Interval arithmetic

We're getting all these sparse matrix problems that now solve with 32-bit posits that used to require a 64-bit floating point to do.

If you're doing something like nuclear, that's where I would reach for interval arithmetic.

If there's one place where you need absolute confidence, that would be the best possible benchmark for high-performance computing.

Because you make FFTs faster, you're going to make everything faster.

They had these partial differential equations that have a massive amount of discretization error.

just in there's not enough grid points to do it very accurately you might get maybe a thousand grid points in each direction so you only have an accuracy of a tenth of a percent but because there's 64-bit arithmetic you say well let's at least make sure that the arithmetic rounding error is is not the problem and that then we can just uh worry about dealing with the the the error that we'll make by pretending that a calculator or a computer can do calculus which it can't You have to find out differences instead of real differentiation.

Well, how does your number format deal with that aspect of things, just like the algorithmic error situation? And I remember our mutual friend, Bill Walster and Interval Arithmetic and other efforts and methods to try to contain errors as computations

Well, my first book, The End of Error, was about fixing all the difficulties of interval arithmetic.