1
2/* @(#)e_acos.c 1.3 95/01/18 */
3/* FreeBSD: head/lib/msun/src/e_acos.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_acos.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;
31
32#ifdef __i386__
33/* XXX Work around the fact that gcc truncates long double constants on i386 */
34static volatile double
35pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
36pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
37#define	pi	((long double)pi1 + pi2)
38#else
39static const long double
40pi =  3.14159265358979323846264338327950280e+00L;
41#endif
42
43long double
44acosl(long double x)
45{
46	union IEEEl2bits u;
47	long double z,p,q,r,w,s,c,df;
48	int16_t expsign, expt;
49	u.e = x;
50	expsign = u.xbits.expsign;
51	expt = expsign & 0x7fff;
52	if(expt >= BIAS) {	/* |x| >= 1 */
53	    if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
54		if (expsign>0) return 0.0;	/* acos(1) = 0  */
55		else return pi+2.0*pio2_lo;	/* acos(-1)= pi */
56	    }
57	    return (x-x)/(x-x);		/* acos(|x|>1) is NaN */
58	}
59	if(expt<BIAS-1) {	/* |x| < 0.5 */
60	    if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
61	    z = x*x;
62	    p = P(z);
63	    q = Q(z);
64	    r = p/q;
65	    return pio2_hi - (x - (pio2_lo-x*r));
66	} else  if (expsign<0) {	/* x < -0.5 */
67	    z = (one+x)*0.5;
68	    p = P(z);
69	    q = Q(z);
70	    s = sqrtl(z);
71	    r = p/q;
72	    w = r*s-pio2_lo;
73	    return pi - 2.0*(s+w);
74	} else {			/* x > 0.5 */
75	    z = (one-x)*0.5;
76	    s = sqrtl(z);
77	    u.e = s;
78	    u.bits.manl = 0;
79	    df = u.e;
80	    c  = (z-df*df)/(s+df);
81	    p = P(z);
82	    q = Q(z);
83	    r = p/q;
84	    w = r*s+c;
85	    return 2.0*(df+w);
86	}
87}
88