1 /* $NetBSD: e_asinl.c,v 1.5 2024/06/09 13:35:38 riastradh Exp $ */
2
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 #include <sys/cdefs.h>
16 __RCSID("$NetBSD: e_asinl.c,v 1.5 2024/06/09 13:35:38 riastradh Exp $");
17
18 /*
19 * See comments in e_asin.c.
20 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
21 */
22
23 #include "namespace.h"
24
25 #include <float.h>
26 #include <machine/ieee.h>
27
28 #include "math.h"
29 #include "math_private.h"
30
31 #ifdef __HAVE_LONG_DOUBLE
32
33 __weak_alias(asinl, _asinl)
34
35 #if LDBL_MANT_DIG == 64
36 #include "../ld80/invtrig.h"
37 #elif LDBL_MANT_DIG == 113
38 #include "../ld128/invtrig.h"
39 #else
40 #error "Unsupported long double format"
41 #endif
42
43 #ifdef LDBL_IMPLICIT_NBIT
44 #define LDBL_NBIT 0
45 #endif
46
47 static const long double
48 one = 1.00000000000000000000e+00,
49 huge = 1.000e+300;
50
51 long double
asinl(long double x)52 asinl(long double x)
53 {
54 union ieee_ext_u u;
55 long double t=0.0,w,p,q,c,r,s;
56 int16_t expsign, expt;
57 u.extu_ld = x;
58 expsign = GET_EXPSIGN(&u);
59 expt = expsign & 0x7fff;
60 if(expt >= BIAS) { /* |x|>= 1 */
61 if(expt==BIAS && ((u.extu_frach&~LDBL_NBIT)|u.extu_fracl)==0)
62 /* asin(1)=+-pi/2 with inexact */
63 return x*pio2_hi+x*pio2_lo;
64 return (x-x)/(x-x); /* asin(|x|>1) is NaN */
65 } else if (expt<BIAS-1) { /* |x|<0.5 */
66 if(expt<ASIN_LINEAR) { /* if |x| is small, asinl(x)=x */
67 if(huge+x>one) return x;/* return x with inexact if x!=0*/
68 }
69 t = x*x;
70 p = P(t);
71 q = Q(t);
72 w = p/q;
73 return x+x*w;
74 }
75 /* 1> |x|>= 0.5 */
76 w = one-fabsl(x);
77 t = w*0.5;
78 p = P(t);
79 q = Q(t);
80 s = sqrtl(t);
81 if(u.extu_frach>=THRESH) { /* if |x| is close to 1 */
82 w = p/q;
83 t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
84 } else {
85 u.extu_ld = s;
86 u.extu_fracl = 0;
87 w = u.extu_ld;
88 c = (t-w*w)/(s+w);
89 r = p/q;
90 p = 2.0*s*r-(pio2_lo-2.0*c);
91 q = pio4_hi-2.0*w;
92 t = pio4_hi-(p-q);
93 }
94 if(expsign>0) return t; else return -t;
95 }
96 #endif
97