BUG: rank with object dtype and small values

[jbrockmendel]

# Based on test_rank_ea_small_values
import pandas as pd

ser = pd.Series(
    [5.4954145e29, -9.791984e-21, 9.3715776e-26, pd.NA, 1.8790257e-28],
    dtype="Float64",
)
ser2 = ser.astype(object)

>>> ser.rank(method="min")
0    4.0
1    1.0
2    3.0
3    NaN
4    2.0
dtype: float64

>>> ser2.rank(method="min")
0    4.0
1    1.0
2    1.0
3    NaN
4    1.0
dtype: float64

I'd expect 1) the values to match and 2) to get NA rather than NaN at least for the Float64 case.

Update: if we convert to float64[pyarrow] first we do get NA back and a uint64[pyarrow] dtype.

[annaadonts]

Take