1
2 /* @(#)s_asinh.c 5.1 93/09/24 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /*
15 FUNCTION
16 <<asinh>>, <<asinhf>>---inverse hyperbolic sine
17
18 INDEX
19 asinh
20 INDEX
21 asinhf
22
23 SYNOPSIS
24 #include <math.h>
25 double asinh(double <[x]>);
26 float asinhf(float <[x]>);
27
28 DESCRIPTION
29 <<asinh>> calculates the inverse hyperbolic sine of <[x]>.
30 <<asinh>> is defined as
31 @ifnottex
32 . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
33 @end ifnottex
34 @tex
35 $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
36 @end tex
37
38 <<asinhf>> is identical, other than taking and returning floats.
39
40 RETURNS
41 <<asinh>> and <<asinhf>> return the calculated value.
42
43 PORTABILITY
44 Neither <<asinh>> nor <<asinhf>> are ANSI C.
45
46 */
47
48 /* asinh(x)
49 * Method :
50 * Based on
51 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
52 * we have
53 * asinh(x) := x if 1+x*x=1,
54 * := sign(x)*(log(x)+ln2)) for large |x|, else
55 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
56 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
57 */
58
59 #include "fdlibm.h"
60
61 #ifdef _NEED_FLOAT64
62
63 static const __float64
64 one = _F_64(1.00000000000000000000e+00), /* 0x3FF00000, 0x00000000 */
65 ln2 = _F_64(6.93147180559945286227e-01), /* 0x3FE62E42, 0xFEFA39EF */
66 huge = _F_64(1.00000000000000000000e+300);
67
68 __float64
asinh64(__float64 x)69 asinh64(__float64 x)
70 {
71 __float64 t, w;
72 __int32_t hx, ix;
73 GET_HIGH_WORD(hx, x);
74 ix = hx & 0x7fffffff;
75 if (ix >= 0x7ff00000)
76 return x + x; /* x is inf or NaN */
77 if (ix < 0x3e300000) { /* |x|<2**-28 */
78 if (huge + x > one)
79 return x; /* return x inexact except 0 */
80 }
81 if (ix > 0x41b00000) { /* |x| > 2**28 */
82 w = log64(fabs64(x)) + ln2;
83 } else if (ix > 0x40000000) { /* 2**28 > |x| > 2.0 */
84 t = fabs64(x);
85 w = log64(_F_64(2.0) * t + one / (sqrt64(x * x + one) + t));
86 } else { /* 2.0 > |x| > 2**-28 */
87 t = x * x;
88 w = log1p64(fabs64(x) + t / (one + sqrt64(one + t)));
89 }
90 if (hx > 0)
91 return w;
92 else
93 return -w;
94 }
95
96 _MATH_ALIAS_d_d(asinh)
97
98 #endif /* _NEED_FLOAT64 */
99
