Re: [Rd] floor and ceiling can't handle more than 15 decimal pla (PR#8591)

From: <ted.harding_at_nessie.mcc.ac.uk>
Date: Sun 12 Feb 2006 - 15:38:07 GMT


On 12-Feb-06 benphalan@gmail.com wrote:
> Full_Name: Ben Phalan
> Version: 2.2.1
> OS: Win XP
> Submission from: (NULL) (131.111.111.231)
>
>
> I have noticed that floor returns the wrong number when there are more
> than 15
> decimal places:
>

>> floor(6.999999999999999)

> [1] 6
>> floor(6.9999999999999999)

> [1] 7
>
> There is a similar problem with ceiling, so this may apply to all/most
> rounding functions?
>
>> ceiling (2.000000000000001)

> [1] 3

>> ceiling (2.0000000000000001)
> [1] 2

This is not a problem (nor a bug) with 'floor' or 'ceiling'. The "problem" (in quotes because the real problem is the user's) is in R, intrinsic to the finite-length floating-point arithmetic which is used. See:

  > 6.999999999999999 - 7
  [1] -8.881784e-16

  > 6.9999999999999999 - 7

  [1] 0
  > 2.000000000000001 - 2
  [1] 8.881784e-16
  > 2.0000000000000001 - 2
  [1] 0

so, in fact, R cannot "see" the 16th decimal place when you enter a number to that precision -- it is simply lost. Exactly the same "problem" would arise at some point whatever the finite precision to which a floating-point number is stored. The effect is not confined to functions 'floor' and 'ceiling' or any similar "rounding" functions. It applies to all functions; it is simply more obvious with the rounding functions.

Enter

  .Machine

and the first two items in the output are:

  $double.eps
  [1] 2.220446e-16

  $double.neg.eps
  [1] 1.110223e-16

showing that the smallest difference which can be "seen" by R is greater than 1-^(-16).

So, when you type it in, you *think* you have entered

    2.0000000000000001

into R, but you have not. So the user has to face the problem of how to cope with the finite-length representation in any situation where the distinction between 2 and 2.0000000000000001 really matters.

Hoping this helps,
Ted.



E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 12-Feb-06                                       Time: 15:37:53
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