On Sun, Oct 4, 2009 at 10:56 PM, rjf <fate...@gmail.com> wrote:
>
>
>
> On Oct 4, 12:35 pm, Fredrik Johansson <fredrik.johans...@gmail.com>
> wrote:
> ...big snip.. which I may respond to later (or not..)
>
>
>> Indeed, without manually setting the precision,
>>
>> sage: maxima('bfloat(exp(1/%pi^1000)-1)')
>> 0.0b0
>>
>> which is wrong, and with no indication that it is wrong.
>
> Actually, it is doing the right thing, which is to compute in the
> default precision
> (initially 56 bits for about 16 decimal digits), the values of pi,
> pi^1000, exp(..) and
> the subtraction. It is doing the arithmetic correctly rounded. The
> result of doing
> the arithmetic correctly rounded in 56-bit arithmetic is 0. If you
> want to do the arithmetic in a different precision, try, for example,
> fpprec:1000 .
Yes, it does the right thing if that's what it claims to do. (For
floating point evaluation in SymPy with every arithmetic operation
done using a fixed precision and correct rounding to nearest, you can
evaluate it in mpmath.)
> bfloat does not claim to do what N[] does in mathematica.
SymPy's evalf claims to do (roughly) what N[] does in Mathematica.
> It is
> plausible that one could obtain similar results by using bfloat in a
> loop --- if one computed with a few different fpprec and got the same
> value, but such a simple scheme can be defeated. But there are no
> guarantees on the accuracy of the RESULT, just best effort to achieve
> the accuracy of each operation to (typically) one unit in the last
> place or better.
>
> There ARE problems with maxima 5.18 in that
> if you ask is (exp(1/%pi^1000)-1 >0) it returns false ... it
> thinks that expression is equal to 0.
>
> The commercial Macsyma has a decision procedure associated with its
> version of "is" computes that the expression is positive.
>
> in fact it computes
> is ((exp
> (1/%pi^1000000000000000000000000000000000000000000000000000000000000000)-1)
>>0);
> in 0.0 milliseconds.
That's very nice. Of course, it won't find the answer for any input.
>
>>So it seems
>> that Maxima does not implement any automatic error checking
>> whatsoever. Or is there another function that accomplishes this?
>
> I don't know of one, but someone could make one up with bfloat, if you
> want something like what you seem to have programmed.
>
> Although there are several rigorous interval arithmetic systems
> available in Lisp,
> none of them have been incorporated in any "automatic" scheme in
> Maxima, so far as I know.
>
> I'm not sure whether this is because of
> (a) lack of interest by users
> (b) lack of interest in programmers
> (c) both?
>
> ... more snip...
>
> RJF
> >
>
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