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DTSTART:19700308T020000
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DTSTAMP:20210402T160553Z
LOCATION:Track 10
DTSTART;TZID=America/New_York:20201111T180500
DTEND;TZID=America/New_York:20201111T183000
UID:submissions.supercomputing.org_SC20_sess205_ws_corr105@linklings.com
SUMMARY:A Statistical Analysis of Error in MPI Reduction Operations
DESCRIPTION:Workshop\n\nA Statistical Analysis of Error in MPI Reduction O
 perations\n\nPollard, Norris\n\nThis work explores the effects of nonassoc
 iativity of floating-point addition on Message Passing Interface (MPI) red
 uction operations. Previous work indicates floating-point summation error 
 is comprised of two independent factors: error based on summation algorith
 m and error based on the summands themselves. We find evidence to suggest,
  for MPI reductions, the error based on summands has a much greater effect
  than the error based on the summation algorithm. We begin by sampling fro
 m the state space of all possible summation orders for MPI reduction algor
 ithms. Next, we show the effect of different random number distributions o
 n summation error, taking a 1000-digit precision floating-point accumulato
 r as ground truth. Our results show empirical error bounds that are much t
 ighter than existing analytical bounds. Last, we simulate different allred
 uce algorithms on the high performance computing (HPC) proxy application N
 ekbone and find that the error is relatively stable across algorithms. Our
  approach provides HPC application developers with more realistic error bo
 unds of MPI reduction operations. Quantifying the small---but nonzero---di
 screpancies between reduction algorithms can help developers ensure correc
 tness and aid reproducibility across MPI implementations and cluster topol
 ogies.\n\nTag: Correctness, MPI, Reproducibility and Transparency\n\nRegis
 tration Category: Workshop Reg Pass
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