What case-insensitivity algorithm is used by Windows to decide if two filenames are the same?

I want to know so I can roughly replicate this in code that doesn't run on Windows. I say "roughly" because apparently this is basically impossible to do robustly, but fortunately that doesn't matter for my use case.

There are some other questions around this such as this one and this one and some articles like this one, but they all assume I can use Win32 APIs to do the case conversion/comparison.

How do I do it if my code is not running on Windows?