arithmetic

John Gustafson presents posits, a proposed drop-in replacement for IEEE 754 floats that is simpler in hardware and more flexible in precision. The seminar includes a live demo and machine learning results.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

A 95-minute recorded debate at the ARITH23 computer arithmetic conference between John Gustafson, proponent of unums/posits, and William Kahan, architect of IEEE 754 floating point. They argue the merits of the new number formats versus conventional floats and interval arithmetic.

Bill Dally of NVIDIA gives a University of Washington lecture on trends in deep learning hardware. It covers numeric formats, specialized instructions, energy per operation and co-design of hardware and software.

Aditya Siram introduces ATS, a statically typed ML-like language that compiles to C and offers type-safe pointer arithmetic and a full proof language. The Strange Loop talk shows off C interop, concurrency and verification features with non-trivial examples.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

A London Haskell talk on the algebra of algebraic data types, showing how sum and product types behave like arithmetic. It frames types as numbers obeying algebraic laws.