1*05a0b428SJohn Marino /* @(#)s_tanh.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* tanhl(x)
14*05a0b428SJohn Marino * Return the Hyperbolic Tangent of x
15*05a0b428SJohn Marino *
16*05a0b428SJohn Marino * Method :
17*05a0b428SJohn Marino * x -x
18*05a0b428SJohn Marino * e - e
19*05a0b428SJohn Marino * 0. tanhl(x) is defined to be -----------
20*05a0b428SJohn Marino * x -x
21*05a0b428SJohn Marino * e + e
22*05a0b428SJohn Marino * 1. reduce x to non-negative by tanhl(-x) = -tanhl(x).
23*05a0b428SJohn Marino * 2. 0 <= x <= 2**-55 : tanhl(x) := x*(one+x)
24*05a0b428SJohn Marino * -t
25*05a0b428SJohn Marino * 2**-55 < x <= 1 : tanhl(x) := -----; t = expm1l(-2x)
26*05a0b428SJohn Marino * t + 2
27*05a0b428SJohn Marino * 2
28*05a0b428SJohn Marino * 1 <= x <= 23.0 : tanhl(x) := 1- ----- ; t=expm1l(2x)
29*05a0b428SJohn Marino * t + 2
30*05a0b428SJohn Marino * 23.0 < x <= INF : tanhl(x) := 1.
31*05a0b428SJohn Marino *
32*05a0b428SJohn Marino * Special cases:
33*05a0b428SJohn Marino * tanhl(NaN) is NaN;
34*05a0b428SJohn Marino * only tanhl(0)=0 is exact for finite argument.
35*05a0b428SJohn Marino */
36*05a0b428SJohn Marino
37*05a0b428SJohn Marino #include <math.h>
38*05a0b428SJohn Marino
39*05a0b428SJohn Marino #include "math_private.h"
40*05a0b428SJohn Marino
41*05a0b428SJohn Marino static const long double one=1.0, two=2.0, tiny = 1.0e-4900L;
42*05a0b428SJohn Marino
43*05a0b428SJohn Marino long double
tanhl(long double x)44*05a0b428SJohn Marino tanhl(long double x)
45*05a0b428SJohn Marino {
46*05a0b428SJohn Marino long double t,z;
47*05a0b428SJohn Marino int32_t se;
48*05a0b428SJohn Marino u_int32_t jj0,jj1,ix;
49*05a0b428SJohn Marino
50*05a0b428SJohn Marino /* High word of |x|. */
51*05a0b428SJohn Marino GET_LDOUBLE_WORDS(se,jj0,jj1,x);
52*05a0b428SJohn Marino ix = se&0x7fff;
53*05a0b428SJohn Marino
54*05a0b428SJohn Marino /* x is INF or NaN */
55*05a0b428SJohn Marino if(ix==0x7fff) {
56*05a0b428SJohn Marino /* for NaN it's not important which branch: tanhl(NaN) = NaN */
57*05a0b428SJohn Marino if (se&0x8000) return one/x-one; /* tanhl(-inf)= -1; */
58*05a0b428SJohn Marino else return one/x+one; /* tanhl(+inf)=+1 */
59*05a0b428SJohn Marino }
60*05a0b428SJohn Marino
61*05a0b428SJohn Marino /* |x| < 23 */
62*05a0b428SJohn Marino if (ix < 0x4003 || (ix == 0x4003 && jj0 < 0xb8000000u)) {/* |x|<23 */
63*05a0b428SJohn Marino if ((ix|jj0|jj1) == 0)
64*05a0b428SJohn Marino return x; /* x == +- 0 */
65*05a0b428SJohn Marino if (ix<0x3fc8) /* |x|<2**-55 */
66*05a0b428SJohn Marino return x*(one+tiny); /* tanh(small) = small */
67*05a0b428SJohn Marino if (ix>=0x3fff) { /* |x|>=1 */
68*05a0b428SJohn Marino t = expm1l(two*fabsl(x));
69*05a0b428SJohn Marino z = one - two/(t+two);
70*05a0b428SJohn Marino } else {
71*05a0b428SJohn Marino t = expm1l(-two*fabsl(x));
72*05a0b428SJohn Marino z= -t/(t+two);
73*05a0b428SJohn Marino }
74*05a0b428SJohn Marino /* |x| > 23, return +-1 */
75*05a0b428SJohn Marino } else {
76*05a0b428SJohn Marino z = one - tiny; /* raised inexact flag */
77*05a0b428SJohn Marino }
78*05a0b428SJohn Marino return (se&0x8000)? -z: z;
79*05a0b428SJohn Marino }
80