xref: /freebsd/lib/msun/src/s_asinh.c (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
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
14 static char rcsid[] = "$FreeBSD$";
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 
31 static const double
32 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
33 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
34 huge=  1.00000000000000000000e+300;
35 
36 double
37 asinh(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 }
58