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/* mpfr_sinh -- hyperbolic sine
Copyright 2001, 2002, 2003, 2004, 2005 Free Software Foundation, Inc.
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"
/* The computation of sinh is done by
sinh(x) = 1/2 [e^(x)-e^(-x)] */
int
mpfr_sinh (mpfr_ptr y, mpfr_srcptr xt, mp_rnd_t rnd_mode)
{
mpfr_t x;
int inexact;
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))
{
MPFR_SET_INF(y);
MPFR_SET_SAME_SIGN(y, xt);
MPFR_RET(0);
}
else /* xt is zero */
{
MPFR_ASSERTD(MPFR_IS_ZERO(xt));
MPFR_SET_ZERO(y); /* sinh(0) = 0 */
MPFR_SET_SAME_SIGN(y, xt);
MPFR_RET(0);
}
}
MPFR_TMP_INIT_ABS (x, xt);
{
mpfr_t t, ti;
mp_exp_t d;
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
int overflow_p = mpfr_overflow_p ();
/* compute the precision of intermediary variable */
Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));
/* the optimal number of bits : see algorithms.ps */
Nt = Nt + MPFR_INT_CEIL_LOG2 (Nt) + 4;
/* If x is near 0, exp(x) - 1/exp(x) = 2*x+x^3/3+O(x^5) */
if (MPFR_GET_EXP (x) < 0)
Nt -= 2*MPFR_GET_EXP (x);
/* initialise of intermediary variable */
mpfr_init2 (t, Nt);
mpfr_init2 (ti, Nt);
/* First computation of sinh */
for (;;) {
/* compute sinh */
mpfr_clear_overflow ();
mpfr_exp (t, x, GMP_RNDD); /* exp(x) */
/* exp(x) can overflow or underflow or return ~1 ! */
d = MPFR_GET_EXP (t);
if (MPFR_UNLIKELY (mpfr_overflow_p ())) {
MPFR_SET_INF (t);
break;
}
mpfr_ui_div (ti, 1, t, GMP_RNDU); /* 1/exp(x) */
mpfr_sub (t, t, ti, GMP_RNDN); /* exp(x) - 1/exp(x) */
mpfr_div_2ui (t, t, 1, GMP_RNDN); /* 1/2(exp(x) - 1/exp(x)) */
/* it may be that t is zero (in fact, it can only occur when te=1,
and thus ti=1 too) */
err = 0;
if (!MPFR_IS_ZERO (t))
{
/* calculation of the error */
d = d - MPFR_GET_EXP (t) + 2;
/* error estimate */
/* err = Nt-(__gmpfr_ceil_log2(1+pow(2,d)));*/
err = Nt - (MAX (d, 0) + 1);
if (mpfr_can_round (t, err, GMP_RNDN, GMP_RNDZ,
MPFR_PREC (y) + (rnd_mode == GMP_RNDN)))
break;
}
/* actualisation of the precision */
Nt += MAX (BITS_PER_MP_LIMB, err);
mpfr_set_prec (t, Nt);
mpfr_set_prec (ti, Nt);
}
inexact = mpfr_set4 (y, t, rnd_mode, MPFR_SIGN (xt));
if (overflow_p != 0)
__gmpfr_flags |= MPFR_FLAGS_OVERFLOW;
mpfr_clear (t);
mpfr_clear (ti);
}
return inexact;
}
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