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 
46 static const __float128 one = 1.0, two = 2.0, tiny = 1.0e-4900Q;
47 
48 __float128
tanhq(__float128 x)49 tanhq (__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