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SMT-based Reasoning About the Fast Inverse Square Root

While there is a mathematical explanation for the choice of 0x5F3759DF in the famous bit-level hack for approximating the multiplicative inverse of the square root of a 32-bit floating-point number, it is not immediately clear to what extent the reasoning is really applicable in the context of machine data types and their peculiarities. This post illustrates how this, and related aspects, can be investigated with SMT-based reasoning about the actual implementation.

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