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/* @(#)z_sineh.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

        <<sinh>>, <<sinhf>>, <<cosh>>, <<coshf>>, <<sineh>>---hyperbolic sine or cosine

INDEX

        sinh

INDEX

        sinhf

INDEX

        cosh

INDEX

        coshf

ANSI_SYNOPSIS

        #include <math.h>

        double sinh(double <[x]>);

        float  sinhf(float <[x]>);

        double cosh(double <[x]>);

        float  coshf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double sinh(<[x]>)

        double <[x]>;

        float  sinhf(<[x]>)

        float <[x]>;

        double cosh(<[x]>)

        double <[x]>;

        float  coshf(<[x]>)

        float <[x]>;

DESCRIPTION

        <<sinh>> and <<cosh>> compute the hyperbolic sine or cosine

        of the argument <[x]>.

        Angles are specified in radians.   <<sinh>>(<[x]>) is defined as

        @ifnottex

        . (exp(<[x]>) - exp(-<[x]>))/2

        @end ifnottex

        @tex

        $${e^x - e^{-x}}\over 2$$

        @end tex

        <<cosh>> is defined as

        @ifnottex

        . (exp(<[x]>) - exp(-<[x]>))/2

        @end ifnottex

        @tex

        $${e^x + e^{-x}}\over 2$$

        @end tex

        <<sinhf>> and <<coshf>> are identical, save that they take

        and returns <<float>> values.

RETURNS

        The hyperbolic sine or cosine of <[x]> is returned.

        When the correct result is too large to be representable (an

        overflow),  the functions return <<HUGE_VAL>> with the

        appropriate sign, and sets the global value <<errno>> to

        <<ERANGE>>.

PORTABILITY

        <<sinh>> is ANSI C.

        <<sinhf>> is an extension.

        <<cosh>> is ANSI C.

        <<coshf>> is an extension.

*/

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

 * Hyperbolic Sine

 *

 * Input:

 *   x - floating point value

 *

 * Output:

 *   hyperbolic sine of x

 *

 * Description:

 *   This routine calculates hyperbolic sines.

 *

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

#include <float.h>

#include "fdlibm.h"

#include "zmath.h"

static const double q[] = { -0.21108770058106271242e+7,

                             0.36162723109421836460e+5,

                            -0.27773523119650701667e+3 };

static const double p[] = { -0.35181283430177117881e+6,

                            -0.11563521196851768270e+5,

                            -0.16375798202630751372e+3,

                            -0.78966127417357099479 };

static const double LNV = 0.6931610107421875000;

static const double INV_V2 = 0.24999308500451499336;

static const double V_OVER2_MINUS1 = 0.13830277879601902638e-4;

double

_DEFUN (sineh, (double, int),

        double x _AND

        int cosineh)

{

  double y, f, P, Q, R, res, z, w;

  int sgn = 1;

  double WBAR = 18.55;

  /* Check for special values. */

  switch (numtest (x))

    {

      case NAN:

        errno = EDOM;

        return (x);

      case INF:

        errno = ERANGE;

        return (ispos (x) ? z_infinity.d : -z_infinity.d);

    }

  y = fabs (x);

  if (!cosineh && x < 0.0)

    sgn = -1;

  if ((y > 1.0 && !cosineh) || cosineh)

    {

      if (y > BIGX)

        {

          w = y - LNV;

          /* Check for w > maximum here. */

          if (w > BIGX)

            {

              errno = ERANGE;

              return (x);

            }

          z = exp (w);

          if (w > WBAR)

            res = z * (V_OVER2_MINUS1 + 1.0);

        }

      else

        {

          z = exp (y);

          if (cosineh)

            res = (z + 1 / z) / 2.0;

          else

            res = (z - 1 / z) / 2.0;

        }

      if (sgn < 0)

        res = -res;

    }

  else

    {

      /* Check for y being too small. */

      if (y < z_rooteps)

        {

          res = x;

        }

      /* Calculate the Taylor series. */

      else

        {

          f = x * x;

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

          P = ((p[3] * f + p[2]) * f + p[1]) * f + p[0];

          R = f * (P / Q);

          res = x + x * R;

        }

    }

  return (res);

}