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chris.bodily@autolivasp.com

2005-Nov-01 16:15 UTC

[R] Unexpected result from binary greater than operator

Hi All,

I recently encountered results that I did not expect, exhibited by the
following code snippet:

test <- function() {
    minX <- 4.2
    min0 <- 4.1
    sigmaG <- 0.1
    Diff <- minX-min0
    print(c(Diff=Diff,sigmaG=sigmaG))
    cat("is Diff > sigmaG?:", Diff > sigmaG,"\n")
    cat("is (4.2 - 4.1) > 0.1?:",(4.2 - 4.1) >
0.1,"\n")
    cat("is 0.1 > 0.1?:", 0.1>0.1,"\n")
}

When I execute the above function I get the following:> test()  Diff sigmaG
   0.1    0.1
is Diff > sigmaG?: TRUE
is (4.2 - 4.1) > 0.1?: TRUE
is 0.1 > 0.1?: FALSE

Can someone please help me understand why R returns TRUE for (4.2 - 4.1) >
0.1 ?

Thanks so much,
Chris


I'm running the precompiled R-2.2.0 binary for Windows on WinXP Pro SP1.
>Sys.getlocale()"LC_COLLATE=English_United States.1252;LC_CTYPE=English_United
States.1252;LC_MONETARY=English_United
States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252"
>version         _
platform i386-pc-mingw32
arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    2.0
year     2005
month    10
day      06
svn rev  35749
language R

Duncan Murdoch

2005-Nov-01 16:22 UTC

head link

[R] Unexpected result from binary greater than operator

On 11/1/2005 11:15 AM, chris.bodily at autolivasp.com wrote:
> Can someone please help me understand why R returns TRUE for (4.2 - 4.1)
>
> 0.1 ?
Rounding error.  See the FAQ item

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

The only numbers that can be represented exactly in R's numeric type are 
integers and fractions whose denominator is a power of 2. Other numbers 
have to be rounded to (typically) 53 binary digits accuracy. As a 
result, two floating point numbers will not reliably be equal unless 
they have been computed by the same algorithm, and not always even then. 
For example

      R> a <- sqrt(2)
      R> a * a == 2
      [1] FALSE
      R> a * a - 2
      [1] 4.440892e-16

The function all.equal() compares two objects using a numeric tolerance 
of .Machine$double.eps ^ 0.5. If you want much greater accuracy than 
this you will need to consider error propagation carefully.

For more information, see e.g. David Goldberg (1991), ?What Every 
Computer Scientist Should Know About Floating-Point Arithmetic?, ACM 
Computing Surveys, 23/1, 5?48, also available via 
http://docs.sun.com/source/806-3568/ncg_goldberg.html

Duncan Murdoch

Sundar Dorai-Raj

2005-Nov-01 16:26 UTC

head link

[R] Unexpected result from binary greater than operator

chris.bodily at autolivasp.com wrote:> Hi All,
> 
> I recently encountered results that I did not expect, exhibited by the
> following code snippet:
> 
> test <- function() {
>     minX <- 4.2
>     min0 <- 4.1
>     sigmaG <- 0.1
>     Diff <- minX-min0
>     print(c(Diff=Diff,sigmaG=sigmaG))
>     cat("is Diff > sigmaG?:", Diff > sigmaG,"\n")
>     cat("is (4.2 - 4.1) > 0.1?:",(4.2 - 4.1) >
0.1,"\n")
>     cat("is 0.1 > 0.1?:", 0.1>0.1,"\n")
> }
> 
> When I execute the above function I get the following:
> 
>>test()
> 
>   Diff sigmaG
>    0.1    0.1
> is Diff > sigmaG?: TRUE
> is (4.2 - 4.1) > 0.1?: TRUE
> is 0.1 > 0.1?: FALSE
> 
> Can someone please help me understand why R returns TRUE for (4.2 - 4.1)
>
> 0.1 ?
> 
> Thanks so much,
> Chris
> 
> 
> I'm running the precompiled R-2.2.0 binary for Windows on WinXP Pro
SP1.
> 
> 
>>Sys.getlocale()
> 
> "LC_COLLATE=English_United States.1252;LC_CTYPE=English_United
> States.1252;LC_MONETARY=English_United
> States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252"
> 
> 
>>version
> 
>          _
> platform i386-pc-mingw32
> arch     i386
> os       mingw32
> system   i386, mingw32
> status
> major    2
> minor    2.0
> year     2005
> month    10
> day      06
> svn rev  35749
> language R
> 
Seems like this is coming up about once a week. See FAQ 7.31.

http://cran.r-project.org/doc/FAQ/R-FAQ.html

Hint:

print(4.2 - 4.1, digits = 16)

--sundar

Peter Dalgaard

2005-Nov-01 16:28 UTC

head link

[R] Unexpected result from binary greater than operator

chris.bodily at autolivasp.com writes:
> Hi All,
> 
> I recently encountered results that I did not expect, exhibited by the
> following code snippet:
> 
> test <- function() {
>     minX <- 4.2
>     min0 <- 4.1
>     sigmaG <- 0.1
>     Diff <- minX-min0
>     print(c(Diff=Diff,sigmaG=sigmaG))
>     cat("is Diff > sigmaG?:", Diff > sigmaG,"\n")
>     cat("is (4.2 - 4.1) > 0.1?:",(4.2 - 4.1) >
0.1,"\n")
>     cat("is 0.1 > 0.1?:", 0.1>0.1,"\n")
> }
> 
> When I execute the above function I get the following:
> > test()
>   Diff sigmaG
>    0.1    0.1
> is Diff > sigmaG?: TRUE
> is (4.2 - 4.1) > 0.1?: TRUE
> is 0.1 > 0.1?: FALSE
> 
> Can someone please help me understand why R returns TRUE for (4.2 - 4.1)
>
> 0.1 ?
Section 7.31 in the FAQ should help:

http://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f
 


-- 
   O__  ---- Peter Dalgaard             ??ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907

Petr Pikal

2005-Nov-01 16:29 UTC

head link

[R] Unexpected result from binary greater than operator

Hi.
Easy. Regardless of OS and R version answer is

binary representation of fractions.
>    (4.2-4.1)>.1[1] TRUE

but
>    (4.3-4.2)>.1[1] FALSE
> print(4.3-4.2, digits=20)[1] 0.099999999999999645

You can not expect precise results using not precise computers.

Use e.g. round
>    round(4.3-4.2)>.1[1] FALSE

HTH
Petr


On 1 Nov 2005 at 9:15, chris.bodily at autolivasp.com wrote:

To:             	r-help at stat.math.ethz.ch
From:           	chris.bodily at autolivasp.com
Date sent:      	Tue, 1 Nov 2005 09:15:50 -0700
Subject:        	[R] Unexpected result from binary greater than operator
> Hi All,
> 
> I recently encountered results that I did not expect, exhibited by the
> following code snippet:
> 
> test <- function() {
>     minX <- 4.2
>     min0 <- 4.1
>     sigmaG <- 0.1
>     Diff <- minX-min0
>     print(c(Diff=Diff,sigmaG=sigmaG))
>     cat("is Diff > sigmaG?:", Diff > sigmaG,"\n")
>     cat("is (4.2 - 4.1) > 0.1?:",(4.2 - 4.1) >
0.1,"\n")
>     cat("is 0.1 > 0.1?:", 0.1>0.1,"\n")
> }
> 
> When I execute the above function I get the following:
> > test()
>   Diff sigmaG
>    0.1    0.1
> is Diff > sigmaG?: TRUE
> is (4.2 - 4.1) > 0.1?: TRUE
> is 0.1 > 0.1?: FALSE
> 
> Can someone please help me understand why R returns TRUE for (4.2 -
> 4.1) > 0.1 ?
> 
> Thanks so much,
> Chris
> 
> 
> I'm running the precompiled R-2.2.0 binary for Windows on WinXP Pro
> SP1.
> 
> >Sys.getlocale()
> "LC_COLLATE=English_United States.1252;LC_CTYPE=English_United
> States.1252;LC_MONETARY=English_United
> States.1252;LC_NUMERIC=C;LC_TIME=English_United States.1252"
> 
> >version
>          _
> platform i386-pc-mingw32
> arch     i386
> os       mingw32
> system   i386, mingw32
> status
> major    2
> minor    2.0
> year     2005
> month    10
> day      06
> svn rev  35749
> language R
> 
> ______________________________________________
> 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
Petr Pikal
petr.pikal at precheza.cz

Andy Bunn

2005-Nov-01 16:34 UTC

head link

[R] Unexpected result from binary greater than operator

Look at ?all.equal and ?identical as well as searching the archives for
those terms. You'll find many an illuminating thread on precision, floating
point arithmetic and other wonders.

minX <- 4.2
min0 <- 4.1
sigmaG <- 0.1
Diff <- minX-min0
all.equal(Diff, sigmaG)
identical(Diff, sigmaG)

HTH, Andy

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