BUG: merge_asof on float does not detect float equality

[RaphaelRosset]

Pandas version checks

• 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 main branch of pandas.

Reproducible Example

left_df = pd.DataFrame({"CONTINUOUS": list(np.arange(100.0, 106.0, 0.8))})
data = [
    (98.0, 103.4, "A", "a"),
    (104.0, 106.8, "B", "b"),
]
right_df = pd.DataFrame(data, columns=["START", "END", "C1", "C2"])
output = pd.merge_asof(
    left_df.sort_values(by="CONTINUOUS"),
    right_df.sort_values(by="START"),
    left_on="CONTINUOUS",
    right_on="START",
    direction="backward",
)
print(output.to_string())

Issue Description

When merge_asof is done with On key being a float number sometimes error due to float precision issue can be seen

CONTINUOUS START END C1
0 100.0 98.0 103.4 A
1 100.8 98.0 103.4 A
2 101.6 98.0 103.4 A
3 102.4 98.0 103.4 A
4 103.2 98.0 103.4 A
5 104.0 98.0 103.4 A <=== 104.0 mapped to A is wrong
6 104.8 104.0 106.8 B
7 105.6 104.0 106.8 B

Note that changing the way CONTINOUS list of values is created makes the output as expected.
For example on my side, these 2 alternative give correct output.
[103.2, 104.0, 104.8] ==> correct output
list(np.arange(103.2, 106.0, 0.8)) ==> correct output

Expected Behavior

CONTINUOUS START END C1
0 100.0 98.0 103.4 A
1 100.8 98.0 103.4 A
2 101.6 98.0 103.4 A
3 102.4 98.0 103.4 A
4 103.2 98.0 103.4 A
5 104.0 98.0 103.4 B <=== 104.0 mapped to B is correct
6 104.8 104.0 106.8 B
7 105.6 104.0 106.8 B

Installed Versions

INSTALLED VERSIONS

commit : d9cdd2e
python : 3.12.2.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.19045
machine : AMD64
processor : Intel64 Family 6 Model 158 Stepping 10, GenuineIntel
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : Norwegian Bokmål_Norway.1252

pandas : 2.2.2
numpy : 2.0.0
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : None
pip : 24.1.1
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pandas_gbq : None
pyarrow : None
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

[abhinav-thimma]

Hi @RaphaelRosset ,
I was triaging your issue on the main branch. Here are my findings:

To make debugging easy, I've set a larger precision for printing numpy.float64's using: np.set_printoptions(precision=15)

Using the Reproducible Example:

(Pdb) left_df
   CONTINUOUS
0       100.0
1       100.8
2       101.6
3       102.4
4       103.2
5       104.0
6       104.8
7       105.6
(Pdb) left_df.iloc[5]
CONTINUOUS    104.0
Name: 5, dtype: float64
(Pdb) left_df.iloc[5]["CONTINUOUS"]
103.99999999999999

• The actual value stored in the 6th row under "CONTINUOUS" column is < 104.0. (This is a well know behavior of floating-point arithmetic by numpy)
• Based on the definition of direction=backward, merge_asof will try to find a key in right_df which is less than or equal to the above value (103.99999999999999) which in this case would be 98.0 from (98.0, 103.4, "A", "a")

If you are not able to control the float numbers in your dataframe, might I recommend setting direction=nearest. Nearest direction produces the following merged dataframe in your case:

   CONTINUOUS  START    END C1 C2
0       100.0   98.0  103.4  A  a
1       100.8   98.0  103.4  A  a
2       101.6  104.0  106.8  B  b
3       102.4  104.0  106.8  B  b
4       103.2  104.0  106.8  B  b
5       104.0  104.0  106.8  B  b
6       104.8  104.0  106.8  B  b
7       105.6  104.0  106.8  B  b

numpy.finfo can be used to understand how floats are stored on your machine.

[RaphaelRosset]

Hi @abhinav-thimma,
yes I fully understand that this issue comes from floating point precision handling and then 104.0 is stored as 103.99999999999999 creating then the issue when looking for closest value less than or equal.

In my use case I cannot switch to nearest because if my value was really 103.99... then mapping to key 98.0 would be correct.
So the result you get using nearest is not the one I expect (see my expected behavior output)

I have currently implemented a workaround to fix this by creating new versions of CONTINUOUS and START columns of the 2 dataframes into integer columns as precision I need which are then used by merge_asof. This is the code of same example using this workaround:

left_df = pd.DataFrame({"CONTINUOUS": list(np.arange(100.0, 106.0, 0.8))})
data = [
    (98.0, 103.4, "A", "a"),
    (104.0, 106.8, "B", "b"),
]
right_df = pd.DataFrame(data, columns=["START", "END", "C1", "C2"])


left_df["CONTINUOUS_integer"] = left_df["CONTINUOUS"].round(6) * 1000000
right_df["START_integer"] = right_df["START"].round(6) * 1000000

output = pd.merge_asof(
    left_df.sort_values(by="CONTINUOUS_integer"),
    right_df.sort_values(by="START_integer"),
    left_on="CONTINUOUS_integer",
    right_on="START_integer",
    direction="backward",
)

output = output.drop(
    columns=[
        "CONTINUOUS_integer",
        "START_integer",
    ]
)

print(output.to_string())