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/* mpfr_asin -- arc-sinus of a floating-point number
Copyright 2001-2021 Free Software Foundation, Inc.
Contributed by the AriC and Caramba projects, INRIA.
This file is part of the GNU MPFR Library.
The GNU 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 3 of the License, or (at your
option) any later version.
The GNU 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 GNU MPFR Library; see the file COPYING.LESSER. If not, see
https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include "mpfr-impl.h"
int
mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
mpfr_t xp;
int compared, inexact;
mpfr_prec_t prec;
mpfr_exp_t xp_exp;
MPFR_SAVE_EXPO_DECL (expo);
MPFR_ZIV_DECL (loop);
MPFR_LOG_FUNC (
("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
("asin[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (asin), mpfr_log_prec, asin,
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_ZERO (asin);
MPFR_SET_SAME_SIGN (asin, x);
MPFR_RET (0); /* exact result */
}
}
/* asin(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
MPFR_FAST_COMPUTE_IF_SMALL_INPUT (asin, x, -2 * MPFR_GET_EXP (x), 2, 1,
rnd_mode, {});
/* Set x_p=|x| (x is a normal number) */
mpfr_init2 (xp, MPFR_PREC (x));
inexact = mpfr_abs (xp, x, MPFR_RNDN);
MPFR_ASSERTD (inexact == 0);
compared = mpfr_cmp_ui (xp, 1);
MPFR_SAVE_EXPO_MARK (expo);
if (MPFR_UNLIKELY (compared >= 0))
{
mpfr_clear (xp);
if (compared > 0) /* asin(x) = NaN for |x| > 1 */
{
MPFR_SAVE_EXPO_FREE (expo);
MPFR_SET_NAN (asin);
MPFR_RET_NAN;
}
else /* x = 1 or x = -1 */
{
if (MPFR_IS_POS (x)) /* 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_CHANGE_SIGN (asin);
}
mpfr_div_2ui (asin, asin, 1, rnd_mode);
}
}
else
{
/* Compute exponent of 1 - ABS(x) */
mpfr_ui_sub (xp, 1, xp, MPFR_RNDD);
MPFR_ASSERTD (MPFR_GET_EXP (xp) <= 0);
MPFR_ASSERTD (MPFR_GET_EXP (x) <= 0);
xp_exp = 2 - MPFR_GET_EXP (xp);
/* Set up initial prec */
prec = MPFR_PREC (asin) + 10 + xp_exp;
/* use asin(x) = atan(x/sqrt(1-x^2)) */
MPFR_ZIV_INIT (loop, prec);
for (;;)
{
mpfr_set_prec (xp, prec);
mpfr_sqr (xp, x, MPFR_RNDN);
mpfr_ui_sub (xp, 1, xp, MPFR_RNDN);
mpfr_sqrt (xp, xp, MPFR_RNDN);
mpfr_div (xp, x, xp, MPFR_RNDN);
mpfr_atan (xp, xp, MPFR_RNDN);
if (MPFR_LIKELY (MPFR_CAN_ROUND (xp, prec - xp_exp,
MPFR_PREC (asin), rnd_mode)))
break;
MPFR_ZIV_NEXT (loop, prec);
}
MPFR_ZIV_FREE (loop);
inexact = mpfr_set (asin, xp, rnd_mode);
mpfr_clear (xp);
}
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (asin, inexact, rnd_mode);
}
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