Adding “Rounding half to even”

[wany-oh]

Description

In python, round() usually means “Rounding half to even”, but polars Series.round()/Expr.round() do not. It should be adding an argument such as to_even to the method. At the very least, there should be a note in the documentation.

round(0.5)  # -> 0
np.round(0.5)  # -> np.float64(0.0)
pd.Series(0.5).round()[0]  # -> np.float64(0.0)

pl.Series([0.5]).round().item()  # -> 1.0

expected:

pl.Series([0.5]).round(to_even=True).item()  # -> 0.0

[eitsupi]

I was surprised that Polars' round is not "bankers rounding".
This could be a fatal weakness for precise calculations.

>>> pl.Series([0.5, 1.5, 2.5]).round()
shape: (3,)
Series: '' [f64]
[
        1.0
        2.0
        3.0
]

Note that this is also introduced in Rust as round_ties_even (rust-lang/rust#96710).

[johnchristopherjones]

It's also specifically not what numpy does:

In [226]: round(0.3125, 3)
Out[226]: 0.312

In [227]: np.round(0.3125, 3)
Out[227]: np.float64(0.312)

In [228]: pl.Series([0.3125]).round(3)
Out[228]: 

shape: (1,)
Series: '' [f64]
[
        0.313
]

It is often useful to be able to switch strategies when coordinating with a party that uses the "wrong" strategy. But, even IEEE754 recommends rounding ties towards even as the default.

The prevalence of the half-up strategy seems to be mostly due C predating IEEE754 and languages directly importing C's default round behavior. Most languages that are either geared towards numerical analysis or are just plain newer seem to default to half-even.

Quick biased survey:

Half-up

• C
• Ruby
• Excel

Half-Even

• Python (builtin, NumPy, Pandas, not Polars)
• Swift
• Julia
• R
• Haskell
• Racket

[cmdlineluser]

I just learned of this difference from a recent Stack Overflow question¹ where a user was trying to speed up a map_elements function that used Python's round().

I see that rounding was just added for Decimal on main which defaults to round to even: #19760

pl.select(pl.lit(0.5).round())
# shape: (1, 1)
# ┌─────────┐
# │ literal │
# │ ---     │
# │ f64     │
# ╞═════════╡
# │ 1.0     │
# └─────────┘

pl.select(pl.lit(0.5, dtype=pl.Decimal).round())
# shape: (1, 1)
# ┌───────────────┐
# │ literal       │
# │ ---           │
# │ decimal[38,0] │
# ╞═══════════════╡
# │ 0             │
# └───────────────┘

Footnotes

1. https://stackoverflow.com/questions/79192572/ ↩

[orlp]

This was fixed in #22248.