Shootout/Nbody
This is a ShootoutEntry for the N-body benchmark.
Each program should model the orbits of Jovian planets, using the same simple symplectic-integrator - see the Java program.
Correct output N = 1000 is
-0.169075164
-0.169087605
Benchmarks[edit]
Finally, we get some decent performance. Timing on Linux/P4, N=1,000,000
| Author | Time | Flags |
|---|---|---|
| current | 8.561 | -O2 -optc-O3 -optc-ffast-math |
| current-fexcess-precision | 6.335 | -O2 -fexcess-precision -optc-O3 -optc-ffast-math |
| chris | 4.515 | -O2 |
| chris | 2.547 | -O2 -fexcess-precision |
| chris | 2.363 | -O2 -fexcess-precision -optc-O -optc-ffast-math |
| C | 1.174 | |
| chris+dons | 1.112 | -O2 -fexcess-precision -optc-O -optc-ffast-math |
| stuarray | 1.073 | -O2 -fexcess-precision -optc-O -optc-ffast-math -funbox-strict-fields |
| stuarray2 | 0.912 | -O3 -fexcess-precision -optc-O -optc-ffast-math -funbox-strict-fields |
| C | 0.518 | -O2 |
Again with N=5,000,000 (as used in shootout):
| Author | Time | Flags |
|---|---|---|
| current | 42.685 | -O2 -optc-O3 -optc-ffast-math |
| chris | 11.753 | -O2 -fexcess-precision -optc-O -optc-ffast-math |
| C | 5.786 | |
| chris+dons | 5.498 | -O2 -fexcess-precision -optc-O -optc-ffast-math |
| stuarray | 5.290 | -O2 -fexcess-precision -optc-O -optc-ffast-math -funbox-strict-fields |
| stuarray2 | 4.489 | -O2 -fexcess-precision -optc-O -optc-ffast-math -funbox-strict-fields |
| C | 2.555 | -O2 |
Hooray!
Need to add my smaller/faster tweak to Joel's entry. -- ChrisKuklewicz
On x86/Linux gcc produces weird numerical errors with the new IOUArray entries (chris and chris+dons), when using the -optc-Ox flags. It cannot be used above -optc-O1
| chris | ERROR | -O2 -optc-O3 -optc-ffast-math |
| chris | ERROR | -O2 -optc-O2 -fexcess-precision -optc-ffast-math |
Architecture differences[edit]
This is very CPU architecture dependent, which means a powerbook G4 is not seeing the same results as linux/x86.
Compiling both with -fglasgow-exts -fexcess-precision -O3 -optc-O3 -optc-ffast-math on a G4:
$ time ./chris 5000000; time ./dons+chris 5000000 -0.169075164 -0.169083134
real 0m27.794s user 0m21.176s sys 0m0.268s -0.169075164 -0.169083134
real 0m25.985s user 0m22.357s sys 0m0.236s
On linux/x86 {{{dons+chris}}} beats {{{chris}}} by a factor of two and on a G4 {{{dons+chris}}} is a few percent slower. Not too surprising, since the floating point hardware differs. The performanace for the this benchmark (AMD Sempron, Inten P4) is untunable on a G4.
So Don: you can submit this when you are happy with the tweaking since I am blind to x86 performance here. Can you try passing architecture switches to -optc such as -mtune? -- ChrisKuklewicz
Conservative extension[edit]
Replace hardcoded sizeof double with Storable instance sizeOf.
{-# OPTIONS -fvia-C -fexcess-precision #-}
--
-- The Computer Language Benchmarks Game
-- http://shootout.alioth.debian.org/
--
-- Contributed by Olof Kraigher and Don Stewart.
--
-- To be compiled with:
--
-- -O2 -fglasgow-exts -funbox-strict-fields -fbang-patterns -optc-O
--
-- Don't enable -optc-mfpmath=sse -optc-msse2, this triggers a gcc bug on x86
--
-- TODO, rewrite in ST.
--
import Foreign
import Foreign.Storable
import Foreign.Marshal.Alloc
import Data.IORef
import Control.Monad
import System
import Text.Printf
main = do
n <- getArgs >>= readIO.head
initialize
offset_momentum
energy 0 planets >>= printf "%.9f\n"
replicateM_ n (advance planets)
energy 0 planets >>= printf "%.9f\n"
offset_momentum = do
m <- foldr (.+.) (Vec 0 0 0)
`fmap` (mapM momentum
. take (nbodies - 1)
. iterate next $ next planets)
setVec (vel planets) $ (-1/solar_mass) *. m
where
momentum p = liftM2 (*.) (mass p) (getVec (vel p))
energy :: Double -> Ptr Double -> IO Double
energy !e p
| p == end = return e
| otherwise = do
p1 <- getVec (pos p)
v1 <- getVec (vel p)
m1 <- mass p
e <- energy2 p1 m1 e p2
energy (e + 0.5 * m1 * magnitude2 v1) p2
where p2 = next p
energy2 :: Vector3 -> Double -> Double -> Ptr Double -> IO Double
energy2 p1 m1 !e p
| p == end = return e
| otherwise = do
p2 <- getVec (pos p)
v2 <- getVec (vel p)
m2 <- mass p
let distance = sqrt . magnitude2 $ p1 .-. p2
energy2 p1 m1 (e - m1 * m2 / distance) (next p)
advance :: Ptr Double -> IO ()
advance p1 = when (p1 /= end) $ do
pos1 <- getVec (pos p1)
m1 <- mass p1
go pos1 m1 p2
advance p2
where
vel1 = vel p1
p2 = next p1
go pos1 m1 p2
| p2 /= end = do
pos2 <- getVec (pos p2)
m2 <- mass p2
let vel2 = vel p2
difference = pos1 .-. pos2
distance2 = magnitude2 difference
distance = sqrt distance2
magnitude = delta_t / (distance2 * distance)
mass_magn = magnitude *. difference
vel1 -= m2 *. mass_magn
vel2 += m1 *. mass_magn
go pos1 m1 (next p2)
| otherwise = do
v1 <- getVec vel1
p1 += delta_t *. v1
------------------------------------------------------------------------
planets :: Ptr Double
planets = unsafePerformIO $ mallocBytes (7 * nbodies * sizeOf (undefined :: Double))
nbodies :: Int
nbodies = 5
solar_mass, delta_t, days_per_year :: Double
days_per_year = 365.24
delta_t = 0.01
solar_mass = 4 * pi ** 2
initialize = mapM_ newPlanet planets
where
dp = days_per_year
planets =
[0, 0, 0,
0, 0, 0,
1 * solar_mass,
4.84143144246472090e+00, (-1.16032004402742839e+00), (-1.03622044471123109e-01),
1.66007664274403694e-03*dp, 7.69901118419740425e-03*dp, (-6.90460016972063023e-05)*dp,
9.54791938424326609e-04 * solar_mass,
8.34336671824457987e+00, 4.12479856412430479e+00, (-4.03523417114321381e-01),
(-2.76742510726862411e-03)*dp, 4.99852801234917238e-03*dp, 2.30417297573763929e-05*dp,
2.85885980666130812e-04 * solar_mass,
1.28943695621391310e+01, (-1.51111514016986312e+01), (-2.23307578892655734e-01),
2.96460137564761618e-03*dp, 2.37847173959480950e-03*dp, (-2.96589568540237556e-05)*dp,
4.36624404335156298e-05 * solar_mass,
1.53796971148509165e+01, (-2.59193146099879641e+01), 1.79258772950371181e-01,
2.68067772490389322e-03*dp, 1.62824170038242295e-03*dp, (-9.51592254519715870e-05)*dp,
5.15138902046611451e-05 * solar_mass
]
------------------------------------------------------------------------
-- Support for 3 dimensional mutable vectors
cursor :: IORef (Ptr Double)
cursor = unsafePerformIO $ newIORef planets
data Vector3 = Vec !Double !Double !Double
end :: Ptr Double
end = inc planets $! nbodies * 7
next :: Ptr Double -> Ptr Double
next p = inc p 7
inc :: Ptr Double -> Int -> Ptr Double
inc ptr n = plusPtr ptr (n * sizeOf (undefined :: Double))
newPlanet :: Double -> IO ()
newPlanet d = do
ptr <- readIORef cursor
pokeElemOff ptr 0 d
writeIORef cursor $! inc ptr 1
pos :: Ptr Double -> Ptr Double
pos ptr = ptr
vel :: Ptr Double -> Ptr Double
vel ptr = inc ptr 3
mass :: Ptr Double -> IO Double
mass ptr = peekElemOff ptr 6
------------------------------------------------------------------------
(Vec x y z) .+. (Vec u v w) = Vec (x+u) (y+v) (z+w)
(Vec x y z) .-. (Vec u v w) = Vec (x-u) (y-v) (z-w)
k *. (Vec x y z) = Vec (k*x) (k*y) (k*z) -- allocates
magnitude2 (Vec x y z) = x*x + y*y + z*z
------------------------------------------------------------------------
getVec p = do
x <- peek p
y <- peekElemOff p 1
z <- peekElemOff p 2
return $! Vec x y z
setVec p (Vec x y z)= do
poke p x
pokeElemOff p 1 y
pokeElemOff p 2 z
infix 4 +=
infix 4 -=
v1 += (Vec u v w) = do
x <- peek v1; poke v1 (x+u)
y <- peekElemOff v1 1; pokeElemOff v1 1 (y+v)
z <- peekElemOff v1 2; pokeElemOff v1 2 (z+w)
v1 -= (Vec u v w) = do
x <- peek v1; poke v1 (x-u)
y <- peekElemOff v1 1; pokeElemOff v1 1 (y-v)
z <- peekElemOff v1 2; pokeElemOff v1 2 (z-w)
Current entry[edit]
Improves on the one below, shorter and at tad faster. I removed the unnecessary inc function and it runs a bit faster. // Olof
{-# OPTIONS -fexcess-precision #-}
--
-- The Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Olof Kraigher, with help from Don Stewart.
--
-- Compile with:
--
-- -funbox-strict-fields -fglasgow-exts -fbang-patterns -O3
-- -optc-O3 -optc-mfpmath=sse -optc-msse2 -optc-march=pentium4
--
import Foreign
import Foreign.Storable
import Foreign.Marshal.Alloc
import Data.IORef
import Control.Monad
import System
import Text.Printf
main = do
n <- getArgs >>= readIO.head
initialize
offset_momentum
energy 0 planets >>= printf "%.9f\n"
replicateM_ n (advance planets)
energy 0 planets >>= printf "%.9f\n"
offset_momentum = do
m <- foldr (.+.) (Vec 0 0 0)
`fmap` (mapM momentum
. take (nbodies - 1)
. iterate next $ next planets)
setVec (vel planets) $ (-1/solar_mass) *. m
where
momentum !p = liftM2 (*.) (mass p) (getVec (vel p))
energy :: Double -> Ptr Double -> IO Double
energy !e !p
| p == end = return e
| otherwise = do
p1 <- getVec (pos p)
v1 <- getVec (vel p)
m1 <- mass p
e <- energy2 p1 m1 e p2
energy (e + 0.5 * m1 * magnitude2 v1) p2
where p2 = next p
energy2 !p1 !m1 !e !p
| p == end = return e
| otherwise = do
p2 <- getVec (pos p)
v2 <- getVec (vel p)
m2 <- mass p
let distance = sqrt . magnitude2 $ p1 .-. p2
energy2 p1 m1 (e - m1 * m2 / distance) (next p)
advance :: Ptr Double -> IO ()
advance !p1 = when (p1 /= end) $ do
pos1 <- getVec $ pos p1
m1 <- mass p1
let go !p2
| p2 /= end = do
pos2 <- getVec (pos p2)
m2 <- mass p2
let vel2 = vel p2
difference = pos1 .-. pos2
distance2 = magnitude2 difference
distance = sqrt distance2
magnitude = delta_t / (distance2 * distance)
mass_magn = magnitude *. difference
vel1 -= m2 *. mass_magn
vel2 += m1 *. mass_magn
go (next p2)
| otherwise = do
v1 <- getVec vel1
p1 += delta_t *. v1
go p2
advance p2
where
vel1 = vel p1
p2 = next p1
------------------------------------------------------------------------
planets :: Ptr Double
planets = unsafePerformIO $ mallocBytes (7 * nbodies * 8) -- sizeOf double = 8
nbodies :: Int
nbodies = 5
solar_mass, delta_t, days_per_year :: Double
days_per_year = 365.24
solar_mass = 4 * pi ** 2;
delta_t = 0.01
initialize = mapM_ newPlanet planets
where
dp = days_per_year
planets =
[0, 0, 0,
0, 0, 0,
1 * solar_mass,
4.84143144246472090e+00, (-1.16032004402742839e+00), (-1.03622044471123109e-01),
1.66007664274403694e-03*dp, 7.69901118419740425e-03*dp, (-6.90460016972063023e-05)*dp,
9.54791938424326609e-04 * solar_mass,
8.34336671824457987e+00, 4.12479856412430479e+00, (-4.03523417114321381e-01),
(-2.76742510726862411e-03)*dp, 4.99852801234917238e-03*dp, 2.30417297573763929e-05*dp,
2.85885980666130812e-04 * solar_mass,
1.28943695621391310e+01, (-1.51111514016986312e+01), (-2.23307578892655734e-01),
2.96460137564761618e-03*dp, 2.37847173959480950e-03*dp, (-2.96589568540237556e-05)*dp,
4.36624404335156298e-05 * solar_mass,
1.53796971148509165e+01, (-2.59193146099879641e+01), 1.79258772950371181e-01,
2.68067772490389322e-03*dp, 1.62824170038242295e-03*dp, (-9.51592254519715870e-05)*dp,
5.15138902046611451e-05 * solar_mass
]
------------------------------------------------------------------------
-- Support for 3 dimensional mutable vectors
data Vector3 = Vec !Double !Double !Double
end :: Ptr Double
end = plusPtr planets $ nbodies * 7 * 8
next :: Ptr Double -> Ptr Double
next p = plusPtr p 56
cursor :: IORef (Ptr Double)
cursor = unsafePerformIO $ newIORef planets
newPlanet :: Double -> IO ()
newPlanet !d = do
ptr <- readIORef cursor
pokeElemOff ptr 0 d
writeIORef cursor (plusPtr ptr 8)
pos :: Ptr Double -> Ptr Double
pos ptr = ptr
vel :: Ptr Double -> Ptr Double
vel ptr = plusPtr ptr 24
mass :: Ptr Double -> IO Double
mass ptr = peekElemOff ptr 6
------------------------------------------------------------------------
(Vec x y z) .+. (Vec u v w) = Vec (x+u) (y+v) (z+w)
(Vec x y z) .-. (Vec u v w) = Vec (x-u) (y-v) (z-w)
k *. (Vec x y z) = Vec (k*x) (k*y) (k*z) -- allocates
magnitude2 (Vec x y z) = x*x + y*y + z*z
------------------------------------------------------------------------
getVec !p = liftM3 Vec (peek p) (f 1) (f 2)
where f = peekElemOff p
setVec p (Vec x y z)= do
poke p x
pokeElemOff p 1 y
pokeElemOff p 2 z
infix 4 +=
infix 4 -=
v1 += (Vec u v w) = do
x <- peek v1; poke v1 (x+u)
y <- peekElemOff v1 1; pokeElemOff v1 1 (y+v)
z <- peekElemOff v1 2; pokeElemOff v1 2 (z+w)
v1 -= (Vec u v w) = do
x <- peek v1; poke v1 (x-u)
y <- peekElemOff v1 1; pokeElemOff v1 1 (y-v)
z <- peekElemOff v1 2; pokeElemOff v1 2 (z-w)Proposed entry[edit]
A fast and relatively nice entry that runs 1.5x the fastest c++ entry.
{-# OPTIONS_GHC -fbang-patterns -fexcess-precision#-}
{-
The Computer Language Shootout
http://shootout.alioth.debian.org/
Contributed by Olof Kraigher, with help from Don Stewart.
Compile with:
-fglasgow-exts -fbang-patterns -fexcess-precision -O3 -optc-O2 -optc-mfpmath=sse -optc-msse2 -optc-march=pentium4
-}
import Foreign.Ptr; import Foreign.Storable; import Foreign.Marshal.Alloc; import Foreign(unsafePerformIO);
import Data.IORef; import Control.Monad; import System; import Text.Printf;
data Vector3 = Vec !Double !Double !Double
nr_of_planets :: Int
nr_of_planets = 5
delta_t :: Double
delta_t = 0.01
days_per_year :: Double
days_per_year = 365.24
solar_mass :: Double
solar_mass = 4 * pi ** 2;
planets :: Ptr Double
planets = unsafePerformIO $ mallocBytes (7 * nr_of_planets * 8) -- sizeOf double = 8
end :: Ptr Double
end = inc planets $ nr_of_planets * 7
cursor :: IORef (Ptr Double)
cursor = unsafePerformIO $ newIORef planets
{-# INLINE inc #-}
inc :: Ptr Double -> Int -> Ptr Double
inc ptr n = plusPtr ptr $ n * 8
{-# INLINE new #-}
new :: Double -> IO ()
new !d = do
ptr <- readIORef cursor
pokeElemOff ptr 0 d
writeIORef cursor (inc ptr 1)
{-# INLINE getVec #-}
getVec :: Ptr Double -> IO Vector3
getVec ptr =
let p = peekElemOff ptr in
liftM3 Vec (p 0) (p 1) (p 2)
{-# INLINE setVec #-}
setVec :: Ptr Double -> Vector3 -> IO ()
setVec ptr (Vec x y z)= do
pokeElemOff ptr 0 x
pokeElemOff ptr 1 y
pokeElemOff ptr 2 z
{-# INLINE pos #-}
pos :: Ptr Double -> Ptr Double
pos ptr = ptr
{-# INLINE vel #-}
vel :: Ptr Double -> Ptr Double
vel ptr = inc ptr 3
{-# INLINE mass #-}
mass :: Ptr Double -> IO Double
mass ptr = peekElemOff ptr 6
{-# INLINE (.+.) #-}
(.+.) :: Vector3 -> Vector3 -> Vector3
(Vec x y z) .+. (Vec u v w) = Vec (x+u) (y+v) (z+w)
{-# INLINE (.-.) #-}
(.-.) :: Vector3 -> Vector3 -> Vector3
(Vec x y z) .-. (Vec u v w) = Vec (x-u) (y-v) (z-w)
{-# INLINE (*.) #-}
(*.) :: Double -> Vector3 -> Vector3
k *. (Vec x y z) = Vec (k*x) (k*y) (k*z)
{-# INLINE magnitude2 #-}
magnitude2 :: Vector3 -> Double
magnitude2 (Vec x y z) = x*x + y*y + z*z
infix 4 +=
infix 4 -=
{-# INLINE (+=) #-}
(+=) :: Ptr Double -> Vector3 -> IO ()
v1 += v2 = do
v1' <- getVec v1
setVec v1 $ v1' .+. v2
{-# INLINE (-=) #-}
(-=) :: Ptr Double -> Vector3 -> IO ()
v1 -= v2 = do
v1' <- getVec v1
setVec v1 $ v1' .-. v2
initialize :: IO ()
initialize =
let dp = days_per_year in
mapM_ new
[ 0, 0, 0,
0, 0, 0,
1 * solar_mass,
4.84143144246472090e+00, (-1.16032004402742839e+00), (-1.03622044471123109e-01),
1.66007664274403694e-03*dp, 7.69901118419740425e-03*dp, (-6.90460016972063023e-05)*dp,
9.54791938424326609e-04 * solar_mass,
8.34336671824457987e+00, 4.12479856412430479e+00, (-4.03523417114321381e-01),
(-2.76742510726862411e-03)*dp, 4.99852801234917238e-03*dp, 2.30417297573763929e-05*dp,
2.85885980666130812e-04 * solar_mass,
1.28943695621391310e+01, (-1.51111514016986312e+01), (-2.23307578892655734e-01),
2.96460137564761618e-03*dp, 2.37847173959480950e-03*dp, (-2.96589568540237556e-05)*dp,
4.36624404335156298e-05 * solar_mass,
1.53796971148509165e+01, (-2.59193146099879641e+01), 1.79258772950371181e-01,
2.68067772490389322e-03*dp, 1.62824170038242295e-03*dp, (-9.51592254519715870e-05)*dp,
5.15138902046611451e-05 * solar_mass
]
advance :: IO ()
advance = do
let advance' !planet1
| planet1 /= end = do
p1 <- getVec $ pos planet1
m1 <- mass planet1
let vel1 = vel planet1
let advance'' !planet2
| planet2 /= end = do
p2 <- getVec $ pos planet2
m2 <- mass planet2
let vel2 = vel planet2
let difference = p1 .-. p2
let distance2 = magnitude2 difference
let distance = sqrt distance2
let magnitude = delta_t / (distance2 * distance)
let mass_magn = magnitude *. difference
vel1 -= (m2 *. mass_magn)
vel2 += (m1 *. mass_magn)
advance'' (inc planet2 7)
| otherwise = do
v1 <- getVec vel1
planet1 += delta_t *. v1
let planet1' = (inc planet1 7)
advance'' planet1'
advance' planet1'
| otherwise = return ()
advance' planets
energy :: IO Double
energy = do
e <- newIORef 0
let energy' !planet1
| planet1 /= end = do
p1 <- getVec $ pos planet1
v1 <- getVec $ vel planet1
m1 <- mass planet1
let energy'' !planet2
| planet2 /= end = do
p2 <- getVec $ pos planet2
v2 <- getVec $ vel planet2
m2 <- mass planet2
let distance = sqrt $ magnitude2 $ p1 .-. p2
modifyIORef e (\x -> x - m1 * m2 / distance)
energy'' (inc planet2 7)
| otherwise = do
modifyIORef e (+ 0.5 * m1 * (magnitude2 v1))
let planet1' = (inc planet1 7)
energy'' planet1'
energy' planet1'
| otherwise = return ()
energy' planets
readIORef e
offset_momentum :: IO ()
offset_momentum = do
let momentum' !planet = do
v <- getVec $ vel planet
m <- mass planet
return $ m *. v
momentum <- return.(foldl (.+.) (Vec 0 0 0)) =<<
(mapM momentum' $ take (nr_of_planets - 1) $ iterate (\x -> inc x 7) (inc planets 7))
setVec (vel planets) $ (-1/solar_mass) *. momentum
main = do
n <- getArgs >>= readIO.head
initialize
offset_momentum
energy >>= printf "%.9f\n"
replicateM_ n advance
energy >>= printf "%.9f\n"Proposed entry[edit]
Complete rewrite, attention paid down to the asm level on the inner loops. Very much faster.
Note that in GHC -fexcess-precision is ignored on the command line!
{-# OPTIONS -fexcess-precision #-}
--
-- The Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Don Stewart
--
-- Compile with:
-- -O -fglasgow-exts -fbang-patterns -optc-O3 -optc-march=pentium4
--
import System
import System.IO.Unsafe
import Text.Printf
import Foreign.Marshal.Array
import Foreign
import Control.Monad
import Bits
import GHC.Exts
------------------------------------------------------------------------
main = do
n <- getArgs >>= readIO . head
offset_momentum
printf "%.9f\n" =<< energy
replicateM_ n advance
printf "%.9f\n" =<< energy
------------------------------------------------------------------------
type Bodies = Ptr Double
nbodies = 5
bodies :: Bodies
bodies = unsafePerformIO . newArray . concat $
[planet 1 0 0 0 0 0 0 -- sun
,planet 9.54791938424326609e-04 -- jupiter
4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01)
( 1.66007664274403694e-03) ( 7.69901118419740425e-03) (-6.90460016972063023e-05)
,planet 2.85885980666130812e-04 -- saturn
8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01)
(-2.76742510726862411e-03) ( 4.99852801234917238e-03) ( 2.30417297573763929e-05)
,planet 4.36624404335156298e-05 -- uranus
1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01)
( 2.96460137564761618e-03) ( 2.37847173959480950e-03) (-2.96589568540237556e-05)
,planet 5.15138902046611451e-05 -- neptune
1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01
( 2.68067772490389322e-03) ( 1.62824170038242295e-03) (-9.51592254519715870e-05)]
where
planet m x y z vx vy vz =
[m*solar_mass,x, y, z, vx*days_per_year, vy*days_per_year, vz*days_per_year, 0]
-- n.b widht of 8 doubles to make bitwise math nice
-- field access
(W# body) `at` (W# field) = I#
(word2Int# (field `or#` (body `uncheckedShiftL#` 3#))) -- sizeof Double
put !body !field = pokeElemOff bodies (body `at` field)
get !body !field = peekElemOff bodies (body `at` field)
--
-- field offsets in flattened array
--
mass = 0
x = 1
y = 2
z = 3
vx = 4
vy = 5
vz = 6
solar_mass = 4 * pi * pi
days_per_year = 365.24
------------------------------------------------------------------------
-- Offset momentum
offset_momentum :: IO ()
offset_momentum = do
(px,py,pz) <- go 0 0 0 0
put 0 vx (- px / solar_mass)
put 0 vy (- py / solar_mass)
put 0 vz (- pz / solar_mass)
where
go !i !px !py !pz
| i >= nbodies = return (px,py,pz)
| otherwise = do
imass <- look mass
ivx <- look vx
ivy <- look vy
ivz <- look vz
go (i+1) (px + ivx * imass)
(py + ivy * imass)
(pz + ivz * imass)
where look = get i
------------------------------------------------------------------------
-- Energy
energy = goI 0 0
goI :: Word -> Double -> IO Double
goI !i !e
| i >= nbodies = return e
| otherwise = do
im <- look mass
ix <- look x -- cache the body offset calculation?
iy <- look y
iz <- look z
ivx <- look vx
ivy <- look vy
ivz <- look vz
e' <- goJ ix iy iz im (i+1) (e + 0.5 * im * (ivx * ivx + ivy * ivy + ivz * ivz))
goI (i+1) e'
where
look = get i
goJ !ix !iy !iz !im !j !e
| j >= nbodies = return e
| otherwise = do
b2m <- look mass
b2x <- look x
b2y <- look y
b2z <- look z
let dx = ix - b2x
dy = iy - b2y
dz = iz - b2z
distance = sqrt $! dx * dx + dy * dy + dz * dz
goJ ix iy iz im (j+1) (e - ((im * b2m) / distance))
where
look = get j
------------------------------------------------------------------------
-- Advance
advance :: IO ()
advance = advanceI 0 >> update
advanceI i@(W# ii) = when (i < nbodies) $ do
bm <- lookI mass
bx <- lookI x -- cache the body offset calculation!
by <- lookI y
bz <- lookI z
bvx <- lookI vx -- float these out to an accumultor
bvy <- lookI vy
bvz <- lookI vz
advanceJ off bm bx by bz bvx bvy bvz (i+1)
advanceI (i+1)
where
off = W# (ii `uncheckedShiftL#` 3#)
lookI x = peekElemOff bodies (fromIntegral $ x .|. off)
setI = put i
advanceJ !i_off !bm !bx !by !bz !bvx !bvy !bvz !j@(W# jj)
| j >= nbodies = do
let setI x = pokeElemOff bodies (fromIntegral $ x .|. i_off)
setI vx bvx
setI vy bvy
setI vz bvz
| otherwise = do
b2mass <- lookJ mass
b2x <- lookJ x
b2y <- lookJ y
b2z <- lookJ z
b2vx <- lookJ vx
b2vy <- lookJ vy
b2vz <- lookJ vz
let dx = bx - b2x
dy = by - b2y
dz = bz - b2z
distance = sqrt (dx * dx + dy * dy + dz * dz)
mag = 0.01 / (distance * distance * distance)
massmag = bm * mag
setJ vx (b2vx + dx * massmag)
setJ vy (b2vy + dy * massmag)
setJ vz (b2vz + dz * massmag)
let mass2mag = - b2mass * mag
advanceJ i_off bm bx by bz (bvx + dx * mass2mag)
(bvy + dy * mass2mag)
(bvz + dz * mass2mag) (j+1)
where
off = W# (jj `uncheckedShiftL#` 3#)
lookJ x = peekElemOff bodies (fromIntegral $ x .|. off)
setJ x = pokeElemOff bodies (fromIntegral $ x .|. off)
update = forM_ [0..nbodies-1] $ \i -> do
let look = get i
set = put i
bx <- look x
by <- look y
bz <- look z
bvx <- look vx
bvy <- look vy
bvz <- look vz
set x (bx + 0.01 * bvx)
set y (by + 0.01 * bvy)
set z (bz + 0.01 * bvz)old entry[edit]
Modifies the ghc flags. Submitted.
{-# OPTIONS -O -fglasgow-exts -fbang-patterns -funbox-strict-fields -fexcess-precision -optc-O -optc-march=pentium4 #-}
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Christoph Bauer
-- Written in Haskell by Chris Kuklewicz, further tweaks by Don Stewart
--
-- -O2 -optc-O -fglasgow-exts -fexcess-precision -optc-ffast-math
--
-- -optc-O3 cannot be used, as at least one version of gcc miscompiles this program
--
import System
import System.IO.Unsafe
import Monad
import Bits
import List
import Data.Array.IO
import Data.Array.Base (unsafeRead,unsafeWrite)
import Text.Printf
import GHC.Base
import GHC.Int
default (Int)
main = do n <- getArgs >>= readIO . head
offsetMomentum
energy >>= printf "%.9f\n"
advance n
energy >>= printf "%.9f\n"
-- Offsets for each field
x = 0; y = 1; z = 2; vx= 3; vy= 4; vz= 5; m = 6
type Bodies = IOUArray Int Double
b :: Bodies = unsafePerformIO $ newListArray (0,pred (length bodiesData)) (bodiesData)
{-# NOINLINE b #-}
set = unsafeWrite b
{-# INLINE set #-}
resetB = zipWithM_ set [0..] bodiesData
-- sun jupiter saturn uranus neptune
-- sun starts at center at rest
bodiesData = concat [ mkB 1 0 0 0 0 0 0
,mkB 9.54791938424326609e-04
4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01)
( 1.66007664274403694e-03) ( 7.69901118419740425e-03) (-6.90460016972063023e-05)
,mkB 2.85885980666130812e-04
8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01)
(-2.76742510726862411e-03) ( 4.99852801234917238e-03) ( 2.30417297573763929e-05)
,mkB 4.36624404335156298e-05
1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01)
( 2.96460137564761618e-03) ( 2.37847173959480950e-03) (-2.96589568540237556e-05)
,mkB 5.15138902046611451e-05
1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01
( 2.68067772490389322e-03) ( 1.62824170038242295e-03) (-9.51592254519715870e-05)]
mkB m x y z vx vy vz =
[x, y, z, vx*days_per_year,vy*days_per_year, vz*days_per_year, m*solar_mass, 0]
solar_mass = 4 * pi * pi
days_per_year = 365.24
nbodies = 4 -- that is 0 to 4
mass :: Int -> IO Double
mass i = unsafeRead b (massOffset .|. (shiftl i 3)) where massOffset = 6
-- Give the sun a small velocity so the total momentum of all bodies totals to zero
offsetMomentum :: IO ()
offsetMomentum = do sm <- mass 0
let act i = mass i >>= \m -> addScaled 3 (-m/sm) (3 .|. (shiftl i 3))
mapM_ act [1..nbodies]
-- Total all kineticE and potentialE
energy = loop 0 0
where loop !i !e
| i > nbodies = return e
| otherwise = do ke <- kineticE i
(loop' (i+1) i $! (e+ke)) >>= loop (i+1)
loop' !j !i !e
| j > nbodies = return e
| otherwise = do pe <- potentialE i j
loop' (j+1) i $! (e + pe)
kineticE !i = do
m <- mass i
vx <- unsafeRead b (f vx)
vy <- unsafeRead b (f vy)
vz <- unsafeRead b (f vz)
return $! 0.5 * m * (vx*vx + vy*vy + vz*vz)
where f = (.|. (shiftl i 3))
potentialE !i !j = do
m1 <- mass i
m2 <- mass j
dx <- liftM2 (-) (unsafeRead b (f x)) (unsafeRead b (g x))
dy <- liftM2 (-) (unsafeRead b (f y)) (unsafeRead b (g y))
dz <- liftM2 (-) (unsafeRead b (f z)) (unsafeRead b (g z))
return $! ((-1)*m1*m2/sqrt (dx*dx + dy*dy + dz*dz))
where
f = (.|.) (shiftl j 3)
g = (.|.) (shiftl i 3)
addScaled !i !a !j = do
set i1 =<< liftM2 scale (unsafeRead b i1) (unsafeRead b j1)
set i2 =<< liftM2 scale (unsafeRead b i2) (unsafeRead b j2)
set i3 =<< liftM2 scale (unsafeRead b i3) (unsafeRead b j3)
where scale old new = old + a * new
i1 = i; i2 = succ i1; i3 = succ i2;
j1 = j; j2 = succ j1; j3 = succ j2;
addScaled3 !i !a !jx !jy !jz = do
set i1 =<< liftM (scale jx) (unsafeRead b i1)
set i2 =<< liftM (scale jy) (unsafeRead b i2)
set i3 =<< liftM (scale jz) (unsafeRead b i3)
where scale new old = a * new + old
i1 = i; i2 = succ i1; i3 = succ i2;
-- This is the main code. Essentially all the time is spent here
advance :: Int -> IO ()
advance n = when (n > 0) $ updateVel 0 >> advance (pred n)
where updateVel i = when (i <= nbodies) $ do
im <- unsafeRead b (f m)
ix <- unsafeRead b (f x)
iy <- unsafeRead b (f y)
iz <- unsafeRead b (f z)
ivx <- unsafeRead b (f vx)
ivy <- unsafeRead b (f vy)
ivz <- unsafeRead b (f vz)
let updateVel' :: Double -> Double -> Double -> Int -> IO ()
updateVel' !ivx !ivy !ivz !j =
if j > nbodies then do
unsafeWrite b (f vx) ivx
unsafeWrite b (f vy) ivy
unsafeWrite b (f vz) ivz
else do
let g = (.|. shiftl j 3)
jm <- unsafeRead b (g m)
dx <- liftM (ix-) (unsafeRead b (g x))
dy <- liftM (iy-) (unsafeRead b (g y))
dz <- liftM (iz-) (unsafeRead b (g z))
let distance = sqrt (dx*dx+dy*dy+dz*dz)
mag = 0.01 / (distance * distance * distance)
addScaled3 (3 .|. (shiftl j 3)) ( im*mag) dx dy dz
let a = -jm*mag
ivx' = ivx+a*dx
ivy' = ivy+a*dy
ivz' = ivz+a*dz
updateVel' ivx' ivy' ivz' $! (j+1)
updateVel' ivx ivy ivz $! (i+1)
addScaled (shiftl i 3) 0.01 (3 .|. (shiftl i 3))
updateVel (i+1)
where
f = (.|. shift i 3)
shiftl = shiftL -- (I# i) (I# j) = I# (word2Int# (uncheckedShiftL# (int2Word# i) j))Old entry[edit]
On a powerbook G4 (GHC 6.4.1, gcc 4.0.1) this is 1.7x time faster than dons+chris. 12.5 seconds versus 21.2 seconds for N=5,000,000 --ChrisKuklewicz Unboxing the strict fields gives a 3x speedup.
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Written by Joel Koerwer.
-- Uses 7 STUArrays for the state.
-- Edited for length by ChrisKuklewicz
--
-- -O3 -optc-O3 -fexcess-precision -funbox-strict-fields -optc-ffast-math
--
-- -funbox-strict-fields is critical
--
-- -optc-ffast-math doesn't speed things up for me.
-- Well, neither does -optc-O3, but that may just be here.
--
import Control.Monad (liftM2,liftM3,liftM4)
import Control.Monad.ST (ST, runST)
import Data.Array.ST (STUArray, newListArray)
import Data.Array.Base (unsafeRead, unsafeWrite)
import System (getArgs)
import Text.Printf (printf)
(!) = unsafeRead :: STUArray s Int Double -> Int -> ST s Double
writeArray = unsafeWrite :: STUArray s Int Double -> Int -> Double -> ST s ()
size :: Int = 5
dt :: Double = 0.01
data PhaseSpace s = PS {ms,rxs,rys,rzs,vxs,vys,vzs :: !(STUArray s Int Double)}
main :: IO ()
main = do n <- getArgs >>= readIO . head
printf "%.9f\n" $ runST (do state <- initialState
offsetMomentum state
energy state)
printf "%.9f\n" $ runST (do state <- initialState
offsetMomentum state
energy state
advance n state
energy state)
advance :: Int -> PhaseSpace s -> ST s ()
advance 0 _ = return ()
advance n sys = do kick sys
drift sys
advance (n-1) sys
readAll (PS m x y z vx vy vz) i = do (x,y,z) <- liftM3 (,,) (x!i) (y!i) (z!i)
(vx,vy,vz) <- liftM3 (,,) (vx!i) (vy!i) (vz!i)
return (x,y,z,vx,vy,vz)
{-# INLINE readAll #-}
kick ps@(PS m rx ry rz vx vy vz) = outer 0 where
outer i | i >= size = return ()
| otherwise = inner (i+1) >> outer (i+1) where
inner j | j >= size = return ()
| otherwise = do
(mi,mj) <- liftM2 (,) (m!i) (m!j)
(rxi,ryi,rzi,vxi,vyi,vzi) <- readAll ps i
(rxj,ryj,rzj,vxj,vyj,vzj) <- readAll ps j
let (dx,dy,dz) = (rxi-rxj, ryi-ryj, rzi-rzj)
dist2 = dx*dx + dy*dy + dz*dz
mag = dt / (dist2 * sqrt dist2)
writeArray vx i (vxi - dx*mj*mag)
writeArray vy i (vyi - dy*mj*mag)
writeArray vz i (vzi - dz*mj*mag)
writeArray vx j (vxj + dx*mi*mag)
writeArray vy j (vyj + dy*mi*mag)
writeArray vz j (vzj + dz*mi*mag)
inner (j+1)
drift ps@(PS _ rxs rys rzs _ _ _) = loop 0 where
loop i | i >= size = return ()
| otherwise = do (x,y,z,vx,vy,vz) <- readAll ps i
writeArray rxs i (x + dt*vx)
writeArray rys i (y + dt*vy)
writeArray rzs i (z + dt*vz)
loop (i+1)
energy sys = liftM2 (+) (kineticEnergy sys) (potentialEnergy sys)
kineticEnergy (PS ms _ _ _ vxs vys vzs) = loop 0 0 where
loop i accum | i >= size = return (0.5 * accum)
| otherwise = do
(m,vx,vy,vz) <- liftM4 (,,,) (ms!i) (vxs!i) (vys!i) (vzs!i)
let v2 = vx*vx + vy*vy + vz*vz
loop (i+1) $! (accum + m*v2)
potentialEnergy (PS ms rxs rys rzs _ _ _) = outer 0 0 where
outer i a | i >= size = return a
| otherwise = inner i (i+1) a >>= outer (i+1)
inner i j a | j >= size = return a
| otherwise = do
(mi,xi,yi,zi) <- liftM4 (,,,) (ms!i) (rxs!i) (rys!i) (rzs!i)
(mj,xj,yj,zj) <- liftM4 (,,,) (ms!j) (rxs!j) (rys!j) (rzs!j)
let (dx,dy,dz) = (xi-xj, yi-yj, zi-zj)
dist = sqrt (dx*dx + dy*dy + dz*dz)
inner i (j+1) $! (a - mi*mj/dist)
offsetMomentum (PS ms rxs rys rzs vxs vys vzs) = do
(px,py,pz) <- calcMomentum 0 (0,0,0)
(mSun,vSunx,vSuny,vSunz) <- liftM4 (,,,) (ms!0) (vxs!0) (vys!0) (vzs!0)
writeArray vxs 0 (vSunx - px/mSun)
writeArray vys 0 (vSuny - py/mSun)
writeArray vzs 0 (vSunz - pz/mSun)
where calcMomentum i (px,py,pz) | i >= size = return (px,py,pz)
| otherwise = do
(m,vx,vy,vz) <- liftM4 (,,,) (ms!i) (vxs!i) (vys!i) (vzs!i)
calcMomentum (i+1) $! (px+vx*m,py+vy*m,pz+vz*m)
initialState = do m <- mkSTUArray masses
x <- mkSTUArray positionXs
y <- mkSTUArray positionYs
z <- mkSTUArray positionZs
vx <- mkSTUArray velocityXs
vy <- mkSTUArray velocityYs
vz <- mkSTUArray velocityZs
return (PS m x y z vx vy vz)
mkSTUArray = newListArray (0,size-1) :: [Double] -> ST s (STUArray s Int Double)
masses = map (4*pi*pi*) [1, 9.54791938424326609e-04, 2.85885980666130812e-04, 4.36624404335156298e-05, 5.15138902046611451e-05]
positionXs = [0, 4.84143144246472090e+00, 8.34336671824457987e+00, 1.28943695621391310e+01, 1.53796971148509165e+01]
positionYs = [0, (-1.16032004402742839e+00), 4.12479856412430479e+00, (-1.51111514016986312e+01), (-2.59193146099879641e+01)]
positionZs = [0, (-1.03622044471123109e-01), (-4.03523417114321381e-01), (-2.23307578892655734e-01), 1.79258772950371181e-01]
velocityXs = map (365.24*) [0, 1.66007664274403694e-03, (-2.76742510726862411e-03), 2.96460137564761618e-03, 2.68067772490389322e-03]
velocityYs = map (365.24*) [0, 7.69901118419740425e-03, 4.99852801234917238e-03, 2.37847173959480950e-03, 1.62824170038242295e-03]
velocityZs = map (365.24*) [0, (-6.90460016972063023e-05), 2.30417297573763929e-05, (-2.96589568540237556e-05), (-9.51592254519715870e-05)]An STUArray Version (Joel Koerwer)[edit]
This one is slightly faster than chris+dons on my machine. The "proposed entry" has ben submitted, so I pushed it and its associated benchmarks down.
I get a speed up from the STUArray versus the dons+chris version on a Powerbook G4. Don+chris is 4.38 s user time, Joel's is 3.74 s user time (17% faster). This makes sense to me, since it does not need to shiftL and .|. the indices. I was cleaning it up without making it slower and I accidentally made it faster (I think by hoisting dt and size). -- ChrisKuklewicz
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Written by Joel Koerwer.
-- Uses 7 STUArrays for the state.
--
-- Performance is very similar to the IOUArray version of
-- Chris Kuklewicz and Don Stewart. This one is slightly faster
-- on my machine at n=5,000,000 (15 s vs 17 s).
--
-- -O3 -optc-O3 -fexcess-precision -funbox-strict-fields
--
-- -optc-ffast-math doesn't speed things up for me.
-- Well, neither does -optc-O3, but that may just be here.
--
import Control.Monad.ST (ST, runST)
import Data.Array.ST (STUArray, newListArray)
import Data.Array.Base (unsafeRead, unsafeWrite)
import System (getArgs)
import Text.Printf (printf)
readArray :: STUArray s Int Double -> Int -> ST s Double
readArray = unsafeRead
writeArray :: STUArray s Int Double -> Int -> Double -> ST s ()
writeArray = unsafeWrite
data PhaseSpace s = PS {size :: !Int,
ms,rxs,rys,rzs,vxs,vys,vzs :: !(STUArray s Int Double)}
advance :: Int -> Double -> PhaseSpace s -> ST s ()
advance 0 _ _ = return ()
advance n dt sys = do
kick dt sys
drift dt sys
advance (n-1) dt sys
kick :: Double -> PhaseSpace s -> ST s ()
kick dt (PS size m rx ry rz vx vy vz) = outer 0
where
outer i | i >= size = return ()
| otherwise = inner (i+1) >> outer (i+1)
where
inner j | j >= size = return ()
| otherwise = do
mi <- readArray m i
mj <- readArray m j
rxi <- readArray rx i
rxj <- readArray rx j
ryi <- readArray ry i
ryj <- readArray ry j
rzi <- readArray rz i
rzj <- readArray rz j
vxi <- readArray vx i
vxj <- readArray vx j
vyi <- readArray vy i
vyj <- readArray vy j
vzi <- readArray vz i
vzj <- readArray vz j
let dx = rxi-rxj
dy = ryi-ryj
dz = rzi-rzj
dist2 = dx*dx + dy*dy + dz*dz
dist = sqrt dist2
mag = dt / (dist*dist2)
writeArray vx i (vxi - dx*mj*mag)
writeArray vy i (vyi - dy*mj*mag)
writeArray vz i (vzi - dz*mj*mag)
writeArray vx j (vxj + dx*mi*mag)
writeArray vy j (vyj + dy*mi*mag)
writeArray vz j (vzj + dz*mi*mag)
inner (j+1)
drift :: Double -> PhaseSpace s -> ST s ()
drift dt (PS size _ rxs rys rzs vxs vys vzs) = loop 0
where
loop i | i >= size = return ()
| otherwise = do
x <- readArray rxs i
y <- readArray rys i
z <- readArray rzs i
vx <- readArray vxs i
vy <- readArray vys i
vz <- readArray vzs i
writeArray rxs i (x + dt*vx)
writeArray rys i (y + dt*vy)
writeArray rzs i (z + dt*vz)
loop (i+1)
energy :: PhaseSpace s -> ST s Double
energy sys = do t <- kineticEnergy sys
u <- potentialEnergy sys
return (t+u)
kineticEnergy :: PhaseSpace s -> ST s Double
kineticEnergy (PS size ms _ _ _ vxs vys vzs) = loop 0 0
where
loop i accum | i >= size = return (0.5 * accum)
| otherwise = do
m <- readArray ms i
vx <- readArray vxs i
vy <- readArray vys i
vz <- readArray vzs i
let v2 = vx*vx + vy*vy + vz*vz
loop (i+1) (accum + m*v2)
potentialEnergy :: PhaseSpace s -> ST s Double
potentialEnergy (PS size ms rxs rys rzs _ _ _) = outer 0 0
where
outer i a | i >= size = return a
| otherwise = inner i (i+1) a >>= outer (i+1)
inner i j a | j >= size = return a
| otherwise = do
mi <- readArray ms i
mj <- readArray ms j
xi <- readArray rxs i
xj <- readArray rxs j
yi <- readArray rys i
yj <- readArray rys j
zi <- readArray rzs i
zj <- readArray rzs j
let dx = xi-xj
dy = yi-yj
dz = zi-zj
dist = sqrt (dx*dx + dy*dy + dz*dz)
inner i (j+1) (a - mi*mj/dist)
offsetMomentum :: PhaseSpace s -> ST s ()
offsetMomentum (PS size ms rxs rys rzs vxs vys vzs) = do
(px,py,pz) <- calcMomentum 0 (0,0,0)
mSun <- readArray ms 0
vSunx <- readArray vxs 0
vSuny <- readArray vys 0
vSunz <- readArray vzs 0
writeArray vxs 0 (vSunx - px/mSun)
writeArray vys 0 (vSuny - py/mSun)
writeArray vzs 0 (vSunz - pz/mSun)
where
calcMomentum i (px,py,pz) | i >= size = return (px,py,pz)
| otherwise = do
m <- readArray ms i
vx <- readArray vxs i
vy <- readArray vys i
vz <- readArray vzs i
let px' = px + vx*m
py' = py + vy*m
pz' = pz + vz*m
calcMomentum (i+1) (px',py',pz')
main = do
n <- getArgs >>= readIO . head
printf "%.9f\n" $ runST (do state <- initialState
offsetMomentum state
energy state)
printf "%.9f\n" $ runST (do state <- initialState
offsetMomentum state
advance n 0.01 state
energy state)
initialState :: ST s (PhaseSpace s)
initialState = do
m <- mkSTUArray masses
x <- mkSTUArray positionXs
y <- mkSTUArray positionYs
z <- mkSTUArray positionZs
vx <- mkSTUArray velocityXs
vy <- mkSTUArray velocityYs
vz <- mkSTUArray velocityZs
return (PS 5 m x y z vx vy vz)
mkSTUArray :: [Double] -> ST s (STUArray s Int Double)
mkSTUArray = newListArray (0,4)
masses = map (4*pi*pi*) [1, 9.54791938424326609e-04, 2.85885980666130812e-04, 4.36624404335156298e-05, 5.15138902046611451e-05]
positionXs = [0, 4.84143144246472090e+00, 8.34336671824457987e+00, 1.28943695621391310e+01, 1.53796971148509165e+01]
positionYs = [0, (-1.16032004402742839e+00), 4.12479856412430479e+00, (-1.51111514016986312e+01), (-2.59193146099879641e+01)]
positionZs = [0, (-1.03622044471123109e-01), (-4.03523417114321381e-01), (-2.23307578892655734e-01), 1.79258772950371181e-01]
velocityXs = map (365.24*) [0, 1.66007664274403694e-03, (-2.76742510726862411e-03), 2.96460137564761618e-03, 2.68067772490389322e-03]
velocityYs = map (365.24*) [0, 7.69901118419740425e-03, 4.99852801234917238e-03, 2.37847173959480950e-03, 1.62824170038242295e-03]
velocityZs = map (365.24*) [0, (-6.90460016972063023e-05), 2.30417297573763929e-05, (-2.96589568540237556e-05), (-9.51592254519715870e-05)]
Proposed Entry (dons+chris)[edit]
A carefully tuned version of Chris' breakthrough entry. Runs faster than unoptimised gcc C. Be sure not to use -optc-O3 on linux, or badness may ensue. The OPTIONS pragma passes -O to gcc last, so it will override any other -O args to gcc passed on the cmd line.
{-# OPTIONS -optc-O #-}
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Christoph Bauer
-- Written in Haskell by Chris Kuklewicz, further tweaks by Don Stewart
--
-- -O2 -optc-O -fglasgow-exts -fexcess-precision -optc-ffast-math
--
-- -optc-O3 cannot be used, as at least one version of gcc miscompiles this program
--
import System
import System.IO.Unsafe
import Monad
import Data.Bits
import Data.List
import Data.Array.IO
import Data.Array.Base(unsafeRead,unsafeWrite)
import Text.Printf
default (Int)
main = do n <- getArgs >>= readIO . head
offsetMomentum
energy >>= printf "%.9f\n"
advance n
energy >>= printf "%.9f\n"
-- Offsets for each field
x = 0; y = 1; z = 2; vx= 3; vy= 4; vz= 5; m = 6
type Bodies = IOUArray Int Double
b :: Bodies = unsafePerformIO $ newListArray (0,pred (length bodiesData)) (bodiesData)
{-# NOINLINE b #-}
set = unsafeWrite b
{-# INLINE set #-}
resetB = zipWithM_ set [0..] bodiesData
-- sun jupiter saturn uranus neptune
-- sun starts at center at rest
bodiesData = concat [ mkB 1 0 0 0 0 0 0
,mkB 9.54791938424326609e-04
4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01)
( 1.66007664274403694e-03) ( 7.69901118419740425e-03) (-6.90460016972063023e-05)
,mkB 2.85885980666130812e-04
8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01)
(-2.76742510726862411e-03) ( 4.99852801234917238e-03) ( 2.30417297573763929e-05)
,mkB 4.36624404335156298e-05
1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01)
( 2.96460137564761618e-03) ( 2.37847173959480950e-03) (-2.96589568540237556e-05)
,mkB 5.15138902046611451e-05
1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01
( 2.68067772490389322e-03) ( 1.62824170038242295e-03) (-9.51592254519715870e-05)]
mkB m x y z vx vy vz =
[x, y, z, vx*days_per_year,vy*days_per_year, vz*days_per_year, m*solar_mass, 0]
solar_mass = 4 * pi * pi
days_per_year = 365.24
nbodies = 4 -- that is 0 to 4
mass i = unsafeRead b (massOffset .|. (shiftL i 3)) where massOffset = 6
-- Give the sun a small velocity so the total momentum of all bodies totals to zero
offsetMomentum :: IO ()
offsetMomentum = do sm <- mass 0
let act i = mass i >>= \m -> addScaled 3 (-m/sm) (3 .|. (shiftL i 3))
mapM_ act [1..nbodies]
-- Total all kineticE and potentialE
energy = loop 0 0
where loop i e | i > nbodies = return e
| otherwise = do ke <- kineticE i
(loop' (i+1) i $! (e+ke)) >>= loop (i+1)
loop' j i e | j > nbodies = return e
| otherwise = do pe <- potentialE i j
loop' (j+1) i $! (e + pe)
kineticE i = let i' = (.|. (shiftL i 3))
in do m <- mass i
vx <- unsafeRead b (i' vx)
vy <- unsafeRead b (i' vy)
vz <- unsafeRead b (i' vz)
return $! 0.5 * m * (vx*vx + vy*vy + vz*vz)
potentialE i j = do
m1 <- mass i
m2 <- mass j
let (i', j') = ((.|. (shiftL i 3)), (.|. (shiftL j 3)))
dx <- liftM2 (-) (unsafeRead b (i' x)) (unsafeRead b (j' x))
dy <- liftM2 (-) (unsafeRead b (i' y)) (unsafeRead b (j' y))
dz <- liftM2 (-) (unsafeRead b (i' z)) (unsafeRead b (j' z))
return $! ((-1)*m1*m2/sqrt (dx*dx + dy*dy + dz*dz))
addScaled i a j | i `seq` a `seq` j `seq` False = undefined -- stricitfy
addScaled i a j = do set i1 =<< liftM2 scale (unsafeRead b i1) (unsafeRead b j1)
set i2 =<< liftM2 scale (unsafeRead b i2) (unsafeRead b j2)
set i3 =<< liftM2 scale (unsafeRead b i3) (unsafeRead b j3)
where scale old new = old + a * new
i1 = i; i2 = succ i1; i3 = succ i2;
j1 = j; j2 = succ j1; j3 = succ j2;
addScaled3 i a jx jy jz | i `seq` a `seq` jx `seq` jy `seq` jz `seq` False = undefined
addScaled3 i a jx jy jz = do set i1 =<< liftM (scale jx) (unsafeRead b i1)
set i2 =<< liftM (scale jy) (unsafeRead b i2)
set i3 =<< liftM (scale jz) (unsafeRead b i3)
where scale new old = a * new + old
i1 = i; i2 = succ i1; i3 = succ i2;
-- This is the main code. Essentially all the time is spent here
advance n = when (n > 0) $ updateVel 0 >> advance (pred n)
where updateVel i = when (i <= nbodies) $ do
let i' = (.|. shift i 3)
im <- unsafeRead b (i' m)
ix <- unsafeRead b (i' x)
iy <- unsafeRead b (i' y)
iz <- unsafeRead b (i' z)
ivx <- unsafeRead b (i' vx)
ivy <- unsafeRead b (i' vy)
ivz <- unsafeRead b (i' vz)
let updateVel' ivx ivy ivz j = ivx `seq` ivy `seq` ivz `seq`
if j > nbodies then do
unsafeWrite b (i' vx) ivx
unsafeWrite b (i' vy) ivy
unsafeWrite b (i' vz) ivz
else do
let j' = (.|. shiftL j 3)
jm <- unsafeRead b (j' m)
dx <- liftM (ix-) (unsafeRead b (j' x))
dy <- liftM (iy-) (unsafeRead b (j' y))
dz <- liftM (iz-) (unsafeRead b (j' z))
let distance = sqrt (dx*dx+dy*dy+dz*dz)
mag = 0.01 / (distance * distance * distance)
addScaled3 (3 .|. (shiftL j 3)) ( im*mag) dx dy dz
let a = -jm*mag
ivx' = ivx+a*dx
ivy' = ivy+a*dy
ivz' = ivz+a*dz
updateVel' ivx' ivy' ivz' $! (j+1)
updateVel' ivx ivy ivz $! (i+1)
addScaled (shiftL i 3) 0.01 (3 .|. (shiftL i 3))
updateVel (i+1)Improved entry (chris)[edit]
I made it go faster! By a factor of 2.5, which is not closing much of the gap. But any speed improvement is a breakthrough at this point. Hopefully someone else can see why it is faster and speed it up further. I am just tweaking things at random now.
All the n-body data (7 doubles: mass x y z vx vy vz) is put into a single IOUArray Int Double. Each body is offset by 8 indices, so there is a padding of 1 double to get an alignment of 8. This let me calculate the offset of each double with {{{shiftL _ 3}}} and . The array itself is a global variable.
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Christoph Bauer
-- Rewritten in Haskell from C by Don Stewart
-- Rewritten again by Chris Kuklewicz
--
-- -O2 -optc-O3 -fglasgow-exts -fexcess-precision -optc-ffast-math
--
-- This code actually runs faster then the previous entry!
--
import Debug.Trace
import System
import System.IO.Unsafe
import Monad
import Data.Bits
import Data.List
import Data.Array.MArray
import Data.Array.IO
import Data.Array.Base(unsafeRead,unsafeWrite)
import Text.Printf
import Data.IORef
default(Int)
main = do
args <- getArgs
let n = if null args then 1000000 else read ( head args )
offsetMomentum
energy >>= printf "%.9f\n"
advance n
energy >>= printf "%.9f\n"
-- Offsets for each field
x = 0
y = 1
z = 2
vx= 3
vy= 4
vz= 5
m = 6
type Bodies = IOUArray Int Double
{-# NOINLINE b #-}
b :: Bodies = unsafePerformIO $ newListArray (0,pred (length bodiesData)) (bodiesData)
get = unsafeRead b
set = unsafeWrite b
resetB = zipWithM_ set [0..] bodiesData
-- sun jupiter saturn uranus neptune
-- sun starts at center at rest
bodiesData = concat [ mkB 1 0 0 0 0 0 0
,mkB 9.54791938424326609e-04
4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01)
( 1.66007664274403694e-03) ( 7.69901118419740425e-03) (-6.90460016972063023e-05)
,mkB 2.85885980666130812e-04
8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01)
(-2.76742510726862411e-03) ( 4.99852801234917238e-03) ( 2.30417297573763929e-05)
,mkB 4.36624404335156298e-05
1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01)
( 2.96460137564761618e-03) ( 2.37847173959480950e-03) (-2.96589568540237556e-05)
,mkB 5.15138902046611451e-05
1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01
( 2.68067772490389322e-03) ( 1.62824170038242295e-03) (-9.51592254519715870e-05)]
mkB m x y z vx vy vz = [x, y, z, vx*days_per_year,
vy*days_per_year, vz*days_per_year, m*solar_mass, 0]
solar_mass = 4 * pi * pi
days_per_year = 365.24
nbodies = 4 -- that is 0 to 4
sh i = shiftL i 3 -- multiply by 8
pos i = sh i
vel i = velOffset .|. sh i where velOffset = 3
mass i = get (massOffset .|. sh i) where massOffset = 6
-- Give the sun a small velocity so the total momentum of all bodies totals to zero
offsetMomentum :: IO ()
offsetMomentum = do sm <- mass 0
let sv = vel 0
act i = mass i >>= \m -> addScaled sv (-m/sm) (vel i)
mapM_ act [1..nbodies]
-- Total all kineticE and potentialE
energy :: IO Double
energy = loop 0 0
where loop i e | i > nbodies = return e
| otherwise = do ke <- kineticE i
(loop' (i+1) i $! (e+ke)) >>= loop (i+1)
loop' j i e | j > nbodies = return e
| otherwise = do pe <- potentialE i j
loop' (j+1) i $! (e + pe)
kineticE i = let i' = (.|. sh i)
in do m <- mass i
vx <- get (i' vx)
vy <- get (i' vy)
vz <- get (i' vz)
return $! 0.5 * m * (vx*vx + vy*vy + vz*vz)
potentialE i j = do
m1 <- mass i
m2 <- mass j
let i' = (.|. (sh i))
j' = (.|. (sh j))
dx <- liftM2 (-) (get (i' x)) (get (j' x))
dy <- liftM2 (-) (get (i' y)) (get (j' y))
dz <- liftM2 (-) (get (i' z)) (get (j' z))
return $! ((-1)*m1*m2/sqrt (dx*dx + dy*dy + dz*dz))
dt = 0.01
addScaled i a j = let scale old new = old + a * new
i1=i; i2=succ i1; i3=succ i2;
j1=j; j2=succ j1; j3=succ j2;
in do set i1 =<< liftM2 scale (get i1) (get j1)
set i2 =<< liftM2 scale (get i2) (get j2)
set i3 =<< liftM2 scale (get i3) (get j3)
addScaled3 i a jx jy jz = do
let scale new old = a * new + old
i1=i; i2=succ i1; i3=succ i2;
set i1 =<< liftM (scale jx) (get i1)
set i2 =<< liftM (scale jy) (get i2)
set i3 =<< liftM (scale jz) (get i3)
-- This is the main code. Essentially all the time is spent here
advance n = when (n>0) $ do
let {-# NOINLINE updateVel #-}
updateVel i = when (i <= nbodies) $ do
let i' = (.|. sh i)
im <- get (i' m)
ix <- get (i' x)
iy <- get (i' y)
iz <- get (i' z)
ivx <- get (i' vx)
ivy <- get (i' vy)
ivz <- get (i' vz)
let {-# INLINE updateVel' #-}
updateVel' ivx ivy ivz j = ivx `seq` ivy `seq` ivz `seq`
if j > nbodies then do
set (i' vx) ivx
set (i' vy) ivy
set (i' vz) ivz
else do
let j' = (.|. sh j)
jm <- get (j' m)
dx <- liftM (ix-) (get (j' x))
dy <- liftM (iy-) (get (j' y))
dz <- liftM (iz-) (get (j' z))
let distance = sqrt (dx*dx+dy*dy+dz*dz)
mag = dt / (distance * distance * distance)
addScaled3 (vel j) ( im*mag) dx dy dz
let a = -jm*mag
ivx' = ivx+a*dx
ivy' = ivy+a*dy
ivz' = ivz+a*dz
updateVel' ivx' ivy' ivz' $! (j+1)
updateVel' ivx ivy ivz $! (i+1)
addScaled (pos i) dt (vel i)
updateVel (i+1)
updateVel 0
advance (pred n)Old attempt by ChrisKuklewicz[edit]
I heavily transformed Don's code. This now runs almost exactly as fast as Einar's code on my machine. So I am niether happy nor sad.
Note that this creates the {{{data MutVec = V ...}}} and {{{data Body = B}}} all at the beginning, puts them into an array, and never constructs any new ones. From them on it just looks up {{{IORef Double}}}'s and works on those.
I cannot find any Haskell idioms for making this run 10x faster, but other languages manage to do it, such as OCaml.
Would peeking and poking unboxed Doubles be the way to go?
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Christoph Bauer
-- Rewritten in Haskell from C by Don Stewart
-- Rewritten again by Chris Kuklewicz
--
-- -O2 -optc-O3 -funbox-strict-fields -fglasgow-exts -fexcess-precision -fasm
--
-- Runs at the same speed as the Haskell#3 open mutable records code
-- by Einar.
--
-- Advance is where ALL the work is done and where any optimization must go.
--
import System
import Control.Monad
import Data.List
import Data.Array.Array
import Text.Printf
import Data.IORef
default()
type Bodies = Array Int Body
data MutVec = V { x, y, z :: !(IORef Double) }
data Body = B { mass :: !Double, pos,vel :: !MutVec }
newV x y z = x `seq` y `seq` z `seq` do liftM3 V (newIORef x) (newIORef y) (newIORef z)
mkB m x y z vx vy vz = liftM2 (B (m*solar_mass)) (newV x y z)
(newV (vx*days_per_year) (vy*days_per_year) (vz*days_per_year))
{-# INLINE mIORef #-}
mIORef r f = readIORef r >>= ( ($!) (writeIORef r) ) . f
{-# INLINE minus #-}
minus x = (\y -> y-x)
{-# INLINE do2 #-}
do2 fm m1 m2 = do x1 <- m1; x2 <- m2; fm x1 x2
{-# INLINE addScaled #-}
addScaled v1@(V x1 y1 z1) a v2@(V x2 y2 z2) = do
(mIORef x1).(+).(*a) =<< readIORef x2
(mIORef y1).(+).(*a) =<< readIORef y2
(mIORef z1).(+).(*a) =<< readIORef z2
{-# INLINE setDiff #-}
setDiff d@(V dx dy dz) v1@(V x1 y1 z1) v2@(V x2 y2 z2) = do
do2 (\a b->writeIORef dx $! (a-b)) (readIORef x1) (readIORef x2)
do2 (\a b->writeIORef dy $! (a-b)) (readIORef y1) (readIORef y2)
do2 (\a b->writeIORef dz $! (a-b)) (readIORef z1) (readIORef z2)
return d
{-# INLINE kineticE #-}
kineticE mass (V x y z) = do vx <- readIORef x ; vy <- readIORef y ; vz <- readIORef z
return $! 0.5 * mass * (vx*vx + vy*vy + vz*vz)
{-# INLINE magV #-}
magV (V x y z) = do
liftM3 (\a b c->sqrt (a*a+b*b+c*c)) (readIORef x) (readIORef y) (readIORef z) >>= (return $!)
{-# INLINE potentialE #-}
potentialE mass1 (V x1 y1 z1) mass2 (V x2 y2 z2) = do
dx <- liftM2 (-) (readIORef x1) (readIORef x2)
dy <- liftM2 (-) (readIORef y1) (readIORef y2)
dz <- liftM2 (-) (readIORef z1) (readIORef z2)
return $! ((-1)*mass1*mass2/sqrt (dx*dx + dy*dy + dz*dz))
mkBodies :: IO Bodies
mkBodies = liftM (listArray (0,nbodies-1)) $ sequence bodiesData
-- sun jupiter saturn uranus neptune
bodiesData = [ mkB 1 0 0 0 0 0 0
,mkB 9.54791938424326609e-04
4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01)
( 1.66007664274403694e-03) ( 7.69901118419740425e-03) (-6.90460016972063023e-05)
,mkB 2.85885980666130812e-04
8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01)
(-2.76742510726862411e-03) ( 4.99852801234917238e-03) ( 2.30417297573763929e-05)
,mkB 4.36624404335156298e-05
1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01)
( 2.96460137564761618e-03) ( 2.37847173959480950e-03) (-2.96589568540237556e-05)
,mkB 5.15138902046611451e-05
1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01
( 2.68067772490389322e-03) ( 1.62824170038242295e-03) (-9.51592254519715870e-05) ]
solar_mass = 4 * pi * pi
days_per_year = 365.24
nbodies = length bodiesData
offsetMomentum :: Bodies -> IO ()
offsetMomentum arr = sequence_ [ addScaled sv (-m/sm) v | (B m _ v) <- tail (elems arr) ]
where (B sm sp sv) = (arr ! 0)
energy :: Int -> Bodies -> IO Double
energy nbodies arr = loop 0 0
where loop i e | i >= nbodies = return e
| otherwise = do let (B mb bp bv) = arr ! i
ke <- kineticE mb bv
(loop' (i+1) bp mb $! (e+ke)) >>= loop (i+1)
loop' j bp mb e | j >= nbodies = return e
| otherwise = do let (B mb2 bp2 _) = arr ! j
pe <- potentialE mb bp mb2 bp2
loop' (j+1) bp mb (e + pe)
main = do
(n::Int) <- getArgs >>= readIO . head
bodies <- mkBodies
dxyz <- newV 0 0 0
let dt = 0.01
advance = do
let updateVel i = when (i < nbodies) $ do
updateVel' (bodies ! i) (i+1)
updateVel (i+1)
updateVel' b1@(B mb1 bp1 bv1) j = if j >= nbodies then return () else do
let (B mb2 bp2 bv2) = bodies ! j
setDiff dxyz bp1 bp2
distance <- magV dxyz
let mag = dt / (distance * distance * distance)
addScaled bv2 (mb1*mag) dxyz
addScaled bv1 (-mb2*mag) dxyz
updateVel' b1 (j+1)
updatePos i = when (i < nbodies) $ do
let (B _ bp bv) = bodies ! i
addScaled bp dt bv
updatePos (i+1)
updateVel 0
updatePos 0
offsetMomentum bodies
energy nbodies bodies >>= printf "%.9f\n"
replicateM_ n advance
energy nbodies bodies >>= printf "%.9f\n"Joel Koerwer's nth attempt[edit]
I suppose the comments say it all.
-- Joel Koerwer's attempt at the Computer Shootout nbody problem.
-- Not as fast as Einar Kartunnen's Open Mutable Records implementation,
-- but I like it!
-- I get about double the runtime of Einar's code.
import System (getArgs)
import Text.Printf (printf)
data Vector3 = V3 !Double !Double !Double deriving (Show, Eq)
instance Num Vector3 where
(V3 x y z) + (V3 u v w) = V3 (x+u) (y+v) (z+w)
(V3 x y z) - (V3 u v w) = V3 (x-u) (y-v) (z-w)
(V3 x y z) * (V3 u v w) = V3 (x*u) (y*v) (z*w)
fromInteger n = V3 (fromInteger n) (fromInteger n) (fromInteger n)
abs (V3 x y z) = V3 (abs x) (abs y) (abs z)
signum (V3 x y z) = V3 (signum x) (signum y) (signum z)
-- Mnemonically read "scalar times vector".
(.*|) :: Double -> Vector3 -> Vector3
a .*| (V3 x y z) = V3 (a*x) (a*y) (a*z)
-- Similarly for "vector divided by scalar".
(|/.) :: Vector3 -> Double -> Vector3
(V3 x y z) |/. a = V3 (x/a) (y/a) (z/a)
dot :: Vector3 -> Vector3 -> Double
(V3 x y z) `dot` (V3 u v w) = x*u + y*v + z*w
norm2 v = v `dot` v
norm = sqrt . norm2
type PhaseSpace = ([Vector3],[Vector3])
advance :: PhaseSpace -> PhaseSpace
advance sys@(rs,vs) = let
vs' = zipWith (+) vs $ getDeltaVs sys
rs' = zipWith ((+) . (dt .*| )) vs' rs
in
(rs', vs')
getDeltaVs :: PhaseSpace -> [Vector3]
getDeltaVs sys@(rs,_) = let
timesMdT = zipWith (.*|) dtms
mags = getMags rs
in
map (sum . timesMdT) mags
-- getMags does the "real work". Given a list of position vectors [r0,r1,..,rN]
-- return the "magnitude matrix"
--
-- [[ 0 m01 m02 .. m0N],
-- [-m01 0 m12 .. m1N],
-- [-m02 -m12 0 .. m2N],
-- [ : : . : ],
-- [ : : . : ],
-- [-m0N -m1N -m2N .. 0 ]]
--
-- where mij = -mji = (rj - ri) / |rj - ri|^3.
--
-- This method is faster than calulating all differences
-- seperately, but not by a whole lot.
getMags :: [Vector3] -> [[Vector3]]
getMags [] = []
getMags (r:rs) = let
mkMag r' = let d = r' - r in d |/. (norm d * norm2 d)
newMags = map mkMag rs
minusMags = map negate newMags
in
(0 : newMags) : zipWith (:) minusMags (getMags rs)
energy :: PhaseSpace -> Double
energy sys = kineticEnergy sys + potentialEnergy sys
-- T = 0.5 * sum_i mi * vi^2
kineticEnergy :: PhaseSpace -> Double
kineticEnergy (_,vs) = 0.5 * (sum $ zipWith (*) ms (map norm2 vs))
-- U = sum_{i/=j} -0.5*mi*mj/|ri-rj|
potentialEnergy :: PhaseSpace -> Double
potentialEnergy (rs,_) = let a = -0.5 :: Double in
(a *) . sum $ zipWith ((*) . sum . zipWith (*) ms) (invDists rs) ms
-- Calculate the inverse distances between positions [r0,..rN].
-- Similar to getMags, but here, mij = |mij| = 1 / |ri-rj|.
invDists :: [Vector3] -> [[Double]]
invDists [] = []
invDists (r:rs) = let
newDs = map ((1/) . norm . (r -)) rs
in
(0 : newDs) : zipWith (:) newDs (invDists rs)
-- offset gives the Sun an initial velocity such that the entire system
-- has zero overall momentum.
offset :: PhaseSpace -> PhaseSpace
offset (rs, vs@(vSun:vPlanets)) = let
pTotal = sum $ zipWith (.*|) ms vs
mSun = head ms
dv = pTotal |/. mSun
in
(rs, vSun-dv : vPlanets)
---------- A strict version of iterate for our loop -----------
seqList [] y = y
seqList (x:xs) y = x `seq` seqList xs y
seqTuple (x,y) z = seqList x $ seqList y z
iterate' f a = let b = f a in seqTuple b $ a : iterate' f b
---------------------------------------------------------------
main = let
sys = offset initialPhaseSpace
print9 = printf "%.9f\n"
in
do
[n'] <- getArgs
let n = read n' :: Int
print9 (energy sys)
print9 . energy $ iterate' advance sys !! n
-- I've stuck all the ugly constants and initial conditions at the end.
dt = 0.01
solarMass = 4*pi*pi
daysPerYear = 365.24
posns =[V3 0 0 0,
V3 4.8414314424647209 (-1.16032004402742839) (-1.03622044471123109e-01),
V3 8.34336671824457987 4.12479856412430479 (-4.03523417114321381e-01),
V3 12.8943695621391310 (-15.1111514016986312) (-2.23307578892655734e-1),
V3 15.3796971148509165 (-25.9193146099879641) (1.79258772950371181e-1)
]
vels' =[
V3 0 0 0,
V3 1.66007664274403694e-3 7.69901118419740425e-3 (-6.90460016972063023e-5),
V3 (-2.76742510726862411e-3) 4.99852801234917238e-3 2.30417297573763929e-5,
V3 2.96460137564761618e-3 2.37847173959480950e-3 (-2.96589568540237556e-5),
V3 2.68067772490389322e-3 1.62824170038242295e-3 (-9.51592254519715870e-5)
]
vels = map (daysPerYear .*|) vels'
initialPhaseSpace = (posns, vels)
dtms = map (dt *) ms -- The masses are only used by themselves in energy, so go
-- ahead and precalculate m*dt.
ms = map (solarMass *) [1, 9.54791938424326609e-04, 2.85885980666130812e-04,
4.36624404335156298e-05, 5.15138902046611451e-05]An imperative entry[edit]
Based on the C version. Too many slow updates on the array still.
{-# OPTIONS -O2 -optc-O3 -funbox-strict-fields -fglasgow-exts #-}
--
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
--
-- Contributed by Christoph Bauer
-- Rewritten in Haskell from C by Don Stewart
--
-- Advance is still too slow.
--
import System
import Control.Monad
import Data.Array.IO
import Data.Array.Base
import Text.Printf
data Planet = P { x, y, z, vx, vy, vz :: !Double } deriving Show
mass = [solar_mass
,9.54791938424326609e-04 * solar_mass
,2.85885980666130812e-04 * solar_mass
,4.36624404335156298e-05 * solar_mass
,5.15138902046611451e-05 * solar_mass]
bodies =[P 0 0 0 0 0 0 -- sun
-- jupiter
,P 4.84143144246472090e+00 -- jupiter
(-1.16032004402742839e+00)
(-1.03622044471123109e-01)
( 1.66007664274403694e-03 * days_per_year)
( 7.69901118419740425e-03 * days_per_year)
(-6.90460016972063023e-05 * days_per_year)
,P 8.34336671824457987e+00 -- saturn
4.12479856412430479e+00
(-4.03523417114321381e-01)
(-2.76742510726862411e-03 * days_per_year)
( 4.99852801234917238e-03 * days_per_year)
( 2.30417297573763929e-05 * days_per_year)
,P 1.28943695621391310e+01 -- uranus
(-1.51111514016986312e+01)
(-2.23307578892655734e-01)
( 2.96460137564761618e-03 * days_per_year)
( 2.37847173959480950e-03 * days_per_year)
(-2.96589568540237556e-05 * days_per_year)
,P 1.53796971148509165e+01 -- neptune
(-2.59193146099879641e+01)
1.79258772950371181e-01
( 2.68067772490389322e-03 * days_per_year)
( 1.62824170038242295e-03 * days_per_year)
(-9.51592254519715870e-05 * days_per_year) ]
solar_mass = 4 * pi * pi :: Double
days_per_year = 365.24
nbodies = 5
offsetMomentum :: Int -> IOArray Int Planet -> IOUArray Int Double -> IO ()
offsetMomentum nbodies arr mass = do
let loop i px py pz
| i >= nbodies = return (px,py,pz)
| otherwise = do
p <- unsafeRead arr i
mp <- unsafeRead mass i
let px' = px + vx p * mp
py' = py + vy p * mp
pz' = pz + vz p * mp
loop (i+1) px' py' pz'
(px,py,pz) <- loop 0 0.0 0.0 0.0
p <- unsafeRead arr 0
unsafeWrite arr 0 $! p { vx = - px / solar_mass
, vy = - py / solar_mass
, vz = - pz / solar_mass }
energy :: Int -> IOArray Int Planet -> IOUArray Int Double -> IO Double
energy nbodies arr mass = loop 0 (0.0 :: Double)
where loop i e
| i >= nbodies = return e
| otherwise = do
b <- unsafeRead arr i
mb<- unsafeRead mass i
let (x,y,z) = (vx b, vy b, vz b)
e' = e + 0.5 * mb * (x*x + y*y + z*z)
e'' <- loop' (i+1) e' b mb
loop (i+1) e''
loop' j e b mb
| j >= nbodies = return e
| otherwise = do
b2 <- unsafeRead arr j
mb2<- unsafeRead mass j
let dx = x b - x b2
dy = y b - y b2
dz = z b - z b2
distance = sqrt $! dx * dx + dy * dy + dz * dz
loop' (j+1) (e - ((mb * mb2) / distance)) b mb
advance :: Int -> IOArray Int Planet -> IOUArray Int Double -> Double -> IO ()
advance nbodies arr mass dt = do
for0 0
for3 0
where
for0 i = when (i < nbodies) $ do
b <- unsafeRead arr i
mb <- unsafeRead mass i
for1 (i+1) mb b >>= unsafeWrite arr i
for0 (i+1)
for1 j mb b = if j >= nbodies then return b else do
b2 <- unsafeRead arr j
mb2<- unsafeRead mass j
let dx = x b - x b2
dy = y b - y b2
dz = z b - z b2
distance = sqrt $! dx * dx + dy * dy + dz * dz
mag = dt / (distance * distance * distance)
(m1,m2) = (mb2 * mag, mb * mag)
unsafeWrite arr j $! b2 { vx = vx b2 + dx * m2
, vy = vy b2 + dy * m2
, vz = vz b2 + dz * m2 }
for1 (j+1) mb $! b { vx = vx b - dx * m1
, vy = vy b - dy * m1
, vz = vz b - dz * m1 }
for3 i = when (i < nbodies) $ do
b <- unsafeRead arr i
unsafeWrite arr i $! b { x = x b + dt * vx b
, y = y b + dt * vy b
, z = z b + dt * vz b }
for3 (i+1)
main = do
(n::Int) <- getArgs >>= readIO . head
arr <- newListArray (0,nbodies-1) bodies :: IO (IOArray Int Planet)
massarr <- newListArray (0,nbodies-1) mass :: IO (IOUArray Int Double)
offsetMomentum nbodies arr massarr
energy nbodies arr massarr >>= printf "%.9f\n"
replicateM_ n $ advance nbodies arr massarr 0.01
energy nbodies arr massarr >>= printf "%.9f\n"
Original entry[edit]
This is the "Haskell GHC #3" entry, the fastest of the three.
-- The Great Computer Language Shootout
-- http://shootout.alioth.debian.org/
-- NBody based on Open Mutable Records
-- Contributed by Einar Karttunen
import Control.Monad
import Control.Monad.Reader
import Data.IORef
import System
import Text.Printf
-- This is a monad for open mutable records programming
newtype OO t r = OO (ReaderT t IO r) deriving(Monad, MonadReader t, MonadIO)
-- run a computation with a record (object)
with :: s -> OO s a -> OO b a
with this (OO c) = liftIO (runReaderT c this)
-- run an OO computation producing an IO value.
ooToIO :: OO s a -> IO a
ooToIO (OO c) = runReaderT c undefined
-- the plain record types
data a :.: r = RC !a !r
infixr :.:
data END = END
-- Next we define a field access method.
class Select r f t | r f -> t where (!) :: r -> f -> Ref t
instance Select (Field f t :.: r) f t where (!) (RC (F x) _) _ = x
instance Select r f t => Select (a :.: r) f t where (!) (RC _ t) = (!) t
-- And finally the type of mutable fields.
type Ref a = IORef a
newtype Field name rtype = F (Ref rtype)
-- Next we define a way to construct record values.
infixr ##
(##) :: v -> OO s r -> OO s ((Field f v) :.: r)
(##) v r = do { h <- liftIO (newIORef v); t <- r; return (RC (F h) t) }
end = return END :: OO s END
-- Get the value of a field.
value :: Select s f t => f -> OO s t
value a = do x <- asks (\s -> s!a)
liftIO (readIORef x)
-- Or set the value of a field.
(<-:) :: Select s f t => f -> t -> OO s ()
a <-: b = do x <- asks (\s -> s!a)
liftIO (writeIORef x b)
-- And as a convenience add value to an double field.
(+=) :: Select s f V3 => f -> V3 -> OO s V3
a += b = do x <- asks (\s -> s!a)
val <- liftIO (readIORef x)
let z = val+b
z `seq` liftIO (writeIORef x z)
return z
-- V3 vector like things.
data V3 = V3 !Double !Double !Double deriving(Show,Eq)
instance Num V3 where
(V3 x1 y1 z1) + (V3 x2 y2 z2) = V3 (x1+x2) (y1+y2) (z1+z2)
(V3 x1 y1 z1) - (V3 x2 y2 z2) = V3 (x1-x2) (y1-y2) (z1-z2)
(V3 x1 y1 z1) * (V3 x2 y2 z2) = V3 (x1*x2) (y1*y2) (z1*z2)
fromInteger o = let v = fromInteger o in V3 v v v
instance Fractional V3 where
(V3 x1 y1 z1) / (V3 x2 y2 z2) = V3 (x1/x2) (y1/y2) (z1/z2)
from field obj = with obj (value field)
dv3 v = V3 v v v
v3len (V3 x y z) = sqrt (x*x + y*y + z*z)
{-# RULE "dv3/mult" forall a b. dv3 a * (V3 x y z) = V3 (a*x) (a*y) (a*z) #-}
-- Bodies
data Base = Base; data Diff = Diff; data Mass = Mass
type Body = Field Base V3 :.: Field Diff V3 :.: Field Mass Double :.: END
-- Create a new body
newBody x1 y1 z1 x2 y2 z2 mass =
V3 x1 y1 z1 ## (dv3 year * V3 x2 y2 z2) ## (mass * solarMass) ## end :: OO s Body
offsetMomemtum bodies@(b:_) = foldM comp 0 bodies >>= (\d -> with b (Diff <-: (-d / dv3 solarMass)))
where comp old body = do diff <- Diff `from` body
mass <- Mass `from` body
return (old + (dv3 mass * diff))
advance dt bodies = advanceLoop dt bodies >> mapM_ comp bodies
where comp body = with body ((\diff -> Base += (dv3 dt * diff)) =<< value Diff)
advanceLoop :: Double -> [Body] -> OO s ()
advanceLoop dt [] = return ()
advanceLoop dt (b:bs) = do
bmass <- Mass `from` b
bbase <- Base `from` b
let inner [] = return ()
inner (p:ps) = do diff <- (Base `from` p >>= \pbase -> return (bbase - pbase))
let dist = v3len diff
let magdiff = dv3 (dt / (dist * dist * dist)) * diff
pmass <- Mass `from` p
with b (Diff += (dv3 pmass * (-magdiff)))
with p (Diff += (dv3 bmass * magdiff))
inner ps
inner bs >> advanceLoop dt bs
energy :: [Body] -> Double -> OO s Double
energy [] e = return e
energy (p:ps) e = do pdiff@(V3 x y z) <- Diff `from` p
pmass <- Mass `from` p
pbase <- Base `from` p
let e' = e + 0.5 * pmass * (x*x + y*y + z*z)
let inner [] e = return e
inner (j:js) e = do jmass <- Mass `from` j
jbase <- Base `from` j
inner js $! (e - ((pmass*jmass)/v3len(pbase - jbase)))
inner ps e' >>= energy ps
solarMass = 4*pi*pi :: Double
year = 365.24 :: Double
createBodies = do
b0 <- newBody 0 0 0 0 0 0 1
b1 <- newBody 4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01)
(1.66007664274403694e-03) (7.69901118419740425e-03) (-6.90460016972063023e-05)
9.54791938424326609e-04
b2 <- newBody 8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01)
(-2.76742510726862411e-03) (4.99852801234917238e-03) (2.30417297573763929e-05)
(2.85885980666130812e-04)
b3 <- newBody 1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01)
2.96460137564761618e-03 2.37847173959480950e-03 (-2.96589568540237556e-05)
4.36624404335156298e-05
b4 <- newBody 1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01
2.68067772490389322e-03 1.62824170038242295e-03 (-9.51592254519715870e-05)
5.15138902046611451e-05
return [b0,b1,b2,b3,b4]
main = do ~[n] <- getArgs
(e1,e2) <- ooToIO (do bodies <- createBodies
offsetMomemtum bodies
e1 <- energy bodies 0
replicateM_ (read n) $ advance 0.01 bodies
e2 <- energy bodies 0
return (e1,e2))
printf "%.9f\n%.9f\n" e1 e2
Smaller code[edit]
Anyone interested in seeing how small we can make the code? Here's my original attempt, which unfortunately suffers from a massive space-leak. I'd be interested in seeing if it is possible to have a succinct version without leaks.
import System(getArgs)
import Numeric
import Data.List
data Vec = V !Double !Double !Double deriving Show
instance Num Vec where
(V a b c) + (V x y z) = (V (a+x) (b+y) (c+z))
(V a b c) - (V x y z) = (V (a-x) (b-y) (c-z))
fromInteger 0 = V 0.0 0.0 0.0 -- for sum function
instance Eq Vec where (V a b c) == (V x y z) = (a==x) && (b==y) && (c==z)
dot (V a b c) (V x y z) = a*x + b*y + c*z
scale (V a b c) n = V (n*a) (n*b) (n*c)
mag (V x y z) = sqrt (x*x + y*y + z*z)
data Planet = Planet Vec Vec Double deriving Show --Position Velocity Mass
dist (Planet p1 _ _) (Planet p2 _ _) = mag $ p1 - p2
mass (Planet _ _ m) = m
vel (Planet _ v _) = v
pos (Planet p _ _) = p
main = do
[arg] <- getArgs
let iter = read arg
let n = 5::Int
let bodies = offset_momentum n [sun, jupiter, saturn, neptune, uranus]
let begin = energy n bodies
putStrLn $ showFFloat (Just 9) begin ""
let final = (iterate (advance n 0.01) bodies)
let end = energy n (final !! iter)
putStrLn $ showFFloat (Just 9) end ""
days_per_year = 365.24
solar_mass = 4.0 * pi * pi
advance :: Int -> Double -> [Planet] -> [Planet]
advance n dt (p:ps) = take n ((Planet (pos p + delta_x)
(new_v) (mass p) ) : advance n dt (ps++[p]))
where
delta_v = sum (map (\q ->
(pos p - pos q) `scale` ((mass q)*dt/(dist p q)^3)) ps)
new_v = (vel p) - delta_v
delta_x = new_v `scale` dt
energy:: Int -> [Planet] -> Double
energy n ps = kinetic - potential
where
kinetic = 0.5 * (sum (map (\q->(mass q)*((vel q) `dot` (vel q))) ps))
potential = sum $ zipWith grav_pot ps (tail (init (tails ps)))
grav_pot x xs = sum $ map (\y -> (mass x)*(mass y)/(dist x y)) xs
offset_momentum n ((Planet p v m):ps) = (Planet p new_v m):ps
where new_v = (sum (map (\n->(vel n) `scale` (mass n)) ps))
`scale` ((-1.0)/solar_mass)
jupiter = (Planet
(V 4.84143144246472090e+00 (-1.16032004402742839e+00) (-1.03622044471123109e-01))
(V ( 1.66007664274403694e-03 * days_per_year)
( 7.69901118419740425e-03 * days_per_year)
((-6.90460016972063023e-05) * days_per_year))
(9.54791938424326609e-04 * solar_mass))
saturn = (Planet
(V 8.34336671824457987e+00 4.12479856412430479e+00 (-4.03523417114321381e-01))
(V (-2.76742510726862411e-03 * days_per_year)
(4.99852801234917238e-03 * days_per_year)
(2.30417297573763929e-05 * days_per_year))
(2.85885980666130812e-04 * solar_mass))
uranus = (Planet
(V 1.28943695621391310e+01 (-1.51111514016986312e+01) (-2.23307578892655734e-01))
(V (2.96460137564761618e-03 * days_per_year)
(2.37847173959480950e-03 * days_per_year)
(-2.96589568540237556e-05 * days_per_year))
(4.36624404335156298e-05 * solar_mass))
neptune = (Planet
(V 1.53796971148509165e+01 (-2.59193146099879641e+01) 1.79258772950371181e-01)
(V (2.68067772490389322e-03 * days_per_year)
(1.62824170038242295e-03 * days_per_year)
(-9.51592254519715870e-05 * days_per_year))
(5.15138902046611451e-05 * solar_mass))
sun = (Planet (V 0.0 0.0 0.0) (V 0.0 0.0 0.0) solar_mass)