Different float values in array impact performance by 10x - why?

Question

please check out my code and the quesion below - thanks

Code:

#include <iostream>
#include <chrono>

using namespace std;

int bufferWriteIndex = 0;
float curSample = 0;

float damping[5] = { 1, 1, 1, 1, 1 };

float modeDampingTermsExp[5] = { 0.447604, 0.0497871, 0.00247875, 0.00012341, 1.37263e-05 };
float modeDampingTermsExp2[5] = { -0.803847, -3, -6, -9, -11.1962 };


int main(int argc, char** argv) {

    float subt = 0;
    int subWriteIndex = 0;
    auto now = std::chrono::high_resolution_clock::now();


    while (true) {

        curSample = 0;

        for (int i = 0; i < 5; i++) {

            //Slow version
            damping[i] = damping[i] * modeDampingTermsExp2[i];

            //Fast version
            //damping[i] = damping[i] * modeDampingTermsExp[i];
            float cosT = 2 * damping[i];

            for (int m = 0; m < 5; m++) {
                curSample += cosT;

            }
        }

        //t += tIncr;
        bufferWriteIndex++;


        //measure calculations per second
        auto elapsed = std::chrono::high_resolution_clock::now() - now;
        if ((elapsed / std::chrono::milliseconds(1)) > 1000) {
            now = std::chrono::high_resolution_clock::now();
            int idx = bufferWriteIndex;
            cout << idx - subWriteIndex << endl;
            subWriteIndex = idx;
        }

    }
}

As you can see im measuring the number of calculations or increments of bufferWriteIndex per second.

Question:

Why is performance faster when using modeDampingTermsExp - Program output:

12625671
12285846
12819392
11179072
12272587
11722863
12648955

vs using modeDampingTermsExp2 ?

1593620
1668170
1614495
1785965
1814576
1851797
1808568
1801945

It's about 10x faster. It seems like the numbers in those 2 arrays have an impact on calculation time. Why?

I am using Visual Studio 2019 with the following flags: /O2 /Oi /Ot /fp:fast

Answer 1

This is because you are hitting denormal numbers (also see this question ).

You can get rid of denormals like so:

#include <cmath>

// [...]

for (int i = 0; i < 5; i++) {
    damping[i] = damping[i] * modeDampingTermsExp2[i];
    if (std::fpclassify(damping[i]) == FP_SUBNORMAL) {
        damping[i] = 0; // Treat denormals as 0.
    }

    float cosT = 2 * damping[i];

    for (int m = 0; m < 5; m++) {
        curSample += cosT;
    }
}