/* mpfr_expm1 -- Compute exp(x)-1

Copyright 2001, 2002, 2003, 2004, 2005 Free Software Foundation.

This file is part of the MPFR Library.

The 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 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 MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin Place, Fifth Floor, Boston,
MA 02110-1301, USA. */

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

 /* The computation of expm1 is done by
    expm1(x)=exp(x)-1
 */

int
mpfr_expm1 (mpfr_ptr y, mpfr_srcptr x , mp_rnd_t rnd_mode) 
{
  int inexact;
  MPFR_SAVE_EXPO_DECL (expo);

  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
    {
      if (MPFR_IS_NAN (x))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      /* check for inf or -inf (expm1(-inf)=-1) */
      else if (MPFR_IS_INF (x))
        { 
          if (MPFR_IS_POS (x))
            {
              MPFR_SET_INF (y);
              MPFR_SET_POS (y);
              MPFR_RET (0);
            }
          else
            return mpfr_set_si (y, -1, rnd_mode);
        }
      else
        {
          MPFR_ASSERTD (MPFR_IS_ZERO (x));
          MPFR_SET_ZERO (y);   /* expm1(+/- 0) = +/- 0 */
          MPFR_SET_SAME_SIGN (y, x);
          MPFR_RET (0);
        }
    }

  /* exp(x)-1 = x +x^2/2 + ... so the error is < 2^(2*EXP(x)-1) */
  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, x, -MPFR_GET_EXP (x)+1,1,rnd_mode,);

  MPFR_SAVE_EXPO_MARK (expo);
  /* General case */
  {
    /* Declaration of the intermediary variable */
    mpfr_t t;
    /* Declaration of the size variable */
    mp_prec_t Ny = MPFR_PREC(y);   /* target precision */
    mp_prec_t Nt;                  /* working precision */
    mp_exp_t err, exp_te;          /* error */
    MPFR_ZIV_DECL (loop);

    /* compute the precision of intermediary variable */
    /* the optimal number of bits : see algorithms.tex */
    Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 6;

    /* if |x| is smaller than 2^(-e), we will loose about e bits in the
       subtraction exp(x) - 1 */
    if (MPFR_EXP(x) < 0)
      Nt += -MPFR_EXP(x);

    /* initialize auxiliary variable */
    mpfr_init2 (t, Nt);

    /* First computation of expm1 */
    MPFR_ZIV_INIT (loop, Nt);
    for (;;)
      {
        mpfr_clear_flags ();
        /* exp(x) may overflow and underflow */
        mpfr_exp (t, x, GMP_RNDN);         /* exp(x)*/
        if (MPFR_UNLIKELY (mpfr_overflow_p ()))
          {
            inexact = mpfr_overflow (y, rnd_mode, MPFR_SIGN_POS);
            MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, MPFR_FLAGS_OVERFLOW);
            break;
          }
        else if (MPFR_UNLIKELY (mpfr_underflow_p ()))
          {
            inexact = mpfr_set_si (y, -1, rnd_mode);
            MPFR_ASSERTD (inexact == 0);
            inexact = -1;
            if (MPFR_IS_LIKE_RNDZ (rnd_mode, 1))
              {
                inexact = 1;
                mpfr_nexttozero (y);
              }
            break;
          }

        exp_te = MPFR_GET_EXP (t);         /* FIXME: exp(x) may overflow! */
        mpfr_sub_ui (t, t, 1, GMP_RNDN);   /* exp(x)-1 */

        /* error estimate */
        /*err=Nt-(__gmpfr_ceil_log2(1+pow(2,MPFR_EXP(te)-MPFR_EXP(t))));*/
        err = Nt - (MAX (exp_te - MPFR_GET_EXP (t), 0) + 1);

        if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
          {
            inexact = mpfr_set (y, t, rnd_mode);
            break;
          }

        /* increase the precision */
        MPFR_ZIV_NEXT (loop, Nt);
        mpfr_set_prec (t, Nt);
      }
    MPFR_ZIV_FREE (loop);

    mpfr_clear (t);
  }

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