Finding normal binary floating-point factors in constant time

06/10/2021

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by   Mak Andrlon, et al.

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Solving the floating-point equation x ⊗ y = z, where x, y and z belong to floating-point intervals, is a common task in automated reasoning for which no efficient algorithm is known in general. We show that it can be solved by computing a constant number of floating-point factors, and give a constant-time algorithm for computing successive normal floating-point factors of normal floating-point numbers in radix 2. This leads to a constant-time procedure for solving the given equation.