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/* asinh(x)
14 * Method :
15 *	Based on
16 *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
17 *	we have
18 *	asinh(x) := x  if  1+x*x=1,
19 *		 := sign(x)*(log(x)+ln2)) for large |x|, else
20 *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
21 *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
22 */
23
24#include <float.h>
25#include <math.h>
26
27#include "math_private.h"
28
29static const double
30one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
31ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
32huge=  1.00000000000000000000e+300;
33
34double
35asinh(double x)
36{
37	double t,w;
38	int32_t hx,ix;
39	GET_HIGH_WORD(hx,x);
40	ix = hx&0x7fffffff;
41	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
42	if(ix< 0x3e300000) {	/* |x|<2**-28 */
43	    if(huge+x>one) return x;	/* return x inexact except 0 */
44	}
45	if(ix>0x41b00000) {	/* |x| > 2**28 */
46	    w = log(fabs(x))+ln2;
47	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
48	    t = fabs(x);
49	    w = log(2.0*t+one/(sqrt(x*x+one)+t));
50	} else {		/* 2.0 > |x| > 2**-28 */
51	    t = x*x;
52	    w =log1p(fabs(x)+t/(one+sqrt(one+t)));
53	}
54	if(hx>0) return w; else return -w;
55}
56DEF_STD(asinh);
57LDBL_MAYBE_CLONE(asinh);
58