Some speech recognizers and machine learning algorithms need to quickly calculate the quantity:
when given only and
. The straightforward algorithm first uses the exponential function to convert the log values to the linear domain representation
and
, then performs the sum, and finally uses the log function to convert back to the log domain:
These conversions between log and linear domains are slow and problems arise when is too large or small for a machine’s floating point representation.
Luckily, there is a clever approximation method that allows quick, accurate calculation with a relatively small precomputed table.