83 lines
2.6 KiB
C++
83 lines
2.6 KiB
C++
/*
|
|
* 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/>.
|
|
*/
|
|
/* Copyright (C) 1997-2001 Ken Turkowski. <turk_at_computer.org>
|
|
*
|
|
* All rights reserved.
|
|
*
|
|
* Warranty Information
|
|
* Even though I have reviewed this software, I make no warranty
|
|
* or representation, either express or implied, with respect to this
|
|
* software, its quality, accuracy, merchantability, or fitness for a
|
|
* particular purpose. As a result, this software is provided "as is,"
|
|
* and you, its user, are assuming the entire risk as to its quality
|
|
* and accuracy.
|
|
*
|
|
* This code may be used and freely distributed as long as it includes
|
|
* this copyright notice and the above warranty information.
|
|
*/
|
|
|
|
#include <math.h>
|
|
|
|
|
|
#define FLOAT float
|
|
#define double_t double
|
|
|
|
/*******************************************************************************
|
|
* FindCubicRoots
|
|
*
|
|
* 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 * 3.14159265) / 3) - a1 / 3;
|
|
x[2] = -2 * sqrtQ * cos((theta + 4 * 3.14159265) / 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);
|
|
}
|
|
}
|