wrong answer for simple expressions

Drew Hoysak <dhoysak at ccs.carleton.ca> writes:

I am experiencing strange (to me) output when trying to do simple
calculations.  Expressions that should equal zero yield non-zero
values.  
Examples:

a <- 4.1-3.1
b <- 5.1-4.1
a-b

[1] -4.440892e-16

(4.1-3.1)-(5.1-4.1)

[1] -4.440892e-16


When this last expression is expanded, I get the right answer:

4.1-3.1-5.1+4.1

[1] 0

Welcome to the world of floating point arithmetic! Since one tenth
cannot be represented exactly in binary, you are going to see these
small deviations once in a while. It is is really no stranger than 

   3/3 - (1/3 + 1/3 + 1/3) = 1.000 -  (0.333 + 0.333 + 0.333) = 0.001

in decimal notaion.

O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
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