1*05a0b428SJohn Marino /* @(#)s_asinh.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* asinhl(x)
14*05a0b428SJohn Marino * Method :
15*05a0b428SJohn Marino * Based on
16*05a0b428SJohn Marino * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
17*05a0b428SJohn Marino * we have
18*05a0b428SJohn Marino * asinhl(x) := x if 1+x*x=1,
19*05a0b428SJohn Marino * := signl(x)*(logl(x)+ln2)) for large |x|, else
20*05a0b428SJohn Marino * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
21*05a0b428SJohn Marino * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
22*05a0b428SJohn Marino */
23*05a0b428SJohn Marino
24*05a0b428SJohn Marino #include <math.h>
25*05a0b428SJohn Marino
26*05a0b428SJohn Marino #include "math_private.h"
27*05a0b428SJohn Marino
28*05a0b428SJohn Marino static const long double
29*05a0b428SJohn Marino one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
30*05a0b428SJohn Marino ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
31*05a0b428SJohn Marino huge= 1.000000000000000000e+4900L;
32*05a0b428SJohn Marino
33*05a0b428SJohn Marino long double
asinhl(long double x)34*05a0b428SJohn Marino asinhl(long double x)
35*05a0b428SJohn Marino {
36*05a0b428SJohn Marino long double t,w;
37*05a0b428SJohn Marino int32_t hx,ix;
38*05a0b428SJohn Marino GET_LDOUBLE_EXP(hx,x);
39*05a0b428SJohn Marino ix = hx&0x7fff;
40*05a0b428SJohn Marino if(ix==0x7fff) return x+x; /* x is inf or NaN */
41*05a0b428SJohn Marino if(ix< 0x3fde) { /* |x|<2**-34 */
42*05a0b428SJohn Marino if(huge+x>one) return x; /* return x inexact except 0 */
43*05a0b428SJohn Marino }
44*05a0b428SJohn Marino if(ix>0x4020) { /* |x| > 2**34 */
45*05a0b428SJohn Marino w = logl(fabsl(x))+ln2;
46*05a0b428SJohn Marino } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
47*05a0b428SJohn Marino t = fabsl(x);
48*05a0b428SJohn Marino w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
49*05a0b428SJohn Marino } else { /* 2.0 > |x| > 2**-28 */
50*05a0b428SJohn Marino t = x*x;
51*05a0b428SJohn Marino w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
52*05a0b428SJohn Marino }
53*05a0b428SJohn Marino if(hx&0x8000) return -w; else return w;
54*05a0b428SJohn Marino }
55