How robust/accurate is 'floor()' in Maxima?

On 8/14/2013 9:34 AM, Henry Baker wrote:
> I've noticed that floor(expression) attempts to evaluate 'expression'
> to an actual integer.
>
> How good is it?
>
> Does floor ask bfloat to compute enough precision, and then come back
> again with more?
Depending on what the expression includes, the determination of what is 
"enough precision" may be
undecidable..  Bill Gosper has written stuff for algebraic expressions, 
but I think that got into
Macsyma not Maxima.  And I don't know if floor used it.

Basically you need some theorems to show that if an expression in a 
certain class is less than
a certain small quantity, then that expression is equivalent to zero.
>
> Is there any way to achieve this kind of evaluation, other than programming
> it myself?
>
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