1 /* $OpenBSD: e_asinl.c,v 1.2 2016/09/12 19:47:02 guenther Exp $ */
2 /* @(#)e_asin.c 1.3 95/01/18 */
3 /* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */
4 /*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15 /*
16 * See comments in e_asin.c.
17 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
18 * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
19 */
20
21 #include <float.h>
22 #include <math.h>
23
24 #include "invtrig.h"
25 #include "math_private.h"
26
27 #ifdef EXT_IMPLICIT_NBIT
28 #define LDBL_NBIT 0
29 #else /* EXT_IMPLICIT_NBIT */
30 #define LDBL_NBIT 0x80000000
31 #endif /* EXT_IMPLICIT_NBIT */
32
33 static const long double
34 one = 1.00000000000000000000e+00,
35 huge = 1.000e+300;
36
37 long double
asinl(long double x)38 asinl(long double x)
39 {
40 union {
41 long double e;
42 struct ieee_ext bits;
43 } u;
44 long double t=0.0,w,p,q,c,r,s;
45 int16_t expsign, expt;
46 u.e = x;
47 expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp;
48 expt = expsign & 0x7fff;
49 if(expt >= BIAS) { /* |x|>= 1 */
50 if(expt==BIAS && ((u.bits.ext_frach&~LDBL_NBIT)
51 #ifdef EXT_FRACHMBITS
52 | u.bits.ext_frachm
53 #endif /* EXT_FRACHMBITS */
54 #ifdef EXT_FRACLMBITS
55 | u.bits.ext_fraclm
56 #endif /* EXT_FRACLMBITS */
57 | u.bits.ext_fracl)==0)
58 /* asin(1)=+-pi/2 with inexact */
59 return x*pio2_hi+x*pio2_lo;
60 return (x-x)/(x-x); /* asin(|x|>1) is NaN */
61 } else if (expt<BIAS-1) { /* |x|<0.5 */
62 if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */
63 if(huge+x>one) return x;/* return x with inexact if x!=0*/
64 }
65 t = x*x;
66 p = P(t);
67 q = Q(t);
68 w = p/q;
69 return x+x*w;
70 }
71 /* 1> |x|>= 0.5 */
72 w = one-fabsl(x);
73 t = w*0.5;
74 p = P(t);
75 q = Q(t);
76 s = sqrtl(t);
77 #ifdef EXT_FRACHMBITS
78 if((((uint64_t)u.bits.ext_frach << EXT_FRACHMBITS)
79 | u.bits.ext_frachm) >= THRESH) {
80 /* if |x| is close to 1 */
81 #else /* EXT_FRACHMBITS */
82 if(u.bits.ext_frach>=THRESH) { /* if |x| is close to 1 */
83 #endif /* EXT_FRACHMBITS */
84 w = p/q;
85 t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
86 } else {
87 u.e = s;
88 u.bits.ext_fracl = 0;
89 #ifdef EXT_FRACLMBITS
90 u.bits.ext_fraclm = 0;
91 #endif /* EXT_FRACLMBITS */
92 w = u.e;
93 c = (t-w*w)/(s+w);
94 r = p/q;
95 p = 2.0*s*r-(pio2_lo-2.0*c);
96 q = pio4_hi-2.0*w;
97 t = pio4_hi-(p-q);
98 }
99 if(expsign>0) return t; else return -t;
100 }
101 DEF_STD(asinl);
102