Add assertions in refiners.

The assertions check that the endpoints of the interval to refine have
different evaluation signs, or they are the same point and its evaluation
is zero.

Algebraic_kernel_d/include/CGAL/RS/bisection_refiner_1.h

@@ -47,7 +47,7 @@ operator()(const Polynomial_&,Bound_&,Bound_&,int){
 
 // This works with any type of polynomial, but only for Gmpfr bounds.
 // TODO: Beyond writing generically, optimize this function. This would
-// remove the need for the next function, which essentially the same.
+// remove the need for the next function, which is essentially the same.
 template<>
 void
 Bisection_refiner_1<Polynomial<Gmpz>,Gmpfr>::
@@ -58,8 +58,6 @@ operator()(const Polynomial<Gmpz> &pol,Gmpfr &left,Gmpfr &right,int prec){
         typedef CGAL::RS_AK1::Signat_1<Polynomial,Gmpfr>
                                                         Signat;
         CGAL_precondition(left<=right);
-        // TODO: add precondition to check whether the interval is a point
-        // or the evaluations on its endpoints have different signs
         //std::cout<<"refining ["<<left<<","<<right<<"]"<<std::endl;
 
         CGAL_RS_GMPFR_MAKE_UNIQUE(left,temp_left);
@@ -72,6 +70,7 @@ operator()(const Polynomial<Gmpz> &pol,Gmpfr &left,Gmpfr &right,int prec){
         mpfr_t center;
 
         sl=signof(left);
+        CGAL_precondition(sl!=signof(right)||(left==right&&sl==ZERO));
         if(sl==ZERO)
                 return;
         pl=left.get_precision();
@@ -120,8 +119,6 @@ operator()(const Polynomial<Gmpq> &pol,Gmpfr &left,Gmpfr &right,int prec){
         typedef CGAL::RS_AK1::Signat_1<Polynomial,Gmpfr>
                                                         Signat;
         CGAL_precondition(left<=right);
-        // TODO: add precondition to check whether the interval is a point
-        // or the evaluations on its endpoints have different signs
         //std::cout<<"refining ["<<left<<","<<right<<"]"<<std::endl;
 
         CGAL_RS_GMPFR_MAKE_UNIQUE(left,temp_left);
@@ -134,6 +131,7 @@ operator()(const Polynomial<Gmpq> &pol,Gmpfr &left,Gmpfr &right,int prec){
         mpfr_t center;
 
         sl=signof(left);
+        CGAL_precondition(sl!=signof(right)||(left==right&&sl==ZERO));
         if(sl==ZERO)
                 return;
         pl=left.get_precision();

Algebraic_kernel_d/include/CGAL/RS/rs3_k_refiner_1.h

@@ -26,6 +26,11 @@
 #include <rs3_fncts.h>
 #include "Gmpfr_make_unique.h"
 
+// If we want assertions, we need to evaluate.
+#ifndef CGAL_NO_ASSERTIONS
+#include "signat_1.h"
+#endif
+
 namespace CGAL{
 namespace RS3{
 
@@ -51,8 +56,15 @@ operator()
         typedef Polynomial_traits_d<Polynomial>         Ptraits;
         typedef Ptraits::Degree                         Degree;
         CGAL_precondition(left<=right);
-        // TODO: add precondition to check whether the interval is a point
+#ifndef CGAL_NO_ASSERTIONS
-        // or the evaluations on its endpoints have different signs
+        typedef Ptraits::Make_square_free               Sfpart;
+        typedef CGAL::RS_AK1::Signat_1<Polynomial,Gmpfr>
+                                                        Signat;
+        Polynomial sfpp=Sfpart()(pol);
+        Signat signof(sfpp);
+        CGAL::Sign sl=signof(left);
+        CGAL_precondition(sl!=signof(right)||(left==right&&sl==ZERO));
+#endif
         //std::cout<<"refining ["<<left<<","<<right<<"]"<<std::endl;
         int deg=Degree()(pol);
         mpz_t* coefficients=(mpz_t*)malloc((deg+1)*sizeof(mpz_t));
@@ -98,12 +110,21 @@ operator()
         typedef Polynomial_traits_d<ZPolynomial>        ZPtraits;
         typedef ZPtraits::Degree                        ZDegree;
         CGAL_precondition(left<=right);
-        // TODO: add precondition to check whether the interval is a point
+#ifndef CGAL_NO_ASSERTIONS
-        // or the evaluations on its endpoints have different signs
+        typedef ZPtraits::Make_square_free              ZSfpart;
+        typedef CGAL::RS_AK1::Signat_1<ZPolynomial,Gmpfr>
+                                                        Signat;
+#endif
         //std::cout<<"refining ["<<left<<","<<right<<"]"<<std::endl;
         Polynomial<Gmpz> zpol=CGAL::RS_AK1::Polynomial_converter_1<
                                         CGAL::Polynomial<Gmpq>,
                                         CGAL::Polynomial<Gmpz> >()(qpol);
+#ifndef CGAL_NO_ASSERTIONS
+        ZPolynomial zsfpp=ZSfpart()(zpol);
+        Signat signof(zsfpp);
+        CGAL::Sign sl=signof(left);
+        CGAL_precondition(sl!=signof(right)||(left==right&&sl==ZERO));
+#endif
         int deg=ZDegree()(zpol);
         mpz_t* coefficients=(mpz_t*)malloc((deg+1)*sizeof(mpz_t));
         __mpfi_struct interval;

Algebraic_kernel_d/include/CGAL/RS/rs3_refiner_1.h

@@ -26,6 +26,11 @@
 #include <rs3_fncts.h>
 #include "Gmpfr_make_unique.h"
 
+// If we want assertions, we need to evaluate.
+#ifndef CGAL_NO_ASSERTIONS
+#include "signat_1.h"
+#endif
+
 namespace CGAL{
 namespace RS3{
 
@@ -51,8 +56,15 @@ operator()
         typedef Polynomial_traits_d<Polynomial>         Ptraits;
         typedef Ptraits::Degree                         Degree;
         CGAL_precondition(left<=right);
-        // TODO: add precondition to check whether the interval is a point
+#ifndef CGAL_NO_ASSERTIONS
-        // or the evaluations on its endpoints have different signs
+        typedef Ptraits::Make_square_free               Sfpart;
+        typedef CGAL::RS_AK1::Signat_1<Polynomial,Gmpfr>
+                                                        Signat;
+        Polynomial sfpp=Sfpart()(pol);
+        Signat signof(sfpp);
+        CGAL::Sign sl=signof(left);
+        CGAL_precondition(sl!=signof(right)||(left==right&&sl==ZERO));
+#endif
         //std::cout<<"refining ["<<left<<","<<right<<"]"<<std::endl;
         int deg=Degree()(pol);
         mpz_t* coefficients=(mpz_t*)malloc((deg+1)*sizeof(mpz_t));
@@ -104,13 +116,22 @@ operator()
         typedef Polynomial_traits_d<ZPolynomial>        ZPtraits;
         typedef ZPtraits::Degree                        ZDegree;
         CGAL_precondition(left<=right);
-        // TODO: add precondition to check whether the interval is a point
+#ifndef CGAL_NO_ASSERTIONS
-        // or the evaluations on its endpoints have different signs
+        typedef ZPtraits::Make_square_free              ZSfpart;
+        typedef CGAL::RS_AK1::Signat_1<ZPolynomial,Gmpfr>
+                                                        Signat;
+#endif
         //std::cout<<"refining ["<<left<<","<<right<<"]"<<std::endl;
         // Construct a Gmpz polynomial from the original Gmpq polynomial.
         Polynomial<Gmpz> zpol=CGAL::RS_AK1::Polynomial_converter_1<
                                         CGAL::Polynomial<Gmpq>,
                                         CGAL::Polynomial<Gmpz> >()(qpol);
+#ifndef CGAL_NO_ASSERTIONS
+        ZPolynomial zsfpp=ZSfpart()(zpol);
+        Signat signof(zsfpp);
+        CGAL::Sign sl=signof(left);
+        CGAL_precondition(sl!=signof(right)||(left==right&&sl==ZERO));
+#endif
         int deg=ZDegree()(zpol);
         mpz_t* coefficients=(mpz_t*)malloc((deg+1)*sizeof(mpz_t));
         __mpfi_struct interval;