How do I optimise this Haskell limit order book (with code, reports, graphs)? - haskell

Question

I've written a haskell version of a limit order book, referencing this version written in C:
https://github.com/jordanbaucke/Limit-Order-Book/blob/master/Others/C%2B%2B/engine.c
A limit order book is the mechanism many stock and currency exchanges use for computing trades of currency and stock.
This haskell version (source code further down) submits 2000 random limit orders to the orderbook, and calculates the average execution price.
main = do
orders <- randomOrders
let (orderBook, events) = foldr (\order (book, ev) -> let (b, e) = processOrder order book in (b, ev++e)) (empty, [])
(take 2000 orders)
let (total, count) = ((fromIntegral $ sum $ map executePrice events), fromIntegral $ length events)
print $ "Average execution price: " ++ show (total / count) ++ ", " ++ (show count) ++ " executions"
I've compiled it with -O2, and running the program without profiling takes almost 10 seconds.
time ./main
"Average execution price: 15137.667036215817, 2706.0 executions"
./main 9.90s user 0.09s system 89% cpu 11.205 total
I've tried to set the program to process 10000 orders, taking 160 seconds.
time ./main
"Average execution price: 15047.099824996354, 13714.0 executions"
./main 161.99s user 2.08s system 57% cpu 4:44.16 total
What can I do to make it dramatically faster without sacrificing functionality? Do you think it is possible to bring it to process 10000 orders per second?
Here are the memory usage charts (with the 2000 orders), generated with +RTS hc/hd/hy and hp2ps:
Here is the source code:
import Data.Array
import Data.List
import Data.Word
import Data.Maybe
import Data.Tuple
import Debug.Trace
import System.Random
import Control.Monad (replicateM)
-- Price is measured in smallest divisible unit of currency.
type Price = Word64
maximumPrice = 30000
type Quantity = Word64
type Trader a = a
type Entry a = (Quantity, Trader a)
type PricePoint a = [Entry a]
data OrderBook a = OrderBook {
pricePoints :: Array Price (PricePoint a),
minAsk :: Price,
maxBid :: Price
} deriving (Show)
data Side = Buy | Sell deriving (Eq, Show, Read, Enum, Bounded)
instance Random Side where
randomR (a, b) g =
case randomR (fromEnum a, fromEnum b) g of
(x, g') -> (toEnum x, g')
random g = randomR (minBound, maxBound) g
data Order a = Order {
side :: Side,
price :: Price,
size :: Quantity,
trader :: Trader a
} deriving (Show)
data Event a =
Execution {
buyer :: Trader a,
seller :: Trader a,
executePrice :: Price,
executeQuantity :: Quantity
} deriving (Show)
empty :: OrderBook a
empty = OrderBook {
pricePoints = array (1, maximumPrice) [(i, []) | i <- [1..maximumPrice]],
minAsk = maximumPrice,
maxBid = 0
}
insertOrder :: Order a -> OrderBook a -> OrderBook a
insertOrder (Order side price size t) (OrderBook pricePoints minAsk maxBid) =
OrderBook {
pricePoints = pricePoints // [(price, (pricePoints!price) ++ [(size, t)])],
maxBid = if side == Buy && maxBid < price then price else maxBid,
minAsk = if side == Sell && minAsk > price then price else minAsk
}
processOrder :: Order a -> OrderBook a -> (OrderBook a, [Event a])
processOrder order orderBook
| size /= 0 && price `comp` current =
let (_order, _ob, _events) = executeForPrice order{price=current} _orderBook
in (\(a,b) c -> (a,c++b)) (processOrder _order{price=price} _ob) _events
| otherwise = (insertOrder order orderBook, [])
where
Order side price size _ = order
(current, comp, _orderBook)
| side == Buy = (minAsk orderBook, (>=), orderBook{minAsk=current+1})
| side == Sell = (maxBid orderBook, (<=), orderBook{maxBid=current-1})
executeForPrice :: Order a -> OrderBook a -> (Order a, OrderBook a, [Event a])
executeForPrice order orderBook
| null pricePoint = (order, orderBook, [])
| entrySize < size = (\(a, b, c) d -> (a, b, d:c))
(executeForPrice order{size=size-entrySize} (set rest)) (execute entrySize)
| otherwise =
let entries
| entrySize > size = (entrySize-size, entryTrader):rest
| otherwise = rest
in (order{size=0}, set entries, [execute size])
where
pricePoint = (pricePoints orderBook)!price
(entrySize, entryTrader):rest = pricePoint
Order side price size trader = order
set = \p -> orderBook{pricePoints=(pricePoints orderBook)//[(price, p)]}
(buyer, seller) = (if side == Buy then id else swap) (trader, entryTrader)
execute = Execution buyer seller price
randomTraders :: IO [Int]
randomTraders = do
g <- newStdGen
return (randomRs (1, 3) g)
randomPrices :: IO [Word64]
randomPrices = do
g <- newStdGen
return (map fromIntegral $ randomRs (1 :: Int, fromIntegral maximumPrice) g)
randomSizes :: IO [Word64]
randomSizes = do
g <- newStdGen
return (map fromIntegral $ randomRs (1 :: Int, 10) g)
randomSides :: IO [Side]
randomSides = do
g <- newStdGen
return (randomRs (Buy, Sell) g)
randomOrders = do
sides <- randomSides
prices <- randomPrices
sizes <- randomSizes
traders <- randomTraders
let zipped = zip4 sides prices sizes traders
let orders = map (\(side, price, size, trader) -> Order side price size trader) zipped
return orders
main = do
orders <- randomOrders
let (orderBook, events) = foldr (\order (book, ev) -> let (b, e) = processOrder order book in (b, ev++e)) (empty, [])
(take 2000 orders)
let (total, count) = ((fromIntegral $ sum $ map executePrice events), fromIntegral $ length events)
print $ "Average execution price: " ++ show (total / count) ++ ", " ++ (show count) ++ " executions"
Here are the profiling reports:
ghc -rtsopts --make -O2 OrderBook.hs -o main -prof -auto-all -caf-all -fforce-recomp
time ./main +RTS -sstderr +RTS -hd -p -K100M && hp2ps -e8in -c main.hp
./main +RTS -sstderr -hd -p -K100M
"Average execution price: 15110.97202536367, 2681.0 executions"
3,184,295,808 bytes allocated in the heap
338,666,300 bytes copied during GC
5,017,560 bytes maximum residency (149 sample(s))
196,620 bytes maximum slop
14 MB total memory in use (2 MB lost due to fragmentation)
Generation 0: 4876 collections, 0 parallel, 1.98s, 2.01s elapsed
Generation 1: 149 collections, 0 parallel, 1.02s, 1.07s elapsed
INIT time 0.00s ( 0.00s elapsed)
MUT time 5.16s ( 5.24s elapsed)
GC time 3.00s ( 3.08s elapsed)
RP time 0.00s ( 0.00s elapsed)
PROF time 0.01s ( 0.01s elapsed)
EXIT time 0.00s ( 0.00s elapsed)
Total time 8.17s ( 8.33s elapsed)
%GC time 36.7% (36.9% elapsed)
Alloc rate 617,232,166 bytes per MUT second
Productivity 63.1% of total user, 61.9% of total elapsed
./main +RTS -sstderr +RTS -hd -p -K100M 8.17s user 0.06s system 98% cpu 8.349 total
cat main.prof
Sun Feb 9 12:03 2014 Time and Allocation Profiling Report (Final)
main +RTS -sstderr -hd -p -K100M -RTS
total time = 0.64 secs (32 ticks # 20 ms)
total alloc = 1,655,532,980 bytes (excludes profiling overheads)
COST CENTRE MODULE %time %alloc
processOrder Main 46.9 81.2
insertOrder Main 21.9 0.0
executeForPrice Main 18.8 9.7
randomPrices Main 9.4 0.1
main Main 3.1 4.5
minAsk Main 0.0 2.1
maxBid Main 0.0 2.0
individual inherited
COST CENTRE MODULE no. entries %time %alloc %time %alloc
MAIN MAIN 1 0 0.0 0.0 100.0 100.0
main Main 392 3 3.1 4.5 100.0 99.8
executePrice Main 417 2681 0.0 0.0 0.0 0.0
processOrder Main 398 5695463 46.9 81.2 87.5 95.0
executeForPrice Main 412 5695252 18.8 9.7 18.8 9.7
pricePoints Main 413 5695252 0.0 0.0 0.0 0.0
insertOrder Main 406 1999 21.9 0.0 21.9 0.0
minAsk Main 405 0 0.0 2.1 0.0 2.1
maxBid Main 400 0 0.0 2.0 0.0 2.0
randomOrders Main 393 1 0.0 0.0 9.4 0.2
randomTraders Main 397 1 0.0 0.0 0.0 0.0
randomSizes Main 396 2 0.0 0.1 0.0 0.1
randomPrices Main 395 2 9.4 0.1 9.4 0.1
randomSides Main 394 1 0.0 0.1 0.0 0.1
CAF:main14 Main 383 1 0.0 0.0 0.0 0.0
randomPrices Main 401 0 0.0 0.0 0.0 0.0
CAF:lvl42_r2wH Main 382 1 0.0 0.0 0.0 0.0
main Main 418 0 0.0 0.0 0.0 0.0
CAF:empty_rqz Main 381 1 0.0 0.0 0.0 0.0
empty Main 403 1 0.0 0.0 0.0 0.0
CAF:lvl40_r2wB Main 380 1 0.0 0.0 0.0 0.0
empty Main 407 0 0.0 0.0 0.0 0.0
CAF:lvl39_r2wz Main 379 1 0.0 0.0 0.0 0.1
empty Main 409 0 0.0 0.1 0.0 0.1
CAF:lvl38_r2wv Main 378 1 0.0 0.0 0.0 0.1
empty Main 410 0 0.0 0.1 0.0 0.1
CAF:maximumPrice Main 377 1 0.0 0.0 0.0 0.0
maximumPrice Main 402 1 0.0 0.0 0.0 0.0
CAF:lvl14_r2vF Main 350 1 0.0 0.0 0.0 0.0
executeForPrice Main 414 0 0.0 0.0 0.0 0.0
CAF:lvl12_r2vB Main 349 1 0.0 0.0 0.0 0.0
processOrder Main 415 0 0.0 0.0 0.0 0.0
CAF:lvl10_r2vx Main 348 1 0.0 0.0 0.0 0.0
processOrder Main 416 0 0.0 0.0 0.0 0.0
CAF:lvl8_r2vt Main 347 1 0.0 0.0 0.0 0.0
processOrder Main 399 0 0.0 0.0 0.0 0.0
CAF:lvl6_r2vp Main 346 1 0.0 0.0 0.0 0.0
empty Main 408 0 0.0 0.0 0.0 0.0
CAF:lvl4_r2vl Main 345 1 0.0 0.0 0.0 0.0
empty Main 411 0 0.0 0.0 0.0 0.0
CAF:lvl2_r2vh Main 344 1 0.0 0.0 0.0 0.0
empty Main 404 0 0.0 0.0 0.0 0.0
CAF GHC.Float 319 8 0.0 0.0 0.0 0.0
CAF GHC.Int 304 2 0.0 0.0 0.0 0.0
CAF GHC.IO.Handle.FD 278 2 0.0 0.0 0.0 0.0
CAF GHC.IO.Encoding.Iconv 239 2 0.0 0.0 0.0 0.0
CAF GHC.Conc.Signal 232 1 0.0 0.0 0.0 0.0
CAF System.Random 222 1 0.0 0.0 0.0 0.0
CAF Data.Fixed 217 3 0.0 0.0 0.0 0.0
CAF Data.Time.Clock.POSIX 214 2 0.0 0.0 0.0 0.0
I'm a newbie in Haskell. How do I interpret these reports, what do they mean and what can I do to make my code faster?

Answer 1

There are two things we can note from the profiling you've made. There seems to be a lot of arrays in memory and also a fair amount of tuples, or rather tuple projections functions. So those seems to be good targets for optimization.
I first tried replacing arrays with Data.Map and for me that cut execution time in half. This is a much bigger win than you reported in one of the comments to your question. You didn't say exactly how you used maps but one thing I did was make sure that the initial map is empty, i.e. I didn't initialize it with lots of empty price points. In order for this to work, I used findWithDefault in Data.Map and let it return an empty list whenever the key wasn't available. If you didn't do that, then that might be the reason I got a much better speedup than you.
I went on to investigate the tuple selection functions. One common trick when writing high performance Haskell is to make sure that things are properly unboxed. Returning tuples from functions can be costly and you do that for the two of the most called functions, executePrice and processOrder. Before rewriting the code I looked at GHC's intermediate code to see if GHC had managed to unbox the tuples by itself. See this post for information on how to look at GHC intermediate representation: Reading GHC Core. The thing to look for is whether the functions has return type (OrderBook a, [Event a]) or (# OrderBook a, [Event a] #). The latter is good, the former is bad.
What I found was that GHC had not been able to unbox the tuples and so I started by unboxing the return type of processOrder by hand. In order to do so I had to replace the foldr in main with a specialized loop, since foldr cannot deal with unboxed tuples. That gave a modest gain. Then I tried to unbox executeForPrice but that resulted in the following bug: https://ghc.haskell.org/trac/ghc/ticket/8762. There might be a way to avoid that bug but I didn't pursue it further.
Another small improvement: unbox all the fields you can in the types OrderBook and Order. It gave me a small gain.
I hope this helps. Good luck with optimizing your Haskell programs.