Thought I'd dive into this cool streaming/approximation algorithms problem I encountered a few months ago.

TLDR: we can create our own custom floating point representation for encoding and decoding integers and use this to index into a tiny 2D histogram, upper-bounding approximation error based on the number of bits per integer we specify to keep.

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Broadly useful for aggregating statistics from massive data streams of user data. Also turns out this is incredibly similar to data structures used in production, like HDRHistogram.