Just sharing some notes I compiled while building Mediant32, an alternative to fixed-point and floating-point for error-aware fraction computations. I was experimenting with continued fractions, the Stern-Brocot tree, and the field of rationals for my programming language. My overarching goal was to find out if I could efficiently represent floats using integer fractions. Along the way, I compiled these notes to share all the algorithms I found for working with powers, inverses, square roots and logarithms (all without converting to floating point) I call it Mediant32 and the number system features: 1. Integer-only inference. (Zero floating point ops) 2. Error aware training and inference. (You can accumulate errors as you go) 3. Built-in quantization for individual matrix elements. (You're working with fractions so you can choose numerators and denominators that align with your goals)