<div dir="ltr">Sorry, I think this does not work for the numbers 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31.</div> <div class="gmail_quote"><div dir="ltr" class="gmail_attr">El mié., 9 oct. 2019 a las 0:34, Andres Valloud via Cuis-dev (<<a href="mailto:cuis-dev@lists.cuis.st">cuis-dev@lists.cuis.st</a>>) escribió: </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">I played a bit with the guard clauses and found the attached one is simpler yet just as fast. On 10/8/19 20:11, Andres Valloud via Cuis-dev wrote: > 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 >> (<<a href="mailto:cuis-dev@lists.cuis.st" target="_blank">cuis-dev@lists.cuis.st</a> <mailto:<a href="mailto:cuis-dev@lists.cuis.st" target="_blank">cuis-dev@lists.cuis.st</a>>>) 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 >> <a href="http://www.cuis-smalltalk.org" rel="noreferrer" target="_blank">www.cuis-smalltalk.org</a> <<a href="http://www.cuis-smalltalk.org" rel="noreferrer" target="_blank">http://www.cuis-smalltalk.org</a>> >> <a href="https://github.com/Cuis-Smalltalk/Cuis-Smalltalk-Dev" rel="noreferrer" target="_blank">https://github.com/Cuis-Smalltalk/Cuis-Smalltalk-Dev</a> >> <a href="https://github.com/jvuletich" rel="noreferrer" target="_blank">https://github.com/jvuletich</a> >> <a href="https://www.linkedin.com/in/juan-vuletich-75611b3" rel="noreferrer" target="_blank">https://www.linkedin.com/in/juan-vuletich-75611b3</a> >> @JuanVuletich >> >> -- Cuis-dev mailing list >> <a href="mailto:Cuis-dev@lists.cuis.st" target="_blank">Cuis-dev@lists.cuis.st</a> <mailto:<a href="mailto:Cuis-dev@lists.cuis.st" target="_blank">Cuis-dev@lists.cuis.st</a>> >> <a href="https://lists.cuis.st/mailman/listinfo/cuis-dev" rel="noreferrer" target="_blank">https://lists.cuis.st/mailman/listinfo/cuis-dev</a> >> >> -- Cuis-dev mailing list <a href="mailto:Cuis-dev@lists.cuis.st" target="_blank">Cuis-dev@lists.cuis.st</a> <a href="https://lists.cuis.st/mailman/listinfo/cuis-dev" rel="noreferrer" target="_blank">https://lists.cuis.st/mailman/listinfo/cuis-dev</a> </blockquote></div>