[R] strange logical results

[Bill.Venables at csiro.au]

Hi Erin,

You would be safe on a machine that represented floating point numbers
in base 10, and I haven't seen one of those for such a long time... All
modern machines use base 2 for floating point numbers.

The moral of the story is not to believe what you see printed.  The
number you see printed innocently as '-0.4' has been arrived at by two
different processes and uses two different *approximations* to the real
thing on a binary machine, and my chance they have arrived at a slightly
different result.  Slight, but enough to make '==' ring the alarm.  Here
is a demo.

> x <- seq(-1,1,by=0.1)
> x[7] - (-0.4)
[1] 1.110223e-16

So the method used by seq() to arrive at an approximation to -0.4 is
just slightly different from the method used by the parser when it reads
the characters '-0.4' and translates them into a floating point number.
It just so happens that for the others you checked the two
approximations agreed, but you can't trust that to happen all the time.

Moral of the story: don't use the '==' or '!=' operators with floating
point numbers.  It's an old tale but still current.

OK, so what can you do to implement the idea of checking equality
'within a tolerance'?  I'm glad you asked.  You can write a couple of
binary operators yourself.  There is an object called .Machine that is a
list of machine constants.  The obvious one to compare the difference
with is .Machine$double.eps

> `%~=%` <- function(a, b) abs(a - b) < .Machine$double.eps
> `%~!%` <- function(a, b) abs(a - b) > .Machine$double.eps
> x %~=% -0.4
 [1] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
FALSE FALSE FALSE
[15] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x %~!% -0.4
 [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE
TRUE  TRUE  TRUE
[15]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE

The world is approximately sane once more.

Bill Venables.

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Erin Hodgess
Sent: Friday, 29 December 2006 8:36 PM
To: r-help at stat.math.ethz.ch
Subject: [R] strange logical results

Dear R People:  

I am getting some odd results when using logical operators:

> x <- seq(from=-1,to=1,by=0.1)

> > x
 [1] -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1  0.0  0.1  0.2
0.3  0.4
[16]  0.5  0.6  0.7  0.8  0.9  1.0
> x == -1
 [1]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x == -0.9
 [1] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x == -0.8
 [1] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x == -0.7
 [1] FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x == -0.6
 [1] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x == -0.5
 [1] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> x == -0.4
 [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
FALSE
[13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
> 

Should this show as true also, please?

I saw this in both Windows and LINUX Versions 2.4.0

Thanks in advance,
Sincerely,
Erin Hodgess
Associate Professor
Department of Computer and Mathematical Sciences
University of Houston - Downtown
mailto: hodgess at gator.uhd.edu

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