1 /* @(#)s_asinh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
10 * ====================================================
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid
[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
20 * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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)))
29 #include "math_private.h"
37 one
= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
38 ln2
= 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
39 huge
= 1.00000000000000000000e+300;
42 double asinh(double x
)
52 if(ix
>=0x7ff00000) return x
+x
; /* x is inf or NaN */
53 if(ix
< 0x3e300000) { /* |x|<2**-28 */
54 if(huge
+x
>one
) return x
; /* return x inexact except 0 */
56 if(ix
>0x41b00000) { /* |x| > 2**28 */
57 w
= __ieee754_log(fabs(x
))+ln2
;
58 } else if (ix
>0x40000000) { /* 2**28 > |x| > 2.0 */
60 w
= __ieee754_log(2.0*t
+one
/(__ieee754_sqrt(x
*x
+one
)+t
));
61 } else { /* 2.0 > |x| > 2**-28 */
63 w
=log1p(fabs(x
)+t
/(one
+__ieee754_sqrt(one
+t
)));
65 if(hx
>0) return w
; else return -w
;
67 libm_hidden_def(asinh
)