Eugene Kirpichov ekirpichov at gmail.com
Thu Feb 26 05:56:20 EST 2009

```Here is a variant that uses mersenne-random-pure64 and works less than
2x slower than C++:

- You don't need to compute samples count an extra time
- You don't need to assemble double pairs from a list
- Notice the strictness in randomDoublePairs: it doubled performance

{-# LANGUAGE BangPatterns #-}

import System.Random.Mersenne.Pure64
import System( getArgs )
import Data.List( foldl' )

isInCircle :: (Double,Double) -> Bool
isInCircle (!x,!y) = sqrt (x*x + y*y) <= 1.0

accumulateHit :: Int -> (Double,Double) -> Int
accumulateHit !hits pair = if isInCircle pair then hits + 1 else hits

monteCarloPi :: Int -> [(Double,Double)] -> Double
monteCarloPi n xs = 4.0 * fromIntegral hits / fromIntegral n
where hits = foldl' accumulateHit 0 . take n \$ xs

randomDoublePairs g = let
!(!x,!g') = randomDouble g
!(!y,!g'') = randomDouble g'
in (x,y):randomDoublePairs g''

main = do
randomNumbers <- randomDoublePairs `fmap` newPureMT
putStrLn . show \$ monteCarloPi samples randomNumbers

jkff@*****:~/montecarlo\$ time ./mc-hs 10000000
3.1417088

real    0m1.141s
user    0m1.140s
sys     0m0.000s
jkff@*****:~/montecarlo\$ time ./mc 10000000
10000000
3.14113

real    0m0.693s
user    0m0.690s
sys     0m0.000s

2009/2/26 Ben Lippmeier <Ben.Lippmeier at anu.edu.au>:
>
> On 26/02/2009, at 9:27 PM, haskell at kudling.de wrote:
>>
>> Currently i can only imagine to define a data type in order to use unboxed
>> Ints instead of the accumulator tuple.
>
> That would probably help a lot. It would also help to use two separate
> Double# parameters instead of the tuple.
>
>> The thing is that i don't see in the profile output yet what to improve.
>> There are some allocations going on in "main", but i don't know what
>> causes it.
>>
>>> The first thing I would do is replace your
>>> isInCircle :: (Floating a, Ord a)  => (a,a) -> Bool
>>> with
>>> isInCircle :: (Double, Double) -> Bool
>>
>> Can you point me to why that matters?
>
> At the machine level, GHC treats the (Floating a, Ord a) as an extra
> argument to the function. This argument holds function pointers that tell it
> how to perform multiplication and <= for the unknown type 'a'. If you use
> Double instead of 'a', then it's more likely to use the actual machine op.
>
> Ben.
>
>
> _______________________________________________