1 /* @(#)e_atanh.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 /* atanhl(x)
14 * Method :
15 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
16 * 2.For x>=0.5
17 * 1 2x x
18 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
19 * 2 1 - x 1 - x
20 *
21 * For x<0.5
22 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
23 *
24 * Special cases:
25 * atanhl(x) is NaN if |x| > 1 with signal;
26 * atanhl(NaN) is that NaN with no signal;
27 * atanhl(+-1) is +-INF with signal.
28 *
29 */
30
31
32
33 static const long double one = 1.0l, huge = 1e4900L;
34
35 static const long double zero = 0.0l;
36
37 long double
atanhl(long double x)38 atanhl(long double x)
39 {
40 long double t;
41 int32_t ix;
42 u_int32_t se,i0,i1;
43 GET_LDOUBLE_WORDS(se,i0,i1,x);
44 ix = se&0x7fff;
45 if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff)
46 /* |x|>1 */
47 return __math_invalidl(x);
48 if(ix==0x3fff)
49 return __math_divzerol(se & 0x8000);
50 if(ix<0x3fe3&&(huge+x)>zero) return x; /* x<2**-28 */
51 SET_LDOUBLE_EXP(x,ix);
52 if(ix<0x3ffe) { /* x < 0.5 */
53 t = x+x;
54 t = 0.5l*log1pl(t+t*x/(one-x));
55 } else
56 t = 0.5l*log1pl((x+x)/(one-x));
57 if(se<=0x7fff) return t; else return -t;
58 }
59
