1/* s_tanhl.c -- __float128 version of s_tanh.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/* Changes for 128-bit __float128 contributed by
18 Stephen L. Moshier <moshier@na-net.ornl.gov> */
19
20/* tanhl(x)
21 * Return the Hyperbolic Tangent of x
22 *
23 * Method :
24 * x -x
25 * e - e
26 * 0. tanhl(x) is defined to be -----------
27 * x -x
28 * e + e
29 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
30 * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x)
31 * -t
32 * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
33 * t + 2
34 * 2
35 * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
36 * t + 2
37 * 40.0 < x <= INF : tanhl(x) := 1.
38 *
39 * Special cases:
40 * tanhl(NaN) is NaN;
41 * only tanhl(0)=0 is exact for finite argument.
42 */
43
44#include "quadmath-imp.h"
45
46static const __float128 one = 1.0Q, two = 2.0Q, tiny = 1.0e-4900Q;
47
48__float128
49tanhq (__float128 x)
50{
51 __float128 t, z;
52 uint32_t jx, ix;
53 ieee854_float128 u;
54
55 /* Words of |x|. */
56 u.value = x;
57 jx = u.words32.w0;
58 ix = jx & 0x7fffffff;
59 /* x is INF or NaN */
60 if (ix >= 0x7fff0000)
61 {
62 /* for NaN it's not important which branch: tanhl(NaN) = NaN */
63 if (jx & 0x80000000)
64 return one / x - one; /* tanhl(-inf)= -1; */
65 else
66 return one / x + one; /* tanhl(+inf)=+1 */
67 }
68
69 /* |x| < 40 */
70 if (ix < 0x40044000)
71 {
72 if (u.value == 0)
73 return x; /* x == +- 0 */
74 if (ix < 0x3fc60000) /* |x| < 2^-57 */
75 {
76 math_check_force_underflow (x);
77 return x * (one + tiny); /* tanh(small) = small */
78 }
79 u.words32.w0 = ix; /* Absolute value of x. */
80 if (ix >= 0x3fff0000)
81 { /* |x| >= 1 */
82 t = expm1q (two * u.value);
83 z = one - two / (t + two);
84 }
85 else
86 {
87 t = expm1q (-two * u.value);
88 z = -t / (t + two);
89 }
90 /* |x| > 40, return +-1 */
91 }
92 else
93 {
94 z = one - tiny; /* raised inexact flag */
95 }
96 return (jx & 0x80000000) ? -z : z;
97}
98