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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: l_interval.hpp,v 1.36 2014/01/30 17:23:46 cxsc Exp $ */ 00025 00026 #ifndef _CXSC_L_INTERVAL_HPP_INCLUDED 00027 #define _CXSC_L_INTERVAL_HPP_INCLUDED 00028 00029 #include <iostream> 00030 #include <string> 00031 #include "real.hpp" 00032 #include "interval.hpp" 00033 #include "l_real.hpp" 00034 #include "except.hpp" 00035 #include "idot.hpp" 00036 00037 namespace cxsc { 00038 00039 class l_interval_Inf; 00040 class l_interval_Sup; 00041 00043 00071 class l_interval 00072 { 00073 friend class l_interval_Inf; 00074 friend class l_interval_Sup; 00075 00076 private: 00077 // ---- Datenelemente --------------------------------------- 00078 00079 // die eigentliche Datenstruktur 00080 // ein l_interval der Praezision n besteht aus n+1 reals , wobei die reals 00081 // 1..n das inf, 00082 // 1..n-1,n+1 das sup darstellen! 00083 // Ein echtes interval liegt also nur in den letzten beiden reals vor! 00084 int prec; 00085 real *data; 00086 00087 00088 public: 00089 // ---- Konstruktoren --------------------------------------- 00090 #if (CXSC_INDEX_CHECK) 00091 00092 inline l_interval() throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00094 inline l_interval(const l_interval &) throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00095 00097 l_interval(const l_real &, const l_real &) throw(ERROR_LINTERVAL_WRONG_STAGPREC,ERROR_LINTERVAL_EMPTY_INTERVAL); 00099 l_interval(const real &, const l_real &) throw(ERROR_LINTERVAL_WRONG_STAGPREC,ERROR_LINTERVAL_EMPTY_INTERVAL); 00101 l_interval(const l_real &, const real &) throw(ERROR_LINTERVAL_WRONG_STAGPREC,ERROR_LINTERVAL_EMPTY_INTERVAL); 00103 inline l_interval(const real &, const real &) throw(ERROR_LINTERVAL_WRONG_STAGPREC,ERROR_LINTERVAL_EMPTY_INTERVAL); 00104 00106 explicit l_interval(const dotprecision &) throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00108 explicit l_interval(const dotprecision &,const dotprecision &) throw(ERROR_LINTERVAL_WRONG_STAGPREC,ERROR_LINTERVAL_EMPTY_INTERVAL); 00110 explicit l_interval(const idotprecision &) throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00111 #else 00112 00113 inline l_interval() throw(); 00115 inline l_interval(const l_interval &) throw(); 00116 00118 l_interval(const l_real &, const l_real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00120 l_interval(const real &, const l_real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00122 l_interval(const l_real &, const real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00124 l_interval(const real &, const real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00125 00127 explicit l_interval(const dotprecision &) throw(); 00129 explicit l_interval(const dotprecision &,const dotprecision &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00131 explicit l_interval(const idotprecision &) throw(); 00132 #endif 00133 00135 explicit inline l_interval(const real &) throw(); 00137 explicit inline l_interval(const l_real &) throw(); 00138 00139 #if(CXSC_INDEX_CHECK) 00140 00141 explicit INLINE l_interval(const l_ivector &) throw(ERROR_LIVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_LIVECTOR_USE_OF_UNINITIALIZED_OBJ); 00143 explicit INLINE l_interval(const l_ivector_slice &) throw(ERROR_LIVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_LIVECTOR_USE_OF_UNINITIALIZED_OBJ); 00145 explicit INLINE l_interval(const l_imatrix &m) throw(ERROR_LIMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_LIMATRIX_USE_OF_UNINITIALIZED_OBJ); 00147 explicit INLINE l_interval(const l_imatrix_slice &m) throw(ERROR_LIMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_LIMATRIX_USE_OF_UNINITIALIZED_OBJ); 00149 friend INLINE interval _l_interval(const l_ivector &) throw(ERROR_LIVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_LIVECTOR_USE_OF_UNINITIALIZED_OBJ); 00151 friend INLINE interval _l_interval(const l_ivector_slice &) throw(ERROR_LIVECTOR_TYPE_CAST_OF_THICK_OBJ,ERROR_LIVECTOR_USE_OF_UNINITIALIZED_OBJ); 00153 friend INLINE interval _l_interval(const l_imatrix &m) throw(ERROR_LIMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_LIMATRIX_USE_OF_UNINITIALIZED_OBJ); 00155 friend INLINE interval _l_interval(const l_imatrix_slice &m) throw(ERROR_LIMATRIX_TYPE_CAST_OF_THICK_OBJ,ERROR_LIMATRIX_USE_OF_UNINITIALIZED_OBJ); 00156 #else 00157 00158 explicit INLINE l_interval(const l_ivector &) throw(); 00160 explicit INLINE l_interval(const l_ivector_slice &) throw(); 00162 explicit INLINE l_interval(const l_imatrix &m) throw(); 00164 explicit INLINE l_interval(const l_imatrix_slice &m) throw(); 00166 friend INLINE interval _l_interval(const l_ivector &) throw(); 00168 friend INLINE interval _l_interval(const l_ivector_slice &) throw(); 00170 friend INLINE interval _l_interval(const l_imatrix &m) throw(); 00172 friend INLINE interval _l_interval(const l_imatrix_slice &m) throw(); 00173 #endif 00174 00175 00176 00178 inline l_interval & operator= (const real & a) throw(); 00180 inline l_interval & operator= (const l_real &a) throw(); 00182 inline l_interval & operator= (const interval & a)throw(); 00184 l_interval & operator= (const l_interval &a)throw(); 00186 l_interval& operator = (const lx_interval&) throw(); 00187 #if (CXSC_INDEX_CHECK) 00188 00189 l_interval & operator= (const dotprecision &a) throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00191 l_interval & operator= (const idotprecision &) throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00192 #else 00193 00194 l_interval & operator= (const dotprecision &a) throw(); 00196 l_interval & operator= (const idotprecision &) throw(); 00197 #endif 00198 00199 // ---- Destruktor ---- 00200 inline ~l_interval() throw(); 00201 00202 // ---- Typwandlungen ---- 00204 explicit inline l_interval(const interval &) throw(); 00205 00206 friend interval::interval(const l_interval &) throw(); 00207 friend interval _interval(const l_interval &) throw(); 00208 friend interval & interval::operator =(const l_interval &) throw(); 00209 00210 friend inline interval _interval(const real &, const l_real &) throw(); // Sollte in l_real!!! 00211 friend inline interval _interval(const l_real &, const real &) throw(); 00212 friend inline interval _interval(const l_real &) throw(); 00213 friend interval _unchecked_interval(const l_real &, const l_real &) throw(); 00214 00215 // friend inline l_interval _l_interval(const real & a) throw() { return l_interval(a); } 00216 // friend inline l_interval _l_interval(const real & a, const real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00217 // friend inline l_interval _l_interval(const l_real & a) throw() { return l_interval(a); } 00218 // friend inline l_interval _l_interval(const l_real & a,const l_real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00219 // friend inline l_interval _l_interval(const real & a, const l_real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00220 // friend inline l_interval _l_interval(const l_real & a, const real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00221 00222 // friend inline l_interval _l_interval(const interval & a) throw() { return l_interval(a); } 00223 // friend inline l_interval _l_interval(const dotprecision & a) throw() { return l_interval(a); } 00224 // friend inline l_interval _l_interval(const dotprecision & a,const dotprecision & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00225 // friend inline l_interval _l_interval(const idotprecision & a) throw() { return l_interval(a); } 00226 00227 friend l_interval _unchecked_l_interval(const l_real &, const l_real &) throw(); 00228 friend idotprecision _idotprecision(const l_interval &) throw(); 00229 friend idotprecision::idotprecision(const l_interval &) throw(); 00230 friend idotprecision & idotprecision::operator =(const l_interval &) throw(); 00231 00232 // ---- Ausgabefunkt. --------------------------------------- 00234 friend std::istream& operator >> (std::istream& s, l_interval & a) throw(); 00236 friend std::ostream& operator << (std::ostream& s, const l_interval & a) throw(); 00238 friend std::string & operator >> (std::string& s, l_interval & a) throw(); 00240 friend std::string & operator << (std::string& s, const l_interval & a) throw(); 00242 friend void operator >> (const std::string& s,l_interval &a) throw(); 00244 friend void operator >> (const char * s,l_interval &a) throw(); 00245 00246 // ---- Standardfunkt ---- (arithmetische Operatoren) 00247 // LI 00249 friend l_interval operator -(const l_interval &) throw(); 00251 friend inline l_interval operator +(const l_interval &) throw(); 00252 00253 // LI-LI 00255 friend l_interval operator +(const l_interval &,const l_interval &) throw(); 00257 friend l_interval operator -(const l_interval &,const l_interval &) throw(); 00259 friend l_interval operator *(const l_interval &,const l_interval &) throw(); 00261 friend l_interval operator /(const l_interval &,const l_interval &) throw(ERROR_LINTERVAL_DIV_BY_ZERO); 00263 friend inline l_interval operator |(const l_interval &,const l_interval &) throw(ERROR_LINTERVAL_IN_EXACT_CH_OR_IS); 00265 friend inline l_interval operator &(const l_interval &,const l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL,ERROR_LINTERVAL_IN_EXACT_CH_OR_IS); 00266 00268 friend inline l_interval & operator +=(l_interval &,const l_interval &) throw(); 00270 friend inline l_interval & operator -=(l_interval &,const l_interval &) throw(); 00272 friend inline l_interval & operator *=(l_interval &,const l_interval &) throw(); 00274 friend inline l_interval & operator /=(l_interval &,const l_interval &) throw(); 00276 friend inline l_interval & operator |=(l_interval &,const l_interval &) throw(); 00278 friend inline l_interval & operator &=(l_interval &,const l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00279 00280 // LI-ID 00282 friend inline idotprecision operator +(const l_interval &,const idotprecision &) throw(); 00284 friend inline idotprecision operator +(const idotprecision &,const l_interval &) throw(); 00286 friend inline idotprecision operator -(const l_interval &,const idotprecision &) throw(); 00288 friend inline idotprecision operator -(const idotprecision &,const l_interval &) throw(); 00290 friend inline idotprecision operator |(const idotprecision &,const l_interval &) throw(); 00292 friend inline idotprecision operator |(const l_interval &,const idotprecision &) throw(); 00294 friend inline idotprecision operator &(const idotprecision &,const l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00296 friend inline idotprecision operator &(const l_interval &,const idotprecision &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00297 00299 friend inline l_interval & operator |=(l_interval &,const idotprecision &) throw(); 00301 friend inline l_interval & operator &=(l_interval &,const idotprecision &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00302 00303 // LI-LR 00305 friend inline l_interval operator +(const l_interval &,const l_real &) throw(); 00307 friend inline l_interval operator +(const l_real &,const l_interval &) throw(); 00309 friend inline l_interval operator -(const l_interval &,const l_real &) throw(); 00311 friend inline l_interval operator -(const l_real &,const l_interval &) throw(); 00313 friend inline l_interval operator *(const l_interval &,const l_real &) throw(); 00315 friend inline l_interval operator *(const l_real &,const l_interval &) throw(); 00317 friend inline l_interval operator /(const l_interval &,const l_real &) throw(); 00319 friend inline l_interval operator /(const l_real &,const l_interval &) throw(); 00321 friend inline l_interval operator |(const l_real &,const l_interval &) throw(); 00323 friend inline l_interval operator |(const l_interval &,const l_real &) throw(); 00325 friend inline l_interval operator |(const l_real &,const l_real &) throw(); 00327 friend inline l_interval operator &(const l_real &,const l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00329 friend inline l_interval operator &(const l_interval &,const l_real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00330 00332 friend inline l_interval & operator +=(l_interval &,const l_real &) throw(); 00334 friend inline l_interval & operator -=(l_interval &,const l_real &) throw(); 00336 friend inline l_interval & operator *=(l_interval &,const l_real &) throw(); 00338 friend inline l_interval & operator /=(l_interval &,const l_real &) throw(); 00340 friend inline l_interval & operator |=(l_interval &,const l_real &) throw(); 00342 friend inline l_interval & operator &=(l_interval &,const l_real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00343 00344 // LI-I 00346 friend inline l_interval operator +(const l_interval &,const interval &) throw(); 00348 friend inline l_interval operator +(const interval &,const l_interval &) throw(); 00350 friend inline l_interval operator -(const l_interval &,const interval &) throw(); 00352 friend inline l_interval operator -(const interval &,const l_interval &) throw(); 00354 friend inline l_interval operator *(const l_interval &,const interval &) throw(); 00356 friend inline l_interval operator *(const interval &,const l_interval &) throw(); 00358 friend inline l_interval operator /(const l_interval &,const interval &) throw(); 00360 friend inline l_interval operator /(const interval &,const l_interval &) throw(); 00362 friend inline l_interval operator |(const interval &,const l_interval &) throw(); 00364 friend inline l_interval operator |(const l_interval &,const interval &) throw(); 00366 friend inline l_interval operator &(const interval &,const l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00368 friend inline l_interval operator &(const l_interval &,const interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00369 00371 friend inline l_interval & operator +=(l_interval &,const interval &) throw(); 00373 friend inline l_interval & operator -=(l_interval &,const interval &) throw(); 00375 friend inline l_interval & operator *=(l_interval &,const interval &) throw(); 00377 friend inline l_interval & operator /=(l_interval &,const interval &) throw(); 00379 friend inline l_interval & operator |=(l_interval &,const interval &) throw(); 00381 friend inline l_interval & operator &=(l_interval &,const interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00382 00383 // LI-R 00385 friend inline l_interval operator +(const l_interval &,const real &) throw(); 00387 friend inline l_interval operator +(const real &,const l_interval &) throw(); 00389 friend inline l_interval operator -(const l_interval &,const real &) throw(); 00391 friend inline l_interval operator -(const real &,const l_interval &) throw(); 00393 friend inline l_interval operator *(const l_interval &,const real &) throw(); 00395 friend inline l_interval operator *(const real &,const l_interval &) throw(); 00397 friend inline l_interval operator /(const l_interval &,const real &) throw(); 00399 friend inline l_interval operator /(const real &,const l_interval &) throw(); 00401 friend inline l_interval operator |(const real &,const l_interval &) throw(); 00403 friend inline l_interval operator |(const l_interval &,const real &) throw(); 00405 friend inline l_interval operator &(const real &,const l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00407 friend inline l_interval operator &(const l_interval &,const real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00408 00410 friend inline l_interval & operator +=(l_interval &,const real &) throw(); 00412 friend inline l_interval & operator -=(l_interval &,const real &) throw(); 00414 friend inline l_interval & operator *=(l_interval &,const real &) throw(); 00416 friend inline l_interval & operator /=(l_interval &,const real &) throw(); 00418 friend inline l_interval & operator |=(l_interval &,const real &) throw(); 00420 friend inline l_interval & operator &=(l_interval &,const real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00421 00422 // LR-I 00424 friend inline l_interval operator +(const l_real &,const interval &) throw(); 00426 friend inline l_interval operator +(const interval &,const l_real &) throw(); 00428 friend inline l_interval operator -(const l_real &,const interval &) throw(); 00430 friend inline l_interval operator -(const interval &,const l_real &) throw(); 00432 friend inline l_interval operator *(const l_real &,const interval &) throw(); 00434 friend inline l_interval operator *(const interval &,const l_real &) throw(); 00436 friend inline l_interval operator /(const l_real &,const interval &) throw(); 00438 friend inline l_interval operator /(const interval &,const l_real &) throw(); 00440 friend inline l_interval operator |(const interval &,const l_real &) throw(); 00442 friend inline l_interval operator |(const l_real &,const interval &) throw(); 00444 friend inline l_interval operator &(const interval &,const l_real &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00446 friend inline l_interval operator &(const l_real &,const interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00447 00448 // ---- Vergleichsop. ---- 00450 friend bool operator !(const l_interval &) throw(); 00451 // operator void *(void) throw(); 00452 00454 friend bool operator ==(const l_interval &,const l_interval &) throw(); 00456 friend inline bool operator !=(const l_interval &,const l_interval &) throw(); 00457 00459 friend inline bool operator ==(const l_real &,const l_interval &) throw(); 00461 friend inline bool operator !=(const l_real &,const l_interval &) throw(); 00463 friend inline bool operator ==(const l_interval &,const l_real &) throw(); 00465 friend inline bool operator !=(const l_interval &,const l_real &) throw(); 00466 00468 friend inline bool operator ==(const interval &,const l_interval &) throw(); 00470 friend inline bool operator !=(const interval &,const l_interval &) throw(); 00472 friend inline bool operator ==(const l_interval &,const interval &) throw(); 00474 friend inline bool operator !=(const l_interval &,const interval &) throw(); 00475 00477 friend inline bool operator ==(const real &,const l_interval &) throw(); 00479 friend inline bool operator !=(const real &,const l_interval &) throw(); 00481 friend inline bool operator ==(const l_interval &,const real &) throw(); 00483 friend inline bool operator !=(const l_interval &,const real &) throw(); 00484 00486 friend inline bool operator ==(const idotprecision &,const l_interval &) throw(); 00488 friend inline bool operator !=(const idotprecision &,const l_interval &) throw(); 00490 friend inline bool operator ==(const l_interval &,const idotprecision &) throw(); 00492 friend inline bool operator !=(const l_interval &,const idotprecision &) throw(); 00493 00495 friend inline bool operator ==(const dotprecision &,const l_interval &) throw(); 00497 friend inline bool operator !=(const dotprecision &,const l_interval &) throw(); 00499 friend inline bool operator ==(const l_interval &,const dotprecision &) throw(); 00501 friend inline bool operator !=(const l_interval &,const dotprecision &) throw(); 00502 00503 // ---- Mengenvergle. ---- 00505 friend bool operator <(const l_interval &,const l_interval &) throw(); 00507 friend bool operator >(const l_interval &,const l_interval &) throw(); 00509 friend bool operator <=(const l_interval &,const l_interval &) throw(); 00511 friend bool operator >=(const l_interval &,const l_interval &) throw(); 00512 00514 friend inline bool operator <(const l_real &,const l_interval &) throw(); 00516 friend inline bool operator >(const l_real &,const l_interval &) throw(); 00518 friend inline bool operator <=(const l_real &,const l_interval &) throw(); 00520 friend inline bool operator >=(const l_real &,const l_interval &) throw(); 00522 friend inline bool operator <(const l_interval &,const l_real &) throw(); 00524 friend inline bool operator >(const l_interval &,const l_real &) throw(); 00526 friend inline bool operator <=(const l_interval &,const l_real &) throw(); 00528 friend inline bool operator >=(const l_interval &,const l_real &) throw(); 00529 00531 friend inline bool operator <(const interval &,const l_interval &) throw(); 00533 friend inline bool operator >(const interval &,const l_interval &) throw(); 00535 friend inline bool operator <=(const interval &,const l_interval &) throw(); 00537 friend inline bool operator >=(const interval &,const l_interval &) throw(); 00539 friend inline bool operator <(const l_interval &,const interval &) throw(); 00541 friend inline bool operator >(const l_interval &,const interval &) throw(); 00543 friend inline bool operator <=(const l_interval &,const interval &) throw(); 00545 friend inline bool operator >=(const l_interval &,const interval &) throw(); 00546 00548 friend inline bool operator <(const real &,const l_interval &) throw(); 00550 friend inline bool operator >(const real &,const l_interval &) throw(); 00552 friend inline bool operator <=(const real &,const l_interval &) throw(); 00554 friend inline bool operator >=(const real &,const l_interval &) throw(); 00556 friend inline bool operator <(const l_interval &,const real &) throw(); 00558 friend inline bool operator >(const l_interval &,const real &) throw(); 00560 friend inline bool operator <=(const l_interval &,const real &) throw(); 00562 friend inline bool operator >=(const l_interval &,const real &) throw(); 00563 00565 friend inline bool operator <(const idotprecision &,const l_interval &) throw(); 00567 friend inline bool operator >(const idotprecision &,const l_interval &) throw(); 00569 friend inline bool operator <=(const idotprecision &,const l_interval &) throw(); 00571 friend inline bool operator >=(const idotprecision &,const l_interval &) throw(); 00573 friend inline bool operator <(const l_interval &,const idotprecision &) throw(); 00575 friend inline bool operator >(const l_interval &,const idotprecision &) throw(); 00577 friend inline bool operator <=(const l_interval &,const idotprecision &) throw(); 00579 friend inline bool operator >=(const l_interval &,const idotprecision &) throw(); 00580 00582 friend inline bool operator <(const dotprecision &,const l_interval &) throw(); 00584 friend inline bool operator >(const dotprecision &,const l_interval &) throw(); 00586 friend inline bool operator <=(const dotprecision &,const l_interval &) throw(); 00588 friend inline bool operator >=(const dotprecision &,const l_interval &) throw(); 00590 friend inline bool operator <(const l_interval &,const dotprecision &) throw(); 00592 friend inline bool operator >(const l_interval &,const dotprecision &) throw(); 00594 friend inline bool operator <=(const l_interval &,const dotprecision &) throw(); 00596 friend inline bool operator >=(const l_interval &,const dotprecision &) throw(); 00597 00598 // ---- Funktionen ---- 00599 00600 // friend inline l_interval_Inf Inf (l_interval &) throw(); 00601 // friend inline l_interval_Sup Sup (l_interval &) throw(); 00603 friend inline l_real Inf (const l_interval &) throw(); 00605 friend inline l_real Sup (const l_interval &) throw(); 00606 00608 friend inline int expo_sm(const l_interval&); 00609 // Calculating expo(x[k]) of the smallest |x[k]|<>0. 00610 00612 friend inline int expo_gr(const l_interval&); 00613 // Calculating expo(x[k]) of the greatest |x[k]|. 00614 00616 friend inline int StagPrec(const l_interval &) throw(); 00617 00619 friend inline l_interval & SetInf (l_interval & a, const l_real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00621 friend inline l_interval & SetSup (l_interval & a, const l_real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00623 friend inline l_interval & SetInf (l_interval & a, const real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00625 friend inline l_interval & SetSup (l_interval & a, const real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00627 friend inline l_interval adjust (const l_interval &) throw(); 00628 00630 friend inline l_interval & UncheckedSetInf (l_interval & a, const l_real & b) throw(); 00632 friend inline l_interval & UncheckedSetSup (l_interval & a, const l_real & b) throw(); 00634 friend inline l_interval & UncheckedSetInf (l_interval & a, const real & b) throw(); 00636 friend inline l_interval & UncheckedSetSup (l_interval & a, const real & b) throw(); 00637 00639 friend void ConvexHull(const l_interval &, const l_interval &, l_interval &, l_interval &) throw(); 00641 friend void Intersection(const l_interval &, const l_interval &, l_interval &, l_interval &) throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 00642 00644 friend inline l_interval abs (const l_interval & a) throw(); 00646 friend l_real mid (const l_interval & a) throw(); 00648 friend inline l_real diam (const l_interval & a) throw(); 00649 00651 friend l_interval pow(const l_interval &, const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // Pow(x,y) 00653 friend l_interval power(const l_interval &, int); // Power(x,n) 00655 friend l_interval sqr(const l_interval &); // Sqr(x) 00656 00658 friend l_interval sqrt(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // Sqrt(x) 00660 friend l_interval sqrt(const l_interval &, int) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // NSqrt(n,x) 00661 00663 friend l_interval sin(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW); // Sin(x) 00665 friend l_interval cos(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW); // Cos(x) 00667 friend l_interval tan(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW,ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // Tan(x) 00669 friend l_interval cot(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW,ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // Cot(x) 00670 00672 friend l_interval asin(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // ASin(x) 00674 friend l_interval acos(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // ACos(x) 00676 friend l_interval atan(const l_interval &) throw(); // ATan(x) 00678 friend l_interval acot(const l_interval &) throw(); // ACot(x) 00679 00681 friend l_interval exp(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW); // Exp(x) 00683 friend l_interval exp2(const l_interval &); // 2^x 00685 friend l_interval exp10(const l_interval &); // 10^x 00687 friend l_interval ln(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF); // Ln(x) 00689 friend l_interval log2(const l_interval &); 00691 friend l_interval log10(const l_interval &); 00693 friend l_interval sinh(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW); // Sinh(x) 00695 friend l_interval cosh(const l_interval &) throw(ERROR_LINTERVAL_FAK_OVERFLOW); // Cosh(x) 00697 friend l_interval tanh(const l_interval &) throw(); // Tanh(x) 00699 friend l_interval coth(const l_interval &) throw(); // Coth(x) 00700 00702 friend l_interval asinh(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW); // ASinh(x) 00704 friend l_interval acosh(const l_interval &) throw(); // ACosh(x) 00706 friend l_interval atanh(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW); // ATanh(x) 00708 friend l_interval acoth(const l_interval &) throw(ERROR_LINTERVAL_STD_FKT_OUT_OF_DEF,ERROR_LINTERVAL_FAK_OVERFLOW); // ACoth(x) 00709 00711 friend l_interval Ln2_l_interval() throw(); // ln(2) 00713 friend l_interval Ln10_l_interval() throw(); // ln(10) 00715 friend l_interval Ln10r_l_interval() throw(); // 1/ln(10) 00717 friend l_interval Pid4_l_interval() throw(); // Pi/4 00719 friend l_interval Sqrt2_l_interval() throw(); // sqrt(2) 00721 friend l_interval Sqrt5_l_interval() throw(); // sqrt(5) 00723 friend l_interval Sqrt7_l_interval() throw(); // sqrt(7) 00724 00725 // obsolete, see also l_imath.hpp and l_imath.cpp 00727 friend inline l_interval li_ln2(); // ln(2) 00729 friend inline l_interval li_ln10(); // ln(10) 00731 friend inline l_interval li_Rln10(); // 1/ln(10) 00733 friend inline l_interval li_pi4(); // Pi/4 00735 friend inline l_interval li_sqrt2(); // sqrt(2) 00736 00738 friend l_interval Ln2r_l_interval() throw(); // 1/ln(2) 00740 friend l_interval Pi_l_interval() throw(); // Pi 00742 friend l_interval Pid2_l_interval() throw(); // Pi/2 00744 friend l_interval Pi2_l_interval() throw(); // 2*Pi 00746 friend l_interval Pid3_l_interval() throw(); // Pi/3 00748 friend l_interval Pir_l_interval() throw(); // 1/Pi 00750 friend l_interval Pi2r_l_interval() throw(); // 1/(2*Pi) 00752 friend l_interval SqrtPi_l_interval() throw(); // sqrt(Pi) 00754 friend l_interval Sqrt2Pi_l_interval() throw(); // sqrt(2*Pi) 00756 friend l_interval SqrtPir_l_interval() throw(); // 1/sqrt(Pi) 00758 friend l_interval Sqrt2Pir_l_interval() throw(); // 1/sqrt(2*Pi) 00760 friend l_interval Pip2_l_interval() throw(); // Pi^2 00762 friend l_interval Sqrt2r_l_interval() throw(); // 1/sqrt(2) 00764 friend l_interval Sqrt3_l_interval() throw(); // sqrt(3) 00766 friend l_interval Sqrt3d2_l_interval() throw(); // sqrt(3)/2 00768 friend l_interval Sqrt3r_l_interval() throw(); // 1/sqrt(3) 00770 friend l_interval LnPi_l_interval() throw(); // ln(Pi) 00772 friend l_interval Ln2Pi_l_interval() throw(); // ln(2*Pi) 00774 friend l_interval E_l_interval() throw(); // e = exp(1) 00776 friend l_interval Er_l_interval() throw(); // 1/e 00778 friend l_interval Ep2_l_interval() throw(); // e^2 00780 friend l_interval Ep2r_l_interval() throw(); // 1/e^2 00782 friend l_interval EpPi_l_interval() throw(); // e^Pi 00784 friend l_interval Ep2Pi_l_interval() throw(); // e^(2*Pi) 00786 friend l_interval EpPid2_l_interval() throw(); // e^(Pi/2) 00788 friend l_interval EpPid4_l_interval() throw(); // e^(Pi/4) 00790 friend l_interval EulerGa_l_interval() throw(); // EulerGamma 00792 friend l_interval Catalan_l_interval() throw(); // Catalan 00793 00794 // Operatoren: l/real op idotprecision 00795 // 00796 // friend inline void accumulate(idotprecision &, const real &, const l_real &) throw(); 00797 // friend inline void accumulate(idotprecision &, const l_real &, const real &) throw(); 00798 00799 // Operatoren: l_real op idotprecision 00800 // 00801 // friend inline void accumulate(idotprecision &, const l_real &, const l_real &) throw(); 00802 00803 // Operatoren: real, l_interval op idotprecision 00804 // 00806 friend inline void accumulate(idotprecision &, const real &, const l_interval &) throw(); 00808 friend inline void accumulate(idotprecision &, const l_interval &, const real &) throw(); 00809 00810 // Operatoren: interval, l_real op idotprecision 00811 // 00813 friend inline void accumulate(idotprecision &, const interval &, const l_real &) throw(); 00815 friend inline void accumulate(idotprecision &, const l_real &, const interval &) throw(); 00816 00817 // Operatoren: l_interval, l_real op idotprecision 00818 // 00820 friend inline void accumulate(idotprecision &, const l_interval &, const l_real &) throw(); 00822 friend inline void accumulate(idotprecision &, const l_real &, const l_interval &) throw(); 00823 00824 // Operatoren: l_interval, interval op idotprecision 00825 // 00827 friend inline void accumulate(idotprecision &, const l_interval &, const interval &) throw(); 00829 friend inline void accumulate(idotprecision &, const interval &, const l_interval &) throw(); 00830 00831 // Operatoren: l_interval op idotprecision 00832 // 00834 friend void accumulate(idotprecision &, const l_interval &, const l_interval &) throw(); 00835 00837 friend inline bool point_intv(const l_interval &); // bool delivers: a is a point interval; 00839 friend inline bool zero_(const l_interval& ) throw(); // Blomquist,27.11.02 00841 friend void times2pown(l_interval&, int) throw(); // Blomquist,28.11.02 00843 friend void Times2pown(l_interval&, const real&) throw(); 00844 friend void l_realz2l_interval(const l_real&, const interval&, 00845 l_interval&) throw(); // Blomquist,28.11.02 00846 00847 #if (CXSC_INDEX_CHECK) 00848 00849 inline real & operator [](int) throw(ERROR_LINTERVAL_ELEMENT_NOT_IN_LONG); 00850 #else 00851 00852 inline real & operator [](int) throw(); 00853 #endif 00854 00855 private: 00856 #if (CXSC_INDEX_CHECK) 00857 inline void _allo(int) throw(ERROR_LINTERVAL_WRONG_STAGPREC); 00858 #else 00859 inline void _allo(int) throw(); 00860 #endif 00861 inline void _clear(int) throw(); 00862 void _akku_out(idotprecision&) throw(); 00863 void _akku_out_inn(idotprecision&) throw(); 00864 void _akku_add(idotprecision &) const throw(); 00865 void _akku_sub(idotprecision &) const throw(); 00866 //void _create_l_interval(l_real &, l_real &); 00867 inline real & elem(int i) { return data[i-1]; } 00868 inline real elem(int i) const { return data[i-1]; } 00869 00870 }; 00871 00872 interval _unchecked_interval(const l_real &, const l_real &) throw(); 00873 00879 inline l_interval _l_interval(const real & a) throw() { return l_interval(a); } 00885 inline l_interval _l_interval(const real & a, const real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00891 inline l_interval _l_interval(const l_real & a) throw() { return l_interval(a); } 00897 inline l_interval _l_interval(const l_real & a,const l_real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00903 inline l_interval _l_interval(const real & a, const l_real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00909 inline l_interval _l_interval(const l_real & a, const real & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00910 00916 inline l_interval _l_interval(const interval & a) throw() { return l_interval(a); } 00922 inline l_interval _l_interval(const dotprecision & a) throw() { return l_interval(a); } 00928 inline l_interval _l_interval(const dotprecision & a,const dotprecision & b) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { return l_interval(a,b); } 00934 inline l_interval _l_interval(const idotprecision & a) throw() { return l_interval(a); } 00935 l_interval _unchecked_l_interval(const l_real &, const l_real &) throw(); 00936 00937 //inline l_interval_Inf Inf (l_interval &) throw(); 00938 //inline l_interval_Sup Sup (l_interval &) throw(); 00939 inline l_real Inf (const l_interval &) throw(); 00940 inline l_real Sup (const l_interval &) throw(); 00941 00942 int in ( const real& x, const l_interval& y ); // Contained-in relation 00943 int in ( const l_real& x, const l_interval& y ); // Contained-in relation 00944 int in ( const interval& x, const l_interval& y ); // Contained-in relation 00945 int in ( const l_interval& x, const l_interval& y ); // Contained-in relation 00946 l_interval Blow (const l_interval& x, const real& eps ); 00947 int Disjoint (const l_interval& a, const l_interval& b ); // Test for disjointedness 00948 l_real AbsMin ( const l_interval& x ); // Absolute minimum of 00949 // an interval 00950 l_real AbsMax (const l_interval& x ); // Absolute maximum of 00951 // an interval 00952 l_real RelDiam ( const l_interval x ); // Relative diameter 00953 // of an interval 00954 inline bool point_intv(const l_interval &a ); // bool delivers: a is a point interval; 00955 00956 void times2pown(l_interval&, int) throw(); // Blomquist,28.11.02 00957 void Times2pown(l_interval&, const real&) throw(); 00958 00960 00963 class l_interval_Inf 00964 { 00965 private: 00966 l_interval & my_l_interval; 00967 public: 00968 // l_interval_Inf(const l_interval_Inf &a) throw() : my_l_interval(a.my_l_interval) {} 00970 l_interval_Inf(l_interval &a) throw() : my_l_interval(a) {} 00971 operator l_real(void) const { return Inf((const l_interval)my_l_interval); } 00973 l_interval & operator =(const l_real & a) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { SetInf(my_l_interval,a); return my_l_interval; } 00975 l_interval & operator =(const real & a) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { SetInf(my_l_interval,_l_real(a)); return my_l_interval; } 00976 // l_interval & operator =(int a) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { SetInf(my_l_interval,_l_real(a)); return my_l_interval; } 00977 }; 00979 00982 class l_interval_Sup 00983 { 00984 private: 00985 l_interval & my_l_interval; 00986 public: 00988 l_interval_Sup(l_interval &a) throw() : my_l_interval(a) {} 00989 operator l_real(void) const { return Sup((const l_interval)my_l_interval); } 00991 l_interval & operator =(const l_real & a) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { SetSup(my_l_interval,a); return my_l_interval; } 00993 l_interval & operator =(const real & a) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { SetSup(my_l_interval,_l_real(a)); return my_l_interval; } 00994 // l_interval & operator =(int a) throw(ERROR_LINTERVAL_EMPTY_INTERVAL) { SetSup(my_l_interval,_l_real(a)); return my_l_interval; } 00995 }; 00996 00997 } // namespace cxsc 00998 00999 #include "l_interval.inl" 01000 01001 #endif // _CXSC_L_INTERVAL_HPP_INCLUDED
1.7.5.1