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

[Raymond T. <toy...@gm...>]

>>>>> "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