X86 SSE/AVX指令集：向量内积

##向量内积

• 向量a和b的内积为：$a \cdot b = a_{1} \times b_{1} + a_{2} \times b_{2} + \cdots + a_{n} \times b_{n} $

##利用_mm256_dp_ps实现double型向量内积

double dot(float* a, float* b, int n)
{
	double res = 0.0;
	int k = n / 4 + 1;
	for(int i = 0; i < k; i++)
	{
		__m256 ai = _mm256_loadu_ps(a + i * 4);//不对齐加载数据
		__m256 bi = _mm256_loadu_ps(b + i * 4);
		__m256 r = _mm256_dp_ps(ai, bi, 0xF1);
		res += r[0];
	}
	fclose(fp);
	return res;
}

##利用_mm256_hadd_ps等实现double型向量内积

double dot1(float* a, float* b, int n)
{	
	double res = 0.0;
	int k = n / 4 + 1;
	FILE* fp = fopen("dot1.txt", "w");
			 
	for(int i = 0; i < k; i++)
	{   
		__m256 ai = _mm256_loadu_ps(a + i * 4); 
		__m256 bi = _mm256_loadu_ps(b + i * 4); 
		__m256 t = _mm256_mul_ps(ai, bi);
		__m256 zero = _mm256_setzero_ps();
		t = _mm256_hadd_ps(t, zero);
		t = _mm256_hadd_ps(t, zero);
		res = res + t[0];
	}
	return res;
}

##调用程序

#include
#include
#include
#include
#include
#include
using namespace std;
int main(int argv, char** argc)
{
	int N = atoi(argc[1]);
	float* d = (float*)malloc(sizeof(float) * N); 
	for(int i = 0; i < N; i++)
	{
		d[i] = (double)rand() / RAND_MAX;
	}
	clock_t start_time = clock();
	double r1 = dot(d, d, N);
	clock_t end_time = clock();
	printf("%f\n", r1);
	printf("pall times = %fs\n" ,(double)(end_time - start_time) / CLOCKS_PER_SEC);	
	start_time = clock();
	double r2 = originalDot(d, d, N);
	end_time = clock();
	printf("%f\n", r2);
	printf("sequence times = %fs\n" ,(double)(end_time - start_time) / CLOCKS_PER_SEC);
	return 1;
}

##编译

g++ mcl.cpp -o mcl -msse -mavx -ffloat-store

##运行结果

• 当向量中的数据较大时精度会损失，本机上实测为大于3000时精度就下降，所以在计算的向量之前要对其进行标准化
• 用SSE指令的速度比正常的顺序执行要快两倍左右，不是标准的4倍，因为还有加载数据的io时间

yfzhongchao@yfzhongchao-pc:~/workspace/cpp/mc$ ./mcl 300000000
sse res = 99995252.458352
sse time = 0.476225s
sequence res = 99995252.457381
sequence time = 0.908160s