
 
 inline extLong BigFloatRep::MSB() const {

CGAL_Core/include/CGAL/CORE/BigFloat_impl.h

@@ -194,8 +194,7 @@ void BigFloatRep :: truncM(const BigFloatRep& B, const extLong& r, const extLong
       err = 2;
       exp = B.exp + t;
     } else //  t < chunkCeil(clLg(B.err))
-      core_error(std::string("BigFloat error: truncM called with stricter")
+      CGAL_error_msg("BigFloat error: truncM called with stricter precision than current error.");
-          + "precision than current error.", __FILE__, __LINE__, true);
   } else {//  B.m == 0
     long t = chunkFloor(- a.asLong()) - B.exp;
 
@@ -204,8 +203,7 @@ void BigFloatRep :: truncM(const BigFloatRep& B, const extLong& r, const extLong
       err = 1;
       exp = B.exp + t;
     } else //  t < chunkCeil(clLg(B.err))
-      core_error(std::string("BigFloat error: truncM called with stricter")
+      CGAL_error_msg("BigFloat error: truncM called with stricter precision than current error.");
-          + "precision than current error.", __FILE__, __LINE__, true);
   }
 }
 
@@ -216,7 +214,7 @@ CGAL_INLINE_FUNCTION
 void BigFloatRep::approx(const BigFloatRep& B,
               const extLong& r, const extLong& a) {
   if (B.err) {
-    if (1 + clLg(B.err) <= bitLength(B.m))
+    if (static_cast<std::size_t>(1 + clLg(B.err)) <= bitLength(B.m))
       truncM(B, r + 1, a);
     else //  1 + clLg(B.err) > lg(B.m)
       truncM(B, CORE_posInfty, a);
@@ -258,7 +256,7 @@ void BigFloatRep::div(const BigInt& N, const BigInt& D,
       exp = 0;
     }
   } else //  D == 0
-    core_error( "BigFloat error: zero divisor.", __FILE__, __LINE__, true);
+    CGAL_error_msg( "BigFloat error: zero divisor.");
 
   // Call normalization globally     -- IP 10/9/98
   normal();
@@ -455,6 +453,7 @@ void BigFloatRep::centerize(const BigFloatRep& a, const BigFloatRep& b) {
   // Zilin & Vikram, 08/24/04
   // err = 1 + longValue(chunkShift(r.m, r.exp - exp));
   BigInt E = chunkShift(r.m, r.exp - exp);
+  E = abs(E);
   bigNormal(E);
 }
 
@@ -538,8 +537,7 @@ void BigFloatRep :: div(const BigFloatRep& x, const BigFloatRep& y,
       bigNormal(bigErr);
     }
   } else {//  y.m <= y.err
-    core_error("BigFloat error: possible zero divisor.",
+    CGAL_error_msg("BigFloat error: possible zero divisor.");
-                    __FILE__, __LINE__, true);
   }
 
   // Call normalization globally     -- IP 10/9/98
@@ -734,8 +732,7 @@ void BigFloatRep::sqrt(const BigFloatRep& x, const extLong& a, const BigFloat& A
       }  // end of case with error in mantissa
     }//else
   } else
-    core_error("BigFloat error: squareroot called with negative operand.",
+    CGAL_error_msg("BigFloat error: squareroot called with negative operand.");
-                    __FILE__, __LINE__, true);
 } //sqrt with initial approximation
 
 //  compareMExp(x)
@@ -822,8 +819,7 @@ BigFloatRep::toDecimal(unsigned int width, bool Scientific) const {
   if (err > 0 && err >= abs(m)) {
     // if err is larger than mantissa, sign and significant values
     // can not be determined.
-    core_error("BigFloat error: Error is too big!",
+    CGAL_CORE_warning_msg(true, "BigFloat error: Error is too big!");
-                    __FILE__, __LINE__, false);
     decOut.rep = "0.0e0";          // error is too big
     decOut.isScientific = false;
     decOut.noSignificant = 0;
@@ -869,7 +865,7 @@ BigFloatRep::toDecimal(unsigned int width, bool Scientific) const {
     M <<= e2;         // M = x * 2^(e2)
   }
 
-  std::string decRep = M.get_str();
+  std::string decRep = M.convert_to<std::string>();
   // Determine the "significant part" of this string, i.e. the part which
   // is guaranteed to be correct in the presence of error,
   // except that the last digit which might be subject to +/- 1.
@@ -1003,8 +999,7 @@ void BigFloatRep :: fromString(const char *str, extLong prec ) {
   // NOTE: prec defaults to get_static_defBigFloatInputDigits() (see BigFloat.h)
   // check that prec is not INFTY
   if (prec.isInfty())
-    core_error("BigFloat error: infinite precision not allowed",
+    CGAL_error_msg("BigFloat error: infinite precision not allowed");
-                        __FILE__, __LINE__, true);
 
   const char *e = strchr(str, 'e');
   int dot = 0;

CGAL_Core/include/CGAL/CORE/BigInt.h

@@ -24,448 +24,113 @@
 #ifndef _CORE_BIGINT_H_
 #define _CORE_BIGINT_H_
 
-#include <CGAL/CORE/Gmp.h>
+#include <CGAL/boost_mp_type.h>
 #include <CGAL/CORE/RefCount.h>
 #include <CGAL/CORE/MemoryPool.h>
 #include <string>
 
+
+#if !(defined(CGAL_CORE_USE_BOOST_BACKEND) && BOOST_VERSION > 107900 && defined(CGAL_USE_BOOST_MP)) && !defined(CGAL_DISABLE_GMP)
+#define CGAL_CORE_USE_GMP_BACKEND 1
+#endif
+
 namespace CORE {
 
+#ifdef CGAL_CORE_USE_GMP_BACKEND
+  typedef boost::multiprecision::mpz_int BigInt;
+#else
+  typedef  boost::multiprecision::cpp_int BigInt;
+#endif
 
-class BigIntRep : public RCRepImpl<BigIntRep> {
-public:
-  BigIntRep() {
-    mpz_init(mp);
-  }
-  // Note : should the copy-ctor be allowed at all ? [Sylvain Pion]
-  BigIntRep(const BigIntRep& z) : RCRepImpl<BigIntRep>() {
-    mpz_init_set(mp, z.mp);
-  }
-  BigIntRep(signed char c) {
-    mpz_init_set_si(mp, c);
-  }
-  BigIntRep(unsigned char c) {
-    mpz_init_set_ui(mp, c);
-  }
-  BigIntRep(signed int i) {
-    mpz_init_set_si(mp, i);
-  }
-  BigIntRep(unsigned int i) {
-    mpz_init_set_ui(mp, i);
-  }
-  BigIntRep(signed short int s) {
-    mpz_init_set_si(mp, s);
-  }
-  BigIntRep(unsigned short int s) {
-    mpz_init_set_ui(mp, s);
-  }
-  BigIntRep(signed long int l) {
-    mpz_init_set_si(mp, l);
-  }
-  BigIntRep(unsigned long int l) {
-    mpz_init_set_ui(mp, l);
-  }
-  BigIntRep(float f) {
-    mpz_init_set_d(mp, f);
-  }
-  BigIntRep(double d) {
-    mpz_init_set_d(mp, d);
-  }
-  BigIntRep(const char* s, int base=0) {
-    mpz_init_set_str(mp, s, base);
-  }
-  BigIntRep(const std::string& s, int base=0) {
-    mpz_init_set_str(mp, s.c_str(), base);
-  }
-  explicit BigIntRep(mpz_srcptr z) {
-    mpz_init_set(mp, z);
-  }
-  ~BigIntRep() {
-    mpz_clear(mp);
-  }
-
-  CGAL_CORE_EXPORT CORE_NEW(BigIntRep)
-  CGAL_CORE_EXPORT CORE_DELETE(BigIntRep)
-
-  mpz_srcptr get_mp() const {
-    return mp;
-  }
-  mpz_ptr get_mp() {
-    return mp;
-  }
-private:
-  mpz_t mp;
-};
-
-typedef RCImpl<BigIntRep> RCBigInt;
-class CGAL_CORE_EXPORT BigInt : public RCBigInt {
-public:
-  /// \name Constructors
-  //@{
-  /// default constructor
-  BigInt() : RCBigInt(new BigIntRep()) {}
-  /// constructor for <tt>signed char</tt>
-  BigInt(signed char x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>unsigned char</tt>
-  BigInt(unsigned char x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>signed short int</tt>
-  BigInt(signed short int x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>unsigned short int</tt>
-  BigInt(unsigned short int x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>signed int</tt>
-  BigInt(signed int x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>unsigned int</tt>
-  BigInt(unsigned int x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>signed long int</tt>
-  BigInt(signed long int x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>unsigned long int</tt>
-  BigInt(unsigned long int x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>float</tt>
-  BigInt(float x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>double</tt>
-  BigInt(double x) : RCBigInt(new BigIntRep(x)) {}
-  /// constructor for <tt>const char*</tt> with base
-  BigInt(const char* s, int base=0) : RCBigInt(new BigIntRep(s, base)) {}
-  /// constructor for <tt>std::string</tt> with base
-  BigInt(const std::string& s, int base=0) : RCBigInt(new BigIntRep(s, base)) {}
-  /// constructor for <tt>mpz_srcptr</tt>
-  explicit BigInt(mpz_srcptr z) : RCBigInt(new BigIntRep(z)) {}
-  //@}
-
-  /// \name Copy-Assignment-Destructor
-  //@{
-  /// copy constructor
-  BigInt(const BigInt& rhs) : RCBigInt(rhs) {
-    rep->incRef();
-  }
-  /// assignment operator
-  BigInt& operator=(const BigInt& rhs) {
-    if (this != &rhs) {
-      rep->decRef();
-      rep = rhs.rep;
-      rep->incRef();
-    }
-    return *this;
-  }
-  /// destructor
-  ~BigInt() {
-    rep->decRef();
-  }
-  //@}
-
-  /// \name Overloaded operators
-  //@{
-  BigInt& operator +=(const BigInt& rhs) {
-    makeCopy();
-    mpz_add(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator -=(const BigInt& rhs) {
-    makeCopy();
-    mpz_sub(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator *=(const BigInt& rhs) {
-    makeCopy();
-    mpz_mul(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator /=(const BigInt& rhs) {
-    makeCopy();
-    mpz_tdiv_q(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator %=(const BigInt& rhs) {
-    makeCopy();
-    mpz_tdiv_r(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator &=(const BigInt& rhs) {
-    makeCopy();
-    mpz_and(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator |=(const BigInt& rhs) {
-    makeCopy();
-    mpz_ior(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator ^=(const BigInt& rhs) {
-    makeCopy();
-    mpz_xor(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigInt& operator <<=(unsigned long ul) {
-    makeCopy();
-    mpz_mul_2exp(get_mp(), get_mp(), ul);
-    return *this;
-  }
-  BigInt& operator >>=(unsigned long ul) {
-    makeCopy();
-    mpz_tdiv_q_2exp(get_mp(), get_mp(), ul);
-    return *this;
-  }
-  //@}
-
-  /// \name unary, increment, decrement operators
-  //@{
-  BigInt operator+() const {
-    return BigInt(*this);
-  }
-  BigInt operator-() const {
-    BigInt r;
-    mpz_neg(r.get_mp(), get_mp());
-    return r;
-  }
-  BigInt& operator++() {
-    makeCopy();
-    mpz_add_ui(get_mp(), get_mp(), 1);
-    return *this;
-  }
-  BigInt& operator--() {
-    makeCopy();
-    mpz_sub_ui(get_mp(), get_mp(), 1);
-    return *this;
-  }
-  BigInt operator++(int) {
-    BigInt r(*this);
-    ++(*this);
-    return r;
-  }
-  BigInt operator--(int) {
-    BigInt r(*this);
-    --(*this);
-    return r;
-  }
-  //@}
-
-  /// \name Helper Functions
-  //@{
-  /// Has Exact Division
-  static bool hasExactDivision() {
-    return false;
-  }
-  /// get mpz pointer (const)
-  mpz_srcptr get_mp() const {
-    return rep->get_mp();
-  }
-  /// get mpz pointer
-  mpz_ptr get_mp() {
-    return rep->get_mp();
-  }
-  //@}
-
-  /// \name String Conversion Functions
-  //@{
-  /// set value from <tt>const char*</tt>
-  int set_str(const char* s, int base = 0) {
-    makeCopy();
-    return mpz_set_str(get_mp(), s, base);
-  }
-  /// convert to <tt>std::string</tt>
-  std::string get_str(int base = 10) const {
-    int n = mpz_sizeinbase (get_mp(), base) + 2;
-    char *buffer = new char[n];
-    mpz_get_str(buffer, base, get_mp());
-    std::string result(buffer);
-    delete [] buffer;
-    return result;
-  }
-  //@}
-
-  /// \name Conversion Functions
-  //@{
-  /// intValue
-  int intValue() const {
-    return static_cast<int>(mpz_get_si(get_mp()));
-  }
-  /// longValue
-  long longValue() const {
-    return mpz_get_si(get_mp());
-  }
-  /// ulongValue
-  unsigned long ulongValue() const {
-    return mpz_get_ui(get_mp());
-  }
-  /// doubleValue
-  double doubleValue() const {
-    return mpz_get_d(get_mp());
-  }
-  //@}
-};
-
-inline BigInt operator+(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_add(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator-(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_sub(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator*(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_mul(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator/(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_tdiv_q(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator%(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_tdiv_r(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator&(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_and(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator|(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_ior(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator^(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_xor(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigInt operator<<(const BigInt& a, unsigned long ul) {
-  BigInt r;
-  mpz_mul_2exp(r.get_mp(), a.get_mp(), ul);
-  return r;
-}
-inline BigInt operator>>(const BigInt& a, unsigned long ul) {
-  BigInt r;
-  mpz_tdiv_q_2exp(r.get_mp(), a.get_mp(), ul);
-  return r;
-}
 
 inline int cmp(const BigInt& x, const BigInt& y) {
-  return mpz_cmp(x.get_mp(), y.get_mp());
+  return x.compare(y);
-}
-inline bool operator==(const BigInt& a, const BigInt& b) {
-  return cmp(a, b) == 0;
-}
-inline bool operator!=(const BigInt& a, const BigInt& b) {
-  return cmp(a, b) != 0;
-}
-inline bool operator>=(const BigInt& a, const BigInt& b) {
-  return cmp(a, b) >= 0;
-}
-inline bool operator>(const BigInt& a, const BigInt& b) {
-  return cmp(a, b) > 0;
-}
-inline bool operator<=(const BigInt& a, const BigInt& b) {
-  return cmp(a, b) <= 0;
-}
-inline bool operator<(const BigInt& a, const BigInt& b) {
-  return cmp(a, b) < 0;
 }
 
-inline std::ostream& operator<<(std::ostream& o, const BigInt& x) {
-  //return CORE::operator<<(o, x.get_mp());
-  return CORE::io_write(o, x.get_mp());
-}
-inline std::istream& operator>>(std::istream& i, BigInt& x) {
-  x.makeCopy();
-  //return CORE::operator>>(i, x.get_mp());
-  return CORE::io_read(i, x.get_mp());
-}
 
-/// sign
+inline int set_str(BigInt& a, const char* s) {
-inline int sign(const BigInt& a) {
+    a = BigInt(s);
-  return mpz_sgn(a.get_mp());
+    return 0;  // should be -1 if not correct in the base (we ignore)
-}
+  }
-/// abs
-inline BigInt abs(const BigInt& a) {
-  BigInt r;
-  mpz_abs(r.get_mp(), a.get_mp());
-  return r;
-}
-/// neg
-inline BigInt neg(const BigInt& a) {
-  BigInt r;
-  mpz_neg(r.get_mp(), a.get_mp());
-  return r;
-}
-/// negate
-inline void negate(BigInt& a) {
-  a.makeCopy();
-  mpz_neg(a.get_mp(), a.get_mp());
-}
-/// cmpabs
-inline int cmpabs(const BigInt& a, const BigInt& b) {
-  return mpz_cmpabs(a.get_mp(), b.get_mp());
-}
 
-/// \name Conversion Functions
+  /// longValue
-//@{
-/// longValue
 inline long longValue(const BigInt& a) {
-  return a.longValue();
+  return a.convert_to<long>();
 }
-/// ulongValue
+
-inline unsigned long ulongValue(const BigInt& a) {
+  /// doubleValue
-  return a.ulongValue();
-}
-/// doubleValue
 inline double doubleValue(const BigInt& a) {
-  return a.doubleValue();
+  return a.convert_to<double>();
 }
-//@}
 
-/// \name File I/O Functions
+  /// isEven
-//@{
-/// read from file
-void readFromFile(BigInt& z, std::istream& in, long maxLength = 0);
-/// write to file
-void writeToFile(const BigInt& z, std::ostream& in, int base=10, int charsPerLine=80);
-//@}
-
-/// \name Misc Functions
-//@{
-/// isEven
 inline bool isEven(const BigInt& z) {
-  return mpz_even_p(z.get_mp());
+  return bit_test(z,0) == 0;
 }
 /// isOdd
 inline bool isOdd(const BigInt& z) {
-  return mpz_odd_p(z.get_mp());
+  return bit_test(z,0) == 1;
 }
 
-/// get exponent of power 2
-inline unsigned long getBinExpo(const BigInt& z) {
-  return mpz_scan1(z.get_mp(), 0);
-}
-/// get exponent of power k
-inline void getKaryExpo(const BigInt& z, BigInt& m, int& e, unsigned long k) {
-  mpz_t f;
-  mpz_init_set_ui(f, k);
-  m.makeCopy();
-  e = mpz_remove(m.get_mp(), z.get_mp(), f);
-  mpz_clear(f);
-}
-
-/// divisible(x,y) = "x | y"
 inline bool isDivisible(const BigInt& x, const BigInt& y) {
-  return mpz_divisible_p(x.get_mp(), y.get_mp()) != 0;
+    BigInt q, r;
+    divide_qr(x, y, q, r);
+    return r.is_zero();
 }
+
 inline bool isDivisible(int x, int y) {
   return x % y == 0;
 }
+
 inline bool isDivisible(long x, long y) {
   return x % y == 0;
+
 }
-/// exact div
+  /// get exponent of power 2
+inline std::size_t getBinExpo(const BigInt& z) {
+    if (z.is_zero()) {
+        return (std::numeric_limits<std::size_t>::max)();
+    }
+    return lsb(abs(z));
+}
+
+  // bit length
+inline std::size_t bitLength(const BigInt& a){
+    if (a.is_zero()) {
+        return 0;
+    }
+  return msb(abs(a))+1;
+}
+
+/// floorLg -- floor of log_2(a)
+/** Convention: a=0, floorLg(a) returns -1.
+ *  This makes sense for integer a.
+ */
+inline long floorLg(const BigInt& a) {
+  assert(std::size_t((std::numeric_limits<long>::max)()) > bitLength(a));
+  return (sign(a) == 0) ? (-1) : static_cast<long>(bitLength(a)-1);
+}
+
+
+/// div_rem
+inline void div_rem(BigInt& q, BigInt& r, const BigInt& a, const BigInt& b) {
+  divide_qr(a, b, q, r);
+}
+
+
+  /// ulongValue
+inline unsigned long ulongValue(const BigInt& a) {
+    assert(a >= BigInt(0));
+  return a.convert_to<unsigned long>();
+}
+
+  /// exact div
 inline void divexact(BigInt& z, const BigInt& x, const BigInt& y) {
-  z.makeCopy();
+  BigInt r;
-  mpz_divexact(z.get_mp(), x.get_mp(), y.get_mp());
+  divide_qr(x, y, z, r );  // was void mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)   Is this faster?
+  assert(r.is_zero());
 }
+
 // Chee (1/12/2004)   The definition of div_exact(x,y) next
 //   ensure that in Polynomials<NT> works with both NT=BigInt and NT=int:
 inline BigInt div_exact(const BigInt& x, const BigInt& y) {
@@ -473,50 +138,19 @@ inline BigInt div_exact(const BigInt& x, const BigInt& y) {
   divexact(z, x, y); // z is set to x/y;
   return z;
 }
+
 inline int div_exact(int x, int y) {
   return x/y;  // precondition: isDivisible(x,y)
 }
+
 inline long div_exact(long x, long y) {
   return x/y;  // precondition: isDivisible(x,y)
 }
 
-
+inline BigInt gcd(const BigInt& a, const BigInt& b){
-/// gcd
+  return boost::multiprecision::gcd(a,b);
-inline BigInt gcd(const BigInt& a, const BigInt& b) {
-  BigInt r;
-  mpz_gcd(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-/// div_rem
-inline void div_rem(BigInt& q, BigInt& r, const BigInt& a, const BigInt& b) {
-  q.makeCopy();
-  r.makeCopy();
-  mpz_tdiv_qr(q.get_mp(), r.get_mp(), a.get_mp(), b.get_mp());
-}
-/// power
-inline void power(BigInt& c, const BigInt& a, unsigned long ul) {
-  c.makeCopy();
-  mpz_pow_ui(c.get_mp(), a.get_mp(), ul);
 }
 
-// pow
-inline BigInt pow(const BigInt& a, unsigned long ui) {
-  BigInt r;
-  power(r, a, ui);
-  return r;
-}
-
-// bit length
-inline int bitLength(const BigInt& a) {
-  return mpz_sizeinbase(a.get_mp(), 2);
-}
-/// floorLg -- floor of log_2(a)
-/** Convention: a=0, floorLg(a) returns -1.
- *  This makes sense for integer a.
- */
-inline long floorLg(const BigInt& a) {
-  return (sign(a) == 0) ? (-1) : (bitLength(a)-1);
-}
 /// ceilLg -- ceiling of log_2(a) where a=BigInt, int or long
 /** Convention: a=0, ceilLg(a) returns -1.
  *  This makes sense for integer a.
@@ -524,20 +158,45 @@ inline long floorLg(const BigInt& a) {
 inline long ceilLg(const BigInt& a) {
   if (sign(a) == 0)
     return -1;
-  unsigned long len = bitLength(a);
+  assert(std::size_t((std::numeric_limits<long>::max)()) > bitLength(a));
-  return (mpz_scan1(a.get_mp(), 0) == len-1) ? (len-1) : len;
+  std::size_t len = static_cast<long>(bitLength(a));
+
+  return (lsb(abs(a)) == len - 1) ? (static_cast<long>(len) - 1) : static_cast<long>(len);
 }
+
 inline long ceilLg(long a) { // need this for Polynomial<long>
   return ceilLg(BigInt(a));
 }
+
 inline long ceilLg(int a) { // need this for Polynomial<int>
   return ceilLg(BigInt(a));
 }
 
-//@}
+
+/// negate
+inline void negate(BigInt& a) {
+  a= - a;
+}
+
+/// get exponent of power k
+inline void getKaryExpo(const BigInt& z, BigInt& m, int& e, unsigned long uk) {
+    BigInt k(uk), q, r;
+    e = 0;
+    m = z;
+    for(;;) {
+        divide_qr(m, k, q, r);
+        if (!r.is_zero()) break;
+        m = q;
+        ++e;
+    }
+}
+
+inline void power(BigInt& c, const BigInt& a, unsigned long ul) {
+  c = pow(a, ul);
+}
+
+} // namespace CORE
 
 
 
-} //namespace CORE
-
 #endif // _CORE_BIGINT_H_

CGAL_Core/include/CGAL/CORE/BigRat.h

@@ -28,354 +28,35 @@
 #include <CGAL/CORE/BigInt.h>
 
 namespace CORE {
+#ifdef CGAL_CORE_USE_GMP_BACKEND
+  typedef boost::multiprecision::mpq_rational BigRat;
+#else
+  typedef  boost::multiprecision::cpp_rational BigRat;
+#endif
 
-class BigRatRep : public RCRepImpl<BigRatRep> {
+
-public:
+  inline BigInt numerator(const BigRat& q)
-  BigRatRep() {
+  {
-    mpq_init(mp);
+    return boost::multiprecision::numerator(q);
-  }
-  // Note : should the copy-ctor be allowed at all ? [Sylvain Pion]
-  BigRatRep(const BigRatRep& z)  : RCRepImpl<BigRatRep>() {
-    mpq_init(mp);
-    mpq_set(mp, z.mp);
-  }
-  BigRatRep(signed char c) {
-    mpq_init(mp);
-    mpq_set_si(mp, c, 1);
-  }
-  BigRatRep(unsigned char c) {
-    mpq_init(mp);
-    mpq_set_ui(mp, c, 1);
-  }
-  BigRatRep(signed int i) {
-    mpq_init(mp);
-    mpq_set_si(mp, i, 1);
-  }
-  BigRatRep(unsigned int i) {
-    mpq_init(mp);
-    mpq_set_ui(mp, i, 1);
-  }
-  BigRatRep(signed short int s) {
-    mpq_init(mp);
-    mpq_set_si(mp, s, 1);
-  }
-  BigRatRep(unsigned short int s) {
-    mpq_init(mp);
-    mpq_set_ui(mp, s, 1);
-  }
-  BigRatRep(signed long int l) {
-    mpq_init(mp);
-    mpq_set_si(mp, l, 1);
-  }
-  BigRatRep(unsigned long int l) {
-    mpq_init(mp);
-    mpq_set_ui(mp, l, 1);
-  }
-  BigRatRep(float f) {
-    mpq_init(mp);
-    mpq_set_d(mp, f);
-  }
-  BigRatRep(double d) {
-    mpq_init(mp);
-    mpq_set_d(mp, d);
-  }
-  BigRatRep(const char* s) {
-    mpq_init(mp);
-    mpq_set_str(mp, s, 0);
-  }
-  BigRatRep(const std::string& s) {
-    mpq_init(mp);
-    mpq_set_str(mp, s.c_str(), 0);
-  }
-  explicit BigRatRep(mpq_srcptr q) {
-    mpq_init(mp);
-    mpq_set(mp, q);
-  }
-  BigRatRep(mpz_srcptr z) {
-    mpq_init(mp);
-    mpq_set_z(mp, z);
-  }
-  BigRatRep(mpz_srcptr n, mpz_srcptr d) {
-    mpq_init(mp);
-    mpz_set(mpq_numref(mp), n);
-    mpz_set(mpq_denref(mp), d);
-    mpq_canonicalize(mp);
-  }
-  ~BigRatRep() {
-    mpq_clear(mp);
   }
 
-  CGAL_CORE_EXPORT CORE_NEW(BigRatRep)
+  inline BigInt denominator(const BigRat& q)
-  CGAL_CORE_EXPORT CORE_DELETE(BigRatRep)
+  {
-
+    return boost::multiprecision::denominator(q);
-  mpq_srcptr get_mp() const {
-    return mp;
-  }
-  mpq_ptr get_mp() {
-    return mp;
-  }
-private:
-  mpq_t mp;
-}; //BigRatRep
-
-class BigFloat;
-
-typedef RCImpl<BigRatRep> RCBigRat;
-class BigRat : public RCBigRat {
-public:
-  /// \name Constructors
-  //@{
-  /// default constructor
-  BigRat() : RCBigRat(new BigRatRep()) {}
-  /// constructor for <tt>signed char</tt>
-  BigRat(signed char x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>unsigned char</tt>
-  BigRat(unsigned char x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>signed short int</tt>
-  BigRat(signed short int x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>unsigned short int</tt>
-  BigRat(unsigned short int x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>signed int</tt>
-  BigRat(signed int x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>unsigned int</tt>
-  BigRat(unsigned int x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>signed long int</tt>
-  BigRat(signed long int x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>unsigned long int</tt>
-  BigRat(unsigned long int x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>float</tt>
-  BigRat(float x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>double</tt>
-  BigRat(double x) : RCBigRat(new BigRatRep(x)) {}
-  /// constructor for <tt>const char*</tt> with base
-  BigRat(const char* s) : RCBigRat(new BigRatRep(s)) {}
-  /// constructor for <tt>std::string</tt> with base
-  BigRat(const std::string& s) : RCBigRat(new BigRatRep(s)) {}
-  /// constructor for <tt>mpq_srcptr</tt>
-  explicit BigRat(mpq_srcptr z) : RCBigRat(new BigRatRep(z)) {}
-  /// constructor for <tt>BigInt</tt>
-  BigRat(const BigInt& z) : RCBigRat(new BigRatRep(z.get_mp())) {}
-  /// constructor for two <tt>BigInts</tt>
-  BigRat(const BigInt& n, const BigInt& d)
-      : RCBigRat(new BigRatRep(n.get_mp(), d.get_mp())) {}
-  /// constructor for <tt>BigFloat</tt>
-  BigRat(const BigFloat&);
-  //@}
-
-  /// \name Copy-Assignment-Destructor
-  //@{
-  /// copy constructor
-  BigRat(const BigRat& rhs) : RCBigRat(rhs) {
-    rep->incRef();
-  }
-  /// assignment operator
-  BigRat& operator=(const BigRat& rhs) {
-    if (this != &rhs) {
-      rep->decRef();
-      rep = rhs.rep;
-      rep->incRef();
-    }
-    return *this;
-  }
-  /// destructor
-  ~BigRat() {
-    rep->decRef();
-  }
-  //@}
-
-  /// \name Overloaded operators
-  //@{
-  BigRat& operator +=(const BigRat& rhs) {
-    makeCopy();
-    mpq_add(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigRat& operator -=(const BigRat& rhs) {
-    makeCopy();
-    mpq_sub(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigRat& operator *=(const BigRat& rhs) {
-    makeCopy();
-    mpq_mul(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigRat& operator /=(const BigRat& rhs) {
-    makeCopy();
-    mpq_div(get_mp(), get_mp(), rhs.get_mp());
-    return *this;
-  }
-  BigRat& operator <<=(unsigned long ul) {
-    makeCopy();
-    mpq_mul_2exp(get_mp(), get_mp(), ul);
-    return *this;
-  }
-  BigRat& operator >>=(unsigned long ul) {
-    makeCopy();
-    mpq_div_2exp(get_mp(), get_mp(), ul);
-    return *this;
-  }
-  //@}
-
-  /// \name div2, unary, increment, decrement operators
-  //@{
-
-  /// exact division by 2 (this method is provided for compatibility)
-  BigRat div2() const {
-    BigRat r; BigRat t(2);     // probably not most efficient way
-    mpq_div(r.get_mp(), get_mp(), t.get_mp());
-    return r;
-  }
-  BigRat operator+() const {
-    return BigRat(*this);
-  }
-  BigRat operator-() const {
-    BigRat r;
-    mpq_neg(r.get_mp(), get_mp());
-    return r;
-  }
-  BigRat& operator++() {
-    makeCopy();
-    mpz_add(get_num_mp(),get_num_mp(),get_den_mp());
-    return *this;
-  }
-  BigRat& operator--() {
-    makeCopy();
-    mpz_sub(get_num_mp(),get_num_mp(),get_den_mp());
-    return *this;
-  }
-  BigRat operator++(int) {
-    BigRat r(*this);
-    ++(*this);
-    return r;
-  }
-  BigRat operator--(int) {
-    BigRat r(*this);
-    --(*this);
-    return r;
-  }
-  //@}
-
-  /// \name Helper Functions
-  //@{
-  /// Canonicalize
-  void canonicalize() {
-    makeCopy();
-    mpq_canonicalize(get_mp());
-  }
-  /// Has Exact Division
-  static bool hasExactDivision() {
-    return true;
   }
 
-  /// return mpz pointer of numerator (const)
+  // Chee (3/19/2004):
-  mpz_srcptr get_num_mp() const {
-    return mpq_numref(get_mp());
-  }
-  /// return mpz pointer of numerator
-  mpz_ptr get_num_mp() {
-    return mpq_numref(get_mp());
-  }
-  /// return mpz pointer of denominator
-  mpz_srcptr get_den_mp() const {
-    return mpq_denref(get_mp());
-  }
-  /// return mpz pointer of denominator
-  mpz_ptr get_den_mp() {
-    return mpq_denref(get_mp());
-  }
-
-  /// get mpq pointer (const)
-  mpq_srcptr get_mp() const {
-    return rep->get_mp();
-  }
-  /// get mpq pointer
-  mpq_ptr get_mp() {
-    return rep->get_mp();
-  }
-  //@}
-
-  /// \name String Conversion Functions
-  //@{
-  /// set value from <tt>const char*</tt>
-  int set_str(const char* s, int base = 0) {
-    makeCopy();
-    return mpq_set_str(get_mp(), s, base);
-  }
-  /// convert to <tt>std::string</tt>
-  std::string get_str(int base = 10) const {
-    int n = mpz_sizeinbase(mpq_numref(get_mp()), base) + mpz_sizeinbase(mpq_denref(get_mp()), base)+ 3;
-    char *buffer = new char[n];
-    mpq_get_str(buffer, base, get_mp());
-    std::string result(buffer);
-    delete [] buffer;
-    return result;
-  }
-  //@}
-
-  /// \name Conversion Functions
-  //@{
-  /// intValue
-  int intValue() const {
-    return static_cast<int>(doubleValue());
-  }
-  /// longValue
-  long longValue() const {
-    return static_cast<long>(doubleValue());
-  }
-  /// doubleValue
-  double doubleValue() const {
-    return mpq_get_d(get_mp());
-  }
-  /// BigIntValue
-  BigInt BigIntValue() const {
-    BigInt r;
-    mpz_tdiv_q(r.get_mp(), get_num_mp(), get_den_mp());
-    return r;
-  }
-  //@}
-}; //BigRat class
-
-inline BigRat operator+(const BigRat& a, const BigRat& b) {
-  BigRat r;
-  mpq_add(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigRat operator-(const BigRat& a, const BigRat& b) {
-  BigRat r;
-  mpq_sub(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigRat operator*(const BigRat& a, const BigRat& b) {
-  BigRat r;
-  mpq_mul(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-inline BigRat operator/(const BigRat& a, const BigRat& b) {
-  BigRat r;
-  mpq_div(r.get_mp(), a.get_mp(), b.get_mp());
-  return r;
-}
-// Chee (3/19/2004):
 //   The following definitions of div_exact(x,y) and gcd(x,y)
 //   ensures that in Polynomial<NT>
 /// divisible(x,y) = "x | y"
-inline BigRat div_exact(const BigRat& x, const BigRat& y) {
+  inline BigRat div_exact(const BigRat& x, const BigRat& y) {
-        BigRat z;
+    BigRat z = x / y;
-        mpq_div(z.get_mp(), x.get_mp(), y.get_mp());
+    return z;
-        return z;
+  }
-}
-/// numerator
-inline BigInt numerator(const BigRat& a) {
-  return BigInt(a.get_num_mp());
-}
-/// denominator
-inline BigInt denominator(const BigRat& a) {
-  return BigInt(a.get_den_mp());
-}
 
-inline BigRat gcd(const BigRat& x, const BigRat& y) {
+  inline BigRat gcd(const BigRat& x , const BigRat& y)
-  //        return BigRat(1);  // Remark: we may want replace this by
+  {
+    //        return BigRat(1);  // Remark: we may want replace this by
                            // the definition of gcd of a quotient field
                            // of a UFD [Yap's book, Chap.3]
   //Here is one possible definition: gcd of x and y is just the
@@ -384,98 +65,17 @@ inline BigRat gcd(const BigRat& x, const BigRat& y) {
   BigInt n = gcd(numerator(x), numerator(y));
   BigInt d = gcd(denominator(x), denominator(y));
   return BigRat(n,d);
+  }
 
-}
+  /// BigIntValue
-// Chee: 8/8/2004: need isDivisible to compile Polynomial<BigRat>
+inline BigInt BigIntValue(const BigRat& br)
-// A trivial implementation is to return true always. But this
+{
-// caused tPolyRat to fail.
+  BigInt r, rem;
-// So we follow the definition of
+  divide_qr(numerator(br), denominator(br), r, rem);
-// Expr::isDivisible(e1, e2) which checks if e1/e2 is an integer.
-inline bool isInteger(const BigRat& x) {
-  return BigInt(x.get_den_mp()) == 1;
-}
-inline bool isDivisible(const BigRat& x, const BigRat& y) {
-  BigRat r;
-  mpq_div(r.get_mp(), x.get_mp(), y.get_mp());
-  return isInteger(r);
-}
-inline BigRat operator<<(const BigRat& a, unsigned long ul) {
-  BigRat r;
-  mpq_mul_2exp(r.get_mp(), a.get_mp(), ul);
-  return r;
-}
-inline BigRat operator>>(const BigRat& a, unsigned long ul) {
-  BigRat r;
-  mpq_div_2exp(r.get_mp(), a.get_mp(), ul);
   return r;
 }
 
-inline int cmp(const BigRat& x, const BigRat& y) {
+} // namespace CORE
-  return mpq_cmp(x.get_mp(), y.get_mp());
-}
-inline bool operator==(const BigRat& a, const BigRat& b) {
-  return cmp(a, b) == 0;
-}
-inline bool operator!=(const BigRat& a, const BigRat& b) {
-  return cmp(a, b) != 0;
-}
-inline bool operator>=(const BigRat& a, const BigRat& b) {
-  return cmp(a, b) >= 0;
-}
-inline bool operator>(const BigRat& a, const BigRat& b) {
-  return cmp(a, b) > 0;
-}
-inline bool operator<=(const BigRat& a, const BigRat& b) {
-  return cmp(a, b) <= 0;
-}
-inline bool operator<(const BigRat& a, const BigRat& b) {
-  return cmp(a, b) < 0;
-}
-
-inline std::ostream& operator<<(std::ostream& o, const BigRat& x) {
-  //return CORE::operator<<(o, x.get_mp());
-  return CORE::io_write(o, x.get_mp());
-}
-inline std::istream& operator>>(std::istream& i, BigRat& x) {
-  x.makeCopy();
-  //return CORE::operator>>(i, x.get_mp());
-  return CORE::io_read(i, x.get_mp());
-}
-
-/// sign
-inline int sign(const BigRat& a) {
-  return mpq_sgn(a.get_mp());
-}
-/// abs
-inline BigRat abs(const BigRat& a) {
-  BigRat r;
-  mpq_abs(r.get_mp(), a.get_mp());
-  return r;
-}
-/// neg
-inline BigRat neg(const BigRat& a) {
-  BigRat r;
-  mpq_neg(r.get_mp(), a.get_mp());
-  return r;
-}
-/// div2
-inline BigRat div2(const BigRat& a) {
-  BigRat r(a);
-  return r.div2();
-}
-/// longValue
-inline long longValue(const BigRat& a) {
-  return a.longValue();
-}
-/// doubleValue
-inline double doubleValue(const BigRat& a) {
-  return a.doubleValue();
-}
-/// return BigInt value
-inline BigInt BigIntValue(const BigRat& a) {
-  return a.BigIntValue();
-}
 
 
-} //namespace CORE
 #endif // _CORE_BIGRAT_H_

CGAL_Core/include/CGAL/CORE/Config.h

@@ -29,4 +29,13 @@
 
 #include <CGAL/export/CORE.h>
 
+#ifdef CGAL_TEST_SUITE
+// disabled for the testsuite to avoid `w`
+#define CGAL_CORE_warning_msg(X ,Y)
+// if (!(X)) CGAL_error_msg(Y)
+#else
+#define CGAL_CORE_warning_msg(X ,Y) CGAL_warning_msg(X ,Y)
+#endif
+
+
 #endif // _CORE_CONFIG_H_

CGAL_Core/include/CGAL/CORE/CoreAux.h

@@ -156,12 +156,6 @@ CGAL_CORE_EXPORT double IntMantissa(double d);
 //      (See CORE_PATH/progs/ieee/frexp.cpp for details)
 CGAL_CORE_EXPORT int IntExponent(double d);
 
-/// Writes out an error or warning message in the local file CORE_DIAGFILE
-/** If last argument (err) is TRUE, then this is considered an error
- *  (not just warning).  In this case, the message is also printed in
- *  std::cerr, using std::perror().
- *  */
-CGAL_CORE_EXPORT void core_error(std::string msg, std::string file, int lineno, bool err);
 
 /// This is for debugging messages
 inline void core_debug(std::string msg){

CGAL_Core/include/CGAL/CORE/CoreAux_impl.h

@@ -31,7 +31,6 @@
 
 #include <CGAL/use.h>
 #include <CGAL/CORE/CoreAux.h>
-#include <CGAL/gmp.h>
 
 namespace CORE {
 
@@ -157,30 +156,5 @@ int IntExponent(double d) {
         return e-53;
 }
 
-/// core_error is the method to write Core Library warning or error messages
-/**         Both warnings and errors are written to a file called CORE_DIAGFILE.
- *        But errors are also written on std::cerr (similar to std::perror()).
- * */
-// Usage: core_error(message, file_with_error, line_number, err_type)
-//   where err_type=0 means WARNING, error_type=0 means ERROR
-CGAL_INLINE_FUNCTION
-void core_error(std::string msg, std::string file, int lineno, bool err) {
-  std::ofstream outFile(CORE_DIAGFILE, std::ios::app);  // open to append
-  if (!outFile) {
-     // perror("CORE ERROR: cannot open Core Diagnostics file");
-     std::cerr << "CORE ERROR: can't open Core Diagnostics file"<<std::endl;
-     std::exit(1); //Note: do not call abort()
-  }
-  outFile << "CORE " << (err? "ERROR" : "WARNING")
-     << " (at " << file << ": " << lineno << "): "
-     << msg << std::endl;
-  outFile.close();
-  if (err) {
-     std::cerr << (std::string("CORE ERROR") + " (file " + file + ", line "
-                   + std::to_string(lineno) +"):" + msg + "\n").c_str();
-     std::exit(1); //Note: do not call abort()
-  }
-}
-
 
 } //namespace CORE

CGAL_Core/include/CGAL/CORE/CoreIO_impl.h

@@ -1,479 +0,0 @@
-/****************************************************************************
- * Core Library Version 1.7, August 2004
- * Copyright (c) 1995-2004 Exact Computation Project
- * All rights reserved.
- *
- * This file is part of CGAL (www.cgal.org).
- *
- * File: CoreIO.cpp
- *
- * Written by
- *       Zilin Du <zilin@cs.nyu.edu>
- *       Chee Yap <yap@cs.nyu.edu>
- *
- * WWW URL: https://cs.nyu.edu/exact/
- * Email: exact@cs.nyu.edu
- *
- * $URL$
- * $Id$
- * SPDX-License-Identifier: LGPL-3.0-or-later
- ***************************************************************************/
-
-#ifndef _COREIO_IMPL_H_
-#define _COREIO_IMPL_H_
-
-#ifdef CGAL_HEADER_ONLY
-#define CGAL_INLINE_FUNCTION inline
-#else
-#define CGAL_INLINE_FUNCTION
-#endif
-
-#include <CGAL/CORE/BigFloatRep.h>
-#include <CGAL/CORE/BigFloat.h>
-#include <CGAL/CORE/BigInt.h>
-
-namespace CORE {
-
-CGAL_INLINE_FUNCTION
-void core_io_error_handler(const char *f, const char *m) {
-  std::cout << "\n error_handler";
-  std::cout << "::" << f << "::" << m << "\n";
-  std::cout.flush();
-  std::abort();
-}
-
-CGAL_INLINE_FUNCTION
-void core_io_memory_handler(char *t, const char *f, const char *m) {
-  if (t == nullptr) {
-    std::cout << "\n memory_handler";
-    std::cout << "::" << f << "::" << m;
-    std::cout << "memory exhausted\n";
-    std::cout.flush();
-    std::abort();
-  }
-}
-
-// s has size old_size and will be resized to new_size.
-CGAL_INLINE_FUNCTION
-void allocate (char * &s, int old_size, int new_size) {
-  if (old_size > new_size)
-    old_size = new_size;
-
-  if (s == nullptr)
-    old_size = 0;
-
-  char *t = new char[new_size];
-  core_io_memory_handler(t, "CoreIO", "allocate::out of memory error");
-
-  int i;
-  for (i = 0; i < old_size; i++)
-    t[i] = s[i];
-
-  delete[] s;
-  s = t;
-}
-
-// appends c to s at position pos.
-// sz is the size of s
-CGAL_INLINE_FUNCTION
-void append_char (char * &s, int & sz, int pos, char c) {
-  if (pos > sz)
-    core_io_error_handler("CoreIO", "append_char::invalid argument");
-
-  if (pos == sz) {
-    allocate(s, sz, 2*sz);
-    sz *= 2;
-  }
-
-  s[pos] = c;
-}
-
-// skip blanks, tabs, line breaks and comment lines
-CGAL_INLINE_FUNCTION
-int skip_comment_line (std::istream & in) {
-  char c;
-
-  do {
-    in.get(c);
-    while ( c == '#' ) {
-      do {
-        in.get(c);
-      } while ( c != '\n' );
-     in.get(c);
-    }
-  } while (c == ' ' || c == '\t' || c == '\n');
-
-  if (in.eof())
-    core_io_error_handler("CoreIO::read_from_file()","unexpected end of file.");
-
-  in.putback(c);
-  return c;
-}
-
-// skips '\\' followed by '\n'
-CGAL_INLINE_FUNCTION
-char skip_backslash_new_line (std::istream & in) {
-  char c;
-  in.get(c);
-
-  while (c == '\\') {
-    in.get(c);
-
-    if (c == '\n')
-      in.get(c);
-    else
-      core_io_error_handler("CoreIO::operator>>", "\\ must be immediately followed by new line.");
-  }
-
-  return c;
-}
-
-CGAL_INLINE_FUNCTION
-void read_string(std::istream& in, char* &buffer, int sz) {
-  char c;
-  int pos=0;
-  skip_comment_line(in);
-
-  while ( in.get(c) ) {
-    if ( c == ' ' || c == '\t' || c == '\n' || c == '#')
-      break;
-    else
-      append_char(buffer, sz, pos++, c);
-  }
-  append_char(buffer, sz, pos, '\0');
-}
-
-CGAL_INLINE_FUNCTION
-void read_base_number(std::istream& in, BigInt& m, long length, long maxBits) {
-  char *buffer;
-  int size, offset;
-  int base;
-  bool is_negate;
-
-  char c;
-  int pos = 0;
-  skip_comment_line(in);
-
-  // read sign
-  in.get(c);
-  if (c == '-') {
-    is_negate = true;
-    in.get(c);
-  } else
-    is_negate = false;
-
-  // read base and compute digits
-  if (c == '0') {
-    in.get(c);
-    if (c == 'b') {
-      base = 2;
-      size = (maxBits == 0 || maxBits > length) ? length : maxBits;
-      offset = length - size;
-    } else if (c == 'x') {
-      base = 16;
-      size = (maxBits == 0) ? length : (maxBits+3) >> 2;
-      size = (size > length) ? length : size;
-      offset = (length - size) << 2;
-    } else {
-      base = 8;
-      size = (maxBits == 0) ? length : (maxBits+2) / 3;
-      size = (size > length) ? length : size;
-      offset = (length - size) * 3;
-      in.putback(c);
-    }
-  } else {
-    base = 10;
-    size = (maxBits == 0) ? length : (int)std::ceil(maxBits*std::log(2.0)/std::log(10.0));
-    size = (size > length) ? length : size;
-    offset = length - size;
-    in.putback(c);
-  }
-
-  buffer = new char[size+2];
-  // read digits
-  for (int i=0; i<size; i++) {
-    c=skip_backslash_new_line(in);
-    if(in.eof()){
-      break;
-    }
-    if (c != ' ' && c != '\t' && c != '\n')
-      append_char(buffer, size, pos++, c);
-  }
-  if (base == 10) {
-    for(int j=0; j<offset; j++)
-      append_char(buffer, size, pos++, '0');
-  }
-  append_char(buffer, size, pos, '\0');
-
-  // convert string to bigint.
-  if (m.set_str(buffer, base) < 0)
-    core_io_error_handler("CoreIO::read_from_file()","bad big number format.");
-  delete[] buffer;
-
-  // shift left if necessary
-  if (offset > 0 && base != 10) {
-    m <<= offset;
-  }
-
-  if (is_negate)
-    negate(m);
-}
-
-
-CGAL_INLINE_FUNCTION
-void write_base_number(std::ostream& out, char* buffer, std::size_t length, int base, int charsPerLine) {
-  // write big number in a format that gmp's mpz_set_str() can
-  // automatically recognize with argument base = 0.
-  if (base == 2)
-    out << "0b";
-  else if (base == 16)
-    out << "0x";
-  else if (base == 8)
-    out << '0';
-
-  // write big number in charsPerLine.
-  char* start, *end, c;
-  for (std::size_t i=0; i<length; i += charsPerLine) {
-    start = buffer + i;
-    if (i + charsPerLine >= length)
-      out << start;
-    else {
-      end = start + charsPerLine;
-      c = *end;
-      *end = '\0';
-
-      out << start << "\\\n";
-      *end = c;
-    }
-  }
-}
-
-CGAL_INLINE_FUNCTION
-void readFromFile(BigInt& z, std::istream& in, long maxLength) {
-  char *buffer;
-  long length;
-
-  // check type name whether it is Integer or not.
-  buffer = new char[8];
-  read_string(in, buffer, sizeof(buffer));
-  if ( std::strcmp(buffer, "Integer") != 0)
-    core_io_error_handler("BigInt::read_from_file()","type name expected.");
-  delete[] buffer;
-
-  // read the bit length field.
-  buffer = new char[100];
-  read_string(in, buffer, sizeof(buffer));
-  length = std::atol(buffer);
-  delete[] buffer;
-
-  // read bigint
-  read_base_number(in, z, length, maxLength);
-}
-
-CGAL_INLINE_FUNCTION
-void writeToFile(const BigInt& z, std::ostream& out, int base, int charsPerLine) {
-  BigInt c = abs(z);
-
-  // get the absolute value string
-  char* buffer = new char[mpz_sizeinbase(c.get_mp(), base) + 2];
-  mpz_get_str(buffer, base, c.get_mp());
-  std::size_t length = std::strlen(buffer);
-
-  // write type name of big number and length
-  //out << "# This is an experimental big number format.\n";
-  out << "Integer " << length << "\n";
-
-  // if bigint is negative, then write an sign '-'.
-  if ( sign(z) < 0  )
-    out << '-';
-
-  write_base_number(out, buffer, length, base, charsPerLine);
-  out << "\n";
-  delete[] buffer;
-}
-
-CGAL_INLINE_FUNCTION
-void readFromFile(BigFloat& bf, std::istream& in, long maxLength) {
-  char *buffer;
-  long length;
-  long exponent;
-  BigInt mantissa;
-
-  // check type name whether it is Float
-  buffer = new char[6];
-  read_string(in, buffer, sizeof(buffer));
-  if (std::strcmp(buffer, "Float") != 0)
-    core_io_error_handler("BigFloat::read_from_file()", "type name expected");
-  delete[] buffer;
-
-  // read base (default is 16384)
-  buffer = new char[8];
-  read_string(in, buffer, sizeof(buffer));
-  if (std::strcmp(buffer, "(16384)") != 0)
-    core_io_error_handler("BigFloat::read_from_file()", "base expected");
-  delete[] buffer;
-
-  // read the bit length field.
-  buffer = new char[100];
-  read_string(in, buffer, sizeof(buffer));
-  length = std::atol(buffer);
-  delete[] buffer;
-
-  // read exponent
-  buffer = new char[100];
-  read_string(in, buffer, sizeof(buffer));
-  exponent = std::atol(buffer);
-  delete[] buffer;
-
-  // read mantissa
-  read_base_number(in, mantissa, length, maxLength);
-
-  // construct BigFloat
-  bf = BigFloat(mantissa, 0, exponent);
-}
-
-CGAL_INLINE_FUNCTION
-void writeToFile(const BigFloat& bf, std::ostream& out, int base, int charsPerLine) {
-  BigInt c(CORE::abs(bf.m()));
-
-  // get the absolute value string
-  char* buffer = new char[mpz_sizeinbase(c.get_mp(), base) + 2];
-  mpz_get_str(buffer, base, c.get_mp());
-  std::size_t length = std::strlen(buffer);
-
-
-  // write type name, base, length
-  //out << "# This is an experimental Big Float format." << std::endl;
-  out << "Float (16384) " << length << std::endl;
-  // write exponent
-  out << bf.exp() << std::endl;
-
-  // write mantissa
-  if ( CORE::sign(bf.m()) < 0 )
-    out << '-';
-
-  write_base_number(out, buffer, length, base, charsPerLine);
-  out << '\n';
-  delete[] buffer;
-}
-
-/* Underconstruction ----
-void BigFloat::read_from_file2(std::istream& in, long maxLength) {
-  long length = 1024;
-  char *buffer;
-
-  // check type name whether it is Float
-  buffer = new char[7];
-  BigInt::read_string(in, buffer, sizeof(buffer));
-  if (strcmp(buffer, "NFloat") != 0)
-    core_io_error_handler("BigFloat::read_from_file2()", "type name expected");
-  delete[] buffer;
-
-  // read base (default is 16)
-  buffer = new char[5];
-  BigInt::read_string(in, buffer, sizeof(buffer));
-  if (strcmp(buffer, "(16)") != 0)
-    core_io_error_handler("BigFloat::read_from_file2()", "base expected");
-  delete[] buffer;
-
-  // read length field
-  buffer = new char[100];
-  BigInt::read_string(in, buffer, sizeof(buffer));
-
-  // get the length field if it is not null.
-  if (buffer[0] != '\0') {
-    length = atol(buffer);
-    if (maxLength > 0 && length >= maxLength)
-      length = maxLength;
-  }
-  delete[] buffer;
-
-  // read exponent
-  buffer = new char[100];
-  BigInt::read_string(in, buffer, sizeof(buffer));
-  long exp16 = atol(buffer);
-  delete[] buffer;
-
-  // read mantissa
-  buffer = new char[length+2];
-  //BigInt::read_base_number(in, buffer, length);
-
-  BigInt m16(buffer);
-  delete[] buffer;
-
-  // convert to base CHUNK_BIT
-  exp16 = exp16 - length + 1;
-  if ( m16.is_negative() )
-    exp16 ++;
-
-  long tmp_exp = exp16 * 4;
-  long q = tmp_exp / CHUNK_BIT;
-  long r = tmp_exp % CHUNK_BIT;
-  if ( r < 0 ) {
-    r += CHUNK_BIT;
-    q --;
-  }
-
-  BigInt mantissa = m16 << r;
-  long exponent = q;
-
-  // construct BigFloat
-  if (--rep->refCount == 0)
-    delete rep;
-
-  rep = new BigFloatRep(mantissa, 0, exponent);
-  rep->refCount++;
-
-}
-
-// write normal float
-// now it assumed to write in hex base, i.e. B=2^4=16
-// (note: our default base B=2^(CHUNK_BIT)=2^14=16384
-void BigFloat::write_to_file2(std::ostream& out, int base, int charsPerLine) {
-  // convert to base 16.
-  long new_base = 4; // 2^4 = 16
-  long tmp_exp = (rep->exp) * CHUNK_BIT;
-  long q = tmp_exp / new_base;
-  long r = tmp_exp % new_base;
-  std::cout << "CORE_DEBUG: q=" << q << ", r=" << r << std::endl;
-  if ( r < 0 ) {
-    r += new_base;
-    q--;
-  }
-  std::cout << "CORE_DEBUG: q=" << q << ", r=" << r << std::endl;
-
-  BigInt m16 = (rep->m) << r;
-
-  int size = mpz_sizeinbase(m16.I, base) + 2;
-  std::cout << "size=" << size << std::endl;
-  char* buffer = new char[size];
-
-  int length = bigint_to_string(m16, buffer, base);
-  std::cout << "length=" << length << std::endl;
-
-  long exp16 = q + length - 1;
-  if ( m16.is_negative() )
-    exp16 --;
-
-  // write type name, base, length
-  out << "# This is an experimental Big Float format." << std::endl;
-  out << "NFloat (16) " << length << std::endl;
-
-  // write exponent
-  out << exp16 << std::endl;
-
-  // write mantissa
-  if ( m16.is_negative() ) {
-    out << '-';
-    buffer ++;
-  }
-
-  BigInt::write_base_number(out, buffer, length, base, charsPerLine);
-  out << '\n';
-  delete[] buffer;
-}
-*/
-
-} //namespace CORE
-
-#endif // _COREIO_IMPL_H_

CGAL_Core/include/CGAL/CORE/Expr.h

@@ -72,9 +72,7 @@ public:
   Expr(float f) : RCExpr(nullptr) { // check for valid numbers
     // (i.e., not infinite and not NaN)
     if (! CGAL_CORE_finite(f)) {
-      core_error(" ERROR : constructed an invalid float! ", __FILE__, __LINE__, false);
+      CGAL_error_msg("ERROR : constructed an invalid float! ");
-      if (get_static_AbortFlag())
-        abort();
       get_static_InvalidFlag() = -1;
     }
     rep = new ConstDoubleRep(f);
@@ -83,9 +81,7 @@ public:
   Expr(double d) : RCExpr(nullptr) { // check for valid numbers
     // (i.e., not infinite and not NaN)
     if (! CGAL_CORE_finite(d)) {
-      core_error(" ERROR : constructed an invalid double! ", __FILE__, __LINE__, false);
+      CGAL_error_msg("ERROR : constructed an invalid double! ");
-      if (get_static_AbortFlag())
-        abort();
       get_static_InvalidFlag() = -2;
     }
     rep = new ConstDoubleRep(d);
@@ -95,6 +91,14 @@ public:
   Expr(const BigInt& I) : RCExpr(new ConstRealRep(Real(I))) {}
   /// constructor for <tt>BigRat</tt>
   Expr(const BigRat& R) : RCExpr(new ConstRealRep(Real(R))) {}
+  /// constructor from expression template
+  template <class TmplExpr,
+            class = std::enable_if_t<
+              boost::multiprecision::is_number_expression<TmplExpr>::value> >
+  Expr(const TmplExpr& R)
+    : RCExpr(new ConstRealRep(Real(
+        std::conditional_t<boost::multiprecision::number_category<TmplExpr>::value == boost::multiprecision::number_kind_integer,
+        BigInt, BigRat>(R)))) {}
 
   /// constructor for <tt>BigFloat</tt>
   Expr(const BigFloat& F) : RCExpr(new ConstRealRep(Real(F))) {}
@@ -173,9 +177,7 @@ public:
   /// /= operator
   Expr& operator/=(const Expr& e) {
     if ((e.rep)->getSign() == 0) {
-      core_error(" ERROR : division by zero ! ",__FILE__, __LINE__, false);
+      CGAL_error_msg("ERROR : division by zero ! ");
-      if (get_static_AbortFlag())
-        abort();
       get_static_InvalidFlag() = -3;
     }
     *this = new DivRep(rep, e.rep);
@@ -376,9 +378,7 @@ inline Expr operator*(const Expr& e1, const Expr& e2) {
 /// division
 inline Expr operator/(const Expr& e1, const Expr& e2) {
   if (e2.sign() == 0) {
-    core_error(" ERROR : division by zero ! ", __FILE__, __LINE__, false);
+    CGAL_error_msg("ERROR : division by zero ! ");
-    if (get_static_AbortFlag())
-      abort();
     get_static_InvalidFlag() = -4;
   }
   return Expr(new DivRep(e1.Rep(), e2.Rep()));
@@ -479,9 +479,7 @@ inline bool isDivisible(const Expr& e1, const Expr& e2) {
 /// square root
 inline Expr sqrt(const Expr& e) {
   if (e.sign() < 0) {
-    core_error(" ERROR : sqrt of negative value ! ", __FILE__, __LINE__, false);
+    CGAL_error_msg("ERROR : sqrt of negative value ! ");
-    if (get_static_AbortFlag())
-      abort();
     get_static_InvalidFlag() = -5;
   }
   return Expr(new SqrtRep(e.Rep()));

CGAL_Core/include/CGAL/CORE/ExprRep.h

@@ -564,9 +564,7 @@ public:
     I = ss.isolateRoot(n);
     // check whether n-th root exists
     if (I.first == 1 && I.second == 0) {
-      core_error("CORE ERROR! root index out of bound",
+      CGAL_error_msg("CORE ERROR! root index out of bound");
-                      __FILE__, __LINE__, true);
-      abort();
     }
     // test if the root isolated in I is 0:
     if ((I.first == 0)&&(I.second == 0))
@@ -583,9 +581,7 @@ public:
     ss.isolateRoots(I.first, I.second, v);
     I = v.front();
     if (v.size() != 1) {
-      core_error("CORE ERROR! non-isolating interval",
+      CGAL_error_msg("CORE ERROR! non-isolating interval");
-                      __FILE__, __LINE__, true);
-      abort();
     }
     ffVal = computeFilteredValue(); // Chee: this line seems unnecessary
   }
@@ -1092,8 +1088,7 @@ void AddSubRep<Operator>::computeExactFlags() {
           uMSB() = newValue.uMSB();   // chen: to get tighers value.
           sign() = newValue.sign();
         } else if (lowBound.isInfty()) {//check if rootbound is too big
-          core_error("AddSubRep:root bound has exceeded the maximum size\n \
+          CGAL_CORE_warning_msg(false, "AddSubRep:root bound has exceeded the maximum size but we still cannot decide zero.");
-            but we still cannot decide zero.\n", __FILE__, __LINE__, false);
         } else {               // Op(first, second) == 0
           lMSB() = CORE_negInfty;
           sign() = 0;
@@ -1186,8 +1181,7 @@ void AddSubRep<Operator>::computeExactFlags() {
           //8/9/01, Chee: implement escape precision here:
           if (i> get_static_EscapePrec()) {
             get_static_EscapePrecFlag() = -i.asLong();//negative means EscapePrec is used
-            core_error("Escape precision triggered at",
+            CGAL_CORE_warning_msg(false, "Escape precision triggered");
-                             __FILE__, __LINE__, false);
             if (get_static_EscapePrecWarning())
               std::cout<< "Escape Precision triggered at "
                       << get_static_EscapePrec() << " bits" << std::endl;
@@ -1204,8 +1198,7 @@ void AddSubRep<Operator>::computeExactFlags() {
 #endif
 
         if (sign() == 0 && ua .isInfty()) {
-          core_error("AddSubRep: root bound has exceeded the maximum size\n \
+          CGAL_error_msg("AddSubRep: root bound has exceeded the maximum size but we still cannot decide zero.");
-            but we still cannot decide zero.\n", __FILE__, __LINE__, true);
         } // if (sign == 0 && ua .isInfty())
       }// else do progressive
     }
@@ -1236,8 +1229,7 @@ void AddSubRep<Operator>::computeApproxValue(const extLong& relPrec,
   {
     std::ostringstream oss;
     oss << "CORE WARNING: a huge lMSB in AddSubRep: " << lMSB();
-    core_error(oss.str(),
+    CGAL_CORE_warning_msg(false, oss.str().c_str());
-                 __FILE__, __LINE__, false);
   }
 
   extLong rf = first->uMSB()-lMSB()+relPrec+EXTLONG_FOUR;  // 2 better

CGAL_Core/include/CGAL/CORE/Expr_impl.h

@@ -702,7 +702,7 @@ void computeExactFlags_temp(ConstRep* t, const Real &value) {
   } else {
     t->uMSB() = value.uMSB();
     t->lMSB() = value.lMSB();
-    core_error("Leaves in DAG is not exact!", __FILE__, __LINE__, true);
+    CGAL_error_msg("Leafs in DAG is not exact!");
   }
 
   t->sign() = value.sign();
@@ -809,8 +809,7 @@ void SqrtRep::computeExactFlags() {
 
   sign() = child->sign();
   if (sign() < 0)
-    core_error("squareroot is called with negative operand.",
+    CGAL_error_msg("square root is called with negative operand.");
-               __FILE__, __LINE__, true);
 
   uMSB() = child->uMSB() / EXTLONG_TWO;
   lMSB() = child->lMSB() / EXTLONG_TWO;
@@ -928,7 +927,7 @@ void DivRep::computeExactFlags() {
     second->computeExactFlags();
 
   if (!second->sign())
-    core_error("zero divisor.", __FILE__, __LINE__, true);
+    CGAL_error_msg("zero divisor.");
 
   if (!first->sign()) {// value must be exactly zero.
     reduceToZero();
@@ -1025,8 +1024,7 @@ void MultRep::computeApproxValue(const extLong& relPrec,
   {
     std::ostringstream oss;
     oss << "CORE WARNING: a huge lMSB in AddSubRep " <<  lMSB();
-    core_error(oss.str(),
+    CGAL_CORE_warning_msg(false, oss.str().c_str());
-                 __FILE__, __LINE__, false);
   }
 
   extLong r   = relPrec + EXTLONG_FOUR;
@@ -1048,8 +1046,7 @@ void DivRep::computeApproxValue(const extLong& relPrec,
   {
     std::ostringstream oss;
     oss << "CORE WARNING: a huge lMSB in AddSubRep " << lMSB();
-    core_error(oss.str(),
+    CGAL_CORE_warning_msg(false, oss.str().c_str());
-                 __FILE__, __LINE__, false);
   }
 
   extLong rr  = relPrec + EXTLONG_SEVEN;                // These rules come from
@@ -1082,7 +1079,9 @@ void Expr::debug(int mode, int level, int depthLimit) const {
   else if (mode == Expr::TREE_MODE)
     rep->debugTree(level, 0, depthLimit);
   else
-    core_error("unknown debugging mode", __FILE__, __LINE__, false);
+  {
+    CGAL_CORE_warning_msg(false, "unknown debugging mode");
+  }
   std::cout << "---- End Expr debug(): " << std::endl;
 }
 
@@ -1215,8 +1214,6 @@ void BinOpRep::debugTree(int level, int indent, int depthLimit) const {
   second->debugTree(level, indent + 2, depthLimit - 1);
 }
 
-CORE_MEMORY_IMPL(BigIntRep)
-CORE_MEMORY_IMPL(BigRatRep)
 CORE_MEMORY_IMPL(ConstDoubleRep)
 CORE_MEMORY_IMPL(ConstRealRep)
 

CGAL_Core/include/CGAL/CORE/Filter.h

@@ -137,8 +137,8 @@ public:
   }
   /// division
   filteredFp operator/ (const filteredFp& x) const {
-    if (x.fpVal == 0.0)
+    CGAL_CORE_warning_msg(x.fpVal != 0.0, "possible zero divisor!");
-      core_error("possible zero divisor!", __FILE__, __LINE__, false);
+
     double xxx = core_abs(x.fpVal) / x.maxAbs - (x.ind+1)*CORE_EPS + DBL_MIN;
     if (xxx > 0) {
       double val =  fpVal / x.fpVal;
@@ -149,8 +149,8 @@ public:
   }
   /// square root
   filteredFp sqrt () const {
-    if (fpVal < 0.0)
+
-      core_error("possible negative sqrt!", __FILE__, __LINE__, false);
+    CGAL_CORE_warning_msg( !(fpVal < 0.0), "possible negative sqrt!");
     if (fpVal > 0.0) {
       double val = std::sqrt(fpVal);
       return filteredFp(val,  ( maxAbs / fpVal ) * val, 1 + ind);

CGAL_Core/include/CGAL/CORE/Gmp.h

@@ -1,37 +0,0 @@
-/****************************************************************************
- * Core Library Version 1.7, August 2004
- * Copyright (c) 1995-2004 Exact Computation Project
- * All rights reserved.
- *
- * This file is part of CGAL (www.cgal.org).
- *
- * $URL$
- * $Id$
- * SPDX-License-Identifier: LGPL-3.0-or-later
- ***************************************************************************/
-
-// CORE LIBRARY FILE
-#ifndef _CORE_GMP_H_
-#define _CORE_GMP_H_
-
-#include <CGAL/CORE/Impl.h>
-#include <gmp.h>
-
-namespace CORE {
-
-CGAL_CORE_EXPORT std::ostream& io_write (std::ostream &, mpz_srcptr);
-CGAL_CORE_EXPORT std::ostream& io_write (std::ostream &, mpq_srcptr);
-CGAL_CORE_EXPORT std::istream& io_read (std::istream &, mpz_ptr);
-CGAL_CORE_EXPORT std::istream& io_read (std::istream &, mpq_ptr);
-//std::ostream& operator<< (std::ostream &, mpz_srcptr);
-//std::ostream& operator<< (std::ostream &, mpq_srcptr);
-//std::istream& operator>> (std::istream &, mpz_ptr);
-//std::istream& operator>> (std::istream &, mpq_ptr);
-
-} //namespace CORE
-
-#ifdef CGAL_HEADER_ONLY
-#include <CGAL/CORE/Gmp_impl.h>
-#endif // CGAL_HEADER_ONLY
-
-#endif // _CORE_GMP_H_

CGAL_Core/include/CGAL/CORE/Gmp_impl.h

@@ -1,265 +0,0 @@
-/****************************************************************************
- * Core Library Version 1.7, August 2004
- * Copyright (c) 1995-2004 Exact Computation Project
- * All rights reserved.
- *
- * file: GmpIO.cpp
- *                 Adapted from multi-files under /cxx in GMP's source distribution
- *
- * Zilin Du, 2003
- *
- * $URL$
- * $Id$
- * SPDX-License-Identifier: LGPL-3.0-only
- ***************************************************************************/
-
-/* Auxiliary functions for C++-style input of GMP types.
-
-Copyright 2001 Free Software Foundation, Inc.
-
-This file is part of the GNU MP Library.
-
-*/
-
-#ifdef CGAL_HEADER_ONLY
-#define CGAL_INLINE_FUNCTION inline
-#else
-#define CGAL_INLINE_FUNCTION
-#endif
-
-#include <CGAL/CORE/Gmp.h>
-#include <cctype>
-#include <iostream>
-#include <string>
-#include <cstdio>
-
-namespace CORE {
-
-CGAL_INLINE_FUNCTION
-int
-__gmp_istream_set_base (std::istream &i, char &c, bool &zero, bool &showbase)
-{
-  int base;
-  using std::ios;
-
-  zero = showbase = false;
-  switch (i.flags() & ios::basefield)
-    {
-    case ios::dec:
-      base = 10;
-      break;
-    case ios::hex:
-      base = 16;
-      break;
-    case ios::oct:
-      base = 8;
-      break;
-    default:
-      showbase = true; // look for initial "0" or "0x" or "0X"
-      if (c == '0')
-        {
-          if (! i.get(c))
-            c = 0; // reset or we might loop indefinitely
-
-          if (c == 'x' || c == 'X')
-            {
-              base = 16;
-              i.get(c);
-            }
-          else
-            {
-              base = 8;
-              zero = true; // if no other digit is read, the "0" counts
-            }
-        }
-      else
-        base = 10;
-      break;
-    }
-
-  return base;
-}
-
-CGAL_INLINE_FUNCTION
-void
-__gmp_istream_set_digits (std::string &s, std::istream &i, char &c, bool &ok, int base)
-{
-  switch (base)
-    {
-    case 10:
-      while (isdigit(c))
-        {
-          ok = true; // at least a valid digit was read
-          s += c;
-          if (! i.get(c))
-            break;
-        }
-      break;
-    case 8:
-      while (isdigit(c) && c != '8' && c != '9')
-        {
-          ok = true; // at least a valid digit was read
-          s += c;
-          if (! i.get(c))
-            break;
-        }
-      break;
-    case 16:
-      while (isxdigit(c))
-        {
-          ok = true; // at least a valid digit was read
-          s += c;
-          if (! i.get(c))
-            break;
-        }
-      break;
-    }
-}
-
-CGAL_INLINE_FUNCTION
-std::istream &
-//operator>> (std::istream &i, mpz_ptr z)
-io_read (std::istream &i, mpz_ptr z)
-{
-  using namespace std;
-  int base;
-  char c = 0;
-  std::string s;
-  bool ok = false, zero, showbase;
-
-  i.get(c); // start reading
-
-  if (i.flags() & ios::skipws) // skip initial whitespace
-    while (isspace(c) && i.get(c))
-      ;
-
-  if (c == '-' || c == '+') // sign
-    {
-      if (c == '-') // mpz_set_str doesn't accept '+'
-        s = "-";
-      i.get(c);
-    }
-
-  while (isspace(c) && i.get(c)) // skip whitespace
-    ;
-
-  base = __gmp_istream_set_base(i, c, zero, showbase); // select the base
-  __gmp_istream_set_digits(s, i, c, ok, base);         // read the number
-
-  if (i.good()) // last character read was non-numeric
-    i.putback(c);
-  else if (i.eof() && (ok || zero)) // stopped just before eof
-    i.clear();
-
-  if (ok)
-    mpz_set_str(z, s.c_str(), base); // extract the number
-  else if (zero)
-    mpz_set_ui(z, 0);
-  else
-    i.setstate(ios::failbit); // read failed
-
-  return i;
-}
-
-CGAL_INLINE_FUNCTION
-std::istream &
-//operator>> (std::istream &i, mpq_ptr q)
-io_read (std::istream &i, mpq_ptr q)
-{
-  using namespace std;
-  int base;
-  char c = 0;
-  std::string s;
-  bool ok = false, zero, showbase;
-
-  i.get(c); // start reading
-
-  if (i.flags() & ios::skipws) // skip initial whitespace
-    while (isspace(c) && i.get(c))
-      ;
-
-  if (c == '-' || c == '+') // sign
-    {
-      if (c == '-')
-        s = "-";
-      i.get(c);
-    }
-
-  while (isspace(c) && i.get(c)) // skip whitespace
-    ;
-
-  base = __gmp_istream_set_base(i, c, zero, showbase); // select the base
-  __gmp_istream_set_digits(s, i, c, ok, base);         // read the numerator
-
-  if (! ok && zero) // the only digit read was "0"
-    {
-      base = 10;
-      s += '0';
-      ok = true;
-    }
-
-  if (c == '/') // there's a denominator
-    {
-      bool zero2 = false;
-      int base2 = base;
-
-      s += '/';
-      ok = false; // denominator is mandatory
-      i.get(c);
-
-      while (isspace(c) && i.get(c)) // skip whitespace
-        ;
-
-      if (showbase) // check base of denominator
-        base2 = __gmp_istream_set_base(i, c, zero2, showbase);
-
-      if (base2 == base || base2 == 10) // read the denominator
-        __gmp_istream_set_digits(s, i, c, ok, base);
-
-      if (! ok && zero2) // the only digit read was "0"
-        {                // denominator is 0, but that's your business
-          s += '0';
-          ok = true;
-        }
-    }
-
-  if (i.good()) // last character read was non-numeric
-    i.putback(c);
-  else if (i.eof() && ok) // stopped just before eof
-    i.clear();
-
-  if (ok)
-    mpq_set_str(q, s.c_str(), base); // extract the number
-  else
-    i.setstate(ios::failbit); // read failed
-
-  return i;
-}
-
-CGAL_INLINE_FUNCTION
-std::ostream&
-//operator<< (std::ostream &o, mpz_srcptr z)
-io_write (std::ostream &o, mpz_srcptr z)
-{
-  char *str = new char [mpz_sizeinbase(z,10) + 2];
-  str = mpz_get_str(str, 10, z);
-  o << str ;
-  delete[] str;
-  return o;
-}
-
-CGAL_INLINE_FUNCTION
-std::ostream&
-//operator<< (std::ostream &o, mpq_srcptr q)
-io_write (std::ostream &o, mpq_srcptr q)
-{
-  // size according to GMP documentation
-  char *str = new char [mpz_sizeinbase(mpq_numref(q), 10) +
-                        mpz_sizeinbase (mpq_denref(q), 10) + 3];
-  str = mpq_get_str(str, 10, q);
-  o << str ;
-  delete[] str;
-  return o;
-}
-
-} //namespace CORE

CGAL_Core/include/CGAL/CORE/MemoryPool.h

@@ -57,7 +57,7 @@ public:
         t = t->next;
       }
     //);
-    //CGAL_warning_msg(count ==  nObjects * blocks.size(),
+    //CGAL_CORE_warning_msg(count ==  nObjects * blocks.size(),
     //                 "Cannot delete memory as there are cyclic references");
 
     if(count ==  nObjects * blocks.size()){

CGAL_Core/include/CGAL/CORE/Promote.h

@@ -26,10 +26,12 @@
  * SPDX-License-Identifier: LGPL-3.0-or-later
  ***************************************************************************/
 
-#ifndef __PROMOTE_H__
+#ifndef _CORE_PROMOTE_H__
-#define __PROMOTE_H__
+#define _CORE_PROMOTE_H__
 
 #include <CGAL/CORE/Impl.h>
+#include <CGAL/CORE/BigInt.h>
+#include <CGAL/CORE/BigRat.h>
 
 namespace CORE {
 
@@ -67,10 +69,10 @@ class Promotion<T, T> {
     typedef T ResultT;
 };
 
-#define MAX_TYPE(T1, T2)                \
+#define CORE_MAX_TYPE(T1, T2)                   \
   typename Promotion<T1, T2>::ResultT
 
-#define DEFINE_MAX_TYPE(T1, T2, Tr)        \
+#define CORE_DEFINE_MAX_TYPE(T1, T2, Tr)        \
   template<> class Promotion<T1, T2> {        \
     public:                                \
       typedef Tr ResultT;                \
@@ -83,15 +85,15 @@ class Promotion<T, T> {
 /*
  * For example:
  *
- * DEFINE_MAX_TYPE(BigInt, BigRat, BigRat)           // define the promotion
+ * CORE_DEFINE_MAX_TYPE(BigInt, BigRat, BigRat)           // define the promotion
  *
  * template<typename T1, typename T2>                 // define function f with type templates
- *   MAX_TYPE(T1, T2) f(T1& , T2& );
+ *   CORE_MAX_TYPE(T1, T2) f(T1& , T2& );
  *
  * or
  *
  * template<typename T1, typename T2>                 // define function f with type templates
- *   const MAX_TYPE(T1, T2)& f(T1& , T2& );
+ *   const CORE_MAX_TYPE(T1, T2)& f(T1& , T2& );
  *
  * BigInt  a  =  1;
  * BigRat  b  = "1/3";
@@ -119,30 +121,30 @@ class Promotion<T, T> {
  *
  */
 
-class BigInt;
+//class BigInt;
 class BigFloat;
-class BigRat;
+//class BigRat;
 class Expr;
 
-DEFINE_MAX_TYPE(long, BigInt, BigInt)
+CORE_DEFINE_MAX_TYPE(long, BigInt, BigInt)
-DEFINE_MAX_TYPE(long, BigFloat, BigFloat)
+CORE_DEFINE_MAX_TYPE(long, BigFloat, BigFloat)
-DEFINE_MAX_TYPE(long, BigRat, BigRat)
+CORE_DEFINE_MAX_TYPE(long, BigRat, BigRat)
-DEFINE_MAX_TYPE(long, Expr, Expr)
+CORE_DEFINE_MAX_TYPE(long, Expr, Expr)
 
-DEFINE_MAX_TYPE(int, BigInt, BigInt)
+CORE_DEFINE_MAX_TYPE(int, BigInt, BigInt)
-DEFINE_MAX_TYPE(int, BigFloat, BigFloat)
+CORE_DEFINE_MAX_TYPE(int, BigFloat, BigFloat)
-DEFINE_MAX_TYPE(int, BigRat, BigRat)
+CORE_DEFINE_MAX_TYPE(int, BigRat, BigRat)
-DEFINE_MAX_TYPE(int, Expr, Expr)
+CORE_DEFINE_MAX_TYPE(int, Expr, Expr)
 
-DEFINE_MAX_TYPE(BigInt, BigFloat, BigFloat)
+CORE_DEFINE_MAX_TYPE(BigInt, BigFloat, BigFloat)
-DEFINE_MAX_TYPE(BigInt, BigRat, BigRat)
+CORE_DEFINE_MAX_TYPE(BigInt, BigRat, BigRat)
-DEFINE_MAX_TYPE(BigInt, Expr, Expr)
+CORE_DEFINE_MAX_TYPE(BigInt, Expr, Expr)
 
-DEFINE_MAX_TYPE(BigFloat, BigRat, BigRat)
+CORE_DEFINE_MAX_TYPE(BigFloat, BigRat, BigRat)
-DEFINE_MAX_TYPE(BigFloat, Expr, Expr)
+CORE_DEFINE_MAX_TYPE(BigFloat, Expr, Expr)
 
-DEFINE_MAX_TYPE(BigRat, Expr, Expr)
+CORE_DEFINE_MAX_TYPE(BigRat, Expr, Expr)
 
 } //namespace CORE
 
-#endif //__PROMOTE_H__
+#endif //_CORE_PROMOTE_H__

CGAL_Core/include/CGAL/CORE/Real.h

@@ -277,12 +277,12 @@ const long halfLongMin = LONG_MIN /2;
 struct _real_add {
   template <class T>
   static Real eval(const T& a, const T& b) {
-    return a+b;
+    return T(a+b);
   }
   // specialized for two long values
   static Real eval(long a, long b) {
     if ((a > halfLongMax && b > halfLongMax) || (a < halfLongMin && b < halfLongMin))
-      return BigInt(a)+BigInt(b);
+      return BigInt(BigInt(a)+ BigInt(b));
     else
       return a+b;
   }
@@ -291,12 +291,12 @@ struct _real_add {
 struct _real_sub {
   template <class T>
   static Real eval(const T& a, const T& b) {
-    return a-b;
+    return T(a-b);
   }
   // specialized for two long values
   static Real eval(long a, long b) {
     if ((a > halfLongMax && b < halfLongMin) || (a < halfLongMin && b > halfLongMax))
-      return BigInt(a)-BigInt(b);
+      return BigInt(BigInt(a)-BigInt(b));
     else
       return a-b;
   }
@@ -305,12 +305,12 @@ struct _real_sub {
 struct _real_mul {
   template <class T>
   static Real eval(const T& a, const T& b) {
-    return a*b;
+    return T(a*b);
   }
   // specialized for two long values
   static Real eval(long a, long b) {
     if (flrLg(a) + flrLg(b) >= static_cast<int>(LONG_BIT-2))
-      return BigInt(a)*BigInt(b);
+      return BigInt(BigInt(a)*BigInt(b));
     else
       return a*b;
   }
@@ -357,7 +357,7 @@ struct real_div {
         bf_a.approx(a.BigRatValue(), bf_b.MSB() - bf_b.flrLgErr() + 1, CORE_posInfty);
         return bf_a.div(bf_b, r);
       } else // both are BigRat
-        return a.BigRatValue()/b.BigRatValue();
+        return BigRat(a.BigRatValue() / b.BigRatValue());
     } else if (a.ID() == REAL_BIGFLOAT || b.ID() == REAL_BIGFLOAT
                || a.ID() == REAL_DOUBLE || b.ID() == REAL_DOUBLE) {
       return a.BigFloatValue().div(b.BigFloatValue(), r);
@@ -478,11 +478,11 @@ inline Real sqrt(const Real& x) {
 // unary minus operator
 template <class T>
 inline Real Realbase_for<T>::operator-() const {
-  return -ker;
+  return T(- T(ker));
 }
 template <>
 inline Real RealLong::operator-() const {
-  return ker < -LONG_MAX ? -BigInt(ker) : -ker;
+  return ker < -LONG_MAX ? BigInt(- BigInt(ker)) : -ker;
 }
 
 inline void init_CORE() {

CGAL_Core/include/CGAL/CORE/RealRep.h

@@ -92,10 +92,10 @@ public:
   int ID() const;
 
   long longValue() const {
-    return ker.longValue();
+    return CORE::longValue(ker);
   }
   double doubleValue() const {
-    return ker.doubleValue();
+    return CORE::doubleValue(ker);
   }
   BigInt BigIntValue() const {
     return BigInt(ker);
@@ -231,7 +231,7 @@ inline BigInt   RealBigInt::BigIntValue() const {
 }
 template<>
 inline BigInt   RealBigRat::BigIntValue() const {
-  return ker.BigIntValue();
+  return CORE::BigIntValue(ker);
 }
 template<>
 inline BigInt RealBigFloat::BigIntValue() const {
@@ -500,11 +500,11 @@ inline unsigned long RealBigRat::height() const {
 // toString()
 template<>
 inline std::string RealBigInt::toString(long, bool) const {
-  return ker.get_str();
+  return ker.convert_to<std::string>();
 }
 template<>
 inline std::string RealBigRat::toString(long, bool) const {
-  return ker.get_str();
+  return ker.convert_to<std::string>();
 }
 template<>
 inline std::string RealBigFloat::toString(long prec, bool sci) const {

CGAL_Core/include/CGAL/CORE/extLong.h

@@ -31,6 +31,9 @@
 #include <CGAL/CORE/Impl.h>
 #include <CGAL/CORE/CoreAux.h>
 
+#include <limits>
+#include <type_traits>
+
 namespace CORE {
 
 #ifndef LONG_MAX
@@ -77,6 +80,9 @@ public:
   extLong(long);
   /// constructor for \c unsigned long
   extLong(unsigned long);
+  /// constructor for \c std::size_t
+  template<typename T, typename = std::enable_if_t<std::is_same_v<T,std::size_t> && !std::is_same_v<unsigned long, std::size_t>>>
+  extLong(T s);
   //@}
 
   /// \name Arithmetic and assignment operators
@@ -149,8 +155,7 @@ const extLong EXTLONG_EIGHT(8);
 //  private comparison function
 inline int extLong::cmp(const extLong& x) const {
   if (isNaN() || x.isNaN()) {
-    core_error("Two extLong NaN's cannot be compared!",
+    CGAL_CORE_warning_msg(false, "Two extLong NaN's cannot be compared!");
-               __FILE__, __LINE__, false);
   }
   return (val == x.val) ? 0 : ((val > x.val) ? 1 : -1);
 }
@@ -189,6 +194,17 @@ inline extLong::extLong(unsigned long u) {
   }
 }
 
+template <typename T, typename>
+inline extLong::extLong(T u) {
+  if (u >= (std::numeric_limits<std::size_t>::max)()) {
+    val  = EXTLONG_MAX;
+    flag = 1;
+  } else {
+    val = static_cast<long>(u);
+    flag = 0;
+  }
+}
+
 // isNaN defaults to false
 inline extLong::extLong(bool isNaN) : val(0), flag(0) {
   if (isNaN) {

CGAL_Core/include/CGAL/CORE/extLong_impl.h

@@ -77,7 +77,7 @@ extLong& extLong::operator+= (const extLong& y) {
   if (flag == 2 || y.flag == 2 || (flag * y.flag < 0)) {
 #ifdef CORE_DEBUG
     if (flag * y.flag < 0) //want a message at the first creation of NaN
-      core_error("extLong NaN Error in addition.", __FILE__, __LINE__, false);
+      CGAL_CORE_warning_msg(false, "extLong NaN Error in addition.");
 #endif
 
     *this = CORE_NaNLong;
@@ -96,7 +96,7 @@ extLong& extLong::operator-= (const extLong& y) {
   if (flag == 2 || y.flag == 2 || (flag * y.flag > 0)) {
 #ifdef CORE_DEBUG
     if (flag * y.flag > 0) //want a message at the first creation of NaN
-      core_error("extLong NaN Error in subtraction.", __FILE__, __LINE__, false);
+      CGAL_CORE_warning_msg(false, "extLong NaN Error in subtraction.");
 #endif
 
     *this = CORE_NaNLong;
@@ -131,7 +131,7 @@ extLong& extLong::operator*= (const extLong& y) {
       *this = CORE_negInfty;
     } else {
 #ifdef CORE_DEBUG
-      core_error("extLong NaN Error in multiplication.",__FILE__,__LINE__,false);
+      CGAL_CORE_warning_msg(false, "extLong NaN Error in multiplication.");
 #endif
       *this = CORE_NaNLong;
     }
@@ -144,9 +144,9 @@ extLong& extLong::operator/= (const extLong& y) {
   if (flag==2 || y.flag==2 || ((flag != 0) && (y.flag != 0)) || (y.val == 0)) {
 #ifdef CORE_DEBUG
     if (y.val == 0)
-      core_error("extLong NaN Error, Divide by Zero.", __FILE__, __LINE__, false);
+      CGAL_CORE_warning_msg(false, "extLong NaN Error, Divide by Zero.");
     else if ((flag !=0) && (y.flag !=0))
-      core_error("extLong NaN Error, +/-Inf/Inf.", __FILE__, __LINE__, false);
+      CGAL_CORE_warning_msg(false, "extLong NaN Error, +/-Inf/Inf.");
 #endif
 
     *this = CORE_NaNLong;
@@ -180,8 +180,7 @@ extLong extLong::operator- () const {
 //    you cannot interpret the returned value!
 CGAL_INLINE_FUNCTION
 int extLong::sign() const {
-  if (flag == 2)
+  CGAL_CORE_warning_msg(flag != 2, "NaN Sign can not be determined!");
-    core_error("NaN Sign can not be determined!", __FILE__, __LINE__, false);
   return ((val == 0) ? 0 : ((val > 0) ? 1 : -1));
 }
 

CGAL_Core/include/CGAL/CORE/poly/Curves.tcc

@@ -1336,7 +1336,7 @@ cout <<"Number of roots at " << xCurr << " are " << numRoots<<endl;
     if (!xCurr.isExact()){
       std::ostringstream oss;
       oss << "xCurr has error! xCurr=" << xCurr;
-      core_error(oss.str(), __FILE__, __LINE__, false);
+      CGAL_CORE_warning_msg(false, oss.str());
     }
    }//main while loop
 
@@ -1426,4 +1426,3 @@ void showIntervals(char* s, BFVecInterval &vI) {
 /*************************************************************************** */
 // END
 /*************************************************************************** */
-

CGAL_Core/include/CGAL/CORE/poly/Poly.h

@@ -48,6 +48,7 @@
 #define CORE_POLY_H
 
 #include <CGAL/CORE/BigFloat.h>
+#include <CGAL/CORE/BigRat.h>
 #include <CGAL/CORE/Promote.h>
 #include <vector>
 #include <CGAL/assertions.h>
@@ -196,12 +197,10 @@ public:
   /// In particular, if the value is 0, we return 0.
   /// @param oldMSB is any estimate of the negative log of the evaluation
   BigFloat evalExactSign(const BigFloat& val, const extLong& oldMSB=54) const;
+
   /// Polynomial evaluation that return the same type as its argument
-  /// Caution: The type T must be greater or equal to the type NT
-  ///         NOTE: Eventually, we will remove this restriction by
-  ///         introduce MaxType(NT,T) for the return type.
   template <class T>
-  MAX_TYPE(NT, T) eval(const T&) const;
+  CORE_MAX_TYPE(NT, T) eval(const T&) const;
 
   // Bounds
   BigFloat CauchyUpperBound() const;  // Cauchy Root Upper Bound

CGAL_Core/include/CGAL/CORE/poly/Poly.tcc

@@ -673,7 +673,7 @@ Polynomial<NT> Polynomial<NT>::pseudoRemainder (
   int bTrueDegree = tmpB.degree;
   C = NT(1);  // Initialized to C=1.
   if (bTrueDegree == -1)  {
-    core_error("ERROR in Polynomial<NT>::pseudoRemainder :\n    -- divide by zero polynomial", __FILE__, __LINE__, false);
+    CGAL_CORE_warning_msg(false, "ERROR in Polynomial<NT>::pseudoRemainder :\n    -- divide by zero polynomial");
     return Polynomial(0);  // Unit Polynomial (arbitrary!)
   }
   if (bTrueDegree > degree) {
@@ -771,8 +771,8 @@ BigFloat Polynomial<NT>::eval(const BigFloat& f) const {        // evaluation
 
 template <class NT>
 template <class T>
-MAX_TYPE(NT, T) Polynomial<NT>::eval(const T& f) const {        // evaluation
+CORE_MAX_TYPE(NT, T) Polynomial<NT>::eval(const T& f) const {        // evaluation
-  typedef MAX_TYPE(NT, T) ResultT;
+  typedef CORE_MAX_TYPE(NT, T) ResultT;
   if (degree == -1)
     return ResultT(0);
   if (degree == 0)
@@ -892,10 +892,10 @@ BigFloat Polynomial<NT>::CauchyUpperBound() const {
   NT mx = 0;
   int deg = getTrueDegree();
   for (int i = 0; i < deg; ++i) {
-    mx = core_max(mx, abs(coeff[i]));
+    mx = core_max(mx, NT(abs(coeff[i])));
   }
   Expr e = mx;
-  e /= Expr(abs(coeff[deg]));
+  e /= Expr(NT(abs(coeff[deg])));
   e.approx(CORE_INFTY, 2);
   // get an absolute approximate value with error < 1/4
   return (e.BigFloatValue().makeExact() + 2);
@@ -922,7 +922,7 @@ BigInt Polynomial<NT>::CauchyBound() const {
     /* compute B^{deg} */
     if (rhs <= lhs) {
       B <<= 1;
-      rhs *= (BigInt(1)<<deg);
+      rhs *= BigFloat(BigInt(BigInt(1)<<deg));
     } else
       break;
   }
@@ -959,7 +959,7 @@ BigInt Polynomial<NT>::UpperBound() const {
     /* compute B^{deg} */
     if (rhs <= (std::max)(lhsPos,lhsNeg)) {
       B <<= 1;
-      rhs *= (BigInt(1)<<deg);
+      rhs *= BigFloat(BigInt(BigInt(1)<<deg));
     } else
       break;
   }
@@ -975,9 +975,9 @@ BigFloat Polynomial<NT>::CauchyLowerBound() const {
   NT mx = 0;
   int deg = getTrueDegree();
   for (int i = 1; i <= deg; ++i) {
-    mx = core_max(mx, abs(coeff[i]));
+    mx = core_max(mx, NT(abs(coeff[i])));
   }
-  Expr e = Expr(abs(coeff[0]))/ Expr(abs(coeff[0]) + mx);
+  Expr e = Expr(NT(abs(coeff[0])))/ Expr(NT(NT(abs(coeff[0])) + mx));
   e.approx(2, CORE_INFTY);
   // get an relative approximate value with error < 1/4
   return (e.BigFloatValue().makeExact().div2());
@@ -1018,8 +1018,8 @@ BigFloat Polynomial<NT>::height() const {
   int deg = getTrueDegree();
   NT ht = 0;
   for (int i = 0; i< deg; i++)
-    if (ht < abs(coeff[i]))
+    if (ht < NT(abs(coeff[i])))
-      ht = abs(coeff[i]);
+      ht = NT(abs(coeff[i]));
   return BigFloat(ht);
 }
 

CGAL_Core/include/CGAL/CORE/poly/Sturm.h

@@ -607,8 +607,7 @@ public:
       if (ff == 0) {
         NEWTON_DIV_BY_ZERO = true;
         del = 0;
-        core_error("Zero divisor in Newton Iteration",
+        CGAL_CORE_warning_msg(false, "Zero divisor in Newton Iteration");
-                __FILE__, __LINE__, false);
         return 0;
       }
 
@@ -680,8 +679,7 @@ public:
       stepsize++; // heuristic
     } while ((del != 0) && ((del.uMSB() >= -prec) && (count >0))) ;
 
-    if (count == 0) core_error("newtonIterE: reached count=0",
+    CGAL_assertion_msg(count != 0, "newtonIterE: reached count=0");
-                            __FILE__, __LINE__, true);
     del = BigFloat(core_abs(del.m()), err, del.exp() );
     del.makeCeilExact();
     return val;

CGAL_Core/package_info/CGAL_Core/license.txt

@@ -1,2 +1 @@
-LGPL (v3)
 LGPL (v3 or later)

Circular_kernel_2/package_info/Circular_kernel_2/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Algebraic_kernel_for_circles
 Arithmetic_kernel
+CGAL_Core
 Cartesian_kernel
 Circular_kernel_2
 Distance_2

Circular_kernel_3/package_info/Circular_kernel_3/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Algebraic_kernel_for_spheres
 Arithmetic_kernel
+CGAL_Core
 Cartesian_kernel
 Circular_kernel_3
 Distance_2

Combinatorial_map/package_info/Combinatorial_map/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Arithmetic_kernel
 BGL
+CGAL_Core
 Cartesian_kernel
 Circulator
 Combinatorial_map

Convex_decomposition_3/package_info/Convex_decomposition_3/dependencies

@@ -2,6 +2,7 @@ Algebraic_foundations
 Arithmetic_kernel
 BGL
 Box_intersection_d
+CGAL_Core
 Cartesian_kernel
 Circulator
 Convex_decomposition_3

Convex_hull_3/package_info/Convex_hull_3/dependencies

@@ -1,6 +1,7 @@
 Algebraic_foundations
 Arithmetic_kernel
 BGL
+CGAL_Core
 Cartesian_kernel
 Circulator
 Convex_hull_2

Data/data/meshes/halfcube.off

@@ -0,0 +1,13 @@
+OFF
+5 4 0
+
+-1 -1 1
+-1 1 1
+1 -1 -1
+-1 1 -1
+-1 -1 -1
+3  0 4 2
+3  2 4 3
+3  4 0 1
+3  1 3 4
+