R help - Sep 2007 - a bug when subtracting vectors?

Hi,

I am calling in some data into R via the read.table function. The 'tail'
of
this data reads
> tail(data)
        Date                   Open   High    Low  Close  Volume
3728 Fri 14-Sep-07     114.19 114.46 113.93 114.08 1117992
3729 Mon 17-Sep-07   113.99 114.37 113.91 114.27  899671
3730 Tue 18-Sep-07    114.30 114.32 113.47 113.85 1346282
3731 Wed 19-Sep-07   113.71 113.71 113.00 113.16 1499423
3732 Thu 20-Sep-07    112.98 113.24 112.28 112.30 1376946
3733 Fri 21-Sep-07      112.41 112.64 112.24 112.47 1052431

The data is saved in a CSV file, which according to Notepad looks like

Fri 14-Sep-07,114.19,114.46,113.93,114.08,1117992
Mon 17-Sep-07,113.99,114.37,113.91,114.27,899671
Tue 18-Sep-07,114.3,114.32,113.47,113.85,1346282
Wed 19-Sep-07,113.71,113.71,113,113.16,1499423
Thu 20-Sep-07,112.98,113.24,112.28,112.3,1376946
Fri 21-Sep-07,112.41,112.64,112.24,112.47,1052431

i.e. all the data is saved to 2 decimal places. To calculate the net change
of the 'Close' variable in the last row I would use
> data[3733,5]-data[3732,5]
[1] 0.17

which is correct. However, when I use the following code to calculate the
net change over all observations i get the following result
> n <- length(data[,1])
> temp <- data[2:n,5]-data[1:(n-1),5]
> tail(temp)
0.039999999999992
0.189999999999998
-0.420000000000002
-0.689999999999998
-0.86
0.170000000000002

When subtracting,  all numbers should be to 2 decimal places. Why is R
calculating it to 15 decimal places -- the output is essentially wrong
112.47-112.30=0.17 NOT 0.170000000000002. I suspect I am encoding this
incorrectly?

Any help would be gratefully appreciated.

Kind regards,

Sam

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Samuel Kemp wrote:
> When subtracting,  all numbers should be to 2 decimal places. Why is R
> calculating it to 15 decimal places -- the output is essentially wrong
> 112.47-112.30=0.17 NOT 0.170000000000002. I suspect I am encoding this
> incorrectly?
>   

Well, two comments...one is not computer related.  If you are 
subtracting two numbers which have two digits after the decimal (i.e., 
two significant figures), you shouldn't be accepting a result of more 
than two digits.  So, the only thing wrong that you're doing is just 
that you're not formatting the output properly by cutting the remaining 
numbers.

As for the second comment, computers cannot represent decimal numbers 
exactly and problems like this occurs very often.  In the above example, 
one of your numbers can be represented exactly as 112.47 or 112.30.  
That's just something everyone has to be aware of when using computers 
to do math.  This, in my opinion, is an excellent paper on the 
problem...it is quite technical, but at least worth a skim:

http://docs.sun.com/source/806-3568/ncg_goldberg.html

I found this sentence near the beginning of the article to be perfect:  
"Squeezing infinitely many real numbers into a finite number of bits 
requires an approximate representation."

I presume there's an FAQ for R on this...not sure where it is, though.  
But, I hope this helps!

Ray

A good answer is found in the FAQ for R, in 

FAQ 7.31 Why doesn't R think these numbers are equal?

-- 
Bj?rn-Helge Mevik