Fix the dead Test-extension guard in the error hint

[devmotion]

Fix the extension name in the error hint. The guard queried :InverseFunctionsTest, but the extension is registered as InverseFunctionsTestExt. Base.get_extension returns nothing for an unknown name rather than erroring, so the guard was permanently true and "Did you forget to load Test?" was appended to every test_inverse MethodError — including ones raised while Test is loaded.

Tests cover both directions: with Test loaded, a wrong-arity MethodError carries no hint; without Test (checked in a subprocess, since Test can't be unloaded), the hint is shown and hasmethod(test_inverse, Tuple{Any,Any}) is false. Tests pass on Julia 1.6, 1.10, 1.11 and 1.13.

An earlier version of this PR also removed __init__ to save load time. That cost turned out to be a @time_imports measurement artifact (see the discussion below), so __init__ and the error hint stay.

Closes #66 (version bumped to 0.1.18 here).

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.50%. Comparing base (0434eba) to head (aabdd9b).

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #67      +/-   ##
==========================================
+ Coverage   98.48%   98.50%   +0.02%     
==========================================
  Files           6        6              
  Lines         132      134       +2     
==========================================
+ Hits          130      132       +2     
  Misses          2        2              

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[timholy]

Could you fix the timing issue with precompile(__init__, ())? If it does, one small plus is that it would keep an external package's hasmethod(test_inverse, ...) giving an informative error.

[devmotion]

Thanks, this made me dig deeper, and the load-time cost I attributed to __init__ turns out to be a @time_imports artifact rather than a real cost.

Under @time_imports, Base.run_module_init prints an extra ┌ … ms Pkg.__init__() line, but only for packages that define __init__. It prints that line inside the timing window used for the package's own line. In a fresh session, printing it is the first use of printstyled/with_output_color/print(::IOStream, ::Float64, …), and compiling those takes ~17 ms on 1.10 and ~35 ms on 1.13 (from jl_dump_compiles). That compile time is reported as the package's "~80% compilation time". (On 1.11/1.12 it isn't counted towards the package line.)

Supporting evidence:

• __init__ itself is reported as 0.0 ms.
• An empty __init__ shows the same overhead.
• Calling the same printstyled/print methods before @time_imports drops InverseFunctions on 1.10 from 19 ms / 88% to 2 ms / 0%.
• With plain @elapsed using InverseFunctions, master, master + precompile(__init__, ()), an empty __init__, and this PR are all within noise (1.10: ~18–20 ms; 1.13: ~3–5 ms). jl_dump_compiles shows nothing from InverseFunctions being compiled during a normal load.

So precompile(__init__, ()) has nothing to fix, and there's no reason to remove __init__. I'll cut this PR down to the extension-name fix, keep the error hint (and with it an informative hasmethod(test_inverse, …)), and add tests for the hint. Probably worth an upstream issue about @time_imports counting its own printing too.

[timholy]

Gotcha. Also, I dug around a bit, and we compile __init__ by default (I didn't check, but there's even a chance that I'm the one that added that 😆 ).

[timholy]

Nice catch on @time_imports by the way, I do think that merits a report.

[devmotion]

I reported the finding in JuliaLang/julia#63850