December 2000 - Haskell-Cafe

Boolean Primes Map (continued)
by Shlomi Fish 17 Jan '01

17 Jan '01

Well, after some thought, I decided to try re-writing the boolean primes map program only using a list instead of an array. I came up with this program: primes :: Int -> [Int] primes how_much = (iterate 2 initial_map) where initial_map :: [Bool] initial_map = (map (\x -> True) [ 0 .. how_much]) iterate :: Int -> [Bool] -> [Int] iterate p (a:as) | p > mybound = process_map p (a:as) | a = p:(iterate (p+1) (mymark (p+1) step (2*p) as)) | (not a) = (iterate (p+1) as) where step :: Int step = if p == 2 then p else 2*p mymark :: Int -> Int -> Int -> [Bool] -> [Bool] mymark cur_pos step next_pos [] = [] mymark cur_pos step next_pos (a:as) = if (cur_pos == next_pos) then False:(mymark (cur_pos+1) step (cur_pos+step) as) else a:(mymark (cur_pos+1) step next_pos as) mybound :: Int mybound = ceiling(sqrt(fromIntegral(how_much))) process_map :: Int -> [Bool] -> [Int] process_map cur_pos [] = [] process_map cur_pos (a:as) | a = cur_pos:(process_map (cur_pos+1) as) | (not a) = (process_map (cur_pos+1) as) I don't know too much about Haskell yet, so it is possible this program can be further optimized using some Haskell built-ins. Now, this program can scale to 100,000 and beyond, as opposed to the array version which only got until 30,000 or 40,000. It's a pity Haskell doesn't handle arrays very well, but I guess every language has its faults. Regards, Shlomi Fish ---------------------------------------------------------------------- Shlomi Fish shlomif(a)vipe.technion.ac.il Home Page: http://t2.technion.ac.il/~shlomif/ Home E-mail: shlomif(a)techie.com The prefix "God Said" has the extraordinary logical property of converting any statement that follows it into a true one.

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RE: GHCi, Hugs (was: Mixture ...)
by Simon Peyton-Jones 17 Jan '01

17 Jan '01

| It'd be good if left-behind tools were using a BSD(-like) licence, in | the event that anybody - commercial or otherwise - who wanted to pick | them up again, were free to do so. GHC does indeed have a BSD-like license. Simon

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RE: Will Haskell be commercialized in the future?
by Doug Ransom 17 Jan '01

17 Jan '01

> -----Original Message----- > From: Benjamin L. Russell [mailto:russell@brainlink.com] > Sent: Sunday, November 26, 2000 11:50 PM > To: Doug Ransom; haskell-cafe(a)haskell.org > Subject: Re: Will Haskell be commercialized in the future? > > > On Fri, 24 Nov 2000 09:15:52 -0800 > Doug Ransom <Doug_Ransom(a)pml.com> wrote: > > > > [stuff deleted] > > > > A lot of the things Haskell excells at (IMO) inferior > > tools are being used > > in place. For example, microsoft has build good XSLT > > translators and two > > new compilers (C#, VB7) in the last couple years. > > Unfortunately, C#, not > > Haskell, will probably be "the" language for the next > > decade. [stuff deleted] > > Just out of curiosity: what makes you so sure about C#? C# > has some potential big problems, too: in particular, the > ability to declare a portion of the code "unsafe," which can > encourage unsafe programming among entrenched C/C++ programmers. Well, first of all, most C++ programmers really hate C++ and will be happy to stay in safe mode and move to C#. There were cheers at the Microsoft Profesional Developers Conference when MS announced garbage collection for the COM replacement and the safety available with C# and managed C++ code. C# is a huge improvement over C++. Why would a C++ programmer want to go into unsafe mode? I guess when they are writing interfaces to device drives, operating system calls, and legacy interfaces. > > I myself am in no big hurry to master C#. I'd rather use a > set of domain-specific languages with interlinked code, > rather than a single language that purports to be as > general-purpose as C# does. Well, I would prefer to master Haskell and use that as my general purpose language. Fat chance since the object models available in the microsoft common language runtime are designed for impertive programming. > > Benjamin L. Russell > russell(a)brainlink.com > "Furuike ya! Kawazu tobikomu mizu no oto." --Matsuo Basho >

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Re: Learning Haskell and FP
by senganb＠ia.nsc.com 28 Dec '00

28 Dec '00

> * The Design Patterns Haskell Companion > by [someone(s) reading this list?] I agree except I would also like to see more on Haskell space-leaks and how to find them. Lazyness is great for structuring programs and garbage collection helps rapid prototyping immensely. However it makes it difficult to find the cause of that 128Mb heap overflow once you have 2000 lines of code. Yes the profiler gives you an idea of which function is using a lot of heap, but not exactly where. E.g. I rewrote my monads ultra stritly and the heap consumption fell by half, even though I'm not convinced being so strict isn't just masking some other problem: > (MN c1) >>= fc2 = MN $ \s0 -> case c1 s0 of { (r1,io1,s1) -> > case fc2 r1 of { ( MN c2 ) -> > case c2 s1 of { (r2,io2,s2) -> > (r2,io1 >> io2,s2) }}} Such a "community written book" might be good for http://www.lightandmatter.com/cgi-bin/asbrowsesubject.cgi?class=Q Sengan

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Haskell question
by Scott 28 Dec '00

28 Dec '00

Hello! I am reading Discrete Mathematics Using a computer by Hall and O'Donnell and in the introduction to hugs section, they give this example: [[x,y] | x<-[1..50],y<-[1..50],z<-[1..50],x**2+y**2==z**2] now I type it in and expect it to return a number of results, but it doesn't, it shows: [[8.0,15.0,17.0],[14.0,48.0,50.0],[15.0,8.0,17.0],[15.0,20.0,25.0],[20.0,15.0,25.0],[21.0,28.0,35.0],[27.0,36.0,45.0],[28.0,21.0,35.0],[30.0,40.0,50.0],[36.0,27.0,45.0],[40.0,30.0,50.0],[48.0,14.0,50.0]] My question is where is [3.0,4.0,5.0],[5.0,12.0,13.0]? I have looked everywhere I could think of to see what I am doing wrong, but I have no idea. Maybe a rounding error somewhere? Thank you, Scott Anderson

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Re: Haskell question
by Mike Gunter 28 Dec '00

28 Dec '00

This is fairly subtle. The fact that the numbers are printed with a decimal point hints that they are floating point numbers. Floating-point arithmetic's inexactness makes equality tests less valuable than for, e.g., Integer arithmetic. If you change the "**"s to "^"s you'll get [3,4], etc. (or [3,4,5] if you change "[x,y]" to "[x,y,z]"). mike gunter E.g.: Main> [[x,y,z] | x<-[1..50],y<-[1..50],z<-[1..50],x^2+y^2==z^2] [[3,4,5],[4,3,5],[5,12,13],[6,8,10],[7,24,25], ... ] > Hello! > I am reading Discrete Mathematics Using a computer by Hall and O'Donnell > and in the introduction to hugs section, they give this example: > [[x,y] | x<-[1..50],y<-[1..50],z<-[1..50],x**2+y**2==z**2] > now I type it in and expect it to return a number of results, but it > doesn't, it shows: > [[8.0,15.0,17.0],[14.0,48.0,50.0],[15.0,8.0,17.0],[15.0,20.0,25.0],[20.0,15.0,25.0],[21.0,28.0,35.0],[27.0,36.0,45.0],[28.0,21.0,35.0],[30.0,40.0,50.0],[36.0,27.0,45.0],[40.0,30.0,50.0],[48.0,14.0,50.0]] > My question is where is [3.0,4.0,5.0],[5.0,12.0,13.0]? > I have looked everywhere I could think of to see what I am doing wrong, but > I have no idea. Maybe a rounding error somewhere? > Thank you, > Scott Anderson

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RE: Haskell question
by Conal Elliott 28 Dec '00

28 Dec '00

It's probably due to rounding. If you use "^" instead of "**", defaulting to integers, you'll get the triples you expected. - Conal -----Original Message----- From: Scott [mailto:adric@wipcradio.cc] Sent: Thursday, December 28, 2000 3:05 PM To: Haskell-Cafe(a)haskell.org Subject: Haskell question Hello! I am reading Discrete Mathematics Using a computer by Hall and O'Donnell and in the introduction to hugs section, they give this example: [[x,y] | x<-[1..50],y<-[1..50],z<-[1..50],x**2+y**2==z**2] now I type it in and expect it to return a number of results, but it doesn't, it shows: [[8.0,15.0,17.0],[14.0,48.0,50.0],[15.0,8.0,17.0],[15.0,20.0,25.0],[20.0,15. 0,25.0],[21.0,28.0,35.0],[27.0,36.0,45.0],[28.0,21.0,35.0],[30.0,40.0,50.0], [36.0,27.0,45.0],[40.0,30.0,50.0],[48.0,14.0,50.0]] My question is where is [3.0,4.0,5.0],[5.0,12.0,13.0]? I have looked everywhere I could think of to see what I am doing wrong, but I have no idea. Maybe a rounding error somewhere? Thank you, Scott Anderson _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe(a)haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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Boolean Primes Map (continued)
by Shlomi Fish 22 Dec '00

22 Dec '00

Well, after some thought, I decided to try re-writing the boolean primes map program only using a list instead of an array. I came up with this program: primes :: Int -> [Int] primes how_much = (iterate 2 initial_map) where initial_map :: [Bool] initial_map = (map (\x -> True) [ 0 .. how_much]) iterate :: Int -> [Bool] -> [Int] iterate p (a:as) | p > mybound = process_map p (a:as) | a = p:(iterate (p+1) (mymark (p+1) step (2*p) as)) | (not a) = (iterate (p+1) as) where step :: Int step = if p == 2 then p else 2*p mymark :: Int -> Int -> Int -> [Bool] -> [Bool] mymark cur_pos step next_pos [] = [] mymark cur_pos step next_pos (a:as) = if (cur_pos == next_pos) then False:(mymark (cur_pos+1) step (cur_pos+step) as) else a:(mymark (cur_pos+1) step next_pos as) mybound :: Int mybound = ceiling(sqrt(fromIntegral(how_much))) process_map :: Int -> [Bool] -> [Int] process_map cur_pos [] = [] process_map cur_pos (a:as) | a = cur_pos:(process_map (cur_pos+1) as) | (not a) = (process_map (cur_pos+1) as) I don't know too much about Haskell yet, so it is possible this program can be further optimized using some Haskell built-ins. Now, this program can scale to 100,000 and beyond, as opposed to the array version which only got until 30,000 or 40,000. It's a pity Haskell doesn't handle arrays very well, but I guess every language has its faults. Regards, Shlomi Fish ---------------------------------------------------------------------- Shlomi Fish shlomif(a)vipe.technion.ac.il Home Page: http://t2.technion.ac.il/~shlomif/ Home E-mail: shlomif(a)techie.com The prefix "God Said" has the extraordinary logical property of converting any statement that follows it into a true one.

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finding primes
by S.D.Mechveliani 21 Dec '00

21 Dec '00

Hello, On generating prime numbers, people wrote ... | import Array | primes n = [ i | i <- [2 ..n], not (primesMap ! i)] where | primesMap = accumArray (||) False (2,n) multList | [..] I think that it is good for functional programming to avoid arrays, as possible. Shlomi Fish <shlomif(a)vipe.technion.ac.il> writes > [..] > primes :: Int -> [Int] > > primes how_much = sieve [2..how_much] where > sieve (p:x) = > p : (if p <= mybound > then sieve (remove (p*p) x) > else x) where > remove what (a:as) | what > how_much = (a:as) > | a < what = a:(remove what as) > | a == what = (remove (what+step) as) > | a > what = a:(remove (what+step) as) > remove what [] = [] > step = (if (p == 2) then p else (2*p)) > sieve [] = [] > mybound = ceiling(sqrt(fromIntegral how_much)) > > I optimized it quite a bit, but the concept remained the same. > > Anyway, this code can scale very well to 100000 and beyond. But it's not > exactly the same algorithm. > [..] C.Runciman <Colin.Runciman(a)cs.york.ac.uk> gives a paper reference about this. Aslo may I ask what do you mean by "can scale to 100000", the value of a prime or its position No in the list? Anyway, here are my attempts: ----------------------------------- 1. primes1 = s [(2::Int)..] :: [Int] where s (p:ns) = p: (s (filter (notm p) ns)) notm p n = (mod n p) /= 0 main = putStr $ shows (primes1!!9000) "\n" After compiling by GHC-4.08 -O2 it yields 93187 in 115 sec on Intel-586, 160 MHz. ----------------------------------- 2. The DoCon program written in Haskell (again, no arrays) gives about 10 sec (for Integer values). Also it finds, for example, first 5 primes after 10^9 as follows: take 5 $ filter isPrime [(10^9 ::Integer) ..] --> [1000000007,1000000009,1000000021,1000000033,1000000087] This takes 0.05 sec. But DoCon uses a particular isPrime test method: Pomerance C., Selfridge J.L., Wagstaff S.S.: The pseudoprimes to 25*10^9. Math.Comput., 1980, v.36, No.151, pp.1003-1026. After 25*10^9 it becomes again, expensive. ------------------ Sergey Mechveliani mechvel(a)botik.ru

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finding primes
by S.D.Mechveliani 21 Dec '00

21 Dec '00

Hello, I wrote recently on generating prime numbers > [..] > The DoCon program written in Haskell (again, no arrays) gives > [..] > take 5 $ filter isPrime [(10^9 ::Integer) ..] > --> > [1000000007,1000000009,1000000021,1000000033,1000000087] > > This takes 0.05 sec. > [..] But it is better to refer to the BAL library for Haskell (basAlgPropos) http://www.botik.ru/pub/local/Mechveliani/basAlgPropos/ It is easier to use. ------------------ Sergey Mechveliani mechvel(a)botik.ru

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