Improve expo analytical integral stability

[swetank18]

Motivation

The analytical integral of exponential TF1 functions computes differences of
exponentials, which can suffer from numerical cancellation or overflow when the
integration bounds are close or the exponent is large.

Changes

• Replace the direct difference of exponentials with a numerically stable
  expm1-based formulation

Impact

• Improves numerical robustness without changing the mathematical result
• No API changes

[hageboeck]

This will clash with #20992. Should we close that one?

[swetank18]

This will clash with #20992. Should we close that one?

Thanks for pointing this out.
Both PRs are mine — the earlier one (#20992) introduced the initial change, and this PR refines it with improved numerical stability.
If you prefer, I’m happy to close #20992 and keep everything here, or alternatively rebase/split to avoid overlap — whatever you think is cleaner.

[hageboeck]

If you prefer, I’m happy to close #20992 and keep everything here, or alternatively rebase/split to avoid overlap — whatever you think is cleaner.

Let's move it here, so we can save a few CI runs.

[github-actions]

Test Results

     7 files       7 suites   14h 51m 57s ⏱️
 3 747 tests  3 746 ✅ 0 💤 1 ❌
21 036 runs  21 031 ✅ 0 💤 5 ❌

For more details on these failures, see this check.

Results for commit f3dcfcc.

[hageboeck]

The tests seem to fail because the commit from #20993 is not in here, but the tests rely on this behaviour. So maybe we should do the following:

• Cherry-pick and rebase.
  • Interactive rebase, squashing the "stabilise" commit with its clang-format.
  • Cherry-pick the commit from Add parameter domain checks to analytical integrals #20993 into this branch.
  • And put the tests last, so everything stays green in between these commits.
  • And maybe update the PR description to reflect these changes.
• Alternatively, one could move the parameter domain test into Add parameter domain checks to analytical integrals #20993, but I doubt that this is less work.

@swetank18, what do you think?

[swetank18]

The tests seem to fail because the commit from #20993 is not in here, but the tests rely on this behaviour. So maybe we should do the following:

* Cherry-pick and rebase.
  
  * Interactive rebase, squashing the "stabilise" commit with its clang-format.
  * Cherry-pick the commit from [Add parameter domain checks to analytical integrals #20993](https://github.com/root-project/root/pull/20993) into this branch.
  * And put the tests last, so everything stays green in between these commits.
  * And maybe update the PR description to reflect these changes.

* Alternatively, one could move the parameter domain test into [Add parameter domain checks to analytical integrals #20993](https://github.com/root-project/root/pull/20993), but I doubt that this is less work.

@swetank18, what do you think?

Thanks, that makes sense to me.
I’m happy to follow that approach: I’ll consolidate the commits with an interactive rebase, cherry-pick the parameter domain checks from #20993, and ensure the tests come last so CI stays green throughout. I’ll also update the PR description accordingly.

[swetank18]

The tests seem to fail because the commit from #20993 is not in here, but the tests rely on this behaviour. So maybe we should do the following:

* Cherry-pick and rebase.
  
  * Interactive rebase, squashing the "stabilise" commit with its clang-format.
  * Cherry-pick the commit from [Add parameter domain checks to analytical integrals #20993](https://github.com/root-project/root/pull/20993) into this branch.
  * And put the tests last, so everything stays green in between these commits.
  * And maybe update the PR description to reflect these changes.

* Alternatively, one could move the parameter domain test into [Add parameter domain checks to analytical integrals #20993](https://github.com/root-project/root/pull/20993), but I doubt that this is less work.

@swetank18, what do you think?
Apologies for the delay — I was unwell for a few days.
I’ve now completed the consolidation as discussed and updated the branch accordingly. Please let me know if you’d like anything adjusted.