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*To*: Gabriel Dos Reis <gdr at codesourcery dot com>*Subject*: Re: What is acceptable for -ffast-math? A numerical viewpoint*From*: Wolfgang Bangerth <wolfgang dot bangerth at iwr dot uni-heidelberg dot de>*Date*: Wed, 1 Aug 2001 16:55:02 +0200 (MET DST)*cc*: dewar at gnat dot com, gcc at gcc dot gnu dot org

On 1 Aug 2001, Gabriel Dos Reis wrote: > | > Finally, as a concrete example, look at the classical problem of > | > approximating the zeros of a univariate polynomial. There you have > | > true degragation. Just take the Wilkinson polynomial of 20th degree, > | > and make slight pertubation to its cofficients (preferably the three > | > leading cofficients) and see what happens. > | There you obviously need high and known precision because the > | problems are unstable. PDE solvers, OTOH, usually use stable ^^^^^^^^^^^^^^^^^^^^^ > | methods. It is only for the latter applications that I said it > | would be useful to have more aggressive/dubious optimizations. > > You seem to believe that we were using unstable methods to approximate > polynomial roots. That is untrue. We are using stable methods, > combined with separation algorithms. The trouble is not really the > methods but the problems at hand: Polynomial roots are very sensitive > to pertubation to coefficients. Of course, it's just like nobody uses Gaussian elimination without pivoting. I understand that it's the problem at hand that makes the difficulties. That's why I wrote "problems", not "algorithms" :-) > My point was bring in a concrete conter-example to the claim that, it > doesn't matter how dubious are the transformations, it suffices to > use stable algorithms. So we agree: there are instable problems where -ffast-math makes no sense because they are too sensitive even when using stable algorithms. And then there are stable problems where stable methods might profit from potentially dubious transformations; for these, a/b/c=a/(b*c) and a*c+b*c=(a+b)*c would make sense. My intention was just to point out that there are non-negligible branches of computational maths where the stability of the problems and algorithms would allow for such transformations and there they'd be useful. Regards Wolfgang ------------------------------------------------------------------------- Wolfgang Bangerth email: wolfgang.bangerth@iwr.uni-heidelberg.de www: http://gaia.iwr.uni-heidelberg.de/~wolf

**Follow-Ups**:**Re: What is acceptable for -ffast-math? A numerical viewpoint***From:*Dima Volodin

**References**:**Re: What is acceptable for -ffast-math? A numerical viewpoint***From:*Gabriel Dos Reis

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