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