vector: add a fixed point math implementation.
name old time/op new time/op delta GlyphAlpha16Over-8 4.48µs ± 1% 3.56µs ± 0% -20.70% (p=0.000 n=9+10) GlyphAlpha16Src-8 4.17µs ± 0% 3.38µs ± 1% -19.09% (p=0.000 n=10+10) GlyphAlpha32Over-8 9.03µs ± 0% 6.74µs ± 0% -25.33% (p=0.000 n=9+10) GlyphAlpha32Src-8 7.46µs ± 1% 5.98µs ± 0% -19.80% (p=0.000 n=10+9) GlyphAlpha64Over-8 21.3µs ± 0% 16.4µs ± 0% -22.84% (p=0.000 n=10+10) GlyphAlpha64Src-8 16.2µs ± 1% 13.1µs ± 0% -19.33% (p=0.000 n=10+10) GlyphAlpha128Over-8 59.8µs ± 0% 47.2µs ± 0% -21.11% (p=0.000 n=9+9) GlyphAlpha128Src-8 41.3µs ± 1% 33.0µs ± 0% -20.26% (p=0.000 n=9+10) GlyphAlpha256Over-8 197µs ± 0% 158µs ± 0% -19.44% (p=0.000 n=9+10) GlyphAlpha256Src-8 124µs ± 0% 98µs ± 0% -21.17% (p=0.000 n=9+9) GlyphAlphaLoose16Over-8 4.73µs ± 0% 3.97µs ± 1% -16.06% (p=0.000 n=10+10) GlyphAlphaLoose16Src-8 4.41µs ± 0% 3.64µs ± 1% -17.50% (p=0.000 n=10+10) GlyphAlphaLoose32Over-8 9.62µs ± 0% 8.47µs ± 0% -11.95% (p=0.000 n=10+10) GlyphAlphaLoose32Src-8 8.25µs ± 0% 7.19µs ± 0% -12.88% (p=0.000 n=9+9) GlyphAlphaLoose64Over-8 25.6µs ± 0% 22.2µs ± 0% -13.01% (p=0.000 n=9+9) GlyphAlphaLoose64Src-8 20.2µs ± 0% 17.2µs ± 1% -14.98% (p=0.000 n=10+10) GlyphAlphaLoose128Over-8 83.4µs ± 1% 68.2µs ± 0% -18.27% (p=0.000 n=10+10) GlyphAlphaLoose128Src-8 59.8µs ± 0% 47.4µs ± 0% -20.77% (p=0.000 n=10+9) GlyphAlphaLoose256Over-8 273µs ± 1% 239µs ± 0% -12.52% (p=0.000 n=10+9) GlyphAlphaLoose256Src-8 187µs ± 0% 155µs ± 1% -16.91% (p=0.000 n=9+10) GlyphRGBA16Over-8 5.99µs ± 0% 5.24µs ± 1% -12.60% (p=0.000 n=9+10) GlyphRGBA16Src-8 5.48µs ± 0% 4.68µs ± 0% -14.68% (p=0.000 n=9+10) GlyphRGBA32Over-8 14.6µs ± 0% 13.5µs ± 0% -7.60% (p=0.000 n=9+9) GlyphRGBA32Src-8 12.6µs ± 0% 11.4µs ± 0% -9.62% (p=0.000 n=9+9) GlyphRGBA64Over-8 44.8µs ± 0% 42.2µs ± 0% -5.69% (p=0.000 n=9+9) GlyphRGBA64Src-8 36.6µs ± 1% 33.5µs ± 1% -8.55% (p=0.000 n=9+9) GlyphRGBA128Over-8 162µs ± 0% 148µs ± 1% -8.85% (p=0.000 n=10+9) GlyphRGBA128Src-8 129µs ± 1% 114µs ± 0% -11.61% (p=0.000 n=9+10) GlyphRGBA256Over-8 588µs ± 0% 573µs ± 0% -2.53% (p=0.000 n=9+10) GlyphRGBA256Src-8 455µs ± 0% 426µs ± 1% -6.51% (p=0.000 n=9+10) GlyphNRGBA16Over-8 27.0µs ± 4% 26.3µs ± 2% -2.65% (p=0.001 n=9+10) GlyphNRGBA16Src-8 19.4µs ± 3% 18.6µs ± 1% -4.35% (p=0.000 n=9+10) GlyphNRGBA32Over-8 97.4µs ± 3% 96.8µs ± 2% ~ (p=0.447 n=9+10) GlyphNRGBA32Src-8 66.6µs ± 3% 64.5µs ± 1% -3.21% (p=0.000 n=10+9) GlyphNRGBA64Over-8 372µs ± 3% 368µs ± 1% ~ (p=0.105 n=10+10) GlyphNRGBA64Src-8 235µs ± 1% 234µs ± 1% ~ (p=0.130 n=8+8) GlyphNRGBA128Over-8 1.45ms ± 2% 1.48ms ± 3% +2.06% (p=0.014 n=9+9) GlyphNRGBA128Src-8 926µs ± 3% 937µs ± 1% ~ (p=0.113 n=10+9) GlyphNRGBA256Over-8 5.76ms ± 2% 5.90ms ± 3% +2.29% (p=0.001 n=9+10) GlyphNRGBA256Src-8 3.59ms ± 1% 3.86ms ± 1% +7.46% (p=0.000 n=9+10) Change-Id: I72f25193b5be4e57af09e9eea4eee50545a34cbf Reviewed-on: https://go-review.googlesource.com/29972 Reviewed-by: David Crawshaw <crawshaw@golang.org>
This commit is contained in:
Nigel Tao
parent
8a20735b0e
commit
992afa5d48
252
vector/raster_fixed.go
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252
vector/raster_fixed.go
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@ -0,0 +1,252 @@
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// Copyright 2016 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package vector
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// This file contains a fixed point math implementation of the vector
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// graphics rasterizer.
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import (
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"golang.org/x/image/math/f32"
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)
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const (
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// ϕ is the number of binary digits after the fixed point.
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//
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// For example, if ϕ == 10 (and int1ϕ is based on the int32 type) then we
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// are using 22.10 fixed point math.
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//
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// When changing this number, also change the assembly code (search for ϕ
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// in the .s files).
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ϕ = 10
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one int1ϕ = 1 << ϕ
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oneAndAHalf int1ϕ = 1<<ϕ + 1<<(ϕ-1)
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oneMinusIota int1ϕ = 1<<ϕ - 1 // Used for rounding up.
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)
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// int1ϕ is a signed fixed-point number with 1*ϕ binary digits after the fixed
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// point.
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type int1ϕ int32
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// int2ϕ is a signed fixed-point number with 2*ϕ binary digits after the fixed
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// point.
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//
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// The Rasterizer's bufU32 field, nominally of type []uint32 (since that slice
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// is also used by other code), can be thought of as a []int2ϕ during the
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// fixedLineTo method. Lines of code that are actually like:
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// buf[i] += uint32(etc) // buf has type []uint32.
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// can be thought of as
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// buf[i] += int2ϕ(etc) // buf has type []int2ϕ.
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type int2ϕ int32
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func fixedMax(x, y int1ϕ) int1ϕ {
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if x > y {
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return x
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}
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return y
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}
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func fixedMin(x, y int1ϕ) int1ϕ {
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if x < y {
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return x
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}
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return y
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}
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func fixedFloor(x int1ϕ) int32 { return int32(x >> ϕ) }
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func fixedCeil(x int1ϕ) int32 { return int32((x + oneMinusIota) >> ϕ) }
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func (z *Rasterizer) fixedLineTo(b f32.Vec2) {
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a := z.pen
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z.pen = b
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dir := int1ϕ(1)
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if a[1] > b[1] {
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dir, a, b = -1, b, a
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}
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// Horizontal line segments yield no change in coverage. Almost horizontal
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// segments would yield some change, in ideal math, but the computation
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// further below, involving 1 / (b[1] - a[1]), is unstable in fixed point
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// math, so we treat the segment as if it was perfectly horizontal.
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if b[1]-a[1] <= 0.000001 {
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return
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}
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dxdy := (b[0] - a[0]) / (b[1] - a[1])
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ay := int1ϕ(a[1] * float32(one))
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by := int1ϕ(b[1] * float32(one))
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x := int1ϕ(a[0] * float32(one))
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y := fixedFloor(ay)
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yMax := fixedCeil(by)
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if yMax > int32(z.size.Y) {
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yMax = int32(z.size.Y)
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}
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width := int32(z.size.X)
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for ; y < yMax; y++ {
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dy := fixedMin(int1ϕ(y+1)<<ϕ, by) - fixedMax(int1ϕ(y)<<ϕ, ay)
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xNext := x + int1ϕ(float32(dy)*dxdy)
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if y < 0 {
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x = xNext
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continue
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}
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buf := z.bufU32[y*width:]
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d := dy * dir
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x0, x1 := x, xNext
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if x > xNext {
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x0, x1 = x1, x0
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}
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x0i := fixedFloor(x0)
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x0Floor := int1ϕ(x0i) << ϕ
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x1i := fixedCeil(x1)
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x1Ceil := int1ϕ(x1i) << ϕ
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if x1i <= x0i+1 {
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xmf := (x+xNext)>>1 - x0Floor
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if i := clamp(x0i+0, width); i < uint(len(buf)) {
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buf[i] += uint32(d * (one - xmf))
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}
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if i := clamp(x0i+1, width); i < uint(len(buf)) {
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buf[i] += uint32(d * xmf)
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}
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} else {
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oneOverS := x1 - x0
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twoOverS := 2 * oneOverS
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x0f := x0 - x0Floor
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oneMinusX0f := one - x0f
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oneMinusX0fSquared := oneMinusX0f * oneMinusX0f
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x1f := x1 - x1Ceil + one
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x1fSquared := x1f * x1f
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// These next two variables are unused, as rounding errors are
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// minimized when we delay the division by oneOverS for as long as
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// possible. These lines of code (and the "In ideal math" comments
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// below) are commented out instead of deleted in order to aid the
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// comparison with the floating point version of the rasterizer.
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//
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// a0 := ((oneMinusX0f * oneMinusX0f) >> 1) / oneOverS
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// am := ((x1f * x1f) >> 1) / oneOverS
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if i := clamp(x0i, width); i < uint(len(buf)) {
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// In ideal math: buf[i] += uint32(d * a0)
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D := oneMinusX0fSquared
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D *= d
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D /= twoOverS
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buf[i] += uint32(D)
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}
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if x1i == x0i+2 {
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if i := clamp(x0i+1, width); i < uint(len(buf)) {
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// In ideal math: buf[i] += uint32(d * (one - a0 - am))
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D := twoOverS<<ϕ - oneMinusX0fSquared - x1fSquared
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D *= d
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D /= twoOverS
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buf[i] += uint32(D)
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}
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} else {
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// This is commented out for the same reason as a0 and am.
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//
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// a1 := ((oneAndAHalf - x0f) << ϕ) / oneOverS
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if i := clamp(x0i+1, width); i < uint(len(buf)) {
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// In ideal math: buf[i] += uint32(d * (a1 - a0))
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//
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// Convert to int64 to avoid overflow. Without that,
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// TestRasterizePolygon fails.
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D := int64((oneAndAHalf-x0f)<<(ϕ+1) - oneMinusX0fSquared)
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D *= int64(d)
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D /= int64(twoOverS)
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buf[i] += uint32(D)
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}
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dTimesS := uint32((d << (2 * ϕ)) / oneOverS)
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for xi := x0i + 2; xi < x1i-1; xi++ {
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if i := clamp(xi, width); i < uint(len(buf)) {
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buf[i] += dTimesS
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}
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}
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// This is commented out for the same reason as a0 and am.
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//
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// a2 := a1 + (int1ϕ(x1i-x0i-3)<<(2*ϕ))/oneOverS
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if i := clamp(x1i-1, width); i < uint(len(buf)) {
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// In ideal math: buf[i] += uint32(d * (one - a2 - am))
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//
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// Convert to int64 to avoid overflow. Without that,
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// TestRasterizePolygon fails.
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D := int64(twoOverS << ϕ)
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D -= int64((oneAndAHalf - x0f) << (ϕ + 1))
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D -= int64((x1i - x0i - 3) << (2*ϕ + 1))
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D -= int64(x1fSquared)
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D *= int64(d)
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D /= int64(twoOverS)
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buf[i] += uint32(D)
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}
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}
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if i := clamp(x1i, width); i < uint(len(buf)) {
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// In ideal math: buf[i] += uint32(d * am)
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D := x1fSquared
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D *= d
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D /= twoOverS
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buf[i] += uint32(D)
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}
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}
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x = xNext
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}
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}
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func fixedAccumulateOpSrc(dst []uint8, src []uint32) {
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acc := int2ϕ(0)
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for i, v := range src {
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acc += int2ϕ(v)
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a := acc
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if a < 0 {
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a = -a
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}
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a >>= 2*ϕ - 8
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if a > 0xff {
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a = 0xff
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}
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dst[i] = uint8(a)
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}
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}
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func fixedAccumulateOpOver(dst []uint8, src []uint32) {
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acc := int2ϕ(0)
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for i, v := range src {
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acc += int2ϕ(v)
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a := acc
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if a < 0 {
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a = -a
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}
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a >>= 2*ϕ - 16
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if a > 0xffff {
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a = 0xffff
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}
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// This algorithm comes from the standard library's image/draw package.
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dstA := uint32(dst[i]) * 0x101
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maskA := uint32(a)
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outA := dstA*(0xffff-maskA)/0xffff + maskA
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dst[i] = uint8(outA >> 8)
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}
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}
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func fixedAccumulateMask(buf []uint32) {
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acc := int2ϕ(0)
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for i, v := range buf {
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acc += int2ϕ(v)
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a := acc
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if a < 0 {
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a = -a
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}
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a >>= 2*ϕ - 16
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if a > 0xffff {
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a = 0xffff
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}
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buf[i] = uint32(a)
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}
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}
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@ -25,6 +25,26 @@ import (
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"golang.org/x/image/math/f32"
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)
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// floatingPointMathThreshold is the width or hight above which the rasterizer
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// chooses to used floating point math instead of fixed point math.
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//
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// Both implementations of line segmentation rasterization (see raster_fixed.go
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// and raster_floating.go) implement the same algorithm (in ideal, infinite
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// precision math) but they perform differently in practice. The fixed point
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// math version is roughtly 1.25x faster (on GOARCH=amd64) on the benchmarks,
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// but at sufficiently large scales, the computations will overflow and hence
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// show rendering artifacts. The floating point math version has more
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// consistent quality over larger scales, but it is significantly slower.
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//
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// This constant determines when to use the faster implementation and when to
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// use the better quality implementation.
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//
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// The rationale for this particular value is that TestRasterizePolygon in
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// vector_test.go checks the rendering quality of polygon edges at various
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// angles, inscribed in a circle of diameter 2048. It may be that a higher
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// value would still produce acceptable quality, but 2048 seems to work.
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const floatingPointMathThreshold = 2048
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func midPoint(p, q f32.Vec2) f32.Vec2 {
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return f32.Vec2{
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(p[0] + q[0]) * 0.5,
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// NewRasterizer returns a new Rasterizer whose rendered mask image is bounded
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// by the given width and height.
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func NewRasterizer(w, h int) *Rasterizer {
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return &Rasterizer{
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bufF32: make([]float32, w*h),
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size: image.Point{w, h},
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}
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z := &Rasterizer{}
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z.Reset(w, h)
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return z
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}
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// Raster is a 2-D vector graphics rasterizer.
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@ -77,11 +96,11 @@ type Rasterizer struct {
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// bufU32[i] = math.Float32bits(x + math.Float32frombits(bufU32[i]))
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//
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// See golang.org/issue/17220 for some discussion.
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//
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// TODO: use bufU32 in the fixed point math implementation.
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bufF32 []float32
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bufU32 []uint32
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useFloatingPointMath bool
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size image.Point
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first f32.Vec2
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pen f32.Vec2
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@ -99,18 +118,33 @@ type Rasterizer struct {
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//
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// This includes setting z.DrawOp to draw.Over.
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func (z *Rasterizer) Reset(w, h int) {
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if n := w * h; n > cap(z.bufF32) {
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z.bufF32 = make([]float32, n)
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} else {
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z.bufF32 = z.bufF32[:n]
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for i := range z.bufF32 {
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z.bufF32[i] = 0
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}
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}
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z.size = image.Point{w, h}
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z.first = f32.Vec2{}
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z.pen = f32.Vec2{}
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z.DrawOp = draw.Over
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z.useFloatingPointMath = w > floatingPointMathThreshold || h > floatingPointMathThreshold
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// Make z.bufF32 or z.bufU32 large enough to hold w*h samples.
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if z.useFloatingPointMath {
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if n := w * h; n > cap(z.bufF32) {
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z.bufF32 = make([]float32, n)
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} else {
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z.bufF32 = z.bufF32[:n]
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for i := range z.bufF32 {
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z.bufF32[i] = 0
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}
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}
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} else {
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if n := w * h; n > cap(z.bufU32) {
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z.bufU32 = make([]uint32, n)
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} else {
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z.bufU32 = z.bufU32[:n]
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for i := range z.bufU32 {
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z.bufU32[i] = 0
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}
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}
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}
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}
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// Size returns the width and height passed to NewRasterizer or Reset.
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@ -147,8 +181,11 @@ func (z *Rasterizer) MoveTo(a f32.Vec2) {
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//
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// The coordinates are allowed to be out of the Rasterizer's bounds.
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func (z *Rasterizer) LineTo(b f32.Vec2) {
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// TODO: add a fixed point math implementation.
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z.floatingLineTo(b)
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if z.useFloatingPointMath {
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z.floatingLineTo(b)
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} else {
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||||
z.fixedLineTo(b)
|
||||
}
|
||||
}
|
||||
|
||||
// QuadTo adds a quadratic Bézier segment, from the pen via b to c, and moves
|
||||
|
|
@ -258,22 +295,29 @@ func (z *Rasterizer) Draw(dst draw.Image, r image.Rectangle, src image.Image, sp
|
|||
}
|
||||
|
||||
func (z *Rasterizer) accumulateMask() {
|
||||
if n := z.size.X * z.size.Y; n > cap(z.bufU32) {
|
||||
z.bufU32 = make([]uint32, n)
|
||||
if z.useFloatingPointMath {
|
||||
if n := z.size.X * z.size.Y; n > cap(z.bufU32) {
|
||||
z.bufU32 = make([]uint32, n)
|
||||
} else {
|
||||
z.bufU32 = z.bufU32[:n]
|
||||
}
|
||||
floatingAccumulateMask(z.bufU32, z.bufF32)
|
||||
} else {
|
||||
z.bufU32 = z.bufU32[:n]
|
||||
fixedAccumulateMask(z.bufU32)
|
||||
}
|
||||
floatingAccumulateMask(z.bufU32, z.bufF32)
|
||||
}
|
||||
|
||||
func (z *Rasterizer) rasterizeDstAlphaSrcOpaqueOpOver(dst *image.Alpha, r image.Rectangle) {
|
||||
// TODO: add SIMD implementations.
|
||||
// TODO: add a fixed point math implementation.
|
||||
// TODO: non-zero vs even-odd winding?
|
||||
if r == dst.Bounds() && r == z.Bounds() {
|
||||
// We bypass the z.accumulateMask step and convert straight from
|
||||
// z.bufF32 to dst.Pix.
|
||||
floatingAccumulateOpOver(dst.Pix, z.bufF32)
|
||||
// z.bufF32 or z.bufU32 to dst.Pix.
|
||||
if z.useFloatingPointMath {
|
||||
floatingAccumulateOpOver(dst.Pix, z.bufF32)
|
||||
} else {
|
||||
fixedAccumulateOpOver(dst.Pix, z.bufU32)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
|
|
@ -294,12 +338,15 @@ func (z *Rasterizer) rasterizeDstAlphaSrcOpaqueOpOver(dst *image.Alpha, r image.
|
|||
|
||||
func (z *Rasterizer) rasterizeDstAlphaSrcOpaqueOpSrc(dst *image.Alpha, r image.Rectangle) {
|
||||
// TODO: add SIMD implementations.
|
||||
// TODO: add a fixed point math implementation.
|
||||
// TODO: non-zero vs even-odd winding?
|
||||
if r == dst.Bounds() && r == z.Bounds() {
|
||||
// We bypass the z.accumulateMask step and convert straight from
|
||||
// z.bufF32 to dst.Pix.
|
||||
floatingAccumulateOpSrc(dst.Pix, z.bufF32)
|
||||
// z.bufF32 or z.bufU32 to dst.Pix.
|
||||
if z.useFloatingPointMath {
|
||||
floatingAccumulateOpSrc(dst.Pix, z.bufF32)
|
||||
} else {
|
||||
fixedAccumulateOpSrc(dst.Pix, z.bufU32)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user