1/* s_tanhl.c -- long double version of s_tanh.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/* Changes for 128-bit long double contributed by
18   Stephen L. Moshier <moshier@na-net.ornl.gov> */
19
20/* tanhq(x)
21 * Return the Hyperbolic Tangent of x
22 *
23 * Method :
24 *                                      x    -x
25 *                                     e  - e
26 *      0. tanhq(x) is defined to be -----------
27 *                                      x    -x
28 *                                     e  + e
29 *      1. reduce x to non-negative by tanhq(-x) = -tanhq(x).
30 *      2.  0      <= x <= 2**-57 : tanhq(x) := x*(one+x)
31 *                                               -t
32 *          2**-57 <  x <=  1     : tanhq(x) := -----; t = expm1q(-2x)
33 *                                              t + 2
34 *                                                    2
35 *          1      <= x <=  40.0  : tanhq(x) := 1-  ----- ; t=expm1q(2x)
36 *                                                  t + 2
37 *          40.0   <  x <= INF    : tanhq(x) := 1.
38 *
39 * Special cases:
40 *      tanhq(NaN) is NaN;
41 *      only tanhq(0)=0 is exact for finite argument.
42 */
43
44#include "quadmath-imp.h"
45
46static const __float128 one = 1.0, two = 2.0, 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: tanhq(NaN) = NaN */
63      if (jx & 0x80000000)
64	return one / x - one;	/* tanhq(-inf)= -1; */
65      else
66	return one / x + one;	/* tanhq(+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