On Fri, Jul 12, 2013 at 4:07 PM, Jeff Walden <jwalden...@mit.edu> wrote:
> On 07/09/2013 06:49 PM, Mark S. Miller wrote:
>> Because Nat includes 2**53, this code actually fails to enforce conservation
>> of currency!!
>
> The problem isn't that Nat includes 2**53. It's that you're performing an
> operation that may compute an inexact value, then you're treating that
> inexact value *as if it were exact*. You should be testing *before*
> performing any operation that might compute an inexact value. Or, you should
> be rejecting values which might be rounded from an inexact value. Which
> would mean your MAX_NAT test should instead be
>
> if (allegedNum >= MAX_NAT) { throw new RangeError('too big'); }
>
> But really, Nat seems like the wrong concept to me. Even if you correct it
> as above, it's only correctly usable if it is applied after *every* floating
> point operation. If you have |a + b|, you can correctly apply a corrected
> Nat to that. But if you have |a + b + c| or |a + b - c| or any more
> floating-point operations than a single operation, Nat can't be correctly
> applied. Corrected Nat as-is gives a false sense of security, by implying
> that you can apply it to a calculation and it'll do the right thing, when
> really it'll only do so if the value you're passing in is the result of no
> more than a single computation.
Mark's Nat() function *does* throw if the input isn't an
exactly-representable number.
~TJ
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