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DTSTART:19700308T020000
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BEGIN:VEVENT
DTSTAMP:20210402T160553Z
LOCATION:Track 10
DTSTART;TZID=America/New_York:20201111T155500
DTEND;TZID=America/New_York:20201111T162000
UID:submissions.supercomputing.org_SC20_sess205_ws_corr104@linklings.com
SUMMARY:Order Matters: A Case Study on Reducing Floating Point Error in Su
 ms through Ordering and Grouping
DESCRIPTION:Workshop\n\nOrder Matters: A Case Study on Reducing Floating P
 oint Error in Sums through Ordering and Grouping\n\nJob, Grove, Fogerty, M
 auney, Neuman...\n\nDue to accumulated round-off error, mathematically equ
 ivalent floating-point summations can yield different computational result
 s. Errors propagated across time steps can be substantial and can lead to 
 significant inaccuracy in the final results. We focus on sums in an adapti
 ve mesh refinement hydrocode. We reduce error in a moderate-length equatio
 n by generating proper ordering and grouping of the terms and verify this 
 on a typical numerical simulation. Our techniques show equivalent accuracy
  to classic methodology like Kahan without the extra overhead. The heurist
 ics presented here could improve accuracy in single and double precision f
 or many codes. With some knowledge and minimal effort, researchers can app
 ly these techniques and see improvement in the accuracy of code at no cost
  in performance. The same approach may facilitate reduced precision comput
 ation.\n\nTag: Correctness, Floating Point, Reproducibility and Transparen
 cy\n\nRegistration Category: Workshop Reg Pass
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