1*49393c00Smartynas /* @(#)s_tanh.c 5.1 93/09/24 */
2*49393c00Smartynas /*
3*49393c00Smartynas * ====================================================
4*49393c00Smartynas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*49393c00Smartynas *
6*49393c00Smartynas * Developed at SunPro, a Sun Microsystems, Inc. business.
7*49393c00Smartynas * Permission to use, copy, modify, and distribute this
8*49393c00Smartynas * software is freely granted, provided that this notice
9*49393c00Smartynas * is preserved.
10*49393c00Smartynas * ====================================================
11*49393c00Smartynas */
12*49393c00Smartynas
13*49393c00Smartynas /* tanhl(x)
14*49393c00Smartynas * Return the Hyperbolic Tangent of x
15*49393c00Smartynas *
16*49393c00Smartynas * Method :
17*49393c00Smartynas * x -x
18*49393c00Smartynas * e - e
19*49393c00Smartynas * 0. tanhl(x) is defined to be -----------
20*49393c00Smartynas * x -x
21*49393c00Smartynas * e + e
22*49393c00Smartynas * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
23*49393c00Smartynas * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
24*49393c00Smartynas * -t
25*49393c00Smartynas * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
26*49393c00Smartynas * t + 2
27*49393c00Smartynas * 2
28*49393c00Smartynas * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
29*49393c00Smartynas * t + 2
30*49393c00Smartynas * 23.0 < x <= INF : tanhl(x) := 1.
31*49393c00Smartynas *
32*49393c00Smartynas * Special cases:
33*49393c00Smartynas * tanhl(NaN) is NaN;
34*49393c00Smartynas * only tanhl(0)=0 is exact for finite argument.
35*49393c00Smartynas */
36*49393c00Smartynas
37*49393c00Smartynas #include <math.h>
38*49393c00Smartynas
39*49393c00Smartynas #include "math_private.h"
40*49393c00Smartynas
41*49393c00Smartynas static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
42*49393c00Smartynas
43*49393c00Smartynas long double
tanhl(long double x)44*49393c00Smartynas tanhl(long double x)
45*49393c00Smartynas {
46*49393c00Smartynas long double t,z;
47*49393c00Smartynas int32_t se;
48*49393c00Smartynas u_int32_t jj0,jj1,ix;
49*49393c00Smartynas
50*49393c00Smartynas /* High word of |x|. */
51*49393c00Smartynas GET_LDOUBLE_WORDS(se,jj0,jj1,x);
52*49393c00Smartynas ix = se&0x7fff;
53*49393c00Smartynas
54*49393c00Smartynas /* x is INF or NaN */
55*49393c00Smartynas if(ix==0x7fff) {
56*49393c00Smartynas /* for NaN it's not important which branch: tanhl(NaN) = NaN */
57*49393c00Smartynas if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */
58*49393c00Smartynas else return one/x+one; /* tanhl(+inf)=+1 */
59*49393c00Smartynas }
60*49393c00Smartynas
61*49393c00Smartynas /* |x| < 23 */
62*49393c00Smartynas if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */
63*49393c00Smartynas if ((ix|jj0|jj1) == 0)
64*49393c00Smartynas return x; /* x == +- 0 */
65*49393c00Smartynas if (ix<0x3fc8) /* |x|<2**-55 */
66*49393c00Smartynas return x*(one+tiny); /* tanh(small) = small */
67*49393c00Smartynas if (ix>=0x3fff) { /* |x|>=1 */
68*49393c00Smartynas t = expm1l(two*fabsl(x));
69*49393c00Smartynas z = one - two/(t+two);
70*49393c00Smartynas } else {
71*49393c00Smartynas t = expm1l(-two*fabsl(x));
72*49393c00Smartynas z= -t/(t+two);
73*49393c00Smartynas }
74*49393c00Smartynas /* |x| > 23, return +-1 */
75*49393c00Smartynas } else {
76*49393c00Smartynas z = one - tiny; /* raised inexact flag */
77*49393c00Smartynas }
78*49393c00Smartynas return (se&0x8000)? -z: z;
79*49393c00Smartynas }
80