G'day Paul,
>>>>> "PM" == Paul Mosquin <[EMAIL PROTECTED]> writes:
PM> Thomas, Thank you for your response. I checked the FAQ and it
PM> provides an example using sqrt(2) where you'd expect numerical
PM> precision to be an issue.
You should expect numerical precision issues in all calculations
involving "real" numbers in finite precision arithmetic. Perhaps the
FAQ should include a link to, say:
http://docs.sun.com/source/806-3568/ncg_goldberg.html
(A copy of Goldberg's "What Every Computer Scientist Should Know About
Floating-Point Arithmetic".)
PM> I guess that I expect R to act pretty much as C or C++ would
PM> do if I were to program the same code.
Well, did you? I am pretty sure that you would have the same results
in C or C++, at least I do (see below). But please, don't go and fill
another bug report for your C or C++ compiler when you see that it
behaves the same way as R. :-)
[bossiaea:test]$ cat test1.c
#include<stdlib.h>
#include<stdio.h>
int
main()
{
double x = 0.2;
if( x*x == 0.04)
printf("The numbers are equal\n");
else
printf("The numbers are *NOT* equal\n");
return EXIT_SUCCESS;
}
[bossiaea:test]$ gcc -o test1 test1.c
[bossiaea:test]$ ./test1
The numbers are *NOT* equal
PM> It's a bit of a surprise that assignment of rationals, well
PM> within precision, followed by multiplication leading to a
PM> result well within precision picks up those extra bits along
PM> the way. Something to watch out for, to be sure.
No surprise at all for anybody who learned about how numbers are
represented in a computer and how finite precision arithmetic works.
Big hint, 0.2 is not exactly representable in a binary basis (and
there have been function posted to the R mailing lists that show you
the binary representation of real numbers on your machine).
Read the link above or a book on numerical analysis, e.g. Chapter 1 in
@Book{gentle:98:na,
author = {Gentle, J. E.},
title = {Numerical Linear Algebra with Applications in Statistics},
publisher = {Springer-Verlag},
year = 1998,
series = {Statistics and Computing},
address = {New York}
}
Cheers,
Berwin
========================== Full address ============================
Berwin A Turlach Tel.: +61 (8) 6488 3338 (secr)
School of Mathematics and Statistics +61 (8) 6488 3383 (self)
The University of Western Australia FAX : +61 (8) 6488 1028
35 Stirling Highway
Crawley WA 6009 e-mail: [EMAIL PROTECTED]
Australia http://www.maths.uwa.edu.au/~berwin
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