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f32: optimize Affine2D
encode/decode seem to introduce significant overhead. Inline them manually. It'll make code harder to read, however the performance wins are significant. name \ time/op before after delta TransformOffset-32 2.64ns ± 0% 0.25ns ± 0% ~ (p=0.100 n=3+3) TransformScale-32 2.64ns ± 0% 0.25ns ± 1% ~ (p=0.100 n=3+3) TransformRotate-32 2.65ns ± 0% 0.24ns ± 3% ~ (p=0.100 n=3+3) TransformTranslateMultiply-32 42.5ns ± 0% 12.9ns ± 0% ~ (p=0.100 n=3+3) TransformScaleMultiply-32 42.6ns ± 0% 12.9ns ± 0% ~ (p=0.100 n=3+3) TransformMultiply-32 42.2ns ± 0% 12.9ns ± 2% ~ (p=0.100 n=3+3) Signed-off-by: Egon Elbre <egonelbre@gmail.com>
This commit is contained in:
Egon Elbre
+27
-44
@@ -24,9 +24,9 @@ type Affine2D struct {
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// in row major order. The rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
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func NewAffine2D(sx, hx, ox, hy, sy, oy float32) Affine2D {
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return Affine2D{
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a: sx, b: hx, c: ox,
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d: hy, e: sy, f: oy,
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}.encode()
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a: sx - 1, b: hx, c: ox,
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d: hy, e: sy - 1, f: oy,
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}
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}
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// Offset the transformation.
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@@ -69,14 +69,13 @@ func (a Affine2D) Shear(origin Point, radiansX, radiansY float32) Affine2D {
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// Mul returns A*B.
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func (A Affine2D) Mul(B Affine2D) (r Affine2D) {
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A, B = A.decode(), B.decode()
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r.a = A.a*B.a + A.b*B.d
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r.b = A.a*B.b + A.b*B.e
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r.c = A.a*B.c + A.b*B.f + A.c
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r.d = A.d*B.a + A.e*B.d
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r.e = A.d*B.b + A.e*B.e
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r.f = A.d*B.c + A.e*B.f + A.f
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return r.encode()
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r.a = (A.a+1)*(B.a+1) + A.b*B.d - 1
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r.b = (A.a+1)*B.b + A.b*(B.e+1)
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r.c = (A.a+1)*B.c + A.b*B.f + A.c
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r.d = A.d*(B.a+1) + (A.e+1)*B.d
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r.e = A.d*B.b + (A.e+1)*(B.e+1) - 1
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r.f = A.d*B.c + (A.e+1)*B.f + A.f
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return r
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}
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// Invert the transformation. Note that if the matrix is close to singular
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@@ -85,70 +84,54 @@ func (a Affine2D) Invert() Affine2D {
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if a.a == 0 && a.b == 0 && a.d == 0 && a.e == 0 {
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return Affine2D{a: 0, b: 0, c: -a.c, d: 0, e: 0, f: -a.f}
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}
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a = a.decode()
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a.a += 1
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a.e += 1
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det := a.a*a.e - a.b*a.d
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a.a, a.e = a.e/det, a.a/det
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a.b, a.d = -a.b/det, -a.d/det
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temp := a.c
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a.c = -a.a*a.c - a.b*a.f
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a.f = -a.d*temp - a.e*a.f
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return a.encode()
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a.a -= 1
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a.e -= 1
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return a
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}
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// Transform p by returning a*p.
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func (a Affine2D) Transform(p Point) Point {
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a = a.decode()
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return Point{
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X: p.X*a.a + p.Y*a.b + a.c,
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Y: p.X*a.d + p.Y*a.e + a.f,
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X: p.X*(a.a+1) + p.Y*a.b + a.c,
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Y: p.X*a.d + p.Y*(a.e+1) + a.f,
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}
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}
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// Elems returns the matrix elements of the transform in row-major order. The
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// rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
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func (a Affine2D) Elems() (sx, hx, ox, hy, sy, oy float32) {
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a = a.decode()
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return a.a, a.b, a.c, a.d, a.e, a.f
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}
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func (a Affine2D) encode() Affine2D {
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// since we store with identity matrix subtracted
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a.a -= 1
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a.e -= 1
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return a
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}
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func (a Affine2D) decode() Affine2D {
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// since we store with identity matrix subtracted
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a.a += 1
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a.e += 1
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return a
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return a.a + 1, a.b, a.c, a.d, a.e + 1, a.f
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}
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func (a Affine2D) scale(factor Point) Affine2D {
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a = a.decode()
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return Affine2D{
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a.a * factor.X, a.b * factor.X, a.c * factor.X,
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a.d * factor.Y, a.e * factor.Y, a.f * factor.Y,
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}.encode()
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(a.a+1)*factor.X - 1, a.b * factor.X, a.c * factor.X,
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a.d * factor.Y, (a.e+1)*factor.Y - 1, a.f * factor.Y,
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}
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}
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func (a Affine2D) rotate(radians float32) Affine2D {
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sin, cos := math.Sincos(float64(radians))
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s, c := float32(sin), float32(cos)
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a = a.decode()
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return Affine2D{
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a.a*c - a.d*s, a.b*c - a.e*s, a.c*c - a.f*s,
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a.a*s + a.d*c, a.b*s + a.e*c, a.c*s + a.f*c,
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}.encode()
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(a.a+1)*c - a.d*s - 1, a.b*c - (a.e+1)*s, a.c*c - a.f*s,
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(a.a+1)*s + a.d*c, a.b*s + (a.e+1)*c - 1, a.c*s + a.f*c,
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}
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}
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func (a Affine2D) shear(radiansX, radiansY float32) Affine2D {
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tx := float32(math.Tan(float64(radiansX)))
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ty := float32(math.Tan(float64(radiansY)))
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a = a.decode()
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return Affine2D{
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a.a + a.d*tx, a.b + a.e*tx, a.c + a.f*tx,
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a.a*ty + a.d, a.b*ty + a.e, a.f*ty + a.f,
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}.encode()
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(a.a + 1) + a.d*tx - 1, a.b + (a.e+1)*tx, a.c + a.f*tx,
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(a.a+1)*ty + a.d, a.b*ty + (a.e + 1) - 1, a.f*ty + a.f,
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}
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}
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@@ -13,6 +13,16 @@ func eq(p1, p2 Point) bool {
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return math.Abs(math.Sqrt(float64(dx*dx+dy*dy))) < tol
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}
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func eqaff(x, y Affine2D) bool {
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tol := 1e-5
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return math.Abs(float64(x.a-y.a)) < tol &&
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math.Abs(float64(x.b-y.b)) < tol &&
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math.Abs(float64(x.c-y.c)) < tol &&
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math.Abs(float64(x.d-y.d)) < tol &&
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math.Abs(float64(x.e-y.e)) < tol &&
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math.Abs(float64(x.f-y.f)) < tol
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}
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func TestTransformOffset(t *testing.T) {
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p := Point{X: 1, Y: 2}
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o := Point{X: 2, Y: -3}
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@@ -84,6 +94,49 @@ func TestTransformMultiply(t *testing.T) {
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}
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}
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func TestPrimes(t *testing.T) {
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xa := NewAffine2D(9, 11, 13, 17, 19, 23)
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xb := NewAffine2D(29, 31, 37, 43, 47, 53)
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pa := Point{X: 2, Y: 3}
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pb := Point{X: 5, Y: 7}
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for _, test := range []struct {
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x Affine2D
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p Point
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exp Point
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}{
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{x: xa, p: pa, exp: Pt(64, 114)},
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{x: xa, p: pb, exp: Pt(135, 241)},
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{x: xb, p: pa, exp: Pt(188, 280)},
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{x: xb, p: pb, exp: Pt(399, 597)},
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} {
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got := test.x.Transform(test.p)
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if !eq(got, test.exp) {
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t.Errorf("%v.Transform(%v): have %v, want %v", test.x, test.p, got, test.exp)
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}
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}
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for _, test := range []struct {
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x Affine2D
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exp Affine2D
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}{
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{x: xa, exp: NewAffine2D(-1.1875, 0.6875, -0.375, 1.0625, -0.5625, -0.875)},
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{x: xb, exp: NewAffine2D(1.5666667, -1.0333333, -3.2000008, -1.4333333, 1-0.03333336, 1.7999992)},
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} {
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got := test.x.Invert()
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if !eqaff(got, test.exp) {
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t.Errorf("%v.Invert(): have %v, want %v", test.x, got, test.exp)
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}
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}
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got := xa.Mul(xb)
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exp := NewAffine2D(734, 796, 929, 1310, 1420, 1659)
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if !eqaff(got, exp) {
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t.Errorf("%v.Mul(%v): have %v, want %v", xa, xb, got, exp)
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}
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}
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func TestTransformScaleAround(t *testing.T) {
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p := Pt(-1, -1)
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target := Pt(-6, -13)
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@@ -119,3 +172,61 @@ func TestMulOrder(t *testing.T) {
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t.Error("multiplication / transform order not as expected")
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}
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}
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func BenchmarkTransformOffset(b *testing.B) {
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p := Point{X: 1, Y: 2}
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o := Point{X: 0.5, Y: 0.5}
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aff := Affine2D{}.Offset(o)
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for i := 0; i < b.N; i++ {
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p = aff.Transform(p)
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}
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_ = p
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}
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func BenchmarkTransformScale(b *testing.B) {
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p := Point{X: 1, Y: 2}
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s := Point{X: 0.5, Y: 0.5}
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aff := Affine2D{}.Scale(Point{}, s)
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for i := 0; i < b.N; i++ {
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p = aff.Transform(p)
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}
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_ = p
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}
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func BenchmarkTransformRotate(b *testing.B) {
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p := Point{X: 1, Y: 2}
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a := float32(math.Pi / 2)
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aff := Affine2D{}.Rotate(Point{}, a)
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for i := 0; i < b.N; i++ {
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p = aff.Transform(p)
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}
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_ = p
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}
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func BenchmarkTransformTranslateMultiply(b *testing.B) {
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a := Affine2D{}.Offset(Point{X: 1, Y: 1}).Rotate(Point{}, math.Pi/3)
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t := Affine2D{}.Offset(Point{X: 0.5, Y: 0.5})
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for i := 0; i < b.N; i++ {
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a = a.Mul(t)
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}
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}
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func BenchmarkTransformScaleMultiply(b *testing.B) {
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a := Affine2D{}.Offset(Point{X: 1, Y: 1}).Rotate(Point{}, math.Pi/3)
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t := Affine2D{}.Offset(Point{X: 0.5, Y: 0.5}).Scale(Point{}, Point{X: 0.4, Y: -0.5})
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for i := 0; i < b.N; i++ {
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a = a.Mul(t)
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}
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}
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func BenchmarkTransformMultiply(b *testing.B) {
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a := Affine2D{}.Offset(Point{X: 1, Y: 1}).Rotate(Point{}, math.Pi/3)
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t := Affine2D{}.Offset(Point{X: 0.5, Y: 0.5}).Rotate(Point{}, math.Pi/7)
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for i := 0; i < b.N; i++ {
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a = a.Mul(t)
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}
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}
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