From: Thomas Lumley (tlumley@u.washington.edu)
Date: Sat 02 Nov 2002 - 02:08:46 EST
Message-id: <Pine.A41.4.44.0211010706051.71068-100000@homer19.u.washington.edu>
On 1 Nov 2002, Peter Dalgaard BSA wrote:
> Neil Klepeis <nklepeis@uclink4.berkeley.edu> writes:
>
> > I'm at a loss on this one:
> >
> > > c(1.253) %in% seq(1.1,1.3,by=0.001)
> > [1] FALSE
> > > c(1.252) %in% seq(1.1,1.3,by=0.001)
> > [1] TRUE
> > > c(1.254) %in% seq(1.1,1.3,by=0.001)
> > [1] TRUE
>
> "Never trust exact equality with floating point operations."
>
> Finite decimal fractions are not finite binary fractions and if you
> compute them in two different ways you'll very likely get differences
> in the last few bits because of rounding errors.
>
> > seq(1.1,1.3,by=0.001)[154]
> [1] 1.253
> > seq(1.1,1.3,by=0.001)[154]-1.253
> [1] 2.220446e-16
>
> It's not different in principle from the fact that in 3-digit decimal
> arithmetic 1/3 * 3 = 0.333 * 3 = 0.999
Though it's a bit unintuitive that
1.253 %in% round(seq(1.1, 1.3,by=0.001), 3)
is also FALSE. However,
round(1.253,3) %in% round( seq(1.1, 1.3, by=0.001), 3)
does work and should be more reliable.
The optimistic version of Peter's general principle is that two real
numbers will compare equal only if they were obtained by the same
computation.
-thomas
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