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1.7.5.1
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C-XSC - A C++ Class Library for Extended Scientific Computing
2.5.4
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00001 /* 00002 ** CXSC is a C++ library for eXtended Scientific Computing (V 2.5.4) 00003 ** 00004 ** Copyright (C) 1990-2000 Institut fuer Angewandte Mathematik, 00005 ** Universitaet Karlsruhe, Germany 00006 ** (C) 2000-2014 Wiss. Rechnen/Softwaretechnologie 00007 ** Universitaet Wuppertal, Germany 00008 ** 00009 ** This library is free software; you can redistribute it and/or 00010 ** modify it under the terms of the GNU Library General Public 00011 ** License as published by the Free Software Foundation; either 00012 ** version 2 of the License, or (at your option) any later version. 00013 ** 00014 ** This library is distributed in the hope that it will be useful, 00015 ** but WITHOUT ANY WARRANTY; without even the implied warranty of 00016 ** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 00017 ** Library General Public License for more details. 00018 ** 00019 ** You should have received a copy of the GNU Library General Public 00020 ** License along with this library; if not, write to the Free 00021 ** Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 00022 */ 00023 00024 /* CVS $Id: real.hpp,v 1.42 2014/01/30 17:23:48 cxsc Exp $ */ 00025 00026 #ifndef _CXSC_REAL_HPP_INCLUDED 00027 #define _CXSC_REAL_HPP_INCLUDED 00028 00029 #include <iostream> 00030 #include <string> 00031 00032 // namespace cxsc { 00033 00034 #include "compiler.h" 00035 #include "RtsTyp.h" 00036 #include "ioflags.hpp" 00037 00038 #include "except.hpp" 00040 00044 namespace cxsc { 00045 00046 class rvector; 00047 class rmatrix; 00048 class rvector_slice; 00049 class rmatrix_slice; 00050 00051 #define addu addup 00052 #define addd adddown 00053 #define subu subup 00054 #define subd subdown 00055 #define mulu multup 00056 #define muld multdown 00057 #define divu divup 00058 #define divd divdown 00059 00060 // --------------------------------------------------------------------------- 00061 // ---- ---- 00062 // ---- class real (declaration) ---- 00063 // ---- ---- 00064 // --------------------------------------------------------------------------- 00065 00067 00113 class real 00114 { 00115 private: 00116 // ---- private data ---------------------------------------- 00117 double w; 00118 00119 public: 00120 // ---- implicit constructors ------------------------------- 00122 real(void) throw () { } 00124 real(const float &a) throw () : w(a) { } 00126 real(const double &a) throw () : w(a) { } 00128 real(const int a) throw () : w(a) { } 00130 real(const long a) throw () : w(a) { } 00131 00132 // ---- explicit constructors ------------------------------- 00134 explicit real(const l_real &) throw(); 00135 00136 // The following are defined in the specific vector, matrix-files 00137 #if(CXSC_INDEX_CHECK) 00138 00139 explicit INLINE real(const rvector &) throw (ERROR_RVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_RVECTOR_USE_OF_UNINITIALIZED_OBJ); 00141 explicit INLINE real(const rvector_slice &) throw (ERROR_RVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_RVECTOR_USE_OF_UNINITIALIZED_OBJ); 00143 explicit INLINE real(const rmatrix &) throw (ERROR_RMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_RMATRIX_USE_OF_UNINITIALIZED_OBJ); 00145 explicit INLINE real(const rmatrix_slice &) throw (ERROR_RMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_RMATRIX_USE_OF_UNINITIALIZED_OBJ); 00146 #else 00147 00148 explicit INLINE real(const rvector &) throw (); 00150 explicit INLINE real(const rvector_slice &) throw (); 00152 explicit INLINE real(const rmatrix &) throw (); 00154 explicit INLINE real(const rmatrix_slice &) throw (); 00155 #endif 00156 00157 00158 // ---- assignments ----------------------------------------- 00159 00160 // ---- compatibility typecasts ----------------------------- 00161 00163 friend inline double _double(const real &a) throw(); 00165 friend inline real _real(const double &a) throw(); 00166 00167 #if(CXSC_INDEX_CHECK) 00168 00169 00174 friend INLINE real _real(const rvector &) throw (ERROR_RVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_RVECTOR_USE_OF_UNINITIALIZED_OBJ); 00176 00181 friend INLINE real _real(const rvector_slice &) throw (ERROR_RVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_RVECTOR_USE_OF_UNINITIALIZED_OBJ); 00183 00188 friend INLINE real _real(const rmatrix &) throw (ERROR_RMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_RMATRIX_USE_OF_UNINITIALIZED_OBJ); 00190 00195 friend INLINE real _real(const rmatrix_slice &) throw (ERROR_RMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_RMATRIX_USE_OF_UNINITIALIZED_OBJ); 00196 #else 00197 00198 00203 friend INLINE real _real(const rvector &) throw (); 00205 00210 friend INLINE real _real(const rvector_slice &) throw (); 00212 00217 friend INLINE real _real(const rmatrix &) throw (); 00219 00224 friend INLINE real _real(const rmatrix_slice &) throw (); 00225 #endif 00226 00227 // ---- Input/Output --------------------------------------- 00228 00230 friend std::ostream & operator <<(std::ostream &,const real &) throw(); 00232 friend std::istream & operator >>(std::istream &,real &) throw(); 00234 friend std::string & operator <<(std::string &,const real &) throw(); 00236 friend std::string & operator >>(std::string &,real &) throw(); 00238 friend void operator >>(const char *,real &) throw(); 00240 friend void operator >>(const std::string &,real &) throw(); 00241 00242 // ---- Std.Operators --------------------------------------- 00243 // As the real-arithmetic should be as fast as double all 00244 // operators are inlined. 00245 00247 friend inline real operator -(const real &) throw (); 00249 friend inline real operator +(const real &) throw (); 00250 00252 friend inline real operator +(const real &,const real &) throw(); 00254 friend inline real operator -(const real &,const real &) throw(); 00256 friend inline real operator *(const real &,const real &) throw(); 00258 friend inline real operator /(const real &,const real &) throw(); 00259 00261 friend inline real& operator +=(real &, const real &) throw(); 00263 friend inline real& operator -=(real &, const real &) throw(); 00265 friend inline real& operator *=(real &, const real &) throw(); 00267 friend inline real& operator /=(real &, const real &) throw(); 00268 00269 // ---- Comp.Operat. --------------------------------------- 00270 00272 friend inline bool operator! (const real& a) throw(); 00274 friend inline bool operator== (const real& a, const real& b) throw(); 00276 friend inline bool operator!= (const real& a, const real& b) throw(); 00278 friend inline bool operator< (const real& a, const real& b) throw(); 00280 friend inline bool operator<= (const real& a, const real& b) throw(); 00282 friend inline bool operator>= (const real& a, const real& b) throw(); 00284 friend inline bool operator> (const real& a, const real& b) throw(); 00285 00287 friend inline bool operator== (const real& a, const int & b) throw(); 00289 friend inline bool operator!= (const real& a, const int & b) throw(); 00291 friend inline bool operator== (const int & a, const real& b) throw(); 00293 friend inline bool operator!= (const int & a, const real& b) throw(); 00295 friend inline bool operator== (const real& a, const long & b) throw(); 00297 friend inline bool operator!= (const real& a, const long & b) throw(); 00299 friend inline bool operator== (const long & a, const real& b) throw(); 00301 friend inline bool operator!= (const long & a, const real& b) throw(); 00303 friend inline bool operator== (const real& a, const float & b) throw(); 00305 friend inline bool operator!= (const real& a, const float & b) throw(); 00307 friend inline bool operator== (const float & a, const real& b) throw(); 00309 friend inline bool operator!= (const float & a, const real& b) throw(); 00311 friend inline bool operator== (const real& a, const double & b) throw(); 00313 friend inline bool operator!= (const real& a, const double & b) throw(); 00315 friend inline bool operator== (const double & a, const real& b) throw(); 00317 friend inline bool operator!= (const double & a, const real& b) throw(); 00318 00319 // ---- Rounding Operators --------------------------------- 00320 00322 friend inline real addup(const real &, const real &); 00324 friend inline real adddown(const real &, const real &); 00326 friend inline real subup(const real &, const real &); 00328 friend inline real subdown(const real &, const real &); 00330 friend inline real multup(const real &, const real &); 00332 friend inline real multdown(const real &, const real &); 00334 friend inline real divup(const real &, const real &); 00336 friend inline real divdown(const real &, const real &); 00337 00338 // ---- Others ------------------------------------------- 00339 00341 friend inline real abs(const real &a) throw(); 00343 friend inline int sign(const real &) throw(); 00344 00346 friend inline real pred(const real &) throw(); 00348 friend inline real succ(const real &) throw(); 00350 friend inline a_intg expo(const real &) throw(); 00352 friend inline real comp(const real &,a_intg) throw(); 00354 friend inline real mant(const real &) throw(); 00355 00356 real & operator = (const lx_real&) throw(); // Blomquist, 12.11.2008; 00357 real & operator = (const l_real&) throw(); // Blomquist, 12.11.2008; 00358 }; // end of class real 00359 00360 inline real comp(const real &,a_intg) throw(); 00361 00362 // --------------------------------------------------------------------------- 00363 // ---- ---- 00364 // ---- friend functions of class real (not inline) ---- 00365 // ---- ---- 00366 // --------------------------------------------------------------------------- 00367 00368 std::ostream & operator <<(std::ostream &,const real &) throw(); 00369 std::istream & operator >>(std::istream &,real &) throw(); 00370 std::string & operator <<(std::string &,const real &) throw(); 00371 std::string & operator >>(std::string &,real &) throw(); 00372 void operator >>(const char *,real &) throw(); 00373 void operator >>(const std::string &,real &) throw(); 00374 00375 // --------------------------------------------------------------------------- 00376 // ---- ---- 00377 // ---- global functions associated with class real ---- 00378 // ---- ---- 00379 // --------------------------------------------------------------------------- 00380 00382 inline real max(const real & a, const real & b); 00384 inline real min(const real & a, const real & b); 00386 inline real Max(const real & a, const real & b); 00387 00388 //---------------------------------------------------------------------- 00389 // MakeHexReal - erstellt aus den binaer angegebenen Einzelteilen einer 00390 // IEEE 64-bit Gleitkommazahl eine solche 00391 00393 const real& MakeHexReal ( 00394 int sign, unsigned int expo, a_btyp manthigh, a_btyp mantlow); 00395 00397 inline bool IsInfinity(const real &a); 00399 inline bool IsQuietNaN(const real &a); 00401 inline bool IsSignalingNaN(const real &a); 00402 00403 //------------------------------------------------------------------------- 00404 // times2pown - Fast multiplication of reference parameter r with 2^n ----- 00406 inline void times2pown(real& r,const int n); // Blomquist 1.10.02. {real.inl} 00407 00409 inline real pow2n(const int n) throw(); // returns 2^n; 00410 00412 string realToHex(const real& a); 00413 00414 // --------------------------------------------------------------------------- 00415 // ---- ---- 00416 // ---- special constants associated with class real ---- 00417 // ---- ---- 00418 // --------------------------------------------------------------------------- 00419 00420 // ---- special constants ----------------------------------------- 00422 extern const real MinReal; 00424 extern const real minreal; 00426 extern const real MaxReal; 00428 extern const real Infinity; 00430 extern const real SignalingNaN; 00432 extern const real QuietNaN; 00434 extern const real Epsilon; 00435 extern const real Factor; 00436 00438 extern const real Pi_real; // Pi 00440 extern const real Pi2_real; // 2*Pi 00442 extern const real Pi3_real; // 3*Pi 00444 extern const real Pid2_real; // Pi/2 00446 extern const real Pid3_real; // Pi/3 00448 extern const real Pid4_real; // Pi/4 00450 extern const real Pir_real; // 1/Pi 00452 extern const real Pi2r_real; // 1/(2*Pi) 00454 extern const real Pip2_real; // Pi^2 00456 extern const real SqrtPi_real; // sqrt(Pi) 00458 extern const real Sqrt2Pi_real; // sqrt(2Pi) 00460 extern const real SqrtPir_real; // 1/sqrt(Pi) 00462 extern const real Sqrt2Pir_real; // 1/sqrt(2Pi) 00464 extern const real Sqrt2_real; // sqrt(2) 00466 extern const real Sqrt5_real; // sqrt(5) 00468 extern const real Sqrt7_real; // sqrt(7) 00470 extern const real Sqrt2r_real; // 1/sqrt(2) 00472 extern const real Sqrt3_real; // sqrt(3) 00474 extern const real Sqrt3d2_real; // sqrt(3)/2 00476 extern const real Sqrt3r_real; // 1/sqrt(3) 00478 extern const real Ln2_real; // ln(2) 00480 extern const real Ln2r_real; // 1/ln(2) 00482 extern const real Ln10_real; // ln(10) 00484 extern const real Ln10r_real; // 1/ln(10) 00486 extern const real LnPi_real; // ln(Pi) 00488 extern const real Ln2Pi_real; // ln(2Pi) 00490 extern const real E_real; // e 00492 extern const real Er_real; // 1/e 00494 extern const real Ep2_real; // e^2 00496 extern const real Ep2r_real; // 1/e^2 00498 extern const real EpPi_real; // e^(Pi) 00500 extern const real Ep2Pi_real; // e^(2Pi) 00502 extern const real EpPid2_real; // e^(Pi/2) 00504 extern const real EpPid4_real; // e^(Pi/4) 00505 00506 } // namespace cxsc 00507 00508 #include "real.inl" 00509 #include "rmath.hpp" 00510 // } 00511 #endif // _CXSC_REAL_HPP_INCLUDED 00512
1.7.5.1