/*
**  ha_rmath.hpp: additional headerfile for the C-XSC library,
**                mathematical standard functions (elementary functions)
**                of high accuracy for real arguments 
**
**  ha_imath.hpp: additional headerfile for the C-XSC library,
**                mathematical standard functions (elementary functions)
**                of high accuracy for interval arguments 
**
**  Copyright  (C) 2002 Dr. W. Hofschuster
**                      Wiss. Rechnen/Softwaretechnologie
**                      Universitaet Wuppertal, Germany   
**
**  This library is free software; you can redistribute it and/or
**  modify it under the terms of the GNU Library General Public
**  License as published by the Free Software Foundation; either
**  version 2 of the License, or (at your option) any later version.
**
**  This library is distributed in the hope that it will be useful,
**  but WITHOUT ANY WARRANTY; without even the implied warranty of
**  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
**  Library General Public License for more details.
**
**  You should have received a copy of the GNU Library General Public
**  License along with this library; if not, write to the Free
**  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/


The headerfiles ha_rmath.hpp and ha_imath.hpp are additional headerfiles
for the C-XSC 2.0 - Library (http://www.math.uni-wuppertal.de/~xsc) and
they are an interface for mathematical standard functions (elementary 
functions) of high accuracy.


When do you need these additional headerfiles?
==============================================

1. You need the elementary functions available in C-XSC for real and 
   interval arguments,
      sqr, sqrt, 
      sin, cos, tan, cot,
      asin, acos, atan, acot,
      exp, ln,
      sinh, cosh, tanh, coth,
      asinh, acos, atanh, acoth,
      pow, power
   with higher accuracy. The computed values of the functions declared
   in the additional headerfiles are accurate to within one or two
   units in the last place. The emphasis is more on accuracy than
   on speed.
   
   Hint: If you want to evaluate your functions fast, use the elementary
   functions of the C-XSC library (headerfile: rmath.hpp or imath.hpp,
   namespace: cxsc). If you need higher accuracy and you accept that the
   computation is more expensive, use the additional headerfiles (header-
   file: ha_rmath.hpp or ha_imath.hpp, namespace: ha_cxsc).

2. You need functions with a larger argument range, e.g.
      real x; sin(x);          with |x|>1e9   or
      interval x,y; pow(x,y);  with Inf(x)<0
          
3. You need one of the additional functions
      atan2(x,y) = arctan(x/y) for real arguments,
      exp2, exp10, log2, log10, loga for real and interval arguments,
   then you must use these additonal headerfiles.


How to use the headerfiles?
===========================
As usual, you include the addional headerfiles in your own program with
   #include "ha_rmath.hpp"   or
   #include "ha_imath.hpp".
The additional functions are in the namespace ha_cxsc, that means you
must use the scope operator to call such a function (e.g. for the 
sine function ha_cxsc::sin(x) ).

Hint: To avoid ambiguity of overloaded function names do not use
"using namespace ha_cxsc;" and "using namespace cxsc;" simultaneously.

Afterwards you can compile your program and link the C-XSC library as
usual.        


Questions, Suggestions, Problems, Solutions are welcome:
========================================================

     Wissenschaftliches Rechnen/Softwaretechnologie
     Fachbereich 7 (Mathematik)
     Bergische Universitaet Wuppertal
     Gaussstrasse 20
     D-42097 Wuppertal

e-mail: xsc@math.uni-wuppertal.de

C-XSC-Homepage: http://www.math.uni-wuppertal.de/~xsc/
             or http://www.xsc.de/