mpfr-2.4.1/gen_inverse.h

/* generic inverse of a function.

Copyright 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
Contributed by the Arenaire and Cacao projects, INRIA.

This file is part of the GNU MPFR Library.

The GNU MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The GNU MPFR 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */

#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"

#ifndef ACTION_SPECIAL
#define ACTION_SPECIAL
#endif

#ifndef ACTION_TINY
#define ACTION_TINY
#endif

/* example of use:
#define FUNCTION mpfr_sec
#define INVERSE  mpfr_cos
#define ACTION_NAN(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
#define ACTION_INF(y) do { MPFR_SET_NAN(y); MPFR_RET_NAN; } while (1)
#define ACTION_ZERO(y) return mpfr_set_ui (y, 1, GMP_RNDN)
#include "gen_inverse.h"
*/

int
FUNCTION (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
  mp_prec_t precy; /* target precision */
  mp_prec_t m;     /* working precision */
  mpfr_t z;        /* temporary variable to store INVERSE(x) */
  int inexact;     /* inexact flag */
  MPFR_ZIV_DECL (loop);
  MPFR_SAVE_EXPO_DECL (expo);

  if (MPFR_UNLIKELY(MPFR_IS_SINGULAR(x)))
    {
      if (MPFR_IS_NAN(x))
        ACTION_NAN(y);
      else if (MPFR_IS_INF(x))
        ACTION_INF(y);
      else /* x = 0 */
        ACTION_ZERO(y,x);
    }

  /* x is neither NaN, Inf nor zero */
  MPFR_SAVE_EXPO_MARK (expo);
  ACTION_TINY (y, x, rnd_mode); /* special case for very small input x */
  precy = MPFR_PREC(y);
  m = precy + MPFR_INT_CEIL_LOG2 (precy) + 3;
  mpfr_init2 (z, m);

  MPFR_ZIV_INIT (loop, m);
  for(;;)
    {
      MPFR_BLOCK_DECL (flags);

      MPFR_BLOCK (flags, INVERSE (z, x, GMP_RNDZ)); /* error k_u < 1 ulp */
      /* FIXME: the following assumes that if an overflow happens with
         MPFR_EMAX_MAX, then necessarily an underflow happens with
         __gmpfr_emin */
      if (MPFR_OVERFLOW (flags))
        {
          int s = MPFR_SIGN(z);
          MPFR_ZIV_FREE (loop);
          mpfr_clear (z);
          MPFR_SAVE_EXPO_FREE (expo);
          return mpfr_underflow (y, (rnd_mode == GMP_RNDN) ?
                                 GMP_RNDZ : rnd_mode, s);
        }
      mpfr_ui_div (z, 1, z, GMP_RNDN);
      /* the error is less than c_w + 2*c_u*k_u (see algorithms.tex),
         where c_w = 1/2, c_u = 1 since z was rounded towards zero,
         thus 1/2 + 2 < 4 */
      if (MPFR_LIKELY (MPFR_CAN_ROUND (z, m - 2, precy, rnd_mode)))
        break;
      ACTION_SPECIAL;
      MPFR_ZIV_NEXT (loop, m);
      mpfr_set_prec (z, m);
    }
  MPFR_ZIV_FREE (loop);

  inexact = mpfr_set (y, z, rnd_mode);
  mpfr_clear (z);

 end:
  MPFR_SAVE_EXPO_FREE (expo);
  return mpfr_check_range (y, inexact, rnd_mode);
}