DDS (direct digital synthesis) was originally developed for producing high quality sine waves.

In a DDS generator the RAM address increment rate is determined from a fixed clock frequency by a digital block comprising a phase increment register and a phase accumulator.

A description of the DDS technique is available here: DDS Technical

Most digital function generators now use DDS which has been further developed into a system for arbitrary waveform generation.  Unless stated otherwise, a typical arbitrary/function generator will use DDS for all its waveforms including arbitrary.