Fast Synthesis of Basic Oscillators

I’ve been working on synthesizers for the GBA and rp2040 the past couple years, and I’ve made some fast oscillators. So first of all, this all applies to doing synthesis with integers. I think for oscillators, even if you do have an FPU, ints are much easier to deal with anyway because of the wrapping. We’ll be doing math entirely with 32-bit values in this post, for two reasons. One is, it’s the native register size on the GBA, and what I’ve been doing with for the past couple years. The other: it’s a very nice sweet spot for pitch resolution. You can represent all pitches within the audible range quite accurately when dealing with a 32-bit phase. As you reduce the bit-depth of your phase, you start losing pitch accuracy in the bass. You can work with that, and many demosceners do, but it becomes something you have to actively think about when composing your music. With 32-bit, its a non-issue. Anything beyond 32-bit doesn’t really provide much benefit. Most of the waveforms I’m…