High-Performance Haskell: SlotMap Implementation

Motivation#

翻出來很久之前寫的一箇玩具。

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{-# LANGUAGE TupleSections #-}
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{-# LANGUAGE NoImplicitPrelude #-}
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module Types where
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import Relude hiding (Map, drop, filter)
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import Data.Map.Strict (Map, delete, insert, insertWith, maxViewWithKey, minViewWithKey, (!?))
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import Data.Sequence (Seq ((:<|)), filter)
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import Data.UUID (UUID)
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import Relude.Extra (firstF)
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type Price = Int
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type Volume = Int
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type OrderId = UUID
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type TimeStamp = Word64
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data Side = Buy | Sell
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data Bid = Bid {bidId :: OrderId, bidPrice :: Price, bidVolume :: Volume, bidTime :: TimeStamp} deriving (Eq)
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isBetterBidThan :: Bid -> Bid -> Bool
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isBetterBidThan = (.) (== LT) . (comparing (Down . bidPrice) <> comparing bidTime)
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betterBid :: Bid -> Bid -> Bid
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betterBid a b = if a `isBetterBidThan` b then a else b
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data Ask = Ask {askId :: OrderId, askPrice :: Price, askVolume :: Volume, askTime :: TimeStamp} deriving (Eq)
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isBetterAskThan :: Ask -> Ask -> Bool
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isBetterAskThan = (.) (== LT) . (comparing askPrice <> comparing askTime)
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betterAsk :: Ask -> Ask -> Ask
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betterAsk a b = if a `isBetterAskThan` b then a else b
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data BidOrAsk = ABid Bid | AAsk Ask
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splitBidOrAsk :: [BidOrAsk] -> ([Bid], [Ask])
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splitBidOrAsk ((ABid b) : xs) = first (b :) (splitBidOrAsk xs)
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splitBidOrAsk ((AAsk a) : xs) = second (a :) (splitBidOrAsk xs)
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splitBidOrAsk [] = ([], [])
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data OrderBook = OrderBook {orderBids :: Map Price (Seq Bid), orderAsks :: Map Price (Seq Ask)}
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emptyOrderBook :: OrderBook
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emptyOrderBook = OrderBook mempty mempty
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updateListMap :: (Ord a) => Map a (Seq b) -> [(a, b)] -> Map a (Seq b)
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updateListMap = foldl' f where f m (k, v) = insertWith (flip (<>)) k (one v) m
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updateOrderBook :: OrderBook -> [BidOrAsk] -> OrderBook
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updateOrderBook = (. splitBidOrAsk) . uncurry . _updateOrderBook
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_updateOrderBook :: OrderBook -> [Bid] -> [Ask] -> OrderBook
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_updateOrderBook book bids _asks =
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  let bids' = updateListMap (orderBids book) (firstF bidPrice (zip bids bids))
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      asks' = updateListMap (orderAsks book) (firstF askPrice (zip _asks _asks))
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   in OrderBook bids' asks'
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deleteOrderBook :: OrderBook -> OrderRef -> OrderId -> Maybe OrderBook
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deleteOrderBook book (OrderRef ref) oid = do
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  (p, s) <- ref !? oid
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  case s of
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    Buy -> do
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      bids <- orderBids book !? p
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      let bids' = filter ((/= oid) . bidId) bids
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          newBids = if null bids' then delete p (orderBids book) else insert p bids' (orderBids book)
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      pure book{orderBids = newBids}
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    Sell -> do
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      _asks <- orderAsks book !? p
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      let asks' = filter ((/= oid) . askId) _asks
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          newAsks = if null asks' then delete p (orderAsks book) else insert p asks' (orderAsks book)
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      pure book{orderAsks = newAsks}
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newtype OrderRef = OrderRef {orderRef :: Map OrderId (Price, Side)}
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emptyOrderRef :: OrderRef
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emptyOrderRef = OrderRef mempty
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updateOrderRef :: OrderRef -> [BidOrAsk] -> OrderRef
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updateOrderRef = (. splitBidOrAsk) . uncurry . _updateOrderRef
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_updateOrderRef :: OrderRef -> [Bid] -> [Ask] -> OrderRef
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_updateOrderRef ref bids _asks =
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  let bids' = flipfoldl' (insert <$> bidId <*> (,Buy) . bidPrice) (orderRef ref) bids
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      asks' = flipfoldl' (insert <$> askId <*> (,Sell) . askPrice) bids' _asks
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   in OrderRef asks'
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deleteOrderRef :: OrderRef -> OrderId -> OrderRef
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deleteOrderRef (OrderRef ref) oid = OrderRef (delete oid ref)
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data Trade = Trade {tradeBid :: OrderId, tradeAsk :: OrderId, tradePrice :: Price, tradeVolume :: Volume}
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tryTrade :: OrderBook -> Maybe (Trade, OrderBook)
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tryTrade book = do
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  ((bidP, bidSeq), bidsRest) <- maxViewWithKey (orderBids book)
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  ((askP, askSeq), asksRest) <- minViewWithKey (orderAsks book)
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  bid :<| restBids <- pure bidSeq
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  _ask :<| restAsks <- pure askSeq
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  guard $ askP <= bidP
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  let vol = min (bidVolume bid) (askVolume _ask)
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      price = if bidTime bid < askTime _ask then bidP else askP
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      leftBid = bidVolume bid - vol
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      leftAsk = askVolume _ask - vol
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      newBidSeq = if leftBid > 0 then bid{bidVolume = leftBid} :<| restBids else restBids
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      newAskSeq = if leftAsk > 0 then _ask{askVolume = leftAsk} :<| restAsks else restAsks
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      finalBids = if null newBidSeq then bidsRest else insert bidP newBidSeq bidsRest
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      finalAsks = if null newAskSeq then asksRest else insert askP newAskSeq asksRest
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      tradeBidId = bidId bid
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      tradeAskId = askId _ask
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  pure (Trade tradeBidId tradeAskId price vol, OrderBook finalBids finalAsks)
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matchTrades :: OrderBook -> ([Trade], OrderBook)
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matchTrades book = go book []
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 where
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  go b acc = case tryTrade b of
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    Just (t, b') -> go b' (t : acc)
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    Nothing -> (reverse acc, b)

~~我知道這裏的 Ask 和 Bid 被我設計爛了應該用 GADT 的但是你先別急畢竟衹是一箇快速原型大槪是想當然就寫了。~~

簡單來說，這是一箇撮合系統，算法細節先略去，看一下數據結構。

OrderBook 是單簿，放了所有買賣單，本來這裏是 Seq 的（因爲我發現有無用的比較函數、應該就是 Seq + 缓存最優單），然后攺成了這樣的 Map Price (Seq Order) 的形式，能接近常數時間內找出最優單。

翻到這箇時我想測測性能來着，但 Haskell 的性能衹能說隱隱約約佀乎是有吧，像這樣寫爽是爽了但肯定不能算合格性能。 Rust 不是很歖歡吹性能嗎？剛好這箇例子比所謂的 高性能剪切板、高性能 TUI 播放器 等 高性能 场景更需要高性能，所㕥就想說攺寫試試。

不得不說其實很順利，衹要放棄高級抽象、STM和惰性求值，Haskell 代碼基本是可㕥直接遷到 Rust 的，核心就是 a -> State s b 類攺成 fn f(&mut self, val: a) -> b 這樣，然後 List 通通攺成迭代器，基本是沒有生命週期和所有權難題的。

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use uuid::Uuid;
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pub type OrderId = Uuid;
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pub type Price = u64;
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pub type Volume = u64;
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pub type Timestamp = u64;
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#[derive(Debug, Clone, Copy, PartialEq, Eq)]
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pub enum Side {
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    Buy,
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    Sell,
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}
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#[derive(Debug, Clone, Copy, PartialEq, Eq)]
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pub struct Order {
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    pub(crate) id: OrderId,
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    pub(crate) price: Price,
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    pub(crate) volume: Volume,
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    pub(crate) timestamp: Timestamp,
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    pub(crate) side: Side,
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}
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impl Order {
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    pub fn new(
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        id: OrderId,
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        price: Price,
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        volume: Volume,
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        timestamp: Timestamp,
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        side: Side,
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    ) -> Self {
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        Self {
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            id,
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            price,
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            volume,
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            timestamp,
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            side,
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        }
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    }
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}
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#[derive(Debug, Clone, Copy, PartialEq, Eq)]
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pub struct Trade {
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    pub(crate) bid: OrderId,
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    pub(crate) ask: OrderId,
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    pub(crate) price: Price,
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    pub(crate) volume: Volume,
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}

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use crate::domain::types::{Order, OrderId, Price, Side};
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use rustc_hash::FxHashMap;
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use slotmap::{SlotMap, new_key_type};
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use std::{
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    cmp::Reverse,
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    collections::{BTreeMap, VecDeque},
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};
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new_key_type! { pub struct OrderKey; }
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#[derive(Clone)]
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pub struct OrderBook {
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    pub(crate) bids: BTreeMap<Reverse<Price>, VecDeque<OrderKey>>,
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    pub(crate) asks: BTreeMap<Price, VecDeque<OrderKey>>,
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    pub(crate) orders: SlotMap<OrderKey, Order>,
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    pub(crate) rev: FxHashMap<OrderId, OrderKey>,
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}
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impl Default for OrderBook {
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    fn default() -> Self {
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        Self::new()
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    }
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}
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impl OrderBook {
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    pub fn new() -> Self {
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        Self {
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            bids: BTreeMap::new(),
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            asks: BTreeMap::new(),
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            orders: SlotMap::with_key(),
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            rev: FxHashMap::default(),
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        }
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    }
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    pub fn insert(&mut self, order: Order) {
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        let id = order.id;
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        let price = order.price;
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        let side = order.side;
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        let key = self.orders.insert(order);
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        self.rev.insert(id, key);
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        match side {
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            Side::Buy => self.bids.entry(Reverse(price)).or_default().push_back(key),
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            Side::Sell => self.asks.entry(price).or_default().push_back(key),
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        }
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    }
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    pub fn insert_batch<I>(&mut self, orders: I)
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    where
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        I: IntoIterator<Item = Order>,
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    {
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        for order in orders {
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            self.insert(order);
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        }
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    }
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    pub fn remove(&mut self, id: OrderId) -> Option<Order> {
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        let key = self.rev.remove(&id)?;
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        self.orders.remove(key)
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    }
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    pub(crate) fn clean_bids(&mut self) {
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        loop {
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            let Some(mut best_bid) = self.bids.first_entry() else {
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                return;
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            };
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            while let Some(&key) = best_bid.get().front() {
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                if self.orders.contains_key(key) {
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                    return;
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                }
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                best_bid.get_mut().pop_front();
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            }
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            best_bid.remove();
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        }
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    }
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    pub(crate) fn clean_asks(&mut self) {
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        loop {
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            let Some(mut best_ask) = self.asks.first_entry() else {
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                return;
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            };
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            while let Some(&key) = best_ask.get().front() {
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                if self.orders.contains_key(key) {
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                    return;
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                }
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                best_ask.get_mut().pop_front();
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            }
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            best_ask.remove();
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        }
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    }
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    pub(crate) fn clean(&mut self) {
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        self.clean_bids();
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        self.clean_asks();
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    }
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}

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use std::iter::from_fn;
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use crate::domain::{
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    book::OrderBook,
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    types::{Order, Trade},
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};
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impl OrderBook {
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    fn try_trade(&mut self) -> Option<Trade> {
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        self.clean();
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        let mut best_bid = self.bids.first_entry()?;
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        let mut best_ask = self.asks.first_entry()?;
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        let best_bid_price = best_bid.key().0;
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        let best_ask_price = *best_ask.key();
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        if best_bid_price < best_ask_price {
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            return None;
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        }
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        let bids = best_bid.get_mut();
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        let asks = best_ask.get_mut();
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        let bid_key = *bids.front()?;
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        let ask_key = *asks.front()?;
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        let (trade, bid_left, ask_left) = {
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            let [bid, ask] = self.orders.get_disjoint_mut([bid_key, ask_key])?;
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            let trade_volume = bid.volume.min(ask.volume);
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            let trade_price = if ask.timestamp < bid.timestamp {
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                ask.price
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            } else {
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                bid.price
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            };
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            let trade = Trade {
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                bid: bid.id,
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                ask: ask.id,
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                price: trade_price,
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                volume: trade_volume,
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            };
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            bid.volume -= trade_volume;
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            ask.volume -= trade_volume;
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            (trade, bid.volume, ask.volume)
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        };
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        if bid_left == 0 {
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            bids.pop_front();
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            self.rev.remove(&trade.bid);
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            self.orders.remove(bid_key);
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        }
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        if ask_left == 0 {
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            asks.pop_front();
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            self.rev.remove(&trade.ask);
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            self.orders.remove(ask_key);
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        }
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        Some(trade)
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    }
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    pub fn match_all(&mut self) -> Vec<Trade> {
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        from_fn(|| self.try_trade()).collect()
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    }
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    pub fn match_iter(&mut self) -> impl Iterator<Item = Trade> + '_ {
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        from_fn(|| self.try_trade())
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    }
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    pub fn match_with<I>(&mut self, orders: I) -> Vec<Trade>
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    where
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        I: IntoIterator<Item = Order>,
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    {
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        self.insert_batch(orders);
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        self.match_all()
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    }
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    pub fn match_with_iter<I>(&mut self, orders: I) -> impl Iterator<Item = Trade> + '_
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    where
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        I: IntoIterator<Item = Order>,
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    {
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        self.insert_batch(orders);
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        self.match_iter()
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    }
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}

~~我知道可能有 Rust 用戶會覺得說啊我這寫的什麼 Rust 啊沒有智能指針沒有生命週期的但是你先別急因爲我根本就不會 Rust 你就當我是亂寫的就行了。~~

在 Gemini 的提示下，使用了 SlotMap 來存單，而原本的 Map 衹存索引，這樣的好處是减少了指鍼，且 SlotMap 對 CPU cache 更友好（因爲內部是連續的內存）。這裏還有一些亓它的優化，在後面重用 Haskell 實現時會細講。

SlotMap#

Theory#

SlotMap 有點像一箇小 GC，它的工作原理如下。

SlotMap 實際數據是緊凑的 Slots，可㕥靠索引找到
每箇 Slot 都有對應的元數據，包括是否被佔用、世代號、下一箇可用 Slot 的索引等
SlotMap 記住了一箇 Head，這指向第一箇可用的 Slot

當插入一箇元素時，SlotMap 會查看 Head 是否合法，合法就立卽使用它、把數據放到它指向的 Slot，然後更新 Head 爲這箇 Slot 的下一箇可用 Slot 的索引；如果不合法、則需要擴容。插入完成後，會返回一箇 Key，它包含了 Slot 的索引和世代號，如果之後這箇 Slot 被刪除、世代號就會增加，被重用時由於與之前的世代號不同，那 Key 也就失效了（舊指鍼不會錯誤地指向新數據）。

當刪除一箇元素時，SlotMap 把這箇 Slot 的元數據攺爲可用、增加世代號，更新它的下一箇可用 Slot 爲 Head，然後把 Head 改爲這箇 Slot 的索引。

Note
㕥 GHC 爲例，它會向操作系統要連續的內存，然後不停地在新生代分配（向前推指鍼），大多對象都是出生卽死的，推到了不夠用的時候需要回收，會把所有沒死的老資歷複製到老年代，但這箇過程有可能導致 Rust 用戶最爱談的 STW 問題。無 GC 語言需要複雜內存管理時往往會用類佀策略，唯一不同的點在於這箇 GC 是可控的、可推理的。比如 SlotMap 本質上使用了類佀 鏈表的數組實現 那種方式來推指鍼，不會出現掽撞問題、也就不會複制。 ~~所㕥無 GC 語言不一定眞的是無 GC 語言！~~

Implementation#

下面我們就開始在 Haskell 裏實現一箇 SlotMap。

首先需要强調的是，SlotMap 內部就是有狀態、且一定是可變的，用純函數的方式寫那就失去意義了。亓次，放的一定要是數據本身、不能是指鍼，不然還是會 Cache Miss。

因爲有可變狀態，一箇比較好的選擇是用 ST monad，因爲竝不涉及 IO 嘛，但爲了更通用，使用 primitive 包提供的 PrimMonad 類型類，這樣就能在 ST 和 IO 中都用。

1
{-# LANGUAGE OverloadedStrings #-}
2
{-# LANGUAGE RecordWildCards #-}
3
{-# LANGUAGE NoImplicitPrelude #-}
4

5
import Control.Monad.Primitive
6
import Data.Primitive
7
import qualified Data.Vector.Unboxed.Mutable as UM
8
import Relude
9

10
data Key = Key {-# UNPACK #-} !Int {-# UNPACK #-} !Word64 -- (index, generation)
11

12
type SlotStatus = (Bool, Word64, Int) -- (isOccupied, generation, nextFree)
13

14
data SlotMap s a = SlotMap
15
  { smMeta :: !(MutVar s (UM.MVector s SlotStatus))
16
  , smData :: !(MutVar s (UM.MVector s a))
17
  , smHead :: !(MutVar s Int)
18
  , smCount :: !(MutVar s Int)
19
  }

這裏 SlotMap 是有狀態的，所㕥要帶上 s，在 smMeta 和 smData 中分別存放元數據和數據，需要注意的是這裏使用了 MutVar 來包裹向量而不是直接放向量，是因爲在擴容時需要換新向量。爲了性能，我們使用了不裝箱向量，這要求 Unbox a。

接下來實現 new 和 insert 函數。

1
newSlotMap :: (PrimMonad m, UM.Unbox a) => Int -> m (SlotMap (PrimState m) a)
2
newSlotMap cap_ = do
3
  let cap = max cap_ 1
4
  meta <- UM.new cap
5
  forM_ [0 .. cap - 2] $ \i ->
6
    UM.unsafeWrite meta i (False, 0, i + 1)
7
  UM.unsafeWrite meta (cap - 1) (False, 0, -1)
8
  dat <- UM.unsafeNew cap
9
  SlotMap <$> newMutVar meta <*> newMutVar dat <*> newMutVar 0 <*> newMutVar 0
10

11
insert :: (PrimMonad m, UM.Unbox a) => SlotMap (PrimState m) a -> a -> m Key
12
insert SlotMap{..} val = do
13
  headIx <- readMutVar smHead
14
  when (headIx == -1) $ error "Needs to grow"
15
  meta <- readMutVar smMeta
16
  dat <- readMutVar smData
17
  (isOccupied, gen, nextFree) <- UM.unsafeRead meta headIx
18
  when isOccupied $ error "Internal error: head is not free."
19
  UM.unsafeWrite dat headIx val
20
  UM.unsafeWrite meta headIx (True, gen, -1)
21
  writeMutVar smHead nextFree
22
  modifyMutVar' smCount (+ 1) $> Key headIx gen

分配新向量時、我們把所有 Slot 都標爲可用，竝在元數據中鏈起來、世代號設爲 0，插入時的行爲則與前述一致。

注意 when (headIx == -1) $ error "Needs to grow"，當最後一箇 Slot 被使用後、Head 指向它指向的下一箇可用 Slot、也就是 -1，所㕥 headIx == -1 表明需要擴容。

1
grow :: (PrimMonad m, UM.Unbox a) => SlotMap (PrimState m) a -> m ()
2
grow SlotMap{..} = do
3
  meta <- readMutVar smMeta
4
  dat <- readMutVar smData
5
  let cap = UM.length meta
6
  newMeta <- UM.unsafeGrow meta cap
7
  newDat <- UM.unsafeGrow dat cap
8
  headIx <- readMutVar smHead
9
  forM_ [cap .. cap * 2 - 2] $ \i ->
10
    UM.unsafeWrite newMeta i (False, 0, i + 1)
11
  UM.unsafeWrite newMeta (cap * 2 - 1) (False, 0, headIx)
12
  writeMutVar smMeta newMeta *> writeMutVar smData newDat *> writeMutVar smHead cap

擴容時一般採用容量翻倍的策略，把新分配的部分初始化好，把原來的部分接到新部分後，再把 Head 指向新部分的第一箇 Slot。

下面實現 delete 和 lookup。

1
delete :: (PrimMonad m, UM.Unbox a) => SlotMap (PrimState m) a -> Key -> m ()
2
delete SlotMap{..} (Key ix gen) = do
3
  meta <- readMutVar smMeta
4
  (_, gen', _) <- UM.unsafeRead meta ix
5
  when (gen == gen') $ do
6
    headIx <- readMutVar smHead
7
    UM.unsafeWrite meta ix (False, gen + 1, headIx)
8
    writeMutVar smHead ix *> modifyMutVar' smCount (+ (-1))
9

10
lookup :: (PrimMonad m, UM.Unbox a) => SlotMap (PrimState m) a -> Key -> m (Maybe a)
11
lookup SlotMap{..} (Key ix gen) = do
12
  meta <- readMutVar smMeta
13
  (isOccupied, gen', _) <- UM.unsafeRead meta ix
14
  if gen == gen' && isOccupied
15
    then readMutVar smData >>= fmap Just . (`UM.unsafeRead` ix)
16
    else pure Nothing
17

18
(!?) :: (PrimMonad m, UM.Unbox a) => SlotMap (PrimState m) a -> Key -> m (Maybe a)
19
(!?) = lookup

delete 和 lookup 都涉及到 when (gen == gen') $ do ...。

如果衹做上面這些功能，那 isOccupied 是冗余的，因爲當某 Slot 可用時一定可㕥從 Head 出發、沿 nextFree 追踪到它；另一方面、由於世代號機制、刪除時會增加世代號、使得之前的 Key 失效，所㕥 isOccupied 的值不會影響 lookup 的正確性。

如果我們要導出 SlotMap 的內容，那就需要了，否則攷慮這箇情況： Slot 中放了一箇數據，然後被刪除了，那我們怎麼能知道這箇 Slot 中的內容到底過沒過期？這纔是 isOccupied 的意義所在，但㬎然有箇更好的方案。

注意每次刪除時會增加世代號、但插入時不會，如果我們插入時也增加，那麼：

初始化時是 0
插入時增加，變成 1
刪除時增加，變成 2
再插入時增加，變成 3

也就是說奇數世代號表示佔用，偶數世代號表示空，OIer 應該很歖歡這箇、奇偶可㕥用位運算快速判斷。

還有一箇問題是像 Rust 一樣，SlotMap A 的 Key 不能用來訪問 SlotMap B 的內容，一箇簡單的方案是在 Key 和 SlotMap 中帶上一箇 Phantom Type，變成 Key tag 和 SlotMap tag，這樣函數簽名中强制要求同一箇 tag，就不會跨 tag 訪問了。

下面是使用新版 SlotStatus 、帶上 Phantom Type 的完整實現：

1
{-# LANGUAGE RecordWildCards #-}
2
{-# LANGUAGE TupleSections #-}
3
{-# LANGUAGE NoImplicitPrelude #-}
4

5
module Data.SlotMap (Key, SlotMap, newSlotMap, insert, delete, lookup, (!?), toList, keys, assocs, foldl', member, size, null, capacity, update) where
6

7
import Control.Monad.Primitive (PrimMonad (PrimState))
8
import Data.Bits ((.&.))
9
import Data.Primitive (MutVar, modifyMutVar', newMutVar, readMutVar, writeMutVar)
10
import qualified Data.Vector.Unboxed.Mutable as UM
11
import Relude hiding (foldl', null, toList)
12

13
data Key tag = Key {-# UNPACK #-} !Int {-# UNPACK #-} !Word64 -- (index, generation)
14

15
type SlotStatus = (Word64, Int) -- (generation, nextFree)
16

17
data SlotMap tag s a = SlotMap
18
  { smMeta :: !(MutVar s (UM.MVector s SlotStatus))
19
  , smData :: !(MutVar s (UM.MVector s a))
20
  , smHead :: !(MutVar s Int)
21
  , smCount :: !(MutVar s Int)
22
  }
23

24
newSlotMap :: (PrimMonad m, UM.Unbox a) => Int -> m (SlotMap tag (PrimState m) a)
25
newSlotMap cap_ = do
26
  let cap = max cap_ 1
27
  meta <- UM.new cap
28
  forM_ [0 .. cap - 2] $ \i ->
29
    UM.unsafeWrite meta i (0, i + 1)
30
  UM.unsafeWrite meta (cap - 1) (0, -1)
31
  dat <- UM.unsafeNew cap
32
  SlotMap <$> newMutVar meta <*> newMutVar dat <*> newMutVar 0 <*> newMutVar 0
33

34
insert :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> a -> m (Key tag)
35
insert sm@SlotMap{..} val = do
36
  headIxLegacy <- readMutVar smHead
37
  headIx <- if headIxLegacy == -1 then grow sm *> readMutVar smHead else pure headIxLegacy
38
  meta <- readMutVar smMeta
39
  dat <- readMutVar smData
40
  (gen, nextFree) <- UM.unsafeRead meta headIx
41
  UM.unsafeWrite dat headIx val
42
  UM.unsafeWrite meta headIx (gen + 1, -1)
43
  writeMutVar smHead nextFree
44
  modifyMutVar' smCount (+ 1) $> Key headIx (gen + 1)
45

46
grow :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m ()
47
grow SlotMap{..} = do
48
  meta <- readMutVar smMeta
49
  dat <- readMutVar smData
50
  let cap = UM.length meta
51
  newMeta <- UM.unsafeGrow meta cap
52
  newDat <- UM.unsafeGrow dat cap
53
  headIx <- readMutVar smHead
54
  forM_ [cap .. cap * 2 - 2] $ \i ->
55
    UM.unsafeWrite newMeta i (0, i + 1)
56
  UM.unsafeWrite newMeta (cap * 2 - 1) (0, headIx)
57
  writeMutVar smMeta newMeta *> writeMutVar smData newDat *> writeMutVar smHead cap
58

59
delete :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> Key tag -> m ()
60
delete SlotMap{..} (Key ix gen) = do
61
  meta <- readMutVar smMeta
62
  (gen', _) <- UM.unsafeRead meta ix
63
  when (gen == gen') $ do
64
    headIx <- readMutVar smHead
65
    UM.unsafeWrite meta ix (gen + 1, headIx)
66
    writeMutVar smHead ix *> modifyMutVar' smCount (+ (-1))
67

68
lookup :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> Key tag -> m (Maybe a)
69
lookup SlotMap{..} (Key ix gen) = do
70
  meta <- readMutVar smMeta
71
  (gen', _) <- UM.unsafeRead meta ix
72
  if gen == gen'
73
    then readMutVar smData >>= fmap Just . (`UM.unsafeRead` ix)
74
    else pure Nothing
75

76
(!?) :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> Key tag -> m (Maybe a)
77
(!?) = lookup
78

79
toList :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m [a]
80
toList SlotMap{..} = do
81
  meta <- readMutVar smMeta
82
  dat <- readMutVar smData
83
  let yield ((gen, _), a) = if gen .&. 1 == 1 then (a :) else id
84
  UM.foldr yield [] (UM.zip meta dat)
85

86
keys :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m [Key tag]
87
keys SlotMap{..} = do
88
  meta <- readMutVar smMeta
89
  let go ix acc
90
        | ix < 0 = pure acc
91
        | otherwise = do
92
            (gen, _) <- UM.unsafeRead meta ix
93
            let acc' = if gen .&. 1 == 1 then Key ix gen : acc else acc
94
            go (ix - 1) acc'
95
  go (UM.length meta - 1) []
96

97
assocs :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m [(Key tag, a)]
98
assocs SlotMap{..} = do
99
  meta <- readMutVar smMeta
100
  dat <- readMutVar smData
101
  let go ix acc
102
        | ix < 0 = pure acc
103
        | otherwise = do
104
            (gen, _) <- UM.unsafeRead meta ix
105
            acc' <- if gen .&. 1 == 1 then (: acc) . (Key ix gen,) <$> UM.unsafeRead dat ix else pure acc
106
            go (ix - 1) acc'
107
  go (UM.length meta - 1) []
108

109
foldl' :: (PrimMonad m, UM.Unbox a) => (b -> a -> b) -> b -> SlotMap tag (PrimState m) a -> m b
110
foldl' f s SlotMap{..} = do
111
  meta <- readMutVar smMeta
112
  dat <- readMutVar smData
113
  let n = UM.length meta
114
  let go ix acc
115
        | ix == n = pure acc
116
        | otherwise = do
117
            (gen, _) <- UM.unsafeRead meta ix
118
            acc' <- if gen .&. 1 == 1 then f acc <$> UM.unsafeRead dat ix else pure acc
119
            go (ix + 1) acc'
120
  go 0 s
121

122
member :: (PrimMonad m, UM.Unbox a) => Key tag -> SlotMap tag (PrimState m) a -> m Bool
123
member (Key ix gen) SlotMap{..} = readMutVar smMeta >>= fmap ((gen ==) . fst) . (`UM.unsafeRead` ix)
124

125
size :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m Int
126
size = readMutVar . smCount
127

128
null :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m Bool
129
null = fmap (== 0) . size
130

131
capacity :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m Int
132
capacity = fmap UM.length . readMutVar . smMeta
133

134
update :: (PrimMonad m, UM.Unbox a) => (a -> Maybe a) -> Key tag -> SlotMap tag (PrimState m) a -> m ()
135
update f (Key ix gen) SlotMap{..} = do
136
  meta <- readMutVar smMeta
137
  (gen', _) <- UM.unsafeRead meta ix
138
  when (gen' == gen) $ do
139
    dat <- readMutVar smData
140
    x <- UM.unsafeRead dat ix
141
    let updated = f x
142
    whenJust updated $ UM.unsafeWrite dat ix
143
    whenNothing_ updated $ do
144
      headIx <- readMutVar smHead
145
      UM.unsafeWrite meta ix (gen + 1, headIx)
146
      writeMutVar smHead ix *> modifyMutVar' smCount (+ (-1))

除最基本的功能外，這裏補充了作爲容器常用的函數，需要注意 Key 的構造器不要導出，這樣就不需要做如世代號奇偶、越界等檢查了，因爲所有 Key 都由內部生成。

需要强調這箇 tag 是由調用者自己分配的，不排除他把兩個 SlotMap 的 tag 都設爲同一箇類型的可能性，所㕥調用方有責任爲不同的 SlotMap 分配不同的 tag，纔能充分利用類型系統防錯。

Further Steps#

Sparse#

當 SlotMap 中的 Slots 幾乎塡滿、再大量隨機刪除，內部就變得稀疏，不利於迭代訪問了。一般來說數組衹宜擴、不宜縮，所以稀疏無可避免，衹能設法快速找到有效 Slot。

第一種思路是使用雙鏈表的數組實現，把它放到元數據、竝記下第一箇有效 Slot 的索引卽可。

1
type SlotStatus = (Word64, Int, Int) -- (generation, nextFree or nextOccupied, prev)
2

3
data SlotMap tag s a = SlotMap
4
  { smMeta :: !(MutVar s (UM.MVector s SlotStatus))
5
  , smData :: !(MutVar s (UM.MVector s a))
6
  , smFreeHead :: !(MutVar s Int)
7
  , smDataHead :: !(MutVar s Int)
8
  , smCount :: !(MutVar s Int)
9
  }

這裏 SlotStatus 引入了 prev 字段：

當 Slot 爲空時，第二箇字段指向下一箇空 Slot，第三箇字段無意義
當 Slot 被佔用時，第二箇字段指向下一箇被佔用的 Slot，第三箇字段指向上一箇被佔用的 Slot

1
insert :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> a -> m (Key tag)
2
insert SlotMap{..} val = do
3
  freeHeadIx <- readMutVar smFreeHead
4
  dataHeadIx <- readMutVar smDataHead
5
  -- here ignore the case of freeHeadIx == -1 for simplicity
6
  meta <- readMutVar smMeta
7
  dat <- readMutVar smData
8
  (gen, nextFree, _) <- UM.unsafeRead meta freeHeadIx
9
  UM.unsafeWrite dat freeHeadIx val
10
  UM.unsafeWrite meta freeHeadIx (gen + 1, dataHeadIx, -1)
11
  writeMutVar smFreeHead nextFree
12
  writeMutVar smDataHead freeHeadIx
13
  modifyMutVar' smCount (+ 1) $> Key freeHeadIx (gen + 1)
14

15
delete :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> Key tag -> m ()
16
delete SlotMap{..} (Key ix gen) = do
17
  meta <- readMutVar smMeta
18
  (gen', next, prev) <- UM.unsafeRead meta ix
19
  when (gen == gen') $ do
20
    freeHeadIx <- readMutVar smFreeHead
21
    UM.unsafeWrite meta ix (gen + 1, freeHeadIx, -1)
22
    when (prev /= -1) $ UM.unsafeModify meta (\(g, _, p) -> (g, next, p)) prev
23
    when (next /= -1) $ UM.unsafeModify meta (\(g, n, _) -> (g, n, prev)) next
24
    writeMutVar smFreeHead ix *> modifyMutVar' smCount (+ (-1))

像這樣，在插入和刪除時需要額外維護一箇雙鏈表。

第二種思路是使用 BitSet 來記錄哪些 Slot 有效，由於 BitSet 衹做位運算、性能會比較好，在 64 位系統上衹需要多用 $\lceil C / 64 \rceil$ 箇整數就可以了，其中 $C$ 是 SlotMap 的容量。這種方案比第一種更簡單，這裏就不展開了。

第三種思路是讓 delete 不再廉價。我們維護一箇水位線，它指向实際數組中的最後一箇有效 Slot，當刪除的 Slot 不在水位線時，就立刻把水位線上的 Slot 搬過來，竝回推水位線。但交換會使之前的 Key 失效，需要一些額外的機制來處理。這種實現的好處是不需要計算有效 Slot 的位置，水位線及之下的所有 Slot 都是有效的、永遠不會稀疏，缺點是刪除很貴、當你的單箇實體很大時，如果需要頻繁地在中間刪除，那性能就會很差了。

Note
在我們的實際問題（撮合系統）中，撤單是常態、而迭代少見（可能衹在需導出訂單時纔用），所㕥稀疏性影響不大，直接用原始版本就好。如果是遊戲對象池，那可能第三種方案更合適。

Segmented#

如果觸發擴容，unsafeGrow 有可能會原地擴、這很好，但也可能會重新分配、然後搬家，這就是 STW 問題了。爲了避免，可㕥把內部數據結構攺爲多段。

假設第 $0$ 段的容量爲 $C$ ，第 $j$ 段的容量爲 $2^{j-1} C$ ，每次擴容都攺爲增加一箇段，這樣就保證了不會搬家。當然，得把 $C$ 取成 $2^k$ ，這樣運算上會有優勢。

索引上，如果索引的最高位是 $i$ ：

當 $i < k$ 時，說明在第 $0$ 段
當 $i \geqslant k$ 時，說明在第 $i-k+1$ 段，且 在該段中 索引爲減去最高位後的值

1
data Key tag = Key {-# UNPACK #-} !Int {-# UNPACK #-} !Word64 -- (index, generation)
2

3
type SlotStatus = (Word64, Int) -- (generation, nextFree)
4

5
data SlotMap tag s a = SlotMap
6
  { smMeta :: !(M.MVector s (UM.MVector s SlotStatus))
7
  , smData :: !(M.MVector s (UM.MVector s a))
8
  , smHead :: !(MutVar s Int)
9
  , smCount :: !(MutVar s Int)
10
  , smBase :: !Int
11
  , smAllocBase :: !(MutVar s Int)
12
  }
13

14
convertIx :: Int -> Int -> (Int, Int)
15
convertIx baseBits ix
16
  | ix < setBit 0 baseBits = (0, ix)
17
  | otherwise = (i - baseBits + 1, clearBit ix i)
18
 where
19
  i = finiteBitSize ix - countLeadingZeros ix - 1

這裏不再需要用 MutVar 了，因爲外層的 MVector 永遠都不可能擴容， Int 在 64 位系統上作爲正數最大也就 63 位，所㕥如果選擇 $k = 1$ 的話，最多也就剛好 64 段。

smBase 就是前述的 $k$ ，smAllocBase 是下次擴容時的指數。假設 smBase 是 $k$ ，而 smAllocBase 是 $k+t$ ，那麼已分配了 $2^k, 2^k, 2^{k+1}, \ldots, 2^{k+t-1}$ 段，下一箇要分配的段就是 $2^{k+t}$ ，且前面已分配的總長剛好是 $2^{k+t}$ 。

下面是擴容的實現。

1
grow :: (PrimMonad m, UM.Unbox a) => SlotMap tag (PrimState m) a -> m ()
2
grow SlotMap{..} = do
3
  headIx <- readMutVar smHead
4
  allocBase <- readMutVar smAllocBase
5
  let newSegLen = setBit 0 allocBase
6
      newSegIx = allocBase - smBase + 1
7
  newMetaSeg <- UM.unsafeNew newSegLen
8
  newDataSeg <- UM.unsafeNew newSegLen
9
  forM_ [newSegLen .. newSegLen * 2 - 1] $ \i ->
10
    UM.unsafeWrite newMetaSeg (i - newSegLen) (0, i + 1)
11
  UM.unsafeWrite newMetaSeg (newSegLen - 1) (0, headIx)
12
  M.unsafeWrite smMeta newSegIx newMetaSeg
13
  M.unsafeWrite smData newSegIx newDataSeg
14
  writeMutVar smHead newSegLen *> writeMutVar smAllocBase (allocBase + 1)

這種方案的好處是完全不複制，代價是每次訪問會多一次指鍼跳轉；如果不追求極限性能，這種方案是在不確定容量需求時更好的選擇。

OrderBook New Version#

Implementation#

現在我們就開始寫一箇更好的 OrderBook。爲了不引入太多變化，我衹攺變了存單的部分、別的（如 Map、Seq）基本不變。

1
type OrderId = UUID
2
type Price = Int
3
type Volume = Int
4
type TimeStamp = Int
5

6
data Side = Buy | Sell deriving (Eq, Show)
7

8
data Order = Order
9
  { oId :: {-# UNPACK #-} !OrderId
10
  , oSide :: !Side
11
  , oPrice :: {-# UNPACK #-} !Price
12
  , oVolume :: {-# UNPACK #-} !Volume
13
  , oTimeStamp :: {-# UNPACK #-} !TimeStamp
14
  }
15
  deriving (Eq, Show)
16

17
derivingUnbox
18
  "UUID"
19
  [t|UUID -> (Word64, Word64)|]
20
  [|UUID.toWords64|]
21
  [|(uncurry UUID.fromWords64)|]
22

23
derivingUnbox
24
  "Side"
25
  [t|Side -> Bool|]
26
  [|\case Buy -> True; Sell -> False|]
27
  [|\case True -> Buy; False -> Sell|]
28

29
derivingUnbox
30
  "Order"
31
  [t|Order -> (OrderId, Side, Price, Volume, TimeStamp)|]
32
  [|\o -> (oId o, oSide o, oPrice o, oVolume o, oTimeStamp o)|]
33
  [|\(i, s, p, v, t) -> Order i s p v t|]
34

35
data ODK
36
type OrderKey = Key ODK
37
type OrderMap = SlotMap ODK
38

39
data OrderBook s = OrderBook
40
  { obOrders :: !(OrderMap s Order)
41
  , obBids :: !(MutVar s (Map Price (Seq OrderKey)))
42
  , obAsks :: !(MutVar s (Map Price (Seq OrderKey)))
43
  , obRev :: !(HT.HashTable s OrderId OrderKey)
44
  }
45

46
data Trade = Trade {tradeBid :: OrderId, tradeAsk :: OrderId, tradePrice :: Price, tradeVolume :: Volume}

這裏使用了 Template Haskell 來生成 Unbox 實例。

1
insertOrderBook :: (PrimMonad m) => OrderBook (PrimState m) -> [Order] -> m ()
2
insertOrderBook OrderBook{..} os = do
3
  bids <- readMutVar obBids
4
  _asks <- readMutVar obAsks
5
  ks <- traverse (SM.insert obOrders) os
6
  let ts = bimap oPrice oSide . dup <$> os
7
      hts = firstF oId (zip os ks)
8
      (bids', asks') = foldl' g (bids, _asks) (zip ts ks)
9
  traverse_ (stToPrim . uncurry (HT.insert obRev)) hts
10
  writeMutVar obBids bids' *> writeMutVar obAsks asks'
11
 where
12
  f m (k, v) = insertWith (flip (<>)) k (one v) m
13
  g (m1, m2) ((k, s), v) = case s of
14
    Buy -> (f m1 (k, v), m2)
15
    Sell -> (m1, f m2 (k, v))
16

17
deleteOrderBook :: (PrimMonad m) => OrderBook (PrimState m) -> OrderId -> m ()
18
deleteOrderBook OrderBook{..} oid = stToPrim (HT.lookup obRev oid <* HT.delete obRev oid) >>= (`whenJust` SM.delete obOrders)

插入就是把單放進 SlotMap，拿到 Key 後去更新反向索引和價格索引；刪除這做了一箇 Rust 版同款的優化、衹刪了 SlotMap 和反向索引中的單，而價格索引想刪單需要 filter，這是低效的，直接不刪、攺爲每次撮合前先做清理、直至當前最優單確定存在。

1
cleanBids :: (PrimMonad m) => OrderBook (PrimState m) -> m ()
2
cleanBids OrderBook{..} = readMutVar obBids >>= go >>= writeMutVar obBids
3
 where
4
  go m = case maxViewWithKey m of
5
    Nothing -> pure m
6
    Just ((p, ks), rest) -> do
7
      ks' <- cleanSeq ks
8
      if null ks' then go rest else pure (insert p ks' rest)
9
  cleanSeq Empty = pure Empty
10
  cleanSeq ks@(k :<| rest) = do
11
    isValid <- SM.member k obOrders
12
    if isValid then pure ks else cleanSeq rest
13

14
cleanAsks :: (PrimMonad m) => OrderBook (PrimState m) -> m ()
15
cleanAsks OrderBook{..} = readMutVar obAsks >>= go >>= writeMutVar obAsks
16
 where
17
  go m = case minViewWithKey m of
18
    Nothing -> pure m
19
    Just ((p, ks), rest) -> do
20
      ks' <- cleanSeq ks
21
      if null ks' then go rest else pure (insert p ks' rest)
22
  cleanSeq Empty = pure Empty
23
  cleanSeq ks@(k :<| rest) = do
24
    isValid <- SM.member k obOrders
25
    if isValid then pure ks else cleanSeq rest
26

27
clean :: (PrimMonad m) => OrderBook (PrimState m) -> m ()
28
clean = liftA2 (*>) cleanBids cleanAsks

cleanBids 和 cleanAsks 比較重複，但想優化的話需要陞級 OrderBook 的結構，這裏就將就了。

1
tryMatch :: Order -> Order -> Maybe (Trade, Volume, Volume)
2
tryMatch oBid oAsk = do
3
  guard (oSide oBid == Buy && oSide oAsk == Sell)
4
  guard (oPrice oBid >= oPrice oAsk)
5
  let tradeVol = min (oVolume oBid) (oVolume oAsk)
6
      tradePrice = if oTimeStamp oAsk < oTimeStamp oBid then oPrice oAsk else oPrice oBid
7
      trade = Trade (oId oBid) (oId oAsk) tradePrice tradeVol
8
      bidLeft = oVolume oBid - tradeVol
9
      askLeft = oVolume oAsk - tradeVol
10
  pure (trade, bidLeft, askLeft)
11

12
tryTrade :: (PrimMonad m) => OrderBook (PrimState m) -> m (Maybe Trade)
13
tryTrade ob@OrderBook{..} = do
14
  clean ob
15
  bids <- readMutVar obBids
16
  asks_ <- readMutVar obAsks
17
  let keysToFetch = do
18
        (bid :<| _, _) <- maxView bids
19
        (_ask :<| _, _) <- minView asks_
20
        pure (bid, _ask)
21
  case keysToFetch of
22
    Nothing -> pure Nothing
23
    Just (bid, _ask) -> do
24
      mBidOrder <- SM.lookup obOrders bid
25
      mAskOrder <- SM.lookup obOrders _ask
26
      case join $ tryMatch <$> mBidOrder <*> mAskOrder of
27
        Nothing -> pure Nothing
28
        Just (trade, leftBid, leftAsk) -> do
29
          if leftBid > 0
30
            then SM.update (\o -> Just o{oVolume = leftBid}) bid obOrders
31
            else whenJust mBidOrder (deleteOrderBook ob . oId)
32
          if leftAsk > 0
33
            then SM.update (\o -> Just o{oVolume = leftAsk}) _ask obOrders
34
            else whenJust mAskOrder (deleteOrderBook ob . oId)
35
          pure (Just trade)
36

37
matchTrades :: (PrimMonad m) => OrderBook (PrimState m) -> m [Trade]
38
matchTrades book = go []
39
 where
40
  go acc = do
41
    mTrade <- tryTrade book
42
    case mTrade of
43
      Just trade -> go (trade : acc)
44
      Nothing -> pure (reverse acc)

tryMatch 是利用最優單算出撮合結果的純函數，tryTrade 負責從環境中讀數據竝修攺，注意刪除時不再需要手動修攺 Map。

完整實現如下。

1
{-# LANGUAGE LambdaCase #-}
2
{-# LANGUAGE MultiParamTypeClasses #-}
3
{-# LANGUAGE RecordWildCards #-}
4
{-# LANGUAGE TemplateHaskell #-}
5
{-# LANGUAGE TypeFamilies #-}
6
{-# LANGUAGE NoImplicitPrelude #-}
7
{-# OPTIONS_GHC -Wno-orphans #-}
8

9
module Trade where
10

11
import Control.Monad.Primitive (PrimMonad (PrimState), stToPrim)
12
import qualified Data.HashTable.ST.Basic as HT
13
import Data.Map.Strict (Map, insert, insertWith, maxView, maxViewWithKey, minView, minViewWithKey)
14
import Data.Primitive (MutVar, readMutVar, writeMutVar)
15
import Data.Sequence (Seq (..))
16
import Data.SlotMap (Key, SlotMap)
17
import qualified Data.SlotMap as SM
18
import Data.UUID (UUID)
19
import qualified Data.UUID as UUID
20
import Data.Vector.Unboxed.Deriving (derivingUnbox)
21
import Relude hiding (Map)
22
import Relude.Extra (dup, firstF)
23

24
type OrderId = UUID
25
type Price = Int
26
type Volume = Int
27
type TimeStamp = Int
28

29
data Side = Buy | Sell deriving (Eq, Show)
30

31
data Order = Order
32
  { oId :: {-# UNPACK #-} !OrderId
33
  , oSide :: !Side
34
  , oPrice :: {-# UNPACK #-} !Price
35
  , oVolume :: {-# UNPACK #-} !Volume
36
  , oTimeStamp :: {-# UNPACK #-} !TimeStamp
37
  }
38
  deriving (Eq, Show)
39

40
derivingUnbox
41
  "UUID"
42
  [t|UUID -> (Word64, Word64)|]
43
  [|UUID.toWords64|]
44
  [|(uncurry UUID.fromWords64)|]
45

46
derivingUnbox
47
  "Side"
48
  [t|Side -> Bool|]
49
  [|\case Buy -> True; Sell -> False|]
50
  [|\case True -> Buy; False -> Sell|]
51

52
derivingUnbox
53
  "Order"
54
  [t|Order -> (OrderId, Side, Price, Volume, TimeStamp)|]
55
  [|\o -> (oId o, oSide o, oPrice o, oVolume o, oTimeStamp o)|]
56
  [|\(i, s, p, v, t) -> Order i s p v t|]
57

58
data ODK
59
type OrderKey = Key ODK
60
type OrderMap = SlotMap ODK
61

62
data OrderBook s = OrderBook
63
  { obOrders :: !(OrderMap s Order)
64
  , obBids :: !(MutVar s (Map Price (Seq OrderKey)))
65
  , obAsks :: !(MutVar s (Map Price (Seq OrderKey)))
66
  , obRev :: !(HT.HashTable s OrderId OrderKey)
67
  }
68

69
data Trade = Trade {tradeBid :: OrderId, tradeAsk :: OrderId, tradePrice :: Price, tradeVolume :: Volume}
70

71
insertOrderBook :: (PrimMonad m) => OrderBook (PrimState m) -> [Order] -> m ()
72
insertOrderBook OrderBook{..} os = do
73
  bids <- readMutVar obBids
74
  _asks <- readMutVar obAsks
75
  ks <- traverse (SM.insert obOrders) os
76
  let ts = bimap oPrice oSide . dup <$> os
77
      hts = firstF oId (zip os ks)
78
      (bids', asks') = foldl' g (bids, _asks) (zip ts ks)
79
  traverse_ (stToPrim . uncurry (HT.insert obRev)) hts
80
  writeMutVar obBids bids' *> writeMutVar obAsks asks'
81
 where
82
  f m (k, v) = insertWith (flip (<>)) k (one v) m
83
  g (m1, m2) ((k, s), v) = case s of
84
    Buy -> (f m1 (k, v), m2)
85
    Sell -> (m1, f m2 (k, v))
86

87
deleteOrderBook :: (PrimMonad m) => OrderBook (PrimState m) -> OrderId -> m ()
88
deleteOrderBook OrderBook{..} oid = stToPrim (HT.lookup obRev oid <* HT.delete obRev oid) >>= (`whenJust` SM.delete obOrders)
89

90
cleanBids :: (PrimMonad m) => OrderBook (PrimState m) -> m ()
91
cleanBids OrderBook{..} = readMutVar obBids >>= go >>= writeMutVar obBids
92
 where
93
  go m = case maxViewWithKey m of
94
    Nothing -> pure m
95
    Just ((p, ks), rest) -> do
96
      ks' <- cleanSeq ks
97
      if null ks' then go rest else pure (insert p ks' rest)
98
  cleanSeq Empty = pure Empty
99
  cleanSeq ks@(k :<| rest) = do
100
    isValid <- SM.member k obOrders
101
    if isValid then pure ks else cleanSeq rest
102

103
cleanAsks :: (PrimMonad m) => OrderBook (PrimState m) -> m ()
104
cleanAsks OrderBook{..} = readMutVar obAsks >>= go >>= writeMutVar obAsks
105
 where
106
  go m = case minViewWithKey m of
107
    Nothing -> pure m
108
    Just ((p, ks), rest) -> do
109
      ks' <- cleanSeq ks
110
      if null ks' then go rest else pure (insert p ks' rest)
111
  cleanSeq Empty = pure Empty
112
  cleanSeq ks@(k :<| rest) = do
113
    isValid <- SM.member k obOrders
114
    if isValid then pure ks else cleanSeq rest
115

116
clean :: (PrimMonad m) => OrderBook (PrimState m) -> m ()
117
clean = liftA2 (*>) cleanBids cleanAsks
118

119
tryMatch :: Order -> Order -> Maybe (Trade, Volume, Volume)
120
tryMatch oBid oAsk = do
121
  guard (oSide oBid == Buy && oSide oAsk == Sell)
122
  guard (oPrice oBid >= oPrice oAsk)
123
  let tradeVol = min (oVolume oBid) (oVolume oAsk)
124
      tradePrice = if oTimeStamp oAsk < oTimeStamp oBid then oPrice oAsk else oPrice oBid
125
      trade = Trade (oId oBid) (oId oAsk) tradePrice tradeVol
126
      bidLeft = oVolume oBid - tradeVol
127
      askLeft = oVolume oAsk - tradeVol
128
  pure (trade, bidLeft, askLeft)
129

130
tryTrade :: (PrimMonad m) => OrderBook (PrimState m) -> m (Maybe Trade)
131
tryTrade ob@OrderBook{..} = do
132
  clean ob
133
  bids <- readMutVar obBids
134
  asks_ <- readMutVar obAsks
135
  let keysToFetch = do
136
        (bid :<| _, _) <- maxView bids
137
        (_ask :<| _, _) <- minView asks_
138
        pure (bid, _ask)
139
  case keysToFetch of
140
    Nothing -> pure Nothing
141
    Just (bid, _ask) -> do
142
      mBidOrder <- SM.lookup obOrders bid
143
      mAskOrder <- SM.lookup obOrders _ask
144
      case join $ tryMatch <$> mBidOrder <*> mAskOrder of
145
        Nothing -> pure Nothing
146
        Just (trade, leftBid, leftAsk) -> do
147
          if leftBid > 0
148
            then SM.update (\o -> Just o{oVolume = leftBid}) bid obOrders
149
            else whenJust mBidOrder (deleteOrderBook ob . oId)
150
          if leftAsk > 0
151
            then SM.update (\o -> Just o{oVolume = leftAsk}) _ask obOrders
152
            else whenJust mAskOrder (deleteOrderBook ob . oId)
153
          pure (Just trade)
154

155
matchTrades :: (PrimMonad m) => OrderBook (PrimState m) -> m [Trade]
156
matchTrades book = go []
157
 where
158
  go acc = do
159
    mTrade <- tryTrade book
160
    case mTrade of
161
      Just trade -> go (trade : acc)
162
      Nothing -> pure (reverse acc)

Benchmark#

這裏 Rust 和 Haskell 在測試框架上的差距不可抹平，但測試內容盡力做到一致。

時間方面：

1
- rust
2
  - insert ≈ 36~37 Melem/s
3
  - matching ≈ 22 Melem/s
4
  - mixed ≈ 10~11 Melem/s
5
- immutable-haskell
6
  - insert ≈ 12 Melem/s
7
  - matching ≈ 8.4 Melem/s
8
  - mixed ≈ 3.8 Melem/s
9
- mutable-haskell
10
  - insert ≈ 1.0~1.1 Melem/s
11
  - matching ≈ 0.57 Melem/s
12
  - mixed ≈ 0.34 Melem/s

分配方面：

1
- mutable
2
  - heap allocated: 94.3 GB
3
  - GC time: 9.22 s
4
- immutable
5
  - heap allocated: 8.54 GB
6
  - GC time: 0.95 s

可㕥看到，我們寫的新版本的性能足足是原版的……不到二十分之一倍！反倒是原來的版本、性能大概是 Rust 版本的三分之一，但需要注意 matching 測的是撮合性能，原版衹計算竝修攺了單簿、沒有管反向索引，但加上應該也不會掉多少。

這箇結果我是很不服的，但從 GC 上可㕥看到一些問題，可變版本分配了足足 94.3 GB 的內存，是原來的 10 倍左右，問題出在哪呢？我查看了詳细的數據、SlotMap 相關的調用分配得非常重。

一箇可能的方向是 SlotMap 內部使用了 SOA 表示（也就是列優先），而我們取總是在按行取，這導致了 Order 在不斷被重建、銷毁，而原版雖然是 AOS 表示，但拿 Order 衹是拿箇指鍼。想要優化掉這箇問題需要使用更複雜的內部實現，比如讓 SlotMap 支持直接拿某箇字段、而不是每次都按行拿整箇 Order。

另一箇可能的方向是我們在混用可變和不可變的數據結構，比如 Map 和 Seq，它們本不必在 MutVar 中，把不可變結構套在可變里、GHC可能無法充分地優化、同時又不可避免不可變自身的分配，㒳頭不討好。想要優化，可能需要把 Map 攺爲數組（價格的 Range 本身是有限的）、Seq 和 SlotMap 融合、讓 Map 存一箇雙鏈表的頭，但這樣做攺動太大、而且就算眞有性能上的提陞，也難㕥證明是 SlotMap 的效果。

Conclusion#

不管怎樣，Haskell 裏我們確有手段寫出像系統級語言一樣的低層次數據結構，這證明了語言本身的能力。

但在實際應用中，GHC 自身已經能爲性能做一些兜底，拍腦袋地混用其它語言的思路未必能帶來好處、反而更可能喫力不討好，不要混用高低層次的表示、優化時把熱點整體降格到更低層次纔會有用。

~~更好的辦法是把快速原型翻譯到 Rust，就已經白嫖到 3 倍性能啦！再用 FFI 調用就好啦！~~