facd737ee4
So making this code change took a few hours. But then deciding that it
was the right one of the many options available took the next 3 days.
When changing to the new rounding function, we had a test that started
failing. It appears as if our new rounding function is not the same in
some way as the one built into python 2.
```
>>> round(.0045*100 + .05)/100
0.0
>>> round_away_from_zero(.0045*100 + .05)/100
0.01
```
Doing the math by hand we see that the new function is actually correct
but the old one is clearly rounding incorrectly in this case. Looking
closer at this I discovered that it was due to a floating point issue
where .0045*100 is represented as 0.44999999999999996 so when we add
0.05 to this number we get 0.49999999999999994. This is all because of
the limitations of floating point arithmetic.
See https://docs.python.org/3/tutorial/floatingpoint.html#tut-fp-issues
for more on that.
Because python does its rounding at the bit level in C code. It treats
the .4999... as below the .5 cutoff and rounds down. Whereas our code
does more simple arithmetic which causes the number to correct itself
before we round and so correctly rounds up to 0.01
The result of this change is that previously, the rounding threshold used to
be that any number > .0045 would ronud to 0.01 and now any number that
is >= .0045 rounds to 0.01
Note that if we only care about the two most significant digits of
number between 0 and 1, this error only manifests itself in such a way
that other than the case of going from 0.00 to 0.01 eg. from 0% to 1%
none of the other cases where we would now round up cause the 2 most
significant digits to change. Given this level of impact, we're fine
with this change.
In our tests we see this for one case, where an incomplete turns into an
F in a test. I'm updating the test here to be more correct.
As we were looking at it we speculated as to why we were adding the .05
to the number. Could it be to counteract this floating point issue? It
turns out not.
Looking at this commit(a1286b1c7d) we see that it
looks like this was intended to always round up to the nearest
percentage point. However, there's a typo here. If you wanted to
ensure that we always rounded up to the nearest percentage point you
would have the math be `round(final_grade_percent*100 + 0.5)/ 100` or a
simpler way to do this would be
`math.ceil(final_grade_percent*100)/100`. However, that is not what
happened and 7 years later, there have been a lot of people graded with
the wrong rounding where essentialy anyone with a grade of 89.45 gets a
90 when the intended impact was supposed to be that anyone with a grade
above an 89.0 would get a grade of 90.
Changing it now requires a lot of conversation and wolud have a large
impact on existing learners. So we are not going to change it as a part
of the python 2 -> python 3 upgrade. I have created
https://openedx.atlassian.net/browse/TNL-6972 to capture this issue if
we want to address it in the future.
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