On Feb 2, 1:16 pm, Julien Puydt <julien.pu...@laposte.net> wrote:
> Le 02/02/2012 23:22, Jonathan Bober a crit :
>
> > Can you think of a reason that the answer should change? Does maxima use
> > less that 53 bits of precision ever?
>
> Well, if I don't err, $10^{17}$ has 18 decimal digits, which is more
> than the 15,95.. that fit in 53 binary digits.

Maxima uses the floating point in the underlying lisp implementation
unless
you specify bigfloats, in which case the floating point precision can
be
set to fewer bits as well as more bits.

I don't understand why you can't work with numbers like 2^(-53) or
2^(-52).
It's not that they take so many digits to write down this way, and it
does
actually reflect what is going on in a fp system with binary base.

>
> In any case, let me repeat : three of the four failing numerical tests
> pass if I add a relative tolerance of 1e-15... the only remaining one is
> the computation of $\Gamma(10)$, where the relative error is
> 1.2832...e-15, for which I don't know if it's acceptable or not, but
> doesn't look that crazy.

I think that's unacceptable.

>
> Snark on #sagemath

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