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 
29 static const long double
30 one=  1.00000000000000000000e+00;
31 
32 #ifdef __i386__
33 /* XXX Work around the fact that gcc truncates long double constants on i386 */
34 static volatile double
35 pi1 =  3.14159265358979311600e+00,	/*  0x1.921fb54442d18p+1  */
36 pi2 =  1.22514845490862001043e-16;	/*  0x1.1a80000000000p-53 */
37 #define	pi	((long double)pi1 + pi2)
38 #else
39 static const long double
40 pi =  3.14159265358979323846264338327950280e+00L;
41 #endif
42 
43 long double
acosl(long double x)44 acosl(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