直到最近，并行编程的前景才引起了我的注意。从那以后，我使用了各种并行编程库。也许我的第一站是英特尔线程构建模块 (TBB)。但是，经常成为瓶颈的是由于诸如舍入和这些程序在不同处理器架构中的不可预测行为等因素导致的错误。下面是一段计算两组值的 Pearsons 相关系数的代码。它采用了 TBB 非常基本的并行模式 - *parallel_for* 和 *parallel_reduce* ：
// A programme to calculate Pearsons Correlation coefficient
#include <math.h>
#include <stdlib.h>
#include <iostream>
#include <tbb/task_scheduler_init.h>
#include <tbb/parallel_for.h>
#include <tbb/parallel_reduce.h>
#include <tbb/blocked_range.h>
#include <tbb/tick_count.h>
using namespace std;
using namespace tbb;
const size_t n=100000;
double global=0;
namespace s //Namesapce for serial part
{
double *a,*b;
int j;
double mean_a,mean_b,sd_a=0,sd_b=0,pcc=0;
double sum_a,sum_b,i;
}
namespace p //Namespace for parallel part
{
double *a,*b;
double mean_a,mean_b,pcc;
double sum_a,sum_b,i;
double sd_a,sd_b;
}
class serials
{
public:
void computemean_serial()
{
using namespace s;
sum_a=0,sum_b=0,i=0;
a=(double*) malloc(n*sizeof(double));
b=(double*) malloc(n*sizeof(double));
for(j=0;j<n;j++,i++)
{
a[j]=sin(i);
b[j]=cos(i);
sum_a=sum_a+a[j];
sum_b=sum_b+b[j];
}
mean_a=sum_a/n;
mean_b=sum_b/n;
cout<<"\nMean of a :"<<mean_a;
cout<<"\nMean of b :"<<mean_b;
}
void computesd_serial()
{
using namespace s;
for(j=0;j<n;j++)
{sd_a=sd_a+pow((a[j]-mean_a),2);
sd_b=sd_b+pow((b[j]-mean_b),2);
}
sd_a=sd_a/n;
sd_a=sqrt(sd_a);
sd_b=sd_b/n;
sd_b=sqrt(sd_b);
cout<<"\nStandard deviation of a :"<<sd_a;
cout<<"\nStandard deviation of b :"<<sd_b;
}
void pearson_correlation_coefficient_serial()
{
using namespace s;
pcc=0;
for(j=0;j<n;j++)
{
pcc+=(a[j]-mean_a)*(b[j]-mean_b);
}
pcc=pcc/(n*sd_a*sd_b);
cout<<"\nPearson Correlation Coefficient: "<<pcc;
}
};
class parallel
{
public:
class compute_mean
{
double *store1,*store2;
public:
double mean_a,mean_b;
void operator()( const blocked_range<size_t>& r)
{
double *a= store1;
double *b= store2;
for(size_t i =r.begin();i!=r.end(); ++i)
{
mean_a+=a[i];
mean_b+=b[i];
}
}
compute_mean( compute_mean& x, split) : store1(x.store1),store2(x.store2),mean_a(0),mean_b(0){}
void join(const compute_mean& y) {mean_a+=y.mean_a;mean_b+=y.mean_b;}
compute_mean(double* a,double* b): store1(a),store2(b),mean_a(0),mean_b(0){}
};
class read_array
{
double *const a,*const b;
public:
read_array(double* vec1, double* vec2) : a(vec1),b(vec2){} // constructor copies the arguments into local store
void operator() (const blocked_range<size_t> &r) const { // opration to be used in parallel_for
for(size_t k = r.begin(); k!=r.end(); k++,global++)
{
a[k]=sin(global);
b[k]=cos(global);
}
}};
void computemean_parallel()
{
using namespace p;
i=0;
a=(double*) malloc(n*sizeof(double));
b=(double*) malloc(n*sizeof(double));
parallel_for(blocked_range<size_t>(0,n,5000),read_array(a,b));
compute_mean sf(a,b);
parallel_reduce(blocked_range<size_t>(0,n,5000),sf);
mean_a=sf.mean_a/n;
mean_b=sf.mean_b/n;
cout<<"\nMean of a :"<<mean_a;
cout<<"\nMean of b :"<<mean_b;
}
class compute_sd
{
double *store1,*store2;
double store3,store4;
public:
double sd_a,sd_b,dif_a,dif_b,temp_pcc;
void operator()( const blocked_range<size_t>& r)
{
double *a= store1;
double *b= store2;
double mean_a=store3;
double mean_b=store4;
for(size_t i =r.begin();i!=r.end(); ++i)
{
dif_a=a[i]-mean_a;
dif_b=b[i]-mean_b;
temp_pcc+=dif_a*dif_b;
sd_a+=pow(dif_a,2);
sd_b+=pow(dif_b,2);
}}
compute_sd( compute_sd& x, split) : store1(x.store1),store2(x.store2),store3(p::mean_a),store4(p::mean_b),sd_a(0),sd_b(0),temp_pcc(0){}
void join(const compute_sd& y) {sd_a+=y.sd_a;sd_b+=y.sd_b;}
compute_sd(double* a,double* b,double mean_a,double mean_b): store1(a),store2(b),store3(mean_a),store4(mean_b),sd_a(0),sd_b(0),temp_pcc(0){}
};
void computesd_and_pearson_correlation_coefficient_parallel()
{
using namespace p;
compute_sd obj2(a,b,mean_a,mean_b);
parallel_reduce(blocked_range<size_t>(0,n,5000),obj2);
sd_a=obj2.sd_a;
sd_b=obj2.sd_b;
sd_a=sd_a/n;
sd_a=sqrt(sd_a);
sd_b=sd_b/n;
sd_b=sqrt(sd_b);
cout<<"\nStandard deviation of a :"<<sd_a;
cout<<"\nStandard deviation of b :"<<sd_b;
pcc=obj2.temp_pcc;
pcc=pcc/(n*sd_a*sd_b);
cout<<"\nPearson Correlation Coefficient: "<<pcc;
}
};
main()
{
serials obj_s;
parallel obj_p;
cout<<"\nSerial Part";
cout<<"\n-----------";
tick_count start_s=tick_count::now();
obj_s.computemean_serial();
obj_s.computesd_serial();
obj_s.pearson_correlation_coefficient_serial();
tick_count end_s=tick_count::now();
cout<<"\n";
task_scheduler_init init;
cout<<"\nParallel Part";
cout<<"\n-------------";
tick_count start_p=tick_count::now();
obj_p.computemean_parallel();
obj_p.computesd_and_pearson_correlation_coefficient_parallel();
tick_count end_p=tick_count::now();
cout<<"\n";
cout<<"\nTime Estimates";
cout<<"\n--------------";
cout<<"\nSerial Time :"<<(end_s-start_s).seconds()<<" Seconds";
cout<<"\nParallel time :"<<(end_p-start_p).seconds()<<" Seconds\n";
}
好 ！它在装有 Core i5 的 Windows 机器上运行良好。它为输出中的每个参数提供了完全相同的值，并行代码流形比串行代码快。这是我的输出：
操作系统：Windows 7 Ultimate 64 位处理器：核心 i5
Serial Part
-----------
Mean of a :1.81203e-05
Mean of b :1.0324e-05
Standard deviation of a :0.707107
Standard deviation of b :0.707107
Pearson Correlation Coefficient: 3.65091e-07
Parallel Part
-------------
Mean of a :1.81203e-05
Mean of b :1.0324e-05
Standard deviation of a :0.707107
Standard deviation of b :0.707107
Pearson Correlation Coefficient: 3.65091e-07
Time Estimates
--------------
Serial Time : 0.0204829 Seconds
Parallel Time : 0.00939971 Seconds
那么其他机器呢？如果我说它会正常工作，那么至少我的一些朋友会说“等等，伙计！有些东西很可疑。” 尽管并行代码总是比串行代码快，但不同机器的答案（并行代码和串行代码产生的答案之间）存在细微差别。那么是什么造成了这些差异呢？我们得出的结论是，这种异常行为是舍入错误，其代价是过度并行性和处理器架构的差异。
这导致了我的问题：
- 当我们在代码中使用并行处理库以利用多核处理器时，我们需要采取哪些预防措施？
- 即使有多个处理器可用，在哪些情况下我们不应该使用并行方法？
- 为了避免舍入错误，我们能做的最好的事情是什么？（让我说明一下，我不是在谈论强制互斥锁和障碍，它们有时可能会限制并行性的扩展，而是关于简单的编程技巧，可以有时很方便）
我很高兴看到您对这些问题的建议。如果您有时间限制，请自由回答最适合您的部分。
编辑 - 我在这里包含了更多结果
操作系统：Linux Ubuntu 64 位处理器：核心 i5
Serial Part
-----------
Mean of a :1.81203e-05
Mean of b :1.0324e-05
Standard deviation of a :0.707107
Standard deviation of b :0.707107
Pearson Correlation Coefficient: 3.65091e-07
Parallel Part
-------------
Mean of a :-0.000233041
Mean of b :0.00414375
Standard deviation of a :2.58428
Standard deviation of b :54.6333
Pearson Correlation Coefficient: -0.000538456
Time Estimates
--------------
Serial Time :0.0161237 Seconds
Parallel Time :0.0103125 Seconds
操作系统：Linux Fedora 64 位处理器：核心 i3
Serial Part
-----------
Mean of a :1.81203e-05
Mean of b :1.0324e-05
Standard deviation of a :0.707107
Standard deviation of b :0.707107
Pearson Correlation Coefficient: 3.65091e-07
Parallel Part
-------------
Mean of a :-0.00197118
Mean of b :0.00124329
Standard deviation of a :0.707783
Standard deviation of b :0.703951
Pearson Correlation Coefficient: -0.129055
Time Estimates
--------------
Serial Time :0.02257 Seconds
Parallel Time :0.0107966 Seconds
编辑：在 timday 建议的更改之后
操作系统：Linux Ubuntu 64 位处理器：corei5
Serial Part
-----------
Mean of a :1.81203e-05
Mean of b :1.0324e-05
Standard deviation of a :0.707107
Standard deviation of b :0.707107
Pearson Correlation Coefficient: 3.65091e-07
Parallel Part
-------------
Mean of a :-0.000304446
Mean of b :0.00172593
Standard deviation of a :0.708465
Standard deviation of b :0.7039
Pearson Correlation Coefficient: -0.140716
Time Estimates
--------------
Serial Time :0.0235391 Seconds
Parallel time :0.00810775 Seconds
最好的祝福。
注意1：我不保证上面的代码是正确的。我相信是的。
注意 2：这段代码也在 Linux 机器上进行了测试。
注 3：尝试了不同的粒度组合和自动分区选项。