Floating points and floor() ?

[Folkes, Michael-2]

Perhaps somebody could clarify for me if the following is a floating
point matter or otherwise, and how am I to correct for it?

> floor(100*.1)
[1] 10

> 100*(1.0-.9)
[1] 10

> floor(100*(1-0.9))
[1] 9


Thanks!
Michael
_______________________________________________________
Michael Folkes
Salmon Stock Assessment
Canadian Dept. of Fisheries & Oceans    
Pacific Biological Station
3190 Hammond Bay Rd.
Nanaimo, B.C., Canada
V9T-6N7
Ph [phone] Fax [phone]  [hidden email]


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[Jeff Newmiller]

You are assuming that 0.1 is exactly represented. Since it is not, either 0.1 or 1-0.9 will be less than 0.1.

As to what you should do about it... that depends on what you are trying to accomplish. Whatever it is, you need to use some other approach. Often the alternative involves using integers as much as possible.
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"Folkes, Michael" <[hidden email]> wrote:

Perhaps somebody could clarify for me if the following is a floating point matter or otherwise, and how am I to correct for it? > floor(100*.1) [1] 10 > 100*(1.0-.9) [1] 10 > floor(100*(1-0.9)) [1] 9 Thanks! Michael_____________________________________________
Michael Folkes Salmon Stock Assessment Canadian Dept. of Fisheries & Oceans Pacific Biological Station 3190 Hammond Bay Rd. Nanaimo, B.C., Canada V9T-6N7 Ph [phone] Fax [phone] [hidden email] [[alternative HTML version deleted]]_____________________________________________
[hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.


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[David Winsemius]

On Mar 3, 2011, at 8:23 PM, Folkes, Michael wrote:

> Perhaps somebody could clarify for me if the following is a floating
> point matter or otherwise, and how am I to correct for it?
>
>> floor(100*.1)
> [1] 10
>
>> 100*(1.0-.9)
> [1] 10
>
>> floor(100*(1-0.9))
> [1] 9
>
>

Yes. It's a "floating point matter". What do you mean by "correct for  
it"? What result would be "correct"?


David Winsemius, MD
Heritage Laboratories
West Hartford, CT

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[rex.dwyer]

Hi Michael,

In floating point calculation, 1.0-.9 is not exactly 0.1.  This is easily seen by subtracting.
> (1.0-.9)-0.1
[1] -2.775558e-17
> (1.0-.9)==0.1
[1] FALSE

David is right, you can't "correct" this.  You can only compensate by taking care that you never, ever test whether 2 FP numbers are equal, because they almost never are.  You must always ask whether the difference is small.

> round(1.0-.9-.1,15)==0
[1] TRUE

Unfortunately, most of us forget this rule once in a while and write a loop like "while (x!=0)..." that won't terminate.
HTH
Rex



-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of Folkes, Michael
Sent: Thursday, March 03, 2011 9:24 PM
To: [hidden email]
Subject: [R] Floating points and floor() ?

Perhaps somebody could clarify for me if the following is a floating
point matter or otherwise, and how am I to correct for it?

> floor(100*.1)
[1] 10

> 100*(1.0-.9)
[1] 10

> floor(100*(1-0.9))
[1] 9


Thanks!
Michael
_______________________________________________________
Michael Folkes
Salmon Stock Assessment
Canadian Dept. of Fisheries & Oceans
Pacific Biological Station
3190 Hammond Bay Rd.
Nanaimo, B.C., Canada
V9T-6N7
Ph [phone] Fax [phone]  [hidden email]


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message may contain confidential information. If you are not the designated recipient, please notify the sender immediately, and delete the original and any copies. Any use of the message by you is prohibited.
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[Petr Savicky-2]

On Thu, Mar 03, 2011 at 06:23:36PM -0800, Folkes, Michael wrote:

> Perhaps somebody could clarify for me if the following is a floating
> point matter or otherwise, and how am I to correct for it?
>
> > floor(100*.1)
> [1] 10
>
> > 100*(1.0-.9)
> [1] 10
>
> > floor(100*(1-0.9))
> [1] 9

As others pointed out, 0.1 is not exactly representable in base 2,
so we get

  formatC(0.1, digits=20)
  [1] "0.10000000000000000555"

  formatC(100*0.1, digits=20, width=-1)
  [1] "10"

  formatC(100*(1 - 0.9), digits=20)
  [1] "9.9999999999999982236"

A correct result may be obtained, if you reorganize your
calculation, so that all intermediate results are integers
and the inaccurate division is only the last operation. Then,
floor(n/10) will be correct and also n %/% 10 may be used.

Alternatively, if you work with decimal numbers with 1 or 2
decimal digits, then also floor(round(x, 1)) or floor(round(x, 2))
work correctly, if x is not too large.

See FAQ 7.31

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

and

  http://rwiki.sciviews.org/doku.php?id=misc:r_accuracy:decimal_numbers

for further examples and some hints.

Hope this helps.

Petr Savicky.

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[Folkes, Michael-2]

This was most helpful Rex.  It makes clear how I can compensate for the matter.
Too bad it's not March 15, I could declare "beware the 0.Ides of March!"
Michael


-----Original Message-----
From: [hidden email] [mailto:[hidden email]]
Sent: Thu 03/03/2011 8:24 PM
To: Folkes, Michael; [hidden email]
Subject: RE: Floating points and floor() ?
 
Hi Michael,

In floating point calculation, 1.0-.9 is not exactly 0.1.  This is easily seen by subtracting.
> (1.0-.9)-0.1
[1] -2.775558e-17
> (1.0-.9)==0.1
[1] FALSE

David is right, you can't "correct" this.  You can only compensate by taking care that you never, ever test whether 2 FP numbers are equal, because they almost never are.  You must always ask whether the difference is small.

> round(1.0-.9-.1,15)==0
[1] TRUE

Unfortunately, most of us forget this rule once in a while and write a loop like "while (x!=0)..." that won't terminate.
HTH
Rex



-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of Folkes, Michael
Sent: Thursday, March 03, 2011 9:24 PM
To: [hidden email]
Subject: [R] Floating points and floor() ?

Perhaps somebody could clarify for me if the following is a floating
point matter or otherwise, and how am I to correct for it?

> floor(100*.1)
[1] 10

> 100*(1.0-.9)
[1] 10

> floor(100*(1-0.9))
[1] 9


Thanks!
Michael
_______________________________________________________
Michael Folkes
Salmon Stock Assessment
Canadian Dept. of Fisheries & Oceans
Pacific Biological Station
3190 Hammond Bay Rd.
Nanaimo, B.C., Canada
V9T-6N7
Ph [phone] Fax [phone]  [hidden email]


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and provide commented, minimal, self-contained, reproducible code.




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