1/* s_atanhl.c -- long double version of s_atan.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/* __ieee754_atanhl(x)
16 * Method :
17 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
18 * 2.For x>=0.5
19 * 1 2x x
20 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
21 * 2 1 - x 1 - x
22 *
23 * For x<0.5
24 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
25 *
26 * Special cases:
27 * atanhl(x) is NaN if |x| > 1 with signal;
28 * atanhl(NaN) is that NaN with no signal;
29 * atanhl(+-1) is +-INF with signal.
30 *
31 */
32
33#include <float.h>
34#include <math.h>
35#include <math-barriers.h>
36#include <math_private.h>
37#include <math-underflow.h>
38#include <libm-alias-finite.h>
39
40static const long double one = 1.0, huge = 1e4900L;
41
42static const long double zero = 0.0;
43
44long double
45__ieee754_atanhl(long double x)
46{
47 long double t;
48 int32_t ix;
49 uint32_t se,i0,i1;
50 GET_LDOUBLE_WORDS(se,i0,i1,x);
51 ix = se&0x7fff;
52 if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff)
53 /* |x|>1 */
54 return (x-x)/(x-x);
55 if(ix==0x3fff)
56 return x/zero;
57 if(ix<0x3fdf) {
58 math_force_eval(huge+x);
59 math_check_force_underflow (x);
60 return x; /* x<2**-32 */
61 }
62 SET_LDOUBLE_EXP(x,ix);
63 if(ix<0x3ffe) { /* x < 0.5 */
64 t = x+x;
65 t = 0.5*__log1pl(t+t*x/(one-x));
66 } else
67 t = 0.5*__log1pl((x+x)/(one-x));
68 if(se<=0x7fff) return t; else return -t;
69}
70libm_alias_finite (__ieee754_atanhl, __atanhl)
71