From 01c75c3765eb305b1a99b794c1d40ad224b071c6 Mon Sep 17 00:00:00 2001 From: Brecht Van Lommel Date: Thu, 31 May 2018 16:36:20 +0200 Subject: 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. --- source/blender/blenlib/intern/math_matrix.c | 91 ++++++++--------------------- 1 file changed, 25 insertions(+), 66 deletions(-) (limited to 'source/blender/blenlib/intern/math_matrix.c') diff --git a/source/blender/blenlib/intern/math_matrix.c b/source/blender/blenlib/intern/math_matrix.c index 3559500bf63..0272fa6f52b 100644 --- a/source/blender/blenlib/intern/math_matrix.c +++ b/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 *******************************/ -- cgit v1.2.3