mirror of
https://gitlab.com/rnger/amath
synced 2026-10-16 12:36:52 +00:00
115 lines
3.7 KiB
C
115 lines
3.7 KiB
C
/* @(#)s_tanh.c 1.3 95/01/18 */
|
|
|
|
/*
|
|
* Copyright (c) 2015-2017 Carsten Sonne Larsen <cs@innolan.dk>
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
|
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
|
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
|
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
|
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
|
|
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*
|
|
* The origin source code can be obtained from:
|
|
* http://www.netlib.org/fdlibm/s_tanh.c
|
|
*
|
|
*/
|
|
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*
|
|
*/
|
|
|
|
#include "prim.h"
|
|
#include "math.h"
|
|
|
|
static const double one=1.0, two=2.0, tiny = 1.0e-300;
|
|
|
|
/**
|
|
* @brief Hyperbolic tangent function.
|
|
* @version 1.3
|
|
* @date 95/01/18
|
|
* @details
|
|
* <pre>
|
|
* Return the Hyperbolic Tangent of x
|
|
*
|
|
* Method :
|
|
* x -x
|
|
* e - e
|
|
* 0. tanh(x) is defined to be -----------
|
|
* x -x
|
|
* e + e
|
|
* 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
|
* 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
|
|
* -t
|
|
* 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
|
* t + 2
|
|
* 2
|
|
* 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
|
* t + 2
|
|
* 22.0 < x <= INF : tanh(x) := 1.
|
|
*
|
|
* Special cases:
|
|
* tanh(NaN) is NaN;
|
|
* only tanh(0)=0 is exact for finite argument.
|
|
* </pre>
|
|
* @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
* @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission
|
|
* to use, copy, modify, and distribute this software is freely granted,
|
|
* provided that this notice is preserved.
|
|
*/
|
|
|
|
double tanh(double x)
|
|
{
|
|
double t,z;
|
|
sword jx,ix;
|
|
|
|
/* High word of |x|. */
|
|
GET_HIGH_WORD(jx,x);
|
|
ix = jx&0x7fffffff;
|
|
|
|
/* x is INF or NaN */
|
|
if(ix>=0x7ff00000) {
|
|
if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
|
else return one/x-one; /* tanh(NaN) = NaN */
|
|
}
|
|
|
|
/* |x| < 22 */
|
|
if (ix < 0x40360000) { /* |x|<22 */
|
|
if (ix<0x3c800000) /* |x|<2**-55 */
|
|
return x*(one+x); /* tanh(small) = small */
|
|
if (ix>=0x3ff00000) { /* |x|>=1 */
|
|
t = expm1(two*fabs(x));
|
|
z = one - two/(t+two);
|
|
} else {
|
|
t = expm1(-two*fabs(x));
|
|
z= -t/(t+two);
|
|
}
|
|
/* |x| > 22, return +-1 */
|
|
} else {
|
|
z = one - tiny; /* raised inexact flag */
|
|
}
|
|
return (jx>=0)? z: -z;
|
|
}
|