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 //__FBSDID("$FreeBSD: src/lib/msun/src/e_acosl.c,v 1.2 2008/08/02 03:56:22 das Exp $");
16
17 /*
18 * See comments in e_acos.c.
19 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
20 */
21
22
23 #include "e_rem_pio2l.h"
24
25 #include "invtrig.h"
26
27 static const long double
28 one= 1.00000000000000000000e+00L;
29
30 #ifdef __i386__
31 /* XXX Work around the fact that gcc truncates long double constants on i386 */
32 static volatile double
33 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
34 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
35 #define pi ((long double)pi1 + (long double)pi2)
36 #else
37 static const long double
38 pi = 3.14159265358979323846264338327950280e+00L;
39 #endif
40
41 long double
acosl(long double x)42 acosl(long double x)
43 {
44 union IEEEl2bits u;
45 long double z,p,q,r,w,s,c,df;
46 int16_t expsign, expt;
47 u.e = x;
48 expsign = u.xbits.expsign;
49 expt = expsign & 0x7fff;
50 if(expt >= BIAS) { /* |x| >= 1 */
51 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
52 if (expsign>0) return 0.0L; /* acos(1) = 0 */
53 else return pi+2.0L*pio2_lo; /* acos(-1)= pi */
54 }
55 return __math_invalidl(x); /* acos(|x|>1) is NaN */
56 }
57 if(expt<BIAS-1) { /* |x| < 0.5 */
58 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
59 z = x*x;
60 p = P(z);
61 q = Q(z);
62 r = p/q;
63 return pio2_hi - (x - (pio2_lo-x*r));
64 } else if (expsign<0) { /* x < -0.5 */
65 z = (one+x)*0.5L;
66 p = P(z);
67 q = Q(z);
68 s = sqrtl(z);
69 r = p/q;
70 w = r*s-pio2_lo;
71 return pi - 2.0L*(s+w);
72 } else { /* x > 0.5 */
73 z = (one-x)*0.5L;
74 s = sqrtl(z);
75 u.e = s;
76 u.bits.manl = 0;
77 df = u.e;
78 c = (z-df*df)/(s+df);
79 p = P(z);
80 q = Q(z);
81 r = p/q;
82 w = r*s+c;
83 return 2.0L*(df+w);
84 }
85 }
86
