I have a gut feeling that there is a faster way to compute logarithms going from least to most significant bit. How would I go about using ML to find it? [Edit

I have a gut feeling that there is a faster way to compute logarithms going from least to most significant bit. How would I go about using ML to find it? [Edit] I think Feynman's algorithm might do it: "Consider the problem of finding the logarithm of a fractional number between 1 and 2. (The algorithm can be generalized without too much difficulty.) Feynman observed that any such number can be uniquely represented as a product of numbers of the form 1 + 2^(-k), where k is an integer. Testing for the presence of each of these factors in a binary representation is simply a matter of a shift and a subtraction. Once the factors are determined, the logarithm can be computed by adding together the precomputed logarithms of the factors. The algorithm fit the Connection Machine especially well because the small table of the logarithms of 1 + 2^(-k) could be shared by all the processors. The entire computation took less time than doing a division."