Math: optimizations for 4x4x matrix inverse, multiplications.

In some heavy rigs matrix inverse can be 10% of computation time. This
reduces it to 2% by using Eigen's optimized 4x4 matrix inverse and SSE
matrix multiplication.

intern/eigen/CMakeLists.txt

@@ -36,10 +36,12 @@ set(SRC
 
 	intern/eigenvalues.cc
 	intern/linear_solver.cc
+	intern/matrix.cc
 	intern/svd.cc
 
 	intern/eigenvalues.h
 	intern/linear_solver.h
+	intern/matrix.h
 	intern/svd.h
 )
 

intern/eigen/eigen_capi.h

@@ -29,6 +29,7 @@
 
 #include "intern/eigenvalues.h"
 #include "intern/linear_solver.h"
+#include "intern/matrix.h"
 #include "intern/svd.h"
 
 #endif  /* __EIGEN_C_API_H__ */

intern/eigen/intern/matrix.cc

@@ -0,0 +1,56 @@
+/*
+ * ***** BEGIN GPL LICENSE BLOCK *****
+ *
+ * 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 2
+ * 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.
+ *
+ * The Original Code is Copyright (C) 2015 Blender Foundation.
+ * All rights reserved.
+ *
+ * Contributor(s): Blender Foundation,
+ *                 Bastien Montagne
+ *
+ * ***** END GPL LICENSE BLOCK *****
+ */
+
+#ifndef __EIGEN3_MATRIX_C_API_CC__
+#define __EIGEN3_MATRIX_C_API_CC__
+
+/* Eigen gives annoying huge amount of warnings here, silence them! */
+#if defined(__GNUC__) && !defined(__clang__)
+#  pragma GCC diagnostic ignored "-Wlogical-op"
+#endif
+
+#ifdef __EIGEN3_MATRIX_C_API_CC__  /* quiet warning */
+#endif
+
+#include <Eigen/Core>
+#include <Eigen/Dense>
+
+#include "matrix.h"
+
+using Eigen::Map;
+using Eigen::Matrix4f;
+
+bool EIG_invert_m4_m4(float inverse[4][4], const float matrix[4][4])
+{
+	Map<Matrix4f> M = Map<Matrix4f>((float*)matrix);
+	Matrix4f R;
+	bool invertible = true;
+	M.computeInverseWithCheck(R, invertible, 0.0f);
+	memcpy(inverse, R.data(), sizeof(float)*4*4);
+	return invertible;
+}
+
+#endif  /* __EIGEN3_MATRIX_C_API_CC__ */

intern/eigen/intern/matrix.h

@@ -0,0 +1,40 @@
+/*
+ * ***** BEGIN GPL LICENSE BLOCK *****
+ *
+ * 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 2
+ * 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.
+ *
+ * The Original Code is Copyright (C) 2015 Blender Foundation.
+ * All rights reserved.
+ *
+ * Contributor(s): Blender Foundation,
+ *                 Bastien Montagne
+ *
+ * ***** END GPL LICENSE BLOCK *****
+ */
+
+#ifndef __EIGEN3_MATRIX_C_API_H__
+#define __EIGEN3_MATRIX_C_API_H__
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+bool EIG_invert_m4_m4(float inverse[4][4], const float matrix[4][4]);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif  /* __EIGEN3_MATRIX_C_API_H__ */

intern/eigen/intern/svd.cc

@@ -37,6 +37,7 @@
 
 #include <Eigen/Core>
 #include <Eigen/SVD>
+#include <Eigen/Dense>
 
 #include "svd.h"
 
@@ -51,6 +52,8 @@ using Eigen::MatrixXf;
 using Eigen::VectorXf;
 using Eigen::Map;
 
+using Eigen::Matrix4f;
+
 void EIG_svd_square_matrix(const int size, const float *matrix, float *r_U, float *r_S, float *r_V)
 {
 	/* Since our matrix is squared, we can use thinU/V. */