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/* mpfr_tanh -- hyperbolic tangent
Copyright 2001, 2002, 2003, 2004 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. */
#include "mpfr-impl.h"
/* The computation of cosh is done by
tanh= [e^(x)^2-1]/[e^(x)^2+1] */
int
mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mp_rnd_t rnd_mode)
{
/****** Declaration ******/
mpfr_t x;
int 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))
{
if (MPFR_IS_POS(xt))
return mpfr_set_ui (y, 1, rnd_mode); /* tanh(inf) = 1 */
else
return mpfr_set_si (y, -1, rnd_mode); /* tanh(-inf) = -1 */
}
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_emin_emax ();
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 Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of output variable */
mp_prec_t Nt; /* Precision of intermediary variables */
long int err; /* Precision of error */
/* Compute the precision of intermediary variable */
Nt = MAX (Nx, Ny);
/* The optimal number of bits: see algorithms.ps */
Nt = Nt + /*__gmpfr_ceil_log2 (9)*/ 4 + __gmpfr_ceil_log2 (Nt);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
mpfr_init2 (te, Nt);
/* First computation of cosh */
for (;;)
{
/* Compute tanh */
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);
/* Estimation of the error */
/*err = Nt-(__gmpfr_ceil_log2(7+pow(2,d+1)));*/
err = Nt - (MAX(d + 1, 3) + 1);
if (mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
Ny + (rnd_mode == GMP_RNDN)))
break;
/* Actualisation of the precision */
Nt += BITS_PER_MP_LIMB;
mpfr_set_prec (t, Nt);
mpfr_set_prec (te, Nt);
}
if (MPFR_IS_NEG (xt) )
MPFR_CHANGE_SIGN(t);
inexact = mpfr_set (y, t, rnd_mode);
mpfr_clear (te);
mpfr_clear (t);
}
mpfr_restore_emin_emax ();
return mpfr_check_range (y, inexact, rnd_mode);
}
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