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

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: l_imath.hpp,v 1.29 2011/06/07 15:17:40 cxsc Exp $ */
00025 
00026 #ifndef _CXSC_L_IMATH_HPP_INCLUDED
00027 #define _CXSC_L_IMATH_HPP_INCLUDED
00028 
00029 #include "l_interval.hpp"
00030 
00031 namespace cxsc {
00032 
00034 l_interval pow     (const l_interval&, const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // Pow(x,y)
00036 l_interval power   (const l_interval&, int);    // Power(x,n)
00038 l_interval sqr     (const l_interval&);         // Sqr(x)
00039 
00041 l_interval sqrt    (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); 
00042                                                 // Sqrt(x)
00044 l_interval sqrt    (const l_interval&, int) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); 
00045                                                 // NSqrt(n,x)
00046 
00048 l_interval sin     (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW);    
00049                                                 // Sin(x)
00051 l_interval cos     (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW);    
00052                                                 // Cos(x)
00054 l_interval tan     (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW,ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF);
00055                                                 // Tan(x)
00057 l_interval cot     (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW,ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF);
00058                                                 // Cot(x)
00059 
00061 l_interval asin    (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF);   
00062                                                 // ASin(x)
00064 l_interval acos    (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF);   
00065                                                 // ACos(x)
00067 l_interval atan    (const l_interval&) throw(); // ATan(x)
00069 l_interval acot    (const l_interval&) throw(); // ACot(x)
00070 
00072 l_interval exp     (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW);    
00073                                                 // exp(x)
00075 l_interval exp2(const l_interval &); // 2^x
00076 
00078 l_interval exp10(const l_interval &); // 10^x
00079 
00081 l_interval expm1(const l_interval & x) throw(); // exp(x)-1;
00083 l_interval expmx2  (const l_interval&);         // e^(-x^2);
00085 l_interval ln      (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF);
00086                                                 // Ln(x)
00088 l_interval log2(const l_interval &);
00090 l_interval log10(const l_interval &);
00092 l_interval lnp1    (const l_interval&) throw(); // ln(1+x)
00094 l_interval sinh    (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW);   
00095                                                 // Sinh(x)
00097 l_interval cosh    (const l_interval&) throw(ERROR_LINTERVAL_FAK_OVERFLOW);   
00098                                                 // Cosh(x)
00100 l_interval tanh    (const l_interval&) throw(); // Tanh(x)
00102 l_interval coth    (const l_interval&) throw(); // Coth(x)           
00103  
00105 l_interval asinh   (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW);  
00106                                                 // ASinh(x)
00108 l_interval acosh   (const l_interval&) throw(); // ACosh(x)
00110 l_interval acoshp1 (const l_interval& x);
00112 l_interval atanh   (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW);
00113                                                 // ATanh(x)
00115 l_interval acoth   (const l_interval&) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW);  
00116                                                 // ACoth(x)
00117 
00119 l_interval sqrt1px2(const l_interval&) throw(); // Sqrt(1+x^2); 
00121 l_interval sqrtx2y2(const l_interval&, const l_interval&) throw(); 
00122                                                 // Sqrt(x^2+y^2); 
00124 l_interval sqrtp1m1(const l_interval&) throw(STD_FKT_OUT_OF_DEF);
00125                                                 // sqrtp1m1(x) calculates an inclusion of sqrt(x+1)-1
00127 l_interval sqrtx2m1(const l_interval&);         // sqrt(x^2-1)
00129 l_interval sqrt1mx2(const l_interval&);         // sqrt(1-x^2) 
00130 
00132 l_interval ln_sqrtx2y2(const l_interval&, const l_interval&) throw();
00133 
00134 // some constants as functions for l_interval
00135 // l_interval li_ln2() throw();                    // ln(2)
00136 // l_interval li_ln10() throw();                   // ln(10)
00137 // l_interval li_Rln10() throw();                  // 1/ln(10)
00138 // l_interval li_pi4() throw();                    // Pi/4
00139 // l_interval li_sqrt2() throw();                  // sqrt(2)
00141 l_interval Ln2_l_interval()   throw();   // ln(2) 
00143 l_interval Ln10_l_interval()  throw();   // ln(10)
00145 l_interval Ln10r_l_interval() throw();   // 1/ln(10)
00147 l_interval Pid4_l_interval()  throw();   // Pi/4
00149 l_interval Sqrt2_l_interval() throw();   // sqrt(2)
00151 l_interval Sqrt5_l_interval() throw();   // sqrt(5)
00153 l_interval Sqrt7_l_interval() throw();   // sqrt(7)
00154 
00155 // obsolete functions, for compability
00157 inline l_interval li_ln2()  {return Ln2_l_interval();}    // ln(2)
00159 inline l_interval li_ln10() {return Ln10_l_interval();}   // ln(10)
00161 inline l_interval li_Rln10(){return Ln10r_l_interval();}  // 1/ln(10)
00163 inline l_interval li_pi4()  {return Pid4_l_interval();}   // Pi/4
00165 inline l_interval li_sqrt2(){return Sqrt2_l_interval();}  // sqrt(2)
00166 
00168 l_interval Ln2r_l_interval() throw();     // 1/ln(2)
00170 l_interval Pi_l_interval() throw();       // Pi
00172 l_interval Pid2_l_interval() throw();     // Pi/2
00174 l_interval Pi2_l_interval() throw();      // 2*Pi
00176 l_interval Pid3_l_interval() throw();     // Pi/3
00178 l_interval Pir_l_interval() throw();      // 1/Pi
00180 l_interval Pi2r_l_interval() throw();     // 1/(2*Pi)
00182 l_interval SqrtPi_l_interval() throw();   // sqrt(Pi)
00184 l_interval Sqrt2Pi_l_interval() throw();  // sqrt(2*Pi)
00186 l_interval SqrtPir_l_interval() throw();  // 1/sqrt(Pi)
00188 l_interval Sqrt2Pir_l_interval() throw(); // 1/sqrt(2*Pi)
00190 l_interval Pip2_l_interval() throw();     // Pi^2
00192 l_interval Sqrt2r_l_interval() throw();   // 1/sqrt(2)
00194 l_interval Sqrt3_l_interval() throw();    // sqrt(3)
00196 l_interval Sqrt3d2_l_interval() throw();  // sqrt(3)/2
00198 l_interval Sqrt3r_l_interval() throw();   // 1/sqrt(3)
00200 l_interval LnPi_l_interval() throw();     // ln(Pi)
00202 l_interval Ln2Pi_l_interval() throw();    // ln(2*Pi)
00204 l_interval E_l_interval() throw();        // e = exp(1)
00206 l_interval Er_l_interval() throw();       // 1/e
00208 l_interval Ep2_l_interval() throw();      // e^2
00210 l_interval Ep2r_l_interval() throw();     // 1/e^2
00212 l_interval EpPi_l_interval() throw();     // e^Pi
00214 l_interval Ep2Pi_l_interval() throw();    // e^(2*Pi)
00216 l_interval EpPid2_l_interval() throw();   // e^(Pi/2)
00218 l_interval EpPid4_l_interval() throw();   // e^(Pi/4)
00220 l_interval EulerGa_l_interval() throw();  // EulerGamma
00222 l_interval Catalan_l_interval() throw();  // Catalan
00223 } // namespace cxsc 
00224 
00225 #endif // _CXSC_L_IMATH_HPP_INCLUDED