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/* @(#)z_sine.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

        <<sin>>, <<cos>>, <<sine>>, <<sinf>>, <<cosf>>, <<sinef>>---sine or cosine

INDEX

sin

INDEX

sinf

INDEX

cos

INDEX

cosf

ANSI_SYNOPSIS

        #include <math.h>

        double sin(double <[x]>);

        float  sinf(float <[x]>);

        double cos(double <[x]>);

        float cosf(float <[x]>);

TRAD_SYNOPSIS

        #include <math.h>

        double sin(<[x]>)

        double <[x]>;

        float  sinf(<[x]>)

        float <[x]>;

        double cos(<[x]>)

        double <[x]>;

        float cosf(<[x]>)

        float <[x]>;

DESCRIPTION

        <<sin>> and <<cos>> compute (respectively) the sine and cosine

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

RETURNS

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

PORTABILITY

        <<sin>> and <<cos>> are ANSI C.

        <<sinf>> and <<cosf>> are extensions.

QUICKREF

        sin ansi pure

        sinf - pure

*/

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

 * sine

 *

 * Input:

 *   x - floating point value

 *   cosine - indicates cosine value

 *

 * Output:

 *   Sine of x.

 *

 * Description:

 *   This routine calculates sines and cosines.

 *

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

#include "fdlibm.h"

#include "zmath.h"

#ifndef _DOUBLE_IS_32BITS

static const double HALF_PI = 1.57079632679489661923;

static const double ONE_OVER_PI = 0.31830988618379067154;

static const double r[] = { -0.16666666666666665052,

                             0.83333333333331650314e-02,

                            -0.19841269841201840457e-03,

                             0.27557319210152756119e-05,

                            -0.25052106798274584544e-07,

                             0.16058936490371589114e-09,

                            -0.76429178068910467734e-12,

                             0.27204790957888846175e-14 };

double

_DEFUN (sine, (double, int),

        double x _AND

        int cosine)

{

  int sgn, N;

  double y, XN, g, R, res;

  double YMAX = 210828714.0;

  switch (numtest (x))

    {

      case NAN:

        errno = EDOM;

        return (x);

      case INF:

        errno = EDOM;

        return (z_notanum.d);

    }

  /* Use sin and cos properties to ease computations. */

  if (cosine)

    {

      sgn = 1;

      y = fabs (x) + HALF_PI;

    }

  else

    {

      if (x < 0.0)

        {

          sgn = -1;

          y = -x;

        }

      else

        {

          sgn = 1;

          y = x;

        }

    }

  /* Check for values of y that will overflow here. */

  if (y > YMAX)

    {

      errno = ERANGE;

      return (x);

    }

  /* Calculate the exponent. */

  if (y < 0.0)

    N = (int) (y * ONE_OVER_PI - 0.5);

  else

    N = (int) (y * ONE_OVER_PI + 0.5);

  XN = (double) N;

  if (N & 1)

    sgn = -sgn;

  if (cosine)

    XN -= 0.5;

  y = fabs (x) - XN * __PI;

  if (-z_rooteps < y && y < z_rooteps)

    res = y;

  else

    {

      g = y * y;

      /* Calculate the Taylor series. */

      R = (((((((r[6] * g + r[5]) * g + r[4]) * g + r[3]) * g + r[2]) * g + r[1]) * g + r[0]) * g);

      /* Finally, compute the result. */

      res = y + y * R;

    }

  res *= sgn;

  return (res);

}

#endif /* _DOUBLE_IS_32BITS */