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and so you can at 1-bit too, and the hardware will be even smaller and cheaper

A LUT is pretty wasteful. You only have a one bit significand, so the mantissa and sign bits are boolean binops, and the exponent is a 2 bit adder.

Low level software engineers use look up tables.

Hardware engineers realise that a compiler will almost always find some combination of gates which is smaller/faster than the contents of any table.