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Re: st: Bug?


From   "Sergiy Radyakin" <serjradyakin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Bug?
Date   Mon, 20 Oct 2008 21:10:51 -0400

No, not a bug.
di ceil(1/0.125)
8

computers work with binary fractions, not decimal fractions. that's
why you should think about numbers like 0.03 as
0.02999999999999999999999999999 or
0.030000000000000000000000000000001, in other words x is (x+epsilon)
where epsilon is small and can be negative - representation error.
There is no such error when the fraction is a power of 2, e.g. one
half=0.5 or one sixteenth 0.0625. This is no different as writing
1/3=0.3333333 in decimal notation. It is not exactly 0.3333333, but we
are most of the times fine with such representation. But functions
floor() and ceil() are by their very nature very sensitive to these
small differences. When using division (multiplication) the error
propagates to higher digits.

This is another example from the same shelf:
  clear
  set obs 10
  generate var1=0.2
  count if var1==0.2
  tab var1

You should get a zero count  when you count, but 10 in the table.
Repeat the same with 0.5 and everything will be as your intuition
tells you. That's why one never compares two real numbers, but rather
one compares their difference with an epsilon.

If you suspect a bug, it is advisable to report Stata's version, and
OS version, unless you are sure that all versions are affected (e.g.
an error in the ado file). In some cases even compile_number may be
requested: display c(compile_number)

Hope this helps.

Best regards, Sergiy Radyakin


On Mon, Oct 20, 2008 at 8:36 PM, Le Wang <statauser@gmail.com> wrote:
> Hi all,
>
> Thanks in advance for your time.
>
> I am trying to use -- ceil() -- to do the following calculations that
> are supposed to give identical results, but the results turn out to be
> different. I couldn't figure out the solution to this problem.
>
> Le
>
> The codes
> -----------------------------------------------------------------------
>
> . di ceil((0.05-0.04)/0.01)
> 2
>
> . di ceil((0.04-0.03)/0.01)
> 2
>
>
> . di (0.04-0.03)/0.01
> 1
>
> -----------------------------------------------------------------------
>
> --
>
> ~~~~~~~~~~~~~~~~~~~~~~~~
> Le Wang, Ph.D
> Assistant Professor
> Department of Economics
> University of New Hampshire
> *
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