Re: [Haskell-cafe] NaN as Integer value

For better or worse; IEEE-754 settled many of these questions. I personally think the standard is a good compromise of what's practical, efficiently implementable, and mathematically sensible. I find the following paper by Rummer and Wahl an especially good read: http://www.ccs.neu.edu/home/wahl/Publications/rw10.pdf The paper focuses on how to formalize floating-point in SMT-solvers; but section 3 is a great read for understanding how floating-point semantics work, regardless whether you care for SMT-solving or not. It could be the basis for a nice software implementation of floating-point, for instance. -Levent. On Wed, Apr 17, 2013 at 10:11 AM, wren ng thornton wrote:

On 4/14/13 8:53 PM, Kim-Ee Yeoh wrote:

...

On Sun, Apr 14, 2013 at 3:28 PM, wren ng thornton wrote:

...

Whereas the problematic values due to infinities are overspecified, so no matter which answer you pick it's guaranteed to be the wrong answer half the time.

Part of this whole problem comes from the fact that floats *do* decide to give a meaning to 1/0 (namely Infinity).

I'm not sure what you mean about overspecification here, but in setting 1/0 as +infinity (as opposed to -infinity), there's an easily overlooked assumption that the limit is obtained "from above" as opposed to "from below."

Setting 1/0 = +inf isn't the problem, or at least not the main one. Of course, there's always the question about which completion of the reals to use--- i.e., whether we have +inf vs -inf, or whether we just have a single point infinity.

Rather, the NaN problem comes from trying to resolve things like:

inf - inf inf * 0 inf / inf 0 / 0

The overspecification problem I mentioned is that each of these expressions has "too many" solutions. For example, we have the following equations:

x * 0 == 0 -- where x is finite inf * y == inf * signum y -- where y /= 0 inf * 0 == ??

x - inf == -inf -- where x is finite inf - y == inf -- where y is finite inf - inf == ??

x / 0 == inf * signum x -- where x /= 0 0 / y == 0 -- where y /= 0 0 / 0 == ??

-- Live well, ~wren

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