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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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 http://mozilla.org/MPL/2.0/.
#ifndef EIGEN_NUMTRAITS_H
#define EIGEN_NUMTRAITS_H
namespace Eigen {
/** \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 \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 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 \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 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 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 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
};
// Division is messy but important, because it is expensive and throughput
// varies significantly. The following numbers are based on min division
// throughput on Haswell.
template<bool Vectorized>
struct Div {
enum {
#ifdef EIGEN_VECTORIZE_AVX
AVX = true,
#else
AVX = false,
#endif
Cost = IsInteger ? (sizeof(T) == 8 ? (IsSigned ? 24 : 21) : (IsSigned ? 8 : 9)):
Vectorized ? (sizeof(T) == 8 ? (AVX ? 16 : 8) : (AVX ? 14 : 7)) : 8
};
};
typedef T Real;
typedef typename internal::conditional<
IsInteger,
typename internal::conditional<sizeof(T)<=2, float, double>::type,
T
>::type NonInteger;
typedef T Nested;
EIGEN_DEVICE_FUNC
static inline Real epsilon()
{
return numext::numeric_limits<T>::epsilon();
}
EIGEN_DEVICE_FUNC
static inline Real dummy_precision()
{
// make sure to override this for floating-point types
return Real(0);
}
EIGEN_DEVICE_FUNC
static inline T highest() {
return (numext::numeric_limits<T>::max)();
}
EIGEN_DEVICE_FUNC
static inline T lowest() {
return IsInteger ? (numext::numeric_limits<T>::min)() : (-(numext::numeric_limits<T>::max)());
}
EIGEN_DEVICE_FUNC
static inline T infinity() {
return numext::numeric_limits<T>::infinity();
}
EIGEN_DEVICE_FUNC
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>
{
EIGEN_DEVICE_FUNC
static inline float dummy_precision() { return 1e-5f; }
};
template<> struct NumTraits<double> : GenericNumTraits<double>
{
EIGEN_DEVICE_FUNC
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;
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
};
EIGEN_DEVICE_FUNC
static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
EIGEN_DEVICE_FUNC
static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); }
};
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;
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
};
EIGEN_DEVICE_FUNC
static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
EIGEN_DEVICE_FUNC
static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
};
} // end namespace Eigen
#endif // EIGEN_NUMTRAITS_H
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