[R] 0.1 + 0.2 != 0.3 revisited

[Duncan Murdoch]

On Fri, 6 Feb 2004 12:55:05 -0000, "Simon Fear"
<Simon.Fear at synequanon.com> wrote :

>Prompted by Peter Dalgard's recent elegant "intbin" function,
>I have been playing with the extension to converting reals to binary
>representation. The decimal part can be done like this:
>
>decbase <- function(x, n=52, base=2) {
>  if(n) {
>    x <- x*base
>    paste(trunc(x), decbase(x%%1, n-1, base), sep="")
>  }
>}
>
>n=52 default because that's the number of bits in the significand of
>a 64-bit float.

Remember that IEEE double formats are complicated, they're not fixed
point formats.

Both 0.1 and 0.2 are less than 1, so the n=52 count is wrong.  I think
0.1 would be stored as (1 + 0.6)*2^(-4) and 0.2 would be stored as (1
+ 0.6)*2^(-3), whereas 0.3 would be stored as (1 + 0.2)*2^(-2).  You
should expect 56 decimal (binary?) place accuracy on 0.1, 55 place
accuracy on 0.2, and 54 place accuracy on 0.3.  It's not surprising
weird things happen!

Duncan Murdoch