mpfr-2.4.1/tanh.c

/* mpfr_tanh -- hyperbolic tangent

Copyright 2001, 2002, 2003, 2004, 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"

int
mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
{
  /****** Declaration ******/
  mpfr_t x;
  int inexact;
  MPFR_SAVE_EXPO_DECL (expo);

  MPFR_LOG_FUNC (("x[%#R]=%R rnd=%d", xt, xt, rnd_mode),
                 ("y[%#R]=%R inexact=%d", y, y, inexact));

  /* Special value checking */
  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (xt)))
    {
      if (MPFR_IS_NAN (xt))
        {
          MPFR_SET_NAN (y);
          MPFR_RET_NAN;
        }
      else if (MPFR_IS_INF (xt))
        {
          /* tanh(inf) = 1 && tanh(-inf) = -1 */
          return mpfr_set_si (y, MPFR_INT_SIGN (xt), rnd_mode);
        }
      else /* tanh (0) = 0 and xt is zero */
        {
          MPFR_ASSERTD (MPFR_IS_ZERO(xt));
          MPFR_SET_ZERO (y);
          MPFR_SET_SAME_SIGN (y, xt);
          MPFR_RET (0);
        }
    }

  /* tanh(x) = x - x^3/3 + ... so the error is < 2^(3*EXP(x)-1) */
  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (y, xt, -2 * MPFR_GET_EXP (xt), 1, 0,
                                    rnd_mode, {});

  MPFR_TMP_INIT_ABS (x, xt);

  MPFR_SAVE_EXPO_MARK (expo);

  /* General case */
  {
    /* Declaration of the intermediary variable */
    mpfr_t t, te;
    mp_exp_t d;

    /* Declaration of the size variable */
    mp_prec_t Ny = MPFR_PREC(y);   /* target precision */
    mp_prec_t Nt;                  /* working precision */
    long int err;                  /* error */
    int sign = MPFR_SIGN (xt);
    MPFR_ZIV_DECL (loop);
    MPFR_GROUP_DECL (group);

    /* First check for BIG overflow of exp(2*x):
       For x > 0, exp(2*x) > 2^(2*x)
       If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */
    if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) {
      /* initialise of intermediary variables
         since 'set_one' label assumes the variables have been
         initialize */
      MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te);
      goto set_one;
    }

    /* Compute the precision of intermediary variable */
    /* The optimal number of bits: see algorithms.tex */
    Nt = Ny + MPFR_INT_CEIL_LOG2 (Ny) + 4;
    /* if x is small, there will be a cancellation in exp(2x)-1 */
    if (MPFR_GET_EXP (x) < 0)
      Nt += -MPFR_GET_EXP (x);

    /* initialise of intermediary variable */
    MPFR_GROUP_INIT_2 (group, Nt, t, te);

    MPFR_ZIV_INIT (loop, Nt);
    for (;;) {
      /* tanh = (exp(2x)-1)/(exp(2x)+1) */
      mpfr_mul_2ui (te, x, 1, GMP_RNDN);  /* 2x */
      /* since x > 0, we can only have an overflow */
      mpfr_exp (te, te, GMP_RNDN);        /* exp(2x) */
      if (MPFR_UNLIKELY (MPFR_IS_INF (te))) {
      set_one:
        inexact = MPFR_FROM_SIGN_TO_INT (sign);
        mpfr_set4 (y, __gmpfr_one, GMP_RNDN, sign);
        if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign)))
          {
            inexact = -inexact;
            mpfr_nexttozero (y);
          }
        break;
      }
      d = MPFR_GET_EXP (te);              /* For Error calculation */
      mpfr_add_ui (t, te, 1, GMP_RNDD);   /* exp(2x) + 1*/
      mpfr_sub_ui (te, te, 1, GMP_RNDU);  /* exp(2x) - 1*/
      d = d - MPFR_GET_EXP (te);
      mpfr_div (t, te, t, GMP_RNDN);      /* (exp(2x)-1)/(exp(2x)+1)*/

      /* Calculation of the error */
      d = MAX(3, d + 1);
      err = Nt - (d + 1);

      if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
        {
          inexact = mpfr_set4 (y, t, rnd_mode, sign);
          break;
        }

      /* if t=1, we still can round since |sinh(x)| < 1 */
      if (MPFR_GET_EXP (t) == 1)
        goto set_one;

      /* Actualisation of the precision */
      MPFR_ZIV_NEXT (loop, Nt);
      MPFR_GROUP_REPREC_2 (group, Nt, t, te);
    }
    MPFR_ZIV_FREE (loop);
    MPFR_GROUP_CLEAR (group);
  }
  MPFR_SAVE_EXPO_FREE (expo);
  inexact = mpfr_check_range (y, inexact, rnd_mode);

  return inexact;
}