[Cuis-dev] Problems in class Number
Andres Valloud
ten at smallinteger.com
Tue Oct 8 20:49:10 PDT 2019
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
>> (<cuis-dev at lists.cuis.st <mailto:cuis-dev at lists.cuis.st>>) 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
>> >> (<cuis-dev at lists.cuis.st <mailto:cuis-dev at lists.cuis.st>
>> <mailto: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>
>> <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>
>> <mailto:Cuis-dev at lists.cuis.st <mailto:Cuis-dev at lists.cuis.st>>
>> >> https://lists.cuis.st/mailman/listinfo/cuis-dev
>> >>
>> >>
>> -- 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
>>
>>
-------------- next part --------------
'From Cuis 5.0 [latest update: #3866] on 8 October 2019 at 8:47:30 pm'!
!Integer methodsFor: 'testing' stamp: 'sqr 10/8/2019 20:46:35'!
isPrimeFast2d
self < 3 ifTrue: [ ^self = 2 ].
self even ifTrue: [^false].
self < 32 ifTrue: [
3 to: self - 1 by: 2 do: [:each |
self \\ each = 0 ifTrue: [ ^false ].
].
^true
].
self \\ 3 = 0 ifTrue: [ ^false ].
self \\ 5 = 0 ifTrue: [ ^false ].
"Now 2, 3 and 5 do not divide self. So, self is of the form
30*k + {1, 7, 11, 13, 17, 19, 23, 29} for integer k >= 0.
The 31 case below is the 30k+1 case, excluding k = 0"
0 to: self sqrtFloor by: 30 do:[:each |
self \\ (each+7) = 0 ifTrue: [ ^false ].
self \\ (each+11) = 0 ifTrue: [ ^false ].
self \\ (each+13) = 0 ifTrue: [ ^false ].
self \\ (each+17) = 0 ifTrue: [ ^false ].
self \\ (each+19) = 0 ifTrue: [ ^false ].
self \\ (each+23) = 0 ifTrue: [ ^false ].
self \\ (each+29) = 0 ifTrue: [ ^false ].
self \\ (each+31) = 0 ifTrue: [ ^false ].
].
^true! !
More information about the Cuis-dev
mailing list