FIFE: engine/core/util/math/fife

00001 /***************************************************************************
00002  *   Copyright (C) 2005-2010 by the FIFE team                              *
00003  *   http://www.fifengine.net                                               *
00004  *   This file is part of FIFE.                                            *
00005  *                                                                         *
00006  *   FIFE is free software; you can redistribute it and/or                 *
00007  *   modify it under the terms of the GNU Lesser General Public            *
00008  *   License as published by the Free Software Foundation; either          *
00009  *   version 2.1 of the License, or (at your option) any later version.    *
00010  *                                                                         *
00011  *   This library is distributed in the hope that it will be useful,       *
00012  *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
00013  *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU     *
00014  *   Lesser General Public License for more details.                       *
00015  *                                                                         *
00016  *   You should have received a copy of the GNU Lesser General Public      *
00017  *   License along with this library; if not, write to the                 *
00018  *   Free Software Foundation, Inc.,                                       *
00019  *   51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA          *
00020  ***************************************************************************/
00021 
00022 #ifndef FIFE_UTIL_FIFE_MATH_H
00023 #define FIFE_UTIL_FIFE_MATH_H
00024 
00025 // Standard C++ library includes
00026 #include <cassert>
00027 #include <cmath>
00028 #include <limits>
00029 
00030 // Platform specific includes
00031 
00032 // 3rd party library includes
00033 
00034 // FIFE includes
00035 // These includes are split up in two parts, separated by one empty line
00036 // First block: files included from the FIFE root src directory
00037 // Second block: files included from the same folder
00038 
00039 #ifndef ABS
00040 #define ABS(x) ((x)<0?-(x):(x))
00041 
00042 #endif
00043 
00044 // Sort out the missing round function in MSVC:
00045 #if defined( WIN32 ) && defined( _MSC_VER )
00046 inline double round(const double x) {
00047     return x < 0.0 ? ceil(x - 0.5) : floor(x + 0.5);
00048 }
00049 #endif
00050 
00051 namespace FIFE {
00052 
00053     static const float FLT_STD_EPSILON = std::numeric_limits<float>::epsilon();
00054     static const float FLT_STD_MAX = std::numeric_limits<float>::max();
00055     static const float FLT_ZERO_TOLERANCE = 1e-06f;
00056     static const float FLT_PI = 4.0f*std::atan(1.0f);
00057     static const float FLT_TWO_PI = 2.0f*FLT_PI;
00058     static const float FLT_HALF_PI = 0.5f*FLT_PI;
00059     static const float FLT_INVERSE_PI = 1.0f/FLT_PI;
00060     static const float FLT_INVERSE_TWO_PI = 1.0f/FLT_TWO_PI;
00061     static const float FLT_DEG_TO_RAD = FLT_PI/180.0f;
00062     static const float FLT_RAD_TO_DEG = 180.0f/FLT_PI;
00063     static const float FLT_LOG_2 = std::log(2.0f);
00064     static const float FLT_LOG_10 = std::log(10.0f);
00065     static const float FLT_INV_LOG_2 = 1.0f/std::log(2.0f);
00066     static const float FLT_INV_LOG_10 = 1.0f/std::log(10.0f);
00067 
00068     static const double DBL_STD_EPSILON = std::numeric_limits<double>::epsilon();
00069     static const double DBL_STD_MAX = std::numeric_limits<double>::max();
00070     static const double DBL_ZERO_TOLERANCE = 1e-08;
00071     static const double DBL_PI = 4.0*std::atan(1.0);
00072     static const double DBL_TWO_PI = 2.0*DBL_PI;
00073     static const double DBL_HALF_PI = 0.5*DBL_PI;
00074     static const double DBL_INVERSE_PI = 1.0/DBL_PI;
00075     static const double DBL_INVERSE_TWO_PI = 1.0/DBL_TWO_PI;
00076     static const double DBL_DEG_TO_RAD = DBL_PI/180.0;
00077     static const double DBL_RAD_TO_DEG = 180.0f/DBL_PI;
00078     static const double DBL_LOG_2 = std::log(2.0);
00079     static const double DBL_LOG_10 = std::log(10.0);
00080     static const double DBL_INV_LOG_2 = 1.0/std::log(2.0);
00081     static const double DBL_INV_LOG_10 = 1.0/std::log(10.0);
00082 
00083     template <class numT>
00084     struct float_traits { };
00085 
00086     template <>
00087     struct float_traits<float> {
00088         typedef float float_type;
00089         static inline float_type epsilon() { return FLT_STD_EPSILON; }
00090         static inline float_type zeroTolerance() { return FLT_ZERO_TOLERANCE; }
00091         static inline float_type max() { return FLT_STD_MAX; }
00092         static inline float_type pi() { return FLT_PI; }
00093         static inline float_type twoPi() { return FLT_TWO_PI; }
00094         static inline float_type halfPi() { return FLT_HALF_PI; }
00095         static inline float_type inversePi() { return FLT_INVERSE_PI; }
00096         static inline float_type inverseTwoPi() { return FLT_INVERSE_TWO_PI; }
00097         static inline float_type degToRad() { return FLT_DEG_TO_RAD; }
00098         static inline float_type radToDeg() { return FLT_RAD_TO_DEG; }
00099         static inline float_type log2() { return FLT_LOG_2; }
00100         static inline float_type log10() { return FLT_LOG_10; }
00101         static inline float_type invLog2() { return FLT_INV_LOG_2; }
00102         static inline float_type invLog10() { return FLT_INV_LOG_10; }
00103     };
00104 
00105     template <>
00106     struct float_traits<double> {
00107         typedef double float_type;
00108         static inline float_type epsilon() { return DBL_STD_EPSILON; }
00109         static inline float_type zeroTolerance() { return DBL_ZERO_TOLERANCE; }
00110         static inline float_type max() { return DBL_STD_MAX; }
00111         static inline float_type pi() { return DBL_PI; }
00112         static inline float_type twoPi() { return DBL_TWO_PI; }
00113         static inline float_type halfPi() { return DBL_HALF_PI; }
00114         static inline float_type inversePi() { return DBL_INVERSE_PI; }
00115         static inline float_type inverseTwoPi() { return DBL_INVERSE_TWO_PI; }
00116         static inline float_type degToRad() { return DBL_DEG_TO_RAD; }
00117         static inline float_type radToDeg() { return DBL_RAD_TO_DEG; }
00118         static inline float_type log2() { return DBL_LOG_2; }
00119         static inline float_type log10() { return DBL_LOG_10; }
00120         static inline float_type invLog2() { return DBL_INV_LOG_2; }
00121         static inline float_type invLog10() { return DBL_INV_LOG_10; }
00122     };
00123 
00124     template <typename T>
00125     class Math {
00126     public:
00127         typedef T num_type;
00128         typedef float_traits<num_type> traits_type;
00129 
00130         static inline num_type epsilon() { return traits_type::epsilon(); }
00131         static inline num_type zeroTolerance() { return traits_type::zeroTolerance(); }
00132         static inline num_type max() { return traits_type::max(); }
00133         static inline num_type pi() { return traits_type::pi(); }
00134         static inline num_type twoPi() { return traits_type::twoPi(); }
00135         static inline num_type halfPi() { return traits_type::halfPi(); }
00136         static inline num_type inversePi() { return traits_type::inversePi(); }
00137         static inline num_type inverseTwoPi() { return traits_type::inverseTwoPi(); }
00138         static inline num_type degToRad() { return traits_type::degToRad(); }
00139         static inline num_type radToDeg() { return traits_type::radToDeg(); }
00140         static inline num_type log2() { return traits_type::log2(); }
00141         static inline num_type log10() { return traits_type::log10(); }
00142         static inline num_type invLog2() { return traits_type::invLog2(); }
00143         static inline num_type invLog10() { return traits_type::invLog10(); }
00144 
00145         static T ACos(T _val);
00146         static T ASin(T _val);
00147         static T ATan(T _val);
00148         static T ATan2(T _x, T _y);
00149         static T Ceil(T _val);
00150         static T Cos(T _val);
00151         static T Exp(T _val);
00152         static T FAbs(T _val);
00153         static T Floor(T _val);
00154         static T FMod (T _x, T _y);
00155         static T InvSqrt(T _val);
00156         static T Log(T _val);
00157         static T Log2(T _val);
00158         static T Log10(T _val);
00159         static T Pow(T _base, T _exponent);
00160         static T Sin(T _val);
00161         static T Sqr(T _val);
00162         static T Sqrt(T _val);
00163         static T Tan(T _val);
00164         static bool Equal(T _val1, T _val2);
00165     };
00166 
00167     typedef Math<float> Mathf;
00168     typedef Math<double> Mathd;
00169 
00170     template<typename T>
00171     inline T Math<T>::ACos(T _val) {
00172         if (-static_cast<T>(1) < _val) {
00173             if (_val < static_cast<T>(1)) {
00174                 return static_cast<T>(std::acos(_val));
00175             }
00176             else {
00177                 return static_cast<T>(0);
00178             }
00179         }
00180         else {
00181             return pi();
00182         }
00183     }
00184 
00185     template <class T>
00186     inline T Math<T>::ASin(T _val) {
00187         if (-static_cast<T>(1) < _val) {
00188             if (_val < static_cast<T>(1)) {
00189                 return static_cast<T>(std::asin(_val));
00190             }
00191             else {
00192                 return halfPi();
00193             }
00194         }
00195         else {
00196             return -halfPi();
00197         }
00198     }
00199 
00200     template <class T>
00201     inline T Math<T>::ATan(T _val) {
00202         return static_cast<T>(std::atan(_val));
00203     }
00204 
00205     template <class T>
00206     inline T Math<T>::ATan2(T _x, T _y) {
00207         return static_cast<T>(std::atan2(_x, _y));
00208     }
00209 
00210     template <class T>
00211     inline T Math<T>::Ceil(T _val) {
00212         return static_cast<T>(std::ceil(_val));
00213     }
00214 
00215     template <class T>
00216     inline T Math<T>::Cos(T _val) {
00217         return static_cast<T>(std::cos(_val));
00218     }
00219 
00220     template <class T>
00221     inline T Math<T>::Exp(T _val){
00222         return static_cast<T>(std::exp(_val));
00223     }
00224 
00225     template <class T>
00226     inline T Math<T>::FAbs(T _val) {
00227         return static_cast<T>(std::fabs(_val));
00228     }
00229 
00230     template <class T>
00231     inline T Math<T>::Floor(T _val) {
00232         return static_cast<T>(std::floor(_val));
00233     }
00234 
00235     template <class T>
00236     inline T Math<T>::FMod(T _x, T _y) {
00237         return static_cast<T>(std::fmod(_x, _y));
00238     }
00239 
00240     template <class T>
00241     inline T Math<T>::InvSqrt(T _val) {
00242         return static_cast<T>(1/std::sqrt(_val));
00243     }
00244 
00245     template <class T>
00246     inline T Math<T>::Log(T _val) {
00247         return static_cast<T>(std::log(_val));
00248     }
00249 
00250     template <class T>
00251     inline T Math<T>::Log2(T _val) {
00252         return invLog2() * static_cast<T>(std::log(_val));
00253     }
00254     template <class T>
00255     inline T Math<T>::Log10(T _val) {
00256 
00257         return invLog10() * static_cast<T>(std::log(_val));
00258     }
00259 
00260     template <class T>
00261     inline T Math<T>::Pow(T _base, T _exponent) {
00262         return static_cast<T>(std::pow(_base, _exponent));
00263     }
00264 
00265     template <class T>
00266     inline T Math<T>::Sin(T _val) {
00267         return static_cast<T>(std::sin(_val));
00268     }
00269 
00270     template <class T>
00271     inline T Math<T>::Sqr(T _val) {
00272         return _val*_val;
00273     }
00274 
00275     template <class T>
00276     inline T Math<T>::Sqrt(T _val) {
00277         return static_cast<T>(std::sqrt(_val));
00278     }
00279 
00280     template <class T>
00281     inline T Math<T>::Tan(T _val) {
00282         return static_cast<T>(std::tan(_val));
00283     }
00284 
00285     template <class T>
00286     inline bool Math<T>::Equal(T _val1, T _val2) {
00287         return std::fabs(_val1 - _val2) < epsilon();
00288     }
00289 
00292     inline unsigned nextPow2(unsigned x)
00293     {
00294         --x;
00295         x |= x >> 1;
00296         x |= x >> 2;
00297         x |= x >> 4;
00298         x |= x >> 8;
00299         x |= x >> 16;
00300         return ++x;
00301     }
00302 } //FIFE
00303 
00304 #endif // FIFE_UTIL_FIFE_MATH_H
fife_math.h
