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/* Copyright (c) <2003-2011> <Julio Jerez, Newton Game Dynamics>
*
* This software is provided 'as-is', without any express or implied
* warranty. In no event will the authors be held liable for any damages
* arising from the use of this software.
*
* Permission is granted to anyone to use this software for any purpose,
* including commercial applications, and to alter it and redistribute it
* freely, subject to the following restrictions:
*
* 1. The origin of this software must not be misrepresented; you must not
* claim that you wrote the original software. If you use this software
* in a product, an acknowledgment in the product documentation would be
* appreciated but is not required.
*
* 2. Altered source versions must be plainly marked as such, and must not be
* misrepresented as being the original software.
*
* 3. This notice may not be removed or altered from any source distribution.
*/
#include "dgStdafx.h"
#include "dgGoogol.h"
#include "dgSmallDeterminant.h"
#define Absolute(a) ((a) >= 0.0 ? (a) : -(a))
dgFloat64 Determinant2x2(const dgFloat64 matrix[2][2], dgFloat64 *const error) {
dgFloat64 a00xa11 = matrix[0][0] * matrix[1][1];
dgFloat64 a01xa10 = matrix[0][1] * matrix[1][0];
*error = Absolute(a00xa11) + Absolute(a01xa10);
return a00xa11 - a01xa10;
}
dgGoogol Determinant2x2(const dgGoogol matrix[2][2]) {
dgGoogol a00xa11(matrix[0][0] * matrix[1][1]);
dgGoogol a01xa10(matrix[0][1] * matrix[1][0]);
return a00xa11 - a01xa10;
}
dgFloat64 Determinant3x3(const dgFloat64 matrix[3][3], dgFloat64 *const error) {
dgFloat64 sign = dgFloat64(-1.0f);
dgFloat64 det = dgFloat64(0.0f);
dgFloat64 accError = dgFloat64(0.0f);
for (dgInt32 i = 0; i < 3; i++) {
dgFloat64 cofactor[2][2];
for (dgInt32 j = 0; j < 2; j++) {
dgInt32 k0 = 0;
for (dgInt32 k = 0; k < 3; k++) {
if (k != i) {
cofactor[j][k0] = matrix[j][k];
k0++;
}
}
}
dgFloat64 parcialError;
dgFloat64 minorDet = Determinant2x2(cofactor, &parcialError);
accError += parcialError * Absolute(matrix[2][i]);
det += sign * minorDet * matrix[2][i];
sign *= dgFloat64(-1.0f);
}
*error = accError;
return det;
}
dgGoogol Determinant3x3(const dgGoogol matrix[3][3]) {
dgGoogol negOne(dgFloat64(-1.0f));
dgGoogol sign(dgFloat64(-1.0f));
dgGoogol det = dgFloat64(0.0f);
for (dgInt32 i = 0; i < 3; i++) {
dgGoogol cofactor[2][2];
for (dgInt32 j = 0; j < 2; j++) {
dgInt32 k0 = 0;
for (dgInt32 k = 0; k < 3; k++) {
if (k != i) {
cofactor[j][k0] = matrix[j][k];
k0++;
}
}
}
dgGoogol minorDet(Determinant2x2(cofactor));
det = det + sign * minorDet * matrix[2][i];
sign = sign * negOne;
}
return det;
}
dgFloat64 Determinant4x4(const dgFloat64 matrix[4][4], dgFloat64 *const error) {
dgFloat64 sign = dgFloat64(1.0f);
dgFloat64 det = dgFloat64(0.0f);
dgFloat64 accError = dgFloat64(0.0f);
for (dgInt32 i = 0; i < 4; i++) {
dgFloat64 cofactor[3][3];
for (dgInt32 j = 0; j < 3; j++) {
dgInt32 k0 = 0;
for (dgInt32 k = 0; k < 4; k++) {
if (k != i) {
cofactor[j][k0] = matrix[j][k];
k0++;
}
}
}
dgFloat64 parcialError;
dgFloat64 minorDet = Determinant3x3(cofactor, &parcialError);
accError += parcialError * Absolute(matrix[3][i]);
det += sign * minorDet * matrix[3][i];
sign *= dgFloat64(-1.0f);
}
*error = accError;
return det;
}
dgGoogol Determinant4x4(const dgGoogol matrix[4][4]) {
dgGoogol sign = dgFloat64(1.0f);
dgGoogol det = dgFloat64(0.0f);
dgGoogol negOne(dgFloat64(-1.0f));
dgGoogol accError = dgFloat64(0.0f);
for (dgInt32 i = 0; i < 4; i++) {
dgGoogol cofactor[3][3];
for (dgInt32 j = 0; j < 3; j++) {
dgInt32 k0 = 0;
for (dgInt32 k = 0; k < 4; k++) {
if (k != i) {
cofactor[j][k0] = matrix[j][k];
k0++;
}
}
}
dgGoogol minorDet = Determinant3x3(cofactor);
det = det + sign * minorDet * matrix[3][i];
sign = sign * negOne;
}
return det;
}
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