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## Re: [Maxima-discuss] a fun demo for variable precision arithmetic

 From: Barton Willis Subject: Re: [Maxima-discuss] a fun demo for variable precision arithmetic Date: Fri, 4 Dec 2015 19:24:07 +0000

 Incidentally: For bounding floating point round off error, the running error is an old-fashioned alternative to interval arithmetic. This method is described in  Higham, Nicholas J. (2002), Accuracy and stability of numerical algorithms.  SIAM. The maxima function nfloat implements the running error method. When the error is too large, nfloat automatically increases the value of fpprec.  Of course if the input data differs from its true value, there isn't any magic that can fix that. (%i19) baz(xx,yy,dig) := nfloat(1335/4*y^6+x^2*(11*x^2*y^2-y^6+(-121)*y^4-2)+11/2*y^8+x/(2*y),[x=xx,y=yy],dig)\$ (%i20) load(hypergeometric)\$ (%i19) for fpprec:10 step 5 thru 50 do print (baz(77617, 33096, fpprec)); -8.2739606b-1 -8.27396059946821b-1 -8.2739605994682136814b-1 -8.273960599468213681411651b-1 -8.2739605994682136814116509548b-1 -8.2739605994682136814116509547981629b-1 -8.27396059946821368141165095479816291999b-1 -8.27396059946821368141165095479816291999033116b-1 -8.2739605994682136814116509547981629199903311578439b-1 (%o19) done   --Barton

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