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("$FreeBSD$");
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 <float.h>
28
29#include "math.h"
30#include "math_private.h"
31
32static const double
33one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
34ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
35huge=  1.00000000000000000000e+300;
36
37double
38asinh(double x)
39{
40	double t,w;
41	int32_t hx,ix;
42	GET_HIGH_WORD(hx,x);
43	ix = hx&0x7fffffff;
44	if(ix>=0x7ff00000) return x+x;	/* x is inf or NaN */
45	if(ix< 0x3e300000) {	/* |x|<2**-28 */
46	    if(huge+x>one) return x;	/* return x inexact except 0 */
47	}
48	if(ix>0x41b00000) {	/* |x| > 2**28 */
49	    w = __ieee754_log(fabs(x))+ln2;
50	} else if (ix>0x40000000) {	/* 2**28 > |x| > 2.0 */
51	    t = fabs(x);
52	    w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
53	} else {		/* 2.0 > |x| > 2**-28 */
54	    t = x*x;
55	    w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
56	}
57	if(hx>0) return w; else return -w;
58}
59
60#if LDBL_MANT_DIG == 53
61__weak_reference(asinh, asinhl);
62#endif
63