Linear Addition from the Log Domain

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.