mirror of https://gitlab.com/rnger/amath
123 lines
3.9 KiB
C
123 lines
3.9 KiB
C
/*-
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* Copyright (c) 2014-2017 Carsten Sonne Larsen <cs@innolan.net>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* Project homepage:
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* https://amath.innolan.net
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*
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* The original source code can be obtained from:
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* http://www.netlib.org/fdlibm/s_tanh.c
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*
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* =================================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* =================================================================
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*/
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/**
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* @file tanh.c
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* @brief Hyperbolic tangent function
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*/
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#include "prim.h"
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static const double
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one = 1.0,
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two = 2.0,
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tiny = 1.0e-300;
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/**
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* @brief Hyperbolic tangent function
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* @return The Hyperbolic Tangent of x
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* @details
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* <pre>
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* Method
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* x -x
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* e - e
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* 0. tanh(x) is defined to be -----------
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* x -x
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* e + e
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*
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* 1. reduce x to non-negative by tanh(-x) = -tanh(x)
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*
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* 2. 0 <= x <= 2**-55 : tanh(x) = x*(one+x)
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* -t
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* 2**-55 < x <= 1 : tanh(x) = -----; t = expm1(-2x)
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* t + 2
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* 2
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* 1 <= x <= 22.0 : tanh(x) = 1- ----- ; t=expm1(2x)
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* t + 2
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* 22.0 < x <= INF : tanh(x) = 1
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*
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* Special cases
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* tanh(NaN) is NaN
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* only tanh(0)=0 is exact for finite argument.
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* </pre>
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*/
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double tanh(double x)
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{
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double t, z;
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int32_t jx, ix;
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/* High word of |x|. */
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GET_HIGH_WORD(jx, x);
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ix = jx & 0x7FFFFFFF;
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/* x is INF or NaN */
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if (ix >= 0x7FF00000)
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{
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if (jx >= 0)
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return one / x + one; /* tanh(+-inf)=+-1 */
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else
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return NAN; /* tanh(NaN) = NaN */
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}
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/* |x| < 22 */
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if (ix < 0x40360000)
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{ /* |x|<22 */
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if (ix < 0x3C800000) /* |x|<2**-55 */
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return x * (one + x); /* tanh(small) = small */
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if (ix >= 0x3FF00000)
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{ /* |x|>=1 */
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t = expm1(two * fabs(x));
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z = one - two / (t + two);
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}
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else
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{
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t = expm1(-two * fabs(x));
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z = -t / (t + two);
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}
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}
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/* |x| > 22, return +-1 */
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else
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{
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z = one - tiny; /* raised inexact flag */
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}
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return (jx >= 0) ? z : -z;
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}
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