1/* s_asinhl.c -- long double version of s_asinh.c.
2 */
3
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15#if defined(LIBM_SCCS) && !defined(lint)
16static char rcsid[] = "$NetBSD: $";
17#endif
18
19/* asinhl(x)
20 * Method :
21 * Based on
22 * asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
23 * we have
24 * asinhl(x) := x if 1+x*x=1,
25 * := signl(x)*(logl(x)+ln2)) for large |x|, else
26 * := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
27 * := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
28 */
29
30#include <float.h>
31#include <math.h>
32#include <math_private.h>
33#include <math-underflow.h>
34#include <libm-alias-ldouble.h>
35
36static const long double
37one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
38ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
39huge= 1.000000000000000000e+4900L;
40
41long double __asinhl(long double x)
42{
43 long double t,w;
44 int32_t hx,ix;
45 GET_LDOUBLE_EXP(hx,x);
46 ix = hx&0x7fff;
47 if(__builtin_expect(ix< 0x3fde, 0)) { /* |x|<2**-34 */
48 math_check_force_underflow (x);
49 if(huge+x>one) return x; /* return x inexact except 0 */
50 }
51 if(__builtin_expect(ix>0x4020,0)) { /* |x| > 2**34 */
52 if(ix==0x7fff) return x+x; /* x is inf or NaN */
53 w = __ieee754_logl(fabsl(x))+ln2;
54 } else {
55 long double xa = fabsl(x);
56 if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
57 w = __ieee754_logl(2.0*xa+one/(sqrtl(xa*xa+one)+xa));
58 } else { /* 2.0 > |x| > 2**-28 */
59 t = xa*xa;
60 w =__log1pl(xa+t/(one+sqrtl(one+t)));
61 }
62 }
63 return copysignl(w, x);
64}
65libm_alias_ldouble (__asinh, asinh)
66