<div dir="ltr"><div>The next step of this idea will be for self of the form 2310*k+{1, 13, 17, ..., 2309} (344 cases !!).</div><div>I wouldn't make that step, but it is okay if you want to add any other optimization. </div><div>I leave you again the implementation, because there was a redundant check in the last one.</div><div>Besides that, I don't see any reason to have a slower implementation of isPrime in the base image. </div></div> <div class="gmail_quote"><div dir="ltr" class="gmail_attr">El mié., 9 oct. 2019 a las 2:18, 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">If you are happy with the code, then we can queue it for integration. Is there anything else you'd like to do to isPrime? At one point I thought it might be possible to merge the small factor loop by letting it evaluate even for large receivers (on the grounds that chances are the faster loop that does not send sqrtFloor is likely to find small factors quickly), but if no factor is found then the rounds of 30 could start at 30 or 60. I couldn't quite find a way to do that and make it run faster. On 10/8/19 21:44, Agustín Sansone via Cuis-dev wrote: > Okay, this should work faster. > > El mié., 9 oct. 2019 a las 1:22, Andres Valloud 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: > > In the larger slicer test, > > 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) > isPrimeFast2e]] > > I get 2627 vs 2430, or about 7.5% faster. > > On 10/8/19 21:19, Andres Valloud via Cuis-dev wrote: > > "The latest code you sent" > > Time millisecondsToRun: > > [10000 timesRepeat: [1 to: 1000 do: [:x | x isPrimeFast1b]]] 767 > > > > "The code from my last email" > > Time millisecondsToRun: > > [10000 timesRepeat: [1 to: 1000 do: [:x | x isPrimeFast2e]]] 704 > > > > The observation is that the boundary of 31 is arbitrary, so we > might as > > well tune it according to the break even point. > > > > On 10/8/19 21:11, Agustín Sansone via Cuis-dev wrote: > >> I don't think there will be any difference by making > optimizations for > >> small numbers. This runs just as fast as the original approach. > >> > >> El mié., 9 oct. 2019 a las 1:01, Andres Valloud 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>> > <mailto:<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: > >> > >> Expanding on the idea to treat tiny integers as special cases, > >> approximating sqrtFloor for tiny integers wins. > >> > >> On 10/8/19 20:49, Andres Valloud via Cuis-dev wrote: > >> > See attached hybrid. > >> > > >> > On 10/8/19 20:44, Andres Valloud via Cuis-dev wrote: > >> >> Right, that won't work. I had tried to avoid doing > something > >> like this, > >> >> > >> >> | mod30Index | > >> >> self < 3 ifTrue: [^self = 2]. > >> >> self < 32 ifTrue: [ > >> >> ^#(false true true false true false true false > false > >> false > >> >> true false true false false false true > false true > >> false > >> >> false false true false false false false > false true > >> false > >> >> true) at: self]. > >> >> mod30Index := self \\ 30 + 1. > >> >> #(false true false false false false false true > false false > >> >> false true false true false false false true > false true > >> >> false false false true false false false false > false > >> true) > >> >> at: mod30Index :: ifFalse: [^false]. > >> >> > >> >> > >> >> but alas it's not as simple as I thought. > >> >> > >> >> Andres. > >> >> > >> >> On 10/8/19 20:40, Agustín Sansone via Cuis-dev wrote: > >> >>> Sorry, I think this does not work for the numbers 3, 5, 7, > >> 11, 13, > >> >>> 17, 19, 23, 29 and 31. > >> >>> > >> >>> El mié., 9 oct. 2019 a las 0:34, Andres Valloud 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>> <mailto:<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>>> > >> <mailto:<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>> <mailto:<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: > >> >>> > >> >>> 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>> > >> <mailto:<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>>> <mailto:<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>> > >> <mailto:<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>>>> > >> >>> <mailto:<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>> > >> <mailto:<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>>> <mailto:<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>> > >> <mailto:<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="http://www.cuis-smalltalk.org" rel="noreferrer" target="_blank">http://www.cuis-smalltalk.org</a>> > >> <<a href="http://www.cuis-smalltalk.org" rel="noreferrer" target="_blank">http://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>> <mailto:<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>>> > >> <mailto:<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>> <mailto:<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>>>> > >> >>> <mailto:<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>> > >> <mailto:<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>>> <mailto:<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>> > >> <mailto:<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> <mailto:<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> <mailto:<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> > <mailto:<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> > <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> <mailto:<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> <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> <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>