Matrix inversion optimizations and benchmark; originally by whunt@google.com.
https://codereview.appspot.com/6901046/
git-svn-id: http://skia.googlecode.com/svn/trunk@6775 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/src/utils/SkMatrix44.cpp b/src/utils/SkMatrix44.cpp
index bc67fa0..acd4ae6 100644
--- a/src/utils/SkMatrix44.cpp
+++ b/src/utils/SkMatrix44.cpp
@@ -418,18 +418,38 @@
return fMat[0][0] * fMat[1][1] * fMat[2][2] * fMat[3][3];
}
- return fMat[0][0] * det3x3(fMat[1][1], fMat[1][2], fMat[1][3],
- fMat[2][1], fMat[2][2], fMat[2][3],
- fMat[3][1], fMat[3][2], fMat[3][3]) -
- fMat[1][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
- fMat[2][1], fMat[2][2], fMat[2][3],
- fMat[3][1], fMat[3][2], fMat[3][3]) +
- fMat[2][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
- fMat[1][1], fMat[1][2], fMat[1][3],
- fMat[3][1], fMat[3][2], fMat[3][3]) -
- fMat[3][0] * det3x3(fMat[0][1], fMat[0][2], fMat[0][3],
- fMat[1][1], fMat[1][2], fMat[1][3],
- fMat[2][1], fMat[2][2], fMat[2][3]);
+ double a00 = fMat[0][0];
+ double a01 = fMat[0][1];
+ double a02 = fMat[0][2];
+ double a03 = fMat[0][3];
+ double a10 = fMat[1][0];
+ double a11 = fMat[1][1];
+ double a12 = fMat[1][2];
+ double a13 = fMat[1][3];
+ double a20 = fMat[2][0];
+ double a21 = fMat[2][1];
+ double a22 = fMat[2][2];
+ double a23 = fMat[2][3];
+ double a30 = fMat[3][0];
+ double a31 = fMat[3][1];
+ double a32 = fMat[3][2];
+ double a33 = fMat[3][3];
+
+ double b00 = a00 * a11 - a01 * a10;
+ double b01 = a00 * a12 - a02 * a10;
+ double b02 = a00 * a13 - a03 * a10;
+ double b03 = a01 * a12 - a02 * a11;
+ double b04 = a01 * a13 - a03 * a11;
+ double b05 = a02 * a13 - a03 * a12;
+ double b06 = a20 * a31 - a21 * a30;
+ double b07 = a20 * a32 - a22 * a30;
+ double b08 = a20 * a33 - a23 * a30;
+ double b09 = a21 * a32 - a22 * a31;
+ double b10 = a21 * a33 - a23 * a31;
+ double b11 = a22 * a33 - a23 * a32;
+
+ // Calculate the determinant
+ return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
}
///////////////////////////////////////////////////////////////////////////////
@@ -478,61 +498,78 @@
return true;
}
- double det = this->determinant();
+ double a00 = fMat[0][0];
+ double a01 = fMat[0][1];
+ double a02 = fMat[0][2];
+ double a03 = fMat[0][3];
+ double a10 = fMat[1][0];
+ double a11 = fMat[1][1];
+ double a12 = fMat[1][2];
+ double a13 = fMat[1][3];
+ double a20 = fMat[2][0];
+ double a21 = fMat[2][1];
+ double a22 = fMat[2][2];
+ double a23 = fMat[2][3];
+ double a30 = fMat[3][0];
+ double a31 = fMat[3][1];
+ double a32 = fMat[3][2];
+ double a33 = fMat[3][3];
+
+ double b00 = a00 * a11 - a01 * a10;
+ double b01 = a00 * a12 - a02 * a10;
+ double b02 = a00 * a13 - a03 * a10;
+ double b03 = a01 * a12 - a02 * a11;
+ double b04 = a01 * a13 - a03 * a11;
+ double b05 = a02 * a13 - a03 * a12;
+ double b06 = a20 * a31 - a21 * a30;
+ double b07 = a20 * a32 - a22 * a30;
+ double b08 = a20 * a33 - a23 * a30;
+ double b09 = a21 * a32 - a22 * a31;
+ double b10 = a21 * a33 - a23 * a31;
+ double b11 = a22 * a33 - a23 * a32;
+
+ // Calculate the determinant
+ double det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
+
if (dabs(det) < TOO_SMALL_FOR_DETERMINANT) {
return false;
}
-
- // We now we will succeed, so return early if the caller doesn't actually
- // want the computed inverse.
if (NULL == inverse) {
return true;
}
+ double invdet = 1.0 / det;
- // we explicitly promote to doubles to keep the intermediate values in
- // higher precision (assuming SkMScalar isn't already a double)
- double m00 = fMat[0][0];
- double m01 = fMat[0][1];
- double m02 = fMat[0][2];
- double m03 = fMat[0][3];
- double m10 = fMat[1][0];
- double m11 = fMat[1][1];
- double m12 = fMat[1][2];
- double m13 = fMat[1][3];
- double m20 = fMat[2][0];
- double m21 = fMat[2][1];
- double m22 = fMat[2][2];
- double m23 = fMat[2][3];
- double m30 = fMat[3][0];
- double m31 = fMat[3][1];
- double m32 = fMat[3][2];
- double m33 = fMat[3][3];
+ b00 *= invdet;
+ b01 *= invdet;
+ b02 *= invdet;
+ b03 *= invdet;
+ b04 *= invdet;
+ b05 *= invdet;
+ b06 *= invdet;
+ b07 *= invdet;
+ b08 *= invdet;
+ b09 *= invdet;
+ b10 *= invdet;
+ b11 *= invdet;
- double tmp[4][4];
+ inverse->fMat[0][0] = SkDoubleToMScalar(a11 * b11 - a12 * b10 + a13 * b09);
+ inverse->fMat[0][1] = SkDoubleToMScalar(a02 * b10 - a01 * b11 - a03 * b09);
+ inverse->fMat[0][2] = SkDoubleToMScalar(a31 * b05 - a32 * b04 + a33 * b03);
+ inverse->fMat[0][3] = SkDoubleToMScalar(a22 * b04 - a21 * b05 - a23 * b03);
+ inverse->fMat[1][0] = SkDoubleToMScalar(a12 * b08 - a10 * b11 - a13 * b07);
+ inverse->fMat[1][1] = SkDoubleToMScalar(a00 * b11 - a02 * b08 + a03 * b07);
+ inverse->fMat[1][2] = SkDoubleToMScalar(a32 * b02 - a30 * b05 - a33 * b01);
+ inverse->fMat[1][3] = SkDoubleToMScalar(a20 * b05 - a22 * b02 + a23 * b01);
+ inverse->fMat[2][0] = SkDoubleToMScalar(a10 * b10 - a11 * b08 + a13 * b06);
+ inverse->fMat[2][1] = SkDoubleToMScalar(a01 * b08 - a00 * b10 - a03 * b06);
+ inverse->fMat[2][2] = SkDoubleToMScalar(a30 * b04 - a31 * b02 + a33 * b00);
+ inverse->fMat[2][3] = SkDoubleToMScalar(a21 * b02 - a20 * b04 - a23 * b00);
+ inverse->fMat[3][0] = SkDoubleToMScalar(a11 * b07 - a10 * b09 - a12 * b06);
+ inverse->fMat[3][1] = SkDoubleToMScalar(a00 * b09 - a01 * b07 + a02 * b06);
+ inverse->fMat[3][2] = SkDoubleToMScalar(a31 * b01 - a30 * b03 - a32 * b00);
+ inverse->fMat[3][3] = SkDoubleToMScalar(a20 * b03 - a21 * b01 + a22 * b00);
+ inverse->dirtyTypeMask();
- tmp[0][0] = m12*m23*m31 - m13*m22*m31 + m13*m21*m32 - m11*m23*m32 - m12*m21*m33 + m11*m22*m33;
- tmp[0][1] = m03*m22*m31 - m02*m23*m31 - m03*m21*m32 + m01*m23*m32 + m02*m21*m33 - m01*m22*m33;
- tmp[0][2] = m02*m13*m31 - m03*m12*m31 + m03*m11*m32 - m01*m13*m32 - m02*m11*m33 + m01*m12*m33;
- tmp[0][3] = m03*m12*m21 - m02*m13*m21 - m03*m11*m22 + m01*m13*m22 + m02*m11*m23 - m01*m12*m23;
- tmp[1][0] = m13*m22*m30 - m12*m23*m30 - m13*m20*m32 + m10*m23*m32 + m12*m20*m33 - m10*m22*m33;
- tmp[1][1] = m02*m23*m30 - m03*m22*m30 + m03*m20*m32 - m00*m23*m32 - m02*m20*m33 + m00*m22*m33;
- tmp[1][2] = m03*m12*m30 - m02*m13*m30 - m03*m10*m32 + m00*m13*m32 + m02*m10*m33 - m00*m12*m33;
- tmp[1][3] = m02*m13*m20 - m03*m12*m20 + m03*m10*m22 - m00*m13*m22 - m02*m10*m23 + m00*m12*m23;
- tmp[2][0] = m11*m23*m30 - m13*m21*m30 + m13*m20*m31 - m10*m23*m31 - m11*m20*m33 + m10*m21*m33;
- tmp[2][1] = m03*m21*m30 - m01*m23*m30 - m03*m20*m31 + m00*m23*m31 + m01*m20*m33 - m00*m21*m33;
- tmp[2][2] = m01*m13*m30 - m03*m11*m30 + m03*m10*m31 - m00*m13*m31 - m01*m10*m33 + m00*m11*m33;
- tmp[2][3] = m03*m11*m20 - m01*m13*m20 - m03*m10*m21 + m00*m13*m21 + m01*m10*m23 - m00*m11*m23;
- tmp[3][0] = m12*m21*m30 - m11*m22*m30 - m12*m20*m31 + m10*m22*m31 + m11*m20*m32 - m10*m21*m32;
- tmp[3][1] = m01*m22*m30 - m02*m21*m30 + m02*m20*m31 - m00*m22*m31 - m01*m20*m32 + m00*m21*m32;
- tmp[3][2] = m02*m11*m30 - m01*m12*m30 - m02*m10*m31 + m00*m12*m31 + m01*m10*m32 - m00*m11*m32;
- tmp[3][3] = m01*m12*m20 - m02*m11*m20 + m02*m10*m21 - m00*m12*m21 - m01*m10*m22 + m00*m11*m22;
-
- double invDet = 1.0 / det;
- for (int i = 0; i < 4; i++) {
- for (int j = 0; j < 4; j++) {
- inverse->fMat[i][j] = SkDoubleToMScalar(tmp[i][j] * invDet);
- }
- }
inverse->dirtyTypeMask();
return true;
}