The result of the following code is very surprising to me. Why does using accumulate produce such a large error? I know that because it is single precisions, it will have a round-off error but when using reduce without any policy (single precision), this round-off error is not so significant! In fact, round-off errors is reasonable. But again, when I use reduce with policy (either of par seq unseq), its result will be the same with such a huge error compared to exact sum. Can anyone explain this?
#include <fstream>
#include <iomanip>
#include <execution>
#include <random>
#include <iostream>
#include <chrono>
#include <cfloat>
using namespace std;
int main() {
const int N=100*1e6;
default_random_engine g(time(0));
uniform_real_distribution<float> d(0.0f,nextafter(1.0f, DBL_MAX));
vector<float> a;
vector<double> b;
double exact{0.0};
float sum;
for(auto i=0; i<N ;i++){
a.push_back(d(g));
b.push_back(static_cast<double>(a[i]));
}
exact=accumulate(b.begin(),b.end(),0.0);
cout<<" exact sum is: "<<exact<<endl;
sum=accumulate(a.begin(),a.end(),0.0f);
cout<<" using accumulate for float : "<<sum<<endl;
sum=reduce(a.begin(),a.end());
cout<<" using reduce for float : "<<sum<<endl;
sum=reduce(execution::unseq,a.begin(),a.end());
cout<<" using reduce with ploicy : "<<sum<<endl;
}
it's result is :
exact sum is: 4.99979e+07
using accumulate for float : 1.67772e+07
using reduce for float : 5.00006e+07
using reduce with ploicy : 1.67772e+07