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/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma ident "@(#)tanhl.c 1.8 06/01/31 SMI"
#if defined(ELFOBJ)
#pragma weak tanhl = __tanhl
#endif
/*
* tanhl(x) returns the hyperbolic tangent of x
*
* Method :
* 1. reduce x to non-negative: tanhl(-x) = - tanhl(x).
* 2.
* 0 < x <= small : tanhl(x) := x
* -expm1l(-2x)
* small < x <= 1 : tanhl(x) := --------------
* expm1l(-2x) + 2
* 2
* 1 <= x <= threshold : tanhl(x) := 1 - ---------------
* expm1l(2x) + 2
* threshold < x <= INF : tanhl(x) := 1.
*
* where
* single : small = 1.e-5 threshold = 11.0
* double : small = 1.e-10 threshold = 22.0
* quad : small = 1.e-20 threshold = 45.0
*
* Note: threshold was chosen so that
* fl(1.0+2/(expm1(2*threshold)+2)) == 1.
*
* Special cases:
* tanhl(NaN) is NaN;
* only tanhl(0.0)=0.0 is exact for finite argument.
*/
#include "libm.h"
static const long double small = 1.0e-20L, one = 1.0, two = 2.0,
#ifndef lint
big = 1.0e+20L,
#endif
threshold = 45.0L;
long double
tanhl(long double x) {
long double t, y, z;
int signx;
if (isnanl(x))
return (x + x); /* x is NaN */
signx = signbitl(x);
t = fabsl(x);
z = one;
if (t <= threshold) {
if (t > one)
z = one - two / (expm1l(t + t) + two);
else if (t > small) {
y = expm1l(-t - t);
z = -y / (y + two);
} else {
#ifndef lint
volatile long double dummy = t + big;
/* inexact if t != 0 */
#endif
return (x);
}
} else if (!finitel(t))
return (copysignl(one, x));
else
return (signx ? -z + small * small : z - small * small);
return (signx ? -z : z);
}
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