%in% not working

Neil Klepeis <nklepeis at 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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