Re: Another weirdest hp50g thing...

In article <1176658041.980159.145450@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
usenet1.20.quaxo@xxxxxxxxxxxxxxx wrote:

Now this is strange... I wonder if I'm dumb or if I always stumble
onto peculiar things...

Take this number: (2^67)-1
And try to factor it with a 50g (3rd item on the "Alg" menu).
After a lengthy time, it returns the input number, as if it can't be
factored. But its factors are actually
193707721 * 761838257287 .
.
.
.
Can someone explain this?

Yes, someone can explain that.

Perhaps I can, in fact. Is it possible that you're running up against
a limitation on the number of significant digits that the calculator is
using?

I'm not sure how different the HP50G is from the HP48G, but if, on my
HP48G, I take 2 and raise it to the 67th power, I get 1.4757395259E+20.
That's eleven digits of precision. Written out the long way, this
number is 147,573,952,590,000,000,000. Obviously, this isn't really the
true representation of 2^67, but it's as close as this calculator is
capable of representing it.

And with this limit of precision, subtracting one doesn't change it at
all. I verified this by doing «2 67 ^ DUP 1 - -», which ought to have
given me a result of one if there were no precision limits, and instead,
it gives me zero.

I'm a bit surprised that your HP50G, in trying to factor this, seems
to decide that it's a prime number. Perhaps it does do because it
recognizes that it's a number that exceeds its precision limits, and
that it therefore knows that it cannot produce a correct result; but it
seems that if that were the case, then it would come to this conclusion
quickly, and not take as long as you say it is taking.

When I try to factor this result on my HP48G, I get
2^29*5*229*457*525313. This is rather surprising. I know that I
couldn't possibly get the correct answer that you're looking for,
because my calculator doesn't have nearly enough precision to do so. I
expected a correct factoring of what I thought was being represented,
which was 147,573,952,590,000,000,000; but since that number is a
multiple of 10^10, there should be at least ten fives in the result, and
there is only one. I suppose my error here was to assume that with a
number that has more digits than the calculator can represent, that the
extra unrepresented digits would be treated as being zeros.


Now the (even weirdest) thing... If I try it with the emulator (flags
set like the actual calc), if the emulator is set to "Authentic
calculator speed", I get the same result as the actual calc;
if instead I run the emulator full speed, unchecking the "Authentic
calculator speed" option, then the emulator gives the correct
answer!!! ?!? What's going on? Is the 50g "quitting", aborting, after
too much time has passed and no solution is found?

I'm not familiar, as I said, with the HP50G, and I am even less
familiar with whatever emulator you are running. A guess I might make
here is that when the emulator is set to "Authentic calculator speed"
that it feels obligated to be as true as possible to the calculator that
it is emulating, but that when it is set otherwise, it takes some
liberties to try to be "better" than the genuine calculator in ways
other than speed. Apparently, one of these other liberties that it
takes is to implement a much higher degree of precision, that allows it
to give you the true answer that you are looking for.

--
"Today, we celebrate the first glorious anniversary of the Information
Purification Directives. ... Our Unification of Thoughts is more powerful
a weapon than any fleet or army on earth. ... Our enemies shall talk
themselves to death and we will bury them with their own confusion."
.

Relevant Pages

  • Re: Calculating Wishes (was hpcatalog.com)
    ... But compared to modern computers, ... Sun-Earth distance useful even if it's know to a precision clearly ... digits of precision. ... > If a calculator offerred say 19 or more digits of precision, ...
    (comp.sys.hp48)
  • Re: how to add two no. of 100 digits or more?
    ... I wonder how many of those digits are significant? ... Probably about 10 digits of actual precision. ... the precision of that calculator doesn't impress me. ... triple-dubya dott tustinfreezone dott org ...
    (comp.lang.c)
  • Re: BigNum -- Floating Point
    ... I require lossless precision. ... You need an infinite number of digits to accurately represent ... The calculator mentioned above uses a Digits class that does have ... > the rounding mode flag as well. ...
    (comp.programming)
  • Re: Another weirdest hp50g thing...
    ... a limitation on the number of significant digits that the calculator is ... That's eleven digits of precision. ... if instead I run the emulator full speed, ...
    (comp.sys.hp48)
  • Re: .99999... still=/= 1
    ... > A scientific calculator does approximate convergence with a certain ... > number significant digits. ... i.e. any partial sum, or do you mean the whole series, which is defined ... The expression you wrote with it stopping after the mth term ...
    (sci.math)
Loading