[Python][C++][Compute] Fix correctness of decimal round_binary kernel #50641

Describe the bug, including details regarding any error messages, version, and platform.

The round_binary kernel for decimal input does not properly compute the halfway remainder point (half_pow10) elementwise based on the actual ndigits. Instead it is always computed as if ndigits is 0. This leads half_pow10 to be off by a factor of 10^(ndigits) and throws off the rounding logic.

import pyarrow as pa
import pyarrow.compute as pc
from decimal import Decimal

>>> pc.round_binary(Decimal("2.89"), 1)
<pyarrow.Decimal128Scalar: Decimal('2.80')>   # should be 2.9
>>> pc.round_binary(Decimal("-5.927"), 2)
<pyarrow.Decimal128Scalar: Decimal('-5.920')>   # should be -5.93
>>> pc.round_binary(Decimal("-134.2"), -1)
<pyarrow.Decimal128Scalar: Decimal('-140.0')>   # should be -130.0
>>> pc.round_binary(Decimal("211"), -2)
<pyarrow.Decimal128Scalar: Decimal('300')>    # should be 200

It also falls through to a no-op for any decimal input with negative scale.

negative_scale_input = pa.scalar(Decimal("3700"), type=pa.decimal128(4, -2))
>>> pc.round_binary(negative_scale_input, -3)
<pyarrow.Decimal128Scalar: Decimal('3.7E+3')>    # should be 4.0E+3

In summary, decimal round_binary returns the wrong answer when ndigits < scale (the standard case when rounding) AND one of the following are true:

• Scale < 0
• One of the rounding modes HALF_DOWN, HALF_UP, HALF_TOWARDS_ZERO, HALF_TOWARDS_INFINITY, HALF_TO_EVEN, or HALF_TO_ODD are used, AND:
  • ndigits > 0 and input is closer to ceil(input, ndigits) than floor(input, ndigits), OR
  • ndigits < 0, abs(input) % 10^(-ndigits) > 0.5 (true 90% of the time for ndigits == -1, and even more likely for ndigits < -1), and input is closer to ceil(input, ndigits) than floor(input, ndigits),

The only cases when decimal round_binary gets the right answer are when:

• ndigits == 0,
• ndigits >= scale (no rounding needed),
• scale >= 0 and either of the following are true:
  • One of the rounding modes DOWN, UP, TOWARDS_ZERO, or TOWARDS_INFINITY are used
  • ndigits < 0 and abs(input) % 10^(-ndigits) <= 0.5, which is rare
• OR a buggy round-to-nearest mode is used and happens to return the nearest number just by luck

Thus we conclude that decimal round_binary is completely unreliable at the moment for the most common rounding modes when ndigits != 0, only getting the correct answer for about 50% of inputs by chance. This is a major issue since the only reason one would want to use round_binary over round in the first place is if some elements should be rounded to nonzero ndigits of precision.

See the current implementation:

Aside: there's also a bug in the decimal implementation of HALF_TO_ODD here:

This should be scaled += remainder.Sign() >= 0 ? 1 : -1; similar to what the HALF_TO_EVEN mode does.

Here is the effect of the bug:

>>> pc.round(Decimal("-52.5"), 0, "half_to_odd")
<pyarrow.Decimal128Scalar: Decimal('-51.0')>   # should be -53.0

Component(s)

C++, Python