1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
|
/* @(#)e_acos.c 1.3 95/01/18 */
/* FreeBSD: head/lib/msun/src/e_acos.c 176451 2008-02-22 02:30:36Z das */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* See comments in e_acos.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include <float.h>
#include "invtrig.h"
#include "math.h"
#include "math_private.h"
static const long double
one= 1.00000000000000000000e+00;
#ifdef __i386__
/* XXX Work around the fact that gcc truncates long double constants on i386 */
static volatile double
pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
#define pi ((long double)pi1 + pi2)
#else
static const long double
pi = 3.14159265358979323846264338327950280e+00L;
#endif
long double
acosl(long double x)
{
union IEEEl2bits u;
long double z,p,q,r,w,s,c,df;
int16_t expsign, expt;
u.e = x;
expsign = u.xbits.expsign;
expt = expsign & 0x7fff;
if(expt >= BIAS) { /* |x| >= 1 */
if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0) {
if (expsign>0) return 0.0; /* acos(1) = 0 */
else return pi+2.0*pio2_lo; /* acos(-1)= pi */
}
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(expt<BIAS-1) { /* |x| < 0.5 */
if(expt<ACOS_CONST) return pio2_hi+pio2_lo;/*x tiny: acosl=pi/2*/
z = x*x;
p = P(z);
q = Q(z);
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (expsign<0) { /* x < -0.5 */
z = (one+x)*0.5;
p = P(z);
q = Q(z);
s = sqrtl(z);
r = p/q;
w = r*s-pio2_lo;
return pi - 2.0*(s+w);
} else { /* x > 0.5 */
z = (one-x)*0.5;
s = sqrtl(z);
u.e = s;
u.bits.manl = 0;
df = u.e;
c = (z-df*df)/(s+df);
p = P(z);
q = Q(z);
r = p/q;
w = r*s+c;
return 2.0*(df+w);
}
}
|
