Alex Shinn <alexshinn@gmail.com> writes:

> On Sat, Dec 22, 2012 at 11:42 AM, John Cowan <cowan@mercury.ccil.org>
> wrote:
>
>     > I think any slow-down is better than giving the wrong answer,
>
>     That's what exact arithmetic is for.
>
> Exact arithmetic can run out of memory.

So can your proposed inexacts.  In order to avoid underflow and
overflow, the number of representable values cannot be finite, because
there can be no maximum or minimum representable magnitude.  Therefore
the amount of memory needed to represent your numbers is unbounded.  No
matter how clever your compression method is, that fact is unavoidable.

     Mark

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