Thomas Lord wrote:
> I don't have a cite handy but maybe someone can play with
> Google to find it. Sun Microsystems, some years ago,
> published a long paper called something like "everything programmers
> need to know about floating point numbers" which I would like
> to recommend.
http://portal.acm.org/citation.cfm?id=103163.
Unfortunately, it's not public :(
Arthur
>
>
>
> Arthur Smyles wrote:
>> Second, +inf and -inf are not ranges they are points.
>
>
> That's wrong too.
>
> 1.0 / 0.0 == +inf for a very specific reason: that "0.0" might not
> actually mean "naught". In particular, "0.0" might mean "a very,
> very small positive Real number (or negative)". Thus, "+inf"
> means "a very, very large Real number."
>
>
> A visualization that I can't do much justice to in ASCII might
> help:
>
> There are a finite number of bit patterns corresponding to floating
> point numbers. These are distributed on the real line (except for
> NaN). They are distributed unevenly:
>
>
> ...============== -1 === 0 === 1 ===============...
> ^ ^ ^ ^ ^ ^ ^ ^^^^^^^^^^^^ ^ ^ ^ ^ ^ ^ ^
>
> Each bit pattern is the name for the interval formed by splitting the
> distance to its neighbors. For example, "0.0" really means "plus
> or minus epsilon".
>
> Since the list of bit patterns is finite, it has a start and end --
> there smallest and largest floating point bit patterns. Each of those
> has no neighbor on one side:
>
>
> ========================
> ^ ^ (no
> neighbor on this side)
> +inf
>
>
> Those "inf" values therefore stand for half-infinite intervals.
>
> When you ask a floating point unit to compute something like x/y
> you are asking, in effect "Suppose I know that there is a number X in
> one interval, and a number Y in another interval -- In what interval
> can I find the quotient of these numbers, if it exists?"
>
> The "+inf" and "-inf" answers tell you "The quotient might exist
> and, if so, it is very very large or very very small".
>
> When an operation gives you "NaN" it is telling you that "Either
> the floating point circuits can prove that no answer exists or
> they can prove that they can not prove that any answer might exist."
>
>
>
>
> -t
>
Received on Fri Jun 22 2007 - 14:31:14 UTC