> a <- 0 ; for(i in (1:200000000)) a <- a + 1/i > b <- 0 ; for(i in (200000000:1)) b <- b + 1/i > c <- sum(1/(1:200000000)) > d <- sum(1/(200000000:1)) > order(c(a,b,c,d)) [1] 1 2 4 3 > b<c [1] TRUE > c==d [1] FALSE
I'd expected b being the largest, since we sum up the smallest numbers first. Instead, c is the largest, which is sum() applied to the vector ordered with largest numbers first. Can anyone shed some light on this? What is the best way in R to compute a sum while avoiding cancellation effects? By the way, sum() in the above example is much faster than the loops, so it would be nice if we could utilize it.
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