e_asinl.c revision 1.1 
1/*	$OpenBSD: e_asinl.c,v 1.1 2008/12/09 20:00:35 martynas 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
33static const long double
34one =  1.00000000000000000000e+00,
35huge = 1.000e+300;
36
37long double
38asinl(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