Re: Possible loss of accuracy

[John W. Eaton]

On 05/15/2013 05:27 AM, Marco Caliari wrote:
> Dear all,
>
> if I compute
>
> t=50
> (1-2^(-t))^(2^t)
>
> I get (different versions, machines, ...)
>
> ans = 3.67879441128629e-01
>
> which is correct to the 10th digit (compared with www.wolframalpha.com).
> I can stay with it, but Matlab is correct to the 15th digit. While
> trying to understand, I wrote the following Fortran code
>
> program test
> integer t
> t = 50
> write(6,'(1x,e24.16)') (1.d0-2.d0**(-t))**(2.d0**t)
> write(6,'(1x,e24.16)') (1.d0-2.d0**(-50))**(2.d0**50)
> stop
> end
>
> If I compile with gfortran test.f (gfortran 4.3.3) and run, I get
>
> 0.3678794411286288E+00 (~ Octave value)
> 0.3678794411714422E+00 (~ Matlab value)
>
> and if I compile with gfortran -O2 test.f and run, I get
>
> 0.3678794411714422E+00
> 0.3678794411714422E+00

I don't know what the problem is, but with Octave 3.6.2 on my system,
I get 0.367879441171442 for your expression.

jwe