On Wednesday 19 September 2007 14:20, Timothy Normand Miller wrote: > We've talked a lot about multipliers recently, and in the past, we've > talked about floating point adders, multipliers, and reciprocal. > > Another interesting function that might be good to implement is the > logarithm. In fact, I think we may actually need that to do > MIP-mapped textures. > > But there are more general applications. I've studied various > problems in AI where numberous probabilities must be multiplied > together, for instance in hidden markov models. (HMMs). To avoid > having to multiply smaller and smaller numbers, people commonly switch > to log space. Instead of multiplying small positive numbers, you add > large negative numbers. Logs of probabilities are commonly referred > to as "likelihoods" or "log likelihoods." I don't remember enough > about the math to explain the advantage, but apparently, there is one.
Am I too old? Adding logs instead of multiplying (And subtracting instead of dividing) was how I learnt to do multiplication adn division before you werte allowed to use calculators in school exams (Early 1980's in NZ :) In the mid-late 80's we also used methods like this for steam calculations (Water table calculations were quite unweildy things to work with in those days. I wonder whether they still use tables or calculate that nowadays). Didn't some early processors (e..g Pentium floating point bug) use a similiar method for multiplication and division by keeping what was essentially a log table in ROM and the microcode would lookup a log, add/subtract & convert back instead of trying to do multiplication/division longhand? Come to think of it, would it be more efficient (Thinking of time & logic vs table lookup space) to use a lookup table to caluclate log/alog like using Eton tables in the old days? Or actually calculating it? Hamish. _______________________________________________ Open-graphics mailing list [email protected] http://lists.duskglow.com/mailman/listinfo/open-graphics List service provided by Duskglow Consulting, LLC (www.duskglow.com)
