1 /* $OpenBSD: e_acosl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $ */
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 * See comments in e_acos.c.
17 * Converted to long double by David Schultz <das@FreeBSD.ORG>.
18 * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
19 */
20
21 #include <float.h>
22 #include <math.h>
23
24 #include "invtrig.h"
25 #include "math_private.h"
26
27 #ifdef EXT_IMPLICIT_NBIT
28 #define LDBL_NBIT 0
29 #else /* EXT_IMPLICIT_NBIT */
30 #define LDBL_NBIT 0x80000000
31 #endif /* EXT_IMPLICIT_NBIT */
32
33 static const long double
34 one= 1.00000000000000000000e+00;
35
36 #if defined(__amd64__) || defined(__i386__)
37 /* XXX Work around the fact that gcc truncates long double constants on i386 */
38 static volatile double
39 pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
40 pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
41 #define pi ((long double)pi1 + pi2)
42 #else
43 static const long double
44 pi = 3.14159265358979323846264338327950280e+00L;
45 #endif
46
47 long double
acosl(long double x)48 acosl(long double x)
49 {
50 union {
51 long double e;
52 struct ieee_ext bits;
53 } u;
54 long double z,p,q,r,w,s,c,df;
55 int16_t expsign, expt;
56 u.e = x;
57 expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp;
58 expt = expsign & 0x7fff;
59 if(expt >= BIAS) { /* |x| >= 1 */
60 if(expt==BIAS && ((u.bits.ext_frach&~LDBL_NBIT)
61 #ifdef EXT_FRACHMBITS
62 | u.bits.ext_frachm
63 #endif /* EXT_FRACHMBITS */
64 #ifdef EXT_FRACLMBITS
65 | u.bits.ext_fraclm
66 #endif /* EXT_FRACLMBITS */
67 | u.bits.ext_fracl)==0) {
68 if (expsign>0) return 0.0; /* acos(1) = 0 */
69 else return pi+2.0*pio2_lo; /* acos(-1)= pi */
70 }
71 return (x-x)/(x-x); /* acos(|x|>1) is NaN */
72 }
73 if(expt<BIAS-1) { /* |x| < 0.5 */
74 if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
75 z = x*x;
76 p = P(z);
77 q = Q(z);
78 r = p/q;
79 return pio2_hi - (x - (pio2_lo-x*r));
80 } else if (expsign<0) { /* x < -0.5 */
81 z = (one+x)*0.5;
82 p = P(z);
83 q = Q(z);
84 s = sqrtl(z);
85 r = p/q;
86 w = r*s-pio2_lo;
87 return pi - 2.0*(s+w);
88 } else { /* x > 0.5 */
89 z = (one-x)*0.5;
90 s = sqrtl(z);
91 u.e = s;
92 u.bits.ext_fracl = 0;
93 #ifdef EXT_FRACLMBITS
94 u.bits.ext_fraclm = 0;
95 #endif /* EXT_FRACLMBITS */
96 df = u.e;
97 c = (z-df*df)/(s+df);
98 p = P(z);
99 q = Q(z);
100 r = p/q;
101 w = r*s+c;
102 return 2.0*(df+w);
103 }
104 }
105