Can you give us a short overview of the SIDs internal architecture ?
It's pretty brute-force, I didn't have time to be elegant. Each "voice" consisted of an Oscillator, a Waveform Generator, a Waveform Selector, a Waveform D/A converter, a Multiplying D/A converter for amplitude control and an Envelope Generator for modulation. The analog output of each voice could be sent through a Multimode Analog Filter or bypass the filter and a final Multiplying D/A converter provided overall manual volume control.
As I recall, the Oscillator is a 24-bit phase-accumulating design of which thelower 16-bits are programmable for pitch control. The output of the accumulator goes directly to a D/A converter through a waveform selector. Normally, the output of a phase-accumulating oscillator would be used as an address into memory which contained a wavetable, but SID had to be entirely self-contained and there was no room at all for a wavetable on the chip.
The Sawtooth waveform was created by sending the upper 12-bits of the accumulator to the 12-bit Waveform D/A.
The Triangle waveform was created by using the MSB of the accumulator to invert the remaining upper 11 accumulator bits using EXOR gates. These 11 bits were then left-shifted (throwing away the MSB) and sent to the Waveform D/A (so the resolution of the triangle waveform was half that of the sawtooth, but the amplitude and frequency were the same).
The Pulse waveform was created by sending the upper 12-bits of the accumulator to a 12-bit digital comparator. The output of the comparator was either a one or a zero. This single output was then sent to all 12 bits of the Waveform D/A.
The Noise waveform was created using a 23-bit pseudo-random <a href="https://www.sequencer.de/specials/sequencer.html">Sequencer</a>uence generator (i.e., a shift register with specific outputs fed back to the input through combinatorial logic). The shift register was clocked by one of the intermediate bits of the accumulator to keep the frequency content of the noise waveform relatively the same as the pitched waveforms. The upper 12-bits of the shift register were sent to the Waveform D/A.
Since all of the waveforms were just digital bits, the Waveform Selector consisted of multiplexers that selected which waveform bits would be sent to the Waveform D/A. The multiplexers were single transistors and did not provide a "lock-out", allowing combinations of the waveforms to be selected. The combination was actually a logical ANDing of the bits of each waveform, which produced unpredictable results, so I didn't encourage this, especially since it could lock up the pseudo-random <a href="https://www.sequencer.de/specials/sequencer.html">Sequencer</a>uence generator by filling it with zeroes.