Bug or feature? sum(c(a, b, c)) != (a + b + c)

Greetings all,

I'm porting an algorithm from MATLAB to R, and noticed some minor
discrepancies in small decimal values using rowSums and colSums which are
exacerbated after heavy iteration and log space transformation. This was
rather perplexing as both programs claimed and appeared to use the IEEE 754
standard for floating point arithmetic (confirmed with manual basic
operations). ?After some tracing and testing, I've managed to isolated a
minimal working example as follows:

a = 0.812672
b = 0.916541
c = 0.797810
sum(c(a, b, c)) == (a + b + c)
[1] FALSE

Its probably to do with the order of summations. With your a,b,c you get:

 > (a+b+c) == (c+b+a)
 [1] TRUE
 > (a+b+c) == (c+a+b)
 [1] FALSE

shock horror, addition is not associative[1]. Lets investigate:

 > sum(c(a,b,c)) == c+a+b
 [1] TRUE
 > sum(c(a,b,c)) == a+c+b
 [1] TRUE

 'sum' seems to get the same answer as adding the first and the third,
then adding the second - explicitly:

 > sum(c(a,b,c)) == (a+c)+b
 [1] TRUE

I'm not sure what it would do for four values in the sum. Have fun
finding out. Does matlab similarly have a+b+c != c+b+a?

Barry

[1] or commutative or distributive or one of those -ives you learn one
day in school. Too lazy to wikipedia it right now...