diff --git a/Number_types/doc_tex/NumberTypeSupport_ref/Gmpfr.tex b/Number_types/doc_tex/NumberTypeSupport_ref/Gmpfr.tex
index 57a67058ad8..3b9b396b0a4 100644
--- a/Number_types/doc_tex/NumberTypeSupport_ref/Gmpfr.tex
+++ b/Number_types/doc_tex/NumberTypeSupport_ref/Gmpfr.tex
@@ -73,7 +73,7 @@ This type is \ccc{ImplicitInteroperable} with \ccc{Gmpz}, \verb-long-,
 \ccConstructor{Gmpfr(const Gmpzf &zf);}
         {Creates a \ccc{Gmpfr}, initialized with the value of \ccc{zf}.}
 
-\ccConstructor{Gmpfr(std::pair<Gmpz,long> ie);}
+\ccConstructor{Gmpfr(const std::pair<Gmpz,long> &ie);}
         {Creates a \ccc{Gmpfr}, initialized with the value of
         \( ie.first \times 2^{ie.second} \) .}
 
@@ -331,8 +331,8 @@ the compared numbers is \ccc{NaN}, the \ccc{erange} flag is set.
 
 \ccMethod{bool is_square(const Gmpfr &y);}
         {Returns \ccc{true} iff \ccVar~is the square of a number
-        representable by an object of this type, calculating it and storing
-        it in \ccc{y}.}
+        representable by an object of this type, computing and storing it
+        in \ccc{y}.}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -348,7 +348,7 @@ the compared numbers is \ccc{NaN}, the \ccc{erange} flag is set.
 
 \ccFunction{std::ostream& operator<<(std::ostream& out, const Gmpfr& f);}
         {If the ostream \ccc{out} is in pretty-print mode, writes a decimal
-        approximatin of \ccc{f} to \ccc{out}. Otherwise, writes \ccc{f} to
+        approximation of \ccc{f} to \ccc{out}. Otherwise, writes \ccc{f} to
         \ccc{out} in the form \(MeE\), where \(M\) is its mantissa and
         \(E\) is its exponent, both in base 10.}
 
diff --git a/Number_types/include/CGAL/GMP/Gmpfr_type.h b/Number_types/include/CGAL/GMP/Gmpfr_type.h
index b476850aa10..863a551988f 100644
--- a/Number_types/include/CGAL/GMP/Gmpfr_type.h
+++ b/Number_types/include/CGAL/GMP/Gmpfr_type.h
@@ -255,7 +255,7 @@ class Gmpfr:
                 }
         }
 
-        Gmpfr(Gmpzf f,
+        Gmpfr(const Gmpzf &f,
               std::float_round_style r,
               Gmpfr::Precision_type p=Gmpfr::get_default_precision()){
                 CGAL_assertion(p>=MPFR_PREC_MIN&&p<=MPFR_PREC_MAX);
@@ -264,7 +264,7 @@ class Gmpfr:
                 mpfr_mul_2si(fr(),fr(),f.exp(),_gmp_rnd(r));
         }
 
-        Gmpfr(Gmpzf f,Gmpfr::Precision_type p){
+        Gmpfr(const Gmpzf &f,Gmpfr::Precision_type p){
                 CGAL_assertion(p>=MPFR_PREC_MIN&&p<=MPFR_PREC_MAX);
                 mpfr_init2(fr(),p);
                 mpfr_set_z(fr(),f.man(),mpfr_get_default_rounding_mode());
@@ -274,7 +274,7 @@ class Gmpfr:
                              mpfr_get_default_rounding_mode());
         }
 
-        Gmpfr(Gmpzf f){
+        Gmpfr(const Gmpzf &f){
                 mpfr_init2(fr(),
                            static_cast<Gmpfr::Precision_type>(
                                    mpz_sizeinbase(f.man(),2)<MPFR_PREC_MIN?
@@ -288,7 +288,7 @@ class Gmpfr:
                 CGAL_assertion_msg(inexact==0,"inexact conversion from Gmpzf");
         }
 
-        Gmpfr(std::pair<Gmpz,long> intexp,
+        Gmpfr(const std::pair<Gmpz,long> &intexp,
               std::float_round_style r=Gmpfr::get_default_rndmode(),
               Gmpfr::Precision_type p=Gmpfr::get_default_precision()){
                 CGAL_assertion(p>=MPFR_PREC_MIN&&p<=MPFR_PREC_MAX);
@@ -297,7 +297,7 @@ class Gmpfr:
                 mpfr_mul_2si(fr(),fr(),intexp.second,_gmp_rnd(r));
         }
 
-        Gmpfr(std::pair<Gmpz,long> intexp,Gmpfr::Precision_type p){
+        Gmpfr(const std::pair<Gmpz,long> &intexp,Gmpfr::Precision_type p){
                 CGAL_assertion(p>=MPFR_PREC_MIN&&p<=MPFR_PREC_MAX);
                 mpfr_init2(fr(),p);
                 mpfr_set_z(fr(),
diff --git a/Number_types/test/Number_types/Gmpfr.cpp b/Number_types/test/Number_types/Gmpfr.cpp
index 0412939457f..e1c1b5d0f96 100644
--- a/Number_types/test/Number_types/Gmpfr.cpp
+++ b/Number_types/test/Number_types/Gmpfr.cpp
@@ -116,15 +116,26 @@ int test_to_integer_exp(CGAL::Gmpfr f){
         }
 }
 
+// This function checks equality between an _NT x and a Gmpfr y.
 template<class _NT>
-int test_constructors(_NT x){
+int are_different(const _NT &x,const CGAL::Gmpfr &y){
+        return x!=y;
+}
+
+template<>
+int are_different(const std::pair<CGAL::Gmpz,long> &x,const CGAL::Gmpfr &y){
+        return(mpfr_cmp_si_2exp(y.fr(),mpz_get_si(x.first.mpz()),x.second));
+}
+
+template<class _NT>
+int test_constructors(const _NT &x){
         typedef CGAL::Gmpfr     Gmpfr;
         typedef _NT             NT;
         bool fail=false;
         Gmpfr::set_default_precision(70);
         Gmpfr f(x);
         // this conversion should be exact
-        if(f!=x){
+        if(are_different(x,f)){
                 std::cerr<<"failed default construction! (inexact)"<<std::endl;
                 fail=true;
         }
@@ -173,6 +184,9 @@ int main(){
   _TEST("constructors Gmpz",
         test_constructors<CGAL::Gmpz>((CGAL::Gmpz(1)<<1000)+CGAL::Gmpz(1));)
   _TEST("constructors Gmpzf",test_constructors<CGAL::Gmpzf>(1025);)
+  typedef std::pair<CGAL::Gmpz,long>                            MantExp;
+  _TEST("constructors pair<Gmpz,long>",
+        test_constructors<MantExp>(std::make_pair(CGAL::Gmpz(4096),35));)
 
   _TEST("operators Gmpfr",test_operators<NT>();)
   _TEST("operators Gmpzf",test_operators<CGAL::Gmpzf>();)