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Complete rework of global math functions and NumTraits.

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* 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.
This commit is contained in:
Benoit Jacob
2010-04-28 18:51:38 -04:00
parent 4f83d6ad19
commit e277586958
26 changed files with 900 additions and 498 deletions
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180
Eigen/src/Core/NumTraits.h
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@@ -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