Thread Subject: pi^2*pi^2==pi^4 gives 0 (untrue)?

Dear Matlab Community,

Why the following?..

pi^2*pi^2==pi^4 gives 0 (untrue)?

exp(5)*exp(5)==exp(10) gives 0 (untrue)?

(2/3)^5*(2/3)^5==(2/3)^10 gives 0 (untrue)?



Is there any problem with the endless digits?


(2/3)*(2/3)==(2/3)^2 gives 1 though..

Thanks in advance

"Leonidas Bantis" <sasm05013@sas.aegean.gr> wrote in message <fm9mcr
$52l$1@fred.mathworks.com>...
> Dear Matlab Community,
>
> Why the following?..
>
> pi^2*pi^2==pi^4 gives 0 (untrue)?
>
> exp(5)*exp(5)==exp(10) gives 0 (untrue)?
>
> (2/3)^5*(2/3)^5==(2/3)^10 gives 0 (untrue)?
>
> Is there any problem with the endless digits?
>
> (2/3)*(2/3)==(2/3)^2 gives 1 though..
>
> Thanks in advance
--------
  You will note that in each case the two quantities that would ideally be
exactly equal, differ in only their least bit out of the 53 bits. That is an error
of only one part in around 10^16. This is about all you can expect of a
computer with this many bits, arriving at a result as it does by two different
computational paths and making roundoff errors along the way.

  I like to give the example of a violation of the basic associative law of
addition:

 3/14 + (3/14 + 15/14) ~= (3/14 + 3/14) + 15/14

According to many computers, digital or binary, these are not equal (though
again they differ only in their least bit.)

Roger Stafford

Leonidas Bantis wrote:
> Dear Matlab Community,
>
> Why the following?..
>
> pi^2*pi^2==pi^4 gives 0 (untrue)?
>
> exp(5)*exp(5)==exp(10) gives 0 (untrue)?
>
> (2/3)^5*(2/3)^5==(2/3)^10 gives 0 (untrue)?


You need to do/evaluate:

"abs(pi^2*pi^2 - pi^4) < tolerance", approx 1e-14 or whatever

etc.


Regards,
Martin

"Leonidas Bantis" <sasm05013@sas.aegean.gr> wrote in news:fm9mcr$52l$1
@fred.mathworks.com:

> Dear Matlab Community,
>
> Why the following?..
>
> pi^2*pi^2==pi^4 gives 0 (untrue)?
>
> exp(5)*exp(5)==exp(10) gives 0 (untrue)?
>
> (2/3)^5*(2/3)^5==(2/3)^10 gives 0 (untrue)?
>
>
>
> Is there any problem with the endless digits?
>
>
> (2/3)*(2/3)==(2/3)^2 gives 1 though..
>
> Thanks in advance


One must be extremely careful when doing equality comparisions on floating
point data. It's generally not a great idea.

--
Scott
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