17 June, 2017

Galois LFSR PRNG in NeoPixel goggles

I've been playing with software to run on my Adafruit Neopixel Goggles. The software gets to make pretty patterns on 32 x 24-bit RGB LEDs arranged in two rings.

One of the modes picks random colours to change each ring to. The Arduino stack supplies a random() function to do this, but it seemed to take up about 600 bytes of the limited 5kb flash program memory on the in-goggles microcontroller.

I wondered if I could make a smaller-but-less-random generator. After all, the colour pattern does not need to be cryptographically secure. I'm just trying to avoid getting the same sequence of colours every time.

Someone pointed me at Linear Feedback Shift Register PRNGs and I implemented one based around a description in Wikipedia. I chose the Galois one because pistols at dawn.

That seemed to work well for the basic generation of random numbers, but the Arduino always started up with the same seed, and so gave the same sequence of colours each time. Luckily, there are 512 bytes of EEPROM on this microcontroller and so I used two other those to generate and store a seed to be used next time.

Initially, I generated two random bytes at power-on, and stored those into the EEPROM. However, this rapidly proved to have a really short period: there were only two different patterns being displayed by the goggles in this mode!

So, next, which seems to work better, the code now initialises the PRNG from EEPROM, takes a single bit from it (and discards it) and then writes out the PRNG state into the EEPROM. That means that the start state advances by one bit every boot.

Code for the goggles is here on github: https://github.com/benclifford/goggles.

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