From: Rozental, Gennadiy (gennadiy.rozental_at_[hidden])
Date: 2003-07-07 13:22:22
> Let t be tmp and e? be error values (smaller than ulp/2).
>
> rounded(rounded(t*t) - t)
> = ((t*t) * (1+e1) - t) * (1+e2)
> = t*t - t + t*t * (e1+e2+e1*e2) - t*e2
>
> So how much is the relative error? For example, if e1=ulp/2
> and e2=0, the absolute error reaches t*t*ulp/2 = 0.605*ulp.
> So the relative error is 0.605*ulp / (11/100) = 5.5*ulp. The
> result may be 6 ulps away! (and maybe
> more)
You seems to be right. My test program produces relative errors up to
2e+7*ulp.
> Thinking rounding errors just add themselves is a
> misunderstanding of floating-point arithmetic (if it was that
> easy, interval arithmetic wouldn't be useful).
>
> Guillaume
I could probably prohibit usage of CHECK_CLOSE with number of rounding
errors provided.
Is there any other general recommendations how to choose the tolerance to FP
computation correctness checking?
Gennadiy.