C-XSC - A C++ Class Library for Extended Scientific Computing: lx

00001 /*
00002 **  CXSC is a C++ library for eXtended Scientific Computing (V 2.5.1)
00003 **
00004 **  Copyright (C) 1990-2000 Institut fuer Angewandte Mathematik,
00005 **                          Universitaet Karlsruhe, Germany
00006 **            (C) 2000-2011 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: lx_real.hpp,v 1.6 2011/06/07 15:17:41 cxsc Exp $ */
00025 
00026 
00027 /*
00028 **  F. Blomquist, University of Wuppertal, 19.09.2007;
00029 */
00030 
00031 /*
00032 **  Implementation of the classes
00033 **
00034 **  lx_real      with all tools and elementary functions for real
00035 **               point and interval aruments
00036 **
00037 */
00038 
00039 #ifndef _CXSC_LX_REAL_HPP_INCLUDED
00040 #define _CXSC_LX_REAL_HPP_INCLUDED
00041 
00042 #include <l_imath.hpp>
00043 #include <sstream>
00044 #include <cmath>
00045 #include <iostream>
00046 
00047 namespace cxsc {
00048 
00049         const real Max_Int_R =  9007199254740991.0; // = 2^(53) - 1
00050         const real Max_Int_N = -9007199254738891.0; // = -Max_Int_R+2100
00051 
00053         inline bool Is_Integer(const real& x);
00054     // returns 1 if x is an integer value and 
00055     //           if |x| <= 2^53 - 1 = 9007199254740991.0;
00056     // otherwise 0 is returnd
00057 
00058         class lx_real
00059         {
00060 
00061                 private:
00062     // ------------- Datenelemente -------------------------------------------
00063                         real ex;
00064                         l_real lr;
00065 
00066                 public:
00067     // ------------- Constructors --------------------------------------------
00068 
00070                         lx_real(void)  throw() {}
00072                         lx_real(const real& n, const l_real &a) throw() 
00073                         { 
00074                                 if ( !(Is_Integer(n)) ) 
00075                                         cxscthrow(REAL_NOT_ALLOWED("lx_real(const real&, const l_real&)"));
00076                                 else
00077                                 {
00078                                         ex = n; lr = a;
00079                                 }
00080                         }
00081 
00083                         lx_real(const real& n, const real &a) throw() 
00084                         { 
00085                                 if ( !(Is_Integer(n)) ) 
00086                                         cxscthrow(REAL_NOT_ALLOWED("lx_real(const real&, const real&)"));
00087                                 else
00088                                 {
00089                                         ex = n; lr = a;
00090                                 }
00091                         }
00092 
00094                         explicit lx_real(const l_real &a) throw() : ex(0), lr(a) { }
00096                         explicit lx_real(const real &a)   throw() : ex(0), lr(a) { }
00098                         lx_real(const real&, const string&) throw();
00099 
00100 
00101     // ------------- Assignments ---------------------------------------------
00102          
00104                         inline lx_real & operator = (const lx_real &) throw();
00106                         inline lx_real & operator = (const l_real &)  throw();
00108                         inline lx_real & operator = (const real &)    throw();
00109 
00110     // ------------- Functions -----------------------------------------------
00111 
00113                         friend inline int StagPrec(const lx_real&) throw(); 
00115                         friend inline real expo(const lx_real&) throw();
00117                         friend inline int sign(const lx_real&) throw();
00119                         friend inline l_real lr_part(const lx_real&) throw();
00121                         friend inline lx_real abs(const lx_real&) throw();
00123                         friend void scale_up  (lx_real &) throw();
00125                         friend void scale_down(lx_real &) throw();
00127                         friend inline lx_real adjust(const lx_real &) throw();
00128 
00130                         friend inline bool eq_zero (const lx_real &a) throw(); // a = 0;
00132                         friend inline bool gr_zero (const lx_real &a) throw(); // a > 0;
00134                         friend inline bool ge_zero (const lx_real &a) throw(); // a >=0;
00136                         friend inline bool sm_zero (const lx_real &a) throw(); // a < 0;
00138                         friend inline bool se_zero (const lx_real &a) throw(); // a <=0;
00139          
00141                         friend inline void times2pown(lx_real &, const real &) throw();
00143                         friend inline void times2pown_neg(lx_real& a, const real& n) throw();
00145                         friend inline bool operator ! (const lx_real &) throw();
00147                         friend inline lx_real operator -(const lx_real &) throw();
00148 
00149 
00150 // ----------------------- Output --------------------------------------------
00151 
00152 //friend inline std::ostream& operator << (std::ostream& s, const lx_real& a) 
00153 //    throw(); // A value a of type lx_real is written to the output channel.
00154 // The above operator is declared and defined in
00155 // lx_interval.hpp (outside the class lx_interval) , lx_interval.inl;
00157 friend std::string & operator << (std::string &s, const lx_real& a) 
00158                                         throw();
00159 // The value of a variable a of type lx_real is copied to a string s.
00160 // s has the form:  {2**(ex)*li};  ex is the exponent to base 2.
00161 
00162 }; // end of class lx_real
00163 
00164 // -------------------------------------------------------------
00165 // ------- friend functions declared in class lx_real: ---------
00166 // -------------------------------------------------------------
00167 
00168 inline int StagPrec(const lx_real&) throw();
00169 inline real expo(const lx_real&) throw();
00170 inline int sign(const lx_real&) throw();
00171 inline l_real lr_part(const lx_real&) throw();
00172 inline lx_real abs(const lx_real&) throw();
00173 inline lx_real adjust(const lx_real &) throw();
00174 inline void times2pown_neg(lx_real&, const real&) throw();
00175 
00176        void scale_up  (lx_real&)   throw();
00177                  void scale_down(lx_real &a) throw();
00178 
00179                  inline bool eq_zero (const lx_real &a) throw(); // a = 0;
00180                  inline bool gr_zero (const lx_real &a) throw(); // a > 0;
00181                  inline bool ge_zero (const lx_real &a) throw(); // a >=0;
00182                  inline bool sm_zero (const lx_real &a) throw(); // a < 0;
00183                  inline bool se_zero (const lx_real &a) throw(); // a <=0;
00184 
00185                  inline void times2pown(lx_real &, const real &) throw();
00186                  inline bool operator ! (const lx_real &) throw();
00187 
00188                  inline lx_real operator -(const lx_real &) throw();
00189 
00190 // -------------------------- Input ------------------------------------
00191 
00193                  string & operator >> (string &s, lx_real &a) throw();
00195                  void operator >> (const string &s, lx_real &a) throw();
00197                  void operator >> (const char *s, lx_real&) throw();
00199                  std::istream & operator >> (std::istream &s, lx_real &a) throw();
00200 
00201 // -------------------------- Output ------------------------------------
00202 
00203    std::string & operator << (std::string &s, const lx_real& a) 
00204                                         throw();
00205 //inline std::ostream& operator << (std::ostream& s, const lx_real& a) 
00206 //    throw(); // A value a of type lx_real is written to the output channel.
00208                  inline std::string & operator << (std::string &s, const lx_real& a) 
00209                                  throw();
00210 // The value of a variable a of type lx_real is copied to a string s.
00211 // s has the form:  {2**(ex),lr}
00212 
00213 // ---- function declarations outside the class lx_real ----
00214 
00216                  inline real add_real(const real &a, const real &b) throw();
00217 
00219                  inline real sub_real(const real &a, const real &b) throw();
00220 
00222                  lx_real upper_bnd(const lx_real& x) throw();
00223 
00225                  lx_real lower_bnd(const lx_real& x) throw();
00227                  inline lx_real operator +(const lx_real &) throw();
00228 
00230                  lx_real operator + (const lx_real &, const lx_real &) throw();
00232                  inline lx_real operator + (const lx_real&, const l_real &) throw();
00234                  inline lx_real operator + (const l_real&, const lx_real &) throw();
00236                  inline lx_real operator + (const lx_real&, const real &) throw();
00238                  inline lx_real operator + (const real&, const lx_real &) throw();
00239 
00241                  inline lx_real & operator +=(lx_real &, const lx_real &) throw();
00243                  inline lx_real & operator +=(lx_real &, const l_real &) throw();
00245                  inline lx_real & operator +=(lx_real &, const real &) throw();
00246 
00248                  inline lx_real operator - (const lx_real &, const lx_real &) throw();
00250                  inline lx_real operator - (const lx_real &, const l_real &) throw();
00252                  inline lx_real operator - (const l_real &, const lx_real &) throw();
00254                  inline lx_real operator - (const lx_real &, const real &) throw();
00256                  inline lx_real operator - (const real &, const lx_real &) throw();
00257 
00259                  inline lx_real & operator -=(lx_real &, const lx_real &) throw();
00261                  inline lx_real & operator -=(lx_real &, const l_real &) throw();
00263                  inline lx_real & operator -=(lx_real &, const real &) throw();
00264 
00266                  lx_real operator * (const lx_real &, const lx_real &) throw();
00268                  inline lx_real operator * (const lx_real&, const l_real &) throw();
00270                  inline lx_real operator * (const l_real&, const lx_real &) throw();
00272                  inline lx_real operator * (const lx_real&, const real &) throw();
00274                  inline lx_real operator * (const real&, const lx_real &) throw();
00275 
00277                  inline lx_real & operator *=(lx_real &, const lx_real &) throw();
00279                  inline lx_real & operator *=(lx_real &, const l_real &) throw();
00281                  inline lx_real & operator *=(lx_real &, const real &) throw();
00282 
00284                  lx_real operator / (const lx_real &, const lx_real &) throw(DIV_BY_ZERO);
00286                  inline lx_real operator / (const lx_real&, const l_real &) throw();
00288                  inline lx_real operator / (const l_real&, const lx_real &) throw();
00290                  inline lx_real operator / (const lx_real&, const real &) throw();
00292                  inline lx_real operator / (const real&, const lx_real &) throw();
00293 
00295                  inline lx_real & operator /=(lx_real &, const lx_real &) throw();
00297                  inline lx_real & operator /=(lx_real &, const l_real &) throw();
00299                  inline lx_real & operator /=(lx_real &, const real &) throw();
00300 
00302                  bool operator == (const lx_real &, const lx_real &) throw();
00304                  inline bool operator == (const lx_real &, const l_real &) throw();
00306                  inline bool operator == (const l_real &, const lx_real &) throw();
00308                  inline bool operator == (const lx_real &, const real &)   throw();
00310                  inline bool operator == (const real &,   const lx_real &) throw();
00311 
00313                  inline bool operator != (const lx_real &, const lx_real &) throw();
00315                  inline bool operator != (const lx_real &, const l_real &) throw();
00317                  inline bool operator != (const l_real &, const lx_real &) throw();
00319                  inline bool operator != (const lx_real &, const real &)   throw();
00321                  inline bool operator != (const real &,   const lx_real &) throw();
00322 
00324                  bool operator > (const lx_real &, const lx_real &) throw();
00325 
00327                  inline bool operator <= (const lx_real &, const lx_real &) throw();
00329                  inline bool operator <  (const lx_real &, const lx_real &) throw();
00331                  inline bool operator >= (const lx_real &, const lx_real &) throw();
00332 
00334                  inline bool operator >  (const real &, const lx_real &) throw();
00336                  inline bool operator <= (const real &, const lx_real &) throw();
00338                  inline bool operator <  (const real &, const lx_real &) throw();
00340                  inline bool operator >= (const real &, const lx_real &) throw();
00341 
00343                  inline bool operator >  (const lx_real &, const real &) throw();
00345                  inline bool operator <= (const lx_real &, const real &) throw();
00347                  inline bool operator <  (const lx_real &, const real &) throw();
00349                  inline bool operator >= (const lx_real &, const real &) throw();
00350 
00352                  inline bool operator >  (const l_real &, const lx_real &) throw();
00354                  inline bool operator <= (const l_real &, const lx_real &) throw();
00356                  inline bool operator <  (const l_real &, const lx_real &) throw();
00358                  inline bool operator >= (const l_real &, const lx_real &) throw();
00359 
00361                  inline bool operator >  (const lx_real &, const l_real &) throw();
00363                  inline bool operator <= (const lx_real &, const l_real &) throw();
00365                  inline bool operator <  (const lx_real &, const l_real &) throw();
00367                  inline bool operator >= (const lx_real &, const l_real &) throw();
00368 
00370                  inline lx_real max(const lx_real&, const lx_real&);
00372                  inline lx_real min(const lx_real&, const lx_real&);
00373 
00375                  inline real cutint(const real& x) throw();
00376 
00377 // ------------------- lx_real Constants ------------------------------------
00378 
00380                  lx_real Pi_lx_real() throw(); // pi
00382                  lx_real Pip2_lx_real() throw(); // pi^2
00384                  lx_real Pi2_lx_real() throw(); // 2*pi
00386                  lx_real Pid4_lx_real() throw(); // Pi/4
00388                  lx_real Pid2_lx_real() throw(); // Pi/2
00390                  lx_real Ln2_lx_real() throw();
00392                  lx_real Ln10_lx_real() throw();
00394                  lx_real Ln10r_lx_real() throw();
00396                  lx_real Pir_lx_real() throw();
00398                  lx_real Pi2r_lx_real() throw();  // 1/(2*pi)
00400                  lx_real SqrtPi_lx_real() throw();
00402                  lx_real Sqrt2Pi_lx_real() throw();
00404                  lx_real Sqrt2_lx_real() throw();
00406                  lx_real Sqrt2r_lx_real() throw();
00408                  lx_real Sqrt3_lx_real() throw();
00410                  lx_real Sqrt3r_lx_real() throw();
00412                  lx_real Sqrt3d2_lx_real() throw();
00414                  lx_real Ln2r_lx_real() throw();
00416                  lx_real Pid3_lx_real() throw();
00418                  lx_real SqrtPir_lx_real() throw();
00420                  lx_real Sqrt2Pir_lx_real() throw();
00422                  lx_real LnPi_lx_real() throw();
00424                  lx_real Ln2Pi_lx_real() throw();
00426                  lx_real E_lx_real() throw();
00428                  lx_real Ep2_lx_real() throw();
00430                  lx_real Ep2r_lx_real() throw();
00432                  lx_real Er_lx_real() throw();
00434                  lx_real EpPi_lx_real() throw();
00436                  lx_real EpPid2_lx_real() throw();
00438                  lx_real EpPid4_lx_real() throw();
00440                  lx_real Ep2Pi_lx_real() throw();
00442                  lx_real EulerGamma_lx_real() throw();
00444                  lx_real Catalan_lx_real() throw();
00446                  lx_real sqrt5_lx_real() throw();
00448                  lx_real sqrt7_lx_real() throw();
00450                  lx_real One_m_lx_real() throw();
00452                  lx_real One_p_lx_real() throw();
00453 
00454 // **********************************************************************
00455 // **********************************************************************
00456 
00457 
00458 
00459 // ------------------- Array of constants ----------------------
00460 
00461 // const real ln_N[180];
00462 // ln_N[0] = ln(2); ln_N[1] = ln(3); ... ln_N[179] = ln(181);
00463 
00464 const real ln_N[180] =
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00645 
00646 // ------------------------------------------------------------------------
00647 // --------------- lx_real elementary functions ---------------------------
00648 // ------------------------------------------------------------------------
00649 
00651  lx_real sqrt(const lx_real&) throw();
00653  lx_real sqr(const lx_real&) throw();
00655  lx_real ln(const lx_real &) throw();
00657  lx_real log2(const lx_real &) throw();
00659  lx_real log10(const lx_real &) throw();
00661  lx_real lnp1(const lx_real &) throw();
00663  lx_real exp(const lx_real &) throw();
00665  lx_real exp2(const lx_real &) throw(); // 2^x
00667  lx_real exp10(const lx_real &) throw(); // 10^x
00669  lx_real expm1(const lx_real &x) throw(); 
00671  lx_real power(const lx_real &, const real &) throw();
00673  lx_real pow(const lx_real &, const lx_real &) throw();
00675  lx_real xp1_pow_y(const lx_real &, const lx_real &) throw(); 
00677  lx_real sin(const lx_real &)throw();
00679  lx_real sin_n(const lx_real &x, const real& n) throw();
00681  lx_real cos(const lx_real &) throw();
00683  lx_real cos_n(const lx_real &x, const real& n) throw();
00685  lx_real tan(const lx_real &) throw();
00687  lx_real cot(const lx_real &) throw();
00689  lx_real sqrt1px2(const lx_real &) throw();
00691  lx_real atan(const lx_real &) throw();
00693  lx_real sqrt1mx2(const lx_real &) throw();
00695  lx_real sqrtx2m1(const lx_real &) throw();
00697  lx_real asin(const lx_real & ) throw();
00699  lx_real acos(const lx_real &) throw();
00701  lx_real acot(const lx_real &) throw();
00703  lx_real sinh(const lx_real &) throw();
00705  lx_real cosh(const lx_real &) throw();
00707  lx_real tanh(const lx_real &) throw();
00709  lx_real coth(const lx_real &) throw();
00711  lx_real sqrtp1m1(const lx_real &) throw();
00713  lx_real asinh(const lx_real &) throw();
00715  lx_real acosh(const lx_real &) throw();
00717  lx_real acoshp1(const lx_real &) throw();
00719  lx_real atanh(const lx_real &) throw();
00721  lx_real atanh1m(const lx_real &) throw();
00723  lx_real atanhm1p(const lx_real &) throw();
00725  lx_real acoth(const lx_real &) throw();
00727  lx_real acothp1(const lx_real &) throw();
00729  lx_real acothm1m(const lx_real &) throw();
00731  lx_real sqrtx2y2(const lx_real &, const lx_real &) throw();
00733  lx_real ln_sqrtx2y2(const lx_real &, const lx_real &) throw();
00735  lx_real sqrt(const lx_real &, int) throw();
00736 
00737 } // end namespace cxsc
00738 
00739 #include "lx_real.inl"
00740 
00741 #endif // _CXSC_LX_REAL_HPP_INCLUDED