beb9675609
Change-Id: Iea92b74ca9533de2ef17534ee3acf4f40c3d03ef Reviewed-on: https://go-review.googlesource.com/30899 Reviewed-by: David Crawshaw <crawshaw@golang.org>
263 lines
6.4 KiB
Go
263 lines
6.4 KiB
Go
// 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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fxOne int1ϕ = 1 << ϕ
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fxOneAndAHalf int1ϕ = 1<<ϕ + 1<<(ϕ-1)
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fxOneMinusIota 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 + fxOneMinusIota) >> 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(fxOne))
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by := int1ϕ(b[1] * float32(fxOne))
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x := int1ϕ(a[0] * float32(fxOne))
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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 * (fxOne - 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 := fxOne - x0f
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oneMinusX0fSquared := oneMinusX0f * oneMinusX0f
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x1f := x1 - x1Ceil + fxOne
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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 * (fxOne - 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 := ((fxOneAndAHalf - 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((fxOneAndAHalf-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 * (fxOne - 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((fxOneAndAHalf - 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 fixedAccumulateOpOver(dst []uint8, src []uint32) {
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// Sanity check that len(dst) >= len(src).
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if len(dst) < len(src) {
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return
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}
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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 fixedAccumulateOpSrc(dst []uint8, src []uint32) {
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// Sanity check that len(dst) >= len(src).
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if len(dst) < len(src) {
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return
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}
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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 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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