weird NaN in mean() of float16 series

I have a shuffled series with a bunch of sinvalues in float16, like this:

   tdata.time_sin
   110405276   -0.183105
   175560878   -0.301270
   ...
   130331292   -0.158813
   6782127     -0.282471
    Name: time_sin, Length: 18490389, dtype: float16

There’s no NaN values, everything’s a sinus of something:

tdata.time_sin[np.isnan(tdata.time_sin) == True].count()
0

But for some reason, mean() chokes somewhere in the middle like it’s overflowing:

tdata.time_sin.mean()
nan

tdata.time_sin[:328720].mean()
0.0

tdata.time_sin[:328721].mean()
nan

tdata.time_sin[328719:328722]
117467643   -0.639648
85318746     0.956055
10829780     0.112000
Name: time_sin, dtype: float16

And it works fine when converted to float32:

foo = tdata.time_sin.astype(np.float32)
foo.mean()

0.20143597

Is this weird or am I missing something about float16?

This behavior persists after pickling and loading and sorting by index, although it now chokes much earlier:

zzz = pickle.load(open('timesin.pkl', 'rb'))
bb = zzz.sort_index()

bb[:74351].mean()
-0.0

bb[:74352].mean()
nan

bb[74350:74355]
749371   -0.898438
749393   -0.898438
749432   -0.898438
749447   -0.898438
749479   -0.898438
Name: time_sin, dtype: float16

Problem description

Expected Output

Output of pd.show_versions()