我试着用本征写一些SSE代码,有些行为让我无法理解。
给定的代码:
#ifndef EIGEN_DONT_VECTORIZE // Not needed with Intel C++ Compiler XE 15.0
#define EIGEN_VECTORIZE_SSE4_2
#define EIGEN_VECTORIZE_SSE4_1
#define EIGEN_VECTORIZE_SSSE3
#define EIGEN_VECTORIZE_SSE3
#endif
#include "stdafx.h"
#include <iostream>
#include <unsupported/Eigen/AlignedVector3>
#include <Eigen/StdVector>
#include <chrono>
int _tmain(int argc, _TCHAR* argv[]) {
static const int SIZE = 4000000;
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> A_SSE(1, 1, 1);
//EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> B_SSE(2, 2, 2);
//std::vector<Eigen::AlignedVector3<float>> C_SSE(SIZE, Eigen::AlignedVector3<float>(0,0,0));
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> A_SSE1(1, 1, 1);
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> A_SSE2(1, 1, 1);
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> A_SSE3(1, 1, 1);
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> A_SSE4(1, 1, 1);
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> B_SSE(2, 2, 2);
EIGEN_ALIGNED_VECTOR3 Eigen::AlignedVector3<float> B_SSE_increment_unroll(16, 16, 16);
A_SSE2 += B_SSE;
A_SSE3 = A_SSE2 + B_SSE;
A_SSE4 = A_SSE3 + B_SSE;
std::vector<Eigen::AlignedVector3<float>> C_SSE(SIZE, Eigen::AlignedVector3<float>(0, 0, 0));
auto start2 = std::chrono::system_clock::now();
// no unroll
for (int iteration = 0; iteration < SIZE; ++iteration) {
A_SSE += B_SSE;
C_SSE[iteration] = A_SSE;
}
//// own unroll
//for (int iteration = 0; iteration < SIZE / 8; ++iteration){
// A_SSE1 += B_SSE_increment_unroll;
// A_SSE2 += B_SSE_increment_unroll;
// A_SSE3 += B_SSE_increment_unroll;
// A_SSE4 += B_SSE_increment_unroll;
// C_SSE[iteration * 2] = A_SSE1;
// C_SSE[iteration * 2 + 1] = A_SSE2;
// C_SSE[iteration * 2 + 2] = A_SSE3;
// C_SSE[iteration * 2 + 3] = A_SSE4;
//}
auto end2 = std::chrono::system_clock::now();
auto elapsed2 = end2 - start2;
std::cout << "Eigen aligned vector " << elapsed2.count() << '\n';
Eigen::Matrix3Xf A = Eigen::Matrix3Xf::Zero(3, SIZE);
Eigen::Vector3f B(3, 3, 3);
Eigen::Vector3f C(2, 2, 2);
auto start1 = std::chrono::system_clock::now();
for (int iteration = 0; iteration < SIZE; ++iteration) {
B += C;
A.col(iteration) = B;
}
auto end1 = std::chrono::system_clock::now();
auto elapsed1 = end1 - start1;
std::cout << "Eigen matrix " << elapsed1.count() << '\n';
float *pResult = (float*)_aligned_malloc(SIZE * sizeof(float) * 4, 16); // align to 16-byte for SSE
auto start3 = std::chrono::system_clock::now();
__m128 x;
__m128 xDelta = _mm_set1_ps(2.0f); // Set the xDelta to (4,4,4,4)
__m128 *pResultSSE = (__m128*) pResult;
x = _mm_set_ps(1.0f, 1.0f, 1.0f, 1.0f); // Set the initial values of x to (4,3,2,1)
for (int iteration = 0; iteration < SIZE; ++iteration)
{
x = _mm_add_ps(x, xDelta);
pResultSSE[iteration] = x;
}
auto end3 = std::chrono::system_clock::now();
auto elapsed3 = end3 - start3;
std::cout << "Own sse " << elapsed3.count() << '\n';
}在我的电脑上,时间似乎很奇怪。
当我检查程序集、对齐版本和自己的SSE时,使用addps movaps,但在手动展开循环之前,我不会获得额外的性能,即使不是在所有运行(50%)中都这样做,我也不会得到任何提升。使用本征矩阵的版本不使用sse,实现相同的性能,内联组装显示在16次迭代中展开。手动展开那么有影响吗?我们是否应该手动为SSE执行此操作,如果使用CPU属性,则取决于此?
编辑:所以总结一下。SSE指令性能不佳,因为无法证明展开循环将保持与未展开循环相同的结果,因此无法隐藏内存存储延迟。但是在汇编代码中,“单一”指令只使用一个寄存器,并在展开循环中递增。如果SSE成瘾是垂直执行的(对齐向量中的单个浮点数累积了相同的加法运算量),编译器应该能够证明展开的相等性。默认情况下,SSE操作是否不经编译器优化?如果展开循环保持执行顺序,那么保留非关联的数学,那么自动展开应该是可能的,为什么它不会发生,以及如何强制编译器这样做呢?
编辑:正如我所建议的那样,我运行测试,但是来自艾根的工作台单元不能在visual studio 2017下工作,所以它被替换为
#include <iostream>
#include <vector>
#include <unsupported/Eigen/AlignedVector3>
#include <chrono>
#include <numeric>
EIGEN_DONT_INLINE
void vector_no_unroll(std::vector<Eigen::AlignedVector3<float>>& out)
{
Eigen::AlignedVector3<float> A_SSE(1, 1, 1);
Eigen::AlignedVector3<float> B_SSE(2, 2, 2);
for (auto &x : out)
{
A_SSE += B_SSE;
x = A_SSE;
}
}
EIGEN_DONT_INLINE
void vector_unrolled(std::vector<Eigen::AlignedVector3<float>>& out)
{
Eigen::AlignedVector3<float> A_SSE1(1, 1, 1);
Eigen::AlignedVector3<float> A_SSE2(1, 1, 1);
Eigen::AlignedVector3<float> A_SSE3(1, 1, 1);
Eigen::AlignedVector3<float> A_SSE4(1, 1, 1);
Eigen::AlignedVector3<float> B_SSE(2, 2, 2);
Eigen::AlignedVector3<float> B_SSE_increment_unroll(16, 16, 16);
A_SSE2 += B_SSE;
A_SSE3 = A_SSE2 + B_SSE;
A_SSE4 = A_SSE3 + B_SSE;
for (size_t i = 0; i<out.size(); i += 4)
{
A_SSE1 += B_SSE_increment_unroll;
A_SSE2 += B_SSE_increment_unroll;
A_SSE3 += B_SSE_increment_unroll;
A_SSE4 += B_SSE_increment_unroll;
out[i + 0] = A_SSE1;
out[i + 1] = A_SSE2;
out[i + 2] = A_SSE3;
out[i + 3] = A_SSE4;
}
}
EIGEN_DONT_INLINE
void eigen_matrix(Eigen::Matrix3Xf& out)
{
Eigen::Vector3f B(1, 1, 1);
Eigen::Vector3f C(2, 2, 2);
for (int i = 0; i < out.cols(); ++i) {
B += C;
out.col(i) = B;
}
}
template<int unrolling> EIGEN_DONT_INLINE
void eigen_matrix_unrolled(Eigen::Matrix3Xf& out)
{
Eigen::Matrix<float, 3, unrolling> B = Eigen::Matrix<float, 1, unrolling>::LinSpaced(3.f, 1 + 2 * unrolling).template replicate<3, 1>();
for (int i = 0; i < out.cols(); i += unrolling) {
out.middleCols<unrolling>(i) = B;
B.array() += float(2 * unrolling);
}
}
int main() {
static const int SIZE = 4000000;
int tries = 30;
int rep = 10;
std::vector<int> Timings(tries, 0);
{
Eigen::Matrix3Xf A(3, SIZE);
#pragma loop( 1 )
for (int iter = 0; iter < tries; ++iter)
{
auto start1 = std::chrono::system_clock::now();
eigen_matrix(A);
Timings[iter] = (std::chrono::system_clock::now() - start1).count();
}
}
std::cout << "eigen matrix Min: " << *std::min_element(Timings.begin(), Timings.end()) << " ms\n";
std::cout << "eigen matrix Mean: " << std::accumulate(Timings.begin(), Timings.end(), 0) / tries << " ms\n";
{
Eigen::Matrix3Xf A(3, SIZE);
#pragma loop( 1 )
for (int iter = 0; iter < tries; ++iter)
{
auto start1 = std::chrono::system_clock::now();
eigen_matrix_unrolled<4>(A);
Timings[iter] = (std::chrono::system_clock::now() - start1).count();
}
}
std::cout << "eigen matrix unrolled 4 min: " << *std::min_element(Timings.begin(), Timings.end()) << " ms\n";
std::cout << "eigen matrix unrolled 4 Mean: " << std::accumulate(Timings.begin(), Timings.end(), 0) / tries << " ms\n";
{
Eigen::Matrix3Xf A(3, SIZE);
#pragma loop( 1 )
for (int iter = 0; iter < tries; ++iter)
{
auto start1 = std::chrono::system_clock::now();
eigen_matrix_unrolled<8>(A);
Timings[iter] = (std::chrono::system_clock::now() - start1).count();
}
}
std::cout << "eigen matrix unrolled 8 min: " << *std::min_element(Timings.begin(), Timings.end()) << " ms\n";
std::cout << "eigen matrix unrolled 8 Mean: " << std::accumulate(Timings.begin(), Timings.end(), 0) / tries << " ms\n";
{
std::vector<Eigen::AlignedVector3<float>> A(SIZE, Eigen::AlignedVector3<float>(0, 0, 0));
#pragma loop( 1 )
for (int iter = 0; iter < tries; ++iter)
{
auto start1 = std::chrono::system_clock::now();
vector_no_unroll(A);
Timings[iter] = (std::chrono::system_clock::now() - start1).count();
}
}
std::cout << "eigen vector min: " << *std::min_element(Timings.begin(), Timings.end()) << " ms\n";
std::cout << "eigen vector Mean: " << std::accumulate(Timings.begin(), Timings.end(), 0) / tries << " ms\n";
{
std::vector<Eigen::AlignedVector3<float>> A(SIZE, Eigen::AlignedVector3<float>(0, 0, 0));
#pragma loop( 1 )
for (int iter = 0; iter < tries; ++iter)
{
auto start1 = std::chrono::system_clock::now();
vector_unrolled(A);
Timings[iter] = (std::chrono::system_clock::now() - start1).count();
}
}
std::cout << "eigen vector unrolled min: " << *std::min_element(Timings.begin(), Timings.end()) << " ms\n";
std::cout << "eigen vector unrolled Mean: " << std::accumulate(Timings.begin(), Timings.end(), 0) / tries << " ms\n";
}并在8台不同的机器(所有窗口)上检查结果,并得到以下结果。
特征矩阵Min: 110477 ms
特征矩阵均值: 131691 ms
特征矩阵展开4分钟: 40099 ms
特征矩阵展开4平均: 54812 ms
特征矩阵展开8 min: 40001 ms
特征矩阵展开8平均: 51482 ms
特征向量最小: 100270 ms
特征向量均值: 117316 ms
特征向量展开最小: 59966 ms
特征向量展开平均: 65847 ms
在我测试的每台机器上,最古老的一台。看起来,在新的机器上,小型展开可能是非常有益的(结果不同,从1.5倍到3.5倍的速度在4倍展开,即使展开是8,16,32,或256次,也不会增加)。
发布于 2017-09-27 21:55:48
您的时间非常不准确(当多次运行您的代码时,我得到了很多变化)。为了获得更好的重现性,您应该多次运行每个变体,并且花费最少的时间。我使用作为特征的一部分的BenchUtils编写了一个基准测试:
#include <iostream>
#include <unsupported/Eigen/AlignedVector3>
#include <bench/BenchUtil.h>
EIGEN_DONT_INLINE
void vector_no_unroll(std::vector<Eigen::AlignedVector3<float>>& out)
{
Eigen::AlignedVector3<float> A_SSE(1, 1, 1);
Eigen::AlignedVector3<float> B_SSE(2, 2, 2);
for(auto &x : out)
{
A_SSE += B_SSE;
x = A_SSE;
}
}
EIGEN_DONT_INLINE
void vector_unrolled(std::vector<Eigen::AlignedVector3<float>>& out)
{
Eigen::AlignedVector3<float> A_SSE1(1, 1, 1);
Eigen::AlignedVector3<float> A_SSE2(1, 1, 1);
Eigen::AlignedVector3<float> A_SSE3(1, 1, 1);
Eigen::AlignedVector3<float> A_SSE4(1, 1, 1);
Eigen::AlignedVector3<float> B_SSE(2, 2, 2);
Eigen::AlignedVector3<float> B_SSE_increment_unroll(16, 16, 16);
A_SSE2 += B_SSE;
A_SSE3 = A_SSE2 + B_SSE;
A_SSE4 = A_SSE3 + B_SSE;
for(size_t i=0; i<out.size(); i+=4)
{
A_SSE1 += B_SSE_increment_unroll;
A_SSE2 += B_SSE_increment_unroll;
A_SSE3 += B_SSE_increment_unroll;
A_SSE4 += B_SSE_increment_unroll;
out[i + 0] = A_SSE1;
out[i + 1] = A_SSE2;
out[i + 2] = A_SSE3;
out[i + 3] = A_SSE4;
}
}
EIGEN_DONT_INLINE
void eigen_matrix(Eigen::Matrix3Xf& out)
{
Eigen::Vector3f B(1, 1, 1);
Eigen::Vector3f C(2, 2, 2);
for (int i = 0; i < out.cols(); ++i) {
B += C;
out.col(i) = B;
}
}
template<int unrolling> EIGEN_DONT_INLINE
void eigen_matrix_unrolled(Eigen::Matrix3Xf& out)
{
Eigen::Matrix<float,3,unrolling> B = Eigen::Matrix<float, 1, unrolling>::LinSpaced(3.f, 1+2*unrolling).template replicate<3,1>();
for (int i = 0; i < out.cols(); i+=unrolling) {
out.middleCols<unrolling>(i) = B;
B.array() += float(2*unrolling);
}
}
int main() {
static const int SIZE = 4000000;
int tries = 10;
int rep = 10;
BenchTimer t;
std::cout.precision(4);
{
std::vector<Eigen::AlignedVector3<float>> A(SIZE, Eigen::AlignedVector3<float>(0, 0, 0));
BENCH(t, tries, rep, vector_no_unroll(A));
std::cout << "no unroll: " << 1e3*t.best(CPU_TIMER) << "ms\n";
}
{
std::vector<Eigen::AlignedVector3<float>> A(SIZE, Eigen::AlignedVector3<float>(0, 0, 0));
BENCH(t, tries, rep, vector_unrolled(A));
std::cout << "unrolled: " << 1e3*t.best(CPU_TIMER) << "ms\n";
}
{
Eigen::Matrix3Xf A(3, SIZE);
BENCH(t, tries, rep, eigen_matrix(A));
std::cout << "eigen matrix: " << 1e3*t.best(CPU_TIMER) << "ms\n";
}
{
Eigen::Matrix3Xf A(3, SIZE);
BENCH(t, tries, rep, eigen_matrix_unrolled<4>(A));
std::cout << "eigen unrd<4>: " << 1e3*t.best(CPU_TIMER) << "ms\n";
}
{
Eigen::Matrix3Xf A(3, SIZE);
BENCH(t, tries, rep, eigen_matrix_unrolled<8>(A));
std::cout << "eigen unrd<8>: " << 1e3*t.best(CPU_TIMER) << "ms\n";
}
}我得到了非常相似的时间,几乎独立于使用-msse2、-msse4.2或-mavx2编译
无展开: 66.72ms展开: 66.83ms特征矩阵: 57.56ms特征unrd<4>:50.39ms特征unrd<8>:51.19ms
值得注意的是,AligenedVector3变体始终是最慢的,在展开和不展开之间没有显着性差异。矩阵变体花费大约7/8的时间,手动展开矩阵变量(每次迭代处理4或8列),将时间减少到原来时间的3/4左右。
这表明内存带宽可能是所有向量化变体的瓶颈。展开矩阵变量可能受到实际操作(或单个标量的手动复制)的限制。
基准测试是在IntelCorei5-4210Ucpu @1.70GHz上进行的,使用的是Ubuntu16.04上的g++5.4.1,并且最近对Eigen开发分支进行了检查。
https://stackoverflow.com/questions/46407332
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