# [R] 0.1 + 0.2 != 0.3 revisited

Simon Fear Simon.Fear at synequanon.com
Fri Feb 6 13:55:05 CET 2004

```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.

Now, `decbase(0.1)` is a bit curious in that the 0.1 is going to be
converted to a binary float by the interpreter ... and then re-converted
by `decbase`, so really I should
insist on character format for the number I want to convert. But
anyway I do get the right answer up to the point of truncation:

> decbase(.1)
[1] "0001100110011001100110011001100110011001100110011001"
> decbase(.2)
[1] "0011001100110011001100110011001100110011001100110011"
> decbase(.3)
[1] "0100110011001100110011001100110011001100110011001100"

That is to say, decbase(.1) + decbase(.2) really does equal
decbase(.3). But not if R does its own arithmetic first:

> decbase(.1+.2)
[1] "0100110011001100110011001100110011001100110011001101"

What has gone on here? Why does R apparently get it's
internal representation of one of .1 or .2 "wrong" ? Does the
end of the internal binary for .1 get rounded up instead of
truncated ? Why wouldn't that show in decbase(.1) ?

Simon Fear
Senior Statistician
Syne qua non Ltd
Tel: +44 (0) 1379 644449
Fax: +44 (0) 1379 644445
email: Simon.Fear at synequanon.com
web: http://www.synequanon.com

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