bug #482: pass scalar arguments by const references. This changeset only concerns the Core and Geometry modules

15 files changed, 58 insertions, 58 deletions

diff --git a/Eigen/src/Core/CwiseNullaryOp.h b/Eigen/src/Core/CwiseNullaryOp.h
index 60def3b59..a3a3238d2 100644
--- a/Eigen/src/Core/CwiseNullaryOp.h
+++ b/Eigen/src/Core/CwiseNullaryOp.h
@@ -310,7 +310,7 @@ DenseBase<Derived>::LinSpaced(const Scalar& low, const Scalar& high)
 /** \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
 template<typename Derived>
 bool DenseBase<Derived>::isApproxToConstant
-(const Scalar& val, RealScalar prec) const
+(const Scalar& val, const RealScalar& prec) const
 {
   for(Index j = 0; j < cols(); ++j)
     for(Index i = 0; i < rows(); ++i)
@@ -324,7 +324,7 @@ bool DenseBase<Derived>::isApproxToConstant
   * \returns true if all coefficients in this matrix are approximately equal to \a value, to within precision \a prec */
 template<typename Derived>
 bool DenseBase<Derived>::isConstant
-(const Scalar& val, RealScalar prec) const
+(const Scalar& val, const RealScalar& prec) const
 {
   return isApproxToConstant(val, prec);
 }
@@ -494,7 +494,7 @@ DenseBase<Derived>::Zero()
   * \sa class CwiseNullaryOp, Zero()
   */
 template<typename Derived>
-bool DenseBase<Derived>::isZero(RealScalar prec) const
+bool DenseBase<Derived>::isZero(const RealScalar& prec) const
 {
   for(Index j = 0; j < cols(); ++j)
     for(Index i = 0; i < rows(); ++i)
@@ -624,7 +624,7 @@ DenseBase<Derived>::Ones()
   */
 template<typename Derived>
 bool DenseBase<Derived>::isOnes
-(RealScalar prec) const
+(const RealScalar& prec) const
 {
   return isApproxToConstant(Scalar(1), prec);
 }
@@ -729,7 +729,7 @@ MatrixBase<Derived>::Identity()
   */
 template<typename Derived>
 bool MatrixBase<Derived>::isIdentity
-(RealScalar prec) const
+(const RealScalar& prec) const
 {
   for(Index j = 0; j < cols(); ++j)
   {
diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h
index 4ff091770..2703f8138 100644
--- a/Eigen/src/Core/DenseBase.h
+++ b/Eigen/src/Core/DenseBase.h
@@ -363,17 +363,17 @@ template<typename Derived> class DenseBase
 
     template<typename OtherDerived>
     bool isApprox(const DenseBase<OtherDerived>& other,
-                  RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+                  const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
     bool isMuchSmallerThan(const RealScalar& other,
-                           RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+                           const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
     template<typename OtherDerived>
     bool isMuchSmallerThan(const DenseBase<OtherDerived>& other,
-                           RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+                           const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
-    bool isApproxToConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
-    bool isConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
-    bool isZero(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
-    bool isOnes(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isApproxToConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isConstant(const Scalar& value, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isZero(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isOnes(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
     inline Derived& operator*=(const Scalar& other);
     inline Derived& operator/=(const Scalar& other);
diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
index c4f758d54..81fb4d913 100644
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -287,7 +287,7 @@ MatrixBase<Derived>::asDiagonal() const
   * \sa asDiagonal()
   */
 template<typename Derived>
-bool MatrixBase<Derived>::isDiagonal(RealScalar prec) const
+bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
 {
   if(cols() != rows()) return false;
   RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
diff --git a/Eigen/src/Core/Dot.h b/Eigen/src/Core/Dot.h
index 67dbbf8ba..1bebaa684 100644
--- a/Eigen/src/Core/Dot.h
+++ b/Eigen/src/Core/Dot.h
@@ -238,7 +238,7 @@ MatrixBase<Derived>::lpNorm() const
 template<typename Derived>
 template<typename OtherDerived>
 bool MatrixBase<Derived>::isOrthogonal
-(const MatrixBase<OtherDerived>& other, RealScalar prec) const
+(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
 {
   typename internal::nested<Derived,2>::type nested(derived());
   typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
@@ -257,7 +257,7 @@ bool MatrixBase<Derived>::isOrthogonal
   * Output: \verbinclude MatrixBase_isUnitary.out
   */
 template<typename Derived>
-bool MatrixBase<Derived>::isUnitary(RealScalar prec) const
+bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
 {
   typename Derived::Nested nested(derived());
   for(Index i = 0; i < cols(); ++i)
diff --git a/Eigen/src/Core/Fuzzy.h b/Eigen/src/Core/Fuzzy.h
index 887641163..e0f93bf3d 100644
--- a/Eigen/src/Core/Fuzzy.h
+++ b/Eigen/src/Core/Fuzzy.h
@@ -34,7 +34,7 @@ namespace internal
 template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
 struct isApprox_selector
 {
-  static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec)
+  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
   {
     using std::min;
     typename internal::nested<Derived,2>::type nested(x);
@@ -46,7 +46,7 @@ struct isApprox_selector
 template<typename Derived, typename OtherDerived>
 struct isApprox_selector<Derived, OtherDerived, true>
 {
-  static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar)
+  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)
   {
     return x.matrix() == y.matrix();
   }
@@ -55,7 +55,7 @@ struct isApprox_selector<Derived, OtherDerived, true>
 template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
 struct isMuchSmallerThan_object_selector
 {
-  static bool run(const Derived& x, const OtherDerived& y, typename Derived::RealScalar prec)
+  static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
   {
     return x.cwiseAbs2().sum() <= abs2(prec) * y.cwiseAbs2().sum();
   }
@@ -64,7 +64,7 @@ struct isMuchSmallerThan_object_selector
 template<typename Derived, typename OtherDerived>
 struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
 {
-  static bool run(const Derived& x, const OtherDerived&, typename Derived::RealScalar)
+  static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)
   {
     return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
   }
@@ -73,7 +73,7 @@ struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
 template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
 struct isMuchSmallerThan_scalar_selector
 {
-  static bool run(const Derived& x, const typename Derived::RealScalar& y, typename Derived::RealScalar prec)
+  static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
   {
     return x.cwiseAbs2().sum() <= abs2(prec * y);
   }
@@ -82,7 +82,7 @@ struct isMuchSmallerThan_scalar_selector
 template<typename Derived>
 struct isMuchSmallerThan_scalar_selector<Derived, true>
 {
-  static bool run(const Derived& x, const typename Derived::RealScalar&, typename Derived::RealScalar)
+  static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)
   {
     return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
   }
@@ -112,7 +112,7 @@ template<typename Derived>
 template<typename OtherDerived>
 bool DenseBase<Derived>::isApprox(
   const DenseBase<OtherDerived>& other,
-  RealScalar prec
+  const RealScalar& prec
 ) const
 {
   return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
@@ -134,7 +134,7 @@ bool DenseBase<Derived>::isApprox(
 template<typename Derived>
 bool DenseBase<Derived>::isMuchSmallerThan(
   const typename NumTraits<Scalar>::Real& other,
-  RealScalar prec
+  const RealScalar& prec
 ) const
 {
   return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
@@ -154,7 +154,7 @@ template<typename Derived>
 template<typename OtherDerived>
 bool DenseBase<Derived>::isMuchSmallerThan(
   const DenseBase<OtherDerived>& other,
-  RealScalar prec
+  const RealScalar& prec
 ) const
 {
   return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index 5a744c5ec..cdaedb92f 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -270,7 +270,7 @@ template<typename Derived> class MatrixBase
     template<unsigned int UpLo> typename ConstSelfAdjointViewReturnType<UpLo>::Type selfadjointView() const;
 
     const SparseView<Derived> sparseView(const Scalar& m_reference = Scalar(0),
-                                         typename NumTraits<Scalar>::Real m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
+                                         const typename NumTraits<Scalar>::Real& m_epsilon = NumTraits<Scalar>::dummy_precision()) const;
     static const IdentityReturnType Identity();
     static const IdentityReturnType Identity(Index rows, Index cols);
     static const BasisReturnType Unit(Index size, Index i);
@@ -286,16 +286,16 @@ template<typename Derived> class MatrixBase
     Derived& setIdentity();
     Derived& setIdentity(Index rows, Index cols);
 
-    bool isIdentity(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
-    bool isDiagonal(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isIdentity(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isDiagonal(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
-    bool isUpperTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
-    bool isLowerTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isUpperTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isLowerTriangular(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
     template<typename OtherDerived>
     bool isOrthogonal(const MatrixBase<OtherDerived>& other,
-                      RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
-    bool isUnitary(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const;
+                      const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
+    bool isUnitary(const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const;
 
     /** \returns true if each coefficients of \c *this and \a other are all exactly equal.
       * \warning When using floating point scalar values you probably should rather use a
diff --git a/Eigen/src/Core/ProductBase.h b/Eigen/src/Core/ProductBase.h
index ee00d9c97..8194354de 100644
--- a/Eigen/src/Core/ProductBase.h
+++ b/Eigen/src/Core/ProductBase.h
@@ -216,7 +216,7 @@ operator*(const ProductBase<Derived,Lhs,Rhs>& prod, typename Derived::Scalar x)
 template<typename Derived,typename Lhs,typename Rhs>
 typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
                       const ScaledProduct<Derived> >::type
-operator*(const ProductBase<Derived,Lhs,Rhs>& prod, typename Derived::RealScalar x)
+operator*(const ProductBase<Derived,Lhs,Rhs>& prod, const typename Derived::RealScalar& x)
 { return ScaledProduct<Derived>(prod.derived(), x); }
 
 
@@ -228,7 +228,7 @@ operator*(typename Derived::Scalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
 template<typename Derived,typename Lhs,typename Rhs>
 typename internal::enable_if<!internal::is_same<typename Derived::Scalar,typename Derived::RealScalar>::value,
                       const ScaledProduct<Derived> >::type
-operator*(typename Derived::RealScalar x,const ProductBase<Derived,Lhs,Rhs>& prod)
+operator*(const typename Derived::RealScalar& x,const ProductBase<Derived,Lhs,Rhs>& prod)
 { return ScaledProduct<Derived>(prod.derived(), x); }
 
 namespace internal {
diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h
index 5e97e4052..8454e1f3d 100644
--- a/Eigen/src/Core/TriangularMatrix.h
+++ b/Eigen/src/Core/TriangularMatrix.h
@@ -793,7 +793,7 @@ MatrixBase<Derived>::triangularView() const
   * \sa isLowerTriangular()
   */
 template<typename Derived>
-bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
+bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
 {
   RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
   for(Index j = 0; j < cols(); ++j)
@@ -818,7 +818,7 @@ bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
   * \sa isUpperTriangular()
   */
 template<typename Derived>
-bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const
+bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
 {
   RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
   for(Index j = 0; j < cols(); ++j)
diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h
index f0e3ff2b3..0631d6df9 100644
--- a/Eigen/src/Geometry/AngleAxis.h
+++ b/Eigen/src/Geometry/AngleAxis.h
@@ -91,7 +91,7 @@ public:
     * \warning If the \a axis vector is not normalized, then the angle-axis object
     *          represents an invalid rotation. */
   template<typename Derived>
-  inline AngleAxis(Scalar angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
+  inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
   /** Constructs and initialize the angle-axis rotation from a quaternion \a q. */
   template<typename QuatDerived> inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
   /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
@@ -152,7 +152,7 @@ public:
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
   { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }
 };
 
diff --git a/Eigen/src/Geometry/Hyperplane.h b/Eigen/src/Geometry/Hyperplane.h
index 6abf1664d..108966d37 100644
--- a/Eigen/src/Geometry/Hyperplane.h
+++ b/Eigen/src/Geometry/Hyperplane.h
@@ -90,7 +90,7 @@ public:
     * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
     * \warning the vector normal is assumed to be normalized.
     */
-  inline Hyperplane(const VectorType& n, Scalar d)
+  inline Hyperplane(const VectorType& n, const Scalar& d)
     : m_coeffs(n.size()+1)
   {
     normal() = n;
@@ -271,7 +271,7 @@ public:
     *
     * \sa MatrixBase::isApprox() */
   template<int OtherOptions>
-  bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
   { return m_coeffs.isApprox(other.m_coeffs, prec); }
 
 protected:
diff --git a/Eigen/src/Geometry/ParametrizedLine.h b/Eigen/src/Geometry/ParametrizedLine.h
index ddbda83dc..1a265b787 100644
--- a/Eigen/src/Geometry/ParametrizedLine.h
+++ b/Eigen/src/Geometry/ParametrizedLine.h
@@ -108,7 +108,7 @@ public:
   VectorType projection(const VectorType& p) const
   { return origin() + direction().dot(p-origin()) * direction(); }
 
-  VectorType pointAt( Scalar t ) const;
+  VectorType pointAt(const Scalar& t) const;
   
   template <int OtherOptions>
   Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
@@ -169,7 +169,7 @@ inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const H
   */
 template <typename _Scalar, int _AmbientDim, int _Options>
 inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
-ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt( _Scalar t ) const
+ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const
 {
   return origin() + (direction()*t); 
 }
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index 75083363c..1ffef63a7 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -176,7 +176,7 @@ public:
     *
     * \sa MatrixBase::isApprox() */
   template<class OtherDerived>
-  bool isApprox(const QuaternionBase<OtherDerived>& other, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
   { return coeffs().isApprox(other.coeffs(), prec); }
 
 	/** return the result vector of \a v through the rotation*/
@@ -263,7 +263,7 @@ public:
     * while internally the coefficients are stored in the following order:
     * [\c x, \c y, \c z, \c w]
     */
-  inline Quaternion(Scalar w, Scalar x, Scalar y, Scalar z) : m_coeffs(x, y, z, w){}
+  inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
 
   /** Constructs and initialize a quaternion from the array data */
   inline Quaternion(const Scalar* data) : m_coeffs(data) {}
diff --git a/Eigen/src/Geometry/Rotation2D.h b/Eigen/src/Geometry/Rotation2D.h
index 4339e0f0f..154c3d853 100644
--- a/Eigen/src/Geometry/Rotation2D.h
+++ b/Eigen/src/Geometry/Rotation2D.h
@@ -74,7 +74,7 @@ protected:
 public:
 
   /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
-  inline Rotation2D(Scalar a) : m_angle(a) {}
+  inline Rotation2D(const Scalar& a) : m_angle(a) {}
 
   /** \returns the rotation angle */
   inline Scalar angle() const { return m_angle; }
@@ -104,7 +104,7 @@ public:
   /** \returns the spherical interpolation between \c *this and \a other using
     * parameter \a t. It is in fact equivalent to a linear interpolation.
     */
-  inline Rotation2D slerp(Scalar t, const Rotation2D& other) const
+  inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
   { return m_angle * (1-t) + other.angle() * t; }
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
@@ -129,7 +129,7 @@ public:
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
   { return internal::isApprox(m_angle,other.m_angle, prec); }
 };
 
diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h
index 080f33794..3d4b254ca 100644
--- a/Eigen/src/Geometry/Scaling.h
+++ b/Eigen/src/Geometry/Scaling.h
@@ -109,7 +109,7 @@ public:
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const UniformScaling& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const UniformScaling& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
   { return internal::isApprox(m_factor, other.factor(), prec); }
 
 };
@@ -132,11 +132,11 @@ static inline UniformScaling<std::complex<RealScalar> > Scaling(const std::compl
 
 /** Constructs a 2D axis aligned scaling */
 template<typename Scalar>
-static inline DiagonalMatrix<Scalar,2> Scaling(Scalar sx, Scalar sy)
+static inline DiagonalMatrix<Scalar,2> Scaling(const Scalar& sx, const Scalar& sy)
 { return DiagonalMatrix<Scalar,2>(sx, sy); }
 /** Constructs a 3D axis aligned scaling */
 template<typename Scalar>
-static inline DiagonalMatrix<Scalar,3> Scaling(Scalar sx, Scalar sy, Scalar sz)
+static inline DiagonalMatrix<Scalar,3> Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
 { return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
 
 /** Constructs an axis aligned scaling expression from vector expression \a coeffs
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index e81305ccc..c4ebe00d2 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -521,8 +521,8 @@ public:
   template<typename OtherDerived>
   inline Transform& prescale(const MatrixBase<OtherDerived> &other);
 
-  inline Transform& scale(Scalar s);
-  inline Transform& prescale(Scalar s);
+  inline Transform& scale(const Scalar& s);
+  inline Transform& prescale(const Scalar& s);
 
   template<typename OtherDerived>
   inline Transform& translate(const MatrixBase<OtherDerived> &other);
@@ -536,8 +536,8 @@ public:
   template<typename RotationType>
   inline Transform& prerotate(const RotationType& rotation);
 
-  Transform& shear(Scalar sx, Scalar sy);
-  Transform& preshear(Scalar sx, Scalar sy);
+  Transform& shear(const Scalar& sx, const Scalar& sy);
+  Transform& preshear(const Scalar& sx, const Scalar& sy);
 
   inline Transform& operator=(const TranslationType& t);
   inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
@@ -594,7 +594,7 @@ public:
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const
+  bool isApprox(const Transform& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
   { return m_matrix.isApprox(other.m_matrix, prec); }
 
   /** Sets the last row to [0 ... 0 1]
@@ -804,7 +804,7 @@ Transform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)
   * \sa prescale(Scalar)
   */
 template<typename Scalar, int Dim, int Mode, int Options>
-inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(Scalar s)
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)
 {
   EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
   linearExt() *= s;
@@ -831,7 +831,7 @@ Transform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &oth
   * \sa scale(Scalar)
   */
 template<typename Scalar, int Dim, int Mode, int Options>
-inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(Scalar s)
+inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)
 {
   EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
   m_matrix.template topRows<Dim>() *= s;
@@ -919,7 +919,7 @@ Transform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)
   */
 template<typename Scalar, int Dim, int Mode, int Options>
 Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::shear(Scalar sx, Scalar sy)
+Transform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)
 {
   EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
   EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
@@ -935,7 +935,7 @@ Transform<Scalar,Dim,Mode,Options>::shear(Scalar sx, Scalar sy)
   */
 template<typename Scalar, int Dim, int Mode, int Options>
 Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::preshear(Scalar sx, Scalar sy)
+Transform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)
 {
   EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
   EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)