1. This site uses cookies. By continuing to use this site, you are agreeing to our use of cookies. Learn More.

Overflow?

Discussion in 'Support' started by vefatica, Jun 13, 2008.

  1. vefatica

    Joined:
    May 20, 2008
    Messages:
    7,888
    Likes Received:
    30
    What causes "overflow", as below, and can I anticipate it?

    g:\projects\4utils\release> echo %@sterling[3249] | wc
    Lines Words Chars
    1 1 10003

    g:\projects\4utils\release> echo %@sterling[3250] | wc
    TCC: Overflow "(2 * acos(-1) * 3250) ** (1 / 2) * (3250 / exp(1)) ** 3250"
    Lines Words Chars
    1 15 60

    Note: Sterling's formula, seen above in the error message, approximates
    N-factorial. The result for N=3250 would have been 3-4 characters longer than
    the result for 3249 (or about 10007 characters). Apparently I have run into
    some limit I'm not aware of.
     
  2. rconn

    rconn Administrator
    Staff Member

    Joined:
    May 14, 2008
    Messages:
    9,809
    Likes Received:
    82
    vefatica wrote:

    An Overflow error will occur if the digits to the left of the decimal
    exceed 10,000 characters.

    Rex Conn
    JP Software
     
  3. logic

    Joined:
    May 30, 2008
    Messages:
    42
    Likes Received:
    0
    From: rconn
    Sent: Friday, June 13, 2008 1:40 PM
    Subject: RE: [Support-t-192] Overflow?

    Rex,

    Can you work with Wolfram Systems for V10 and integrate Mathematica into the
    TCC code base? The increased startup time would be more than compensated-for
    by the improvement in expression processing. ;-)

    I jest,

    Jonathan Gilbert_
    \\\ / / / \ |_) |_/
    \\\/ \/ \__/ | \ | \
    Software Systems
     
  4. Steve Fabian

    Joined:
    May 20, 2008
    Messages:
    3,523
    Likes Received:
    4
    vefatica wrote:
    | Note: Sterling's formula, seen above in the error message,
    | approximates N-factorial.

    That's "Stirling's formula"...
    --
    Steve
     
  5. vefatica

    Joined:
    May 20, 2008
    Messages:
    7,888
    Likes Received:
    30
    On Fri, 13 Jun 2008 15:42:37 -0500, you wrote:


    It's the one I know:

    n! ~ sqrt(2*pi*n)(n/e)^n

    Maybe he has others. He has a bunch of numbers too.

    Oh!, now I get it. Indeed, it's Stirling's formula.
     
  6. rconn

    rconn Administrator
    Staff Member

    Joined:
    May 14, 2008
    Messages:
    9,809
    Likes Received:
    82
    logic wrote:


    I've had people nagging me for years for > 80 bit precision in @EVAL. I
    thought that 20,000 digit precision (10k to the left & 10k to the right
    of the decimal) ought to be sufficient to satisfy even the fussiest
    user; I should have known better.

    Though exactly *why* anybody needs numbers larger than the number of
    subatomic particles in the universe is still a mystery to me ...

    Rex Conn
    JP Software
     
  7. Charles Dye

    Charles Dye Super Moderator
    Staff Member

    Joined:
    May 20, 2008
    Messages:
    3,288
    Likes Received:
    39
    Permutations and combinations of the number of subatomic particles in the universe?
     
  8. rconn

    rconn Administrator
    Staff Member

    Joined:
    May 14, 2008
    Messages:
    9,809
    Likes Received:
    82
    Charles Dye wrote:

    Nope, still got that covered. 10^10000 is a REALLY big number ...

    Rex Conn
    JP Software
     
  9. Steve Fabian

    Joined:
    May 20, 2008
    Messages:
    3,523
    Likes Received:
    4
    Charles Dye wrote:
    | ---Quote (Originally by rconn)---
    | Though exactly *why* anybody needs numbers larger than the number of
    | subatomic particles in the universe is still a mystery to me ...
    | ---End Quote---
    | Permutations and combinations of the number of subatomic particles in
    | the universe?

    National debt?
    --
    Steve
     
  10. logic

    Joined:
    May 30, 2008
    Messages:
    42
    Likes Received:
    0
    From: rconn
    Sent: Monday, June 16, 2008 9:58 AM
    Subject: RE: [Support-t-192] Re: Overflow?


    Actually I don't think you have got it covered. A conservative estimate of
    the number of particles in the universe is 10^80. To count all of the
    possible permutations of all of the subatomic particles in the universe, you
    need to be able to store (10^80)! numerically. This is a REALLY, REALLY,
    REALLY big number!

    Stirling's approximation:

    N! ~= sqrt(2 pi N) * (N/e)^N

    N in this case is 10^80 -- 1 followed by 80 zeroes. Putting this into the
    formula yields:

    sqrt(2 pi 10^80) * (10^80 / e) ^ 10^80

    The first factor breaks down to sqrt(2 pi) * sqrt(10^80), which is 10^40 *
    sqrt(2 pi). The second factor takes a number marginally under 10^80 and puts
    it to the power of 10^80. The exact base being exponentiated can be
    determined as follows:

    ln(10^80 / e)
    10^80 / e = e
    (ln(10^80) - ln(e))
    = e
    (184.2068 - 1)
    = e
    183.2068
    = e
    183.2068 / ln(10)
    = 10
    79.5657
    = 10

    This leaves us with:

    _ _ 10^80
    | 79.5657 | (79.5657 * 10^80)
    | 10 | = 10
    |_ _|
    7.95657 * 10^81
    = 10

    This number is slightly less than 1 followed by (10^81 + 8) zeroes. There is
    no way you could store this in a variable with room for 1 followed by 10,000
    zeroes. 10^81 is significantly larger than 10^4. :-)

    Jonathan Gilbert_
    \\\ / / / \ |_) |_/
    \\\/ \/ \__/ | \ | \
    Software Systems
     
  11. logic

    Joined:
    May 30, 2008
    Messages:
    42
    Likes Received:
    0
    From: logic
    Sent: Monday, June 16, 2008 10:27 AM
    Subject: RE: [Support-t-192] Re: Overflow?

    [snip]

    Oh, and of course I forgot to include the first factor. In fact we're
    looking at

    40 7.95657 * 10^81
    sqrt(2 pi) * 10 * 10

    Not that adding an additional 40 zeroes makes much difference when you
    already have 10^81 zeroes. Not 81 zeroes, but 10^81 zeroes.

    It is a number so large that the human brain struggles to comprehend it. It
    is the same league as taking a googol and putting it to the power of a
    googol.

    Jonathan Gilbert_
    \\\ / / / \ |_) |_/
    \\\/ \/ \__/ | \ | \
    Software Systems
     
  12. joshjeppson

    Joined:
    Jun 2, 2008
    Messages:
    42
    Likes Received:
    0
    Yes, that is a very big number, but why would any one want to work with numbers like that in a command processor or shell?

    Use Mathematica, eh?

    - Josh
     
  13. BillMc

    BillMc Guest

    On Mon 16-Jun-08 10:27am -0600, logic wrote:





    I don't remember where I got this, but my functions include
    lfac (which computes log(x!) -- the natural log). Given
    that, solving the problem is simple. There are six lines
    below - some of them may spill over in your email programs:

    [Caution: this will not work in 4nt - use tcc.]

    function lfac=`%@eval[%1*log(%1)-%1+log(%1*(1+4*%1*(1+2*%1)))/6+.5723649429247001]`
    set x=%@eval[%@lfac[10**80]/log(10)]
    set y=%@eval[%x-.5=0.0]
    set z=%@eval[10**(%x-%y)=0.4]
    echo %z * 10 ** %y
    unset x y z

    You should see the approximate answer as:

    3.5476 * 10 ** 7956570551809674817234887108108339491770560299419633343388554621683413535079112945

    That is 3.5476 times 10 to the N, where N is a 82 digit
    integer.

    --
    Best regards,
    Bill
     
  14. Charles Dye

    Charles Dye Super Moderator
    Staff Member

    Joined:
    May 20, 2008
    Messages:
    3,288
    Likes Received:
    39
    I think that the message is very clear here: somewhere outside of and beyond our universe is an operating system, coded up over incalculable spans of time by some kind of hacker-demiurge. The cosmic operating system uses a command-line interface. It runs on something like a teletype, with lots of noise and heat; punched-out bits flutter down into its hopper like drifting stars. The demiurge sits at his teletype, pounding out one command line after another, specifying the values of fundamental constants of physics:

    universe -G 6.672e-11 -e 1.602e-19 -h 6.626e-34 -protonmass 1.673e-27....

    and when he's finished typing out the command line, his right pinky hesitates above the ENTER key for an aeon or two, wondering what's going to happen; then down it comes--and the WHACK you hear is another Big Bang.

    -- Neal Stephenson, In the Beginning Was the Command Line
     
  15. DMcCunney

    Joined:
    Jun 7, 2008
    Messages:
    96
    Likes Received:
    3
    On Tue, Jun 17, 2008 at 11:27 AM, Charles Dye <> wrote:


    Boot Universe. No sync.


    ______
    Dennis
     

Share This Page