blob: dd61195bc200ed9dacb509519cd49cf49a5fa3aa [file] [log] [blame]
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
// Copyright (C) 2006-2010 Benoit Jacob <>
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at
namespace Eigen {
namespace internal {
// default implementation of digits10(), based on numeric_limits if specialized,
// 0 for integer types, and log10(epsilon()) otherwise.
template< typename T,
bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
bool is_integer = NumTraits<T>::IsInteger>
struct default_digits10_impl
static int run() { return std::numeric_limits<T>::digits10; }
template<typename T>
struct default_digits10_impl<T,false,false> // Floating point
static int run() {
using std::log10;
using std::ceil;
typedef typename NumTraits<T>::Real Real;
return int(ceil(-log10(NumTraits<Real>::epsilon())));
template<typename T>
struct default_digits10_impl<T,false,true> // Integer
static int run() { return 0; }
} // end namespace internal
/** \class NumTraits
* \ingroup Core_Module
* \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
* \tparam T the numeric type at hand
* This class stores enums, typedefs and static methods giving information about a numeric type.
* The provided data consists of:
* \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
* then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
* is a typedef to \a U.
* \li A typedef \c 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 internal::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 \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c std::complex<U>, Literal is defined as \c U.
* Of course, this type must be fully compatible with \a T. In doubt, just use \a T here.
* \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 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 enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must
* be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1 otherwise.
* \li An epsilon() function which, unlike <a href="">std::numeric_limits::epsilon()</a>,
* it returns a \a Real instead of a \a T.
* \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.
* \li digits10() function returning the number of decimal digits that can be represented without change. This is
* the analogue of <a href="">std::numeric_limits<T>::digits10</a>
* which is used as the default implementation if specialized.
template<typename T> struct GenericNumTraits
enum {
IsInteger = std::numeric_limits<T>::is_integer,
IsSigned = std::numeric_limits<T>::is_signed,
IsComplex = 0,
RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
ReadCost = 1,
AddCost = 1,
MulCost = 1
typedef T Real;
typedef typename internal::conditional<
typename internal::conditional<sizeof(T)<=2, float, double>::type,
>::type NonInteger;
typedef T Nested;
typedef T Literal;
static inline Real epsilon()
return numext::numeric_limits<T>::epsilon();
static inline int digits10()
return internal::default_digits10_impl<T>::run();
static inline Real dummy_precision()
// make sure to override this for floating-point types
return Real(0);
static inline T highest() {
return (numext::numeric_limits<T>::max)();
static inline T lowest() {
return IsInteger ? (numext::numeric_limits<T>::min)() : (-(numext::numeric_limits<T>::max)());
static inline T infinity() {
return numext::numeric_limits<T>::infinity();
static inline T quiet_NaN() {
return numext::numeric_limits<T>::quiet_NaN();
template<typename T> struct NumTraits : GenericNumTraits<T>
template<> struct NumTraits<float>
: GenericNumTraits<float>
static inline float dummy_precision() { return 1e-5f; }
template<> struct NumTraits<double> : GenericNumTraits<double>
static inline 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> >
: GenericNumTraits<std::complex<_Real> >
typedef _Real Real;
typedef typename NumTraits<_Real>::Literal Literal;
enum {
IsComplex = 1,
RequireInitialization = NumTraits<_Real>::RequireInitialization,
ReadCost = 2 * NumTraits<_Real>::ReadCost,
AddCost = 2 * NumTraits<Real>::AddCost,
MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
static inline int digits10() { return NumTraits<Real>::digits10(); }
template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> >
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;
typedef typename NumTraits<Scalar>::Literal Literal;
enum {
IsComplex = NumTraits<Scalar>::IsComplex,
IsInteger = NumTraits<Scalar>::IsInteger,
IsSigned = NumTraits<Scalar>::IsSigned,
RequireInitialization = 1,
ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost,
AddCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost,
MulCost = ArrayType::SizeAtCompileTime==Dynamic ? HugeCost : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost
static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
template<> struct NumTraits<std::string>
: GenericNumTraits<std::string>
enum {
RequireInitialization = 1,
ReadCost = HugeCost,
AddCost = HugeCost,
MulCost = HugeCost
static inline int digits10() { return 0; }
static inline std::string epsilon();
static inline std::string dummy_precision();
static inline std::string lowest();
static inline std::string highest();
static inline std::string infinity();
static inline std::string quiet_NaN();
// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
template<> struct NumTraits<void> {};
} // end namespace Eigen