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作者： zyl910
一、背景
先前的2篇文章，说了向量类型的类型选择问题。本文讨论一个使用方面的问题——循环展开。
现在的CPU采用了流水线、超标量等机制来提高运算性能。如果完全是顺序代码，那么流水线的效果会非常好。
但是程序中不可避免的需要 分支 与 循环来处理各种复杂的逻辑。分支与循环会被编译为跳转指令，而跳转指令会导致CPU流水线失效，对性能的影响很大。虽然现代处理器增加了分支预测技术，但总会有预测失败的概率。
尤其是在使用向量类型进行SIMD运算时，因向量类型仅尽可能榨干CPU内部的ALU（算术逻辑单元），于是在跳转时的性能损失更大。
故在使用向量类型处理大规模数学计算时，应尽可能的避免分支与循环。
对于分支，最好尽量将分支挪到内循环外。若是内循环中必须的分支，可尽量用位掩码等办法来写无分支代码。
对于循环，一般可使用循环展开技术，来避免短的循环。
1.1 循环展开简介
摘录——
循环展开（Loop unrolling）技术是一种提升程序执行速度的非常有效的优化方法，它可以由程序员手工编写，也可由编译器自动优化。循环展开的本质是，利用CPU指令级并行，来降低循环的开销，当然，同时也有利于指令流水线的高效调度。 …… 循环展开的优点： 第一，减少了分支预测失败的可能性。 第二，增加了循环体内语句并发执行的可能性，当然，这需要循环体内各语句不存在数据相关性。 循环展开的缺点： 第一，造成代码膨胀，导致ELF文件（或Windows PE文件）尺寸增大。 第二，代码可读性显著降低，前一个人写的循环展开代码，很可能被不熟悉的后续维护人员改回去。 1.2 测试准备
注意，循环展开提高的是流水线性能，对小循环效果明显。此时分支造成的延时，大多与内循环的运算耗时差不多。
对于有些复杂的大循环，内循环的运算耗时已经很大了，而分支造成的延时仍是常数值，比例下降了很多。此时循环展开的收益就少了。
由于循环展开是程序员手工编写的，故必须在编码前就确定好展开次数。
本文就来探讨一下大多数时候的展开次数选择。
展开2倍的话，性能最多为原来2倍，即大多数情况下只有1倍多的性能提升，提升不大。
展开2倍的话，性能最多为原来4倍。区间大了，很多时候能达到2倍以上的提升。
故一开始可以用展开4倍来测试。下面将进行测试。
测试电脑的配置信息为：lntel(R) Core(TM) i5-8250U CPU @ 1.60GHz、Windows 10。
二、在C#中使用
为了对比测试 Avx指令的效果，故可在 BenchmarkVectorCore30 工程里进行测试。因是64位操作系统，故选取 x64、Release版的测试结果.
2.1 对基础算法做循环展开
回顾一下基础算法:
private static float SumBase(float[] src, int count, int loops) { float rt = 0; // Result. for (int j=0; j< loops; ++j) { for(int i=0; i< count; ++i) { rt += src[i]; } } return rt; } 改为循环展开4倍后，代码为:
private static float SumBaseU4(float[] src, int count, int loops) { float rt = 0; // Result. float rt1 = 0; float rt2 = 0; float rt3 = 0; int nBlockWidth = 4; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. int p; // Index for src data. int i; for (int j = 0; j < loops; ++j) { p = 0; // Block processs. for (i = 0; i < cntBlock; ++i) { rt += src; rt1 += src
; rt2 += src
; rt3 += src
; p += nBlockWidth; } // Remainder processs. //p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. rt = rt + rt1 + rt2 + rt3; return rt; }
之前内循环只处理1个数据，现在内循环处理了4个数据。
注意内循环在处理者4个数据时，并不是直接将结果全部累加到 rt 变量，而是使用新增的 rt1、rt2、rt3 变量来临时存储累加值。这是为了消除变量之间的相关性，因为变量之间的相关性会影响流水线性能，故分别使用独立的变量就好了。
最后在 Reduce 阶段，将 rt1、rt2、rt3 的值累加到 rt。
2.1.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 可以发现，基础算法使用4倍循环展开后，性能是原先的 2.6336 倍。
2.2 对 Vector4 版算法做循环展开
回顾一下Vector4 版算法:
private static float SumVector4(float[] src, int count, int loops) { float rt = 0; // Result. const int VectorWidth = 4; int nBlockWidth = VectorWidth; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector4 vrt = Vector4.Zero; // Vector result. int p; // Index for src data. int i; // Load. Vector4[] vsrc = new Vector4[cntBlock]; // Vector src. p = 0; for (i = 0; i < vsrc.Length; ++i) { vsrc[i] = new Vector4(src, src
, src
, src
); p += VectorWidth; } // Body. for (int j = 0; j < loops; ++j) { // Vector processs. for (i = 0; i < cntBlock; ++i) { // Equivalent to scalar model: rt += src[i]; vrt += vsrc[i]; // Add. } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. rt += vrt.X + vrt.Y + vrt.Z + vrt.W; return rt; }
改为循环展开4倍后，代码为:
private static float SumVector4U4(float[] src, int count, int loops) { float rt = 0; // Result. const int LoopUnrolling = 4; const int VectorWidth = 4; int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector4 vrt = Vector4.Zero; // Vector result. Vector4 vrt1 = Vector4.Zero; Vector4 vrt2 = Vector4.Zero; Vector4 vrt3 = Vector4.Zero; int p; // Index for src data. int i; // Load. Vector4[] vsrc = new Vector4[count / VectorWidth]; // Vector src. p = 0; for (i = 0; i < vsrc.Length; ++i) { vsrc[i] = new Vector4(src, src
, src
, src
); p += VectorWidth; } // Body. for (int j = 0; j < loops; ++j) { p = 0; // Vector processs. for (i = 0; i < cntBlock; ++i) { vrt += vsrc
; // Add. vrt1 += vsrc
; vrt2 += vsrc
; vrt3 += vsrc
; p += LoopUnrolling; } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. vrt = vrt + vrt1 + vrt2 + vrt3; rt += vrt.X + vrt.Y + vrt.Z + vrt.W; return rt; }
跟刚才的办法一样，使用新增的 rt1、rt2、rt3 变量来临时存储累加值，消除变量之间的相关性。
最后在 Reduce 阶段，将 vrt1、vrt2、vrt3 的值累加到 vrt。
2.2.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVector4: 2.748779E+11 # msUsed=1218, MFLOPS/s=3362.8899835796387, scale=4.054187192118227 SumVector4U4: 1.0995116E+12 # msUsed=532, MFLOPS/s=7699.248120300752, scale=9.281954887218046 SumVector4U4对比基础算法（SumBase），性能倍数是 9.281954887218046。
SumVector4U4对比未循环展开的算法（SumVector4），倍数是 9.281954887218046/4.054187192118227=2.2894736842105263092984587836542
2.3 对 Vector<T> 版算法做循环展开
回顾一下 Vector<T> 版算法:
private static float SumVectorT(float[] src, int count, int loops) { float rt = 0; // Result. int VectorWidth = Vector<float>.Count; // Block width. int nBlockWidth = VectorWidth; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector<float> vrt = Vector<float>.Zero; // Vector result. int p; // Index for src data. int i; // Load. Vector<float>[] vsrc = new Vector<float>[cntBlock]; // Vector src. p = 0; for (i = 0; i < vsrc.Length; ++i) { vsrc[i] = new Vector<float>(src, p); p += VectorWidth; } // Body. for (int j = 0; j < loops; ++j) { // Vector processs. for (i = 0; i < cntBlock; ++i) { vrt += vsrc[i]; // Add. } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src; } } // Reduce. for (i = 0; i < VectorWidth; ++i) { rt += vrt[i]; } return rt; }
改为循环展开4倍后，代码为:
private static float SumVectorTU4(float[] src, int count, int loops) { float rt = 0; // Result. const int LoopUnrolling = 4; int VectorWidth = Vector<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector<float> vrt = Vector<float>.Zero; // Vector result. Vector<float> vrt1 = Vector<float>.Zero; Vector<float> vrt2 = Vector<float>.Zero; Vector<float> vrt3 = Vector<float>.Zero; int p; // Index for src data. int i; // Load. Vector<float>[] vsrc = new Vector<float>[count / VectorWidth]; // Vector src. p = 0; for (i = 0; i < vsrc.Length; ++i) { vsrc[i] = new Vector<float>(src, p); p += VectorWidth; } // Body. for (int j = 0; j < loops; ++j) { p = 0; // Vector processs. for (i = 0; i < cntBlock; ++i) { vrt += vsrc; // Add. vrt1 += vsrc
; vrt2 += vsrc
; vrt3 += vsrc
; p += LoopUnrolling; } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. vrt = vrt + vrt1 + vrt2 + vrt3; for (i = 0; i < VectorWidth; ++i) { rt += vrt[i]; } return rt; }
跟刚才的办法一样，使用新增的 rt1、rt2、rt3 变量来临时存储累加值，消除变量之间的相关性。
最后在 Reduce 阶段，将 vrt1、vrt2、vrt3 的值累加到 vrt。
2.3.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVectorT: 5.497558E+11 # msUsed=609, MFLOPS/s=6725.7799671592775, scale=8.108374384236454 SumVectorTU4: 2.1990233E+12 # msUsed=203, MFLOPS/s=20177.339901477833, scale=24.32512315270936 SumVectorTU4对比基础算法（SumBase），性能倍数是 24.32512315270936。
SumVectorTU4对比未循环展开的算法（SumVectorT），倍数是 24.32512315270936/8.108374384236454=2.9999999999999997533414337788579
初步发现 Vector<T>循环展开（2.9999）带来的性能提升, 比VectorT循环展开（2.2894）更高一些。
2.4 对 Avx版算法做循环展开
先前分别尝试用 数组、Span、指针 的办法来操纵数据、使用Avx指令集。现在对这3种办法，均写一套循环展开4次的代码:
/// <summary> /// Sum - Vector AVX. /// </summary> /// <param name="src">Soure array.</param> /// <param name="count">Soure array count.</param> /// <param name="loops">Benchmark loops.</param> /// <returns>Return the sum value.</returns> private static float SumVectorAvx(float[] src, int count, int loops) { #if Allow_Intrinsics float rt = 0; // Result. //int VectorWidth = 32 / 4; // sizeof(__m256) / sizeof(float); int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. int p; // Index for src data. int i; // Load. Vector256<float>[] vsrc = new Vector256<float>[cntBlock]; // Vector src. p = 0; for (i = 0; i < cntBlock; ++i) { vsrc[i] = Vector256.Create(src, src
, src
, src
, src
, src
, src
, src
); // Load. p += VectorWidth; } // Body. for (int j = 0; j < loops; ++j) { // Vector processs. for (i = 0; i < cntBlock; ++i) { vrt = Avx.Add(vrt, vsrc[i]); // Add. vrt += vsrc[i]; } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; #else throw new NotSupportedException(); #endif } /// <summary> /// Sum - Vector AVX - Loop unrolling *4. /// </summary> /// <param name="src">Soure array.</param> /// <param name="count">Soure array count.</param> /// <param name="loops">Benchmark loops.</param> /// <returns>Return the sum value.</returns> private static float SumVectorAvxU4(float[] src, int count, int loops) { #if Allow_Intrinsics float rt = 0; // Result. const int LoopUnrolling = 4; int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. Vector256<float> vrt1 = Vector256<float>.Zero; Vector256<float> vrt2 = Vector256<float>.Zero; Vector256<float> vrt3 = Vector256<float>.Zero; int p; // Index for src data. int i; // Load. Vector256<float>[] vsrc = new Vector256<float>[count / VectorWidth]; // Vector src. p = 0; for (i = 0; i < vsrc.Length; ++i) { vsrc[i] = Vector256.Create(src
, src
, src
, src
, src
, src
, src
, src
); // Load. p += VectorWidth; } // Body. for (int j = 0; j < loops; ++j) { p = 0; // Vector processs. for (i = 0; i < cntBlock; ++i) { vrt = Avx.Add(vrt, vsrc
); // Add. vrt += vsrc
; vrt1 = Avx.Add(vrt1, vsrc
); vrt2 = Avx.Add(vrt2, vsrc
); vrt3 = Avx.Add(vrt3, vsrc
); p += LoopUnrolling; } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. vrt = Avx.Add(Avx.Add(vrt, vrt1), Avx.Add(vrt2, vrt3)); // vrt = vrt + vrt1 + vrt2 + vrt3; for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; #else throw new NotSupportedException(); #endif } /// <summary> /// Sum - Vector AVX - Span. /// </summary> /// <param name="src">Soure array.</param> /// <param name="count">Soure array count.</param> /// <param name="loops">Benchmark loops.</param> /// <returns>Return the sum value.</returns> private static float SumVectorAvxSpan(float[] src, int count, int loops) { #if Allow_Intrinsics float rt = 0; // Result. int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. int p; // Index for src data. ReadOnlySpan<Vector256<float>> vsrc; // Vector src. int i; // Body. for (int j = 0; j < loops; ++j) { // Vector processs. vsrc = System.Runtime.InteropServices.MemoryMarshal.Cast<float, Vector256<float> >(new Span<float>(src)); // Reinterpret cast. `float*` to `Vector256<float>*`. for (i = 0; i < cntBlock; ++i) { vrt = Avx.Add(vrt, vsrc[i]); // Add. vrt += vsrc[i]; } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; #else throw new NotSupportedException(); #endif } /// <summary> /// Sum - Vector AVX - Span - Loop unrolling *4. /// </summary> /// <param name="src">Soure array.</param> /// <param name="count">Soure array count.</param> /// <param name="loops">Benchmark loops.</param> /// <returns>Return the sum value.</returns> private static float SumVectorAvxSpanU4(float[] src, int count, int loops) { #if Allow_Intrinsics float rt = 0; // Result. const int LoopUnrolling = 4; int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. Vector256<float> vrt1 = Vector256<float>.Zero; Vector256<float> vrt2 = Vector256<float>.Zero; Vector256<float> vrt3 = Vector256<float>.Zero; int p; // Index for src data. ReadOnlySpan<Vector256<float>> vsrc; // Vector src. int i; // Body. for (int j = 0; j < loops; ++j) { p = 0; // Vector processs. vsrc = System.Runtime.InteropServices.MemoryMarshal.Cast<float, Vector256<float>>(new Span<float>(src)); // Reinterpret cast. `float*` to `Vector256<float>*`. for (i = 0; i < cntBlock; ++i) { vrt = Avx.Add(vrt, vsrc
); // Add. vrt += vsrc
; vrt1 = Avx.Add(vrt1, vsrc
); vrt2 = Avx.Add(vrt2, vsrc
); vrt3 = Avx.Add(vrt3, vsrc
); p += LoopUnrolling; } // Remainder processs. p = cntBlock * nBlockWidth; for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. vrt = Avx.Add(Avx.Add(vrt, vrt1), Avx.Add(vrt2, vrt3)); // vrt = vrt + vrt1 + vrt2 + vrt3; for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; #else throw new NotSupportedException(); #endif } /// <summary> /// Sum - Vector AVX - Ptr. /// </summary> /// <param name="src">Soure array.</param> /// <param name="count">Soure array count.</param> /// <param name="loops">Benchmark loops.</param> /// <returns>Return the sum value.</returns> private static float SumVectorAvxPtr(float[] src, int count, int loops) { #if Allow_Intrinsics && UNSAFE unsafe { float rt = 0; // Result. int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. Vector256<float> vload; float* p; // Pointer for src data. int i; // Body. fixed(float* p0 = &src[0]) { for (int j = 0; j < loops; ++j) { p = p0; // Vector processs. for (i = 0; i < cntBlock; ++i) { vload = Avx.LoadVector256(p); // Load. vload = *(*__m256)p; vrt = Avx.Add(vrt, vload); // Add. vrt += vsrc[i]; p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } } // Reduce. for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; } #else throw new NotSupportedException(); #endif } /// <summary> /// Sum - Vector AVX - Ptr - Loop unrolling *4. /// </summary> /// <param name="src">Soure array.</param> /// <param name="count">Soure array count.</param> /// <param name="loops">Benchmark loops.</param> /// <returns>Return the sum value.</returns> private static float SumVectorAvxPtrU4(float[] src, int count, int loops) { #if Allow_Intrinsics && UNSAFE unsafe { float rt = 0; // Result. const int LoopUnrolling = 4; int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. Vector256<float> vrt1 = Vector256<float>.Zero; Vector256<float> vrt2 = Vector256<float>.Zero; Vector256<float> vrt3 = Vector256<float>.Zero; Vector256<float> vload; Vector256<float> vload1; Vector256<float> vload2; Vector256<float> vload3; float* p; // Pointer for src data. int i; // Body. fixed (float* p0 = &src[0]) { for (int j = 0; j < loops; ++j) { p = p0; // Vector processs. for (i = 0; i < cntBlock; ++i) { vload = Avx.LoadVector256(p); // Load. vload = *(*__m256)p; vload1 = Avx.LoadVector256(p + VectorWidth * 1); vload2 = Avx.LoadVector256(p + VectorWidth * 2); vload3 = Avx.LoadVector256(p + VectorWidth * 3); vrt = Avx.Add(vrt, vload); // Add. vrt += vsrc[i]; vrt1 = Avx.Add(vrt1, vload1); vrt2 = Avx.Add(vrt2, vload2); vrt3 = Avx.Add(vrt3, vload3); p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } } // Reduce. vrt = Avx.Add(Avx.Add(vrt, vrt1), Avx.Add(vrt2, vrt3)); // vrt = vrt + vrt1 + vrt2 + vrt3; for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; } #else throw new NotSupportedException(); #endif }
2.4.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVectorAvx: 5.497558E+11 # msUsed=609, MFLOPS/s=6725.7799671592775, scale=8.108374384236454 SumVectorAvxSpan: 5.497558E+11 # msUsed=625, MFLOPS/s=6553.6, scale=7.9008 SumVectorAvxPtr: 5.497558E+11 # msUsed=610, MFLOPS/s=6714.754098360656, scale=8.095081967213115 SumVectorAvxU4: 2.1990233E+12 # msUsed=328, MFLOPS/s=12487.80487804878, scale=15.054878048780488 SumVectorAvxSpanU4: 2.1990233E+12 # msUsed=312, MFLOPS/s=13128.205128205129, scale=15.826923076923078 SumVectorAvxPtrU4: 2.1990233E+12 # msUsed=157, MFLOPS/s=26089.171974522294, scale=31.452229299363058 未做循环展开时，这3钟办法的性能拉不开差距，都是8倍左右。
而现在用了循环展开后，数组版（SumVectorAvxU4）、Span版（SumVectorAvxSpanU4）只有15倍左右的性能提升。而指针版有 31倍性能提升，是 数组版、Span版 的2倍。
可能是因为指针更贴近底层硬件、更易于编译器优化。故当使用内在函数时，推荐优先使用指针。
SumVectorAvxPtrU4 对比基础算法（SumBase），性能倍数是 31.452229299363058。
SumVectorAvxPtrU4 对比未循环展开的算法（SumVectorAvxPtr），倍数是 31.452229299363058/8.095081967213115=3.8853503184713375449974589366746。
2.5 对 Avx版算法做循环展开16次
刚才尝试了4倍循环展开，故理论上限是4倍。而SumVectorAvxPtrU4版有约 3.8853 倍性能提升，故可考虑进一步加大，于是可测试一下 4*4=16 次的循环展开。
将 SumVectorAvxPtr 改造为循环展开16次的，代码如下:
private static float SumVectorAvxPtrU16(float[] src, int count, int loops) { #if Allow_Intrinsics && UNSAFE unsafe { float rt = 0; // Result. const int LoopUnrolling = 16; int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. Vector256<float> vrt = Vector256<float>.Zero; // Vector result. Vector256<float> vrt1 = Vector256<float>.Zero; Vector256<float> vrt2 = Vector256<float>.Zero; Vector256<float> vrt3 = Vector256<float>.Zero; Vector256<float> vrt4 = Vector256<float>.Zero; Vector256<float> vrt5 = Vector256<float>.Zero; Vector256<float> vrt6 = Vector256<float>.Zero; Vector256<float> vrt7 = Vector256<float>.Zero; Vector256<float> vrt8 = Vector256<float>.Zero; Vector256<float> vrt9 = Vector256<float>.Zero; Vector256<float> vrt10 = Vector256<float>.Zero; Vector256<float> vrt11 = Vector256<float>.Zero; Vector256<float> vrt12 = Vector256<float>.Zero; Vector256<float> vrt13 = Vector256<float>.Zero; Vector256<float> vrt14 = Vector256<float>.Zero; Vector256<float> vrt15 = Vector256<float>.Zero; float* p; // Pointer for src data. int i; // Body. fixed (float* p0 = &src[0]) { for (int j = 0; j < loops; ++j) { p = p0; // Vector processs. for (i = 0; i < cntBlock; ++i) { //vload = Avx.LoadVector256(p); // Load. vload = *(*__m256)p; vrt = Avx.Add(vrt, Avx.LoadVector256(p)); // Add. vrt[k] += *((*__m256)(p)+k); vrt1 = Avx.Add(vrt1, Avx.LoadVector256(p + VectorWidth * 1)); vrt2 = Avx.Add(vrt2, Avx.LoadVector256(p + VectorWidth * 2)); vrt3 = Avx.Add(vrt3, Avx.LoadVector256(p + VectorWidth * 3)); vrt4 = Avx.Add(vrt4, Avx.LoadVector256(p + VectorWidth * 4)); vrt5 = Avx.Add(vrt5, Avx.LoadVector256(p + VectorWidth * 5)); vrt6 = Avx.Add(vrt6, Avx.LoadVector256(p + VectorWidth * 6)); vrt7 = Avx.Add(vrt7, Avx.LoadVector256(p + VectorWidth * 7)); vrt8 = Avx.Add(vrt8, Avx.LoadVector256(p + VectorWidth * 8)); vrt9 = Avx.Add(vrt9, Avx.LoadVector256(p + VectorWidth * 9)); vrt10 = Avx.Add(vrt10, Avx.LoadVector256(p + VectorWidth * 10)); vrt11 = Avx.Add(vrt11, Avx.LoadVector256(p + VectorWidth * 11)); vrt12 = Avx.Add(vrt12, Avx.LoadVector256(p + VectorWidth * 12)); vrt13 = Avx.Add(vrt13, Avx.LoadVector256(p + VectorWidth * 13)); vrt14 = Avx.Add(vrt14, Avx.LoadVector256(p + VectorWidth * 14)); vrt15 = Avx.Add(vrt15, Avx.LoadVector256(p + VectorWidth * 15)); p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } } // Reduce. vrt = Avx.Add( Avx.Add( Avx.Add(Avx.Add(vrt, vrt1), Avx.Add(vrt2, vrt3)) , Avx.Add(Avx.Add(vrt4, vrt5), Avx.Add(vrt6, vrt7)) ) , Avx.Add( Avx.Add(Avx.Add(vrt8, vrt9), Avx.Add(vrt10, vrt11)) , Avx.Add(Avx.Add(vrt12, vrt13), Avx.Add(vrt14, vrt15)) ) ) ; // vrt = vrt + vrt1 + vrt2 + vrt3 + ... vrt15; for (i = 0; i < VectorWidth; ++i) { rt += vrt.GetElement(i); } return rt; } #else throw new NotSupportedException(); #endif } 2.5.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVectorAvxPtr: 5.497558E+11 # msUsed=610, MFLOPS/s=6714.754098360656, scale=8.095081967213115 SumVectorAvxPtrU4: 2.1990233E+12 # msUsed=157, MFLOPS/s=26089.171974522294, scale=31.452229299363058 SumVectorAvxPtrU16: 8.386202E+12 # msUsed=125, MFLOPS/s=32768, scale=39.504 SumVectorAvxPtrU16 对比基础算法（SumBase），性能倍数是 39.504。
SumVectorAvxPtrU16 对比未循环展开的算法（SumVectorAvxPtr），倍数是 39.504/8.095081967213115=4.8799999999999998517618469015796。
SumVectorAvxPtrU16 对比循环展开4次的算法（SumVectorAvxPtrU4），倍数是 39.504/31.452229299363058=1.2559999999999999730384771162414。
从循环展开4次，改为循环展开16次，性能倍数只是从 31倍多，提升到 39 倍多，仅提升 25% 左右。
性能提升的少，但编码麻烦多了。看来循环展开16次的性价比很低，故一般情况下用循环展开4次就行了。
2.6 尝试用数组来存储循环展开的临时变量
使用循环展开N次时，将会导致临时变量数量是非循环展开版的N倍。例如刚才的 SumVectorAvxPtrU16 函数，因循环展开16次，导致临时变量是非循环展开版的16倍，写起了很啰嗦。
这些变量的类型是一样的，放到数组中的话，代码会清晰不少，但会不会影响性能呢？
于是做了一个测试，代码如下：
private static float SumVectorAvxPtrU16A(float[] src, int count, int loops) { #if Allow_Intrinsics && UNSAFE unsafe { float rt = 0; // Result. const int LoopUnrolling = 16; int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. int i; //Vector256<float>[] vrt = new Vector256<float>[LoopUnrolling]; // Vector result. Vector256<float>* vrt = stackalloc Vector256<float>[LoopUnrolling]; ; // Vector result. for (i = 0; i< LoopUnrolling; ++i) { vrt[i] = Vector256<float>.Zero; } float* p; // Pointer for src data. // Body. fixed (float* p0 = &src[0]) { for (int j = 0; j < loops; ++j) { p = p0; // Vector processs. for (i = 0; i < cntBlock; ++i) { //vload = Avx.LoadVector256(p); // Load. vload = *(*__m256)p; vrt[0] = Avx.Add(vrt[0], Avx.LoadVector256(p)); // Add. vrt[k] += *((*__m256)(p)+k); vrt[1] = Avx.Add(vrt[1], Avx.LoadVector256(p + VectorWidth * 1)); vrt[2] = Avx.Add(vrt[2], Avx.LoadVector256(p + VectorWidth * 2)); vrt[3] = Avx.Add(vrt[3], Avx.LoadVector256(p + VectorWidth * 3)); vrt[4] = Avx.Add(vrt[4], Avx.LoadVector256(p + VectorWidth * 4)); vrt[5] = Avx.Add(vrt[5], Avx.LoadVector256(p + VectorWidth * 5)); vrt[6] = Avx.Add(vrt[6], Avx.LoadVector256(p + VectorWidth * 6)); vrt[7] = Avx.Add(vrt[7], Avx.LoadVector256(p + VectorWidth * 7)); vrt[8] = Avx.Add(vrt[8], Avx.LoadVector256(p + VectorWidth * 8)); vrt[9] = Avx.Add(vrt[9], Avx.LoadVector256(p + VectorWidth * 9)); vrt[10] = Avx.Add(vrt[10], Avx.LoadVector256(p + VectorWidth * 10)); vrt[11] = Avx.Add(vrt[11], Avx.LoadVector256(p + VectorWidth * 11)); vrt[12] = Avx.Add(vrt[12], Avx.LoadVector256(p + VectorWidth * 12)); vrt[13] = Avx.Add(vrt[13], Avx.LoadVector256(p + VectorWidth * 13)); vrt[14] = Avx.Add(vrt[14], Avx.LoadVector256(p + VectorWidth * 14)); vrt[15] = Avx.Add(vrt[15], Avx.LoadVector256(p + VectorWidth * 15)); p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } } // Reduce. for (i = 1; i < LoopUnrolling; ++i) { vrt[0] = Avx.Add(vrt[0], vrt[i]); // vrt[0] += vrt[i] } for (i = 0; i < VectorWidth; ++i) { rt += vrt[0].GetElement(i); } return rt; } #else throw new NotSupportedException(); #endif } 2.6.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVectorAvxPtr: 5.497558E+11 # msUsed=610, MFLOPS/s=6714.754098360656, scale=8.095081967213115 SumVectorAvxPtrU4: 2.1990233E+12 # msUsed=157, MFLOPS/s=26089.171974522294, scale=31.452229299363058 SumVectorAvxPtrU16: 8.386202E+12 # msUsed=125, MFLOPS/s=32768, scale=39.504 SumVectorAvxPtrU16A: 8.3862026E+12 # msUsed=187, MFLOPS/s=21903.74331550802, scale=26.406417112299465 可以发现 SumVectorAvxPtrU16A 的性能比 SumVectorAvxPtrU16 差。
曾经以为是因为数组是在堆中分配的（new Vector256）引起的，有堆内存分配的开销，且需要多次寻址才能定位变量。
随后改为栈中分配的数组（stackalloc Vector256），且用最贴近硬件的指针来操作，可性能几乎一致。故猜测可能是编译优化时难以将它们优化为寄存器变量。
故在使用循环展开时，临时变量不要用数组来存，还是逐个定义局部变量比较好。
2.7 尝试用栈数组来减少相关性
还尝试了用栈数组来减少相关性，代码如下：
private static float SumVectorAvxPtrUX(float[] src, int count, int loops, int LoopUnrolling) { #if Allow_Intrinsics && UNSAFE unsafe { float rt = 0; // Result. //const int LoopUnrolling = 16; if (LoopUnrolling <= 0) throw new ArgumentOutOfRangeException("LoopUnrolling", "Argument LoopUnrolling must >0 !"); int VectorWidth = Vector256<float>.Count; // Block width. int nBlockWidth = VectorWidth * LoopUnrolling; // Block width. int cntBlock = count / nBlockWidth; // Block count. int cntRem = count % nBlockWidth; // Remainder count. int i; //Vector256<float>[] vrt = new Vector256<float>[LoopUnrolling]; // Vector result. Vector256<float>* vrt = stackalloc Vector256<float>[LoopUnrolling]; ; // Vector result. for (i = 0; i < LoopUnrolling; ++i) { vrt[i] = Vector256<float>.Zero; } float* p; // Pointer for src data. // Body. fixed (float* p0 = &src[0]) { for (int j = 0; j < loops; ++j) { p = p0; // Vector processs. for (i = 0; i < cntBlock; ++i) { for(int k=0; k< LoopUnrolling; ++k) { vrt[k] = Avx.Add(vrt[k], Avx.LoadVector256(p + VectorWidth * k)); // Add. vrt[k] += *(*__m256)(p+k); } p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } } // Reduce. for (i = 1; i < LoopUnrolling; ++i) { vrt[0] = Avx.Add(vrt[0], vrt[i]); // vrt[0] += vrt[i] } // vrt = vrt + vrt1 + vrt2 + vrt3 + ... vrt15; for (i = 0; i < VectorWidth; ++i) { rt += vrt[0].GetElement(i); } return rt; } #else throw new NotSupportedException(); #endif } 测试代码:
// SumVectorAvxPtrUX. int[] LoopUnrollingArray = { 4, 8, 16 }; foreach (int loopUnrolling in LoopUnrollingArray) { tickBegin = Environment.TickCount; rt = SumVectorAvxPtrUX(src, count, loops, loopUnrolling); msUsed = Environment.TickCount - tickBegin; mFlops = countMFlops * 1000 / msUsed; scale = mFlops / mFlopsBase; tw.WriteLine(indent + string.Format("SumVectorAvxPtrUX[{4}]:t{0}t# msUsed={1}, MFLOPS/s={2}, scale={3}", rt, msUsed, mFlops, scale, loopUnrolling)); } 2.7.1 测试结果:
测试结果摘录如下：
SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVectorAvxPtr: 5.497558E+11 # msUsed=610, MFLOPS/s=6714.754098360656, scale=8.095081967213115 SumVectorAvxPtrU4: 2.1990233E+12 # msUsed=157, MFLOPS/s=26089.171974522294, scale=31.452229299363058 SumVectorAvxPtrU16: 8.386202E+12 # msUsed=125, MFLOPS/s=32768, scale=39.504 SumVectorAvxPtrU16A: 8.3862026E+12 # msUsed=187, MFLOPS/s=21903.74331550802, scale=26.406417112299465 SumVectorAvxPtrUX[4]: 2.1990233E+12 # msUsed=547, MFLOPS/s=7488.117001828154, scale=9.027422303473491 SumVectorAvxPtrUX[8]: 4.3980465E+12 # msUsed=500, MFLOPS/s=8192, scale=9.876 SumVectorAvxPtrUX[16]: 8.3862026E+12 # msUsed=500, MFLOPS/s=8192, scale=9.876 可以发现 SumVectorAvxPtrUX 版的性能比 非循环展开版（SumVectorAvxPtr）的性能要好一些，从8倍左右，达到9倍。
调整栈数组长度，达到8之后，性能几乎差不多，看来已经达到瓶颈了。
该办法的性能提升少，性价比不高。故还是推荐用经典的循环展开办法。
2.8 测试结果汇总
测试结果汇总如下：
BenchmarkVectorCore30 IsRelease: True EnvironmentVariable(PROCESSOR_IDENTIFIER): Intel64 Family 6 Model 142 Stepping 10, GenuineIntel Environment.ProcessorCount: 8 Environment.Is64BitOperatingSystem: True Environment.Is64BitProcess: True Environment.OSVersion: Microsoft Windows NT 6.2.9200.0 Environment.Version: 3.1.26 RuntimeEnvironment.GetRuntimeDirectory: C:Program FilesdotnetsharedMicrosoft.NETCore.App3.1.26 RuntimeInformation.FrameworkDescription: .NET Core 3.1.26 BitConverter.IsLittleEndian: True IntPtr.Size: 8 Vector.IsHardwareAccelerated: True Vector<byte>.Count: 32 # 256bit Vector<float>.Count: 8 # 256bit Vector<double>.Count: 4 # 256bit Vector4.Assembly.CodeBase: file:///C:/Program Files/dotnet/shared/Microsoft.NETCore.App/3.1.26/System.Numerics.Vectors.dll Vector<T>.Assembly.CodeBase: file:///C:/Program Files/dotnet/shared/Microsoft.NETCore.App/3.1.26/System.Private.CoreLib.dll Benchmark: count=4096, loops=1000000, countMFlops=4096 SumBase: 6.871948E+10 # msUsed=4938, MFLOPS/s=829.485621709194 SumBaseU4: 2.748779E+11 # msUsed=1875, MFLOPS/s=2184.5333333333333, scale=2.6336 SumVector4: 2.748779E+11 # msUsed=1218, MFLOPS/s=3362.8899835796387, scale=4.054187192118227 SumVector4U4: 1.0995116E+12 # msUsed=532, MFLOPS/s=7699.248120300752, scale=9.281954887218046 SumVectorT: 5.497558E+11 # msUsed=609, MFLOPS/s=6725.7799671592775, scale=8.108374384236454 SumVectorTU4: 2.1990233E+12 # msUsed=203, MFLOPS/s=20177.339901477833, scale=24.32512315270936 SumVectorAvx: 5.497558E+11 # msUsed=609, MFLOPS/s=6725.7799671592775, scale=8.108374384236454 SumVectorAvxSpan: 5.497558E+11 # msUsed=625, MFLOPS/s=6553.6, scale=7.9008 SumVectorAvxPtr: 5.497558E+11 # msUsed=610, MFLOPS/s=6714.754098360656, scale=8.095081967213115 SumVectorAvxU4: 2.1990233E+12 # msUsed=328, MFLOPS/s=12487.80487804878, scale=15.054878048780488 SumVectorAvxSpanU4: 2.1990233E+12 # msUsed=312, MFLOPS/s=13128.205128205129, scale=15.826923076923078 SumVectorAvxPtrU4: 2.1990233E+12 # msUsed=157, MFLOPS/s=26089.171974522294, scale=31.452229299363058 SumVectorAvxPtrU16: 8.386202E+12 # msUsed=125, MFLOPS/s=32768, scale=39.504 SumVectorAvxPtrU16A: 8.3862026E+12 # msUsed=187, MFLOPS/s=21903.74331550802, scale=26.406417112299465 SumVectorAvxPtrUX[4]: 2.1990233E+12 # msUsed=547, MFLOPS/s=7488.117001828154, scale=9.027422303473491 SumVectorAvxPtrUX[8]: 4.3980465E+12 # msUsed=500, MFLOPS/s=8192, scale=9.876 SumVectorAvxPtrUX[16]: 8.3862026E+12 # msUsed=500, MFLOPS/s=8192, scale=9.876 三、在C++中使用
3.1 修改代码
参考上面的经验，现在来将 C++ 版程序也改为循环展开的。
BenchmarkVectorCpp.cpp 的全部代码如下:
// BenchmarkVectorCpp.cpp : This file contains the 'main' function. Program execution begins and ends there. // #include <immintrin.h> #include <malloc.h> #include <stdio.h> #include <time.h> #ifndef EXCEPTION_EXECUTE_HANDLER #define EXCEPTION_EXECUTE_HANDLER (1) #endif // !EXCEPTION_EXECUTE_HANDLER // Sum - base. float SumBase(const float* src, size_t count, int loops) { float rt = 0; // Result. size_t i; for (int j = 0; j < loops; ++j) { for (i = 0; i < count; ++i) { rt += src[i]; } } return rt; } // Sum - base - Loop unrolling *4. float SumBaseU4(const float* src, size_t count, int loops) { float rt = 0; // Result. float rt1=0; float rt2 = 0; float rt3 = 0; size_t nBlockWidth = 4; // Block width. size_t cntBlock = count / nBlockWidth; // Block count. size_t cntRem = count % nBlockWidth; // Remainder count. size_t p; // Index for src data. size_t i; for (int j = 0; j < loops; ++j) { p = 0; // Block processs. for (i = 0; i < cntBlock; ++i) { rt += src; rt1 += src
; rt2 += src
; rt3 += src
; p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += src
; } } // Reduce. rt = rt + rt1 + rt2 + rt3; return rt; } // Sum - Vector AVX. float SumVectorAvx(const float* src, size_t count, int loops) { float rt = 0; // Result. size_t VectorWidth = sizeof(__m256) / sizeof(float); // Block width. size_t nBlockWidth = VectorWidth; // Block width. size_t cntBlock = count / nBlockWidth; // Block count. size_t cntRem = count % nBlockWidth; // Remainder count. __m256 vrt = _mm256_setzero_ps(); // Vector result. [AVX] Set zero. __m256 vload; // Vector load. const float* p; // Pointer for src data. size_t i; // Body. for (int j = 0; j < loops; ++j) { p = src; // Vector processs. for (i = 0; i < cntBlock; ++i) { vload = _mm256_load_ps(p); // Load. vload = *(*__m256)p; vrt = _mm256_add_ps(vrt, vload); // Add. vrt += vload; p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } // Reduce. p = (const float*)&vrt; for (i = 0; i < VectorWidth; ++i) { rt += p[i]; } return rt; } // Sum - Vector AVX - Loop unrolling *4. float SumVectorAvxU4(const float* src, size_t count, int loops) { float rt = 0; // Result. const int LoopUnrolling = 4; size_t VectorWidth = sizeof(__m256) / sizeof(float); // Block width. size_t nBlockWidth = VectorWidth * LoopUnrolling; // Block width. size_t cntBlock = count / nBlockWidth; // Block count. size_t cntRem = count % nBlockWidth; // Remainder count. __m256 vrt = _mm256_setzero_ps(); // Vector result. [AVX] Set zero. __m256 vrt1 = _mm256_setzero_ps(); __m256 vrt2 = _mm256_setzero_ps(); __m256 vrt3 = _mm256_setzero_ps(); __m256 vload; // Vector load. __m256 vload1, vload2, vload3; const float* p; // Pointer for src data. size_t i; // Body. for (int j = 0; j < loops; ++j) { p = src; // Block processs. for (i = 0; i < cntBlock; ++i) { vload = _mm256_load_ps(p); // Load. vload = *(*__m256)p; vload1 = _mm256_load_ps(p + VectorWidth * 1); vload2 = _mm256_load_ps(p + VectorWidth * 2); vload3 = _mm256_load_ps(p + VectorWidth * 3); vrt = _mm256_add_ps(vrt, vload); // Add. vrt += vload; vrt1 = _mm256_add_ps(vrt1, vload1); vrt2 = _mm256_add_ps(vrt2, vload2); vrt3 = _mm256_add_ps(vrt3, vload3); p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } // Reduce. vrt = _mm256_add_ps(_mm256_add_ps(vrt, vrt1), _mm256_add_ps(vrt2, vrt3)); // vrt = vrt + vrt1 + vrt2 + vrt3; p = (const float*)&vrt; for (i = 0; i < VectorWidth; ++i) { rt += p[i]; } return rt; } // Sum - Vector AVX - Loop unrolling *16. float SumVectorAvxU16(const float* src, size_t count, int loops) { float rt = 0; // Result. const int LoopUnrolling = 16; size_t VectorWidth = sizeof(__m256) / sizeof(float); // Block width. size_t nBlockWidth = VectorWidth * LoopUnrolling; // Block width. size_t cntBlock = count / nBlockWidth; // Block count. size_t cntRem = count % nBlockWidth; // Remainder count. __m256 vrt = _mm256_setzero_ps(); // Vector result. [AVX] Set zero. __m256 vrt1 = _mm256_setzero_ps(); __m256 vrt2 = _mm256_setzero_ps(); __m256 vrt3 = _mm256_setzero_ps(); __m256 vrt4 = _mm256_setzero_ps(); __m256 vrt5 = _mm256_setzero_ps(); __m256 vrt6 = _mm256_setzero_ps(); __m256 vrt7 = _mm256_setzero_ps(); __m256 vrt8 = _mm256_setzero_ps(); __m256 vrt9 = _mm256_setzero_ps(); __m256 vrt10 = _mm256_setzero_ps(); __m256 vrt11 = _mm256_setzero_ps(); __m256 vrt12 = _mm256_setzero_ps(); __m256 vrt13 = _mm256_setzero_ps(); __m256 vrt14 = _mm256_setzero_ps(); __m256 vrt15 = _mm256_setzero_ps(); const float* p; // Pointer for src data. size_t i; // Body. for (int j = 0; j < loops; ++j) { p = src; // Block processs. for (i = 0; i < cntBlock; ++i) { vrt = _mm256_add_ps(vrt, _mm256_load_ps(p)); // Add. vrt += *((*__m256)(p)+k); vrt1 = _mm256_add_ps(vrt1, _mm256_load_ps(p + VectorWidth * 1)); vrt2 = _mm256_add_ps(vrt2, _mm256_load_ps(p + VectorWidth * 2)); vrt3 = _mm256_add_ps(vrt3, _mm256_load_ps(p + VectorWidth * 3)); vrt4 = _mm256_add_ps(vrt4, _mm256_load_ps(p + VectorWidth * 4)); vrt5 = _mm256_add_ps(vrt5, _mm256_load_ps(p + VectorWidth * 5)); vrt6 = _mm256_add_ps(vrt6, _mm256_load_ps(p + VectorWidth * 6)); vrt7 = _mm256_add_ps(vrt7, _mm256_load_ps(p + VectorWidth * 7)); vrt8 = _mm256_add_ps(vrt8, _mm256_load_ps(p + VectorWidth * 8)); vrt9 = _mm256_add_ps(vrt9, _mm256_load_ps(p + VectorWidth * 9)); vrt10 = _mm256_add_ps(vrt10, _mm256_load_ps(p + VectorWidth * 10)); vrt11 = _mm256_add_ps(vrt11, _mm256_load_ps(p + VectorWidth * 11)); vrt12 = _mm256_add_ps(vrt12, _mm256_load_ps(p + VectorWidth * 12)); vrt13 = _mm256_add_ps(vrt13, _mm256_load_ps(p + VectorWidth * 13)); vrt14 = _mm256_add_ps(vrt14, _mm256_load_ps(p + VectorWidth * 14)); vrt15 = _mm256_add_ps(vrt15, _mm256_load_ps(p + VectorWidth * 15)); p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } // Reduce. vrt = _mm256_add_ps(_mm256_add_ps(_mm256_add_ps(_mm256_add_ps(vrt, vrt1), _mm256_add_ps(vrt2, vrt3)) , _mm256_add_ps(_mm256_add_ps(vrt4, vrt5), _mm256_add_ps(vrt6, vrt7))) , _mm256_add_ps(_mm256_add_ps(_mm256_add_ps(vrt8, vrt9), _mm256_add_ps(vrt10, vrt11)) , _mm256_add_ps(_mm256_add_ps(vrt12, vrt13), _mm256_add_ps(vrt14, vrt15)))) ; // vrt = vrt + vrt1 + vrt2 + vrt3 + ... vrt15; p = (const float*)&vrt; for (i = 0; i < VectorWidth; ++i) { rt += p[i]; } return rt; } // Sum - Vector AVX - Loop unrolling *16 - Array. float SumVectorAvxU16A(const float* src, size_t count, int loops) { float rt = 0; // Result. const int LoopUnrolling = 16; size_t VectorWidth = sizeof(__m256) / sizeof(float); // Block width. size_t nBlockWidth = VectorWidth * LoopUnrolling; // Block width. size_t cntBlock = count / nBlockWidth; // Block count. size_t cntRem = count % nBlockWidth; // Remainder count. size_t i; __m256 vrt[LoopUnrolling]; // Vector result. for (i = 0; i < LoopUnrolling; ++i) { vrt[i] = _mm256_setzero_ps(); // [AVX] Set zero. } const float* p; // Pointer for src data. // Body. for (int j = 0; j < loops; ++j) { p = src; // Block processs. for (i = 0; i < cntBlock; ++i) { vrt[0] = _mm256_add_ps(vrt[0], _mm256_load_ps(p)); // Add. vrt += *((*__m256)(p)+k); vrt[1] = _mm256_add_ps(vrt[1], _mm256_load_ps(p + VectorWidth * 1)); vrt[2] = _mm256_add_ps(vrt[2], _mm256_load_ps(p + VectorWidth * 2)); vrt[3] = _mm256_add_ps(vrt[3], _mm256_load_ps(p + VectorWidth * 3)); vrt[4] = _mm256_add_ps(vrt[4], _mm256_load_ps(p + VectorWidth * 4)); vrt[5] = _mm256_add_ps(vrt[5], _mm256_load_ps(p + VectorWidth * 5)); vrt[6] = _mm256_add_ps(vrt[6], _mm256_load_ps(p + VectorWidth * 6)); vrt[7] = _mm256_add_ps(vrt[7], _mm256_load_ps(p + VectorWidth * 7)); vrt[8] = _mm256_add_ps(vrt[8], _mm256_load_ps(p + VectorWidth * 8)); vrt[9] = _mm256_add_ps(vrt[9], _mm256_load_ps(p + VectorWidth * 9)); vrt[10] = _mm256_add_ps(vrt[10], _mm256_load_ps(p + VectorWidth * 10)); vrt[11] = _mm256_add_ps(vrt[11], _mm256_load_ps(p + VectorWidth * 11)); vrt[12] = _mm256_add_ps(vrt[12], _mm256_load_ps(p + VectorWidth * 12)); vrt[13] = _mm256_add_ps(vrt[13], _mm256_load_ps(p + VectorWidth * 13)); vrt[14] = _mm256_add_ps(vrt[14], _mm256_load_ps(p + VectorWidth * 14)); vrt[15] = _mm256_add_ps(vrt[15], _mm256_load_ps(p + VectorWidth * 15)); p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } // Reduce. vrt[0] = _mm256_add_ps(_mm256_add_ps(_mm256_add_ps(_mm256_add_ps(vrt[0], vrt[1]), _mm256_add_ps(vrt[2], vrt[3])) , _mm256_add_ps(_mm256_add_ps(vrt[4], vrt[5]), _mm256_add_ps(vrt[6], vrt[7]))) , _mm256_add_ps(_mm256_add_ps(_mm256_add_ps(vrt[8], vrt[9]), _mm256_add_ps(vrt[10], vrt[11])) , _mm256_add_ps(_mm256_add_ps(vrt[12], vrt[13]), _mm256_add_ps(vrt[14], vrt[15])))) ; // vrt = vrt + vrt1 + vrt2 + vrt3 + ... vrt15; p = (const float*)&vrt; for (i = 0; i < VectorWidth; ++i) { rt += p[i]; } return rt; } // Sum - Vector AVX - Loop unrolling *X - Array. float SumVectorAvxUX(const float* src, size_t count, int loops, const int LoopUnrolling) { float rt = 0; // Result. size_t VectorWidth = sizeof(__m256) / sizeof(float); // Block width. size_t nBlockWidth = VectorWidth * LoopUnrolling; // Block width. size_t cntBlock = count / nBlockWidth; // Block count. size_t cntRem = count % nBlockWidth; // Remainder count. size_t i; __m256* vrt = new __m256[LoopUnrolling]; // Vector result. for (i = 0; i < LoopUnrolling; ++i) { vrt[i] = _mm256_setzero_ps(); // [AVX] Set zero. } const float* p; // Pointer for src data. // Body. for (int j = 0; j < loops; ++j) { p = src; // Block processs. for (i = 0; i < cntBlock; ++i) { for (int k = 0; k < LoopUnrolling; ++k) { vrt[k] = _mm256_add_ps(vrt[k], _mm256_load_ps(p + VectorWidth * k)); // Add. vrt += *((*__m256)(p)+k); } p += nBlockWidth; } // Remainder processs. for (i = 0; i < cntRem; ++i) { rt += p[i]; } } // Reduce. for (i = 1; i < LoopUnrolling; ++i) { vrt[0] = _mm256_add_ps(vrt[0], vrt[i]); // vrt[0] += vrt[i] } // vrt = vrt + vrt1 + vrt2 + vrt3 + ... vrt15; p = (const float*)&vrt[0]; for (i = 0; i < VectorWidth; ++i) { rt += p[i]; } delete[] vrt; return rt; } // Do Benchmark. void Benchmark() { const size_t alignment = 256 / 8; // sizeof(__m256) / sizeof(BYTE); // init. clock_t tickBegin, msUsed; double mFlops; // MFLOPS/s . double scale; float rt; const int count = 1024 * 4; const int loops = 1000 * 1000; //const int loops = 1; const double countMFlops = count * (double)loops / (1000.0 * 1000); float* src = (float*)_aligned_malloc(sizeof(float)*count, alignment); // new float[count]; if (NULL == src) { printf("Memory alloc fail!"); return; } for (int i = 0; i < count; ++i) { src[i] = (float)i; } printf("Benchmark: tcount=%d, loops=%d, countMFlops=%fn", count, loops, countMFlops); // SumBase. tickBegin = clock(); rt = SumBase(src, count, loops); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; printf("SumBase:t%gt# msUsed=%d, MFLOPS/s=%fn", rt, (int)msUsed, mFlops); double mFlopsBase = mFlops; // SumBaseU4. tickBegin = clock(); rt = SumBaseU4(src, count, loops); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; scale = mFlops / mFlopsBase; printf("SumBaseU4:t%gt# msUsed=%d, MFLOPS/s=%f, scale=%fn", rt, (int)msUsed, mFlops, scale); // SumVectorAvx. __try { tickBegin = clock(); rt = SumVectorAvx(src, count, loops); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; scale = mFlops / mFlopsBase; printf("SumVectorAvx:t%gt# msUsed=%d, MFLOPS/s=%f, scale=%fn", rt, (int)msUsed, mFlops, scale); // SumVectorAvxU4. tickBegin = clock(); rt = SumVectorAvxU4(src, count, loops); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; scale = mFlops / mFlopsBase; printf("SumVectorAvxU4:t%gt# msUsed=%d, MFLOPS/s=%f, scale=%fn", rt, (int)msUsed, mFlops, scale); // SumVectorAvxU16. tickBegin = clock(); rt = SumVectorAvxU16(src, count, loops); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; scale = mFlops / mFlopsBase; printf("SumVectorAvxU16:t%gt# msUsed=%d, MFLOPS/s=%f, scale=%fn", rt, (int)msUsed, mFlops, scale); // SumVectorAvxU16A. tickBegin = clock(); rt = SumVectorAvxU16A(src, count, loops); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; scale = mFlops / mFlopsBase; printf("SumVectorAvxU16A:t%gt# msUsed=%d, MFLOPS/s=%f, scale=%fn", rt, (int)msUsed, mFlops, scale); // SumVectorAvxUX. int LoopUnrollingArray[] = { 4, 8, 16 }; for (int i = 0; i < sizeof(LoopUnrollingArray) / sizeof(LoopUnrollingArray[0]); ++i) { int loopUnrolling = LoopUnrollingArray[i]; tickBegin = clock(); rt = SumVectorAvxUX(src, count, loops, loopUnrolling); msUsed = clock() - tickBegin; mFlops = countMFlops * CLOCKS_PER_SEC / msUsed; scale = mFlops / mFlopsBase; printf("SumVectorAvxUX[%d]:t%gt# msUsed=%d, MFLOPS/s=%f, scale=%fn", loopUnrolling, rt, (int)msUsed, mFlops, scale); } } __except (EXCEPTION_EXECUTE_HANDLER) { printf("Run SumVectorAvx fail!"); } // done. _aligned_free(src); } int main() { printf("BenchmarkVectorCppn"); printf("n"); printf("Pointer size:t%dn", (int)(sizeof(void*))); #ifdef _DEBUG printf("IsRelease:tFalsen"); #else printf("IsRelease:tTruen"); #endif // _DEBUG #ifdef _MSC_VER printf("_MSC_VER:t%dn", _MSC_VER); #endif // _MSC_VER #ifdef __AVX__ printf("__AVX__:t%dn", __AVX__); #endif // __AVX__ printf("n"); // Benchmark. Benchmark(); }
3.2 测试结果
测试结果汇总如下：
BenchmarkVectorCpp Pointer size: 8 IsRelease: True _MSC_VER: 1916 __AVX__: 1 Benchmark: count=4096, loops=1000000, countMFlops=4096.000000 SumBase: 6.87195e+10 # msUsed=4938, MFLOPS/s=829.485622 SumBaseU4: 2.74878e+11 # msUsed=1229, MFLOPS/s=3332.790887, scale=4.017901 SumVectorAvx: 5.49756e+11 # msUsed=616, MFLOPS/s=6649.350649, scale=8.016234 SumVectorAvxU4: 2.19902e+12 # msUsed=247, MFLOPS/s=16582.995951, scale=19.991903 SumVectorAvxU16: 8.3862e+12 # msUsed=89, MFLOPS/s=46022.471910, scale=55.483146 SumVectorAvxU16A: 8.3862e+12 # msUsed=89, MFLOPS/s=46022.471910, scale=55.483146 SumVectorAvxUX[4]: 2.19902e+12 # msUsed=465, MFLOPS/s=8808.602151, scale=10.619355 SumVectorAvxUX[8]: 4.39805e+12 # msUsed=336, MFLOPS/s=12190.476190, scale=14.696429 SumVectorAvxUX[16]: 8.3862e+12 # msUsed=323, MFLOPS/s=12681.114551, scale=15.287926 先前做未循环展开时，C# 与 Visual C++ 程序的性能差距不大。而现在使用循环展开后，发现差距拉大了——
- SumBaseU4：C++版的MFLOPS/s为 3332.790887，C#版的MFLOPS/s为 2184.5333333333333。3332.790887/2184.5333333333333=1.5256305940246582264042754215188，即大约是 1.5256 倍。
- SumVectorAvxU4：C++版的MFLOPS/s为 16582.995951，C#版的MFLOPS/s为 12487.80487804878。16582.995951/12487.80487804878=1.3279352226386719268724696343231，即大约是 1.3279 倍。
- SumVectorAvxU16：C++版的MFLOPS/s为 46022.471910，C#版的MFLOPS/s为 32768。46022.471910/32768=1.40449438201904296875，即大约是 1.4045 倍。
而且还发现——
- SumVectorAvxU16A 与 SumVectorAvxU16 的性能差不多，表示C++编译器能很好地优化数组访问，能达到局部变量同级别的速度。故C++中可以放心使用数组来存储循环展开的临时变量。
- SumVectorAvxUX 的 C++ 版性能比C#好一些。而且临时数组长度大于8时，也能带来一定的性能提升。只可惜还是存在性价比不高的问题，还是经典的循环展开更好用。
四、小结
C#中使用循环展开的心得总结——
- 使用循环展开能提高性能，但由于编码比较麻烦，且会增加代码维护的成本。故应作为最后手段，应该先尝试其他优化手段。
- 使用循环展开后，指针版代码比数组版、Span版要高一些，可能是因为指针更贴近底层硬件、更易于编译器优化。故推荐优先使用指针。
- 在C#中做循环展开，一般展开4次就行。展开16次只有少量提升，性价比不高。
- 循环展开会引起临时变量倍增，应该坚持逐个定义局部变量。若用数组会造成性能下降，包括用指针操作栈分配数组也会下降。
对于循环展开这样的运算量重的情况，Visual C++编译优化的更好。但性能大多只有1倍多，总体差距不大。
C++还有个优点，是可以用数组来存储循环展开的临时变量，且性能不会下降。
源码地址——
https://github.com/zyl910/BenchmarkVector/tree/main/BenchmarkVector
参考文献
- zyl910《
C# 使用SIMD向量类型加速浮点数组求和运算（1）：使用Vector4、Vector<T>》. https://www.cnblogs.com/zyl910/p/dotnet_simd_BenchmarkVector1.html - zyl910《
C# 使用SIMD向量类型加速浮点数组求和运算（2）：C#通过Intrinsic直接使用AVX指令集操作 Vector256<T>，及C++程序对比》. https://www.cnblogs.com/zyl910/p/dotnet_simd_BenchmarkVector2.html - 有色金属《C 语言性能优化：循环展开》. https://zhuanlan.zhihu.com/p/359032198
