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/* @(#)z_tanh.c 1.0 98/08/13 */

/*****************************************************************

 * The following routines are coded directly from the algorithms

 * and coefficients given in "Software Manual for the Elementary

 * Functions" by William J. Cody, Jr. and William Waite, Prentice

 * Hall, 1980.

 *****************************************************************/

/*

FUNCTION

        <<tanh>>, <<tanhf>>---hyperbolic tangent

INDEX

tanh

INDEX

tanhf

ANSI_SYNOPSIS

        #include <math.h>

        double tanh(double <[x]>);

        float tanhf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double tanh(<[x]>)

        double <[x]>;

        float tanhf(<[x]>)

        float <[x]>;

DESCRIPTION

<<tanh>> computes the hyperbolic tangent of

the argument <[x]>.  Angles are specified in radians.

<<tanh(<[x]>)>> is defined as

. sinh(<[x]>)/cosh(<[x]>)

<<tanhf>> is identical, save that it takes and returns <<float>> values.

RETURNS

The hyperbolic tangent of <[x]> is returned.

PORTABILITY

<<tanh>> is ANSI C.  <<tanhf>> is an extension.

*/

/******************************************************************

 * Hyperbolic Tangent

 *

 * Input:

 *   x - floating point value

 *

 * Output:

 *   hyperbolic tangent of x

 *

 * Description:

 *   This routine calculates hyperbolic tangent.

 *

 *****************************************************************/

#include <float.h>

#include "fdlibm.h"

#include "zmath.h"

#ifndef _DOUBLE_IS_32BITS

static const double LN3_OVER2 = 0.54930614433405484570;

static const double p[] = { -0.16134119023996228053e+4,

                            -0.99225929672236083313e+2,

                            -0.96437492777225469787 };

static const double q[] = { 0.48402357071988688686e+4,

                            0.22337720718962312926e+4,

                            0.11274474380534949335e+3 };

double

_DEFUN (tanh, (double),

        double x)

{

  double f, res, g, P, Q, R;

  f = fabs (x);

  /* Check if the input is too big. */

  if (f > BIGX)

    res = 1.0;

  else if (f > LN3_OVER2)

    res = 1.0 - 2.0 / (exp (2 * f) + 1.0);

  /* Check if the input is too small. */

  else if (f < z_rooteps)

    res = f;

  /* Calculate the Taylor series. */

  else

    {

      g = f * f;

      P = (p[2] * g + p[1]) * g + p[0];

      Q = ((g + q[2]) * g + q[1]) * g + q[0];

      R = g * (P / Q);

      res = f + f * R;

    }

  if (x < 0.0)

    res = -res;

  return (res);

}

#endif /* _DOUBLE_IS_32BITS */