R help - Sep 2006 - exactly representable numbers

Hi

Given a real number x,  I want to know how accurately R can represent  
numbers near x.

In particular, I want to know the infinum of exactly representable
numbers greater than x, and the supremum of exactly representable  
numbers
less than x.  And then the interesting thing is the difference  
between these two.


I have a little function that does some of this:


f <- function(x,FAC=1.1){
   delta <- x
while(x+delta > x){
   delta <- delta/FAC
}
return(delta*FAC)
}

But this can't be optimal.

Is there a better way?



--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

Robin Hankin said the following on 9/11/2006 3:52 AM:
> Hi
> 
> Given a real number x,  I want to know how accurately R can represent  
> numbers near x.
> 
> In particular, I want to know the infinum of exactly representable
> numbers greater than x, and the supremum of exactly representable  
> numbers
> less than x.  And then the interesting thing is the difference  
> between these two.
> 
> 
> I have a little function that does some of this:
> 
> 
> f <- function(x,FAC=1.1){
>    delta <- x
> while(x+delta > x){
>    delta <- delta/FAC
> }
> return(delta*FAC)
> }
> 
> But this can't be optimal.
> 
> Is there a better way?
> 
> 
> 
I believe this is what .Machine$double.eps is. From ?.Machine

double.eps: the smallest positive floating-point number 'x' such that
           '1 + x != 1'.  It equals 'base^ulp.digits' if either
'base'
           is 2 or 'rounding' is 0;  otherwise, it is
'(base^ulp.digits)
           / 2'.

See also .Machine$double.neg.eps. Is this what you need?

--sundar