[Cuis-dev] Problems in class Number
Agustín Sansone
agustinsansone7 at gmail.com
Tue Oct 8 20:36:30 PDT 2019
I don't know if one less iteration will make much difference, however I
also agree the each+31 case should be the last one.
El mié., 9 oct. 2019 a las 0:11, Andres Valloud via Cuis-dev (<
cuis-dev at lists.cuis.st>) escribió:
> Regarding each+31, sure, 30*k+1 comes first, except when k = 0 because
> why would anyone try dividing by 1. So this is why that case is shifted
> by 30. However, when written this way, the actual divisor evaluation
> order is 31, 7, 11, and so on. It's more likely that a random integer
> is 0 mod 7 than 0 mod 31, and the sooner one detects exact division, the
> sooner the computation can stop. Because of that, I think the each+31
> case should be the last one in the division loop.
>
> On 10/8/19 19:17, Agustín Sansone via Cuis-dev wrote:
> > Hello!
> >
> > I agree with you. I don't think isPrime should send isProbablyPrime
> > because it could fail in the future.
> > I leave you here the implementation with this taken care of.
> > I wrote the (each+31) case first in the trial division loop, because it
> > is testing the 30*k+1 case, wich I also wrote first in the comment.
> >
> > Thanks,
> > Agustín
> >
> > El mar., 8 oct. 2019 a las 8:11, Juan Vuletich via Cuis-dev
> > (<cuis-dev at lists.cuis.st <mailto:cuis-dev at lists.cuis.st>>) escribió:
> >
> > Hi Folks,
> >
> > I agree with Andrés comments, and will just focusing on the proposed
> > changes.
> > (snip)
> >
> > On 10/8/2019 2:20 AM, Andres Valloud via Cuis-dev wrote:
> > > Agustin, nice to see someone looking into these kinds of things
> :).
> > > ...
> > >> * The *raisedToInteger: exp modulo: m *method**in Integer has
> > a very
> > >> big problem. If we compute, for example, /"5 raisedTo: 0
> modulo:
> > >> 0"/, this returns 1. This means, that according to
> > Smalltalk, the
> > >> rest of the division by 0 of 1(=5^0) is equal to 1 (Yes,
> > division by
> > >> zero!!). I think you can see the problem. This is due the
> > first line
> > >> of the method, that says /"(exp = 0) ifTrue: [^ 1].", /does
> > >> not check anything else. This problem can be easily fixed by
> > >> checking if m=0 just before.
> > >
> > > I agree, the current code appears to be wrong. The initials on
> the
> > > code belong to Juan Vuletich and Nicolas Cellier. Guys, is there
> > > reason why e.g. 5 raisedTo: 0 modulo: 0 should answer 1 rather
> than
> > > fail? I don't see any, but...
> > >
> > > Assuming the code is broken and needs to be fixed, alternatively
> one
> > > could also write the initial guard clause like this:
> > >
> > > n = 0 ifTrue: [^1 \\ m].
> > >
> > > because the case m = 0 will fail.
> > > ...
> >
> > Just added this suggestion as an update to GitHub. Andrés, I did it
> > with
> > your author initials, it's your code!
> >
> > > ...
> > >> * The *isPrime *method in Integer makes some optimization in
> > order to
> > >> run the algorithm in O(sqrt(self)) instead of the naive way
> in
> > >> O(self). This is very intelligent, but the constant factor
> > of this
> > >> method can be still improved significantly. I share with you
> my
> > >> implementation of *isPrimeFast *with a small explanation.
> This
> > >> implementation runs in general more than 3 times faster than
> the
> > >> actual one. I leave you a test that checks the correctness
> > of it as
> > >> well, and some other tests that check this complexity I
> > mentioned.
> > >
> > > I see what you did there, but I do not know how to reproduce the
> > time
> > > tests you mention. I built a sample of integers between 1 and
> > 2^32 (I
> > > didn't go up to 2^64 because that would require O(2^32) operations
> > > each, and I want that to finish in reasonable time), and I get
> > > something like a 2x performance improvement rather than 3x. This
> > > seems to make sense because the approach you propose halves the \\
> > > operations (8 remain out of the 16 the current code is doing, for
> > > every batch of 30 potential divisors).
> > >
> > > slicer := 1024.
> > > thickness := 255.
> > > maxK := 1 bitShift: 32.
> > > integers := 1 to: maxK by: maxK // slicer
> > > :: inject: OrderedCollection new
> > > into: [:t :x |
> > > t add: x.
> > > thickness timesRepeat: [t add: t last + 1].
> > > t yourself]
> > > :: asArray.
> > > Time millisecondsToRun:
> > > [1 to: integers size do:
> > > [:x | (integers at: x) isPrime]]
> > >
> > > Using the above code (which I could not format more nicely in this
> > > email), I get about 4.8s for isPrime, and about 2.4s for
> isPrimeFast.
> > >
> > > Generally, isPrime shouldn't send isProbablyPrime because isPrime
> is
> > > meant to be deterministic, and one shouldn't assume that the
> > > probabilistic algorithm today will happen to provide the correct
> > > deterministic answer tomorrow.
> > >
> > > Why is the (each+31) case first in the trial division loop?
> > >
> > > Andres.
> >
> > I'll wait for your consensus on what to do here. Making isPrime not
> > send
> > isProbablyPrime sounds reasonable to me, but folks, I prefer to wait
> > for
> > your suggestion.
> >
> > Thanks,
> >
> > --
> > Juan Vuletich
> > www.cuis-smalltalk.org <http://www.cuis-smalltalk.org>
> > https://github.com/Cuis-Smalltalk/Cuis-Smalltalk-Dev
> > https://github.com/jvuletich
> > https://www.linkedin.com/in/juan-vuletich-75611b3
> > @JuanVuletich
> >
> > --
> > Cuis-dev mailing list
> > Cuis-dev at lists.cuis.st <mailto:Cuis-dev at lists.cuis.st>
> > https://lists.cuis.st/mailman/listinfo/cuis-dev
> >
> >
> --
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