1/* mpfr_asin -- arc-sinus of a floating-point number
2
3Copyright 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc.
4Contributed by the AriC and Caramel projects, INRIA.
5
6This file is part of the GNU MPFR Library.
7
8The GNU MPFR Library is free software; you can redistribute it and/or modify
9it under the terms of the GNU Lesser General Public License as published by
10the Free Software Foundation; either version 3 of the License, or (at your
11option) any later version.
12
13The GNU MPFR Library is distributed in the hope that it will be useful, but
14WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
15or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
16License for more details.
17
18You should have received a copy of the GNU Lesser General Public License
19along with the GNU MPFR Library; see the file COPYING.LESSER.  If not, see
20http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
2151 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
22
23#include "mpfr-impl.h"
24
25int
26mpfr_asin (mpfr_ptr asin, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
27{
28  mpfr_t xp;
29  int compared, inexact;
30  mpfr_prec_t prec;
31  mpfr_exp_t xp_exp;
32  MPFR_SAVE_EXPO_DECL (expo);
33  MPFR_ZIV_DECL (loop);
34
35  MPFR_LOG_FUNC (
36    ("x[%Pu]=%.*Rg rnd=%d", mpfr_get_prec (x), mpfr_log_prec, x, rnd_mode),
37    ("asin[%Pu]=%.*Rg inexact=%d", mpfr_get_prec (asin), mpfr_log_prec, asin,
38     inexact));
39
40  /* Special cases */
41  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
42    {
43      if (MPFR_IS_NAN (x) || MPFR_IS_INF (x))
44        {
45          MPFR_SET_NAN (asin);
46          MPFR_RET_NAN;
47        }
48      else /* x = 0 */
49        {
50          MPFR_ASSERTD (MPFR_IS_ZERO (x));
51          MPFR_SET_ZERO (asin);
52          MPFR_SET_SAME_SIGN (asin, x);
53          MPFR_RET (0); /* exact result */
54        }
55    }
56
57  /* asin(x) = x + x^3/6 + ... so the error is < 2^(3*EXP(x)-2) */
58  MPFR_FAST_COMPUTE_IF_SMALL_INPUT (asin, x, -2 * MPFR_GET_EXP (x), 2, 1,
59                                    rnd_mode, {});
60
61  /* Set x_p=|x| (x is a normal number) */
62  mpfr_init2 (xp, MPFR_PREC (x));
63  inexact = mpfr_abs (xp, x, MPFR_RNDN);
64  MPFR_ASSERTD (inexact == 0);
65
66  compared = mpfr_cmp_ui (xp, 1);
67
68  MPFR_SAVE_EXPO_MARK (expo);
69
70  if (MPFR_UNLIKELY (compared >= 0))
71    {
72      mpfr_clear (xp);
73      if (compared > 0)                  /* asin(x) = NaN for |x| > 1 */
74        {
75          MPFR_SAVE_EXPO_FREE (expo);
76          MPFR_SET_NAN (asin);
77          MPFR_RET_NAN;
78        }
79      else                              /* x = 1 or x = -1 */
80        {
81          if (MPFR_IS_POS (x)) /* asin(+1) = Pi/2 */
82            inexact = mpfr_const_pi (asin, rnd_mode);
83          else /* asin(-1) = -Pi/2 */
84            {
85              inexact = -mpfr_const_pi (asin, MPFR_INVERT_RND(rnd_mode));
86              MPFR_CHANGE_SIGN (asin);
87            }
88          mpfr_div_2ui (asin, asin, 1, rnd_mode);
89        }
90    }
91  else
92    {
93      /* Compute exponent of 1 - ABS(x) */
94      mpfr_ui_sub (xp, 1, xp, MPFR_RNDD);
95      MPFR_ASSERTD (MPFR_GET_EXP (xp) <= 0);
96      MPFR_ASSERTD (MPFR_GET_EXP (x) <= 0);
97      xp_exp = 2 - MPFR_GET_EXP (xp);
98
99      /* Set up initial prec */
100      prec = MPFR_PREC (asin) + 10 + xp_exp;
101
102      /* use asin(x) = atan(x/sqrt(1-x^2)) */
103      MPFR_ZIV_INIT (loop, prec);
104      for (;;)
105        {
106          mpfr_set_prec (xp, prec);
107          mpfr_sqr (xp, x, MPFR_RNDN);
108          mpfr_ui_sub (xp, 1, xp, MPFR_RNDN);
109          mpfr_sqrt (xp, xp, MPFR_RNDN);
110          mpfr_div (xp, x, xp, MPFR_RNDN);
111          mpfr_atan (xp, xp, MPFR_RNDN);
112          if (MPFR_LIKELY (MPFR_CAN_ROUND (xp, prec - xp_exp,
113                                           MPFR_PREC (asin), rnd_mode)))
114            break;
115          MPFR_ZIV_NEXT (loop, prec);
116        }
117      MPFR_ZIV_FREE (loop);
118      inexact = mpfr_set (asin, xp, rnd_mode);
119
120      mpfr_clear (xp);
121    }
122
123  MPFR_SAVE_EXPO_FREE (expo);
124  return mpfr_check_range (asin, inexact, rnd_mode);
125}
126