From 500caaeda74dd9c660279036293f4b2997cf0b03 Mon Sep 17 00:00:00 2001 From: Dimitri Sokolyuk Date: Sat, 9 Sep 2017 09:42:37 +0200 Subject: Add vendor --- vendor/golang.org/x/image/vector/raster_fixed.go | 327 +++++++++++++++++++++++ 1 file changed, 327 insertions(+) create mode 100644 vendor/golang.org/x/image/vector/raster_fixed.go (limited to 'vendor/golang.org/x/image/vector/raster_fixed.go') diff --git a/vendor/golang.org/x/image/vector/raster_fixed.go b/vendor/golang.org/x/image/vector/raster_fixed.go new file mode 100644 index 0000000..5b0fe7a --- /dev/null +++ b/vendor/golang.org/x/image/vector/raster_fixed.go @@ -0,0 +1,327 @@ +// 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. + +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 = 9 + + fxOne int1ϕ = 1 << ϕ + fxOneAndAHalf int1ϕ = 1<<ϕ + 1<<(ϕ-1) + fxOneMinusIota 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 + fxOneMinusIota) >> ϕ) } + +func (z *Rasterizer) fixedLineTo(bx, by float32) { + ax, ay := z.penX, z.penY + z.penX, z.penY = bx, by + dir := int1ϕ(1) + if ay > by { + dir, ax, ay, bx, by = -1, bx, by, ax, ay + } + // 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 / (by - ay), is unstable in fixed point math, + // so we treat the segment as if it was perfectly horizontal. + if by-ay <= 0.000001 { + return + } + dxdy := (bx - ax) / (by - ay) + + ayϕ := int1ϕ(ay * float32(fxOne)) + byϕ := int1ϕ(by * float32(fxOne)) + + x := int1ϕ(ax * float32(fxOne)) + y := fixedFloor(ayϕ) + yMax := fixedCeil(byϕ) + 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, byϕ) - fixedMax(int1ϕ(y)<<ϕ, ayϕ) + xNext := x + int1ϕ(float32(dy)*dxdy) + if y < 0 { + x = xNext + continue + } + buf := z.bufU32[y*width:] + d := dy * dir // d ranges up to ±1<<(1*ϕ). + 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 * (fxOne - 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 := fxOne - x0f + oneMinusX0fSquared := oneMinusX0f * oneMinusX0f + x1f := x1 - x1Ceil + fxOne + 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 ranges up to ±1<<(2*ϕ). + D *= d // D ranges up to ±1<<(3*ϕ). + 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 * (fxOne - a0 - am)) + // + // (x1i == x0i+2) and (twoOverS == 2 * (x1 - x0)) implies + // that twoOverS ranges up to +1<<(1*ϕ+2). + D := twoOverS<<ϕ - oneMinusX0fSquared - x1fSquared // D ranges up to ±1<<(2*ϕ+2). + D *= d // D ranges up to ±1<<(3*ϕ+2). + D /= twoOverS + buf[i] += uint32(D) + } + } else { + // This is commented out for the same reason as a0 and am. + // + // a1 := ((fxOneAndAHalf - x0f) << ϕ) / oneOverS + + if i := clamp(x0i+1, width); i < uint(len(buf)) { + // In ideal math: + // buf[i] += uint32(d * (a1 - a0)) + // or equivalently (but better in non-ideal, integer math, + // with respect to rounding errors), + // buf[i] += uint32(A * d / twoOverS) + // where + // A = (a1 - a0) * twoOverS + // = a1*twoOverS - a0*twoOverS + // Noting that twoOverS/oneOverS equals 2, substituting for + // a0 and then a1, given above, yields: + // A = a1*twoOverS - oneMinusX0fSquared + // = (fxOneAndAHalf-x0f)<<(ϕ+1) - oneMinusX0fSquared + // = fxOneAndAHalf<<(ϕ+1) - x0f<<(ϕ+1) - oneMinusX0fSquared + // + // This is a positive number minus two non-negative + // numbers. For an upper bound on A, the positive number is + // P = fxOneAndAHalf<<(ϕ+1) + // < (2*fxOne)<<(ϕ+1) + // = fxOne<<(ϕ+2) + // = 1<<(2*ϕ+2) + // + // For a lower bound on A, the two non-negative numbers are + // N = x0f<<(ϕ+1) + oneMinusX0fSquared + // ≤ x0f<<(ϕ+1) + fxOne*fxOne + // = x0f<<(ϕ+1) + 1<<(2*ϕ) + // < x0f<<(ϕ+1) + 1<<(2*ϕ+1) + // ≤ fxOne<<(ϕ+1) + 1<<(2*ϕ+1) + // = 1<<(2*ϕ+1) + 1<<(2*ϕ+1) + // = 1<<(2*ϕ+2) + // + // Thus, A ranges up to ±1<<(2*ϕ+2). It is possible to + // derive a tighter bound, but this bound is sufficient to + // reason about overflow. + D := (fxOneAndAHalf-x0f)<<(ϕ+1) - oneMinusX0fSquared // D ranges up to ±1<<(2*ϕ+2). + D *= d // D ranges up to ±1<<(3*ϕ+2). + D /= 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 * (fxOne - a2 - am)) + // or equivalently (but better in non-ideal, integer math, + // with respect to rounding errors), + // buf[i] += uint32(A * d / twoOverS) + // where + // A = (fxOne - a2 - am) * twoOverS + // = twoOverS<<ϕ - a2*twoOverS - am*twoOverS + // Noting that twoOverS/oneOverS equals 2, substituting for + // am and then a2, given above, yields: + // A = twoOverS<<ϕ - a2*twoOverS - x1f*x1f + // = twoOverS<<ϕ - a1*twoOverS - (int1ϕ(x1i-x0i-3)<<(2*ϕ))*2 - x1f*x1f + // = twoOverS<<ϕ - a1*twoOverS - int1ϕ(x1i-x0i-3)<<(2*ϕ+1) - x1f*x1f + // Substituting for a1, given above, yields: + // A = twoOverS<<ϕ - ((fxOneAndAHalf-x0f)<<ϕ)*2 - int1ϕ(x1i-x0i-3)<<(2*ϕ+1) - x1f*x1f + // = twoOverS<<ϕ - (fxOneAndAHalf-x0f)<<(ϕ+1) - int1ϕ(x1i-x0i-3)<<(2*ϕ+1) - x1f*x1f + // = B<<ϕ - x1f*x1f + // where + // B = twoOverS - (fxOneAndAHalf-x0f)<<1 - int1ϕ(x1i-x0i-3)<<(ϕ+1) + // = (x1-x0)<<1 - (fxOneAndAHalf-x0f)<<1 - int1ϕ(x1i-x0i-3)<<(ϕ+1) + // + // Re-arranging the defintions given above: + // x0Floor := int1ϕ(x0i) << ϕ + // x0f := x0 - x0Floor + // x1Ceil := int1ϕ(x1i) << ϕ + // x1f := x1 - x1Ceil + fxOne + // combined with fxOne = 1<<ϕ yields: + // x0 = x0f + int1ϕ(x0i)<<ϕ + // x1 = x1f + int1ϕ(x1i-1)<<ϕ + // so that expanding (x1-x0) yields: + // B = (x1f-x0f + int1ϕ(x1i-x0i-1)<<ϕ)<<1 - (fxOneAndAHalf-x0f)<<1 - int1ϕ(x1i-x0i-3)<<(ϕ+1) + // = (x1f-x0f)<<1 + int1ϕ(x1i-x0i-1)<<(ϕ+1) - (fxOneAndAHalf-x0f)<<1 - int1ϕ(x1i-x0i-3)<<(ϕ+1) + // A large part of the second and fourth terms cancel: + // B = (x1f-x0f)<<1 - (fxOneAndAHalf-x0f)<<1 - int1ϕ(-2)<<(ϕ+1) + // = (x1f-x0f)<<1 - (fxOneAndAHalf-x0f)<<1 + 1<<(ϕ+2) + // = (x1f - fxOneAndAHalf)<<1 + 1<<(ϕ+2) + // The first term, (x1f - fxOneAndAHalf)<<1, is a negative + // number, bounded below by -fxOneAndAHalf<<1, which is + // greater than -fxOne<<2, or -1<<(ϕ+2). Thus, B ranges up + // to ±1<<(ϕ+2). One final simplification: + // B = x1f<<1 + (1<<(ϕ+2) - fxOneAndAHalf<<1) + const C = 1<<(ϕ+2) - fxOneAndAHalf<<1 + D := x1f<<1 + C // D ranges up to ±1<<(1*ϕ+2). + D <<= ϕ // D ranges up to ±1<<(2*ϕ+2). + D -= x1fSquared // D ranges up to ±1<<(2*ϕ+3). + D *= d // D ranges up to ±1<<(3*ϕ+3). + D /= 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 ranges up to ±1<<(2*ϕ). + D *= d // D ranges up to ±1<<(3*ϕ). + D /= twoOverS + buf[i] += uint32(D) + } + } + + x = xNext + } +} + +func fixedAccumulateOpOver(dst []uint8, src []uint32) { + // Sanity check that len(dst) >= len(src). + if len(dst) < len(src) { + return + } + + 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 fixedAccumulateOpSrc(dst []uint8, src []uint32) { + // Sanity check that len(dst) >= len(src). + if len(dst) < len(src) { + return + } + + 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 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) + } +} -- cgit v1.2.3