1*49393c00Smartynas /* @(#)s_asinh.c 5.1 93/09/24 */
2*49393c00Smartynas /*
3*49393c00Smartynas * ====================================================
4*49393c00Smartynas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*49393c00Smartynas *
6*49393c00Smartynas * Developed at SunPro, a Sun Microsystems, Inc. business.
7*49393c00Smartynas * Permission to use, copy, modify, and distribute this
8*49393c00Smartynas * software is freely granted, provided that this notice
9*49393c00Smartynas * is preserved.
10*49393c00Smartynas * ====================================================
11*49393c00Smartynas */
12*49393c00Smartynas
13*49393c00Smartynas /* asinhl(x)
14*49393c00Smartynas * Method :
15*49393c00Smartynas * Based on
16*49393c00Smartynas * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
17*49393c00Smartynas * we have
18*49393c00Smartynas * asinhl(x) := x if 1+x*x=1,
19*49393c00Smartynas * := signl(x)*(logl(x)+ln2)) for large |x|, else
20*49393c00Smartynas * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
21*49393c00Smartynas * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
22*49393c00Smartynas */
23*49393c00Smartynas
24*49393c00Smartynas #include <math.h>
25*49393c00Smartynas
26*49393c00Smartynas #include "math_private.h"
27*49393c00Smartynas
28*49393c00Smartynas static const long double
29*49393c00Smartynas one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
30*49393c00Smartynas ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
31*49393c00Smartynas huge= 1.000000000000000000e+4900L;
32*49393c00Smartynas
33*49393c00Smartynas long double
asinhl(long double x)34*49393c00Smartynas asinhl(long double x)
35*49393c00Smartynas {
36*49393c00Smartynas long double t,w;
37*49393c00Smartynas int32_t hx,ix;
38*49393c00Smartynas GET_LDOUBLE_EXP(hx,x);
39*49393c00Smartynas ix = hx&0x7fff;
40*49393c00Smartynas if(ix==0x7fff) return x+x; /* x is inf or NaN */
41*49393c00Smartynas if(ix< 0x3fde) { /* |x|<2**-34 */
42*49393c00Smartynas if(huge+x>one) return x; /* return x inexact except 0 */
43*49393c00Smartynas }
44*49393c00Smartynas if(ix>0x4020) { /* |x| > 2**34 */
45*49393c00Smartynas w = logl(fabsl(x))+ln2;
46*49393c00Smartynas } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
47*49393c00Smartynas t = fabsl(x);
48*49393c00Smartynas w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
49*49393c00Smartynas } else { /* 2.0 > |x| > 2**-28 */
50*49393c00Smartynas t = x*x;
51*49393c00Smartynas w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
52*49393c00Smartynas }
53*49393c00Smartynas if(hx&0x8000) return -w; else return w;
54*49393c00Smartynas }
55