Haskell vs C speed: Sieve of Eratosthenes - c

Question

Haskell one is implemented using optimized Data.IntSet with complexity O(lg n). However, there is a 15x (previously 30x) speed difference for n = 2000000 despite Haskell code is already optimized for even number cases. I would like to know whether/why my implementation in Haskell is imperfect.
Original Haskell
primesUpTo :: Int -> [Int]
primesUpTo n = 2 : put S.empty [3,5..n]
where put :: S.IntSet -> [Int] -> [Int]
put _ [] = []
put comps (x:xs) =
if S.member x comps
then put comps xs
else x : put (S.union comps multiples) xs
where multiples = S.fromList [x*2, x*3 .. n]
Update
fromDistinctAscList gives a 4x speed increase. 2-3-5-7-Wheel speeds up by another 50%.
primesUpTo :: Int -> [Int]
primesUpTo n = 2 : 3 : 5 : 7 : put S.empty (takeWhile (<=n) (spin wheel 11))
where put :: S.IntSet -> [Int] -> [Int]
put _ [] = []
put comps (x:xs) =
if S.member x comps
then put comps xs
else x : put (S.union comps multiples) xs
where multiples = S.fromDistinctAscList [x*x, x*(x+2) .. n]
spin (x:xs) n = n : spin xs (n + x)
wheel = 2:4:2:4:6:2:6:4:2:4:6:6:2:6:4:2:6:4:6:8:4:2:4:2:4:8:6:4:6:2:4:6:2:6:6:4:2:4:6:2:6:4:2:4:2:10:2:10:wheel
Benchmarking
All time are measured by *nix time command, real space
Haskell original : 2e6: N/A; 2e7: >30s
Haskell optimized: 2e6: 0.396s; 2e7: 6.273s
C++ Set (ordered): 2e6: 4.694s; 2e7: >30s
C++ Bool Array : 2e6: 0.039s; 2e7: 0.421s
Haskell optimized is slower than C++ Bool by 10~15x, and faster than C++ Set by 10x.
Source code
C Compiler options: g++ 5.3.1, g++ -std=c++11
Haskell options: ghc 7.8.4, ghc
C code (Bool array) http://pastebin.com/W0s7cSWi
prime[0] = prime[1] = false;
for (int i=2; i<=limit; i++) { //edited
if (!prime[i]) continue;
for (int j=2*i; j<=n; j+=i)
prime[j] = false;
}
C code (Set) http://pastebin.com/sNpghrU4
nonprime.insert(1);
for (int i=2; i<=limit; i++) { //edited
if (nonprime.count(i) > 0) continue;
for (int j=2*i; j<=n; j+=i)
nonprime.insert(j);
}
Haskell code http://pastebin.com/HuMqwvRW
Code as written above.

Answer 1

I would like to know whether/why my implementation in Haskell is imperfect.
Instead of fromList you better use fromDistinctAscList which performs linearly. You may also add only odd multiples starting with x*x not x*2, because all the smaller odd multiples have already been added. Style-wise, a right fold may fit better than recursion.
Doing so, I get more than 3 times performance improvement for n equal to 2,000,000:
import Data.IntSet (member, union, empty, fromDistinctAscList)
sieve :: Int -> [Int]
sieve n = 2: foldr go (const []) [3,5..n] empty
where
go i run obs
| member i obs = run obs
| otherwise = i: run (union obs inc)
where inc = fromDistinctAscList [i*i, i*(i + 2)..n]
Nevertheless, an array has both O(1) access and cache friendly memory allocation. Using mutable arrays, I see more than 15 times performance improvement over your Haskell code (again n equal to 2,000,000):
{-# LANGUAGE FlexibleContexts #-}
import Data.Array.ST (STUArray)
import Control.Monad (forM_, foldM)
import Control.Monad.ST (ST, runST)
import Data.Array.Base (newArray, unsafeWrite, unsafeRead)
sieve :: Int -> [Int]
sieve n = reverse $ runST $ do
arr <- newArray (0, n) False :: ST s (STUArray s Int Bool)
foldM (go arr) [2] [3,5..n]
where
go arr acc i = do
b <- unsafeRead arr i
if b then return acc else do
forM_ [i*i, i*(i + 2).. n] $ \k -> unsafeWrite arr k True
return $ i: acc