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DTSTAMP:20211207T055338Z
LOCATION:Online
DTSTART;TZID=America/Chicago:20211119T084000
DTEND;TZID=America/Chicago:20211119T090000
UID:submissions.supercomputing.org_SC21_sess107_ws_corr107@linklings.com
SUMMARY:Finding Large Poisson Polynomials Using Four-Level Variable Precis
 ion
DESCRIPTION:Workshop\n\nFinding Large Poisson Polynomials Using Four-Level
  Variable Precision\n\nBailey\n\nThe tension between ``correct and reprodu
 cible'' computing and ``high-performance'' computing is particularly acute
  in computational mathematics applications, some of which require very hig
 h numeric precision (hundreds or thousands of digits) to produce correct a
 nd reproducible results, resulting in very long run times.  One solution i
 s to employ a variable precision design, namely using ordinary single- or 
 double-precision arithmetic as much as possible, and shifting to higher le
 vels of precision only when necessary.  But managing a large variable prec
 ision computation is a significant programming challenge.\n\nThis study pr
 esents results using a new arbitrary precision package and a new four-leve
 l variable precision application code to study a class of polynomials aris
 ing from the Poisson potential function of mathematical physics.  The appl
 ication employs four levels of precision: IEEE double, IEEE quad, medium p
 recision (typically 100-1,000 digits) and full precision (typically 5,000 
 to 50,000 digits).  Using this software, we have computed the minimal poly
 nomials associated with the Poisson potential function, not just in the sp
 ecial case $x = 1/s$ and $y = 1/s$ (for integers $1 \leq s \leq 50$), as i
 n an earlier study, but also for many instances of the  broader class of r
 ationals $x = p/s$ and $y = q/s$, for $1 \leq p,q < s/2 \leq 50$.  In this
  paper, we present some initial results of these computations, and also pr
 esent some lessons learned from using extreme variable precision in a comp
 utational mathematics application.\n\nTag: Online Only, Correctness, Relia
 bility and Resiliency, Software Engineering\n\nRegistration Category: Work
 shop Reg Pass
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