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[web] Optimize Matrix4.identity #22622

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Dec 1, 2020
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[web] Optimize Matrix4.identity #22622

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53c9e15
Optimize Matrix4.identity
ferhatb Nov 19, 2020
d4ed243
Add comment for range check optimization
ferhatb Nov 20, 2020
23dfbee
Merge remote-tracking branch 'upstream/master' into identitymatrix
ferhatb Nov 30, 2020
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76 changes: 42 additions & 34 deletions lib/web_ui/lib/src/engine/vector_math.dart
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Original file line number Diff line number Diff line change
Expand Up @@ -67,7 +67,12 @@ class Matrix4 {
Matrix4.zero() : _m4storage = Float32List(16);

/// Identity matrix.
factory Matrix4.identity() => Matrix4.zero()..setIdentity();
Matrix4.identity() : _m4storage = Float32List(16) {
_m4storage[15] = 1.0;
_m4storage[0] = 1.0;
_m4storage[5] = 1.0;
_m4storage[10] = 1.0;
}

/// Copies values from [other].
factory Matrix4.copy(Matrix4 other) => Matrix4.zero()..setFrom(other);
Expand Down Expand Up @@ -98,14 +103,12 @@ class Matrix4 {
..setRotationZ(radians);

/// Translation matrix.
factory Matrix4.translation(Vector3 translation) => Matrix4.zero()
..setIdentity()
factory Matrix4.translation(Vector3 translation) => Matrix4.identity()
..setTranslation(translation);

/// Translation matrix.
factory Matrix4.translationValues(double x, double y, double z) =>
Matrix4.zero()
..setIdentity()
Matrix4.identity()
..setTranslationRaw(x, y, z);

/// Scale matrix.
Expand Down Expand Up @@ -198,6 +201,9 @@ class Matrix4 {
/// Copy into [arg].
Matrix4 copyInto(Matrix4 arg) {
final Float32List argStorage = arg._m4storage;
// Start reading from the last element to eliminate range checks
// in subsequent reads.
argStorage[15] = _m4storage[15];
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thanks for the optimization! Shall we also add a comment about the compiler optimization we are doing(why are we accessing the 15th index before all the others)?

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Done.

argStorage[0] = _m4storage[0];
argStorage[1] = _m4storage[1];
argStorage[2] = _m4storage[2];
Expand All @@ -213,7 +219,6 @@ class Matrix4 {
argStorage[12] = _m4storage[12];
argStorage[13] = _m4storage[13];
argStorage[14] = _m4storage[14];
argStorage[15] = _m4storage[15];
return arg;
}

Expand Down Expand Up @@ -248,6 +253,7 @@ class Matrix4 {
final double sy = y ?? x;
final double sz = z ?? x;
const double sw = 1.0;
_m4storage[15] *= sw;
_m4storage[0] *= sx;
_m4storage[1] *= sx;
_m4storage[2] *= sx;
Expand All @@ -263,7 +269,6 @@ class Matrix4 {
_m4storage[12] *= sw;
_m4storage[13] *= sw;
_m4storage[14] *= sw;
_m4storage[15] *= sw;
}

/// Create a copy of [this] scaled by a [Vector3], [Vector4] or [x],[y], and
Expand All @@ -272,6 +277,7 @@ class Matrix4 {

/// Zeros [this].
void setZero() {
_m4storage[15] = 0.0;
_m4storage[0] = 0.0;
_m4storage[1] = 0.0;
_m4storage[2] = 0.0;
Expand All @@ -287,11 +293,11 @@ class Matrix4 {
_m4storage[12] = 0.0;
_m4storage[13] = 0.0;
_m4storage[14] = 0.0;
_m4storage[15] = 0.0;
}

/// Makes [this] into the identity matrix.
void setIdentity() {
_m4storage[15] = 1.0;
_m4storage[0] = 1.0;
_m4storage[1] = 0.0;
_m4storage[2] = 0.0;
Expand All @@ -307,7 +313,6 @@ class Matrix4 {
_m4storage[12] = 0.0;
_m4storage[13] = 0.0;
_m4storage[14] = 0.0;
_m4storage[15] = 1.0;
}

/// Returns the tranpose of this.
Expand Down Expand Up @@ -337,34 +342,35 @@ class Matrix4 {

/// Returns the determinant of this matrix.
double determinant() {
final Float32List m = _m4storage;
final double det2_01_01 =
_m4storage[0] * _m4storage[5] - _m4storage[1] * _m4storage[4];
m[0] * m[5] - m[1] * m[4];
final double det2_01_02 =
_m4storage[0] * _m4storage[6] - _m4storage[2] * _m4storage[4];
m[0] * m[6] - m[2] * m[4];
final double det2_01_03 =
_m4storage[0] * _m4storage[7] - _m4storage[3] * _m4storage[4];
m[0] * m[7] - m[3] * m[4];
final double det2_01_12 =
_m4storage[1] * _m4storage[6] - _m4storage[2] * _m4storage[5];
m[1] * m[6] - m[2] * m[5];
final double det2_01_13 =
_m4storage[1] * _m4storage[7] - _m4storage[3] * _m4storage[5];
m[1] * m[7] - m[3] * m[5];
final double det2_01_23 =
_m4storage[2] * _m4storage[7] - _m4storage[3] * _m4storage[6];
final double det3_201_012 = _m4storage[8] * det2_01_12 -
_m4storage[9] * det2_01_02 +
_m4storage[10] * det2_01_01;
final double det3_201_013 = _m4storage[8] * det2_01_13 -
_m4storage[9] * det2_01_03 +
_m4storage[11] * det2_01_01;
final double det3_201_023 = _m4storage[8] * det2_01_23 -
_m4storage[10] * det2_01_03 +
_m4storage[11] * det2_01_02;
final double det3_201_123 = _m4storage[9] * det2_01_23 -
_m4storage[10] * det2_01_13 +
_m4storage[11] * det2_01_12;
return -det3_201_123 * _m4storage[12] +
det3_201_023 * _m4storage[13] -
det3_201_013 * _m4storage[14] +
det3_201_012 * _m4storage[15];
m[2] * m[7] - m[3] * m[6];
final double det3_201_012 = m[8] * det2_01_12 -
m[9] * det2_01_02 +
m[10] * det2_01_01;
final double det3_201_013 = m[8] * det2_01_13 -
m[9] * det2_01_03 +
m[11] * det2_01_01;
final double det3_201_023 = m[8] * det2_01_23 -
m[10] * det2_01_03 +
m[11] * det2_01_02;
final double det3_201_123 = m[9] * det2_01_23 -
m[10] * det2_01_13 +
m[11] * det2_01_12;
return -det3_201_123 * m[12] +
det3_201_023 * m[13] -
det3_201_013 * m[14] +
det3_201_012 * m[15];
}

/// Returns a new vector or matrix by multiplying [this] with [arg].
Expand All @@ -387,6 +393,7 @@ class Matrix4 {
/// defined by [this].
Vector3 perspectiveTransform(Vector3 arg) {
final Float32List argStorage = arg._v3storage;

final double x = (_m4storage[0] * argStorage[0]) +
(_m4storage[4] * argStorage[1]) +
(_m4storage[8] * argStorage[2]) +
Expand Down Expand Up @@ -733,6 +740,7 @@ class Matrix4 {

/// Multiply [this] by [arg].
void multiply(Matrix4 arg) {
final double m33 = _m4storage[15];
final double m00 = _m4storage[0];
final double m01 = _m4storage[4];
final double m02 = _m4storage[8];
Expand All @@ -748,8 +756,8 @@ class Matrix4 {
final double m30 = _m4storage[3];
final double m31 = _m4storage[7];
final double m32 = _m4storage[11];
final double m33 = _m4storage[15];
final Float32List argStorage = arg._m4storage;
final double n33 = argStorage[15];
final double n00 = argStorage[0];
final double n01 = argStorage[4];
final double n02 = argStorage[8];
Expand All @@ -765,7 +773,6 @@ class Matrix4 {
final double n30 = argStorage[3];
final double n31 = argStorage[7];
final double n32 = argStorage[11];
final double n33 = argStorage[15];
_m4storage[0] = (m00 * n00) + (m01 * n10) + (m02 * n20) + (m03 * n30);
_m4storage[4] = (m00 * n01) + (m01 * n11) + (m02 * n21) + (m03 * n31);
_m4storage[8] = (m00 * n02) + (m01 * n12) + (m02 * n22) + (m03 * n32);
Expand All @@ -789,6 +796,7 @@ class Matrix4 {

/// Multiply a transposed [this] with [arg].
void transposeMultiply(Matrix4 arg) {
final double m33 = _m4storage[15];
final double m00 = _m4storage[0];
final double m01 = _m4storage[1];
final double m02 = _m4storage[2];
Expand All @@ -804,7 +812,7 @@ class Matrix4 {
final double m30 = _m4storage[12];
final double m31 = _m4storage[13];
final double m32 = _m4storage[14];
final double m33 = _m4storage[15];

final Float32List argStorage = arg._m4storage;
_m4storage[0] = (m00 * argStorage[0]) +
(m01 * argStorage[1]) +
Expand Down