Re: [Maxima-discuss] A proposal to solve Re: float(exp(10000)) works, but float(exp(10000/3)) doesn't

[Stavros M. (Σ. Μ. <mac...@al...>]

Yes, calling floats "approximate numbers" is a shorthand.

It really means "the numbers of the form a*2^b (or 10^b) for certain ranges
of a and b". Some calculations on such numbers result in numbers of the
same form, in which case the calculation can be exact, but most
calculations on most such numbers do not have an exact representation of
that form. Yes, 2.0/3.0 results in the "exact" number 6004799503160661 *
2^-53, but no one is really interested in that number except as an
approximation to 2/3.

So I don't find it misleading to call floats "approximate numbers" for
beginners.

           -s

On Thu, Jan 28, 2016 at 1:29 PM, Raymond Toy <toy...@gm...> wrote:

> >>>>> "Stavros" == Stavros Macrakis <(Σταῦρος Μακράκης)" <
> mac...@al...>> writes:
>
>     Stavros> ​Maxima has had arbitrary-precision exact integers and
>     Stavros> rationals for about 40 years, long before Python 3.
>
>     Stavros> Fateman's proposal is not about "exact decimal numbers";
>     Stavros> it is about approximate (finite-precision) numbers using
>     Stavros> base 10 instead of base 2. Decimal floating point (with
>     Stavros> arbitrarily large powers of 10) is still
>     Stavros> approximate. Though 2/5 can be represented exactly in
>     Stavros> decimal floating point, 2/3 cannot.
>
> Just want to say that, as a friend told me, floating point numbers
> (binary, decimal) should really be thought of as exact rationals of a
> certain form.  It is the operations on them that are approximations.
>
> Thinking about floats this way makes it much easier to understand.
> Especially for things like cos(float(2^120)).  2^120 is exactly
> representable as a binary float; no approximations or any other
> fuzziness.
>
> --
> Ray
>
>
>
> ------------------------------------------------------------------------------
> Site24x7 APM Insight: Get Deep Visibility into Application Performance
> APM + Mobile APM + RUM: Monitor 3 App instances at just $35/Month
> Monitor end-to-end web transactions and take corrective actions now
> Troubleshoot faster and improve end-user experience. Signup Now!
> http://pubads.g.doubleclick.net/gampad/clk?id=267308311&iu=/4140
> _______________________________________________
> Maxima-discuss mailing list
> Max...@li...
> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>