Is there a different IEEE spec or CAS that distinguishes between 1/x and 2/x where x=0?
assert 1/0 != 2/0 != math.inf/0 On Mon, Nov 23, 2020, 2:44 PM <johnmelendow...@gmail.com> wrote: > IEEE 754 is incredibly consistent with mathematics. > > The easiest way to determine if a float operation would return inf, -inf, > or NaN is to quite literally make an expression and take the limit of it as > a certain variable approaches infinity. > > 0/0, inf/inf, 0*inf, inf-inf are standard Indeterminant Forms (IDF). If > you are taking a limit, and come across this the general procedural to > algebraically manipulate to remove the IDF, or apply L'Hospital. If after > those attempts, you are still an IDF then that's that. In IEEE 754, an IDF > is represented as a NaN. > > There are some special cases, wiki would describe 0^0 1^inf and infinity^0 > as IDF through certain manipulations. However, I think most people would > argue otherwise and IEEE 754 handles them accordingly, which actually > evaluates them (or maybe its language specific, both Matlab and Numpy > return 1, 1, and 1 respectively which is correct to me). > > Limits that turn into infinity are quite literally represented by infinity > in IEEE 754. So limit 1/x as x -> 0 is infinity. 1/x as x -> infinity is > zero or as close to zero as IEEE 754 allows. > > Very interesting example is log(0) > > log(x) as x->0 = -inf > > Which mathematically makes sense. As log(x) is asking e raised to what > value a produces x. In other words, e^(a) = x or e^(a) = 0 > > Well the easiest thing to do is choose a << 0 i.e. 1/e^(a) and what would > bring that to 0? making a sufficiently large hence -inf > > Base python should be consistent with IEEE 754 in my opinion. > _______________________________________________ > Python-ideas mailing list -- python-ideas@python.org > To unsubscribe send an email to python-ideas-le...@python.org > https://mail.python.org/mailman3/lists/python-ideas.python.org/ > Message archived at > https://mail.python.org/archives/list/python-ideas@python.org/message/JUGC7SCTVVYUF2J7B2L5S57JJWDXV4K7/ > Code of Conduct: http://python.org/psf/codeofconduct/ >
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