cache optimization

Kaze Emanuar searches for the best sine approximation for the Nintendo 64, comparing the lookup tables in Mario 64 and Ocarina of Time with polynomial alternatives. It walks through numerics and 3rd, 4th and 5th order approximations.

Matt Parker follows the community effort to speed up his slow Wordle-solving code, which ended up running hundreds of millions of times faster. He walks through the techniques contributors used.

A walkthrough of the Quake III fast inverse square root, explaining where the constant 0x5f3759df comes from. It covers IEEE 754 floats, the bit hack that approximates a logarithm, and a Newton's method refinement.

Tom 7 (suckerpinch) delivers a long, comedic digression on gradient descent and floating-point imprecision. He shows how rounding behavior can supply the nonlinearity needed to build a neural network.

3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.