[C++][Python] tdigest and hash_tdigest return NaN for q outside [0, 1]; quantile raises #55372

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

pyarrow.compute.tdigest and hash_tdigest accept a q outside [0, 1] and return NaN, while quantile rejects the same value with ArrowInvalid. TDigestOptions documents the range as a requirement.

import pyarrow as pa
import pyarrow.compute as pc

print(pa.__version__)
a = pa.array([1.0, 2.0, 3.0])
for fn in (pc.quantile, pc.tdigest):
    try:
        print(fn.__name__, fn(a, q=[0.5, 1.5]).to_pylist())
    except pa.ArrowInvalid as e:
        print(fn.__name__, type(e).__name__, e)

t = pa.table({"k": [1, 1, 1], "v": [1.0, 2.0, 3.0]})
agg = t.group_by("k").aggregate([("v", "tdigest", pc.TDigestOptions(q=[7.0]))])
print(agg.to_pylist())

$ python -I td.py    # pyarrow 26.0.0 wheel, Python 3.12, Linux x86_64
26.0.0
quantile ArrowInvalid Quantile must be between 0 and 1
tdigest [2.0, nan]
[{'k': 1, 'v_tdigest': [nan]}]

contract: TDigestOptions.q in python/pyarrow/_compute.pyx:2388 ("All values must be in [0, 1]"), and cpp/src/arrow/compute/api_aggregate.h ("probability level of quantile must be between 0 and 1 inclusive").

CheckQuantileOptions (cpp/src/arrow/compute/kernels/aggregate_quantile.cc:482, a99464f on main) returns Status::Invalid("Quantile must be between 0 and 1") for any q outside the range. Neither aggregate_tdigest.cc nor GroupedTDigestImpl in hash_aggregate_numeric.cc (the separate hash_tdigest kernel) checks q, and TDigest::Quantile in cpp/src/arrow/util/tdigest.cc returns NAN for q < 0 || q > 1.

Expected: ArrowInvalid for any q outside [0, 1], from a shared check called by both the tdigest and hash_tdigest inits, with the message quantile uses.

I read the source at a99464f and ran the 26.0.0 wheel, not a source build. I did not check how q=NaN should behave: quantile also lets it through.

I can open a PR with the check and tests in test_compute.py, kernels/aggregate_test.cc and acero/hash_aggregate_test.cc. Would you take it?

Component(s)

C++, Python