> 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. _______________________________________________ Unsubscribe & other changes: http://lists.boost.org/mailman/listinfo.cgi/boost
