fix: enforce incomplete gamma argument domains

[truemagic-coder]

Summary

Fix incomplete gamma handling to match the documented stdlib specification.

For x >= 0, p may be a positive integer or positive real.

For x < 0, p must be a positive integer. Real-p overloads reject the call.

Changes

• Keep negative-x support for integer-p overloads.
• Reject negative x in real-p overloads.
• Validate p > 0 before special-case returns.
• Fix log_lower_incomplete_gamma(p, 0) to return -Inf.
• Remove the invalid real-p negative-x path.
• Keep generated gamma code clean under strict uninitialized diagnostics.

Tests

Added coverage for:

• positive integer and non-integer p with nonnegative x
• positive integer p with negative x
• rejection of real p with negative x
• rejection of zero and negative p
• lower and upper incomplete gamma
• logarithmic lower and upper incomplete gamma
• log_lower_incomplete_gamma(p, 0) == -Inf
• generated single- and double-precision paths

Negative-x integer-p regressions use a relative tolerance of 128*epsilon(kind).

Verification

GNU Fortran 15.2.0 locally:

• focused gamma tests: 2/2 passed
• strict -Werror=maybe-uninitialized check: passed
• full stdlib suite: 428/428 passed twice

Independent verification by FalseGreen also passed the branch-specific gamma/specification gates.

Assisted-By: Codex

[jvdp1]

Thank youj for this fix, @truemagic-coder .
Should the specs be also updated?

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 68.33%. Comparing base (9a15c77) to head (32979dc).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1203      +/-   ##
==========================================
+ Coverage   68.20%   68.33%   +0.12%     
==========================================
  Files          19       19              
  Lines        2378     2378              
==========================================
+ Hits         1622     1625       +3     
+ Misses        756      753       -3     

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[truemagic-coder]

I missed the documented constraint for negative x. For x < 0, p must be a positive integer.

I’m fixing the implementation and tests against the spec now, then I’ll rerun the full test suite and verification.

[truemagic-coder]

I found two contract issues while checking this against the spec.

Real p must reject negative x. Also, the public wrappers currently return early for x == 0, which lets p <= 0 bypass validation.

I’m fixing both and adding explicit rejection tests before pushing the update.

[truemagic-coder]

Hi @jvdp1

I missed part of the written spec in the first pass.

After going back through it, the spec does not need to be updated. It is already clear that for x < 0, p must be a positive integer.

I found a few implementation issues while aligning the code to that contract.

Real p now rejects negative x, and p <= 0 is checked before the x == 0 special cases. log_lower_incomplete_gamma(p, 0) also returned 0 instead of -Inf, which is now fixed.

Those cases now have regression coverage.

The focused gamma tests pass, the strict compiler diagnostic passes, and the full suite passes 428/428 twice locally with GNU Fortran 15.2.0.

Updated commit: 32979dc.

Thanks!

[Copilot]

Pull request overview

This PR updates stdlib_specialfunctions_gamma to enforce the documented argument domains for incomplete gamma routines, especially around negative x handling and p > 0 validation, and expands the test suite to cover these domain rules and edge cases like log_lower_incomplete_gamma(p, 0).

Changes:

• Enforce p > 0 checks and reject negative x for real-p incomplete gamma overloads; preserve negative-x behavior for integer-p overloads.
• Fix log_lower_incomplete_gamma(p, 0) to return -Inf (instead of 0).
• Add new tests for negative-x integer-p behavior, x=0 log-lower behavior, and invalid-argument rejection (via a separate test program).

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
test/specialfunctions/test_specialfunctions_gamma.fypp	Adds new positive/negative-domain and x=0 log-lower tests.
test/specialfunctions/test_specialfunctions_gamma_invalid.fypp	New test program that asserts invalid domains are rejected.
test/specialfunctions/CMakeLists.txt	Registers the new invalid-argument test in CMake.
src/specialfunctions/stdlib_specialfunctions_gamma.fypp	Enforces domain rules, fixes log_lower_incomplete_gamma(p,0), and addresses uninitialized-result warnings.
CHANGELOG.md	Notes the incomplete-gamma domain enforcement and diagnostics fix under Unreleased.

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