golang-image/vector/raster_fixed.go

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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>
2016-09-28 11:29:02 +02:00
// Copyright 2016 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package vector
// This file contains a fixed point math implementation of the vector
// graphics rasterizer.
import (
"golang.org/x/image/math/f32"
)
const (
// ϕ is the number of binary digits after the fixed point.
//
// For example, if ϕ == 10 (and int1ϕ is based on the int32 type) then we
// are using 22.10 fixed point math.
//
// When changing this number, also change the assembly code (search for ϕ
// in the .s files).
ϕ = 10
one int1ϕ = 1 << ϕ
oneAndAHalf int1ϕ = 1<<ϕ + 1<<(ϕ-1)
oneMinusIota int1ϕ = 1<<ϕ - 1 // Used for rounding up.
)
// int1ϕ is a signed fixed-point number with 1*ϕ binary digits after the fixed
// point.
type int1ϕ int32
// int2ϕ is a signed fixed-point number with 2*ϕ binary digits after the fixed
// point.
//
// The Rasterizer's bufU32 field, nominally of type []uint32 (since that slice
// is also used by other code), can be thought of as a []int2ϕ during the
// fixedLineTo method. Lines of code that are actually like:
// buf[i] += uint32(etc) // buf has type []uint32.
// can be thought of as
// buf[i] += int2ϕ(etc) // buf has type []int2ϕ.
type int2ϕ int32
func fixedMax(x, y int1ϕ) int1ϕ {
if x > y {
return x
}
return y
}
func fixedMin(x, y int1ϕ) int1ϕ {
if x < y {
return x
}
return y
}
func fixedFloor(x int1ϕ) int32 { return int32(x >> ϕ) }
func fixedCeil(x int1ϕ) int32 { return int32((x + oneMinusIota) >> ϕ) }
func (z *Rasterizer) fixedLineTo(b f32.Vec2) {
a := z.pen
z.pen = b
dir := int1ϕ(1)
if a[1] > b[1] {
dir, a, b = -1, b, a
}
// Horizontal line segments yield no change in coverage. Almost horizontal
// segments would yield some change, in ideal math, but the computation
// further below, involving 1 / (b[1] - a[1]), is unstable in fixed point
// math, so we treat the segment as if it was perfectly horizontal.
if b[1]-a[1] <= 0.000001 {
return
}
dxdy := (b[0] - a[0]) / (b[1] - a[1])
ay := int1ϕ(a[1] * float32(one))
by := int1ϕ(b[1] * float32(one))
x := int1ϕ(a[0] * float32(one))
y := fixedFloor(ay)
yMax := fixedCeil(by)
if yMax > int32(z.size.Y) {
yMax = int32(z.size.Y)
}
width := int32(z.size.X)
for ; y < yMax; y++ {
dy := fixedMin(int1ϕ(y+1)<<ϕ, by) - fixedMax(int1ϕ(y)<<ϕ, ay)
xNext := x + int1ϕ(float32(dy)*dxdy)
if y < 0 {
x = xNext
continue
}
buf := z.bufU32[y*width:]
d := dy * dir
x0, x1 := x, xNext
if x > xNext {
x0, x1 = x1, x0
}
x0i := fixedFloor(x0)
x0Floor := int1ϕ(x0i) << ϕ
x1i := fixedCeil(x1)
x1Ceil := int1ϕ(x1i) << ϕ
if x1i <= x0i+1 {
xmf := (x+xNext)>>1 - x0Floor
if i := clamp(x0i+0, width); i < uint(len(buf)) {
buf[i] += uint32(d * (one - xmf))
}
if i := clamp(x0i+1, width); i < uint(len(buf)) {
buf[i] += uint32(d * xmf)
}
} else {
oneOverS := x1 - x0
twoOverS := 2 * oneOverS
x0f := x0 - x0Floor
oneMinusX0f := one - x0f
oneMinusX0fSquared := oneMinusX0f * oneMinusX0f
x1f := x1 - x1Ceil + one
x1fSquared := x1f * x1f
// These next two variables are unused, as rounding errors are
// minimized when we delay the division by oneOverS for as long as
// possible. These lines of code (and the "In ideal math" comments
// below) are commented out instead of deleted in order to aid the
// comparison with the floating point version of the rasterizer.
//
// a0 := ((oneMinusX0f * oneMinusX0f) >> 1) / oneOverS
// am := ((x1f * x1f) >> 1) / oneOverS
if i := clamp(x0i, width); i < uint(len(buf)) {
// In ideal math: buf[i] += uint32(d * a0)
D := oneMinusX0fSquared
D *= d
D /= twoOverS
buf[i] += uint32(D)
}
if x1i == x0i+2 {
if i := clamp(x0i+1, width); i < uint(len(buf)) {
// In ideal math: buf[i] += uint32(d * (one - a0 - am))
D := twoOverS<<ϕ - oneMinusX0fSquared - x1fSquared
D *= d
D /= twoOverS
buf[i] += uint32(D)
}
} else {
// This is commented out for the same reason as a0 and am.
//
// a1 := ((oneAndAHalf - x0f) << ϕ) / oneOverS
if i := clamp(x0i+1, width); i < uint(len(buf)) {
// In ideal math: buf[i] += uint32(d * (a1 - a0))
//
// Convert to int64 to avoid overflow. Without that,
// TestRasterizePolygon fails.
D := int64((oneAndAHalf-x0f)<<(ϕ+1) - oneMinusX0fSquared)
D *= int64(d)
D /= int64(twoOverS)
buf[i] += uint32(D)
}
dTimesS := uint32((d << (2 * ϕ)) / oneOverS)
for xi := x0i + 2; xi < x1i-1; xi++ {
if i := clamp(xi, width); i < uint(len(buf)) {
buf[i] += dTimesS
}
}
// This is commented out for the same reason as a0 and am.
//
// a2 := a1 + (int1ϕ(x1i-x0i-3)<<(2*ϕ))/oneOverS
if i := clamp(x1i-1, width); i < uint(len(buf)) {
// In ideal math: buf[i] += uint32(d * (one - a2 - am))
//
// Convert to int64 to avoid overflow. Without that,
// TestRasterizePolygon fails.
D := int64(twoOverS << ϕ)
D -= int64((oneAndAHalf - x0f) << (ϕ + 1))
D -= int64((x1i - x0i - 3) << (2*ϕ + 1))
D -= int64(x1fSquared)
D *= int64(d)
D /= int64(twoOverS)
buf[i] += uint32(D)
}
}
if i := clamp(x1i, width); i < uint(len(buf)) {
// In ideal math: buf[i] += uint32(d * am)
D := x1fSquared
D *= d
D /= twoOverS
buf[i] += uint32(D)
}
}
x = xNext
}
}
func fixedAccumulateOpSrc(dst []uint8, src []uint32) {
acc := int2ϕ(0)
for i, v := range src {
acc += int2ϕ(v)
a := acc
if a < 0 {
a = -a
}
a >>= 2*ϕ - 8
if a > 0xff {
a = 0xff
}
dst[i] = uint8(a)
}
}
func fixedAccumulateOpOver(dst []uint8, src []uint32) {
acc := int2ϕ(0)
for i, v := range src {
acc += int2ϕ(v)
a := acc
if a < 0 {
a = -a
}
a >>= 2*ϕ - 16
if a > 0xffff {
a = 0xffff
}
// This algorithm comes from the standard library's image/draw package.
dstA := uint32(dst[i]) * 0x101
maskA := uint32(a)
outA := dstA*(0xffff-maskA)/0xffff + maskA
dst[i] = uint8(outA >> 8)
}
}
func fixedAccumulateMask(buf []uint32) {
acc := int2ϕ(0)
for i, v := range buf {
acc += int2ϕ(v)
a := acc
if a < 0 {
a = -a
}
a >>= 2*ϕ - 16
if a > 0xffff {
a = 0xffff
}
buf[i] = uint32(a)
}
}