# [R] Beyond double-precision?

Berwin A Turlach berwin at maths.uwa.edu.au
Sat May 9 18:17:56 CEST 2009

```G'day all,

On Sat, 09 May 2009 08:01:40 -0700
spencerg <spencer.graves at prodsyse.com> wrote:

>       The harmonic mean is exp(mean(logs)).  Therefore, log(harmonic
> mean) = mean(logs).
>
>       Does this make sense?

I think you are talking here about the geometric mean and not the
harmonic mean. :)

The harmonic mean is a bit more complicated.  If x_i are positive
values, then the harmonic mean is

H= n / (1/x_1 + 1/x_2 + ... + 1/x_n)

so

log(H) = log(n) - log( 1/x_1 + 1/x_2 + ... + 1/x_n)

now log(1/x_i) = -log(x_i) so if log(x_i) is available, the logarithm
of the individual terms are easily calculated.  But we need to
calculate the logarithm of a sum from the logarithms of the individual
terms.

At the C level R's API has the function logspace_add for such tasks, so
it would be easy to do this at the C level.  But one could also
implement the equivalent of the C routine using R commands.  The way to
calculate log(x+y) from lx=log(x) and ly=log(y) according to

max(lx,ly) + log1p(exp(-abs(lx-ly)))

So the following function may be helpful:

max(lx, ly) + log1p(exp(-abs(lx-ly)))

len_x <- length(x)
if(len_x > 1){
if( len_x > 2 ){
for(i in 3:len_x)
}
}else{
res <- x
}
res
}

R> set.seed(1)
R> x <- runif(50)
R> lx <- log(x)
R> log(1/mean(1/x))  ## logarithm of harmonic mean
[1] -1.600885
[1] -1.600885

Cheers,

Berwin

Berwin A Turlach                            Tel.: +65 6515 4416 (secr)
Dept of Statistics and Applied Probability        +65 6515 6650 (self)
Faculty of Science                          FAX : +65 6872 3919
National University of Singapore
6 Science Drive 2, Blk S16, Level 7          e-mail: statba at nus.edu.sg
Singapore 117546                    http://www.stat.nus.edu.sg/~statba

```