AVX2指令集浮点乘法性能分析

一、AVX2指令集介绍

AVX2是SIMD(单指令多数据流)指令集，支持在一个指令周期内同时对256位内存进行操作。包含乘法，加法，位运算等功能。下附Intel官网使用文档。

我们本次要用到的指令有 **__m256 _mm256_mul_ps(__m256 a, __m256 b), __m256d_mm256_mul_pd(__m256d a, __m256d b)**等，（p代表精度precision，s代表single，d代表double）

它们可以一次取256位的内存，并按32/64位一个浮点进行乘法运算。下附官网描述。

Synopsis

__m256d _mm256_mul_pd (__m256d a, __m256d b)

#include <immintrin.h>

Instruction: vmulpd ymm, ymm, ymm

CPUID Flags: AVX

Description

Multiply packed double-precision (64-bit) floating-point elements in a and b, and store the results in dst.

Operation

FOR j := 0 to 3
	i := j*64
	dst[i+63:i] := a[i+63:i] * b[i+63:i]
ENDFOR
dst[MAX:256] := 0

Performance

Architecture	Latency	Throughput (CPI)
Icelake	4	0.5
Skylake	4	0.5
Broadwell	3	0.5
Haswell	5	0.5
Ivy Bridge	5	1

二、代码实现

0. 数据生成

为了比较结果，我们用1+1e-8填充。这里利用模版兼容不同数据类型。由于AVX2指令集一次要操作多个数据，为了防止访存越界，我们将大小扩展到256的整数倍位比特，也就是32字节的整数倍。

uint64_t lowbit(uint64_t x)
{
    return x & (-x);
}
uint64_t extTo2Power(uint64_t n, int i)//arraysize datasize
{
    while(lowbit(n) < i)
        n += lowbit(n);
    return n;
}

template <typename T>
T* getArray(uint64_t size)
{
    uint64_t ExSize = extTo2Power(size, 32/sizeof(T));
    T* arr = new T[ExSize];
    for (uint64_t i = 0; i < size; i++)
        arr[i] = 1.0+1e-8;
    for (uint64_t i = size; i < ExSize; i++)
        arr[i] = 1.0;
    return arr;
}
}

1. 普通连乘

为了比较性能差异，我们先实现一份普通连乘。这里也使用模版。

template <typename T>
T simpleProduct(T* arr, uint64_t size)
{
    T product = 1;
    for (uint64_t i = 0; i < size; i++)
        product *= arr[i];
    return product;
}

2. AVX2指令集乘法：单精度浮点(float)

这里我们预开一个avx2的整形变量，每次从数组中取8个32位浮点，乘到这个变量上，最后在对这8个32位浮点进行连乘。

float avx2Product(float* arr, uint64_t size)
{
    float product[8] = {1};
    __m256 product256 = _mm256_setr_ps(1, 1, 1, 1, 1, 1, 1, 1);
    __m256 load256 = _mm256_setzero_ps();
    for (uint64_t i = 0; i < size; i += 8)
    {
        load256 = _mm256_loadu_ps(&arr[i]);
        product256 = _mm256_mul_ps(product256, load256);
    }
    _mm256_storeu_ps(product, product256);
    product[0] *= product[1] * product[2] * product[3] * product[4] * product[5] * product[6] * product[7];
    return product[0];
}

3. AVX2指令集乘法：双精度浮点(double)

double avx2Product(double* arr, uint64_t size)
{
    double product[4] = {1};
    __m256d product256 = _mm256_setr_pd(1, 1, 1, 1);
    __m256d load256 = _mm256_setzero_pd();
    for (uint64_t i = 0; i < size; i += 4)
    {
        load256 = _mm256_loadu_pd(&arr[i]);
        product256 = _mm256_mul_pd(product256, load256);
    }
    _mm256_storeu_pd(product, product256);
    product[0] *= product[1] * product[2] * product[3];
    return product[0];
}

三、性能测试

测试环境

Device	Description
CPU	Intel Core i9-9880H 8-core 2.3GHz
Memory	DDR4-2400MHz Dual-Channel 32GB
complier	Apple Clang-1300.0.29.30

计时方式

利用chrono库获取系统时钟计算运行时间，精确到毫秒级

uint64_t getTime()
{
    uint64_t timems = std::chrono::duration_cast<std::chrono::milliseconds>(std::chrono::system_clock::now().time_since_epoch()).count();
    return timems;
}

测试内容

	uint64_t N = 1e8;
    // compare the performance of simpleProduct and avx2Product
    uint64_t start, end;
    //compare float
    cout << "compare float product" << endl;
    float* arr = getArray<float>(N);
    start = getTime();
    float simpleProductResult = simpleProduct(arr, N);
    end = getTime();
    cout << "Simple product: " << simpleProductResult << endl;
    cout << "Time: " << end - start << " ms" << endl;
    cout << endl;
    start = getTime();
    float avx2ProductResult = avx2Product(arr, N);
    end = getTime();
    cout << "AVX2 product: " << avx2ProductResult << endl;
    cout << "Time: " << end - start << " ms" << endl;
    cout << endl;
    delete[] arr;
    //compare double
    cout << "compare double product" << endl;
    double* arr2 = getArray<double>(N);
    start = getTime();
    double simpleProductResult2 = simpleProduct(arr2, N);
    end = getTime();
    cout << "Simple product: " << simpleProductResult2 << endl;
    cout << "Time: " << end - start << " ms" << endl;
    cout << endl;
    start = getTime();
    double avx2ProductResult2 = avx2Product(arr2, N);
    end = getTime();
    cout << "AVX2 product: " << avx2ProductResult2 << endl;
    cout << "Time: " << end - start << " ms" << endl;
    cout << endl;
    delete[] arr2;

进行性能测试

第一次测试

测试命令

g++ -mavx2 avx_product.cpp 
./a.out

测试结果方法耗时(ms)AVX2乘法单精度57普通乘法单精度232AVX2乘法双精度121普通乘法双精度243

这里能看到单精度下已经出现了比较明显的误差，同时由于CPU内部没有普通的单精度浮点运算器，所以单精度运算和双精度耗时所差无几。

第二次测试