They are more closely related than you suggest. Both methods are using an approximation of log2 to get an initial guess. One gets it from "FPS(n)", the other gets it from the floating point representation of n, where you can roughly find the log2(n) by looking at the exponent of n in the float representation. You can also use the mantissa to refine the guess further.
They are related a little, around the log2 (exponent), I totally agree. I guess I figured the magic number subtraction that turns it into n^(-1/2) is so wild that it puts the Quake trick in a bit of a different class. This right shift thing is a lot older and there’s probably a lineage of ideas from the right shift on integers to the Quake trick. I discovered another fun one on my own that is probably already well known in bit-math circles, but simply inverting the bits of a floating point exponent is a very rough approximation to the reciprocal, good for a Newton initial guess.
