While browsing around StackOverflow I found a page about Square root function implementation. One of the answer points to an article containing different implementations of square root.

One of the things I like to do is pointing out obvious errors in benchmarks. It’s not that I don’t have an intimate understanding of these things, but if I can point out the error, is has to be obvious. One of the obvious errors in time measurement can be shown using a short pseudo code example.

```
Begin = Time();
For (I = N; I > 0; I--) {
F();
}
End = Time();
AvgTime = (End - Begin) / N
```

This program starts by retrieving the time at the start. Then the function `F`

is called `N`

times. At the end we set `End`

to the current time. The absolute
difference between `Begin`

and `End`

is the time it took to call the function
`F`

, `N`

times. We divide by `N`

to find the time it took to call the function
once.

A benchmark should be structured like this. It reduces the error of your measurement. Benchmarks that are nog structured like this are wrong.

Now back to the code in the article. On the surface the code looks a lot like my pseudo code. I will show why it isn’t the same.

```
for (int j = 0; j < AVG; j++) {
dur.Start();
for (int i = 1; i < M; i++) {
RefTotalPrecision+=sqrt((float) i);
}
dur.Stop();
Temp+=dur.GetDuration();
}
RefTotalPrecision/=AVG;
Temp/=AVG;
RefSpeed=(float)(Temp)/CLOCKS_PER_SEC;
```

In this code the variable `AVG`

is set to `10`

and `M`

is set to `10.000`

. After running the
variable `RefTotalPrecision`

will contain the average precision of `M`

`sqrt`

calls. The variable `RefSpeed`

should contain the average speed of `M`

`sqrt`

calls. It – however – doesn’t.

The `M`

loop makes it look like we average over many calls. We don’t because
the value we average with is `AVG`

, which is used in the outer loop. To show
what happens we remove the code that is measured. I also removed the averaging
code at the end.

```
for (int j = 0; j < AVG; j++) {
dur.Start();
// insert code to be measured
dur.Stop();
Temp+=dur.GetDuration();
}
```

The code measures the time `2 * AVG`

times, while it should only be measured
twice, once at the start, and once at the end. To fix this, we need to move two
lines and remove one character.

```
dur.Start();
for (int j = 0; j < AVG; j++)
{
// insert code to be measured
}
dur.Stop();
Temp = dur.GetDuration();
```

We move the `Start`

and `Stop`

calls outside the loop. The error introduced by
the measuring functions will now be divided by `AVG`

, which is `AVG`

times
smaller. I also removed the `+`

, it wasn’t needed anymore.