include/algebramix/series_elementary.hpp

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/******************************************************************************
* MODULE     : series_elementary.hpp
* DESCRIPTION: Power series expansions of elementary functions
* COPYRIGHT  : (C) 2004  Joris van der Hoeven
*******************************************************************************
* This software falls under the GNU general public license and comes WITHOUT
* ANY WARRANTY WHATSOEVER. See the file $TEXMACS_PATH/LICENSE for more details.
* If you don't have this file, write to the Free Software Foundation, Inc.,
* 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
******************************************************************************/

#ifndef __MMX_SERIES_ELEMENTARY__HPP
#define __MMX_SERIES_ELEMENTARY__HPP
#include <numerix/floating.hpp>
#include <algebramix/series.hpp>
#include <algebramix/series_vector.hpp>

namespace mmx {
#define TMPL template<typename C, typename V>
#define TMPLW template<typename C, typename V, typename W>
#define Series series<C,V>

/******************************************************************************
* Elementary functions
******************************************************************************/

TMPL inline Series
sqrt (const Series& f) {
  if (is_exact_zero (f)) return Series (CF(f));
  return unary_recursive_series<sqrt_op> (f);
}

TMPL inline Series
sqrt_init (const Series& f, const C& c) {
  return unary_recursive_series<sqrt_op> (f, c);
}

TMPL inline Series
exp (const Series& f) {
  return unary_recursive_series<exp_op> (f);
}

TMPL inline Series
log (const Series& f) {
  return unary_recursive_series<log_op> (f);
}

TMPL inline Series
log_init (const Series& f, const C& c) {
  return unary_recursive_series<log_op> (f, c);
}

TMPL inline Series
pow (const Series& f, const C& c) {
  return exp (c * log (f));
}

TMPL inline Series
pow (const Series& f, const Series& g) {
  return exp (g * log (f));
}

TMPL inline Series
acos (const Series& f) {
  return unary_recursive_series<acos_op> (f);
}

TMPL inline Series
acos_init (const Series& f, const C& c) {
  return unary_recursive_series<acos_op> (f, c);
}

TMPL inline Series
asin (const Series& f) {
  return unary_recursive_series<asin_op> (f);
}

TMPL inline Series
asin_init (const Series& f, const C& c) {
  return unary_recursive_series<asin_op> (f, c);
}

TMPL inline Series
atan (const Series& f) {
  return unary_recursive_series<atan_op> (f);
}

TMPL inline Series
atan_init (const Series& f, const C& c) {
  return unary_recursive_series<atan_op> (f, c);
}

INV_TRIGO_SUGAR(TMPL,Series)
HYPER_SUGAR(TMPL,Series)
INV_HYPER_SUGAR(TMPL,Series)
ARG_HYPER_SUGAR(TMPL,Series)

/******************************************************************************
* Trigonometric functions
******************************************************************************/

TMPLW inline series<vector<C,W>,V>
trig (const series<vector<C,W>,V>& f) {
  return unary_recursive_series<trig_op> (f);
}

template<typename C,typename V> inline vector<Series >
cos_sin (const Series& f) {
  return as_vector (trig (as_series (vec (f))));
}

template<typename C,typename V> inline Series
cos (const Series& f) {
  return unary_recursive_series<cos_op> (f);
}

template<typename C,typename V> inline Series
sin (const Series& f) {
  return unary_recursive_series<sin_op> (f);
}

template<typename C,typename V> inline Series
tan (const Series& f) {
  return unary_recursive_series<tan_op> (f);
}

#undef TMPL
#undef TMPLW
#undef Series
} // namespace mmx
#endif // __MMX_SERIES_ELEMENTARY__HPP

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