[Cuis-dev] Problems in class Number

[Agustín Sansone]

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>) 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
> 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
> https://lists.cuis.st/mailman/listinfo/cuis-dev
>
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