Invited Talk: Soundly Approximating Numerical Kernels & Beyond

"Computing resources are fundamentally limited and sometimes an exact solution may not even exist. Thus, when implementing real-world systems, approximations are inevitable, as are the errors they introduce. The magnitude of errors is problem-dependent but higher accuracy generally comes at a cost in terms of memory, energy or runtime, effectively creating an accuracy-efficiency tradeoff. To take advantage of this tradeoff, we need to ensure that the computed results are sufficiently accurate, otherwise we risk disastrously incorrect results or system failures. Unfortunately, the current way of programming with approximations is mostly manual, and consequently costly, error prone and often produces suboptimal results. I will show how we can already approximate straight-line numerical kernels fully automatically, while guaranteeing a user-provided error bound, and discuss our work towards supporting programs beyond kernels that feature conditional statements and loops."