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UID:3cfbe0ffbf6924cd07dc30ae0c58dc2a-395
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DESCRIPTION:A Case for Correctly Rounded Math Libraries
URL;VALUE=URI:https://www.csa.iisc.ac.in/newweb/event/395/a-case-for-correctly-rounded-math-libraries/
SUMMARY: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 or
equal to 32-bits.
DTSTART:20230313T120000Z
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