A Hardware-Independent Fast Logarithm Approximation with Adjustable Accuracy

Many multimedia applications rely on the computation of logarithms, for example, when estimating log-likelihoods for Gaussian Mixture Models. Knowing of the demand to compute logarithms and other basic math functions rapidly, many hardware manufacturers provide libraries to perform calculations in hardware. Of course, these libraries are especially popular for the use in computer vision or audio analysis algorithms where a large amounts of data have to be processed. A downside of using specialized hardware though is that it increases the investment cost and the user is forced to use the same hardware, which is especially cumbersome when algorithms optimized for different specialized hardware are to be combined. This article presents the realization of a novel platform-independent, fast C-language implementation of the logarithm function. The idea behind the approach is to take advantage of the large amount of cache available in current processors. The logarithm implementation is compared to the current state of the art and we demonstrate the practical use of the algorithm in an actual speech analysis application.