Rounding error in Timestamp.floor()

[frexvahi]

Code Sample, a copy-pastable example if possible

>>> pd.Timestamp('2117-01-01 00:00:45').floor('15s')
Timestamp('2117-01-01 00:00:30')

>>> pd.Timestamp('1823-01-01 00:00:01').floor('1s')
Timestamp('1823-01-01 00:00:00')

Problem description

For some timestamps more than a hundred years or so in the past or future, Timestamp.floor() rounds an already-round timestamp down to the next round value. I came up against the problem because I was assuming that Timestamp.floor() is idempotent.

I've looked at #14572 and #14440, these have both been closed as fixed but this bug is still present.

Expected Output

>>> pd.Timestamp('2117-01-01 00:00:45').floor('15s')
Timestamp('2117-01-01 00:00:45')

>>> pd.Timestamp('1823-01-01 00:00:01').floor('1s')
Timestamp('1823-01-01 00:00:01')

Output of pd.show_versions()

``` INSTALLED VERSIONS ------------------ commit: None python: 3.6.4.final.0 python-bits: 64 OS: Linux OS-release: 4.10.0-42-generic machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_GB.UTF-8 LOCALE: en_GB.UTF-8

pandas: 0.22.0
pytest: 3.3.0
pip: 9.0.1
setuptools: 36.5.0.post20170921
Cython: 0.27.3
numpy: 1.13.3
scipy: 1.0.0
pyarrow: None
xarray: 0.10.0
IPython: 6.2.1
sphinx: 1.6.3
patsy: 0.4.1
dateutil: 2.6.1
pytz: 2017.3
blosc: None
bottleneck: 1.2.1
tables: 3.4.2
numexpr: 2.6.2
feather: None
matplotlib: 2.1.0
openpyxl: 2.4.8
xlrd: 1.1.0
xlwt: 1.3.0
xlsxwriter: 1.0.2
lxml: 4.1.1
bs4: 4.6.0
html5lib: 0.999999999
sqlalchemy: 1.1.13
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: None

</details>

[jreback]

hmm, must be an error in the offset computation we are essentially doing

In [1]: from pandas.tseries.frequencies import to_offset

In [2]: divisor = to_offset('1s').nanos

In [4]: pd.Timestamp(np.floor(divisor * pd.Timestamp('1823-01-01 00:00:01').value / divisor))
Out[4]: Timestamp('1823-01-01 00:00:00.999999488')

We have some compensation for nanos freq, but I think that needs to be bigger as we are losing precision

[jreback]

PR welcome!

[cbertinato]

Definitely a round-off issue with large numbers. Some curious behavior of true division in Python 3. I would have thought that int / float(int) would be equivalent to int / int. It is when numbers are not large, but in this case:

>>> value = pd.Timestamp('1823-01-01 00:00:01').value
>>> value
-4638902399000000000
>>> unit = to_offset('1s')
>>> unit
1000000000
>>> value / unit
-4638902399.0
>>> value / float(unit)
-4638902399.000001

Changing the division in the offset calculation from int / float(int) to int / int solves the problem, but raises issues for Python 2, which __future__ division did appear to fix, even though it works in the terminal.