[R] [External] Funky calculations

[Jeff Newmiller]

Please don't be dense. Not "some languages"... the discussion here has tried very hard to explain why this affects all of them. Including C/C++ (R is written in C). Look at [1] if you don't believe us.

[1] https://0.30000000000000004.com/


On February 1, 2022 7:00:44 PM PST, Nathan Boeger <nboeger using gmail.com> wrote:
>Thank you for this explanation!
>
>I have a long background in C/C++ and never realized this was such an issue
>with some languages. At least, with trivial single digit decimals. I
>understand accuracy issues with very large decimals, repeating or
>non-terminating rationals and I have handled them in the past. It makes me
>worried about all the R scripts I have written before (yikes!).
>
>Cheers
>
>-nb
>
>On Wed, 2 Feb 2022 at 02:44, Richard M. Heiberger <rmh using temple.edu> wrote:
>
>> RShowDoc('FAQ')
>>
>> then search for 7.31
>>
>>
>> This statement
>> "If you stop at a 5 or 7 or 8 and back up to the previous digit, you round
>> up. Else you leave the previous result alone."
>> is not quite right.  The recommendation in IEEE 754, and this is how R
>> does arithmetic, is to Round Even.
>>
>> I ilustrate here with decimal, even though R and other programs use binary.
>>
>> > x <- c(1.4, 1.5, 1.6, 2.4, 2.5, 2.6, 3.4, 3.5, 3.6, 4.4, 4.5, 4.6)
>> > r <- round(x)
>> > cbind(x, r)
>>         x r
>>  [1,] 1.4 1
>>  [2,] 1.5 2
>>  [3,] 1.6 2
>>  [4,] 2.4 2
>>  [5,] 2.5 2
>>  [6,] 2.6 3
>>  [7,] 3.4 3
>>  [8,] 3.5 4
>>  [9,] 3.6 4
>> [10,] 4.4 4
>> [11,] 4.5 4
>> [12,] 4.6 5
>> >
>>
>> Numbers whose last digit is not 5 (when in decimal) round to the nearest
>> integer.
>> Numbers who last digit is 5 (1.5, 2.5, 3.5, 4.5 above)
>> round to the nearest EVEN integer.
>> Hence 1.5 and 3.5 round up to the even numbers 2 and 4.
>> 2.5 and 4.5 round down do the even numbers 2 and 4.
>>
>> This way the round ups and downs average out to 0.  If we always went up
>> from .5 we would have
>> an updrift over time.
>>
>> For even more detail click on the link in FAQ 7.31 to my appendix
>> https:// link.springer.com/content/pdf/bbm%3A978-1-4939-2122-5%2F1.pdf
>> and search for "Appendix G".
>>
>> Section G.5 explains Round to Even.
>> Sections G.6 onward illustrate specific examples, such as the one that
>> started this email thread.
>>
>> Rich
>
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>
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-- 
Sent from my phone. Please excuse my brevity.