i think i came to the conclusion of 0x5f375a84 at the end of that article. at least by the criteria the test program used to measure error.
the differences are tiny though, and there are other measures that can be used (which will result in different constants)
in any case, on most modern hardware it is not relevant since there is some lookup based instruction that is more accurate, and faster.
the problems here aren't enormous, a smart programmer will work them out for himself, but they are misleading. i think there is some confusion just because this is a low-level API, essentially a hardware abstraction layer, but the user is expecting high level features like a complete maths library. (maybe?)
Also, what's the final verdict on Fast InvSqrt()? Is the optimal magic number Q3's 0x5f3759df, Chris's 0x5f375a86, or your 0x5F375A7F?