From: <savicky_at_cs.cas.cz>

Date: Mon, 14 Dec 2009 23:11:24 +0100 (CET)

R-devel_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-devel Received on Mon 14 Dec 2009 - 22:22:19 GMT

Date: Mon, 14 Dec 2009 23:11:24 +0100 (CET)

On Mon, Dec 14, 2009 at 06:10:16PM +0100, bersch_at_lycos.com wrote:

*>
**> > pnorm(1.35,0,1)
**> [1] 0.911492
**> > pnorm(1.36,0,1)
**> [1] 0.913085
**>
*

> > options(digits=4)

*>
**> > pnorm(1.35,0,1)
**> [1] 0.9115
**> > pnorm(1.36,0,1)
**> [1] 0.913 rounding error?
*

The technical explanation is as follows. If options(digits=k) is set, then the number of significant digits for printing a single number x is determined as min(k, d), where d is the minimum number of digits, for which the relative error of the printed number is less than 10^-k.

If we have

x <- 0.913085

y <- 0.913

then the relative error of y as an approximation of x is
abs(y - x)/x # [1] 9.3091e-05

Since this is less than 10^-4, the 3 digit precision is chosen
for printing x.

A safer way of rounding is to use functions round() and signif().
For example,

round(x, digits=4) # [1] 0.9131

I do not know the history of the R printing algorithm. It is designed primarily for printing vectors, where the rules are more complicated to achieve a good unified format for all numbers. May be, someone else can say more about it. The above analysis may be obtained by inspecting the R source code.

Petr Savicky.

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https://stat.ethz.ch/mailman/listinfo/r-devel Received on Mon 14 Dec 2009 - 22:22:19 GMT

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