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This is a colloquium style talk which presents the idea of the "posit", a possible replacement for IEEE 754 floats. He starts talking about posits at the 15 minute mark.
Original paper [here](https://herbie.uwplse.org/pldi15-paper.pdf).
High Performance Correctly Rounded Math Libraries for 32-bit Floating Point Representations
(cs.rutgers.edu)
Abstract: "This paper proposes a set of techniques to develop correctly
rounded math libraries for 32-bit float and posit types. It
enhances our RLibm approach that frames the problem of
generating correctly rounded libraries as a linear programming problem in the context of 16-bit types to scale...