A decoder D̂: {0,1}^B → ℝ is bit-manipulation decodable (BMD) if expressible as a fixed-length straight-line program over {+,−,×,≫,≪,&,|,⊕} on machine-word integers with output reinterpreted as float via type punning. Three BMD realizations for log-uniform decoding: lookup table (O(N) storage), reinterpret cast / Quake trick (3 ops), and quadratic approximation (5 ops, 0.27% max error).
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