1 /* @(#)s_tanh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
18 * Return the Hyperbolic Tangent of x
23 * 0. tanh(x) is defined to be -----------
26 * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
27 * 2. 0 <= x <= 2**-57 : tanh(x) := x*(one+x)
29 * 2**-57 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
32 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
34 * 22.0 < x <= INF : tanh(x) := 1.
38 * only tanh(0)=0 is exact for finite argument.
42 #include "math_private.h"
43 #include <math_ldbl_opt.h>
45 static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
47 long double __tanhl(long double x)
52 /* High word of |x|. */
53 GET_LDOUBLE_WORDS64(jx,lx,x);
54 ix = jx&0x7fffffffffffffffLL;
57 if(ix>=0x7ff0000000000000LL) {
58 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
59 else return one/x-one; /* tanh(NaN) = NaN */
63 if (ix < 0x4036000000000000LL) { /* |x|<22 */
64 if ((ix | (lx&0x7fffffffffffffffLL)) == 0)
65 return x; /* x == +-0 */
66 if (ix<0x3c60000000000000LL) /* |x|<2**-57 */
67 return x*(one+x); /* tanh(small) = small */
68 if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */
69 t = __expm1l(two*fabsl(x));
70 z = one - two/(t+two);
72 t = __expm1l(-two*fabsl(x));
75 /* |x| > 22, return +-1 */
77 z = one - tiny; /* raised inexact flag */
79 return (jx>=0)? z: -z;
81 long_double_symbol (libm, __tanhl, tanhl);