From c56c5b02419ea8e578cb89f0dee9abe30fe83e26 Mon Sep 17 00:00:00 2001
From: Marc Glisse <marc.glisse@inria.fr>
Date: Tue, 13 Sep 2016 14:31:58 +0200
Subject: [PATCH 1/6] Derive all NumTraits specializations from
 GenericNumTraits.

---
 Number_types/include/CGAL/CORE_BigFloat.h                  | 2 ++
 Number_types/include/CGAL/CORE_BigInt.h                    | 2 ++
 Number_types/include/CGAL/CORE_BigRat.h                    | 2 ++
 Number_types/include/CGAL/CORE_Expr.h                      | 2 ++
 Number_types/include/CGAL/Gmpfi.h                          | 2 ++
 Number_types/include/CGAL/Gmpfr.h                          | 2 ++
 Number_types/include/CGAL/Gmpq.h                           | 2 ++
 Number_types/include/CGAL/Gmpz.h                           | 2 ++
 Number_types/include/CGAL/Interval_nt.h                    | 2 ++
 Number_types/include/CGAL/Lazy_exact_nt.h                  | 2 ++
 Number_types/include/CGAL/MP_Float.h                       | 2 ++
 Number_types/include/CGAL/Mpzf.h                           | 2 ++
 Number_types/include/CGAL/Quotient.h                       | 2 ++
 Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h | 2 ++
 14 files changed, 28 insertions(+)

diff --git a/Number_types/include/CGAL/CORE_BigFloat.h b/Number_types/include/CGAL/CORE_BigFloat.h
index 2488af7d00d..59530c4faea 100644
--- a/Number_types/include/CGAL/CORE_BigFloat.h
+++ b/Number_types/include/CGAL/CORE_BigFloat.h
@@ -526,7 +526,9 @@ template <> class Real_embeddable_traits< CORE::BigFloat >
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::BigFloat>
+   : GenericNumTraits<CORE::BigFloat>
   {
     typedef CORE::BigFloat Real;
     typedef CORE::BigFloat NonInteger;
diff --git a/Number_types/include/CGAL/CORE_BigInt.h b/Number_types/include/CGAL/CORE_BigInt.h
index 288ebedbd0b..f3ce522670d 100644
--- a/Number_types/include/CGAL/CORE_BigInt.h
+++ b/Number_types/include/CGAL/CORE_BigInt.h
@@ -202,7 +202,9 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::BigInt>
+   : GenericNumTraits<CORE::BigInt>
   {
     typedef CORE::BigInt Real;
     typedef CORE::BigRat NonInteger;
diff --git a/Number_types/include/CGAL/CORE_BigRat.h b/Number_types/include/CGAL/CORE_BigRat.h
index 0be849bec7e..1895faa3681 100644
--- a/Number_types/include/CGAL/CORE_BigRat.h
+++ b/Number_types/include/CGAL/CORE_BigRat.h
@@ -236,7 +236,9 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::BigRat>
+   : GenericNumTraits<CORE::BigRat>
   {
     typedef CORE::BigRat Real;
     typedef CORE::BigRat NonInteger;
diff --git a/Number_types/include/CGAL/CORE_Expr.h b/Number_types/include/CGAL/CORE_Expr.h
index 579a2090e5a..976393dfaa6 100644
--- a/Number_types/include/CGAL/CORE_Expr.h
+++ b/Number_types/include/CGAL/CORE_Expr.h
@@ -191,7 +191,9 @@ template <> class Real_embeddable_traits< CORE::Expr >
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::Expr>
+   : GenericNumTraits<CORE::Expr>
   {
     typedef CORE::Expr Real;
     typedef CORE::Expr NonInteger;
diff --git a/Number_types/include/CGAL/Gmpfi.h b/Number_types/include/CGAL/Gmpfi.h
index 97bb80d8647..073bbf89633 100644
--- a/Number_types/include/CGAL/Gmpfi.h
+++ b/Number_types/include/CGAL/Gmpfi.h
@@ -337,7 +337,9 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpfi>
+   : GenericNumTraits<CGAL::Gmpfi>
   {
     typedef CGAL::Gmpfi Real;
     typedef CGAL::Gmpfi NonInteger;
diff --git a/Number_types/include/CGAL/Gmpfr.h b/Number_types/include/CGAL/Gmpfr.h
index 5179425ff19..4607f8e5cbf 100644
--- a/Number_types/include/CGAL/Gmpfr.h
+++ b/Number_types/include/CGAL/Gmpfr.h
@@ -157,7 +157,9 @@ public INTERN_RET::Real_embeddable_traits_base<Gmpfr,CGAL::Tag_true>{
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpfr>
+   : GenericNumTraits<CGAL::Gmpfr>
   {
     typedef CGAL::Gmpfr Real;
     typedef CGAL::Gmpfr NonInteger;
diff --git a/Number_types/include/CGAL/Gmpq.h b/Number_types/include/CGAL/Gmpq.h
index 38fd09242c4..08f0fc4db4b 100644
--- a/Number_types/include/CGAL/Gmpq.h
+++ b/Number_types/include/CGAL/Gmpq.h
@@ -136,7 +136,9 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpq>
+   : GenericNumTraits<CGAL::Gmpq>
   {
     typedef CGAL::Gmpq Real;
     typedef CGAL::Gmpq NonInteger;
diff --git a/Number_types/include/CGAL/Gmpz.h b/Number_types/include/CGAL/Gmpz.h
index b196789c267..69600c43a54 100644
--- a/Number_types/include/CGAL/Gmpz.h
+++ b/Number_types/include/CGAL/Gmpz.h
@@ -210,7 +210,9 @@ class Modular_traits< Gmpz > {
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpz>
+   : GenericNumTraits<CGAL::Gmpz>
   {     
     typedef CGAL::Gmpz Real;
     typedef CGAL::Gmpq NonInteger;
diff --git a/Number_types/include/CGAL/Interval_nt.h b/Number_types/include/CGAL/Interval_nt.h
index e725e74621e..6fa983d6c7a 100644
--- a/Number_types/include/CGAL/Interval_nt.h
+++ b/Number_types/include/CGAL/Interval_nt.h
@@ -1263,7 +1263,9 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<bool b> struct NumTraits<CGAL::Interval_nt<b> >
+    : GenericNumTraits<CGAL::Interval_nt<b> >
   {
     typedef CGAL::Interval_nt<b> Real;
     typedef CGAL::Interval_nt<b> NonInteger;
diff --git a/Number_types/include/CGAL/Lazy_exact_nt.h b/Number_types/include/CGAL/Lazy_exact_nt.h
index 4c0678a7976..1d76ce403bc 100644
--- a/Number_types/include/CGAL/Lazy_exact_nt.h
+++ b/Number_types/include/CGAL/Lazy_exact_nt.h
@@ -1422,7 +1422,9 @@ class Modular_traits<Lazy_exact_nt<ET> >
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<typename ET> struct NumTraits<CGAL::Lazy_exact_nt<ET> >
+   : GenericNumTraits<CGAL::Lazy_exact_nt<ET> >
   {
     typedef CGAL::Lazy_exact_nt<ET> Real;
     // typedef CGAL::Lazy_exact_nt<ET> NonInteger;
diff --git a/Number_types/include/CGAL/MP_Float.h b/Number_types/include/CGAL/MP_Float.h
index 0e1312be337..3103c45944a 100644
--- a/Number_types/include/CGAL/MP_Float.h
+++ b/Number_types/include/CGAL/MP_Float.h
@@ -883,7 +883,9 @@ CGAL_DEFINE_COERCION_TRAITS_FROM_TO(int, MP_Float)
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::MP_Float>
+   : GenericNumTraits<CGAL::MP_Float>
   {
     typedef CGAL::MP_Float Real;
     typedef CGAL::Quotient<CGAL::MP_Float> NonInteger;
diff --git a/Number_types/include/CGAL/Mpzf.h b/Number_types/include/CGAL/Mpzf.h
index 55ceb4ecb61..80f35024936 100644
--- a/Number_types/include/CGAL/Mpzf.h
+++ b/Number_types/include/CGAL/Mpzf.h
@@ -1129,7 +1129,9 @@ CGAL_DEFINE_COERCION_TRAITS_FROM_TO(mpz_class,Mpzf)
  */
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Mpzf>
+   : GenericNumTraits<CGAL::Mpzf>
   {
     typedef CGAL::Mpzf Real;
     /* Should this be Quotient<Mpzf>? Gmpq?  */
diff --git a/Number_types/include/CGAL/Quotient.h b/Number_types/include/CGAL/Quotient.h
index a1934fc12ee..548ceb180d0 100644
--- a/Number_types/include/CGAL/Quotient.h
+++ b/Number_types/include/CGAL/Quotient.h
@@ -854,7 +854,9 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template<class NT> struct NumTraits<CGAL::Quotient<NT> >
+   : GenericNumTraits<CGAL::Quotient<NT> >
   {
     typedef CGAL::Quotient<NT> Real;
     typedef CGAL::Quotient<NT> NonInteger;
diff --git a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
index c9d28d8a993..0f4a524dca2 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
@@ -24,8 +24,10 @@
 
 namespace Eigen {
   template<class> struct NumTraits;
+  template<class> struct GenericNumTraits;
   template <class NT,class ROOT, class ACDE_TAG, class FP_TAG>
   struct NumTraits<CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> >
+   : GenericNumTraits<CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> >
   {
     typedef CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> Real;
     typedef Real NonInteger;

From ddb5bf91e80922ba9c24e1328e3fc02c2d62bbfe Mon Sep 17 00:00:00 2001
From: Marc Glisse <marc.glisse@inria.fr>
Date: Tue, 13 Sep 2016 14:38:47 +0200
Subject: [PATCH 2/6] Optimize NumTraits::Literal for intervals.

---
 Number_types/include/CGAL/Interval_nt.h | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Number_types/include/CGAL/Interval_nt.h b/Number_types/include/CGAL/Interval_nt.h
index 6fa983d6c7a..eb80c7b0c6f 100644
--- a/Number_types/include/CGAL/Interval_nt.h
+++ b/Number_types/include/CGAL/Interval_nt.h
@@ -1270,6 +1270,7 @@ namespace Eigen {
     typedef CGAL::Interval_nt<b> Real;
     typedef CGAL::Interval_nt<b> NonInteger;
     typedef CGAL::Interval_nt<b> Nested;
+    typedef double Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }

From c86749ba016f42a9b861e846b154d08a73c17986 Mon Sep 17 00:00:00 2001
From: Marc Glisse <marc.glisse@inria.fr>
Date: Wed, 14 Sep 2016 13:04:05 +0200
Subject: [PATCH 3/6] Revert "Derive all NumTraits specializations from
 GenericNumTraits."

This reverts commit c56c5b02419ea8e578cb89f0dee9abe30fe83e26.
---
 Number_types/include/CGAL/CORE_BigFloat.h                  | 2 --
 Number_types/include/CGAL/CORE_BigInt.h                    | 2 --
 Number_types/include/CGAL/CORE_BigRat.h                    | 2 --
 Number_types/include/CGAL/CORE_Expr.h                      | 2 --
 Number_types/include/CGAL/Gmpfi.h                          | 2 --
 Number_types/include/CGAL/Gmpfr.h                          | 2 --
 Number_types/include/CGAL/Gmpq.h                           | 2 --
 Number_types/include/CGAL/Gmpz.h                           | 2 --
 Number_types/include/CGAL/Interval_nt.h                    | 2 --
 Number_types/include/CGAL/Lazy_exact_nt.h                  | 2 --
 Number_types/include/CGAL/MP_Float.h                       | 2 --
 Number_types/include/CGAL/Mpzf.h                           | 2 --
 Number_types/include/CGAL/Quotient.h                       | 2 --
 Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h | 2 --
 14 files changed, 28 deletions(-)

diff --git a/Number_types/include/CGAL/CORE_BigFloat.h b/Number_types/include/CGAL/CORE_BigFloat.h
index 59530c4faea..2488af7d00d 100644
--- a/Number_types/include/CGAL/CORE_BigFloat.h
+++ b/Number_types/include/CGAL/CORE_BigFloat.h
@@ -526,9 +526,7 @@ template <> class Real_embeddable_traits< CORE::BigFloat >
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::BigFloat>
-   : GenericNumTraits<CORE::BigFloat>
   {
     typedef CORE::BigFloat Real;
     typedef CORE::BigFloat NonInteger;
diff --git a/Number_types/include/CGAL/CORE_BigInt.h b/Number_types/include/CGAL/CORE_BigInt.h
index f3ce522670d..288ebedbd0b 100644
--- a/Number_types/include/CGAL/CORE_BigInt.h
+++ b/Number_types/include/CGAL/CORE_BigInt.h
@@ -202,9 +202,7 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::BigInt>
-   : GenericNumTraits<CORE::BigInt>
   {
     typedef CORE::BigInt Real;
     typedef CORE::BigRat NonInteger;
diff --git a/Number_types/include/CGAL/CORE_BigRat.h b/Number_types/include/CGAL/CORE_BigRat.h
index 1895faa3681..0be849bec7e 100644
--- a/Number_types/include/CGAL/CORE_BigRat.h
+++ b/Number_types/include/CGAL/CORE_BigRat.h
@@ -236,9 +236,7 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::BigRat>
-   : GenericNumTraits<CORE::BigRat>
   {
     typedef CORE::BigRat Real;
     typedef CORE::BigRat NonInteger;
diff --git a/Number_types/include/CGAL/CORE_Expr.h b/Number_types/include/CGAL/CORE_Expr.h
index 976393dfaa6..579a2090e5a 100644
--- a/Number_types/include/CGAL/CORE_Expr.h
+++ b/Number_types/include/CGAL/CORE_Expr.h
@@ -191,9 +191,7 @@ template <> class Real_embeddable_traits< CORE::Expr >
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CORE::Expr>
-   : GenericNumTraits<CORE::Expr>
   {
     typedef CORE::Expr Real;
     typedef CORE::Expr NonInteger;
diff --git a/Number_types/include/CGAL/Gmpfi.h b/Number_types/include/CGAL/Gmpfi.h
index 073bbf89633..97bb80d8647 100644
--- a/Number_types/include/CGAL/Gmpfi.h
+++ b/Number_types/include/CGAL/Gmpfi.h
@@ -337,9 +337,7 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpfi>
-   : GenericNumTraits<CGAL::Gmpfi>
   {
     typedef CGAL::Gmpfi Real;
     typedef CGAL::Gmpfi NonInteger;
diff --git a/Number_types/include/CGAL/Gmpfr.h b/Number_types/include/CGAL/Gmpfr.h
index 4607f8e5cbf..5179425ff19 100644
--- a/Number_types/include/CGAL/Gmpfr.h
+++ b/Number_types/include/CGAL/Gmpfr.h
@@ -157,9 +157,7 @@ public INTERN_RET::Real_embeddable_traits_base<Gmpfr,CGAL::Tag_true>{
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpfr>
-   : GenericNumTraits<CGAL::Gmpfr>
   {
     typedef CGAL::Gmpfr Real;
     typedef CGAL::Gmpfr NonInteger;
diff --git a/Number_types/include/CGAL/Gmpq.h b/Number_types/include/CGAL/Gmpq.h
index 08f0fc4db4b..38fd09242c4 100644
--- a/Number_types/include/CGAL/Gmpq.h
+++ b/Number_types/include/CGAL/Gmpq.h
@@ -136,9 +136,7 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpq>
-   : GenericNumTraits<CGAL::Gmpq>
   {
     typedef CGAL::Gmpq Real;
     typedef CGAL::Gmpq NonInteger;
diff --git a/Number_types/include/CGAL/Gmpz.h b/Number_types/include/CGAL/Gmpz.h
index 69600c43a54..b196789c267 100644
--- a/Number_types/include/CGAL/Gmpz.h
+++ b/Number_types/include/CGAL/Gmpz.h
@@ -210,9 +210,7 @@ class Modular_traits< Gmpz > {
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Gmpz>
-   : GenericNumTraits<CGAL::Gmpz>
   {     
     typedef CGAL::Gmpz Real;
     typedef CGAL::Gmpq NonInteger;
diff --git a/Number_types/include/CGAL/Interval_nt.h b/Number_types/include/CGAL/Interval_nt.h
index eb80c7b0c6f..5dfa8b33bc4 100644
--- a/Number_types/include/CGAL/Interval_nt.h
+++ b/Number_types/include/CGAL/Interval_nt.h
@@ -1263,9 +1263,7 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<bool b> struct NumTraits<CGAL::Interval_nt<b> >
-    : GenericNumTraits<CGAL::Interval_nt<b> >
   {
     typedef CGAL::Interval_nt<b> Real;
     typedef CGAL::Interval_nt<b> NonInteger;
diff --git a/Number_types/include/CGAL/Lazy_exact_nt.h b/Number_types/include/CGAL/Lazy_exact_nt.h
index 1d76ce403bc..4c0678a7976 100644
--- a/Number_types/include/CGAL/Lazy_exact_nt.h
+++ b/Number_types/include/CGAL/Lazy_exact_nt.h
@@ -1422,9 +1422,7 @@ class Modular_traits<Lazy_exact_nt<ET> >
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<typename ET> struct NumTraits<CGAL::Lazy_exact_nt<ET> >
-   : GenericNumTraits<CGAL::Lazy_exact_nt<ET> >
   {
     typedef CGAL::Lazy_exact_nt<ET> Real;
     // typedef CGAL::Lazy_exact_nt<ET> NonInteger;
diff --git a/Number_types/include/CGAL/MP_Float.h b/Number_types/include/CGAL/MP_Float.h
index 3103c45944a..0e1312be337 100644
--- a/Number_types/include/CGAL/MP_Float.h
+++ b/Number_types/include/CGAL/MP_Float.h
@@ -883,9 +883,7 @@ CGAL_DEFINE_COERCION_TRAITS_FROM_TO(int, MP_Float)
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::MP_Float>
-   : GenericNumTraits<CGAL::MP_Float>
   {
     typedef CGAL::MP_Float Real;
     typedef CGAL::Quotient<CGAL::MP_Float> NonInteger;
diff --git a/Number_types/include/CGAL/Mpzf.h b/Number_types/include/CGAL/Mpzf.h
index 80f35024936..55ceb4ecb61 100644
--- a/Number_types/include/CGAL/Mpzf.h
+++ b/Number_types/include/CGAL/Mpzf.h
@@ -1129,9 +1129,7 @@ CGAL_DEFINE_COERCION_TRAITS_FROM_TO(mpz_class,Mpzf)
  */
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<> struct NumTraits<CGAL::Mpzf>
-   : GenericNumTraits<CGAL::Mpzf>
   {
     typedef CGAL::Mpzf Real;
     /* Should this be Quotient<Mpzf>? Gmpq?  */
diff --git a/Number_types/include/CGAL/Quotient.h b/Number_types/include/CGAL/Quotient.h
index 548ceb180d0..a1934fc12ee 100644
--- a/Number_types/include/CGAL/Quotient.h
+++ b/Number_types/include/CGAL/Quotient.h
@@ -854,9 +854,7 @@ public:
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template<class NT> struct NumTraits<CGAL::Quotient<NT> >
-   : GenericNumTraits<CGAL::Quotient<NT> >
   {
     typedef CGAL::Quotient<NT> Real;
     typedef CGAL::Quotient<NT> NonInteger;
diff --git a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
index 0f4a524dca2..c9d28d8a993 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
@@ -24,10 +24,8 @@
 
 namespace Eigen {
   template<class> struct NumTraits;
-  template<class> struct GenericNumTraits;
   template <class NT,class ROOT, class ACDE_TAG, class FP_TAG>
   struct NumTraits<CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> >
-   : GenericNumTraits<CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> >
   {
     typedef CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> Real;
     typedef Real NonInteger;

From b7b492d9c85a1139c95c00464ba2d29b59e781df Mon Sep 17 00:00:00 2001
From: Marc Glisse <marc.glisse@inria.fr>
Date: Wed, 14 Sep 2016 13:12:35 +0200
Subject: [PATCH 4/6] Manually define Eigen::NumTraits<NT>::Literal for each
 specialization.

Defined to NT, no try is made to optimize for now.
---
 Number_types/include/CGAL/CORE_BigFloat.h                  | 1 +
 Number_types/include/CGAL/CORE_BigInt.h                    | 1 +
 Number_types/include/CGAL/CORE_BigRat.h                    | 1 +
 Number_types/include/CGAL/CORE_Expr.h                      | 1 +
 Number_types/include/CGAL/Gmpfi.h                          | 1 +
 Number_types/include/CGAL/Gmpfr.h                          | 1 +
 Number_types/include/CGAL/Gmpq.h                           | 1 +
 Number_types/include/CGAL/Gmpz.h                           | 1 +
 Number_types/include/CGAL/Lazy_exact_nt.h                  | 1 +
 Number_types/include/CGAL/MP_Float.h                       | 1 +
 Number_types/include/CGAL/Mpzf.h                           | 1 +
 Number_types/include/CGAL/Quotient.h                       | 1 +
 Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h | 1 +
 13 files changed, 13 insertions(+)

diff --git a/Number_types/include/CGAL/CORE_BigFloat.h b/Number_types/include/CGAL/CORE_BigFloat.h
index 2488af7d00d..09302bcdfa3 100644
--- a/Number_types/include/CGAL/CORE_BigFloat.h
+++ b/Number_types/include/CGAL/CORE_BigFloat.h
@@ -531,6 +531,7 @@ namespace Eigen {
     typedef CORE::BigFloat Real;
     typedef CORE::BigFloat NonInteger;
     typedef CORE::BigFloat Nested;
+    typedef CORE::BigFloat Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/CORE_BigInt.h b/Number_types/include/CGAL/CORE_BigInt.h
index 288ebedbd0b..a3c18b16101 100644
--- a/Number_types/include/CGAL/CORE_BigInt.h
+++ b/Number_types/include/CGAL/CORE_BigInt.h
@@ -207,6 +207,7 @@ namespace Eigen {
     typedef CORE::BigInt Real;
     typedef CORE::BigRat NonInteger;
     typedef CORE::BigInt Nested;
+    typedef CORE::BigInt Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/CORE_BigRat.h b/Number_types/include/CGAL/CORE_BigRat.h
index 0be849bec7e..6ab81031299 100644
--- a/Number_types/include/CGAL/CORE_BigRat.h
+++ b/Number_types/include/CGAL/CORE_BigRat.h
@@ -241,6 +241,7 @@ namespace Eigen {
     typedef CORE::BigRat Real;
     typedef CORE::BigRat NonInteger;
     typedef CORE::BigRat Nested;
+    typedef CORE::BigRat Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/CORE_Expr.h b/Number_types/include/CGAL/CORE_Expr.h
index 579a2090e5a..4bd38945006 100644
--- a/Number_types/include/CGAL/CORE_Expr.h
+++ b/Number_types/include/CGAL/CORE_Expr.h
@@ -196,6 +196,7 @@ namespace Eigen {
     typedef CORE::Expr Real;
     typedef CORE::Expr NonInteger;
     typedef CORE::Expr Nested;
+    typedef CORE::Expr Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpfi.h b/Number_types/include/CGAL/Gmpfi.h
index 97bb80d8647..479f1608a4b 100644
--- a/Number_types/include/CGAL/Gmpfi.h
+++ b/Number_types/include/CGAL/Gmpfi.h
@@ -342,6 +342,7 @@ namespace Eigen {
     typedef CGAL::Gmpfi Real;
     typedef CGAL::Gmpfi NonInteger;
     typedef CGAL::Gmpfi Nested;
+    typedef CGAL::Gmpfi Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpfr.h b/Number_types/include/CGAL/Gmpfr.h
index 5179425ff19..94bb613b61e 100644
--- a/Number_types/include/CGAL/Gmpfr.h
+++ b/Number_types/include/CGAL/Gmpfr.h
@@ -162,6 +162,7 @@ namespace Eigen {
     typedef CGAL::Gmpfr Real;
     typedef CGAL::Gmpfr NonInteger;
     typedef CGAL::Gmpfr Nested;
+    typedef CGAL::Gmpfr Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpq.h b/Number_types/include/CGAL/Gmpq.h
index 38fd09242c4..2fde983a7b3 100644
--- a/Number_types/include/CGAL/Gmpq.h
+++ b/Number_types/include/CGAL/Gmpq.h
@@ -141,6 +141,7 @@ namespace Eigen {
     typedef CGAL::Gmpq Real;
     typedef CGAL::Gmpq NonInteger;
     typedef CGAL::Gmpq Nested;
+    typedef CGAL::Gmpq Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Gmpz.h b/Number_types/include/CGAL/Gmpz.h
index b196789c267..5a1b15dbb35 100644
--- a/Number_types/include/CGAL/Gmpz.h
+++ b/Number_types/include/CGAL/Gmpz.h
@@ -215,6 +215,7 @@ namespace Eigen {
     typedef CGAL::Gmpz Real;
     typedef CGAL::Gmpq NonInteger;
     typedef CGAL::Gmpz Nested;
+    typedef CGAL::Gmpz Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Lazy_exact_nt.h b/Number_types/include/CGAL/Lazy_exact_nt.h
index 4c0678a7976..77350845ba6 100644
--- a/Number_types/include/CGAL/Lazy_exact_nt.h
+++ b/Number_types/include/CGAL/Lazy_exact_nt.h
@@ -1428,6 +1428,7 @@ namespace Eigen {
     // typedef CGAL::Lazy_exact_nt<ET> NonInteger;
     typedef CGAL::Lazy_exact_nt<typename NumTraits<ET>::NonInteger> NonInteger;
     typedef CGAL::Lazy_exact_nt<ET> Nested;
+    typedef CGAL::Lazy_exact_nt<ET> Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/MP_Float.h b/Number_types/include/CGAL/MP_Float.h
index 0e1312be337..06436b64731 100644
--- a/Number_types/include/CGAL/MP_Float.h
+++ b/Number_types/include/CGAL/MP_Float.h
@@ -888,6 +888,7 @@ namespace Eigen {
     typedef CGAL::MP_Float Real;
     typedef CGAL::Quotient<CGAL::MP_Float> NonInteger;
     typedef CGAL::MP_Float Nested;
+    typedef CGAL::MP_Float Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Mpzf.h b/Number_types/include/CGAL/Mpzf.h
index 55ceb4ecb61..930f6bdea40 100644
--- a/Number_types/include/CGAL/Mpzf.h
+++ b/Number_types/include/CGAL/Mpzf.h
@@ -1135,6 +1135,7 @@ namespace Eigen {
     /* Should this be Quotient<Mpzf>? Gmpq?  */
     typedef CGAL::Mpzf NonInteger;
     typedef CGAL::Mpzf Nested;
+    typedef CGAL::Mpzf Literal;
 
     static inline Real epsilon() { return 0; }
     static inline Real dummy_precision() { return 0; }
diff --git a/Number_types/include/CGAL/Quotient.h b/Number_types/include/CGAL/Quotient.h
index a1934fc12ee..2617ac92dd8 100644
--- a/Number_types/include/CGAL/Quotient.h
+++ b/Number_types/include/CGAL/Quotient.h
@@ -859,6 +859,7 @@ namespace Eigen {
     typedef CGAL::Quotient<NT> Real;
     typedef CGAL::Quotient<NT> NonInteger;
     typedef CGAL::Quotient<NT> Nested;
+    typedef CGAL::Quotient<NT> Literal;
 
     static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
     static inline Real dummy_precision() { return NumTraits<NT>::dummy_precision(); }
diff --git a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
index c9d28d8a993..725e8b177e2 100644
--- a/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
+++ b/Number_types/include/CGAL/Sqrt_extension/Eigen_NumTraits.h
@@ -30,6 +30,7 @@ namespace Eigen {
     typedef CGAL::Sqrt_extension<NT, ROOT, ACDE_TAG, FP_TAG> Real;
     typedef Real NonInteger;
     typedef Real Nested;
+    typedef Real Literal;
 
     static inline Real epsilon() { return NumTraits<NT>::epsilon(); }
 

From 147ebae4d6ba604a1f1be5b942007ebcbdc7492a Mon Sep 17 00:00:00 2001
From: Andreas Fabri <andreas.fabri@geometryfactory.com>
Date: Wed, 31 Aug 2016 09:13:38 +0200
Subject: [PATCH 5/6] Fix bug in polyline simplification: We had hardwired that
 we use Exact_predicates_tag which is slow for EPEC in particular with
 Quotient<MP_float> or leda::real

We determine the appropriate tag using Algebraic_structure_traits<FT>::Is_exact
---
 .../CGAL/Polyline_simplification_2/simplify.h        |  4 ++--
 .../include/CGAL/Constrained_triangulation_2.h       | 12 ++++++++++++
 2 files changed, 14 insertions(+), 2 deletions(-)

diff --git a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
index 9f0f46f38e5..9b6a4002b39 100644
--- a/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
+++ b/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/simplify.h
@@ -339,7 +339,7 @@ template <class Traits, class Container, class CostFunction, class StopFunction>
   typedef Vertex_base_2< K > Vb;
   typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
   typedef CGAL::Triangulation_data_structure_2<Vb,Fb> TDS;
-  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, CGAL::Exact_predicates_tag> CDT;
+  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS,typename internal::Itag<K>::type>  CDT;
   typedef CGAL::Constrained_triangulation_plus_2<CDT>       PCT;
   typedef typename PCT::Constraint_id Constraint_id;
   typedef typename PCT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
@@ -387,7 +387,7 @@ Simplifies an open or closed polyline given as an iterator range of 2D \cgal poi
   typedef Vertex_base_2< K > Vb;
   typedef CGAL::Constrained_triangulation_face_base_2<K> Fb;
   typedef CGAL::Triangulation_data_structure_2<Vb,Fb> TDS;
-  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS, CGAL::Exact_predicates_tag> CDT;
+  typedef CGAL::Constrained_Delaunay_triangulation_2<K, TDS,typename internal::Itag<K>::type > CDT;
   typedef CGAL::Constrained_triangulation_plus_2<CDT>       PCT;
   typedef typename PCT::Constraint_id Constraint_id;
   typedef typename PCT::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;
diff --git a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
index 4ffa91894a0..46c422d016e 100644
--- a/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_triangulation_2.h
@@ -32,12 +32,24 @@
 #include <CGAL/intersections.h>
 #include <CGAL/squared_distance_2.h>
 
+#include <boost/mpl/if.hpp>
+
 namespace CGAL {
 
 struct No_intersection_tag{};
 struct Exact_intersections_tag{}; // to be used with an exact number type
 struct Exact_predicates_tag{}; // to be used with filtered exact number
 
+namespace internal {
+
+template <typename K>
+struct Itag {
+  typedef typename boost::mpl::if_<typename Algebraic_structure_traits<typename K::FT>::Is_exact,
+                                   Exact_intersections_tag,
+                                   Exact_predicates_tag>::type type;
+};
+
+} // namespace internal
 
 template < class Gt, 
            class Tds = Triangulation_data_structure_2 <

From 343fb726fa8a19666a6c18c44ed30250d17f362e Mon Sep 17 00:00:00 2001
From: Sebastien Loriot <sloriot.ml@gmail.com>
Date: Thu, 15 Sep 2016 15:52:47 +0200
Subject: [PATCH 6/6] Add missing include directive

---
 .../CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h  | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
index 7ab4762e60f..5b9a0299b62 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/polygon_soup_to_polygon_mesh.h
@@ -25,6 +25,7 @@
 #include <CGAL/Polyhedron_incremental_builder_3.h>
 #include <CGAL/boost/graph/Euler_operations.h>
 #include <CGAL/property_map.h>
+#include <CGAL/algorithm.h>
 #include <set>
 
 namespace CGAL