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/* mpfr_asin -- arc-sinus 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_asin (mpfr_ptr asin, mpfr_srcptr x, mp_rnd_t rnd_mode)
{
mpfr_t xp;
mpfr_t arcs;
int sign, supplement;
mpfr_t tmp;
int Prec;
int prec_asin;
int realprec;
int estimated_delta;
int compared;
int inexact;
/* Special cases */
if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) ))
{
if (MPFR_IS_NAN(x) || MPFR_IS_INF(x))
{
MPFR_SET_NAN(asin);
MPFR_RET_NAN;
}
else /* x = 0 */
{
MPFR_ASSERTD(MPFR_IS_ZERO(x));
mpfr_set_ui (asin, 0, GMP_RNDN);
MPFR_RET(0); /* exact result */
}
MPFR_ASSERTN(0);
}
MPFR_CLEAR_FLAGS(asin);
/* 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 (MPFR_UNLIKELY(compared > 0)) /* asin(x) = NaN for |x| > 1 */
{
MPFR_SET_NAN(asin);
mpfr_clear (xp);
MPFR_RET_NAN;
}
if (MPFR_UNLIKELY(compared == 0)) /* x = 1 or x = -1 */
{
if (MPFR_IS_POS_SIGN(sign)) /* asin(+1) = Pi/2 */
inexact = mpfr_const_pi (asin, rnd_mode);
else /* asin(-1) = -Pi/2 */
{
inexact = -mpfr_const_pi (asin, MPFR_INVERT_RND(rnd_mode));
mpfr_neg (asin, asin, rnd_mode);
}
MPFR_SET_EXP (asin, MPFR_GET_EXP (asin) - 1);
mpfr_clear (xp);
return inexact;
}
mpfr_save_emin_emax ();
prec_asin = MPFR_PREC(asin);
mpfr_ui_sub (xp, 1, xp, GMP_RNDD);
supplement = 2 - MPFR_GET_EXP (xp);
realprec = prec_asin + 10;
mpfr_init (tmp);
mpfr_init (arcs);
/* use asin(x) = atan(x/sqrt(1-x^2)) */
for (;;)
{
estimated_delta = 1 + supplement;
Prec = realprec+estimated_delta;
/* Fix prec */
mpfr_set_prec (tmp, Prec);
mpfr_set_prec (arcs, Prec);
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 (arcs, tmp, GMP_RNDN);
if (mpfr_can_round (arcs, realprec, GMP_RNDN, GMP_RNDZ,
MPFR_PREC(asin) + (rnd_mode == GMP_RNDN)))
break;
realprec += __gmpfr_ceil_log2 ((double) realprec);
}
inexact = mpfr_set (asin, arcs, rnd_mode);
mpfr_clear (tmp);
mpfr_clear (arcs);
mpfr_clear (xp);
mpfr_restore_emin_emax ();
return mpfr_check_range (asin, inexact, rnd_mode);
}
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