Solving differential equations on a 6502 with Woz's floating point code (opens in new tab)

I liked this piece for the attempt to imagine what using an early personal computer was like and getting it wrong in good and interesting ways - statistically nobody had an Apple I and everything later had BASIC and higher level (i.e. not just monitor) CLIs - that was the big selling point. Later there's a bit about maybe using a decimal FP representation and my first thought was 'no, that's nuts' but your mention of the 800XL sent me to the wikipedia page:

"The first is that all numeric values in [Atari] BASIC are stored in floating-point binary coded decimal (BCD) format"

Having spent many hours recently futzing writing code for the 65816, including writing an emulator for a machine based around it, and spending many hours investigating writing a C compiler for it...

I think I might have cured myself of my 6502 nostalgia. I don't want to look at one again for a while.

Were you using a CORDIC algorithm? Bit shifts and adds, no multiplies required.

There's also "Sweet 16", Woz's "16-bit virtual machine" that's in the Apple ][ Integer basic ROMs. Another piece of pure genius code.

https://en.wikipedia.org/wiki/SWEET16

It's the easiest approach to solve the ODL: Euler Forward (yes, first order). The approximation could be much better and almost exact with a smaller step size. Runge-Kutta is used for higher ODL's, where the Euler method would fail (especially with periodic solutions).