Solving differential equations on a 6502 with Woz's floating point code • Hacker News Board

Re: Solving differential equations on a 6502 with Woz's floating point code

#11

Post by pvg » Fri, Aug 02, 2019, 4:00 AM UTC

keithnz wrote: post #5

I find it funny that people enjoy the nostalgia of things like 6502... I loved my Atari 800XL, but wistfully dreamed that computers might one day be able to handle 320x240 with 256 colours.... boy... that would be good! Meanwhile I was hand assembling 6502 into data sections in basic so I could try and draw a circle... who knew drawing circles was so ridculously difficult and slow? Having said that, I do like this st…

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"

Re: Solving differential equations on a 6502 with Woz's floating point code

#12

Post by ben165 » Fri, Aug 02, 2019, 5:23 AM UTC

diydsp wrote: post #8

Is that first-order approximation appropriate for iteratively solving the Diff EQ? Or does a higher order method such as Runge-Kutta have to be used? I notice the graphs don't align perfectly...

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).

Re: Solving differential equations on a 6502 with Woz's floating point code

#13

Post by pascal_cuoq » Fri, Aug 02, 2019, 10:39 AM UTC

markrages wrote: post #6

keithnz wrote: post #5

I find it funny that people enjoy the nostalgia of things like 6502... I loved my Atari 800XL, but wistfully dreamed that computers might one day be able to handle 320x240 with 256 colours.... boy... that would be good! Meanwhile I was hand assembling 6502 into data sections in basic so I could try and draw a circle... who knew drawing circles was so ridculously difficult and slow? Having said that, I do like this st…

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

Using a CORDIC algorithm would mean having many iterations to compute trigonometric functions for each drawn point (well, for each 8 points considering the symmetries). A variant of the Bresenham line algorithm for circles lets you draw a circle using only a few operations per 8 points (and the operations are also limited to add and shift):

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

Re: Solving differential equations on a 6502 with Woz's floating point code

#14

Post by cmrdporcupine » Fri, Aug 02, 2019, 1:07 PM UTC

keithnz wrote: post #5

I find it funny that people enjoy the nostalgia of things like 6502... I loved my Atari 800XL, but wistfully dreamed that computers might one day be able to handle 320x240 with 256 colours.... boy... that would be good! Meanwhile I was hand assembling 6502 into data sections in basic so I could try and draw a circle... who knew drawing circles was so ridculously difficult and slow? Having said that, I do like this st…

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.