st: round() for values ending in 5

["Lacy,Michael" <Michael.Lacy@colostate.edu>]

Greetings,

I'd like to clarify what rounding rules Stata implements. In the
grand scheme of things, the answer is trivial, but several examples
have aroused my curiosity.  I did find 
http://www.stata.com/statalist/archive/2005-12/msg00403.html
in the archives, but it doesn't quite fit the current situation.

Background:
Someone I was helping wondered why I had rounded 4.5 to 4 when rounding to 
the nearest integer. I explained that to my knowledge, banker's rounding, 
i.e., rounding values ending in 5 so that the result ends in an even digit,
had been the standard for many decades. I discovered later that this 
rule is no longer universally taught, and has been replaced by the biased
but simpler rule of "always round upward values ending in 5."  (Shocking to 
me, but ...) This prompted me to wonder what Stata did. I presumed it 
implemented banker's rounding. The following thus surprised me:

-display round(4.5,1)-  = 5    and
-display round(4.55,0.1) = 4.5  

It first occurred to me that this might be a floating point precision
issue, but I thought not, since 4.5 has an exact binary representation.
(I also found that the equivalent function call  in Excel agrees on the 
first instance but not the second, but that's another matter.)

This prompted me to check out the IEEE rules on rounding, of which the 
recommended default (loosely stated) is to round so as to make the least 
significant bit of the result even, i.e., 0.  On this rule round(4.55, 0.1) 
might give 4.5, depending on the place at which the least significant bit 
occurs, but I'm not sure what this rule would mean for round(4.5,1). 
4.5 would clearly round to 4 (100b vs. 101b)  in integer arithmetic, 
but the floating point representations of both 4.0 and 5.0 both end in 
0, i.e. 100.000 etc. and 101.000 etc., so that leaves me wondering.

I had the thought that Stata's behavior was perhaps documented somewhere, but I 
didn't happen to find it.  And, lastly, I could imagine this behavior varying
from one hardware platform to another, if round() ends up using a hardware call.  

So, can someone clarify what rule round() implements?


Regards, 

Mike Lacy
Fort Collins CO 
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