feat(libc): implement the tgammaf export

[Prophet069]

What

Provide the missing single-precision gamma export through the host standard math implementation. Tests exercise factorial values, gamma(1/2), signs, NaNs/infinities, poles, errno, floating-point exceptions and the guest SysV ABI. No nextafter/nextafterf implementation is bundled.

Replaces the obsolete base of closed #2964, which was automatically closed for intake pause. Closed alternatives #4133/#4146 remain unmerged; this draft is for reviewing our existing PR rather than opening another duplicate.

Tested

Windows 10 Pro 22H2 x64 (build 19045), MinGW GCC 15.2.0: built the complete candidate libc.prx from this branch and ran the functional guest_tgammaf regression successfully. Tests use synthetic guest-ABI inputs; no game startup, Linux/macOS build or maintainer CI run is claimed.

Based on main dacd78525e537a779682032c0ace7f7af120af05; candidate d7340163a813c4cceab2622908053dc8ceb87c17. No dumps, runtime packages, investigation reports or images are included. No speed improvement is claimed.

Checklist

• Based on current main; no other open PR implements the same functions
• One topic per PR; follow-ups go in a new PR
• No comments in code except technical debt
• Unimplemented paths throw; no silent success stub added
• No notes, investigation .md files or images added to the repository
• New third-party code: none
• Generic behaviour, not specific to one title
• Depends on: none
• Unblocks: issue for TitleID PPSA02015
• GPUs tested: n/a (libc change)
• AI-assisted: yes; prepared with Codex; the submitting author is responsible for every line

[github-actions]

Progress report (dacd785 → d734016)

➖ System libraries: 88.15% (+0.0%, +1 implemented functions)

✅ 1 implemented

Library	Name
libc	tgammaf_nid_postfix

[CnRJay]

The implementation itself looks fine. The description doesn't name a title that imports tgammaf, though. Since #1205/#1208/#950, reviewers ask new-export PRs for the title ID and the log line where that title stops at the export on main (FAIL: unresolved ELF import ... from libc.prx), and export-only PRs without one have been closed. If you know of a title that reaches it (tools/import_audit.py over a title's imports will show it), adding that to the description should be all that's missing.

[oneandonlydean]

Closing: no title is known to reach this. With the queue at 700+ open PRs, please hold off on new PRs that don't name a title needing the change until it's down. If a title stops on this on current main, reopen with the title ID and the log line.