e_asinl.c revision 1.5 
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
47static const long double
48one =  1.00000000000000000000e+00,
49huge = 1.000e+300;
50
51long double
52asinl(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