1 /* s_atanhl.c -- __float128 version of s_atan.c.
2 * Conversion to __float128 by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
4 */
5
6 /*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17 /* atanhq(x)
18 * Method :
19 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
20 * 2.For x>=0.5
21 * 1 2x x
22 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
23 * 2 1 - x 1 - x
24 *
25 * For x<0.5
26 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
27 *
28 * Special cases:
29 * atanhl(x) is NaN if |x| > 1 with signal;
30 * atanhl(NaN) is that NaN with no signal;
31 * atanhl(+-1) is +-INF with signal.
32 *
33 */
34
35 #include "quadmath-imp.h"
36
37 static const __float128 one = 1.0Q, huge = 1e4900Q;
38 static const __float128 zero = 0.0Q;
39
40 __float128
atanhq(__float128 x)41 atanhq (__float128 x)
42 {
43 __float128 t;
44 uint32_t jx, ix;
45 ieee854_float128 u;
46
47 u.value = x;
48 jx = u.words32.w0;
49 ix = jx & 0x7fffffff;
50 u.words32.w0 = ix;
51 if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
52 {
53 if (u.value == one)
54 return x/zero;
55 else
56 return (x-x)/(x-x);
57 }
58 if(ix<0x3fc60000 && (huge+x)>zero) return x; /* x < 2^-57 */
59
60 if(ix<0x3ffe0000) { /* x < 0.5 */
61 t = u.value+u.value;
62 t = 0.5*log1pq(t+t*u.value/(one-u.value));
63 } else
64 t = 0.5*log1pq((u.value+u.value)/(one-u.value));
65 if(jx & 0x80000000) return -t; else return t;
66 }
67