1
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#include <sys/cdefs.h>
16__FBSDID("$FreeBSD$");
17
18/*
19 * See comments in e_asin.c.
20 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
21 */
22
23#include <float.h>
24
25#include "invtrig.h"
26#include "math.h"
27#include "math_private.h"
28
29static const long double
30one =  1.00000000000000000000e+00,
31huge = 1.000e+300;
32
33long double
34asinl(long double x)
35{
36	union IEEEl2bits u;
37	long double t=0.0,w,p,q,c,r,s;
38	int16_t expsign, expt;
39	u.e = x;
40	expsign = u.xbits.expsign;
41	expt = expsign & 0x7fff;
42	if(expt >= BIAS) {		/* |x|>= 1 */
43		if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0)
44		    /* asin(1)=+-pi/2 with inexact */
45		    return x*pio2_hi+x*pio2_lo;
46	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */
47	} else if (expt<BIAS-1) {	/* |x|<0.5 */
48	    if(expt<ASIN_LINEAR) {	/* if |x| is small, asinl(x)=x */
49		if(huge+x>one) return x;/* return x with inexact if x!=0*/
50	    }
51	    t = x*x;
52	    p = P(t);
53	    q = Q(t);
54	    w = p/q;
55	    return x+x*w;
56	}
57	/* 1> |x|>= 0.5 */
58	w = one-fabsl(x);
59	t = w*0.5;
60	p = P(t);
61	q = Q(t);
62	s = sqrtl(t);
63	if(u.bits.manh>=THRESH) { 	/* if |x| is close to 1 */
64	    w = p/q;
65	    t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
66	} else {
67	    u.e = s;
68	    u.bits.manl = 0;
69	    w = u.e;
70	    c  = (t-w*w)/(s+w);
71	    r  = p/q;
72	    p  = 2.0*s*r-(pio2_lo-2.0*c);
73	    q  = pio4_hi-2.0*w;
74	    t  = pio4_hi-(p-q);
75	}
76	if(expsign>0) return t; else return -t;
77}
78