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 ANSI_SYNOPSIS
24 	#include <math.h>
25 	double asinh(double <[x]>);
26 	float asinhf(float <[x]>);
27 
28 TRAD_SYNOPSIS
29 	#include <math.h>
30 	double asinh(<[x]>)
31 	double <[x]>;
32 
33 	float asinhf(<[x]>)
34 	float <[x]>;
35 
36 DESCRIPTION
37 <<asinh>> calculates the inverse hyperbolic sine of <[x]>.
38 <<asinh>> is defined as
39 @ifnottex
40 . sgn(<[x]>) * log(abs(<[x]>) + sqrt(1+<[x]>*<[x]>))
41 @end ifnottex
42 @tex
43 $$sign(x) \times ln\Bigl(|x| + \sqrt{1+x^2}\Bigr)$$
44 @end tex
45 
46 <<asinhf>> is identical, other than taking and returning floats.
47 
48 RETURNS
49 <<asinh>> and <<asinhf>> return the calculated value.
50 
51 PORTABILITY
52 Neither <<asinh>> nor <<asinhf>> are ANSI C.
53 
54 */
55 
56 /* asinh(x)
57  * Method :
58  *	Based on
59  *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
60  *	we have
61  *	asinh(x) := x  if  1+x*x=1,
62  *		 := sign(x)*(log(x)+ln2)) for large |x|, else
63  *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
64  *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
65  */
66 
67 #include "fdlibm.h"
68 
69 #ifndef _DOUBLE_IS_32BITS
70 
71 #ifdef __STDC__
72 static const double
73 #else
74 static double
75 #endif
76 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
77 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
78 huge=  1.00000000000000000000e+300;
79 
80 #ifdef __STDC__
asinh(double x)81 	double asinh(double x)
82 #else
83 	double asinh(x)
84 	double x;
85 #endif
86 {
87 	double t,w;
88 	__int32_t hx,ix;
89 	GET_HIGH_WORD(hx,x);
90 	ix = hx&0x7fffffff;
91 	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
92 	if(ix< 0x3e300000) {	/* |x|<2**-28 */
93 	    if(huge+x>one) return x;	/* return x inexact except 0 */
94 	}
95 	if(ix>0x41b00000) {	/* |x| > 2**28 */
96 	    w = __ieee754_log(fabs(x))+ln2;
97 	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
98 	    t = fabs(x);
99 	    w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
100 	} else {		/* 2.0 > |x| > 2**-28 */
101 	    t = x*x;
102 	    w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
103 	}
104 	if(hx>0) return w; else return -w;
105 }
106 
107 #endif /* _DOUBLE_IS_32BITS */
108