**Root cause:** accumulation of floating point rounding error combined with a tolerance on the equality check

**Lesson:** use exact equality checks with floating point numbers

Oh please donâ€™t. This will bite you far more often than the example in the video. Youâ€™ll be totally scratching your head wondering why

```
x = 0.1
y = 0.2
z = 0.3
if (x + y == z) print *, "Success!"
```

doesnâ€™t seem to work.

0.1 is not 0.1,

but 0.125 is 0.125.

If you watch the video, the real problem seems to be a form of race condition. There are two flags, one that is set with a tolerance and one that is not.

Oh the finitely countable joys of floating point numbers!

Note that I posted that on April 1st (at least in my timezone).

phew I didnâ€™t read it till after, so wasnâ€™t sure.

Yes writing sophisticated code like this

```
real(REAL64) :: a
real :: b
If ((a-b) == 0.0) then
a = 1.0
b = 2
End If
```

is best left to us experienced programmers

Surprisingly, I still see nonsense like this in codes written in the last few years by people who should know better.

Isnâ€™t this a result of the fact tha 0.125 can be exactly represented in binary but 0.1 donâ€™t?

Yes :

- 0.125 = 1/8 = 0b0.001
- 0.1 = 1/10 = 0b0.0001100110011001101â€¦

A number with a finite number of digits in a base can have an infinite number of digits in another base.

But if there is a finite number of digits in binary, there should always be a finite number in decimal, as it is a sum of 1/2^n. But in other bases?

Dont know the answer, but I think with larger bases there are more number that can be represented exactly.

It sounds reasonable.

I guess itâ€™s a matter of prime factors in the base. Base two has only one prime factor and therefore can only exactly represent numbers which can be represented as the sum \sum_{k=m}^{n} a_k2^k.

Base ten has two prime factors: 2 and 5. Therefore, every number, that can be represented exactly with a finite amount of digits with base two, can be represented exactly with base 10, but not the other way around.

Makes a lot of sense