Re: st: rounding error

[Nick Cox <njcoxstata@gmail.com>]

Maarten makes the main point, which is a VFAQ on this list.

In addition, a detail with -display- is that if no format is
specified, -display- tends to round fairly intelligently. This is
usually a feature, but conversely -display- without a format is not a
reliable guide to what a number "really" is.

-round()- can have two arguments, and it is certainly useful on
occasion to be able to do things like -round(x, 5)- or -round(x, 10)-.
But it is hard to see that rounding to a fractional argument serves
_any_ useful purpose. Certainly there have many posts over several
years in which it is evident that people think that -round(x, 0.1)-
is, or should be, the way to get display to 1 decimal place. That is
the job of formats, not rounding functions.

Nick

On Tue, Dec 20, 2011 at 2:32 PM, Maarten Buis <maartenlbuis@gmail.com> wrote:
> On Tue, Dec 20, 2011 at 2:57 PM, Richard Fox <r.p.fox@bham.ac.uk> wrote:
>> The results are generally as expected but sometimes the rounding does not seem to work.
>>
>> I capture the information I need as in the following example (this is just a small extract from the program, obviously there are argument definitions and tabulations etc.);
>>
>> local acc = .1
>> qui su `x' if New`v' == Tnam[`i',1] & New`w'==Wnam`i'[`j',1],d
>> local Median_`i'_`j' = round(r(p50),`acc')
>>
>> The results I obtain (see 2 examples below) often have values that have many decimal places which appears to suggest that the rounding is not working. However if I run a basic summary of the particular variable the results I get do not have the numerous decimal places so I'm not sure if the issue is with the rounding statement. Any ideas?
>
> The problem is that computers store numbers in binary, and a number
> like 84.3 in binary is like 1/3 in decimal; you cannot store it in a
> finite number of digits. There are nice discussions on this topic at
> the Stata blog:
>
> http://blog.stata.com/2011/02/02/how-to-read-the-percent-21x-format/
> http://blog.stata.com/2011/02/10/how-to-read-the-percent-21x-format-part-2/
> http://blog.stata.com/2011/06/17/precision-yet-again-part-i/
> http://blog.stata.com/2011/06/23/precision-yet-again-part-ii/
>
> There has also been a nice article in the Stata Journal:
> William Gould (2006) Mata Matters: Precision. The Stata Journal. 6(4):550-560.
> http://www.stata-journal.com/article.html?article=pr0025
>
> One solution is to realize that macros contain strings, and a computer
> has no trouble storing the string "84.3", even though it cannot
> exactly store the numer that string represents. Here the extended
> macro function -display- can be helpful, for more see -help
> extended_fcn- (*). So if you want to "round" a number like 84.34 to to
> 84.3 and store it as a string you type:
>
> local rounded: display %3.1f 84.34
>
> Hope this helps,
> Maarten
>
> (*) In practice I always type -help macro- and than click on the link
> to extended macro functions.

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