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.

build_files/cmake/Modules/GTestTesting.cmake

@@ -32,6 +32,7 @@ macro(BLENDER_SRC_GTEST_EX NAME SRC EXTRA_LIBS DO_ADD_TEST)
 		                      ${EXTRA_LIBS}
 		                      ${PLATFORM_LINKLIBS}
 		                      bf_testing_main
+		                      bf_intern_eigen
 		                      bf_intern_guardedalloc
 		                      extern_gtest
 		                      extern_gmock

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. */

source/blender/blenlib/intern/math_matrix.c

@@ -33,6 +33,8 @@
 
 #include "BLI_strict_flags.h"
 
+#include "eigen_capi.h"
+
 /********************************* Init **************************************/
 
 void zero_m2(float m[2][2])
@@ -192,6 +194,25 @@ void mul_m4_m4m4_uniq(float R[4][4], const float A[4][4], const float B[4][4])
 	BLI_assert(R != A && R != B);
 
 	/* matrix product: R[j][k] = A[j][i] . B[i][k] */
+#ifdef __SSE2__
+    __m128 A0 = _mm_loadu_ps(A[0]);
+    __m128 A1 = _mm_loadu_ps(A[1]);
+    __m128 A2 = _mm_loadu_ps(A[2]);
+    __m128 A3 = _mm_loadu_ps(A[3]);
+
+    for (int i = 0; i < 4; i++) {
+        __m128 B0 = _mm_set1_ps(B[i][0]);
+        __m128 B1 = _mm_set1_ps(B[i][1]);
+        __m128 B2 = _mm_set1_ps(B[i][2]);
+        __m128 B3 = _mm_set1_ps(B[i][3]);
+
+        __m128 sum = _mm_add_ps(
+			_mm_add_ps(_mm_mul_ps(B0, A0), _mm_mul_ps(B1, A1)),
+			_mm_add_ps(_mm_mul_ps(B2, A2), _mm_mul_ps(B3, A3)));
+
+        _mm_storeu_ps(R[i], sum);
+    }
+#else
 	R[0][0] = B[0][0] * A[0][0] + B[0][1] * A[1][0] + B[0][2] * A[2][0] + B[0][3] * A[3][0];
 	R[0][1] = B[0][0] * A[0][1] + B[0][1] * A[1][1] + B[0][2] * A[2][1] + B[0][3] * A[3][1];
 	R[0][2] = B[0][0] * A[0][2] + B[0][1] * A[1][2] + B[0][2] * A[2][2] + B[0][3] * A[3][2];
@@ -211,6 +232,7 @@ void mul_m4_m4m4_uniq(float R[4][4], const float A[4][4], const float B[4][4])
 	R[3][1] = B[3][0] * A[0][1] + B[3][1] * A[1][1] + B[3][2] * A[2][1] + B[3][3] * A[3][1];
 	R[3][2] = B[3][0] * A[0][2] + B[3][1] * A[1][2] + B[3][2] * A[2][2] + B[3][3] * A[3][2];
 	R[3][3] = B[3][0] * A[0][3] + B[3][1] * A[1][3] + B[3][2] * A[2][3] + B[3][3] * A[3][3];
+#endif
 }
 
 void mul_m4_m4_pre(float R[4][4], const float A[4][4])
@@ -875,74 +897,11 @@ bool invert_m4(float m[4][4])
 	return success;
 }
 
-/*
- * invertmat -
- *      computes the inverse of mat and puts it in inverse.  Returns
- *  true on success (i.e. can always find a pivot) and false on failure.
- *  Uses Gaussian Elimination with partial (maximal column) pivoting.
- *
- *					Mark Segal - 1992
- */
-
 bool invert_m4_m4(float inverse[4][4], const float mat[4][4])
 {
-	int i, j, k;
-	double temp;
-	float tempmat[4][4];
-	float max;
-	int maxj;
-
-	BLI_assert(inverse != mat);
-
-	/* Set inverse to identity */
-	for (i = 0; i < 4; i++)
-		for (j = 0; j < 4; j++)
-			inverse[i][j] = 0;
-	for (i = 0; i < 4; i++)
-		inverse[i][i] = 1;
-
-	/* Copy original matrix so we don't mess it up */
-	for (i = 0; i < 4; i++)
-		for (j = 0; j < 4; j++)
-			tempmat[i][j] = mat[i][j];
-
-	for (i = 0; i < 4; i++) {
-		/* Look for row with max pivot */
-		max = fabsf(tempmat[i][i]);
-		maxj = i;
-		for (j = i + 1; j < 4; j++) {
-			if (fabsf(tempmat[j][i]) > max) {
-				max = fabsf(tempmat[j][i]);
-				maxj = j;
-			}
-		}
-		/* Swap rows if necessary */
-		if (maxj != i) {
-			for (k = 0; k < 4; k++) {
-				SWAP(float, tempmat[i][k], tempmat[maxj][k]);
-				SWAP(float, inverse[i][k], inverse[maxj][k]);
-			}
-		}
-
-		if (UNLIKELY(tempmat[i][i] == 0.0f)) {
-			return false;  /* No non-zero pivot */
-		}
-		temp = (double)tempmat[i][i];
-		for (k = 0; k < 4; k++) {
-			tempmat[i][k] = (float)((double)tempmat[i][k] / temp);
-			inverse[i][k] = (float)((double)inverse[i][k] / temp);
-		}
-		for (j = 0; j < 4; j++) {
-			if (j != i) {
-				temp = tempmat[j][i];
-				for (k = 0; k < 4; k++) {
-					tempmat[j][k] -= (float)((double)tempmat[i][k] * temp);
-					inverse[j][k] -= (float)((double)inverse[i][k] * temp);
-				}
-			}
-		}
-	}
-	return true;
+	/* Use optimized matrix inverse from Eigen, since performance
+	 * impact of this function is significant in complex rigs. */
+	return EIG_invert_m4_m4(inverse, mat);
 }
 
 /****************************** Linear Algebra *******************************/