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