Eigen `sum()` function gives different for same vector in two versions of program

Question

I am using Eigen c++ library for linear algebra operations.

There is a variable v in my code that is a VectorXd type, and I need to calculate its sum, so I called v.sum().

However, when I updated my program to a new version, although the value of v remain same(read from the same input file), the sum() function give slightly different value.

Here is a piece of code that explains my problem:

double vsum1 = v.sum();
double vsum2 = 0; // compare with manually calculated sum
for(size_t i = 0; i < v.size(); ++i)
{
    vsum2 += v(i);
}
cout << "sum1: " << vsum1 << endl;
cout << "sum2: " << vsum2 << endl;

for the old version, the result is

sum1: 94.8117866666666487
sum2: 94.8117866666666202

for the new version , the result is

sum1: 94.8117866666666345
sum2: 94.8117866666666202

The manually calculated sum vsum2 remains unchanged, so I think the origin vector v didn't change, then why would sum() give different result? Is it because of some SIMD optimization performed by Eigen?

The difference is actually neligible, but that leads to a failure of regression test.

Answer 1

5gon12eder's comment is right. Eigen3.3 perform AVX vctorization if available (4 double at once) compared to SSE only in Eigen3.2 (2 double at once). In any case, you must use some tolerance when comparing floating-point numbers to account for round-off errors. You can take inspiration from Eigen's unit tests.