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/* @(#)z_tanh.c 1.0 98/08/13 */
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/* @(#)z_tanh.c 1.0 98/08/13 */
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/*****************************************************************
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/*****************************************************************
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* The following routines are coded directly from the algorithms
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* The following routines are coded directly from the algorithms
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* and coefficients given in "Software Manual for the Elementary
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* and coefficients given in "Software Manual for the Elementary
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* Functions" by William J. Cody, Jr. and William Waite, Prentice
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* Functions" by William J. Cody, Jr. and William Waite, Prentice
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* Hall, 1980.
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* Hall, 1980.
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*****************************************************************/
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*****************************************************************/
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/*
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/*
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FUNCTION
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FUNCTION
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<<tanh>>, <<tanhf>>---hyperbolic tangent
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<<tanh>>, <<tanhf>>---hyperbolic tangent
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INDEX
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INDEX
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tanh
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tanh
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INDEX
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INDEX
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tanhf
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tanhf
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ANSI_SYNOPSIS
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ANSI_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double tanh(double <[x]>);
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double tanh(double <[x]>);
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float tanhf(float <[x]>);
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float tanhf(float <[x]>);
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TRAD_SYNOPSIS
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TRAD_SYNOPSIS
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#include <math.h>
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#include <math.h>
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double tanh(<[x]>)
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double tanh(<[x]>)
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double <[x]>;
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double <[x]>;
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float tanhf(<[x]>)
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float tanhf(<[x]>)
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float <[x]>;
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float <[x]>;
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DESCRIPTION
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DESCRIPTION
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<<tanh>> computes the hyperbolic tangent of
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<<tanh>> computes the hyperbolic tangent of
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the argument <[x]>. Angles are specified in radians.
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the argument <[x]>. Angles are specified in radians.
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<<tanh(<[x]>)>> is defined as
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<<tanh(<[x]>)>> is defined as
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. sinh(<[x]>)/cosh(<[x]>)
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. sinh(<[x]>)/cosh(<[x]>)
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<<tanhf>> is identical, save that it takes and returns <<float>> values.
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<<tanhf>> is identical, save that it takes and returns <<float>> values.
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RETURNS
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RETURNS
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The hyperbolic tangent of <[x]> is returned.
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The hyperbolic tangent of <[x]> is returned.
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PORTABILITY
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PORTABILITY
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<<tanh>> is ANSI C. <<tanhf>> is an extension.
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<<tanh>> is ANSI C. <<tanhf>> is an extension.
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*/
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*/
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/******************************************************************
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/******************************************************************
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* Hyperbolic Tangent
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* Hyperbolic Tangent
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*
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*
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* Input:
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* Input:
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* x - floating point value
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* x - floating point value
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*
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*
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* Output:
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* Output:
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* hyperbolic tangent of x
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* hyperbolic tangent of x
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*
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*
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* Description:
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* Description:
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* This routine calculates hyperbolic tangent.
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* This routine calculates hyperbolic tangent.
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*
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*
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*****************************************************************/
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*****************************************************************/
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#include <float.h>
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#include <float.h>
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#include "fdlibm.h"
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#include "fdlibm.h"
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#include "zmath.h"
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#include "zmath.h"
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#ifndef _DOUBLE_IS_32BITS
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#ifndef _DOUBLE_IS_32BITS
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static const double LN3_OVER2 = 0.54930614433405484570;
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static const double LN3_OVER2 = 0.54930614433405484570;
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static const double p[] = { -0.16134119023996228053e+4,
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static const double p[] = { -0.16134119023996228053e+4,
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-0.99225929672236083313e+2,
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-0.99225929672236083313e+2,
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-0.96437492777225469787 };
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-0.96437492777225469787 };
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static const double q[] = { 0.48402357071988688686e+4,
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static const double q[] = { 0.48402357071988688686e+4,
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0.22337720718962312926e+4,
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0.22337720718962312926e+4,
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0.11274474380534949335e+3 };
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0.11274474380534949335e+3 };
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double
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double
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_DEFUN (tanh, (double),
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_DEFUN (tanh, (double),
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double x)
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double x)
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{
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{
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double f, res, g, P, Q, R;
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double f, res, g, P, Q, R;
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f = fabs (x);
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f = fabs (x);
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/* Check if the input is too big. */
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/* Check if the input is too big. */
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if (f > BIGX)
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if (f > BIGX)
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res = 1.0;
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res = 1.0;
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else if (f > LN3_OVER2)
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else if (f > LN3_OVER2)
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res = 1.0 - 2.0 / (exp (2 * f) + 1.0);
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res = 1.0 - 2.0 / (exp (2 * f) + 1.0);
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/* Check if the input is too small. */
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/* Check if the input is too small. */
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else if (f < z_rooteps)
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else if (f < z_rooteps)
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res = f;
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res = f;
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/* Calculate the Taylor series. */
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/* Calculate the Taylor series. */
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else
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else
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{
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{
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g = f * f;
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g = f * f;
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P = (p[2] * g + p[1]) * g + p[0];
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P = (p[2] * g + p[1]) * g + p[0];
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Q = ((g + q[2]) * g + q[1]) * g + q[0];
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Q = ((g + q[2]) * g + q[1]) * g + q[0];
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R = g * (P / Q);
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R = g * (P / Q);
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res = f + f * R;
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res = f + f * R;
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}
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}
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if (x < 0.0)
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if (x < 0.0)
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res = -res;
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res = -res;
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return (res);
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return (res);
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}
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}
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#endif /* _DOUBLE_IS_32BITS */
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#endif /* _DOUBLE_IS_32BITS */
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