1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
/* 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;
int compared, inexact;
mp_prec_t prec;
mp_exp_t xp_exp;
MPFR_SAVE_EXPO_DECL (expo);
/* 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_RET (0); /* exact result */
}
}
/* Set x_p=|x| (x is a normal number) */
mpfr_init2 (xp, MPFR_PREC (x));
inexact = mpfr_abs (xp, x, GMP_RNDN);
MPFR_ASSERTD (inexact == 0);
compared = mpfr_cmp_ui (xp, 1);
if (MPFR_UNLIKELY (compared >= 0))
{
mpfr_clear (xp);
if (compared > 0) /* asin(x) = NaN for |x| > 1 */
{
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); /* May underflow */
return inexact;
}
}
MPFR_SAVE_EXPO_MARK (expo);
/* Compute exponent of 1 - ABS(x) */
mpfr_ui_sub (xp, 1, xp, GMP_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;
/* If x ~ 2^-N, asin(x) ~ x + x^3/6
If Prec < 2*N, we can't round since x^3/6 won't be count. */
if (MPFR_PREC (asin) >= MPFR_PREC (x)
&& prec <= -2*MPFR_GET_EXP (x) + 10)
prec = -2*MPFR_GET_EXP (x) + 10;
/* use asin(x) = atan(x/sqrt(1-x^2)) */
for (;;)
{
mpfr_set_prec (xp, prec);
mpfr_sqr (xp, x, GMP_RNDN);
mpfr_ui_sub (xp, 1, xp, GMP_RNDN);
mpfr_sqrt (xp, xp, GMP_RNDN);
mpfr_div (xp, x, xp, GMP_RNDN);
mpfr_atan (xp, xp, GMP_RNDN);
if (mpfr_can_round (xp, prec - xp_exp, GMP_RNDN, GMP_RNDZ,
MPFR_PREC (asin) + (rnd_mode == GMP_RNDN)))
break;
prec += BITS_PER_MP_LIMB;
}
inexact = mpfr_set (asin, xp, rnd_mode);
mpfr_clear (xp);
MPFR_SAVE_EXPO_FREE (expo);
return mpfr_check_range (asin, inexact, rnd_mode);
}
|
