This is absolutely wild. Rendering graphics with just combinational logic and no frame buffer is the kind of constraint that breeds creativity.
The HAKMEM sine/cosine generator is such an elegant choice - it's numerically stable in fixed-point and requires only adds and bit-shifts. Perfect for hardware. I used a similar approach once for generating test patterns in an FPGA.
The fact that you can iterate on this in simulation, then deploy to actual silicon via Tiny Tapeout for $150 is honestly mind-blowing. We're living in the future.
How does this compare to CORDIC for sin/cos generation? Which is more accurate, etc ?
Good question! CORDIC and HAKMEM Item 149 are both hardware-friendly, but have different trade-offs:
CORDIC: - Iterative algorithm (needs multiple clock cycles) - Accuracy improves with more iterations - Generates both magnitude and phase - Typical hardware implementation: 12-16 iterations for decent precision
HAKMEM (Item 149): - Single-cycle computation (just two adds per step) - Uses the recurrence: x' = x - εy, y' = y + εx - Accuracy depends on word width and epsilon choice - Numerically stable in exact arithmetic if ε² < 2
CORDIC is more accurate, but takes as many iterations as you have bits of precision in your angle. Another demo called Warp in this contest used pipelined CORDIC to do atan2 on every pixel to create a tunnel, which is super impressive.
https://www.youtube.com/watch?v=K9mu3getxhU&t=780s
> The fact that you can iterate on this in simulation, then deploy to actual silicon via Tiny Tapeout for $150 is honestly mind-blowing. We're living in the future.
It's really cool but it doesn't seem practical at all. They aren't setting up print runs, just one-offs (https://tinytapeout.com/faq/#how-many-chips-will-i-receive-c...) and $150 could get you... many orders of magnitude more power than that.
... For that matter, apparently the microcontroller in the dev kit is a https://en.wikipedia.org/wiki/RP2040 , which seems like a beast in comparison. And it's still available for less than $1 USD on PiShop.
Tiny Tapeout's schtick is that for $150 you can get your chip design made at all. It's not a mass production run.
Remind me to participate in the next one!