Complete rework of global math functions and NumTraits.

* Now completely generic so all standard integer types (like char...) are supported.
** add unit test for that (integer_types).
* NumTraits does no longer inherit numeric_limits
* All math functions are now templated
* Better guard (static asserts) against using certain math functions on integer types.

Eigen/src/Core/Dot.h

@@ -161,7 +161,7 @@ bool MatrixBase<Derived>::isUnitary(RealScalar prec) const
   typename Derived::Nested nested(derived());
   for(int i = 0; i < cols(); ++i)
   {
-    if(!ei_isApprox(nested.col(i).squaredNorm(), static_cast<Scalar>(1), prec))
+    if(!ei_isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
       return false;
     for(int j = 0; j < i; ++j)
       if(!ei_isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))

Eigen/src/Core/Functors.h

@@ -180,7 +180,7 @@ struct ei_functor_traits<ei_scalar_quotient_op<Scalar> > {
     Cost = 2 * NumTraits<Scalar>::MulCost,
     PacketAccess = ei_packet_traits<Scalar>::size>1
                   #if (defined EIGEN_VECTORIZE)
-                  && NumTraits<Scalar>::HasFloatingPoint
+                  && !NumTraits<Scalar>::IsInteger
                   #endif
   };
 };
@@ -384,7 +384,7 @@ template<typename Scalar1,typename Scalar2>
 struct ei_functor_traits<ei_scalar_multiple2_op<Scalar1,Scalar2> >
 { enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
 
-template<typename Scalar, bool HasFloatingPoint>
+template<typename Scalar, bool IsInteger>
 struct ei_scalar_quotient1_impl {
   typedef typename ei_packet_traits<Scalar>::type PacketScalar;
   // FIXME default copy constructors seems bugged with std::complex<>
@@ -396,11 +396,11 @@ struct ei_scalar_quotient1_impl {
   const Scalar m_other;
 };
 template<typename Scalar>
-struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,true> >
+struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,false> >
 { enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = ei_packet_traits<Scalar>::size>1 }; };
 
 template<typename Scalar>
-struct ei_scalar_quotient1_impl<Scalar,false> {
+struct ei_scalar_quotient1_impl<Scalar,true> {
   // FIXME default copy constructors seems bugged with std::complex<>
   EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const ei_scalar_quotient1_impl& other) : m_other(other.m_other) { }
   EIGEN_STRONG_INLINE ei_scalar_quotient1_impl(const Scalar& other) : m_other(other) {}
@@ -408,7 +408,7 @@ struct ei_scalar_quotient1_impl<Scalar,false> {
   typename ei_makeconst<typename NumTraits<Scalar>::Nested>::type m_other;
 };
 template<typename Scalar>
-struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,false> >
+struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,true> >
 { enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
 
 /** \internal
@@ -420,13 +420,13 @@ struct ei_functor_traits<ei_scalar_quotient1_impl<Scalar,false> >
   * \sa class CwiseUnaryOp, MatrixBase::operator/
   */
 template<typename Scalar>
-struct ei_scalar_quotient1_op : ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::HasFloatingPoint > {
+struct ei_scalar_quotient1_op : ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger > {
   EIGEN_STRONG_INLINE ei_scalar_quotient1_op(const Scalar& other)
-    : ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::HasFloatingPoint >(other) {}
+    : ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger >(other) {}
 };
 template<typename Scalar>
 struct ei_functor_traits<ei_scalar_quotient1_op<Scalar> >
-: ei_functor_traits<ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::HasFloatingPoint> >
+: ei_functor_traits<ei_scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger> >
 {};
 
 // nullary functors

Eigen/src/Core/Fuzzy.h

@@ -26,6 +26,8 @@
 #ifndef EIGEN_FUZZY_H
 #define EIGEN_FUZZY_H
 
+// TODO support small integer types properly i.e. do exact compare on coeffs --- taking a HS norm is guaranteed to cause integer overflow.
+
 #ifndef EIGEN_LEGACY_COMPARES
 
 /** \returns \c true if \c *this is approximately equal to \a other, within the precision

Eigen/src/Core/IO.h

@@ -153,13 +153,13 @@ std::ostream & ei_print_matrix(std::ostream & s, const Derived& _m, const IOForm
   }
   else if(fmt.precision == FullPrecision)
   {
-    if (NumTraits<Scalar>::HasFloatingPoint)
+    if (NumTraits<Scalar>::IsInteger)
     {
-      explicit_precision = ei_significant_decimals_impl<Scalar>::run();
+      explicit_precision = 0;
     }
     else
     {
-      explicit_precision = 0;
+      explicit_precision = ei_significant_decimals_impl<Scalar>::run();
     }
   }
   else

Eigen/src/Core/NumTraits.h

@@ -1,7 +1,7 @@
 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
 //
 // Eigen is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
@@ -27,157 +27,121 @@
 
 /** \class NumTraits
   *
-  * \brief Holds some data about the various numeric (i.e. scalar) types allowed by Eigen.
+  * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
   *
-  * \param T the numeric type about which this class provides data. Recall that Eigen allows
-  *          only the following types for \a T: \c int, \c float, \c double,
-  *          \c std::complex<float>, \c std::complex<double>, and \c long \c double (especially
-  *          useful to enforce x87 arithmetics when SSE is the default).
+  * \param T the numeric type at hand
   *
-  * The provided data consists of everything that is supported by std::numeric_limits, plus:
+  * This class stores enums, typedefs and static methods giving information about a numeric type.
+  *
+  * The provided data consists of:
   * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real,
   *     then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real
   *     is a typedef to \a U.
-  * \li A typedef \a FloatingPoint, giving the "floating-point type" of \a T. If \a T is
-  *     \c int, then \a FloatingPoint is a typedef to \c double. Otherwise, \a FloatingPoint
-  *     is a typedef to \a T.
+  * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values,
+  *     such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
+  *     \a T again. Note however that many Eigen functions such as ei_sqrt simply refuse to
+  *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
+  *     only intended as a helper for code that needs to explicitly promote types.
+  * \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you don't know what
+  *     this means, just use \a T here.
   * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex
   *     type, and to 0 otherwise.
-  * \li An enum \a HasFloatingPoint. It is equal to \c 0 if \a T is \c int,
-  *     and to \c 1 otherwise.
+  * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int,
+  *     and to \c 0 otherwise.
+  * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed
+  *     to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers.
+  *     Stay vague here. No need to do architecture-specific stuff.
+  * \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T is unsigned.
   * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T.
-  * \li A dummy_precision() function returning a weak epsilon value. It is mainly used by the fuzzy comparison operators.
-  * \li Two highest() and lowest() functions returning the highest and lowest possible values respectively.
+  * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default
+  *     value by the fuzzy comparison operators.
+  * \li highest() and lowest() functions returning the highest and lowest possible values respectively.
   */
-template<typename T> struct NumTraits;
 
-template<typename T> struct ei_default_float_numtraits
-  : std::numeric_limits<T>
+template<typename T> struct GenericNumTraits
 {
-  inline static T highest() { return  std::numeric_limits<T>::max(); }
-  inline static T lowest()  { return -std::numeric_limits<T>::max(); }
-};
+  enum {
+    IsInteger = std::numeric_limits<T>::is_integer,
+    IsSigned = std::numeric_limits<T>::is_signed,
+    IsComplex = 0,
+    ReadCost = 1,
+    AddCost = 1,
+    MulCost = 1
+  };
 
-template<typename T> struct ei_default_integral_numtraits
-  : std::numeric_limits<T>
-{
-  inline static T dummy_precision() { return T(0); }
+  typedef T Real;
+  typedef typename ei_meta_if<
+                     IsInteger,
+                     typename ei_meta_if<sizeof(T)<=2, float, double>::ret,
+                     T
+                   >::ret NonInteger;
+  typedef T Nested;
+
+  inline static Real epsilon() { return std::numeric_limits<T>::epsilon(); }
+  inline static Real dummy_precision()
+  {
+    // make sure to override this for floating-point types
+    return Real(0);
+  }
   inline static T highest() { return std::numeric_limits<T>::max(); }
   inline static T lowest()  { return std::numeric_limits<T>::min(); }
 };
 
-template<> struct NumTraits<int>
-  : ei_default_integral_numtraits<int>
-{
-  typedef int Real;
-  typedef double FloatingPoint;
-  typedef int Nested;
-  enum {
-    IsComplex = 0,
-    HasFloatingPoint = 0,
-    ReadCost = 1,
-    AddCost = 1,
-    MulCost = 1
-  };
-};
+template<typename T> struct NumTraits : GenericNumTraits<T>
+{};
 
 template<> struct NumTraits<float>
-  : ei_default_float_numtraits<float>
+  : GenericNumTraits<float>
 {
-  typedef float Real;
-  typedef float FloatingPoint;
-  typedef float Nested;
-  enum {
-    IsComplex = 0,
-    HasFloatingPoint = 1,
-    ReadCost = 1,
-    AddCost = 1,
-    MulCost = 1
-  };
-
   inline static float dummy_precision() { return 1e-5f; }
 };
 
-template<> struct NumTraits<double>
-  : ei_default_float_numtraits<double>
+template<> struct NumTraits<double> : GenericNumTraits<double>
 {
-  typedef double Real;
-  typedef double FloatingPoint;
-  typedef double Nested;
-  enum {
-    IsComplex = 0,
-    HasFloatingPoint = 1,
-    ReadCost = 1,
-    AddCost = 1,
-    MulCost = 1
-  };
-
   inline static double dummy_precision() { return 1e-12; }
 };
 
+template<> struct NumTraits<long double>
+  : GenericNumTraits<long double>
+{
+  static inline long double dummy_precision() { return 1e-15l; }
+};
+
 template<typename _Real> struct NumTraits<std::complex<_Real> >
-  : ei_default_float_numtraits<std::complex<_Real> >
+  : GenericNumTraits<std::complex<_Real> >
 {
   typedef _Real Real;
-  typedef std::complex<_Real> FloatingPoint;
-  typedef std::complex<_Real> Nested;
   enum {
     IsComplex = 1,
-    HasFloatingPoint = NumTraits<Real>::HasFloatingPoint,
     ReadCost = 2,
     AddCost = 2 * NumTraits<Real>::AddCost,
     MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
   };
 
-  inline static Real epsilon() { return std::numeric_limits<Real>::epsilon(); }
+  inline static Real epsilon() { return NumTraits<Real>::epsilon(); }
   inline static Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
 };
 
-template<> struct NumTraits<long long int>
-  : ei_default_integral_numtraits<long long int>
+template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
+struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
 {
-  typedef long long int Real;
-  typedef long double FloatingPoint;
-  typedef long long int Nested;
+  typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
+  typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
+  typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
+  typedef ArrayType & Nested;
+  
   enum {
-    IsComplex = 0,
-    HasFloatingPoint = 0,
-    ReadCost = 1,
-    AddCost = 1,
-    MulCost = 1
+    IsComplex = NumTraits<Scalar>::IsComplex,
+    IsInteger = NumTraits<Scalar>::IsInteger,
+    IsSigned  = NumTraits<Scalar>::IsSigned,
+    ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
+    AddCost  = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
+    MulCost  = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
   };
 };
 
-template<> struct NumTraits<long double>
-  : ei_default_float_numtraits<long double>
-{
-  typedef long double Real;
-  typedef long double FloatingPoint;
-  typedef long double Nested;
-  enum {
-    IsComplex = 0,
-    HasFloatingPoint = 1,
-    ReadCost = 1,
-    AddCost = 1,
-    MulCost = 1
-  };
 
-  static inline long double dummy_precision() { return NumTraits<double>::dummy_precision(); }
-};
-
-template<> struct NumTraits<bool>
-  : ei_default_integral_numtraits<bool>
-{
-  typedef bool Real;
-  typedef float FloatingPoint;
-  typedef bool Nested;
-  enum {
-    IsComplex = 0,
-    HasFloatingPoint = 0,
-    ReadCost = 1,
-    AddCost = 1,
-    MulCost = 1
-  };
-};
 
 #endif // EIGEN_NUMTRAITS_H

Eigen/src/Core/SelfCwiseBinaryOp.h

@@ -133,9 +133,11 @@ inline Derived& DenseBase<Derived>::operator*=(const Scalar& other)
 template<typename Derived>
 inline Derived& DenseBase<Derived>::operator/=(const Scalar& other)
 {
-  SelfCwiseBinaryOp<typename ei_meta_if<NumTraits<Scalar>::HasFloatingPoint,ei_scalar_product_op<Scalar>,ei_scalar_quotient_op<Scalar> >::ret, Derived> tmp(derived());
+  SelfCwiseBinaryOp<typename ei_meta_if<NumTraits<Scalar>::IsInteger,
+                                        ei_scalar_quotient_op<Scalar>,
+                                        ei_scalar_product_op<Scalar> >::ret, Derived> tmp(derived());
   typedef typename Derived::PlainObject PlainObject;
-  tmp = PlainObject::Constant(rows(),cols(), NumTraits<Scalar>::HasFloatingPoint ? Scalar(1)/other : other);
+  tmp = PlainObject::Constant(rows(),cols(), NumTraits<Scalar>::IsInteger ? other : Scalar(1)/other);
   return derived();
 }
 

Eigen/src/Core/util/StaticAssert.h

@@ -65,7 +65,7 @@
         YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR,
         YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR,
         UNALIGNED_LOAD_AND_STORE_OPERATIONS_UNIMPLEMENTED_ON_ALTIVEC,
-        NUMERIC_TYPE_MUST_BE_FLOATING_POINT,
+        THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES,
         NUMERIC_TYPE_MUST_BE_REAL,
         COEFFICIENT_WRITE_ACCESS_TO_SELFADJOINT_NOT_SUPPORTED,
         WRITING_TO_TRIANGULAR_PART_WITH_UNIT_DIAGONAL_IS_NOT_SUPPORTED,
@@ -158,6 +158,9 @@
        ) \
      )
 
+#define EIGEN_STATIC_ASSERT_NON_INTEGER(TYPE) \
+  EIGEN_STATIC_ASSERT(!NumTraits<TYPE>::IsInteger, THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
+
 // static assertion failing if it is guaranteed at compile-time that the two matrix expression types have different sizes
 #define EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(TYPE0,TYPE1) \
   EIGEN_STATIC_ASSERT( \