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 /* asinhl(x)
14 * Method :
15 * Based on
16 * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
17 * we have
18 * asinhl(x) := x if 1+x*x=1,
19 * := signl(x)*(logl(x)+ln2)) for large |x|, else
20 * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
21 * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
22 */
23
24
25
26 static const long double
27 one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
28 ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
29 huge= 1.000000000000000000e+4900L;
30
31 long double
asinhl(long double x)32 asinhl(long double x)
33 {
34 long double t,w;
35 int32_t hx,ix;
36 GET_LDOUBLE_EXP(hx,x);
37 ix = hx&0x7fff;
38 if(ix==0x7fff) return x+x; /* x is inf or NaN */
39 if(ix< 0x3fde) { /* |x|<2**-34 */
40 if(huge+x>one) return x; /* return x inexact except 0 */
41 }
42 if(ix>0x4020) { /* |x| > 2**34 */
43 w = logl(fabsl(x))+ln2;
44 } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
45 t = fabsl(x);
46 w = logl(2.0l*t+one/(sqrtl(x*x+one)+t));
47 } else { /* 2.0 > |x| > 2**-28 */
48 t = x*x;
49 w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
50 }
51 if(hx&0x8000) return -w; else return w;
52 }
53
