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

[Alonso Del Arte]

Thanks to everyone who helped me understand what's going on here. At one
point I did try 13! - 2^31, but that was no help, I was off in the
exponent. When Sean said 2^32, it all fell into place.

> should we have new sequences for "overflown" versions of the factorials,
one for signed 4 byte integers with the usual implementation using 2's
complement ... and another one for 8 byte signed integers?

I've been going back and forth on this question. Surely other Java students
will come across the 32-bit sequence and it would be good to have it in the
OEIS. On the other hand, I can also foresee the day when both the 32-bit
and 64-bit sequences will be of purely historical interest.

Al

On Fri, Jun 30, 2017 at 3:16 AM, <john.mason at lispa.it> wrote:

> In Java, use : import java.math.BigInteger;
> john
> __________________________________
>
>
>
>
>
> Da:     Alonso Del Arte <alonso.delarte at gmail.com>
> Per:    Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Data:   29/06/2017 23:43
> Oggetto:        [seqfan] Factorials (A000142) "compressed" through the int
> data type
> Inviato da:     "SeqFan" <seqfan-bounces at list.seqfan.eu>
>
>
>
> 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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> Seqfan Mailing list - http://list.seqfan.eu/
>
>
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>



-- 
Alonso del Arte
Author at SmashWords.com
<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>