/* specfunc/elementary.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program is distributed in the hope that it will be useful, but

 * WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

/* Author:  G. Jungman */

#include <config.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_sf_elementary.h>

#include "error.h"

#include "check.h"

int

gsl_sf_multiply_e(const double x, const double y, gsl_sf_result * result)

{

  const double ax = fabs(x);

  const double ay = fabs(y);

  if(x == 0.0 || y == 0.0) {

    /* It is necessary to eliminate this immediately.

     */

    result->val = 0.0;

    result->err = 0.0;

    return GSL_SUCCESS;

  }

  else if((ax <= 1.0 && ay >= 1.0) || (ay <= 1.0 && ax >= 1.0)) {

    /* Straddling 1.0 is always safe.

     */

    result->val = x*y;

    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);

    return GSL_SUCCESS;

  }

  else {

    const double f = 1.0 - 2.0 * GSL_DBL_EPSILON;

    const double min = GSL_MIN_DBL(fabs(x), fabs(y));

    const double max = GSL_MAX_DBL(fabs(x), fabs(y));

    if(max < 0.9 * GSL_SQRT_DBL_MAX || min < (f * DBL_MAX)/max) {

      result->val = GSL_COERCE_DBL(x*y);

      result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);

      CHECK_UNDERFLOW(result);

      return GSL_SUCCESS;

    }

    else {

      OVERFLOW_ERROR(result);

    }

  }

}

int

gsl_sf_multiply_err_e(const double x, const double dx,

                         const double y, const double dy,

                         gsl_sf_result * result)

{

  int status = gsl_sf_multiply_e(x, y, result);

  result->err += fabs(dx*y) + fabs(dy*x);

  return status;

}

/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/

#include "eval.h"

double gsl_sf_multiply(const double x, const double y)

{

  EVAL_RESULT(gsl_sf_multiply_e(x, y, &result));

}