1 /* s_tanhl.c -- long double version of s_tanh.c.
2 */
3
4 /*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15 /* tanhl(x)
16 * Return the Hyperbolic Tangent of x
17 *
18 * Method :
19 * x -x
20 * e - e
21 * 0. tanhl(x) is defined to be -----------
22 * x -x
23 * e + e
24 * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
25 * 2. 0 <= x <= 2**-57 : tanhl(x) := x*(one+x)
26 * -t
27 * 2**-57 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
28 * t + 2
29 * 2
30 * 1 <= x <= 40.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
31 * t + 2
32 * 40.0 < x <= INF : tanhl(x) := 1.
33 *
34 * Special cases:
35 * tanhl(NaN) is NaN;
36 * only tanhl(0)=0 is exact for finite argument.
37 */
38
39 #include <float.h>
40 #include <math.h>
41 #include <math_private.h>
42 #include <math-underflow.h>
43 #include <libm-alias-ldouble.h>
44
45 static const _Float128 one = 1.0, two = 2.0, tiny = L(1.0e-4900);
46
47 _Float128
__tanhl(_Float128 x)48 __tanhl (_Float128 x)
49 {
50 _Float128 t, z;
51 uint32_t jx, ix;
52 ieee854_long_double_shape_type u;
53
54 /* Words of |x|. */
55 u.value = x;
56 jx = u.parts32.w0;
57 ix = jx & 0x7fffffff;
58 /* x is INF or NaN */
59 if (ix >= 0x7fff0000)
60 {
61 /* for NaN it's not important which branch: tanhl(NaN) = NaN */
62 if (jx & 0x80000000)
63 return one / x - one; /* tanhl(-inf)= -1; */
64 else
65 return one / x + one; /* tanhl(+inf)=+1 */
66 }
67
68 /* |x| < 40 */
69 if (ix < 0x40044000)
70 {
71 if (u.value == 0)
72 return x; /* x == +- 0 */
73 if (ix < 0x3fc60000) /* |x| < 2^-57 */
74 {
75 math_check_force_underflow (x);
76 return x * (one + tiny); /* tanh(small) = small */
77 }
78 u.parts32.w0 = ix; /* Absolute value of x. */
79 if (ix >= 0x3fff0000)
80 { /* |x| >= 1 */
81 t = __expm1l (two * u.value);
82 z = one - two / (t + two);
83 }
84 else
85 {
86 t = __expm1l (-two * u.value);
87 z = -t / (t + two);
88 }
89 /* |x| > 40, return +-1 */
90 }
91 else
92 {
93 z = one - tiny; /* raised inexact flag */
94 }
95 return (jx & 0x80000000) ? -z : z;
96 }
97 libm_alias_ldouble (__tanh, tanh)
98