[seqfan] Re: Factorials (A000142) "compressed" through the int data type

[Sean A. Irvine]

It just arithmetic mod 2^32, e.g. in Maple:

> R:=IntegerRing(2^32);
> R!Factorial(13);
1932053504
> R!Factorial(14);
1278945280

also, the int type in Java is signed, so for a result exceeding 2^31-1 you
actually end up with a negative value in the same equivalence class.

Sean.


On 30 June 2017 at 09:43, Alonso Del Arte <alonso.delarte at gmail.com> wrote:

> One of the things we take for granted in Maple and Mathematica is that
> integers can be arbitrarily large. There are practical limitations, of
> course, but in those programs we can deal with larger numbers than in
> BASIC, FORTRAN, Pascal, etc., without having to worry about overflows and
> such things.
>
> I'm taking a Java course. The instructor told one of my classmates that a
> function can't call itself. I suppose that's proper at this point in the
> class, no pun intended. But it got me thinking about the classic example of
> the function that calls itself, the factorial function implemented
> recursively.
>
>   public static int factorial(int n) {
>     if (n > 0) {
>       return n * factorial(n - 1);
>     } else {
>       return 1;
>     }
>   }
>
> It works up to 12! But for 13! the overflow should trigger some kind of
> runtime error and stop program execution, right? It doesn't.
>
> 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800,
> 479001600, 1932053504, 1278945280, 2004310016, 2004189184, -288522240,
> -898433024, 109641728, -2102132736, -1195114496, -522715136, 862453760,
> -775946240, 2076180480, -1853882368, 1484783616, -1375731712, -1241513984,
> 1409286144, 738197504, -2147483648, -2147483648, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
> 0, 0, 0, 0, 0, 0, 0, BUILD SUCCESSFUL (total time: 1 second)
>
> Of course there are larger data types that can be chosen, but that only
> postpones the inevitable overflow.
>
> Somehow it makes sense to me that this says 32! = 0. And it also makes
> sense that there are negative values for 17! and 18! and a few more after
> that.
>
> But I'm not understanding how the overflow from 13 * 12! gives 1932053504.
> I'm hoping someone here can give some insight on this.
>
> Al
>
> --
> Alonso del Arte
> Author at SmashWords.com
> <https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
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