1/* @(#)s_asinh.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#ifndef lint
14static char rcsid[] = "$FreeBSD: head/lib/msun/src/s_asinh.c 97413 2002-05-28 18:15:04Z alfred $";
15#endif
16
17/* asinh(x)
18 * Method :
19 * Based on
20 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
21 * we have
22 * asinh(x) := x if 1+x*x=1,
23 * := sign(x)*(log(x)+ln2)) for large |x|, else
24 * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
25 * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
26 */
27
28#include "math.h"
29#include "math_private.h"
30
31static const double
32one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
33ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
34huge= 1.00000000000000000000e+300;
35
36double
37asinh(double x)
38{
39 double t,w;
40 int32_t hx,ix;
41 GET_HIGH_WORD(hx,x);
42 ix = hx&0x7fffffff;
43 if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
44 if(ix< 0x3e300000) { /* |x|<2**-28 */
45 if(huge+x>one) return x; /* return x inexact except 0 */
46 }
47 if(ix>0x41b00000) { /* |x| > 2**28 */
48 w = __ieee754_log(fabs(x))+ln2;
49 } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */
50 t = fabs(x);
51 w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
52 } else { /* 2.0 > |x| > 2**-28 */
53 t = x*x;
54 w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
55 }
56 if(hx>0) return w; else return -w;
57}