[C#] Bgr24彩色位图转为灰度的Bgr24位图的跨平台SIMD硬件加速向量算法已关闭评论
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摘要

在上一篇文章里，我们讲解了“Bgr24彩色位图转为Gray8灰度位图”算法。本文将探讨“Bgr24彩色位图转为灰度的Bgr24位图”。区别在于目标位图也是Bgr24格式的，只是将像素数据由彩色转为了灰度。这些算法也是跨平台的，同一份源代码，能在 X86及Arm架构上运行，且均享有SIMD硬件加速。

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一、标量算法

1.1 算法实现

算法原理与上一篇文章是一样，唯一区别是目标位图的地址计算与写入处理。因为现在对于每一个像素，需要写入3个字节。
源代码如下。

public static unsafe void ScalarDoBatch(byte* pSrc, int strideSrc, int width, int height, byte* pDst, int strideDst) {     const int cbPixel = 3; // Bgr24     const int shiftPoint = 16;     const int mulPoint = 1 << shiftPoint; // 0x10000     const int mulRed = (int)(0.299 * mulPoint + 0.5); // 19595     const int mulGreen = (int)(0.587 * mulPoint + 0.5); // 38470     const int mulBlue = mulPoint - mulRed - mulGreen; // 7471     byte* pRow = pSrc;     byte* qRow = pDst;     for (int i = 0; i < height; i++) {         byte* p = pRow;         byte* q = qRow;         for (int j = 0; j < width; j++) {             byte gray = (byte)((p[2] * mulRed + p[1] * mulGreen + p[0] * mulBlue) >> shiftPoint);             q[0] = q[1] = q[2] = gray;             p += cbPixel; // Bgr24             q += cbPixel; // Bgr24 store grayscale.         }         pRow += strideSrc;         qRow += strideDst;     } }

1.2 基准测试代码

使用 BenchmarkDotNet 进行基准测试。
可以使用上一篇文章的公共函数，写好标量算法的基准测试代码。源代码如下。

[Benchmark(Baseline = true)] public void Scalar() {     ScalarDo(_sourceBitmapData, _destinationBitmapData, 0); }  [Benchmark] public void ScalarParallel() {     ScalarDo(_sourceBitmapData, _destinationBitmapData, 1); }  public static unsafe void ScalarDo(BitmapData src, BitmapData dst, int parallelFactor = 0) {     int width = src.Width;     int height = src.Height;     int strideSrc = src.Stride;     int strideDst = dst.Stride;     byte* pSrc = (byte*)src.Scan0.ToPointer();     byte* pDst = (byte*)dst.Scan0.ToPointer();     int processorCount = Environment.ProcessorCount;     int batchSize = 0;     if (parallelFactor > 1) {         batchSize = height / (processorCount * parallelFactor);     } else if (parallelFactor == 1) {         if (height >= processorCount) batchSize = 1;     }     bool allowParallel = (batchSize > 0) && (processorCount > 1);     if (allowParallel) {         int batchCount = (height + batchSize - 1) / batchSize; // ceil((double)length / batchSize)         Parallel.For(0, batchCount, i => {             int start = batchSize * i;             int len = batchSize;             if (start + len > height) len = height - start;             byte* pSrc2 = pSrc + start * strideSrc;             byte* pDst2 = pDst + start * strideDst;             ScalarDoBatch(pSrc2, strideSrc, width, len, pDst2, strideDst);         });     } else {         ScalarDoBatch(pSrc, strideSrc, width, height, pDst, strideDst);     } }

二、向量算法

2.1 算法思路

对于24位转8位灰度，可以使用这种办法: 每次从源位图读取3个向量，进行3-元素组的解交织运算，得到 R,G,B 平面数据。随后使用向量化的乘法与加法，来计算灰度值。最后将存储了灰度值的那一个向量，进行3-元素组的交织运算，便能存储到目标位图。

它与“Bgr24彩色位图转为Gray8灰度位图”向量算法的区别，在于最后需做“3-元素组的交织运算”。

例如 Sse指令集使用的是128位向量，此时1个向量为16字节。每次从源位图读取3个向量，就是读取了48字节，即16个RGB像素。最后将灰度向量做“3-元素组的交织运算”，结果是3个向量。将那3个向量存储到目标位图，就是写入了48字节，即16个RGB像素。

对于3-元素组的交织，可以使用 shuffle 类别的指令来实现。例如对于X86架构的 128位向量，可以使用 SSSE3 的 _mm_shuffle_epi8 指令，它对应 NET 中的 Ssse3.Shuffle 方法。源代码如下。

static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_X_Part0 = Vector128.Create((sbyte)0, -1, -1, 1, -1, -1, 2, -1, -1, 3, -1, -1, 4, -1, -1, 5).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_X_Part1 = Vector128.Create((sbyte)-1, 0, -1, -1, 1, -1, -1, 2, -1, -1, 3, -1, -1, 4, -1, -1).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_X_Part2 = Vector128.Create((sbyte)-1, -1, 0, -1, -1, 1, -1, -1, 2, -1, -1, 3, -1, -1, 4, -1).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_Y_Part0 = Vector128.Create((sbyte)-1, -1, 6, -1, -1, 7, -1, -1, 8, -1, -1, 9, -1, -1, 10, -1).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_Y_Part1 = Vector128.Create((sbyte)5, -1, -1, 6, -1, -1, 7, -1, -1, 8, -1, -1, 9, -1, -1, 10).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_Y_Part2 = Vector128.Create((sbyte)-1, 5, -1, -1, 6, -1, -1, 7, -1, -1, 8, -1, -1, 9, -1, -1).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_Z_Part0 = Vector128.Create((sbyte)-1, 11, -1, -1, 12, -1, -1, 13, -1, -1, 14, -1, -1, 15, -1, -1).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_Z_Part1 = Vector128.Create((sbyte)-1, -1, 11, -1, -1, 12, -1, -1, 13, -1, -1, 14, -1, -1, 15, -1).AsByte(); static readonly Vector128<byte> YGroup3Zip_Shuffle_Byte_Z_Part2 = Vector128.Create((sbyte)10, -1, -1, 11, -1, -1, 12, -1, -1, 13, -1, -1, 14, -1, -1, 15).AsByte();  public static Vector128<byte> YGroup3Zip_Shuffle(Vector128<byte> x, Vector128<byte> y, Vector128<byte> z, out Vector128<byte> data1, out Vector128<byte> data2) {     var f0A = YGroup3Zip_Shuffle_Byte_X_Part0;     var f0B = YGroup3Zip_Shuffle_Byte_X_Part1;     var f0C = YGroup3Zip_Shuffle_Byte_X_Part2;     var f1A = YGroup3Zip_Shuffle_Byte_Y_Part0;     var f1B = YGroup3Zip_Shuffle_Byte_Y_Part1;     var f1C = YGroup3Zip_Shuffle_Byte_Y_Part2;     var f2A = YGroup3Zip_Shuffle_Byte_Z_Part0;     var f2B = YGroup3Zip_Shuffle_Byte_Z_Part1;     var f2C = YGroup3Zip_Shuffle_Byte_Z_Part2;     var rt0 = Sse2.Or(Sse2.Or(Ssse3.Shuffle(x, f0A), Ssse3.Shuffle(y, f0B)), Ssse3.Shuffle(z, f0C));     var rt1 = Sse2.Or(Sse2.Or(Ssse3.Shuffle(x, f1A), Ssse3.Shuffle(y, f1B)), Ssse3.Shuffle(z, f1C));     var rt2 = Sse2.Or(Sse2.Or(Ssse3.Shuffle(x, f2A), Ssse3.Shuffle(y, f2B)), Ssse3.Shuffle(z, f2C));     data1 = rt1;     data2 = rt2;     return rt0; }

VectorTraits 库已经集成了上述算法，提供了“Vectors.YGroup3Zip”方法。该方法能够跨平台，它会使用各个平台的shuffle指令。

2.2 算法实现

有了 YGroup3Unzip、YGroup3Zip 方法后，便能方便的编写彩色转灰度的算法了。灰度系数有8位精度，于是需要将 8位数据变宽为16位后，再来计算乘法与加法。最后再将 16位数据，变窄为8位。源代码如下。

public static unsafe void UseVectorsDoBatch(byte* pSrc, int strideSrc, int width, int height, byte* pDst, int strideDst) {     const int cbPixel = 3; // Bgr24     const int shiftPoint = 8;     const int mulPoint = 1 << shiftPoint; // 0x100     const ushort mulRed = (ushort)(0.299 * mulPoint + 0.5); // 77     const ushort mulGreen = (ushort)(0.587 * mulPoint + 0.5); // 150     const ushort mulBlue = mulPoint - mulRed - mulGreen; // 29     Vector<ushort> vmulRed = new Vector<ushort>(mulRed);     Vector<ushort> vmulGreen = new Vector<ushort>(mulGreen);     Vector<ushort> vmulBlue = new Vector<ushort>(mulBlue);     int vectorWidth = Vector<byte>.Count;     int maxX = width - vectorWidth;     byte* pRow = pSrc;     byte* qRow = pDst;     for (int i = 0; i < height; i++) {         Vector<byte>* pLast = (Vector<byte>*)(pRow + maxX * cbPixel); // Bgr24         Vector<byte>* qLast = (Vector<byte>*)(qRow + maxX * cbPixel); // Bgr24 store grayscale.         Vector<byte>* p = (Vector<byte>*)pRow;         Vector<byte>* q = (Vector<byte>*)qRow;         for (; ; ) {             Vector<byte> r, g, b, gray, gray0, gray1, gray2;             Vector<ushort> wr0, wr1, wg0, wg1, wb0, wb1;             // Load.             b = Vectors.YGroup3Unzip(p[0], p[1], p[2], out g, out r);             // widen(r) * mulRed + widen(g) * mulGreen + widen(b) * mulBlue             Vector.Widen(r, out wr0, out wr1);             Vector.Widen(g, out wg0, out wg1);             Vector.Widen(b, out wb0, out wb1);             wr0 = Vectors.Multiply(wr0, vmulRed);             wr1 = Vectors.Multiply(wr1, vmulRed);             wg0 = Vectors.Multiply(wg0, vmulGreen);             wg1 = Vectors.Multiply(wg1, vmulGreen);             wb0 = Vectors.Multiply(wb0, vmulBlue);             wb1 = Vectors.Multiply(wb1, vmulBlue);             wr0 = Vector.Add(wr0, wg0);             wr1 = Vector.Add(wr1, wg1);             wr0 = Vector.Add(wr0, wb0);             wr1 = Vector.Add(wr1, wb1);             // Shift right and narrow.             wr0 = Vectors.ShiftRightLogical_Const(wr0, shiftPoint);             wr1 = Vectors.ShiftRightLogical_Const(wr1, shiftPoint);             gray = Vector.Narrow(wr0, wr1);             // Store.             gray0 = Vectors.YGroup3Zip(gray, gray, gray, out gray1, out gray2);             q[0] = gray0;             q[1] = gray1;             q[2] = gray2;             // Next.             if (p >= pLast) break;             p += cbPixel;             q += cbPixel;             if (p > pLast) p = pLast; // The last block is also use vector.             if (q > qLast) q = qLast;         }         pRow += strideSrc;         qRow += strideDst;     } }

2.3 基准测试代码

随后为该算法编写基准测试代码。

[Benchmark] public void UseVectors() {     UseVectorsDo(_sourceBitmapData, _destinationBitmapData, 0); }  [Benchmark] public void UseVectorsParallel() {     UseVectorsDo(_sourceBitmapData, _destinationBitmapData, 1); }  public static unsafe void UseVectorsDo(BitmapData src, BitmapData dst, int parallelFactor = 0) {     int vectorWidth = Vector<byte>.Count;     int width = src.Width;     int height = src.Height;     if (width <= vectorWidth) {         ScalarDo(src, dst, parallelFactor);         return;     }     int strideSrc = src.Stride;     int strideDst = dst.Stride;     byte* pSrc = (byte*)src.Scan0.ToPointer();     byte* pDst = (byte*)dst.Scan0.ToPointer();     int processorCount = Environment.ProcessorCount;     int batchSize = 0;     if (parallelFactor > 1) {         batchSize = height / (processorCount * parallelFactor);     } else if (parallelFactor == 1) {         if (height >= processorCount) batchSize = 1;     }     bool allowParallel = (batchSize > 0) && (processorCount > 1);     if (allowParallel) {         int batchCount = (height + batchSize - 1) / batchSize; // ceil((double)length / batchSize)         Parallel.For(0, batchCount, i => {             int start = batchSize * i;             int len = batchSize;             if (start + len > height) len = height - start;             byte* pSrc2 = pSrc + start * strideSrc;             byte* pDst2 = pDst + start * strideDst;             UseVectorsDoBatch(pSrc2, strideSrc, width, len, pDst2, strideDst);         });     } else {         UseVectorsDoBatch(pSrc, strideSrc, width, height, pDst, strideDst);     } }

完整源码在 Bgr24ToGrayBgr24Benchmark.cs

三、基准测试结果

3.1 X86 架构

X86架构下的基准测试结果如下。

BenchmarkDotNet v0.14.0, Windows 11 (10.0.22631.4460/23H2/2023Update/SunValley3) AMD Ryzen 7 7840H w/ Radeon 780M Graphics, 1 CPU, 16 logical and 8 physical cores .NET SDK 8.0.403   [Host]     : .NET 8.0.10 (8.0.1024.46610), X64 RyuJIT AVX-512F+CD+BW+DQ+VL+VBMI   DefaultJob : .NET 8.0.10 (8.0.1024.46610), X64 RyuJIT AVX-512F+CD+BW+DQ+VL+VBMI   | Method               | Width | Mean         | Error      | StdDev     | Ratio | |--------------------- |------ |-------------:|-----------:|-----------:|------:| | Scalar               | 1024  |  1,128.81 us |   4.436 us |   3.932 us |  1.00 | | ScalarParallel       | 1024  |    157.96 us |   1.007 us |   0.942 us |  0.14 | | UseVectors           | 1024  |    123.79 us |   1.144 us |   1.014 us |  0.11 | | UseVectorsParallel   | 1024  |     26.05 us |   0.503 us |   0.471 us |  0.02 | |                      |       |              |            |            |       | | Scalar               | 2048  |  4,279.99 us |  37.658 us |  35.226 us |  1.00 | | ScalarParallel       | 2048  |    622.01 us |   3.989 us |   3.537 us |  0.15 | | UseVectors           | 2048  |    631.53 us |   6.741 us |   6.305 us |  0.15 | | UseVectorsParallel   | 2048  |    330.47 us |   5.479 us |   4.857 us |  0.08 | |                      |       |              |            |            |       | | Scalar               | 4096  | 17,252.90 us | 106.215 us |  99.353 us |  1.00 | | ScalarParallel       | 4096  |  3,743.78 us |  25.989 us |  24.310 us |  0.22 | | UseVectors           | 4096  |  3,273.92 us |  32.645 us |  30.537 us |  0.19 | | UseVectorsParallel   | 4096  |  3,746.83 us |  11.083 us |   9.255 us |  0.22 |

Scalar: 标量算法。
ScalarParallel: 并发的标量算法。
UseVectors: 矢量算法。
UseVectorsParallel: 并发的矢量算法。

3.2 Arm 架构

同样的源代码可以在 Arm 架构上运行。基准测试结果如下。

BenchmarkDotNet v0.14.0, macOS Sequoia 15.0.1 (24A348) [Darwin 24.0.0] Apple M2, 1 CPU, 8 logical and 8 physical cores .NET SDK 8.0.204   [Host]     : .NET 8.0.4 (8.0.424.16909), Arm64 RyuJIT AdvSIMD   DefaultJob : .NET 8.0.4 (8.0.424.16909), Arm64 RyuJIT AdvSIMD   | Method               | Width | Mean         | Error      | StdDev     | Median       | Ratio | RatioSD | |--------------------- |------ |-------------:|-----------:|-----------:|-------------:|------:|--------:| | Scalar               | 1024  |    719.32 us |   0.215 us |   0.201 us |    719.34 us |  1.00 |    0.00 | | ScalarParallel       | 1024  |    157.38 us |   1.423 us |   1.111 us |    157.25 us |  0.22 |    0.00 | | UseVectors           | 1024  |    169.25 us |   0.538 us |   0.503 us |    169.40 us |  0.24 |    0.00 | | UseVectorsParallel   | 1024  |     57.81 us |   0.998 us |   2.149 us |     58.11 us |  0.08 |    0.00 | |                      |       |              |            |            |              |       |         | | Scalar               | 2048  |  2,963.48 us |   6.674 us |   5.211 us |  2,961.39 us |  1.00 |    0.00 | | ScalarParallel       | 2048  |    627.47 us |  11.680 us |  25.142 us |    616.63 us |  0.21 |    0.01 | | UseVectors           | 2048  |    716.27 us |   2.097 us |   1.961 us |    717.02 us |  0.24 |    0.00 | | UseVectorsParallel   | 2048  |    368.49 us |   7.320 us |  21.469 us |    378.95 us |  0.12 |    0.01 | |                      |       |              |            |            |              |       |         | | Scalar               | 4096  | 12,449.32 us | 177.868 us | 157.676 us | 12,508.13 us |  1.00 |    0.02 | | ScalarParallel       | 4096  |  2,510.22 us |  34.541 us |  30.620 us |  2,501.37 us |  0.20 |    0.00 | | UseVectors           | 4096  |  2,968.72 us |  20.503 us |  18.175 us |  2,965.71 us |  0.24 |    0.00 | | UseVectorsParallel   | 4096  |  1,728.46 us |   4.362 us |   4.080 us |  1,729.00 us |  0.14 |    0.00 |

四、对算法进行检查

以往想对算法进行检查法时，直接对各个字节做相等比较就行了。
但“Bgr24彩色位图转为灰度的Bgr24位图”不适合那样的验证。由于整数运算有精度损失，造成部分像素值会有一些小的偏差。若直接对各个字节做相等比较，那么结果总是 false.
于是可以编写一个统计误差的函数。可通过误差的大小，来判断算法是否正确，以及比较算法的优劣。

private unsafe long SumDifference(BitmapData expected, BitmapData dst, out long countByteDifference, out int maxDifference) {     const int cbPixel = 3; // Bgr24 store grayscale.     long totalDifference = 0;     countByteDifference = 0;     maxDifference = 0;     int maxPosX = -1, maxPosY = -1;     int width = expected.Width;     int height = expected.Height;     int strideSrc = expected.Stride;     int strideDst = dst.Stride;     byte* pRow = (byte*)expected.Scan0.ToPointer();     byte* qRow = (byte*)dst.Scan0.ToPointer();     for (int i = 0; i < height; i++) {         byte* p = pRow;         byte* q = qRow;         for (int j = 0; j < width; j++) {             for (int k = 0; k < cbPixel; ++k) {                 int difference = Math.Abs((int)(*q) - *p);                 if (0 != difference) {                     totalDifference += difference;                     ++countByteDifference;                     if (maxDifference < difference) {                         maxDifference = difference;                         maxPosX = j;                         maxPosY = i;                     }                 }                 ++p;                 ++q;             }         }         pRow += strideSrc;         qRow += strideDst;     }     if (maxDifference > 0) {         //Console.WriteLine(string.Format("SumDifference maxDifference={0}, at ({1}, {2})", maxDifference, maxPosX, maxPosY));     }     return totalDifference; }

在 Setup 方法里增加检查代码。

// Check. bool allowCheck = true; if (allowCheck) {     try {         TextWriter writer = Console.Out;         long totalDifference, countByteDifference;         int maxDifference;         double averageDifference;         long totalByte = Width * Height * 3;         double percentDifference;         // Baseline         ScalarDo(_sourceBitmapData, _expectedBitmapData);         // ScalarParallel         ScalarParallel();         totalDifference = SumDifference(_expectedBitmapData, _destinationBitmapData, out countByteDifference, out maxDifference);         averageDifference = (countByteDifference > 0) ? (double)totalDifference / countByteDifference : 0;         percentDifference = 100.0 * countByteDifference / totalByte;         writer.WriteLine(string.Format("Difference of ScalarParallel: {0}/{1}={2}, max={3}, percentDifference={4:0.000000}%", totalDifference, countByteDifference, averageDifference, maxDifference, percentDifference));         // UseVectors         UseVectors();         totalDifference = SumDifference(_expectedBitmapData, _destinationBitmapData, out countByteDifference, out maxDifference);         averageDifference = (countByteDifference > 0) ? (double)totalDifference / countByteDifference : 0;         percentDifference = 100.0 * countByteDifference / totalByte;         writer.WriteLine(string.Format("Difference of UseVectors: {0}/{1}={2}, max={3}, percentDifference={4:0.000000}%", totalDifference, countByteDifference, averageDifference, maxDifference, percentDifference));         // UseVectorsParallel         UseVectorsParallel();         totalDifference = SumDifference(_expectedBitmapData, _destinationBitmapData, out countByteDifference, out maxDifference);         averageDifference = (countByteDifference > 0) ? (double)totalDifference / countByteDifference : 0;         percentDifference = 100.0 * countByteDifference / totalByte;         writer.WriteLine(string.Format("Difference of UseVectorsParallel: {0}/{1}={2}, max={3}, percentDifference={4:0.000000}%", totalDifference, countByteDifference, averageDifference, maxDifference, percentDifference));     } catch (Exception ex) {         Debug.WriteLine(ex.ToString());     } }

字段说明:

totalDifference: 所有像素误差值总和。
countByteDifference: 发生误差的字节总数。
averageDifference: 平均每个字节的误差值。越小越好。
maxDifference: 最大误差值。即输出信息里的“max”。0表示完全匹配，1_{2是正常，3}4表示误差较大，超过5一般是算法存在问题。
percentDifference: 发生误差的字节总数，在整个图片中的比例。越小越好。

运行程序，可以看到相关的输出信息。

Difference of ScalarParallel: 0/0=0, max=0, percentDifference=0.000000% Difference of UseVectors: 422400/422400=1, max=1, percentDifference=13.427734% Difference of UseVectorsParallel: 422400/422400=1, max=1, percentDifference=13.427734%

“max”最大为“1”，表示字节的最大误差只有1。整数算法本身是存在舍入误差的，而现在只有1，表示误差已经控制的很好了，算法的质量很高了。