python - Rounding to nearest int with numpy.rint() not consistent for .5

Question

numpy's round int doesn't seem to be consistent with how it deals with xxx.5

In [2]: np.rint(1.5)
Out[2]: 2.0

In [3]: np.rint(10.5)
Out[3]: 10.0

1.5 is rounded up while 10.5 is rounded down. Is there a reason for this? Is it just and artifact of the inaccuracy of floats?

Edit

Is there a way to get the desired functionality where n.5 is rounded up i.e. to n+1 for both n = even or odd?

Answer 1

This is in fact exactly the rounding specified by the IEEE floating point standard IEEE 754 (1985 and 2008). It is intended to make rounding unbiased. In normal probability theory, a random number between two integers has zero probability of being exactly N + 0.5, so it shouldn't matter how you round it because that case never happens. But in real programs, numbers are not random and N + 0.5 occurs quite often. (In fact, you have to round 0.5 every time a floating point number loses 1 bit of precision!) If you always round 0.5 up to the next largest number, then the average of a bunch rounded numbers is likely to be slightly larger than the average of the unrounded numbers: this bias or drift can have very bad effects on some numerical algorithms and make them inaccurate.

The reason rounding to even is better than rounding to odd is that the last digit is guaranteed to be zero, so if you have to divide by 2 and round again, you don't lose any information at all.

In summary, this kind of rounding is the best that mathematicians have been able to devise, and you should WANT it under most circumstances. Now all we need to do is get schools to start teaching it to children.