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C# 使用SIMD向量类型加速浮点数组求和运算（3）：循环展开

2023-02-18 15:31:13 时间

作者： zyl910

目录

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[p];
            rt1 += src[p + 1];
            rt2 += src[p + 2];
            rt3 += src[p + 3];
            p += nBlockWidth;
        }
        // Remainder processs.
        //p = cntBlock * nBlockWidth;
        for (i = 0; i < cntRem; ++i) {
            rt += src[p + i];
        }
    }
    // 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[p], src[p + 1], src[p + 2], src[p + 3]);
        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[p + i];
        }
    }
    // 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[p], src[p + 1], src[p + 2], src[p + 3]);
        p += VectorWidth;
    }
    // Body.
    for (int j = 0; j < loops; ++j) {
        p = 0;
        // Vector processs.
        for (i = 0; i < cntBlock; ++i) {
            vrt += vsrc[p]; // Add.
            vrt1 += vsrc[p + 1];
            vrt2 += vsrc[p + 2];
            vrt3 += vsrc[p + 3];
            p += LoopUnrolling;
        }
        // Remainder processs.
        p = cntBlock * nBlockWidth;
        for (i = 0; i < cntRem; ++i) {
            rt += src[p + i];
        }
    }
    // 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[p + i];
        }
    }
    // 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[p]; // Add.
            vrt1 += vsrc[p + 1];
            vrt2 += vsrc[p + 1];
            vrt3 += vsrc[p + 1];
            p += LoopUnrolling;
        }
        // Remainder processs.
        p = cntBlock * nBlockWidth;
        for (i = 0; i < cntRem; ++i) {
            rt += src[p + i];
        }
    }
    // 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[p], src[p + 1], src[p + 2], src[p + 3], src[p + 4], src[p + 5], src[p + 6], src[p + 7]); // 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[p + i];
        }
    }
    // 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[p], src[p + 1], src[p + 2], src[p + 3], src[p + 4], src[p + 5], src[p + 6], src[p + 7]); // 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[p]);    // Add. vrt += vsrc[p];
            vrt1 = Avx.Add(vrt1, vsrc[p + 1]);
            vrt2 = Avx.Add(vrt2, vsrc[p + 2]);
            vrt3 = Avx.Add(vrt3, vsrc[p + 3]);
            p += LoopUnrolling;
        }
        // Remainder processs.
        p = cntBlock * nBlockWidth;
        for (i = 0; i < cntRem; ++i) {
            rt += src[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
}

/// <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[p + i];
        }
    }
    // 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[p]);    // Add. vrt += vsrc[p];
            vrt1 = Avx.Add(vrt1, vsrc[p + 1]);
            vrt2 = Avx.Add(vrt2, vsrc[p + 2]);
            vrt3 = Avx.Add(vrt3, vsrc[p + 3]);
            p += LoopUnrolling;
        }
        // Remainder processs.
        p = cntBlock * nBlockWidth;
        for (i = 0; i < cntRem; ++i) {
            rt += src[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
}

/// <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 Files\dotnet\shared\Microsoft.NETCore.App\3.1.26\
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[p];
            rt1 += src[p + 1];
            rt2 += src[p + 2];
            rt3 += src[p + 3];
            p += nBlockWidth;
        }
        // Remainder processs.
        for (i = 0; i < cntRem; ++i) {
            rt += src[p + i];
        }
    }
    // 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=%f\n", count, loops, countMFlops);
    // SumBase.
    tickBegin = clock();
    rt = SumBase(src, count, loops);
    msUsed = clock() - tickBegin;
    mFlops = countMFlops * CLOCKS_PER_SEC / msUsed;
    printf("SumBase:\t%g\t# msUsed=%d, MFLOPS/s=%f\n", 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%g\t# msUsed=%d, MFLOPS/s=%f, scale=%f\n", 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%g\t# msUsed=%d, MFLOPS/s=%f, scale=%f\n", 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%g\t# msUsed=%d, MFLOPS/s=%f, scale=%f\n", 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%g\t# msUsed=%d, MFLOPS/s=%f, scale=%f\n", 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%g\t# msUsed=%d, MFLOPS/s=%f, scale=%f\n", 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%g\t# msUsed=%d, MFLOPS/s=%f, scale=%f\n", loopUnrolling, rt, (int)msUsed, mFlops, scale);
        }
    }
    __except (EXCEPTION_EXECUTE_HANDLER) {
        printf("Run SumVectorAvx fail!");
    }
    // done.
    _aligned_free(src);
}

int main() {
    printf("BenchmarkVectorCpp\n");
    printf("\n");
    printf("Pointer size:\t%d\n", (int)(sizeof(void*)));
#ifdef _DEBUG
    printf("IsRelease:\tFalse\n");
#else
    printf("IsRelease:\tTrue\n");
#endif // _DEBUG
#ifdef _MSC_VER
    printf("_MSC_VER:\t%d\n", _MSC_VER);
#endif // _MSC_VER
#ifdef __AVX__
    printf("__AVX__:\t%d\n", __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

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