1 /* s_atanhl.c -- long double version of s_atan.c.
2 * Conversion to long double 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*log1pq(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, huge = 1e4900Q;
38
39 static const __float128 zero = 0;
40
41 __float128
atanhq(__float128 x)42 atanhq(__float128 x)
43 {
44 __float128 t;
45 uint32_t jx, ix;
46 ieee854_float128 u;
47
48 u.value = x;
49 jx = u.words32.w0;
50 ix = jx & 0x7fffffff;
51 u.words32.w0 = ix;
52 if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
53 {
54 if (u.value == one)
55 return x/zero;
56 else
57 return (x-x)/(x-x);
58 }
59 if(ix<0x3fc60000 && (huge+x)>zero) /* x < 2^-57 */
60 {
61 math_check_force_underflow (x);
62 return x;
63 }
64
65 if(ix<0x3ffe0000) { /* x < 0.5 */
66 t = u.value+u.value;
67 t = 0.5*log1pq(t+t*u.value/(one-u.value));
68 } else
69 t = 0.5*log1pq((u.value+u.value)/(one-u.value));
70 if(jx & 0x80000000) return -t; else return t;
71 }
72