I am experiencing strange (to me) output when trying to do simple calculations. Expressions that should equal zero yield non-zero values. Examples:> a <- 4.1-3.1 > b <- 5.1-4.1 > a-b[1] -4.440892e-16> (4.1-3.1)-(5.1-4.1)[1] -4.440892e-16 When this last expression is expanded, I get the right answer:> 4.1-3.1-5.1+4.1[1] 0 I am using the binary packaged version R-2.0.0-0.fdr.1.fc2.i386.rpm for Linux Fedora Core 2. I had the same problem with version 1.9.0-0 Can anyone tell me what is going on? Thanks, Drew Hoysak
Drew Hoysak <dhoysak at ccs.carleton.ca> writes:> I am experiencing strange (to me) output when trying to do simple > calculations. Expressions that should equal zero yield non-zero > values. > Examples: > > > a <- 4.1-3.1 > > b <- 5.1-4.1 > > a-b > [1] -4.440892e-16 > > > > (4.1-3.1)-(5.1-4.1) > [1] -4.440892e-16 > > > When this last expression is expanded, I get the right answer: > > > 4.1-3.1-5.1+4.1 > [1] 0Welcome to the world of floating point arithmetic! Since one tenth cannot be represented exactly in binary, you are going to see these small deviations once in a while. It is is really no stranger than 3/3 - (1/3 + 1/3 + 1/3) = 1.000 - (0.333 + 0.333 + 0.333) = 0.001 in decimal notaion. -- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
On Thu, 11 Nov 2004, Drew Hoysak wrote:> I am experiencing strange (to me) output when trying to do simple > calculations. Expressions that should equal zero yield non-zero > values.No. There is no reason why these expressions should yield zero values. Remember that computers work in base 2, and that 0.1 has an infinitely recurring binary expansion in base 2. You should expect that 0.1 computed two different ways should differ in the last few bits. You have managed to get zero to 52 bits accuracy, which is not bad when you consider that the machine only works to 54 bits. -thomas> Examples: > >> a <- 4.1-3.1 >> b <- 5.1-4.1 >> a-b > [1] -4.440892e-16 > > >> (4.1-3.1)-(5.1-4.1) > [1] -4.440892e-16 > > > When this last expression is expanded, I get the right answer: > >> 4.1-3.1-5.1+4.1 > [1] 0 > > > I am using the binary packaged version R-2.0.0-0.fdr.1.fc2.i386.rpm for > Linux Fedora Core 2. I had the same problem with version 1.9.0-0 > > Can anyone tell me what is going on? > > Thanks, > > > Drew Hoysak > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html >Thomas Lumley Assoc. Professor, Biostatistics tlumley at u.washington.edu University of Washington, Seattle
R does double precision arithmetic and accumulates roundoff error
like any other double precision computations. I would therefore expect
it to accumulate roundoff error as you have reported. In most cases
like you mentioned, a difference of 4e-16 is "not material", to use
Accounting jargon. If it is an issue, you either need to do error
analysis or use something like Mathematica that does infinite precision
arithmetic.
hope this helps. spencer graves
Drew Hoysak wrote:
>I am experiencing strange (to me) output when trying to do simple
>calculations. Expressions that should equal zero yield non-zero
>values.
>Examples:
>
>
>
>>a <- 4.1-3.1
>>b <- 5.1-4.1
>>a-b
>>
>>
>[1] -4.440892e-16
>
>
>
>
>>(4.1-3.1)-(5.1-4.1)
>>
>>
>[1] -4.440892e-16
>
>
>When this last expression is expanded, I get the right answer:
>
>
>
>>4.1-3.1-5.1+4.1
>>
>>
>[1] 0
>
>
>I am using the binary packaged version R-2.0.0-0.fdr.1.fc2.i386.rpm for
>Linux Fedora Core 2. I had the same problem with version 1.9.0-0
>
>Can anyone tell me what is going on?
>
>Thanks,
>
>
>Drew Hoysak
>
>______________________________________________
>R-help at stat.math.ethz.ch mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>
>
--
Spencer Graves, PhD, Senior Development Engineer
O: (408)938-4420; mobile: (408)655-4567
On Thu, 2004-11-11 at 12:24 -0500, Drew Hoysak wrote:> I am experiencing strange (to me) output when trying to do simple > calculations. Expressions that should equal zero yield non-zero > values. > Examples: > > > a <- 4.1-3.1 > > b <- 5.1-4.1 > > a-b > [1] -4.440892e-16 > > > > (4.1-3.1)-(5.1-4.1) > [1] -4.440892e-16 > > > When this last expression is expanded, I get the right answer: > > > 4.1-3.1-5.1+4.1 > [1] 0 > > > I am using the binary packaged version R-2.0.0-0.fdr.1.fc2.i386.rpm for > Linux Fedora Core 2. I had the same problem with version 1.9.0-0> Can anyone tell me what is going on?A lack of understanding as to how floating point numbers are represented by computers under the IEEE 754 floating point standard. Hint: Take note of the following:> print(0.1, digits = 20)[1] 0.10000000000000000555> print(4.1, digits = 20)[1] 4.0999999999999996447> print(4.1 - 3.1, digits = 20)[1] 0.99999999999999955591> print(4.1 - 3.1 - 5.1, digits = 20)[1] -4.0999999999999996447 Read the last FAQ "Why is 0.1 not 0.1?" here: http://grouper.ieee.org/groups/754/faq.html#binary-decimal and read David Goldberg's article, "What Every Computer Scientist Should Know about Floating-Point Arithmetic", which is available here: http://grouper.ieee.org/groups/754/ in a Postscript file or here in an edited form in HTML: http://docs.sun.com/source/806-3568/ncg_goldberg.html HTH, Marc Schwartz
Hi On 11 Nov 2004 at 12:24, Drew Hoysak wrote:> I am experiencing strange (to me) output when trying to do simple > calculations. Expressions that should equal zero yield non-zero > values. Examples: > > > a <- 4.1-3.1 > > b <- 5.1-4.1 > > a-b > [1] -4.440892e-16 > > > > (4.1-3.1)-(5.1-4.1) > [1] -4.440892e-16 > > > When this last expression is expanded, I get the right answer: > > > 4.1-3.1-5.1+4.1 > [1] 0 > > > I am using the binary packaged version R-2.0.0-0.fdr.1.fc2.i386.rpm > for Linux Fedora Core 2. I had the same problem with version 1.9.0-0 > > Can anyone tell me what is going on?Floating point arithmetic is imprecise. Cheers Petr> > Thanks, > > > Drew Hoysak > > ______________________________________________ > R-help at stat.math.ethz.ch mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide! > http://www.R-project.org/posting-guide.htmlPetr Pikal petr.pikal at precheza.cz