71 lines
2.3 KiB
C++
71 lines
2.3 KiB
C++
/* Copyright (C) 1997-2001 Ken Turkowski. <turk_at_computer.org>
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*
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* Permission is hereby granted, free of charge, to any person obtaining
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* a copy of this software and associated documentation files (the
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* "Software"), to deal in the Software without restriction, including
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* without limitation the rights to use, copy, modify, merge, publish,
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* distribute, sublicense, and/or sell copies of the Software, and to
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* permit persons to whom the Software is furnished to do so, subject to
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* the following conditions:
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*
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* The above copyright notice and this permission notice shall be included
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* in all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
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* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
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* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
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* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*/
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#include <math.h>
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#define FLOAT float
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#define double_t double
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/*******************************************************************************
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* FindCubicRoots
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*
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* Solve:
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* coeff[3] * x^3 + coeff[2] * x^2 + coeff[1] * x + coeff[0] = 0
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*
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* returns:
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* 3 - 3 real roots
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* 1 - 1 real root (2 complex conjugate)
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*******************************************************************************/
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long
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FindCubicRoots(const FLOAT coeff[4], FLOAT x[3])
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{
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FLOAT a1 = coeff[2] / coeff[3];
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FLOAT a2 = coeff[1] / coeff[3];
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FLOAT a3 = coeff[0] / coeff[3];
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double_t Q = (a1 * a1 - 3 * a2) / 9;
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double_t R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) / 54;
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double_t Qcubed = Q * Q * Q;
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double_t d = Qcubed - R * R;
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/* Three real roots */
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if (d >= 0) {
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double_t theta = acos(R / sqrt(Qcubed));
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double_t sqrtQ = sqrt(Q);
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x[0] = -2 * sqrtQ * cos( theta / 3) - a1 / 3;
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x[1] = -2 * sqrtQ * cos((theta + 2 * 3.14159265) / 3) - a1 / 3;
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x[2] = -2 * sqrtQ * cos((theta + 4 * 3.14159265) / 3) - a1 / 3;
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return (3);
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}
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/* One real root */
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else {
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double_t e = pow(sqrt(-d) + fabs(R), 1. / 3.);
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if (R > 0)
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e = -e;
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x[0] = (e + Q / e) - a1 / 3.;
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return (1);
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}
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}
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