NumTraits.h revision 7faaa9f3f0df9d23790277834d426c3d992ac3ba
1551ccae044b0ff658fe629dd67edd5ffe75d10e8Reid Spencer// This file is part of Eigen, a lightweight C++ template library 27a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell// for linear algebra. 3582a23c686aa544c8a44d07601d4520d4ea18980Reid Spencer// 4582a23c686aa544c8a44d07601d4520d4ea18980Reid Spencer// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com> 5582a23c686aa544c8a44d07601d4520d4ea18980Reid Spencer// 67a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell// This Source Code Form is subject to the terms of the Mozilla 77a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell// Public License v. 2.0. If a copy of the MPL was not distributed 87a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 97a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell 107a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell#ifndef EIGEN_NUMTRAITS_H 117a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell#define EIGEN_NUMTRAITS_H 127a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell 137a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswellnamespace Eigen { 140a262ba7c3250ef02833fae864459ccc905a2e9bReid Spencer 150a262ba7c3250ef02833fae864459ccc905a2e9bReid Spencer/** \class NumTraits 160a262ba7c3250ef02833fae864459ccc905a2e9bReid Spencer * \ingroup Core_Module 177a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * 187a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen. 197a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * 207a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * \param T the numeric type at hand 217a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * 227a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * This class stores enums, typedefs and static methods giving information about a numeric type. 237a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell * 248c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * The provided data consists of: 258c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li A typedef \a Real, giving the "real part" type of \a T. If \a T is already real, 268c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * then \a Real is just a typedef to \a T. If \a T is \c std::complex<U> then \a Real 278c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * is a typedef to \a U. 288c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li A typedef \a NonInteger, giving the type that should be used for operations producing non-integral values, 298c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives 308c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to 318c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is 328c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * only intended as a helper for code that needs to explicitly promote types. 338c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \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 348c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * this means, just use \a T here. 358c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c std::complex 368c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * type, and to 0 otherwise. 378c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type such as \c int, 388c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * and to \c 0 otherwise. 398c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of the number of CPU cycles needed 408c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * to by move / add / mul instructions respectively, assuming the data is already stored in CPU registers. 418c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * Stay vague here. No need to do architecture-specific stuff. 428c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \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. 438c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type \a T must 448c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * 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. 450c803894985f80e894b36ad4de58ea4c2e906b07Brian Gaeke * \li An epsilon() function which, unlike std::numeric_limits::epsilon(), returns a \a Real instead of a \a T. 460c803894985f80e894b36ad4de58ea4c2e906b07Brian Gaeke * \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a default 470c803894985f80e894b36ad4de58ea4c2e906b07Brian Gaeke * value by the fuzzy comparison operators. 488c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer * \li highest() and lowest() functions returning the highest and lowest possible values respectively. 498c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer */ 508c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer 514046846d2cb36a6281b853c73776584063cca19dJohn Criswelltemplate<typename T> struct GenericNumTraits 524046846d2cb36a6281b853c73776584063cca19dJohn Criswell{ 534046846d2cb36a6281b853c73776584063cca19dJohn Criswell enum { 54f4bb9b1fa76564704a4ab6c27d5d72180b493e9aReid Spencer IsInteger = std::numeric_limits<T>::is_integer, 55f4bb9b1fa76564704a4ab6c27d5d72180b493e9aReid Spencer IsSigned = std::numeric_limits<T>::is_signed, 56f4bb9b1fa76564704a4ab6c27d5d72180b493e9aReid Spencer IsComplex = 0, 578c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1, 588c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer ReadCost = 1, 598c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer AddCost = 1, 608c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer MulCost = 1 618c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer }; 628c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer 638c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer typedef T Real; 648c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer typedef typename internal::conditional< 658c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer IsInteger, 668c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer typename internal::conditional<sizeof(T)<=2, float, double>::type, 678c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer T 688c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer >::type NonInteger; 698c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer typedef T Nested; 708c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer 718c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer static inline Real epsilon() { return std::numeric_limits<T>::epsilon(); } 728c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer static inline Real dummy_precision() 738c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer { 748c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer // make sure to override this for floating-point types 75394855a87d52d71b702cfbf0ec1a223bda9163d4Reid Spencer return Real(0); 76cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke } 77cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke static inline T highest() { return (std::numeric_limits<T>::max)(); } 78cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke static inline T lowest() { return IsInteger ? (std::numeric_limits<T>::min)() : (-(std::numeric_limits<T>::max)()); } 79cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke 80cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke#ifdef EIGEN2_SUPPORT 81cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke enum { 828c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer HasFloatingPoint = !IsInteger 838c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer }; 848c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer typedef NonInteger FloatingPoint; 85caf0ecec9ed4411280f16b81f43bcca1940a32deReid Spencer#endif 86caf0ecec9ed4411280f16b81f43bcca1940a32deReid Spencer}; 87caf0ecec9ed4411280f16b81f43bcca1940a32deReid Spencer 88ecbd242833cadb8b22006143d5ee4c1152bc81e3Reid Spencertemplate<typename T> struct NumTraits : GenericNumTraits<T> 89ecbd242833cadb8b22006143d5ee4c1152bc81e3Reid Spencer{}; 90ecbd242833cadb8b22006143d5ee4c1152bc81e3Reid Spencer 918c8af327b83a210aed30634c908bb4b39f41eedbReid Spencertemplate<> struct NumTraits<float> 928c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer : GenericNumTraits<float> 938c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer{ 948c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer static inline float dummy_precision() { return 1e-5f; } 958c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer}; 968c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer 978c8af327b83a210aed30634c908bb4b39f41eedbReid Spencertemplate<> struct NumTraits<double> : GenericNumTraits<double> 988c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer{ 998c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer static inline double dummy_precision() { return 1e-12; } 1000c803894985f80e894b36ad4de58ea4c2e906b07Brian Gaeke}; 1010c803894985f80e894b36ad4de58ea4c2e906b07Brian Gaeke 1020c803894985f80e894b36ad4de58ea4c2e906b07Brian Gaeketemplate<> struct NumTraits<long double> 1037a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell : GenericNumTraits<long double> 1047a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell{ 105d59a64797b12dab9dae1842171b4ca9fba302765Brian Gaeke static inline long double dummy_precision() { return 1e-15l; } 106af362fc492bf0bfc6e43e3025621834ea031a29eReid Spencer}; 1076802b55b6b4b46a2dc965eeeb1f75f1fdc33ba35Brian Gaeke 1087a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswelltemplate<typename _Real> struct NumTraits<std::complex<_Real> > 109f4bb9b1fa76564704a4ab6c27d5d72180b493e9aReid Spencer : GenericNumTraits<std::complex<_Real> > 110f4bb9b1fa76564704a4ab6c27d5d72180b493e9aReid Spencer{ 111f4bb9b1fa76564704a4ab6c27d5d72180b493e9aReid Spencer typedef _Real Real; 1124046846d2cb36a6281b853c73776584063cca19dJohn Criswell enum { 1134046846d2cb36a6281b853c73776584063cca19dJohn Criswell IsComplex = 1, 1144046846d2cb36a6281b853c73776584063cca19dJohn Criswell RequireInitialization = NumTraits<_Real>::RequireInitialization, 1157a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell ReadCost = 2 * NumTraits<_Real>::ReadCost, 1167a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell AddCost = 2 * NumTraits<Real>::AddCost, 1177a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost 1187a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell }; 1197a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell 1207a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell static inline Real epsilon() { return NumTraits<Real>::epsilon(); } 1215c039879649f12c17f6c52c08be9a82d838525f9Brian Gaeke static inline Real dummy_precision() { return NumTraits<Real>::dummy_precision(); } 1225c039879649f12c17f6c52c08be9a82d838525f9Brian Gaeke}; 1235c039879649f12c17f6c52c08be9a82d838525f9Brian Gaeke 1247a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswelltemplate<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols> 1257a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswellstruct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> > 1267a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell{ 1274046846d2cb36a6281b853c73776584063cca19dJohn Criswell typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType; 1284046846d2cb36a6281b853c73776584063cca19dJohn Criswell typedef typename NumTraits<Scalar>::Real RealScalar; 1294046846d2cb36a6281b853c73776584063cca19dJohn Criswell typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real; 1304046846d2cb36a6281b853c73776584063cca19dJohn Criswell typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar; 1314046846d2cb36a6281b853c73776584063cca19dJohn Criswell typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger; 1324046846d2cb36a6281b853c73776584063cca19dJohn Criswell typedef ArrayType & Nested; 1334046846d2cb36a6281b853c73776584063cca19dJohn Criswell 1344046846d2cb36a6281b853c73776584063cca19dJohn Criswell enum { 1354046846d2cb36a6281b853c73776584063cca19dJohn Criswell IsComplex = NumTraits<Scalar>::IsComplex, 1364046846d2cb36a6281b853c73776584063cca19dJohn Criswell IsInteger = NumTraits<Scalar>::IsInteger, 1374046846d2cb36a6281b853c73776584063cca19dJohn Criswell IsSigned = NumTraits<Scalar>::IsSigned, 1384046846d2cb36a6281b853c73776584063cca19dJohn Criswell RequireInitialization = 1, 1398a2246f32ec6480b6430078ff2c5740a0a11a3fbReid Spencer ReadCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::ReadCost, 1408a2246f32ec6480b6430078ff2c5740a0a11a3fbReid Spencer AddCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::AddCost, 1418a2246f32ec6480b6430078ff2c5740a0a11a3fbReid Spencer MulCost = ArrayType::SizeAtCompileTime==Dynamic ? Dynamic : ArrayType::SizeAtCompileTime * NumTraits<Scalar>::MulCost 142be13028264888b01ac6fcd46667cf31a7e84e9cfReid Spencer }; 143be13028264888b01ac6fcd46667cf31a7e84e9cfReid Spencer 144be13028264888b01ac6fcd46667cf31a7e84e9cfReid Spencer static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); } 1458c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer static inline RealScalar dummy_precision() { return NumTraits<RealScalar>::dummy_precision(); } 1468c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer}; 1478c8af327b83a210aed30634c908bb4b39f41eedbReid Spencer 148cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke} // end namespace Eigen 149cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke 150cbeedf73d403ca0b65b3d4151b5630c5e335055bBrian Gaeke#endif // EIGEN_NUMTRAITS_H 1517a73b80b9052136c8cd2234eb3433a07df7cf38eJohn Criswell