Mesa (main): util: Move the 4x4 matrix inverse function to u_math
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Fri Jun 18 22:42:31 UTC 2021
Module: Mesa
Branch: main
Commit: f31bfda34abaf5fdd3c31497b476b11f23f728f3
URL: http://cgit.freedesktop.org/mesa/mesa/commit/?id=f31bfda34abaf5fdd3c31497b476b11f23f728f3
Author: Jason Ekstrand <jason at jlekstrand.net>
Date: Mon Jun 22 15:13:29 2020 -0500
util: Move the 4x4 matrix inverse function to u_math
Reviewed-by: Bas Nieuwenhuizen <bas at basnieuwenhuizen.nl>
Part-of: <https://gitlab.freedesktop.org/mesa/mesa/-/merge_requests/11078>
---
src/mesa/math/m_matrix.c | 117 +----------------------------
src/util/u_math.c | 186 +++++++++++++++++++++++++++++++++++++++++++++++
src/util/u_math.h | 2 +
3 files changed, 189 insertions(+), 116 deletions(-)
diff --git a/src/mesa/math/m_matrix.c b/src/mesa/math/m_matrix.c
index 46f379b1f61..62303bc4e7f 100644
--- a/src/mesa/math/m_matrix.c
+++ b/src/mesa/math/m_matrix.c
@@ -333,13 +333,6 @@ _math_matrix_print( const GLmatrix *m )
/** \name Matrix inversion */
/*@{*/
-/**
- * Swaps the values of two floating point variables.
- *
- * Used by invert_matrix_general() to swap the row pointers.
- */
-#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
-
/**
* Compute inverse of 4x4 transformation matrix.
*
@@ -357,116 +350,8 @@ _math_matrix_print( const GLmatrix *m )
*/
static GLboolean invert_matrix_general( GLmatrix *mat )
{
- const GLfloat *m = mat->m;
- GLfloat *out = mat->inv;
- GLfloat wtmp[4][8];
- GLfloat m0, m1, m2, m3, s;
- GLfloat *r0, *r1, *r2, *r3;
-
- r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
-
- r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
- r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
- r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
-
- r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
- r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
- r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
-
- r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
- r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
- r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
-
- r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
- r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
- r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
-
- /* choose pivot - or die */
- if (fabsf(r3[0])>fabsf(r2[0])) SWAP_ROWS(r3, r2);
- if (fabsf(r2[0])>fabsf(r1[0])) SWAP_ROWS(r2, r1);
- if (fabsf(r1[0])>fabsf(r0[0])) SWAP_ROWS(r1, r0);
- if (0.0F == r0[0]) return GL_FALSE;
-
- /* eliminate first variable */
- m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
- s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
- s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
- s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
- s = r0[4];
- if (s != 0.0F) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r0[5];
- if (s != 0.0F) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r0[6];
- if (s != 0.0F) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r0[7];
- if (s != 0.0F) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
- /* choose pivot - or die */
- if (fabsf(r3[1])>fabsf(r2[1])) SWAP_ROWS(r3, r2);
- if (fabsf(r2[1])>fabsf(r1[1])) SWAP_ROWS(r2, r1);
- if (0.0F == r1[1]) return GL_FALSE;
-
- /* eliminate second variable */
- m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
- r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
- r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
- s = r1[4]; if (0.0F != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
- s = r1[5]; if (0.0F != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
- s = r1[6]; if (0.0F != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
- s = r1[7]; if (0.0F != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }
-
- /* choose pivot - or die */
- if (fabsf(r3[2])>fabsf(r2[2])) SWAP_ROWS(r3, r2);
- if (0.0F == r2[2]) return GL_FALSE;
-
- /* eliminate third variable */
- m3 = r3[2]/r2[2];
- r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
- r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
- r3[7] -= m3 * r2[7];
-
- /* last check */
- if (0.0F == r3[3]) return GL_FALSE;
-
- s = 1.0F/r3[3]; /* now back substitute row 3 */
- r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;
-
- m2 = r2[3]; /* now back substitute row 2 */
- s = 1.0F/r2[2];
- r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
- r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
- m1 = r1[3];
- r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
- r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
- m0 = r0[3];
- r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
- r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
-
- m1 = r1[2]; /* now back substitute row 1 */
- s = 1.0F/r1[1];
- r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
- r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
- m0 = r0[2];
- r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
- r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
-
- m0 = r0[1]; /* now back substitute row 0 */
- s = 1.0F/r0[0];
- r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
- r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
-
- MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
- MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
- MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
- MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
- MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
- MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
- MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
- MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];
-
- return GL_TRUE;
+ return util_invert_mat4x4(mat->inv, mat->m);
}
-#undef SWAP_ROWS
/**
* Compute inverse of a general 3d transformation matrix.
diff --git a/src/util/u_math.c b/src/util/u_math.c
index 278a93736bc..7913285a15b 100644
--- a/src/util/u_math.c
+++ b/src/util/u_math.c
@@ -123,3 +123,189 @@ util_fpstate_set(unsigned mxcsr)
}
#endif
}
+
+/**
+ * Compute inverse of 4x4 matrix.
+ *
+ * \return false if the source matrix is singular.
+ *
+ * \author
+ * Code contributed by Jacques Leroy jle at star.be
+ *
+ * Calculates the inverse matrix by performing the gaussian matrix reduction
+ * with partial pivoting followed by back/substitution with the loops manually
+ * unrolled.
+ */
+bool
+util_invert_mat4x4(float *out, const float *m)
+{
+ float wtmp[4][8];
+ float m0, m1, m2, m3, s;
+ float *r0, *r1, *r2, *r3;
+
+#define MAT(m, r, c) (m)[(c)*4 + (r)]
+#define SWAP_ROWS(a, b) \
+ { \
+ float *_tmp = a; \
+ (a) = (b); \
+ (b) = _tmp; \
+ }
+
+ r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
+
+ r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1), r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
+ r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
+
+ r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1), r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
+ r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
+
+ r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1), r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
+ r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
+
+ r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1), r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
+ r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
+
+ /* choose pivot - or die */
+ if (fabsf(r3[0]) > fabsf(r2[0]))
+ SWAP_ROWS(r3, r2);
+ if (fabsf(r2[0]) > fabsf(r1[0]))
+ SWAP_ROWS(r2, r1);
+ if (fabsf(r1[0]) > fabsf(r0[0]))
+ SWAP_ROWS(r1, r0);
+ if (0.0F == r0[0])
+ return false;
+
+ /* eliminate first variable */
+ m1 = r1[0] / r0[0];
+ m2 = r2[0] / r0[0];
+ m3 = r3[0] / r0[0];
+ s = r0[1];
+ r1[1] -= m1 * s;
+ r2[1] -= m2 * s;
+ r3[1] -= m3 * s;
+ s = r0[2];
+ r1[2] -= m1 * s;
+ r2[2] -= m2 * s;
+ r3[2] -= m3 * s;
+ s = r0[3];
+ r1[3] -= m1 * s;
+ r2[3] -= m2 * s;
+ r3[3] -= m3 * s;
+ s = r0[4];
+ if (s != 0.0F) {
+ r1[4] -= m1 * s;
+ r2[4] -= m2 * s;
+ r3[4] -= m3 * s;
+ }
+ s = r0[5];
+ if (s != 0.0F) {
+ r1[5] -= m1 * s;
+ r2[5] -= m2 * s;
+ r3[5] -= m3 * s;
+ }
+ s = r0[6];
+ if (s != 0.0F) {
+ r1[6] -= m1 * s;
+ r2[6] -= m2 * s;
+ r3[6] -= m3 * s;
+ }
+ s = r0[7];
+ if (s != 0.0F) {
+ r1[7] -= m1 * s;
+ r2[7] -= m2 * s;
+ r3[7] -= m3 * s;
+ }
+
+ /* choose pivot - or die */
+ if (fabsf(r3[1]) > fabsf(r2[1]))
+ SWAP_ROWS(r3, r2);
+ if (fabsf(r2[1]) > fabsf(r1[1]))
+ SWAP_ROWS(r2, r1);
+ if (0.0F == r1[1])
+ return false;
+
+ /* eliminate second variable */
+ m2 = r2[1] / r1[1];
+ m3 = r3[1] / r1[1];
+ r2[2] -= m2 * r1[2];
+ r3[2] -= m3 * r1[2];
+ r2[3] -= m2 * r1[3];
+ r3[3] -= m3 * r1[3];
+ s = r1[4];
+ if (0.0F != s) {
+ r2[4] -= m2 * s;
+ r3[4] -= m3 * s;
+ }
+ s = r1[5];
+ if (0.0F != s) {
+ r2[5] -= m2 * s;
+ r3[5] -= m3 * s;
+ }
+ s = r1[6];
+ if (0.0F != s) {
+ r2[6] -= m2 * s;
+ r3[6] -= m3 * s;
+ }
+ s = r1[7];
+ if (0.0F != s) {
+ r2[7] -= m2 * s;
+ r3[7] -= m3 * s;
+ }
+
+ /* choose pivot - or die */
+ if (fabsf(r3[2]) > fabsf(r2[2]))
+ SWAP_ROWS(r3, r2);
+ if (0.0F == r2[2])
+ return false;
+
+ /* eliminate third variable */
+ m3 = r3[2] / r2[2];
+ r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
+ r3[7] -= m3 * r2[7];
+
+ /* last check */
+ if (0.0F == r3[3])
+ return false;
+
+ s = 1.0F / r3[3]; /* now back substitute row 3 */
+ r3[4] *= s;
+ r3[5] *= s;
+ r3[6] *= s;
+ r3[7] *= s;
+
+ m2 = r2[3]; /* now back substitute row 2 */
+ s = 1.0F / r2[2];
+ r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
+ r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
+ m1 = r1[3];
+ r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
+ m0 = r0[3];
+ r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
+
+ m1 = r1[2]; /* now back substitute row 1 */
+ s = 1.0F / r1[1];
+ r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
+ r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
+ m0 = r0[2];
+ r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
+
+ m0 = r0[1]; /* now back substitute row 0 */
+ s = 1.0F / r0[0];
+ r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
+ r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
+
+ MAT(out, 0, 0) = r0[4];
+ MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
+ MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
+ MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
+ MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
+ MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
+ MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
+ MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
+ MAT(out, 3, 3) = r3[7];
+
+#undef MAT
+#undef SWAP_ROWS
+
+ return true;
+}
diff --git a/src/util/u_math.h b/src/util/u_math.h
index becae90714c..0223ecb9965 100644
--- a/src/util/u_math.h
+++ b/src/util/u_math.h
@@ -778,6 +778,8 @@ util_is_vbo_upload_ratio_too_large(unsigned draw_vertex_count,
return upload_vertex_count > draw_vertex_count * 16;
}
+bool util_invert_mat4x4(float *out, const float *m);
+
#ifdef __cplusplus
}
#endif
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