/
asinl.c
105 lines (99 loc) · 4.5 KB
/
asinl.c
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
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8 :vi │
╚──────────────────────────────────────────────────────────────────────────────╝
│ │
│ Musl Libc │
│ Copyright © 2005-2014 Rich Felker, et al. │
│ │
│ Permission is hereby granted, free of charge, to any person obtaining │
│ a copy of this software and associated documentation files (the │
│ "Software"), to deal in the Software without restriction, including │
│ without limitation the rights to use, copy, modify, merge, publish, │
│ distribute, sublicense, and/or sell copies of the Software, and to │
│ permit persons to whom the Software is furnished to do so, subject to │
│ the following conditions: │
│ │
│ The above copyright notice and this permission notice shall be │
│ included in all copies or substantial portions of the Software. │
│ │
│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
│ │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/tinymath/internal.h"
#include "libc/tinymath/invtrigl.internal.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)
__static_yoink("fdlibm_notice");
__static_yoink("musl_libc_notice");
/* origin: FreeBSD /usr/src/lib/msun/src/e_asinl.c */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* See comments in asin.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#if LDBL_MANT_DIG == 64
#define CLOSETO1(u) (u.i.m>>56 >= 0xf7)
#define CLEARBOTTOM(u) (u.i.m &= -1ULL << 32)
#elif LDBL_MANT_DIG == 113
#define CLOSETO1(u) (u.i.top >= 0xee00)
#define CLEARBOTTOM(u) (u.i.lo = 0)
#endif
/**
* Returns arc sine of 𝑥.
*
* @define atan2(𝑥,sqrt((1-𝑥)*(1+𝑥)))
* @domain -1 ≤ 𝑥 ≤ 1
*/
long double asinl(long double x)
{
union ldshape u = {x};
long double z, r, s;
uint16_t e = u.i.se & 0x7fff;
int sign = u.i.se >> 15;
if (e >= 0x3fff) { /* |x| >= 1 or nan */
/* asin(+-1)=+-pi/2 with inexact */
if (x == 1 || x == -1)
return x*pio2_hi + 0x1p-120f;
return 0/(x-x);
}
if (e < 0x3fff - 1) { /* |x| < 0.5 */
if (e < 0x3fff - (LDBL_MANT_DIG+1)/2) {
/* return x with inexact if x!=0 */
FORCE_EVAL(x + 0x1p120f);
return x;
}
return x + x*__invtrigl_R(x*x);
}
/* 1 > |x| >= 0.5 */
z = (1.0 - fabsl(x))*0.5;
s = sqrtl(z);
r = __invtrigl_R(z);
if (CLOSETO1(u)) {
x = pio2_hi - (2*(s+s*r)-pio2_lo);
} else {
long double f, c;
u.f = s;
CLEARBOTTOM(u);
f = u.f;
c = (z - f*f)/(s + f);
x = 0.5*pio2_hi-(2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f));
}
return sign ? -x : x;
}
#endif /* long double is long */