R devel - Jan 2005 - Inaccuracy in seq() function (PR#7503)

Full_Name: Vlad Stolin
Version: R 2.0.0
OS: Windows 2000
Submission from: (NULL) (204.128.232.211)


When generating the sequence using seq() function with non-integer numbers
result is somewhat unpredictable. Example:
> v1<-seq(1.60,1.90,.05)
> v2<-c(1.60,1.65,1.70,1.75,1.80,1.85,1.90)
> v1-v2
[1] 0.000000e+00 2.220446e-16 2.220446e-16 0.000000e+00 0.000000e+00
0.000000e+00 2.220446e-16
> v1==v2
[1]  TRUE FALSE FALSE  TRUE  TRUE  TRUE FALSE
> v1>1.70 & v2<1.80
[1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE

And the bug is?

You don't expect 1.60 + 0.05 == 1.65 do you?  None of those numbers can be 
represented exactly in a binary computer, so there are bound to be small 
errors as you have noted.

See the warning in help("=="), and the section on BUGS in the FAQ.


On Wed, 12 Jan 2005 vstolin@lordabbett.com wrote:
> Full_Name: Vlad Stolin
> Version: R 2.0.0
> OS: Windows 2000
> Submission from: (NULL) (204.128.232.211)
>
>
> When generating the sequence using seq() function with non-integer numbers
> result is somewhat unpredictable. Example:
>> v1<-seq(1.60,1.90,.05)
>> v2<-c(1.60,1.65,1.70,1.75,1.80,1.85,1.90)
>> v1-v2
> [1] 0.000000e+00 2.220446e-16 2.220446e-16 0.000000e+00 0.000000e+00
> 0.000000e+00 2.220446e-16
>> v1==v2
> [1]  TRUE FALSE FALSE  TRUE  TRUE  TRUE FALSE
>> v1>1.70 & v2<1.80
> [1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE
-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

On 12-Jan-05 vstolin@lordabbett.com wrote:
> [...]
> When generating the sequence using seq() function with
> non-integer numbers result is somewhat unpredictable.
> Example:
>> v1<-seq(1.60,1.90,.05)
>> v2<-c(1.60,1.65,1.70,1.75,1.80,1.85,1.90)
>> v1-v2
> [1] 0.000000e+00 2.220446e-16 2.220446e-16 0.000000e+00 0.000000e+00
> 0.000000e+00 2.220446e-16
>> v1==v2
> [1]  TRUE FALSE FALSE  TRUE  TRUE  TRUE FALSE
>> v1>1.70 & v2<1.80
> [1] FALSE FALSE  TRUE  TRUE FALSE FALSE FALSE
This sort of thing is inevitable as a consequence of the
fact that most decimal fractions are not stored accurately
in a finite binary representation. It's not a bug in seq().

Example:

  1.65-(1.60+0.05)
  [1] -2.220446e-16

(compare your second term in v1-v2).

Personally I always prefer to use scaled integer sequences
when creating fractional sequences:

  v3 <- seq(160,190,5)/100

  v1-v3
  [1] 0.000000e+00 2.220446e-16 2.220446e-16 0.000000e+00
  [5] 0.000000e+00 0.000000e+00 2.220446e-16

  v3-v2
  [1] 0 0 0 0 0 0 0

so my method agrees with your hand-forced v2.

But be watchful:

  v4 <- seq(160,190,5)*0.01
  v3-v4
  [1]  0.000000e+00 -2.220446e-16  0.000000e+00  0.000000e+00 
  [5]  0.000000e+00  0.000000e+00 -2.220446e-16

so "/100" is not the same as "*0.01"! And you can similarly
check that not only is v4 != v3, but neither is v4 != v1 nor
is v4 != v2. So now we have three different results (v1,
v2 == v3, v4).

Since (1.60+0.05) corresponds to the method used by seq(),
and is not equal to 1.65, you might argue that seq() is wrong,
but since the method used by seq() consists of adding the "by"
the result of seq() is correct -- in its own terms!

If you know that your intended sequence should only have a
fixed number of decimal places (in your case 2), you can force
all methods to give the same result by using round():

  v1a <- round(seq(1.60,1.90,0.05),2)
  v2a <- round(c(1.60,1.65,1.70,1.75,1.80,1.85,1.90),2)
  v3a <- round(seq(160,190,5)/100,2)
  v4a <- round(seq(160,190,5)*0.01,2)

  v1a-v2a
  [1] 0 0 0 0 0 0 0

  v1a-v3a
  [1] 0 0 0 0 0 0 0

  v1a-v4a
  [1] 0 0 0 0 0 0 0

so now they are indeed all equal. Also note that

  v2-v2a
  [1] 0 0 0 0 0 0 0
  v3-v3a
  [1] 0 0 0 0 0 0 0


so my "seq(160.190.5)/100" gives the same result as the rounded
result, and as your hand-forced version. This is why I prefer it!

Best wishes,
Ted.


--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861  [NB: New number!]
Date: 12-Jan-05                                       Time: 20:52:26
------------------------------ XFMail ------------------------------