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/* mpfr_tanh -- hyperbolic tangent
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., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, 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);
}
}
MPFR_SAVE_EXPO_MARK (expo);
MPFR_TMP_INIT_ABS (x, xt);
/* 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 */
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) + 4;
Nt += ABS (MPFR_GET_EXP (x));
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
mpfr_init2 (te, Nt);
MPFR_ZIV_INIT (loop, Nt);
for (;;) {
/* tanh = (exp(2x)-1)/(exp(2x)+1) */
mpfr_mul_2ui (te, x, 1, GMP_RNDN); /* 2x */
mpfr_exp (te, te, GMP_RNDN); /* exp(2x) */
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*/
mpfr_div (t, te, t, GMP_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/
/* Calculation of the error*/
d = d - MPFR_GET_EXP (t);
err = Nt - (MAX(d + 1, 3) + 1);
if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd_mode)))
break;
/* if t=1, we still can round */
if (MPFR_GET_EXP (t) == 1) {
if (err > Ny + (rnd_mode == GMP_RNDN))
if ((rnd_mode == GMP_RNDZ) ||
(rnd_mode == GMP_RNDD && MPFR_IS_POS (t)) ||
(rnd_mode == GMP_RNDU && MPFR_IS_NEG (t)))
mpfr_nexttozero (t);
break;
}
/* Actualisation of the precision */
MPFR_ZIV_NEXT (loop, Nt);
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
mpfr_clear (te);
mpfr_clear (t);
}
MPFR_SAVE_EXPO_FREE (expo);
inexact = mpfr_check_range (y, inexact, rnd_mode);
return inexact;
}
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