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/* mpfr_acos -- arc-cosinus of a floating-point number
Copyright 2001, 2002, 2003, 2004 Free Software Foundation.
This file is part of the MPFR Library, and was contributed by Mathieu Dutour.
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"
int
mpfr_acos (mpfr_ptr acos, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t xp;
mpfr_t arcc;
int sign, supplement;
mpfr_t tmp;
int Prec;
int prec_acos;
int good = 0;
int realprec;
int compared;
int inexact = 0;
/* Special cases */
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
{
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
{
MPFR_SET_NAN(acos);
MPFR_RET_NAN;
}
else /* necessarily x=0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
/* acos(0)=Pi/2 */
inexact = mpfr_const_pi (acos, rnd_mode);
MPFR_SET_EXP (acos, MPFR_GET_EXP (acos) - 1);
return mpfr_check_range (acos, inexact, rnd_mode);
}
}
MPFR_CLEAR_FLAGS(x);
/* Set x_p=|x| */
sign = MPFR_SIGN(x);
mpfr_init2 (xp, MPFR_PREC(x));
mpfr_abs (xp, x, rnd_mode);
compared = mpfr_cmp_ui (xp, 1);
if (compared > 0) /* acos(x) = NaN for x > 1 */
{
mpfr_clear (xp);
MPFR_SET_NAN(acos);
MPFR_RET_NAN;
}
if (compared == 0)
{
mpfr_clear (xp);
if (MPFR_IS_POS_SIGN(sign)) /* acos(+1) = 0 */
return mpfr_set_ui (acos, 0, rnd_mode);
else /* acos(-1) = Pi */
{
mpfr_const_pi (acos, rnd_mode);
return 1; /* inexact */
}
}
mpfr_save_emin_emax ();
prec_acos = MPFR_PREC(acos);
mpfr_ui_sub (xp, 1, xp, GMP_RNDD);
if (MPFR_IS_POS_SIGN(sign))
supplement = 2 - 2 * MPFR_GET_EXP (xp);
else
supplement = 2 - MPFR_GET_EXP(xp);
realprec = prec_acos + 10;
while (!good)
{
Prec = realprec + supplement;
/* Initialisation */
mpfr_init2 (tmp, Prec);
mpfr_init2 (arcc, Prec);
/* acos(x) = Pi/2 - asin(x) = Pi/2 - atan(x/sqrt(1-x^2)) */
mpfr_mul (tmp, x, x, GMP_RNDN);
mpfr_ui_sub (tmp, 1, tmp, GMP_RNDN);
mpfr_sqrt (tmp, tmp, GMP_RNDN);
mpfr_div (tmp, x, tmp, GMP_RNDN);
mpfr_atan (arcc, tmp, GMP_RNDN);
mpfr_const_pi (tmp, GMP_RNDN);
mpfr_div_2ui (tmp, tmp, 1, GMP_RNDN);
mpfr_sub (arcc, tmp, arcc, GMP_RNDN);
if (mpfr_can_round (arcc, realprec, GMP_RNDN, GMP_RNDZ,
MPFR_PREC(acos) + (rnd_mode == GMP_RNDN)))
{
inexact = mpfr_set (acos, arcc, rnd_mode);
good = 1;
}
else
realprec += __gmpfr_ceil_log2 ((double) realprec);
mpfr_clear (tmp);
mpfr_clear (arcc);
}
mpfr_clear (xp);
mpfr_restore_emin_emax ();
return mpfr_check_range (acos, inexact, rnd_mode);
}
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