/*
 *  This file is part of RawTherapee.
 *
 *  Copyright (c) 2004-2010 Gabor Horvath <hgabor@rawtherapee.com>
 *
 *  RawTherapee 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.
 * 
 *  RawTherapee 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 RawTherapee.  If not, see <http://www.gnu.org/licenses/>.
 */
inline double tightestroot (double L, double a, double b, double r1, double r2, double r3);

#ifndef __COLORCLIP__
#define __COLORCLIP__

#include <cmath>
#include "median.h"

// gives back the tightest >0 amplification by which color clipping occures

inline double tightestroot (double L, double a, double b, double r1, double r2, double r3) {
  
  double an = a/500.0, bn = b/200.0, p = (L+16.0)/116.0;

  double coeff3 = r1*an*an*an - r3*bn*bn*bn;
  double coeff2 = 3.0 * p * (r1*an*an + r3*bn*bn);
  double coeff1 = 3.0 * p*p * (r1*an - r3*bn);
  double coeff0 = p*p*p*(r1+r2+r3) - 1.0;

  double a1 = coeff2 / coeff3;
  double a2 = coeff1 / coeff3;
  double a3 = coeff0 / coeff3;

  double Q = (a1 * a1 - 3.0 * a2) / 9.0;
  double R = (2.0 * a1 * a1 * a1 - 9.0 * a1 * a2 + 27.0 * a3) / 54.0;
  double Qcubed = Q * Q * Q;
  double d = Qcubed - R * R;

//  printf ("input L=%g, a=%g, b=%g\n", L, a, b);
//  printf ("c1=%g, c2=%g, c3=%g, c4=%g\n", coeff3, coeff2, coeff1, coeff0);


  /* Three real roots */
  if (d >= 0) {
    double theta = acos(R / sqrt(Qcubed));
    double sqrtQ = sqrt(Q);
    double x0 = -2.0 * sqrtQ * cos( theta               / 3.0) - a1 / 3.0;
    double x1 = -2.0 * sqrtQ * cos((theta + 2.0 * M_PI) / 3.0) - a1 / 3.0;
    double x2 = -2.0 * sqrtQ * cos((theta + 4.0 * M_PI) / 3.0) - a1 / 3.0;
    
//    printf ("3 roots: %g, %g, %g\n", x0, x1, x2);

    SORT3 (x0,x1,x2,a1,a2,a3);
    if (a1>0)
      return a1;
    if (a2>0)
      return a2;
    if (a3>0)
      return a3;
    return -1;
  }

  /* One real root */
  else {
//    double e = pow(sqrt(-d) + fabs(R), 1.0 / 3.0);
    double e = exp (1.0 / 3.0 * log (sqrt(-d) + fabs(R)));

    if (R > 0)
      e = -e;

    double x0 = (e + Q / e) - a1 / 3.0;

//    printf ("1 root: %g\n", x0);

    if (x0<0)
      return -1;
    else
      return x0;
  }
}


/*******************************************************************************
 * FindCubicRoots
 * --------------
 *
 * Copyright (C) 1997-2001 Ken Turkowski. <turk_at_computer.org>
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 * 
 * The above copyright notice and this permission notice shall be included
 * in all copies or substantial portions of the Software.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * ------------------------------------------------------------------------
 *
 *	Solve:
 *		coeff[3] * x^3 + coeff[2] * x^2 + coeff[1] * x + coeff[0] = 0
 *
 *	returns:
 *		3 - 3 real roots
 *		1 - 1 real root (2 complex conjugate)
 *		
 *******************************************************************************/

/*long
FindCubicRoots(const FLOAT coeff[4], FLOAT x[3])
{
	FLOAT a1 = coeff[2] / coeff[3];
	FLOAT a2 = coeff[1] / coeff[3];
	FLOAT a3 = coeff[0] / coeff[3];

	double_t Q = (a1 * a1 - 3 * a2) / 9;
	double_t R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) / 54;
	double_t Qcubed = Q * Q * Q;
	double_t d = Qcubed - R * R;

	// Three real roots
	if (d >= 0) {
		double_t theta = acos(R / sqrt(Qcubed));
		double_t sqrtQ = sqrt(Q);
		x[0] = -2 * sqrtQ * cos( theta           / 3) - a1 / 3;
		x[1] = -2 * sqrtQ * cos((theta + 2 * pi) / 3) - a1 / 3;
		x[2] = -2 * sqrtQ * cos((theta + 4 * pi) / 3) - a1 / 3;
		return (3);
	}

	// One real root
	else {
		double_t e = pow(sqrt(-d) + fabs(R), 1. / 3.);
		if (R > 0)
			e = -e;
		x[0] = (e + Q / e) - a1 / 3.;
		return (1);
	}
}
*/
#endif