1 | |
---|
2 | /* @(#)e_acosh.c 5.1 93/09/24 */ |
---|
3 | |
---|
4 | /* |
---|
5 | FUNCTION |
---|
6 | <<acosh>>, <<acoshf>>---inverse hyperbolic cosine |
---|
7 | |
---|
8 | INDEX |
---|
9 | acosh |
---|
10 | INDEX |
---|
11 | acoshf |
---|
12 | |
---|
13 | SYNOPSIS |
---|
14 | #include <math.h> |
---|
15 | double acosh(double <[x]>); |
---|
16 | float acoshf(float <[x]>); |
---|
17 | |
---|
18 | DESCRIPTION |
---|
19 | <<acosh>> calculates the inverse hyperbolic cosine of <[x]>. |
---|
20 | <<acosh>> is defined as |
---|
21 | @ifnottex |
---|
22 | . log(<[x]> + sqrt(<[x]>*<[x]>-1)) |
---|
23 | @end ifnottex |
---|
24 | @tex |
---|
25 | $$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$ |
---|
26 | @end tex |
---|
27 | |
---|
28 | <[x]> must be a number greater than or equal to 1. |
---|
29 | |
---|
30 | <<acoshf>> is identical, other than taking and returning floats. |
---|
31 | |
---|
32 | RETURNS |
---|
33 | <<acosh>> and <<acoshf>> return the calculated value. If <[x]> |
---|
34 | less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>. |
---|
35 | |
---|
36 | You can change the error-handling behavior with the non-ANSI |
---|
37 | <<matherr>> function. |
---|
38 | |
---|
39 | PORTABILITY |
---|
40 | Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended |
---|
41 | for portable programs. |
---|
42 | |
---|
43 | |
---|
44 | QUICKREF |
---|
45 | ansi svid posix rentrant |
---|
46 | acos n,n,n,m |
---|
47 | acosf n,n,n,m |
---|
48 | |
---|
49 | MATHREF |
---|
50 | acosh, NAN, arg,DOMAIN,EDOM |
---|
51 | acosh, < 1.0, NAN,DOMAIN,EDOM |
---|
52 | acosh, >=1.0, acosh(arg),,, |
---|
53 | |
---|
54 | MATHREF |
---|
55 | acoshf, NAN, arg,DOMAIN,EDOM |
---|
56 | acoshf, < 1.0, NAN,DOMAIN,EDOM |
---|
57 | acoshf, >=1.0, acosh(arg),,, |
---|
58 | |
---|
59 | */ |
---|
60 | |
---|
61 | /* |
---|
62 | * ==================================================== |
---|
63 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
---|
64 | * |
---|
65 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
---|
66 | * Permission to use, copy, modify, and distribute this |
---|
67 | * software is freely granted, provided that this notice |
---|
68 | * is preserved. |
---|
69 | * ==================================================== |
---|
70 | * |
---|
71 | */ |
---|
72 | |
---|
73 | /* acosh(x) |
---|
74 | * Method : |
---|
75 | * Based on |
---|
76 | * acosh(x) = log [ x + sqrt(x*x-1) ] |
---|
77 | * we have |
---|
78 | * acosh(x) := log(x)+ln2, if x is large; else |
---|
79 | * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else |
---|
80 | * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. |
---|
81 | * |
---|
82 | * Special cases: |
---|
83 | * acosh(x) is NaN with signal if x<1. |
---|
84 | * acosh(NaN) is NaN without signal. |
---|
85 | */ |
---|
86 | |
---|
87 | #include "fdlibm.h" |
---|
88 | |
---|
89 | #ifndef _DOUBLE_IS_32BITS |
---|
90 | |
---|
91 | #ifdef __STDC__ |
---|
92 | static const double |
---|
93 | #else |
---|
94 | static double |
---|
95 | #endif |
---|
96 | one = 1.0, |
---|
97 | ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ |
---|
98 | |
---|
99 | #ifdef __STDC__ |
---|
100 | double acosh(double x) |
---|
101 | #else |
---|
102 | double acosh(x) |
---|
103 | double x; |
---|
104 | #endif |
---|
105 | { |
---|
106 | double t; |
---|
107 | __int32_t hx; |
---|
108 | __uint32_t lx; |
---|
109 | EXTRACT_WORDS(hx,lx,x); |
---|
110 | if(hx<0x3ff00000) { /* x < 1 */ |
---|
111 | return (x-x)/(x-x); |
---|
112 | } else if(hx >=0x41b00000) { /* x > 2**28 */ |
---|
113 | if(hx >=0x7ff00000) { /* x is inf of NaN */ |
---|
114 | return x+x; |
---|
115 | } else |
---|
116 | return log(x)+ln2; /* acosh(huge)=log(2x) */ |
---|
117 | } else if(((hx-0x3ff00000)|lx)==0) { |
---|
118 | return 0.0; /* acosh(1) = 0 */ |
---|
119 | } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ |
---|
120 | t=x*x; |
---|
121 | return log(2.0*x-one/(x+sqrt(t-one))); |
---|
122 | } else { /* 1<x<2 */ |
---|
123 | t = x-one; |
---|
124 | return log1p(t+sqrt(2.0*t+t*t)); |
---|
125 | } |
---|
126 | } |
---|
127 | |
---|
128 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
---|