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 <w...@freegeek.org>wrote: > On 4/14/13 8:53 PM, Kim-Ee Yeoh wrote: > > On Sun, Apr 14, 2013 at 3:28 PM, wren ng thornton <w...@freegeek.org> > 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 > > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >

_______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe