Eigen/src/Core/NumTraits.h - eigen/fuchsia - Git at Google

 // 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.
   *
   * \param 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 PacketAccess>
   struct Div {
     enum {
 #ifdef EIGEN_VECTORIZE_AVX
       AVX = true,
 #else
       AVX = false,
 #endif
       Cost = IsInteger ? (sizeof(T) == 8 ? (IsSigned ? 24 : 21) : (IsSigned ? 8 : 9)):
           PacketAccess ? (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()
   {
 #if defined(__CUDA_ARCH__)
     return internal::device::numeric_limits<T>::epsilon();
 #else
     return std::numeric_limits<T>::epsilon();
 #endif
   }
   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() {
 #if defined(__CUDA_ARCH__)
     return internal::device::numeric_limits<T>::max();
 #else
     return (std::numeric_limits<T>::max)();
 #endif
   }

   EIGEN_DEVICE_FUNC
   static inline T lowest()  {
 #if defined(__CUDA_ARCH__)
     return internal::device::numeric_limits<T>::lowest();
 #else
     return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)());
 #endif
   }

   EIGEN_DEVICE_FUNC
   static inline T infinity() {
 #if defined(__CUDA_ARCH__)
     return internal::device::numeric_limits<T>::infinity();
 #else
     return std::numeric_limits<T>::infinity();
 #endif
   }

   EIGEN_DEVICE_FUNC
   static inline T quiet_NaN() {
 #if defined(__CUDA_ARCH__)
     return internal::device::numeric_limits<T>::quiet_NaN();
 #else
     return std::numeric_limits<T>::quiet_NaN();
 #endif
   }

 #ifdef EIGEN2_SUPPORT
   enum {
     HasFloatingPoint = !IsInteger
   };
   typedef NonInteger FloatingPoint;
 #endif
 };

 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
   };

   template<bool PacketAccess>
   struct Div {
     enum {
       Cost = 6 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost +
              2 * NumTraits<Real>::template Div<PacketAccess>::Cost
     };
   };

   static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
   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 ? 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<bool PacketAccess>
   struct Div {
     enum {
       Cost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic :
           ArrayType::SizeAtCompileTime * NumTraits<Scalar>::template Div<PacketAccess>::Cost
     };
   };

   static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
   static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
 };


 namespace internal {

 // Internal helper defining the cost of a scalar division for the type T.
 // The default heuristic can be specialized for each scalar type and architecture.
 template<typename T, bool Vectorized=false, typename EnableIf = void>
 struct scalar_div_cost {
   enum { value = NumTraits<T>::template Div<Vectorized>::Cost };
 };

 } // end namespace internal

 } // end namespace Eigen

 #endif // EIGEN_NUMTRAITS_H
	// 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.
	*
	* \param 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 PacketAccess>
	struct Div {
	enum {
	#ifdef EIGEN_VECTORIZE_AVX
	AVX = true,
	#else
	AVX = false,
	#endif
	Cost = IsInteger ? (sizeof(T) == 8 ? (IsSigned ? 24 : 21) : (IsSigned ? 8 : 9)):
	PacketAccess ? (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()
	{
	#if defined(__CUDA_ARCH__)
	return internal::device::numeric_limits<T>::epsilon();
	#else
	return std::numeric_limits<T>::epsilon();
	#endif
	}
	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() {
	#if defined(__CUDA_ARCH__)
	return internal::device::numeric_limits<T>::max();
	#else
	return (std::numeric_limits<T>::max)();
	#endif
	}

	EIGEN_DEVICE_FUNC
	static inline T lowest() {
	#if defined(__CUDA_ARCH__)
	return internal::device::numeric_limits<T>::lowest();
	#else
	return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)());
	#endif
	}

	EIGEN_DEVICE_FUNC
	static inline T infinity() {
	#if defined(__CUDA_ARCH__)
	return internal::device::numeric_limits<T>::infinity();
	#else
	return std::numeric_limits<T>::infinity();
	#endif
	}

	EIGEN_DEVICE_FUNC
	static inline T quiet_NaN() {
	#if defined(__CUDA_ARCH__)
	return internal::device::numeric_limits<T>::quiet_NaN();
	#else
	return std::numeric_limits<T>::quiet_NaN();
	#endif
	}

	#ifdef EIGEN2_SUPPORT
	enum {
	HasFloatingPoint = !IsInteger
	};
	typedef NonInteger FloatingPoint;
	#endif
	};

	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
	};

	template<bool PacketAccess>
	struct Div {
	enum {
	Cost = 6 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost +
	2 * NumTraits<Real>::template Div<PacketAccess>::Cost
	};
	};

	static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
	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 ? 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<bool PacketAccess>
	struct Div {
	enum {
	Cost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic :
	ArrayType::SizeAtCompileTime * NumTraits<Scalar>::template Div<PacketAccess>::Cost
	};
	};

	static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
	static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); }
	};


	namespace internal {

	// Internal helper defining the cost of a scalar division for the type T.
	// The default heuristic can be specialized for each scalar type and architecture.
	template<typename T, bool Vectorized=false, typename EnableIf = void>
	struct scalar_div_cost {
	enum { value = NumTraits<T>::template Div<Vectorized>::Cost };
	};

	} // end namespace internal

	} // end namespace Eigen

	#endif // EIGEN_NUMTRAITS_H