s_asinhl.c revision 176451 
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#include <sys/cdefs.h>
14__FBSDID("$FreeBSD: head/lib/msun/src/s_asinh.c 176451 2008-02-22 02:30:36Z das $");
15
16/* asinh(x)
17 * Method :
18 *	Based on
19 *		asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
20 *	we have
21 *	asinh(x) := x  if  1+x*x=1,
22 *		 := sign(x)*(log(x)+ln2)) for large |x|, else
23 *		 := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
24 *		 := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
25 */
26
27#include "math.h"
28#include "math_private.h"
29
30static const double
31one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
32ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
33huge=  1.00000000000000000000e+300;
34
35double
36asinh(double x)
37{
38	double t,w;
39	int32_t hx,ix;
40	GET_HIGH_WORD(hx,x);
41	ix = hx&0x7fffffff;
42	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
43	if(ix< 0x3e300000) {	/* |x|<2**-28 */
44	    if(huge+x>one) return x;	/* return x inexact except 0 */
45	}
46	if(ix>0x41b00000) {	/* |x| > 2**28 */
47	    w = __ieee754_log(fabs(x))+ln2;
48	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
49	    t = fabs(x);
50	    w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
51	} else {		/* 2.0 > |x| > 2**-28 */
52	    t = x*x;
53	    w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
54	}
55	if(hx>0) return w; else return -w;
56}
57