[R] Rounding error in seq(...)

[William Dunlap]

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Martin Batholdy
> Sent: Wednesday, September 30, 2009 12:18 PM
> To: Duncan Murdoch
> Cc: r help
> Subject: Re: [R] Rounding error in seq(...)
> 
> hum,
> 
> can you explain that a little more detailed?
> Perhaps I miss the background knowledge - but it seems just 
> absurd to  
> me.
> 
> 0.1+0.1+0.1 is 0.3 - there is no rounding involved, is there?
> 
> why is
> x <- 0.1 + 0.1 +0.1
> not equal to
> y <- 0.3
> 

Let's do this in base 10, since it is more familiar.  Suppose
we decide, for efficiency reasons to store all numbers to
2 significant decimal digits.  Then 1/3 gets stored as 0.33 and
stored(1/3)+stored(1/3)+stored(1/3) is stored(0.99), not 1.0.
(Here stored() is the function that maps a number to the
2 decimal digit number closest to it.)

For efficiency reasons standard computer representation of
number with fractional part involves 52 significant binary digits.

1/10 in base 10 is like 1/3 in base 2: it cannot be represented
exactly with 52 significant binary digits.  Hence we cannot
expect that
   as.double(1/10)+ <8 reps> +as.double(1/10) will be
exactly 1.0.  (Here, as.double is not the R function but the
mathematical function that maps a number to the double
precision number closest to it.)

Bill Dunlap
TIBCO Software Inc - Spotfire Division
wdunlap tibco.com 

> ?
> 
> 
> 
> Am 30.09.2009 um 21:04 schrieb Duncan Murdoch:
> 
> > On 9/30/2009 2:50 PM, Michael Knudsen wrote:
> >> On Wed, Sep 30, 2009 at 8:44 PM, Duncan Murdoch  
> >> <murdoch at stats.uwo.ca> wrote:
> >>> Why?  You asked for an increment of 1 in the second case 
> (which is  
> >>> exactly
> >>> represented in R), then divided by 10, so you'll get the same as  
> >>> 0.3 gives
> >>> you.  In the seq() case you asked for an increment of a number  
> >>> close to but
> >>> not equal to 1/10 (because 1/10 is not exactly representable in  
> >>> R), so you
> >>> got something different.
> >> Well, the problem is that I don't know how seq is 
> implemented. I just
> >> assumed that it wouldn't behave like this.
> >
> > It doesn't really matter how it is implemented:  if you ask 
> to start  
> > at 0.1 and increment by 0.1, you should expect the result 
> to be the  
> > same as
> >
> > 0.1
> > 0.1+0.1
> > 0.1+0.1+0.1
> > etc.
> >
> > and I think it is.  The problem is that 0.1+0.1+0.1 is not 
> the same  
> > as 0.3, due to rounding.  Neither 0.1 nor 0.3 can be represented  
> > exactly in the standard IEEE floating point formats that R uses.
> >
> > Duncan Murdoch
> >
> > ______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> 
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>