[R] [External] Funky calculations

[Nathan Boeger]

I understand this and with C the data type used is important. For this type
of calculation, I would normally use a float (basic single precision is all
I require).

#include <stdio.h>

void main() {
  float foo = (0.4 + 0.2 + 0.30 + 0.1) ;
  printf("foo: %f , foo > 1: %s \n", foo, (foo > 1.0 ? "true" : "false"));
  double bar = (0.4 + 0.2 + 0.30 + 0.1) ;
  printf("bar: %lf , bar > 1: %s \n", bar, (bar > 1.0 ? "true" : "false"));
}

gcc  c-check.c -o c-check
./c-check
foo: 1.000000 , foo > 1: false
bar: 1.000000 , bar > 1: true

Again, it was my mistake for not reading the R-FAQ. I had no idea it would
spark such a long thread.

Cheers

-nb

On Wed, 2 Feb 2022 at 10:30, Bill Dunlap <williamwdunlap using gmail.com> wrote:

> The base 2 representation of 0.4 repeats the digit sequence 1001
> infinitely, hence must be rounded.  The problem occurs in C the same as it
> does in R.
>
> bill using Bill-T490:~$ cat a.c
> #include <stdio.h>
>
> int main(int argc, char* argv[])
> {
>     double d = 0.4 + 0.3 + 0.2 + 0.1;
>     printf("0.4+0.3+0.2+0.1 -> %24.17g\n", d);
>     printf("0.4+0.3+0.2+0.1 == 1.0 -> %s\n", d == 1.0 ? "true" : "false");
>     return 0;
> }
> bill using Bill-T490:~$ gcc a.c
> bill using Bill-T490:~$ ./a.out
> 0.4+0.3+0.2+0.1 ->      0.99999999999999989
> 0.4+0.3+0.2+0.1 == 1.0 -> false
>
> -Bill
>
> On Tue, Feb 1, 2022 at 7:01 PM 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
>>
>>         [[alternative HTML version deleted]]
>>
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>>
>

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