Simple description : This is a custom binary number system designed to calculate vector dot products.

Technical description : FMA's complement is a fixed-point representation of binary numbers created — as an alternative to 2’s complement and 1’s complement — to perform the Fused Multiply-Add instruction.

We combine linear algebra and arithmetic codes (from data compression theory) to make a number system great for finding dot products.

Motivation I took a gap year to start a data compression startup (this was a mistake, I know) so I spent the past year working with Arithmetic Coders. I was trying to build a lookup table with random matrices and I saw patterns.

From my year's long experience with data compressors - patterns should NOT exist in random data. I built this because, I could (with reasonable accuracy) estimate dot products using a lookup table.

This is the GitHub repo accompanying the article - https://github.com/Fileforma/FMA-Complement