lx_interval.hpp

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_interval.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_interval  with all tools and elementary functions for real
00035 **               point and interval aruments
00036 **
00037 */
00038 
00039 #ifndef _CXSC_LX_INTERVAL_HPP_INCLUDED
00040 #define _CXSC_LX_INTERVAL_HPP_INCLUDED
00041 
00042 #include <l_imath.hpp>
00043 #include <lx_real.hpp>
00044 #include <sstream>
00045 #include <cmath>
00046 #include <iostream>
00047 
00048 namespace cxsc {
00049         
00050 class lx_interval {
00051         
00052 private:
00053     // ------------- Data Elements -------------------------------------------
00054     real ex;
00055     l_interval li;
00056     // The mathematical value of an object of type lx_interval is
00057     // interpreted as:  2^(ex) * li;
00058 
00059 public:
00060     // ------------- Constructors --------------------------------------------
00061 
00063     lx_interval(void)  throw() {}
00064 
00066     lx_interval(const real& n, const l_interval& a) throw() 
00067     {
00068         if ( !(Is_Integer(n)) ) 
00069             cxscthrow(REAL_NOT_ALLOWED("lx_interval(const real&, const l_interval&)"));
00070         else
00071         {
00072             ex = n; li = a;
00073         }
00074     }
00075 
00077     lx_interval(const real& n, const l_real& a) throw() 
00078     { 
00079         if ( !(Is_Integer(n)) ) 
00080             cxscthrow(REAL_NOT_ALLOWED("lx_interval(const real& n, const l_real& a)"));
00081         else
00082         {
00083             ex = n; li = a;
00084         }
00085     }
00086 
00088     lx_interval(const real& n, const interval& a) throw()
00089     { 
00090         if ( !(Is_Integer(n)) ) 
00091             cxscthrow(REAL_NOT_ALLOWED("lx_interval(const real&, const interval&)"));
00092         else
00093         {
00094             ex = n; li = a;
00095         }
00096     }
00097 
00099     explicit lx_interval(const real& n, const real& a) throw()
00100     { 
00101                 if ( !(Is_Integer(n)) ) 
00102                 cxscthrow(REAL_NOT_ALLOWED("lx_interval(const real&, const real&)"));
00103                 else
00104                 {
00105                 ex = n; li = a;
00106                 }
00107     }
00109     explicit lx_interval(const l_interval& a) throw() : ex(0), li(a) { }
00111     explicit lx_interval(const l_real& a)     throw() : ex(0), li(a) { }
00113     lx_interval(const l_real& a, const l_real& b)  throw() : ex(0),li(a,b) { }
00115     explicit lx_interval(const interval& a)   throw() : ex(0), li(a)   { }
00117     explicit lx_interval(const real& a)       throw() : ex(0), li(a)   { }
00119     lx_interval(const lx_real&, const lx_real&) throw();
00121     explicit lx_interval(const lx_real& a)     
00122                                  throw() : ex(expo(a)), li(lr_part(a)) { }
00124     lx_interval(const real&, const string&) throw(); 
00125 
00126     // ------------- Assignments ---------------------------------------------
00127 
00129     inline lx_interval & operator = (const lx_interval & a) throw();
00131     inline lx_interval & operator = (const l_interval & a) throw();
00133     inline lx_interval & operator = (const l_real & a)     throw();
00135     inline lx_interval & operator = (const real & a)       throw();
00137     inline lx_interval & operator = (const interval & a)   throw();
00139     inline lx_interval & operator = (const lx_real & a)     throw();
00140 
00141     // l_interval & operator = (const lx_interval &a) throw(); declared
00142     // in l_interval.hpp and implemented in lx_interval.cpp; 
00143          
00144          // interval & operator = (const lx_interval &a) throw(); declared
00145     // in interval.hpp and implemented in lx_interval.cpp; 
00146 
00147     // ------------- Functions -----------------------------------------------
00148 
00150     friend inline int StagPrec(const lx_interval&) throw(); 
00152     friend inline real expo(const lx_interval&) throw();
00154     friend inline l_interval li_part(const lx_interval&) throw();
00156     friend void scale_down(lx_interval &a);
00158     friend void scale_up  (lx_interval &a);
00159 
00161     friend inline lx_interval adjust(const lx_interval &) throw();
00163     friend inline lx_interval abs(const lx_interval &) throw();
00165     friend inline bool point_intv(const lx_interval &);
00167     friend inline bool operator ! (const lx_interval &) throw(); 
00169     friend inline bool IsEmpty(const lx_interval &) throw(); 
00171     friend inline void times2pown(lx_interval &, const real &) throw();
00173     friend inline lx_interval Blow(const lx_interval &) throw(); 
00175     friend inline void times2pown_neg(lx_interval &, const real&) throw();
00177     friend inline lx_real RelDiam( const lx_interval &);
00179     friend inline lx_real diam(const lx_interval &) throw();
00181     friend inline lx_real mid(const lx_interval &) throw();
00183     friend inline lx_real Inf(const lx_interval &) throw();
00185     friend inline lx_real Sup(const lx_interval &) throw();
00186 
00187     // ---------------- Monadic arithmetic operator ---------------------
00188 
00190     friend inline lx_interval operator-(const lx_interval & a) throw();
00191 
00192 
00193     // ----------------------- Output -----------------------------------
00194 
00196     friend std::ostream& operator << (std::ostream&, const lx_interval&) 
00197         throw();
00198 
00200     friend std::string & operator << (std::string&, const lx_interval&) 
00201         throw();
00202 
00203 }; // end of class lx_interval
00204 
00205 
00206 // -------------------------------------------------------------------
00207 //    Declaration of friend functions outside the class lx_interval 
00208 // -------------------------------------------------------------------
00209 
00210 inline int StagPrec(const lx_interval &a) throw();
00211 inline real expo(const lx_interval &a) throw();
00212 inline l_interval li_part(const lx_interval &a) throw();
00213 
00214        void scale_down(lx_interval &);
00215        void scale_up  (lx_interval &);
00216 inline bool point_intv(const lx_interval &);
00217 inline bool IsEmpty(const lx_interval &) throw();
00218 inline void times2pown(lx_interval &, const real &) throw();
00219 inline lx_interval Blow(const lx_interval &) throw();
00220 inline void times2pown_neg(lx_interval &, const real&) throw();
00221 inline lx_real RelDiam(const lx_interval &);
00222 inline lx_real Inf(const lx_interval &) throw();
00223 inline lx_real Sup(const lx_interval &) throw();
00224 inline lx_interval abs(const lx_interval &) throw();
00225 inline lx_interval adjust(const lx_interval &) throw();
00226 inline lx_real diam(const lx_interval &) throw();
00227 inline lx_real mid(const lx_interval &) throw();
00228 
00229 // ------------------------ Input --------------------------------------
00230 
00232     std::string & operator >> (std::string &s, lx_interval &a) throw();
00234     void operator >> (const std::string &s, lx_interval &a) throw();
00236     void operator >> (const char *s, lx_interval&) throw();
00237 
00239     std::istream & operator >> (std::istream&, lx_interval&) throw();
00240 
00241 // ------------------------ Output --------------------------------------
00242 
00243 std::ostream& operator << (std::ostream& s,const lx_interval& a) throw();
00244 // A value a of type lx_interval is written to the 
00245 // output channel as decimal number in the form: 
00246 // { exponent p to base 10, interval mantissa m } = 10^p * m;
00247 
00248 std::string & operator << (std::string &s,const lx_interval& a) throw();
00249 // The value of a variable a of type lx_interval is copied to a string s.
00250 // s has the form:  {2**(ex), li} = 2^ex * li;
00251 
00252 
00253 // -------------------------------------------------------------------
00254 // ------- Function declarations outside the class lx_interval --------
00255 // -------------------------------------------------------------------
00256 
00257 void Bin2Dec(const lx_interval& a, real& p, l_interval& m);
00258 
00260 lx_interval expo2zero(const lx_interval &) throw(OVERFLOW_ERROR);
00262 inline int Disjoint(const lx_interval &, const lx_interval &);
00264 inline int in (const lx_interval&, const lx_interval&);
00266 inline int in (const l_interval&, const lx_interval&);
00268 inline int in (const interval&, const lx_interval&);
00269 
00271 inline int in (const lx_real&, const lx_interval&);
00273 inline int in (const l_real&, const lx_interval&);
00275 inline int in (const real&, const lx_interval&);
00276 
00278 inline lx_interval Blow( const lx_interval&, const real& );
00280 inline lx_real AbsMin (const lx_interval&); 
00282 inline lx_real AbsMax (const lx_interval&); 
00283 
00284 // -----------------------------------------------------------------------
00285 // ------------- set comparisons -----------------------------------------
00286 // -----------------------------------------------------------------------
00287 
00288 // ---- lx_interval--lx_interval
00289 
00291 inline bool operator <  (const lx_interval&, const lx_interval&) throw();
00293 inline bool operator <= (const lx_interval&, const lx_interval&) throw();
00295 inline bool operator >  (const lx_interval&, const lx_interval&) throw();
00297 inline bool operator >= (const lx_interval&, const lx_interval&) throw();
00298 
00299 // ---- lx_interval--l_interval
00300 
00302 inline bool operator <  (const lx_interval&, const l_interval&) throw();
00304 inline bool operator <= (const lx_interval&, const l_interval&) throw();
00306 inline bool operator <  (const l_interval&, const lx_interval&) throw();
00308 inline bool operator <= (const l_interval&, const lx_interval&) throw();
00310 inline bool operator >  (const lx_interval&, const l_interval&) throw();
00311 inline bool operator >= (const lx_interval&, const l_interval&) throw();
00313 inline bool operator >  (const l_interval&, const lx_interval&) throw();
00315 inline bool operator >= (const l_interval&, const lx_interval&) throw();
00316 
00317 // ---- lx_interval--interval
00318 
00320 inline bool operator <  (const lx_interval&, const interval&) throw();
00322 inline bool operator <= (const lx_interval&, const interval&) throw();
00324 inline bool operator <  (const interval&, const lx_interval&) throw();
00326 inline bool operator <= (const interval&, const lx_interval&) throw();
00328 inline bool operator >  (const lx_interval&, const interval&) throw();
00330 inline bool operator >= (const lx_interval&, const interval&) throw();
00332 inline bool operator >  (const interval&, const lx_interval&) throw();
00334 inline bool operator >= (const interval&, const lx_interval&) throw();
00335 
00336 // ---- lx_interval--real
00337 
00339 inline bool operator <  (const real &, const lx_interval &) throw();
00341 inline bool operator <= (const real &, const lx_interval &) throw();
00343 inline bool operator >  (const lx_interval &, const real &) throw();
00345 inline bool operator >= (const lx_interval &, const real &) throw();
00346 
00347 // ---- lx_interval--l_real
00348 
00350 inline bool operator <  (const l_real &, const lx_interval &) throw();
00352 inline bool operator <= (const l_real &, const lx_interval &) throw();
00354 inline bool operator >  (const lx_interval &, const l_real &) throw();
00356 inline bool operator >= (const lx_interval &, const l_real &) throw();
00357 
00358 // ---- lx_interval--lx_real
00359 
00361 inline bool operator <  (const lx_real &, const lx_interval &) throw();
00363 inline bool operator <= (const lx_real &, const lx_interval &) throw();
00365 inline bool operator >  (const lx_interval &, const lx_real &) throw();
00367 inline bool operator >= (const lx_interval &, const lx_real &) throw();
00368 
00369 
00370 // -------------------------- comparisons --------------------------------
00371 
00373 inline bool operator ! (const lx_interval &) throw();
00374 
00376 inline bool operator == (const lx_interval &, const lx_interval &) throw();
00378 inline bool operator == (const lx_interval &, const l_interval &) throw();
00380 inline bool operator == (const l_interval &, const lx_interval &) throw();
00382 inline bool operator == (const lx_interval &, const interval &) throw();
00384 inline bool operator == (const interval &, const lx_interval &) throw();
00386 inline bool operator == (const lx_interval &, const real &) throw();
00388 inline bool operator == (const real &, const lx_interval &) throw();
00390 inline bool operator == (const lx_interval &, const l_real &) throw();
00392 inline bool operator == (const l_real &, const lx_interval &) throw();
00394 inline bool operator == (const lx_interval &, const lx_real &) throw();
00396 inline bool operator == (const lx_real &, const lx_interval &) throw();
00397 
00399 inline bool operator != (const lx_interval &, const lx_interval &) throw();
00401 inline bool operator != (const lx_interval &, const l_interval &) throw();
00403 inline bool operator != (const l_interval &, const lx_interval &) throw();
00405 inline bool operator != (const lx_interval &, const interval &) throw();
00407 inline bool operator != (const interval &, const lx_interval &) throw();
00409 inline bool operator != (const lx_interval &, const real &) throw();
00411 inline bool operator != (const real &, const lx_interval &) throw();
00413 inline bool operator != (const lx_interval &, const l_real &) throw();
00415 inline bool operator != (const l_real &, const lx_interval &) throw();
00417 inline bool operator != (const lx_interval &, const lx_real &) throw();
00419 inline bool operator != (const lx_real &, const lx_interval &) throw();
00420 
00422 inline lx_interval operator+(const lx_interval &) throw();
00424 inline lx_interval operator-(const lx_interval &) throw();
00425 
00427 lx_interval operator + (const lx_interval &, const lx_interval &) throw();
00428 
00430 inline lx_interval operator + (const lx_interval &, const l_interval &) 
00431                                                                  throw();
00433 inline lx_interval operator + (const l_interval &, const lx_interval &) 
00434                                                                  throw();
00436 inline lx_interval operator + (const lx_interval &, const l_real &) 
00437                                                                  throw();
00439 inline lx_interval operator + (const l_real &, const lx_interval &) 
00440                                                                  throw();
00442 inline lx_interval operator + (const lx_interval &, const lx_real &) 
00443                                                                  throw();
00445 inline lx_interval operator + (const lx_real &, const lx_interval &) 
00446                                                                  throw();
00448 inline lx_interval operator + (const lx_interval &, const real &) 
00449                                                                  throw();
00451 inline lx_interval operator + (const real &, const lx_interval &) 
00452                                                                  throw();
00454 inline lx_interval operator + (const lx_interval &, const interval &) 
00455                                                                  throw();
00457 inline lx_interval operator + (const interval &, const lx_interval &)
00458                                                                  throw();
00459 
00461 inline lx_interval & operator +=(lx_interval &, const lx_interval &) throw();
00463 inline lx_interval & operator +=(lx_interval &, const l_interval &) throw();
00465 inline lx_interval & operator +=(lx_interval &, const l_real     &) throw();
00467 inline lx_interval & operator +=(lx_interval &, const lx_real     &) throw();
00469 inline lx_interval & operator +=(lx_interval &, const real       &) throw();
00471 inline lx_interval & operator +=(lx_interval &, const interval   &) throw();
00472 
00474 inline lx_interval operator - (const lx_interval &, const lx_interval &) 
00475                                                                  throw();
00477 inline lx_interval operator - (const lx_interval &, const l_interval &) 
00478                                                                  throw();
00480 inline lx_interval operator - (const l_interval &, const lx_interval &) 
00481                                                                  throw();
00483 inline lx_interval operator - (const lx_interval &, const l_real &) 
00484                                                                  throw();
00486 inline lx_interval operator - (const l_real &, const lx_interval &) 
00487                                                                  throw();
00489 inline lx_interval operator - (const lx_interval &, const lx_real &) 
00490                                                                  throw();
00492 inline lx_interval operator - (const lx_real &, const lx_interval &) 
00493                                                                  throw();
00495 inline lx_interval operator - (const lx_interval &, const real &) 
00496                                                                  throw();
00498 inline lx_interval operator - (const real &, const lx_interval &) 
00499                                                                  throw();
00501 inline lx_interval operator - (const lx_interval &, const interval &) 
00502                                                                  throw();
00504 inline lx_interval operator - (const interval &, const lx_interval &) 
00505                                                                  throw();
00506 
00508 inline lx_interval & operator -=(lx_interval &, const lx_interval &) throw();
00510 inline lx_interval & operator -=(lx_interval &, const l_interval &) throw();
00512 inline lx_interval & operator -=(lx_interval &, const l_real     &) throw();
00514 inline lx_interval & operator -=(lx_interval &, const lx_real     &) throw();
00516 inline lx_interval & operator -=(lx_interval &, const real       &) throw();
00518 inline lx_interval & operator -=(lx_interval &, const interval   &) throw();
00519 
00521 lx_interval operator * (const lx_interval &, const lx_interval &) 
00522     throw();
00523 
00525 inline lx_interval operator * (const lx_interval &, const l_interval &) 
00526     throw();
00528 inline lx_interval operator * (const l_interval &, const lx_interval &) 
00529     throw();
00531 inline lx_interval operator * (const lx_interval &, const l_real &) 
00532     throw();
00534 inline lx_interval operator * (const l_real &, const lx_interval &) 
00535     throw();
00537 inline lx_interval operator * (const lx_interval &, const lx_real &) 
00538     throw();
00540 inline lx_interval operator * (const lx_real &, const lx_interval &) 
00541     throw();
00543 inline lx_interval operator * (const lx_interval &, const real &) 
00544     throw();
00546 inline lx_interval operator * (const real &, const lx_interval &) 
00547     throw();
00549 inline lx_interval operator * (const lx_interval &, const interval &) 
00550     throw();
00552 inline lx_interval operator * (const interval &, const lx_interval &) 
00553     throw();
00554 
00556 inline lx_interval & operator *=(lx_interval &, const lx_interval &) throw();
00558 inline lx_interval & operator *=(lx_interval &, const l_interval &) throw();
00560 inline lx_interval & operator *=(lx_interval &, const l_real     &) throw();
00562 inline lx_interval & operator *=(lx_interval &, const lx_real     &) throw();
00564 inline lx_interval & operator *=(lx_interval &, const real       &) throw();
00566 inline lx_interval & operator *=(lx_interval &, const interval   &) throw();
00567 
00569 lx_interval operator / (const lx_interval &, const lx_interval &) 
00570     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00571 
00573 inline lx_interval operator / (const lx_interval &, const l_interval &) 
00574     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00576 inline lx_interval operator / (const l_interval &, const lx_interval &) 
00577     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00579 inline lx_interval operator / (const lx_interval &, const l_real &) 
00580     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00582 inline lx_interval operator / (const l_real &, const lx_interval &) 
00583     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00585 inline lx_interval operator / (const lx_interval &, const real &) 
00586     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00588 inline lx_interval operator / (const real &, const lx_interval &) 
00589     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00591 inline lx_interval operator / (const lx_interval &, const interval &) 
00592     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00594 inline lx_interval operator / (const interval &, const lx_interval &) 
00595     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00597 inline lx_interval operator / (const lx_interval &, const lx_real &) 
00598     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00600 inline lx_interval operator / (const lx_real &, const lx_interval &) 
00601     throw(ERROR_LINTERVAL_DIV_BY_ZERO);
00602 
00604 inline lx_interval & operator /=(lx_interval &, const lx_interval &) throw();
00606 inline lx_interval & operator /=(lx_interval &, const l_interval &) throw();
00608 inline lx_interval & operator /=(lx_interval &, const l_real     &) throw();
00610 inline lx_interval & operator /=(lx_interval &, const lx_real     &) throw();
00612 inline lx_interval & operator /=(lx_interval &, const real       &) throw();
00614 inline lx_interval & operator /=(lx_interval &, const interval   &) throw();
00615 
00616 // ----------------------------- Convex hull -------------------------------
00617 
00619     inline lx_interval operator | (const lx_interval&, const lx_interval&) 
00620         throw();
00622     inline lx_interval operator | (const lx_interval&, const l_interval&) 
00623         throw();
00625     inline lx_interval operator | (const l_interval&, const lx_interval&) 
00626         throw();
00628     inline lx_interval operator | (const lx_interval&, const interval&) 
00629         throw();
00631     inline lx_interval operator | (const interval&, const lx_interval&) 
00632         throw();
00634     inline lx_interval & operator |= (lx_interval&, const lx_interval&) 
00635         throw();
00637     inline lx_interval & operator |= (lx_interval&, const l_interval&) 
00638         throw();
00640     inline lx_interval & operator |= (lx_interval&, const interval&) 
00641         throw();
00643     inline lx_interval operator | (const lx_real&, const lx_interval&) 
00644         throw();
00646     inline lx_interval operator | (const real&, const lx_interval&) 
00647         throw();
00649     inline lx_interval operator | (const lx_interval&, const lx_real&) 
00650         throw();
00652     inline lx_interval operator | (const lx_interval&, const real&) 
00653         throw();
00655     inline lx_interval operator | (const lx_interval&, const l_real&) 
00656         throw();
00658     inline lx_interval operator | (const l_real&, const lx_interval&) 
00659         throw();
00661     inline lx_interval & operator |= (lx_interval&, const real&)
00662         throw();
00664     inline lx_interval & operator |= (lx_interval&, const l_real&)
00665         throw();
00667     inline lx_interval & operator |= (lx_interval&, const lx_real&)
00668         throw();
00670     inline lx_interval operator | (const lx_real&, const lx_real&) 
00671         throw();
00672 
00673 // --------------------------- Intersection -----------------------------
00674 
00676     inline lx_interval operator & (const lx_interval&, const lx_interval&) 
00677         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00679     inline lx_interval operator & (const lx_interval&, const l_interval&) 
00680         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00682     inline lx_interval & operator &= (lx_interval&, const l_interval&) 
00683         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00685     inline lx_interval operator & (const l_interval&, const lx_interval&) 
00686         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00688     inline lx_interval operator & (const lx_interval&, const interval&) 
00689         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00691     inline lx_interval & operator &= (lx_interval &a, const interval &b) 
00692         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00694     inline lx_interval operator & (const interval&, const lx_interval&) 
00695         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00697     inline lx_interval & operator &= (lx_interval&, const lx_interval&) 
00698         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00700     inline lx_interval operator & (const lx_interval&, const lx_real&) 
00701         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00703     inline lx_interval operator & (const lx_interval&, const l_real&) 
00704         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00706     inline lx_interval operator & (const lx_interval&, const real&) 
00707         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00709     inline lx_interval operator & (const lx_real&, const lx_interval&) 
00710         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00712     inline lx_interval operator & (const l_real&, const lx_interval&) 
00713         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00715     inline lx_interval operator & (const real&, const lx_interval&) 
00716         throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00718     inline lx_interval & operator &= (lx_interval&, const lx_real&) 
00719         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00721     inline lx_interval & operator &= (lx_interval&, const l_real&) 
00722         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00724     inline lx_interval & operator &= (lx_interval&, const real&) 
00725         throw(ERROR_LINTERVAL_EMPTY_INTERVAL); 
00726 
00727 // ------------------------- SetInf, SetSup -----------------------------
00728 
00730 inline lx_interval & SetInf(lx_interval&, const lx_real&) 
00731     throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00733 inline lx_interval & SetInf(lx_interval&, const l_real&) 
00734     throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00736 inline lx_interval & SetInf(lx_interval&, const real&) 
00737     throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00738 
00740 inline lx_interval & SetSup(lx_interval&, const lx_real&) 
00741     throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00743 inline lx_interval & SetSup(lx_interval&, const l_real&) 
00744     throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00746 inline lx_interval & SetSup(lx_interval&, const real&) 
00747     throw(ERROR_LINTERVAL_EMPTY_INTERVAL);
00748 
00749 // ------------------------- Help Functions: ----------------------------
00750 
00751 // ----------------- Intervals for test calculations -------------------- 
00752 
00754 l_interval point_max(void);
00755 // returns a staggered point interval with maximum exponent 1020,
00756 // whereby nearly all mantissa bits are set. 
00757 
00759 l_interval point_any(int n);
00760 // returns a staggered point interval with exponent n,
00761 // whereby nearly all mantissa bits are set.
00762 // -1074 <= n <= +1020; 
00763 
00765 l_interval wide_max(void);
00766 // returns a staggered interval a with maximum exponent 1020
00767 // and diam(a)>0, whereby nearly all mantissa bits are set. 
00768 
00770 l_interval wide_any(int n);
00771 // returns a wide staggered interval a with exponent n,
00772 // and diam(a)>0, whereby nearly all mantissa bits are set.
00773 // -1074 <= n <= +1020;
00774 
00775 
00776 // --------------------------------------------------------------------
00777 // ----------------- lx_interval Constants ----------------------------
00778 // --------------------------------------------------------------------
00779 
00781  lx_interval Pi_lx_interval() throw(); // pi
00783  lx_interval Pip2_lx_interval() throw(); // pi^2
00785  lx_interval Pi2_lx_interval() throw(); // 2*pi
00787  lx_interval Pi2r_lx_interval() throw(); // 1/(2*pi)
00789  lx_interval Pid4_lx_interval() throw(); // pi/4
00791  lx_interval Pid2_lx_interval() throw(); // pi/2
00793  lx_interval Ln2_lx_interval() throw(); // ln(2)
00795  lx_interval Ln10_lx_interval() throw(); // ln(10)
00797  lx_interval Ln10r_lx_interval() throw(); // 1/ln(10)
00799  lx_interval Pir_lx_interval() throw();  // 1/pi
00801  lx_interval SqrtPi_lx_interval() throw();  // sqrt(pi)
00803  lx_interval Sqrt2Pi_lx_interval() throw(); // sqrt(2pi)
00805  lx_interval Sqrt2_lx_interval() throw();  // sqrt(2)
00807  lx_interval Sqrt2r_lx_interval() throw();  // sqrt(2)
00809  lx_interval Sqrt3_lx_interval() throw();  // sqrt(3)
00811  lx_interval Sqrt3d2_lx_interval() throw();  // sqrt(3)/2
00813  lx_interval Sqrt3r_lx_interval() throw();  // 1/sqrt(3)
00815  lx_interval Ln2r_lx_interval() throw();  // 1/ln(2)
00817  lx_interval Pid3_lx_interval() throw();  // pi/3
00819  lx_interval SqrtPir_lx_interval() throw();  // 1/sqrt(pi)
00821  lx_interval Sqrt2Pir_lx_interval() throw(); // 1/sqrt(2pi)
00823  lx_interval LnPi_lx_interval() throw();  // ln(pi)
00825  lx_interval Ln2Pi_lx_interval() throw();  // ln(2pi)
00827  lx_interval E_lx_interval() throw();  // e
00829  lx_interval Ep2_lx_interval() throw();  // e^2
00831  lx_interval Ep2r_lx_interval() throw();  // 1/e^2
00833  lx_interval Er_lx_interval() throw();  // 1/e
00835  lx_interval EpPi_lx_interval() throw();  // e^pi
00837  lx_interval EpPid2_lx_interval() throw();  // e^(pi/2)
00839  lx_interval EpPid4_lx_interval() throw();  // e^(pi/4)
00841  lx_interval Ep2Pi_lx_interval() throw();  // e^(2*pi)
00843  lx_interval EulerGamma_lx_interval() throw();
00845  lx_interval Catalan_lx_interval() throw();
00847  lx_interval sqrt5_lx_interval() throw();  // sqrt(5)
00849  lx_interval sqrt7_lx_interval() throw();   // sqrt(7)
00851  lx_interval One_m_lx_interval() throw();
00853  lx_interval One_p_lx_interval() throw();
00854 
00855 // -------------------------------------------------------------------------
00856 // ---------------- lx_interval: elementary functions ----------------------
00857 // -------------------------------------------------------------------------
00858  
00860  lx_interval sqrt(const lx_interval&) throw();
00862  lx_interval sqr(const lx_interval&) throw();
00864  lx_interval ln(const lx_interval &) throw();
00866  lx_interval log2(const lx_interval &) throw();
00868  lx_interval log10(const lx_interval &) throw();
00870  lx_interval lnp1(const lx_interval &) throw();
00872  lx_interval exp(const lx_interval &) throw();
00874  lx_interval exp2(const lx_interval &) throw(); // 2^x
00876  lx_interval exp10(const lx_interval &) throw(); // 10^x
00878  lx_interval expm1(const lx_interval &x) throw(); 
00880  lx_interval power(const lx_interval &, const real &) throw();
00882  lx_interval pow(const lx_interval &, const lx_interval &) throw();
00884  lx_interval xp1_pow_y(const lx_interval &, const lx_interval &) throw(); 
00886  lx_interval sin(const lx_interval &)throw();
00888  lx_interval sin_n(const lx_interval &x, const real& n) throw();
00890  lx_interval cos(const lx_interval &) throw();
00892  lx_interval cos_n(const lx_interval &x, const real& n) throw();
00894  lx_interval tan(const lx_interval &) throw();
00896  lx_interval cot(const lx_interval &) throw();
00898  lx_interval sqrt1px2(const lx_interval &) throw();
00900  lx_interval atan(const lx_interval &) throw();
00902  lx_interval sqrt1mx2(const lx_interval &) throw();
00904  lx_interval sqrtx2m1(const lx_interval &) throw();
00906  lx_interval asin(const lx_interval & ) throw();
00908  lx_interval acos(const lx_interval &) throw();
00910  lx_interval acot(const lx_interval &) throw();
00912  lx_interval sinh(const lx_interval &) throw();
00914  lx_interval cosh(const lx_interval &) throw();
00916  lx_interval tanh(const lx_interval &) throw();
00918  lx_interval coth(const lx_interval &) throw();
00920  lx_interval sqrtp1m1(const lx_interval &) throw();
00922  lx_interval asinh(const lx_interval &) throw();
00924  lx_interval acosh(const lx_interval &) throw();
00926  lx_interval acoshp1(const lx_interval &) throw();
00928  lx_interval atanh(const lx_interval &) throw();
00930  lx_interval atanh1m(const lx_interval &) throw();
00932  lx_interval atanhm1p(const lx_interval &) throw();
00934  lx_interval acoth(const lx_interval &) throw();
00936  lx_interval acothp1(const lx_interval &) throw();
00938  lx_interval acothm1m(const lx_interval &) throw();
00940  lx_interval sqrtx2y2(const lx_interval &, const lx_interval &) throw();
00942  lx_interval ln_sqrtx2y2(const lx_interval &, const lx_interval &) throw();
00944  lx_interval sqrt(const lx_interval &, int) throw();
00945 
00946 } // end namespace cxsc
00947 
00948 #include "lx_interval.inl"
00949 
00950 #endif // _CXSC_LX_INTERVAL_HPP_INCLUDED
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