[PWGCF] FactorialMoments: replace subsampling error calculation with merge-safe slot pooling

[baasingh]

1. The task no longer subsamples events: each event is hashed into one of nSlots buckets (slot = splitmix64(globalBC) % nSlots) and only merge-safe partial sums are stored — slots/nEv, slots/sumOcc_pt{i}, slots/sumFq_pt{i}_o{q} — as plain histograms, so hadd adds them cell-by-cell; a merged campaign file is then the same object as a single one-go run (no per-file counter, no RNG in the subsampling).
2. The subsample size K becomes a post-processing choice: local code pools consecutive non-empty slots greedily into K-event groups (any K; keepTail option; K=0 = ratio-of-sums limit) and evaluates Fq exactly as the old path did: Fq = mean over groups of (Sfq/n)/(Socc/n)^q.
3. slots/params (bin1 = number of jobs, bin2 = sum of their nSlots) makes a hadd mixing jobs with different nSlots fail loudly — otherwise invisible, because hadd keeps the first axis and the event totals still balance.
4. Fixes vs the current upstream task: explicit falling-factorial product loop (upstream's TMath::Factorial overflows for n ≥ 171 and poisons pt bin 1, M=4 at all orders); smearPhi option (Gaussian phi randomisation, default off; shipped configs on).`

[github-actions]

O2 linter results: ❌ 0 errors, ⚠️ 21 warnings, 🔕 0 disabled

[alibuild]

Error while checking build/O2Physics/staging for 6a47396 at 2026-10-16 14:40:

## sw/BUILD/O2Physics-latest/log
collect2: error: ld returned 1 exit status
ninja: build stopped: subcommand failed.

Full log here.

[alibuild]

Error while checking build/O2Physics/code-check for 6a47396 at 2026-10-17 08:03:

## sw/BUILD/O2Physics-code-check-latest/log
--
========== List of issues found ==========
++ echo 'To reproduce the results below locally, run: '\''aliBuild build O2Physics-code-check -e ALIBUILD_BASE_HASH=upstream/master'\''.'
To reproduce the results below locally, run: 'aliBuild build O2Physics-code-check -e ALIBUILD_BASE_HASH=upstream/master'.
++ echo 'To apply all automatic fixes, add the '\''-e O2PHYSICS_CHECKER_FIX=1'\'' option.'
To apply all automatic fixes, add the '-e O2PHYSICS_CHECKER_FIX=1' option.
++ echo 'See the documentation for more details at: <https://aliceo2group.github.io/analysis-framework/docs/tools/#running-with-o2physics-code-check>.'
See the documentation for more details at: <https://aliceo2group.github.io/analysis-framework/docs/tools/#running-with-o2physics-code-check>.
++ echo 'Found 3 errors and 0 warnings.'
Found 3 errors and 0 warnings.
++ [[ 3 -gt 0 ]]
++ cat /sw/BUILD/afbd8fd5dd9dc4f7eaa2eadb8686f0f4876c1499/O2Physics-code-check/errors.txt
PWGCF/EbyEFluctuations/Tasks/FactorialMomentsTask.cxx:42:1: error: included header RtypesCore.h is not used directly [misc-include-cleaner,-warnings-as-errors]
PWGCF/EbyEFluctuations/Tasks/FactorialMomentsTask.cxx:132:5: error: no header providing "o2::framework::OutputObjHandlingPolicy" is directly included [misc-include-cleaner,-warnings-as-errors]
PWGCF/EbyEFluctuations/Tasks/FactorialMomentsTask.cxx:560:46: error: no header providing "BIT" is directly included [misc-include-cleaner,-warnings-as-errors]
++ [[ 0 -gt 0 ]]
++ [[ 3 -gt 0 ]]
++ exit 1
--

Full log here.

[vkucera]

Hi @baasingh , please try to make it clearer from the PR title what you changed and where. You can find some tips in the contribution guidelines. https://aliceo2group.github.io/analysis-framework/docs/gettingstarted/contributingtocode.html#pull-requests

[baasingh]

Hi @baasingh , please try to make it clearer from the PR title what you changed and where. You can find some tips in the contribution guidelines. https://aliceo2group.github.io/analysis-framework/docs/gettingstarted/contributingtocode.html#pull-requests

Thanks — Renamed PR to name the task and the change.

[vkucera]

Hi @baasingh , please try to make it clearer from the PR title what you changed and where. You can find some tips in the contribution guidelines. https://aliceo2group.github.io/analysis-framework/docs/gettingstarted/contributingtocode.html#pull-requests

Thanks — Renamed PR to name the task and the change.

Thank you!