A Case for Correctly Rounded Math Libraries

Papers We Love Conf 2022 https://pwlconf.org/2022/santosh-naga... Transcript: https://pwlconf.org/2022/transcripts/... Santosh Nagarakatte / Rutgers University This talk will provide an overview of the RLIBM project where we are building a collection of correctly rounded elementary functions for multiple representations and rounding modes. Historically, polynomial approximations for elementary functions have been designed by approximating the real value. In contrast, we make a case for approximating the correctly rounded result of an elementary function rather than the real value of an elementary function in the RLIBM project. Once we approximate the correctly rounded result, there is an interval of real values around the correctly rounded result such that producing a real value in this interval rounds to the correct result. This interval is the freedom that the polynomial approximation has for an input, which is larger than the ones with the mini-max approach. Using these intervals, we structure the problem of generating polynomial approximations that produce correctly rounded results for all inputs as a linear programming problem. The results from the RLIBM project makes a strong case for mandating correctly rounded results at least for any representation that has fewer than orequal to 32-bits. ---- Video Sponsor: Cerner - https://engineering.cerner.com/?promo...