BUG: Parquet format does not support saving float16 columns

[Anirudhsekar96]

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the master branch of pandas.

Reproducible Example

import pandas as pd
import numpy as np

data = np.arange(2, 10, dtype=np.float16)
df = pd.DataFrame(data=data, columns=['fp16'])
df.to_parquet('./fp16.parquet')

Issue Description

Pandas does not validate presence of float16 columns in DataFrame as parquet format does not support saving float 16 values.

Additional references:

• Issue: halffloat implementation in pyarrow parquet apache/arrow#2691
• https://stackoverflow.com/questions/54150865/arrownotimplementederror-halffloat-error-on-applying-pandas-to-feather-on-a-dat

Expected Behavior

Raise ValueError while validating DataFrame before saving.

Installed Versions

INSTALLED VERSIONS

commit : b7991da
python : 3.8.12.final.0
python-bits : 64
OS : Linux
OS-release : 5.11.0-41-generic
Version : #45~20.04.1-Ubuntu SMP Wed Nov 10 10:20:10 UTC 2021
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.4.0.dev0+1356.gb7991da361.dirty
numpy : 1.21.4
pytz : 2021.3
dateutil : 2.8.2
pip : 21.3.1
setuptools : 59.4.0
Cython : 0.29.25
pytest : 6.2.5
hypothesis : 6.31.3
sphinx : 4.3.1
blosc : None
feather : None
xlsxwriter : 3.0.2
lxml.etree : 4.6.4
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 7.30.1
pandas_datareader: None
bs4 : 4.10.0
bottleneck : 1.3.2
fsspec : 2021.11.0
fastparquet : 0.7.2
gcsfs : 2021.11.0
matplotlib : 3.5.0
numexpr : 2.8.0
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : 6.0.1
pyxlsb : None
s3fs : 2021.11.0
scipy : 1.7.3
sqlalchemy : 1.4.28
tables : 3.6.1
tabulate : 0.8.9
xarray : 0.18.2
xlrd : 2.0.1
xlwt : 1.3.0
numba : 0.53.1

[Anirudhsekar96]

Opened a new bug report because the issue is also observed in other dtypes unsupported by pyarrow.

#44914