1
2 /* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /*
15 * See comments in e_acos.c.
16 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
17 */
18
19 #include <float.h>
20
21 #include "invtrig.h"
22 #include "math.h"
23 #include "math_private.h"
24
25 static const long double
26 one= 1.00000000000000000000e+00;
27
28 #ifdef __i386__
29 /* XXX Work around the fact that gcc truncates long double constants on i386 */
30 static volatile double
31 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
32 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
33 #define pi ((long double)pi1 + pi2)
34 #else
35 static const long double
36 pi = 3.14159265358979323846264338327950280e+00L;
37 #endif
38
39 long double
acosl(long double x)40 acosl(long double x)
41 {
42 union IEEEl2bits u;
43 long double z,p,q,r,w,s,c,df;
44 int16_t expsign, expt;
45 u.e = x;
46 expsign = u.xbits.expsign;
47 expt = expsign & 0x7fff;
48 if(expt >= BIAS) { /* |x| >= 1 */
49 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
50 if (expsign>0) return 0.0; /* acos(1) = 0 */
51 else return pi+2.0*pio2_lo; /* acos(-1)= pi */
52 }
53 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
54 }
55 if(expt<BIAS-1) { /* |x| < 0.5 */
56 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
57 z = x*x;
58 p = P(z);
59 q = Q(z);
60 r = p/q;
61 return pio2_hi - (x - (pio2_lo-x*r));
62 } else if (expsign<0) { /* x < -0.5 */
63 z = (one+x)*0.5;
64 p = P(z);
65 q = Q(z);
66 s = sqrtl(z);
67 r = p/q;
68 w = r*s-pio2_lo;
69 return pi - 2.0*(s+w);
70 } else { /* x > 0.5 */
71 z = (one-x)*0.5;
72 s = sqrtl(z);
73 u.e = s;
74 u.bits.manl = 0;
75 df = u.e;
76 c = (z-df*df)/(s+df);
77 p = P(z);
78 q = Q(z);
79 r = p/q;
80 w = r*s+c;
81 return 2.0*(df+w);
82 }
83 }
84