1 |
|
|
/* @(#)e_acosh.c 5.1 93/09/24 */ |
2 |
|
|
/* |
3 |
|
|
* ==================================================== |
4 |
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 |
|
|
* |
6 |
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business. |
7 |
|
|
* Permission to use, copy, modify, and distribute this |
8 |
|
|
* software is freely granted, provided that this notice |
9 |
|
|
* is preserved. |
10 |
|
|
* ==================================================== |
11 |
|
|
*/ |
12 |
|
|
|
13 |
|
|
/* acoshl(x) |
14 |
|
|
* Method : |
15 |
|
|
* Based on |
16 |
|
|
* acoshl(x) = logl [ x + sqrtl(x*x-1) ] |
17 |
|
|
* we have |
18 |
|
|
* acoshl(x) := logl(x)+ln2, if x is large; else |
19 |
|
|
* acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else |
20 |
|
|
* acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1. |
21 |
|
|
* |
22 |
|
|
* Special cases: |
23 |
|
|
* acoshl(x) is NaN with signal if x<1. |
24 |
|
|
* acoshl(NaN) is NaN without signal. |
25 |
|
|
*/ |
26 |
|
|
|
27 |
|
|
#include <math.h> |
28 |
|
|
|
29 |
|
|
#include "math_private.h" |
30 |
|
|
|
31 |
|
|
static const long double |
32 |
|
|
one = 1.0, |
33 |
|
|
ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */ |
34 |
|
|
|
35 |
|
|
long double |
36 |
|
|
acoshl(long double x) |
37 |
|
|
{ |
38 |
|
|
long double t; |
39 |
|
|
u_int32_t se,i0,i1; |
40 |
|
|
GET_LDOUBLE_WORDS(se,i0,i1,x); |
41 |
|
|
if(se<0x3fff || se & 0x8000) { /* x < 1 */ |
42 |
|
|
return (x-x)/(x-x); |
43 |
|
|
} else if(se >=0x401d) { /* x > 2**30 */ |
44 |
|
|
if(se >=0x7fff) { /* x is inf of NaN */ |
45 |
|
|
return x+x; |
46 |
|
|
} else |
47 |
|
|
return logl(x)+ln2; /* acoshl(huge)=logl(2x) */ |
48 |
|
|
} else if(((se-0x3fff)|i0|i1)==0) { |
49 |
|
|
return 0.0; /* acosh(1) = 0 */ |
50 |
|
|
} else if (se > 0x4000) { /* 2**28 > x > 2 */ |
51 |
|
|
t=x*x; |
52 |
|
|
return logl(2.0*x-one/(x+sqrtl(t-one))); |
53 |
|
|
} else { /* 1<x<2 */ |
54 |
|
|
t = x-one; |
55 |
|
|
return log1pl(t+sqrtl(2.0*t+t*t)); |
56 |
|
|
} |
57 |
|
|
} |