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

[Jack Brennen]

By the way, here's PARI/GP code that gives the sequence for any
number of bits, just change Bits:

Bits=32;N=Mod(1,2^Bits);j=0;until(N==0,print(-centerlift(-N));\
   j+=1;N*=j);

The trick of using -centerlift(-N) instead of centerlift(N) is to
get 2^(Bits-1) to display as a negative number, consistent with
two's complement representation.

- Jack


On 6/30/2017 2:01 PM, Alonso Del Arte wrote:
> 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>
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
> 
> 
>