I apologize if my tone came across wrong. I enjoy reading your comments on
this list.
My goal was to describe what the IEEE and R interpret "careful coding" to be.
> On Feb 01, 2022, at 20:42, Avi Gross <avigr...@verizon.net> wrote:
>
> Richard,
>
> I think it was fairly clear I was explaining how people do arithmetic
> manually and often truncate or round to some number of decimal places. I said
> nothing about what R does or what the IEEE standards say and I do not
> particularly care when making MY point.
>
> My point is that humans before computers also had trouble writing down any
> decimals that continue indefinitely. It cannot be expected computer versions
> of arithmetic can do much better. Different people can opt to do the
> calculation with the same or different numbers of digits ad when compared to
> each other they may not match.
>
> I do care what it does in my programs, of course. My goal here was to explain
> to someone that the anomaly found was not really an anomaly and that careful
> coding may be required in these situations.
>
>
> -----Original Message-----
> From: Richard M. Heiberger <r...@temple.edu>
> To: Avi Gross <avigr...@verizon.net>
> Cc: Nathan Boeger <nboe...@gmail.com>; r-help@r-project.org
> <r-help@r-project.org>
> Sent: Tue, Feb 1, 2022 2:44 pm
> Subject: Re: [External] [R] Funky calculations
>
>
> 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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