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>

f32/affine.go

@@ -24,9 +24,9 @@ type Affine2D struct {
 // in row major order. The rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
 func NewAffine2D(sx, hx, ox, hy, sy, oy float32) Affine2D {
 	return Affine2D{
-		a: sx, b: hx, c: ox,
-		d: hy, e: sy, f: oy,
-	}.encode()
+		a: sx - 1, b: hx, c: ox,
+		d: hy, e: sy - 1, f: oy,
+	}
 }
 
 // Offset the transformation.
@@ -69,14 +69,13 @@ func (a Affine2D) Shear(origin Point, radiansX, radiansY float32) Affine2D {
 
 // Mul returns A*B.
 func (A Affine2D) Mul(B Affine2D) (r Affine2D) {
-	A, B = A.decode(), B.decode()
-	r.a = A.a*B.a + A.b*B.d
-	r.b = A.a*B.b + A.b*B.e
-	r.c = A.a*B.c + A.b*B.f + A.c
-	r.d = A.d*B.a + A.e*B.d
-	r.e = A.d*B.b + A.e*B.e
-	r.f = A.d*B.c + A.e*B.f + A.f
-	return r.encode()
+	r.a = (A.a+1)*(B.a+1) + A.b*B.d - 1
+	r.b = (A.a+1)*B.b + A.b*(B.e+1)
+	r.c = (A.a+1)*B.c + A.b*B.f + A.c
+	r.d = A.d*(B.a+1) + (A.e+1)*B.d
+	r.e = A.d*B.b + (A.e+1)*(B.e+1) - 1
+	r.f = A.d*B.c + (A.e+1)*B.f + A.f
+	return r
 }
 
 // Invert the transformation. Note that if the matrix is close to singular
@@ -85,70 +84,54 @@ func (a Affine2D) Invert() Affine2D {
 	if a.a == 0 && a.b == 0 && a.d == 0 && a.e == 0 {
 		return Affine2D{a: 0, b: 0, c: -a.c, d: 0, e: 0, f: -a.f}
 	}
-	a = a.decode()
+	a.a += 1
+	a.e += 1
 	det := a.a*a.e - a.b*a.d
 	a.a, a.e = a.e/det, a.a/det
 	a.b, a.d = -a.b/det, -a.d/det
 	temp := a.c
 	a.c = -a.a*a.c - a.b*a.f
 	a.f = -a.d*temp - a.e*a.f
-	return a.encode()
+	a.a -= 1
+	a.e -= 1
+	return a
 }
 
 // Transform p by returning a*p.
 func (a Affine2D) Transform(p Point) Point {
-	a = a.decode()
 	return Point{
-		X: p.X*a.a + p.Y*a.b + a.c,
-		Y: p.X*a.d + p.Y*a.e + a.f,
+		X: p.X*(a.a+1) + p.Y*a.b + a.c,
+		Y: p.X*a.d + p.Y*(a.e+1) + a.f,
 	}
 }
 
 // Elems returns the matrix elements of the transform in row-major order. The
 // rows are: [sx, hx, ox], [hy, sy, oy], [0, 0, 1].
 func (a Affine2D) Elems() (sx, hx, ox, hy, sy, oy float32) {
-	a = a.decode()
-	return a.a, a.b, a.c, a.d, a.e, a.f
-}
-
-func (a Affine2D) encode() Affine2D {
-	// since we store with identity matrix subtracted
-	a.a -= 1
-	a.e -= 1
-	return a
-}
-
-func (a Affine2D) decode() Affine2D {
-	// since we store with identity matrix subtracted
-	a.a += 1
-	a.e += 1
-	return a
+	return a.a + 1, a.b, a.c, a.d, a.e + 1, a.f
 }
 
 func (a Affine2D) scale(factor Point) Affine2D {
-	a = a.decode()
 	return Affine2D{
-		a.a * factor.X, a.b * factor.X, a.c * factor.X,
-		a.d * factor.Y, a.e * factor.Y, a.f * factor.Y,
-	}.encode()
+		(a.a+1)*factor.X - 1, a.b * factor.X, a.c * factor.X,
+		a.d * factor.Y, (a.e+1)*factor.Y - 1, a.f * factor.Y,
+	}
 }
 
 func (a Affine2D) rotate(radians float32) Affine2D {
 	sin, cos := math.Sincos(float64(radians))
 	s, c := float32(sin), float32(cos)
-	a = a.decode()
 	return Affine2D{
-		a.a*c - a.d*s, a.b*c - a.e*s, a.c*c - a.f*s,
-		a.a*s + a.d*c, a.b*s + a.e*c, a.c*s + a.f*c,
-	}.encode()
+		(a.a+1)*c - a.d*s - 1, a.b*c - (a.e+1)*s, a.c*c - a.f*s,
+		(a.a+1)*s + a.d*c, a.b*s + (a.e+1)*c - 1, a.c*s + a.f*c,
+	}
 }
 
 func (a Affine2D) shear(radiansX, radiansY float32) Affine2D {
 	tx := float32(math.Tan(float64(radiansX)))
 	ty := float32(math.Tan(float64(radiansY)))
-	a = a.decode()
 	return Affine2D{
-		a.a + a.d*tx, a.b + a.e*tx, a.c + a.f*tx,
-		a.a*ty + a.d, a.b*ty + a.e, a.f*ty + a.f,
-	}.encode()
+		(a.a + 1) + a.d*tx - 1, a.b + (a.e+1)*tx, a.c + a.f*tx,
+		(a.a+1)*ty + a.d, a.b*ty + (a.e + 1) - 1, a.f*ty + a.f,
+	}
 }