spica/cache.ts

Supervisor, Coroutine, Channel, select, AtomicPromise, Cancellation, Cache, List, Queue, Stack, and some utils.

import { max, min } from './alias';
import { now } from './chrono';
import { IterableDict } from './dict';
import { List } from './clist';
import { Heap } from './heap';
import { extend } from './assign';

// Dual Window Cache

/*
LFU論理寿命：
小容量で小効果のみにつきLRU下限で代替し無効化。

LRU下限：
小容量で大効果につき採用。

統計解像度：
効果ないが検証用に残置。

サイクリックスィープ：
LRU汚染対策。
大効果につき採用。

履歴標本：
大効果につき採用。

*/

/*
比較検討

LRU:
低性能。

CLOCK:
非常に高速かつLRUよりややヒット率が高い。
容量制限付きマップなどヒット率より速度を優先する場合に最適。
ただし最悪時間計算量O(n)。

CAR/CDW(CLOCK+DWC)/CLOCK-Pro:
最悪時間計算量O(n)。
CARとCLOCK-Proは合計2倍の履歴を持つ。

ARC:
キャッシュサイズの2倍のキーを保持する。
すでにARCに近いヒット率を達成しているため2倍のキーサイズとリスト操作による
空間効率と速度の低下を正当化できるワークロードでのみ優位性がある。
Loop耐性が欠如しておりGLIやDS1などLoop耐性を要するワークロードではDWCが大幅に優れている。

DWC:
時間空間ともに定数計算量かつすべての基本的耐性を持つ。
情報量(履歴)の不足を補うため全体的に統計精度への依存度が上がっており標本サイズが小さくなるほど
情報量(標本に含まれるシグナルの比率)の加速的減少と統計精度の低下により性能低下しやすくなる。

LIRS:
キャッシュサイズの3倍以上のキーを保持する。
LIRS論文全著者を共著者とするLIRS2論文筆頭著者の実装によると最大2500倍、事実上無制限。
にもかかわらずARCより安定して十分に性能が高いとは言えないうえ大幅に性能の劣るケースも散見される。
履歴に現実的な上限を与えた場合の実際の性能が不明でありまともな比較資料がない。
キーを無制限に走査するGC的処理があるためキャッシュサイズに比例して大きな遅延が入る可能性が上がり
遅延が許容できない水準に達する可能性がある。
まともなアルゴリズムではない。

TinyLFU:
TinyLFUはキーの数値またはポインタのアドレスでブルームフィルタを生成するためJavaScriptでは
文字列やオブジェクトなどからアドレスを取得または代替値を高速に割り当てる方法がなく汎用的に使用できない。
またポインタのアドレスを使用する場合もアドレスの再利用により偽陽性および偽陰性が生じヒット率が低下する
可能性がありどのような状況でどの程度低下するかは未知数。
OSや言語のメモリ割り当て方法によってはメモリアドレスの頻繁な再利用によりヒット率が著しく低下する可能性
があり信頼性が低い。
ベンチマークに使用されているブロックアクセスにおいても書き込み範囲のアドレスにおいて同じ問題が生じる
はずでありブルームフィルタから減算するとしないとにかかわらず精度が低下するが公式実装であるCaffeine
においてもこの精度低下が生じない方法で測定(書き込み範囲はキャッシュに追加または無効化されなければ
ならないはずだが単に処理が省略されている)されているため書き込みを含むワークロードの公表されている
ヒット率は誤った測定方法による不正確なものである疑いがある。
オーバーヘッドが大きくメモ化など同期処理に耐える速度を要件とする用途には適さないと思われる。
ブルームフィルタが削除操作不可であるため一定期間内のキャッシュの任意または有効期限超過による
削除数に比例して性能が低下する。
キャッシュサイズ分の挿入ごとにブルームフィルタがリセットのため全走査されるため
キャッシュサイズに比例した大きさの遅延が入る。
TinyLFUはバーストアクセスに脆弱であるため基本的にW-TinyLFU以外選択肢に入れるべきではない。

https://github.com/ben-manes/caffeine/wiki/Efficiency

*/

/*
# lru-cacheの最適化分析

非常に高いヒット率では素朴な実装より高速化するがそれ以外の場合は低速化する。
この最適化により素朴な実装より速くなる範囲が非常に狭く全体的には低速化している。
巨大な配列を複数要するため空間オーバーヘッドも大きく消費メモリ基準では容量とヒット率が低下する。

## Map値の数値化

Mapは値が数値の場合setが2倍高速化される。
getは変わらないため読み取り主体の場合効果が低い。

## インデクスアクセス化

すべての状態を状態別の配列に格納しインデクスアクセスに変換することで高速化している。
DWCはこの高速化を行っても状態数の多さに比例して増加したオーバーヘッドに相殺され効果を得られない。

## TypedArray

インデクスアクセス化にTypedArrayを使うことで配列の書き込みが2倍高速化される。
これによりリスト操作が高速化されるがもともと高速なため全体的な寄与は小さいと思われる。

*/

class Entry<K, V> implements List.Node {
  constructor(
    public key: K,
    public value: V,
    public size: number,
    public expiration: number,
  ) {
  }
  public partition: 'LRU' | 'LFU' = 'LRU';
  public affiliation: 'LRU' | 'LFU' = 'LRU';
  public enode?: Heap.Node<Entry<K, V>, number> = undefined;
  public next?: this = undefined;
  public prev?: this = undefined;
}

function segment(expiration: number): number {
  return expiration >>> 4;
}

export namespace Cache {
  export interface Options<K, V = undefined> {
    // Max entries.
    // Range: 1-
    readonly capacity?: number;
    // Max costs.
    // Range: L-
    readonly resource?: number;
    readonly age?: number;
    readonly eagerExpiration?: boolean;
    // WARNING: Don't add any new key in disposing.
    readonly disposer?: (value: V, key: K) => void;
    readonly capture?: {
      readonly delete?: boolean;
      readonly clear?: boolean;
    };
    // Mainly for experiments.
    // Min LRU ratio.
    // Range: 0-100
    readonly window?: number;
    // Sample ratio of LRU in LFU.
    // Range: 0-100
    readonly sample?: number;
    readonly sweep?: {
      readonly threshold?: number;
      readonly window?: number;
      readonly room?: number;
      readonly ground?: number;
      readonly interval?: number;
      readonly slide?: number;
    };
  }
}
export class Cache<K, V> implements IterableDict<K, V> {
  constructor(capacity: number, sweep?: boolean);
  constructor(capacity: number, opts?: Cache.Options<K, V>);
  constructor(opts: Cache.Options<K, V>);
  constructor(
    capacity: number | Cache.Options<K, V>,
    opts: boolean | Cache.Options<K, V> = {},
  ) {
    switch (opts) {
      case true:
        opts = {};
        break;
      case false:
        opts = {
          sweep: {
            threshold: 0,
          },
        };
        break;
    }
    if (typeof capacity === 'object') {
      opts = capacity;
      capacity = opts.capacity ?? 0;
    }
    const settings = extend(this.settings, opts, {
      capacity,
    });
    this.capacity = capacity = settings.capacity!;
    assert(capacity > 0);
    this.window = capacity * settings.window! / 100 >>> 0 || 1;
    this.partition = capacity - this.window;
    this.resource = settings.resource! ?? capacity;
    this.sample = settings.sample!;
    this.age = settings.age!;
    if (settings.eagerExpiration) {
      this.expirations = new Heap(Heap.min, { stable: false });
    }
    this.sweeper = settings.sweep?.threshold! > 0
      ? new Sweeper(this.LRU, this as any, {
          threshold: settings.sweep!.threshold!,
          window: settings.sweep!.window!,
          room: settings.sweep!.room!,
          ground: settings.sweep!.ground!,
          interval: settings.sweep!.interval!,
          slide: settings.sweep!.slide!,
        })
      : undefined;
    this.disposer = settings.disposer!;
    assert(settings.resource === opts.resource);
  }
  private readonly settings: Cache.Options<K, V> = {
    capacity: 0,
    window: 1,
    sample: 1,
    age: Infinity,
    eagerExpiration: false,
    capture: {
      delete: true,
      clear: true,
    },
    sweep: {
      threshold: 20,
      window: 1,
      room: 50,
      ground: 90,
      interval: 1,
      slide: 2,
    },
  };
  private capacity: number;
  private partition: number;
  private window: number;
  private dict = new Map<K, Entry<K, V>>();
  private LRU = new List<Entry<K, V>>();
  private LFU = new List<Entry<K, V>>();
  private overlapLRU = 0;
  private overlapLFU = 0;
  private expiration = false;
  private readonly age: number;
  private readonly expirations?: Heap<Entry<K, V>, number>;
  public get length(): number {
    const { LRU, LFU } = this;
    return LRU.length + LFU.length;
  }
  private resource: number;
  private $size = 0;
  public get size(): number {
    return this.$size;
  }
  private readonly disposer?: (value: V, key: K) => void;
  public resize(capacity: number, resource?: number): void {
    assert(capacity > 0);
    this.partition = this.partition / this.capacity * capacity >>> 0;
    this.capacity = capacity;
    const { settings } = this;
    this.window = capacity * settings.window! / 100 >>> 0 || 1;
    this.resource = resource ?? settings.resource ?? capacity;
    this.sweeper?.resize();
    this.ensure(0);
  }
  public clear(): void {
    const { LRU, LFU } = this;
    this.$size = 0;
    this.partition = this.capacity - this.window;
    this.injection = 100;
    this.declination = 1;
    this.dict = new Map();
    this.LRU = new List();
    this.LFU = new List();
    this.overlapLRU = 0;
    this.overlapLFU = 0;
    this.expiration = false;
    this.expirations?.clear();
    this.sweeper?.clear();
    this.sweeper?.replace(this.LRU);
    if (!this.disposer || !this.settings.capture!.clear) return;
    for (const { key, value } of LRU) {
      this.disposer(value, key);
    }
    for (const { key, value } of LFU) {
      this.disposer(value, key);
    }
  }
  private evict$(entry: Entry<K, V>, callback: boolean): void {
    assert(this.LRU.length + this.LFU.length === this.dict.size);
    //assert(this.dict.size <= this.capacity);
    assert(entry.next);
    this.overlap(entry, true);
    assert(this.overlapLRU >= 0);
    assert(this.overlapLFU >= 0);
    if (entry.enode !== undefined) {
      this.expirations!.delete(entry.enode);
      entry.enode = undefined;
    }
    entry.partition === 'LRU'
      ? this.LRU.delete(entry)
      : this.LFU.delete(entry);
    assert(this.LRU.length + this.LFU.length === this.dict.size - 1);
    this.dict.delete(entry.key);
    assert(this.LRU.length + this.LFU.length === this.dict.size);
    //assert(this.dict.size <= this.capacity);
    this.$size -= entry.size;
    callback && this.disposer?.(entry.value, entry.key);
  }
  private readonly sample: number;
  private get overflow(): boolean {
    return this.overlapLRU * 100 > this.LFU.length * this.sample;
  }
  private overlap(entry: Entry<K, V>, eviction = false): Entry<K, V> {
    if (entry.partition === 'LRU') {
      if (entry.affiliation === 'LRU') {
        if (eviction) return entry;
        ++this.overlapLRU;
        assert(this.overlapLRU - 1 <= this.LFU.length);
      }
      else {
        --this.overlapLFU;
        assert(this.overlapLFU >= 0);
      }
    }
    else {
      if (entry.affiliation === 'LFU') {
        if (eviction) return entry;
        ++this.overlapLFU;
        assert(this.overlapLFU - 1 <= this.LRU.length);
      }
      else {
        --this.overlapLRU;
        assert(this.overlapLRU >= 0);
        if (this.declination !== 1 && !this.overflow) {
          this.declination = 1;
        }
      }
    }
    return entry;
  }
  private readonly sweeper?: Sweeper<List<Entry<K, V>>>;
  private injection = 100;
  private declination = 1;
  // Update and deletion are reentrant but addition is not.
  private ensure(margin: number, target?: Entry<K, V>, capture = false): Entry<K, V> | undefined {
    let size = target?.size ?? 0;
    assert(margin - size <= this.resource || !capture);
    const { LRU, LFU } = this;
    while (this.size + margin - size > this.resource) {
      assert(this.length >= 1 + +!!target);
      this.injection = min(this.injection + this.sample, 100 * this.declination);
      let victim = this.expirations?.peek()?.value;
      if (victim !== undefined && victim !== target && victim.expiration < now()) {
      }
      else if (LRU.length === 0) {
        assert(LFU.head!.prev);
        victim = LFU.head!.prev!;
        victim = victim !== target
          ? victim
          : victim.prev!;
      }
      else {
        assert(LRU.head!.prev);
        if (LRU.length >= this.window && this.injection === 100 * this.declination) {
          const entry = LRU.head!.prev!;
          if (entry.affiliation === 'LRU') {
            LRU.delete(entry);
            LFU.unshift(this.overlap(entry));
            entry.partition = 'LFU';
            this.injection = 0;
            this.declination = !this.overflow
              ? 1
              : 8;
          }
        }
        if (this.sweeper?.isActive()) {
          this.sweeper.sweep();
        }
        if (LFU.length > this.partition) {
          assert(LFU.head!.prev);
          let entry = LFU.head!.prev;
          entry = entry !== target
            ? entry
            : LFU.length !== 1
              ? entry!.prev
              : undefined;
          if (entry !== undefined) {
            assert(entry !== target);
            assert(entry.partition === 'LFU');
            LFU.delete(entry);
            LRU.unshift(this.overlap(entry));
            entry.partition = 'LRU';
          }
        }
        if (LRU.length !== 0) {
          victim = LRU.head!.prev!;
          victim = victim !== target
            ? victim
            : LRU.length !== 1
              ? victim.prev
              : undefined;
          assert(victim || target === LRU.head!.prev);
          if (capture && target === undefined && victim !== undefined) {
            assert(victim === LRU.head!.prev);
            target = victim;
            size = target.size;
            continue;
          }
          victim ??= LFU.head!.prev!;
        }
        else {
          assert(!target || LFU.length >= 2);
          victim = LFU.head!.prev!;
          victim = victim !== target
            ? victim
            : victim.prev!;
        }
      }
      assert(victim !== target);
      assert(this.dict.has(victim.key));
      this.evict$(victim, true);
      target = target?.next && target;
      size = target?.size ?? 0;
    }
    assert(!target || target.next);
    return target;
  }
  private update(entry: Entry<K, V>, key: K, value: V, size: number, expiration: number): void {
    assert(entry.next);
    const key$ = entry.key;
    const value$ = entry.value;
    entry.key = key;
    entry.value = value;
    this.$size += size - entry.size;
    assert(0 < this.size && this.size <= this.resource);
    entry.size = size;
    entry.expiration = expiration;
    if (this.expiration && this.expirations !== undefined && expiration !== Infinity) {
      entry.enode !== undefined
        ? this.expirations.update(entry.enode, segment(expiration))
        : entry.enode = this.expirations.insert(entry, segment(expiration));
      assert(this.expirations.length <= this.length);
    }
    else if (entry.enode !== undefined) {
      this.expirations!.delete(entry.enode);
      entry.enode = undefined;
    }
    assert(this.LRU.length + this.LFU.length === this.dict.size);
    this.disposer?.(value$, key$);
  }
  private replace(entry: Entry<K, V>): void {
    const { LRU, LFU } = this;
    if (entry.partition === 'LRU') {
      if (entry.affiliation === 'LRU') {
        // 消しても敵対的パターンへの耐性は下がらないがJumpパターンでの回復力が下がる。
        // 消したほうがヒット率が上がりそうだがベンチマーク結果はほぼ変わらないので残しておく。
        if (entry === LRU.head && this.sweeper?.isActive() !== true) return;
        entry.affiliation = 'LFU';
      }
      else {
        assert(this.overlapLFU > 0);
        const delta = LFU.length <= this.partition
          ? max(LRU.length / (LFU.length || 1) * max(this.overlapLRU / this.overlapLFU, 1) | 0, 1)
          : 0;
        assert(delta >= 0);
        this.partition = min(this.partition + delta, this.capacity - this.window);
        this.overlap(entry);
      }
      assert(this.LFU.length < this.capacity);
      LRU.delete(entry);
      LFU.unshift(entry);
      entry.partition = 'LFU';
    }
    else {
      if (entry.affiliation === 'LFU') {
      }
      else {
        assert(this.overlapLRU > 0);
        const delta = LRU.length <= this.capacity - this.partition
          ? max(LFU.length / (LRU.length || 1) * max(this.overlapLFU / this.overlapLRU, 1) | 0, 1)
          : 0;
        assert(delta >= 0);
        this.partition = max(this.partition - delta, 0);
        this.overlap(entry);
        entry.affiliation = 'LFU';
      }
      if (entry === LFU.head) return;
      LFU.delete(entry);
      LFU.unshift(entry);
    }
  }
  private validate(size: number, age: number): boolean {
    if (1 <= age) {
      this.expiration ||= age !== Infinity;
    }
    else {
      return false;
    }
    return 1 <= size && size <= this.resource;
  }
  public evict(): [K, V] | undefined {
    const victim = this.LRU.last ?? this.LFU.last;
    if (victim === undefined) return;
    this.evict$(victim, true);
    return [victim.key, victim.value];
  }
  public add(key: K, value: V, opts?: { size?: number; age?: number; }, victim?: Entry<K, V>): boolean;
  public add(this: Cache<K, undefined>, key: K, value?: V, opts?: { size?: number; age?: number; }, victim?: Entry<K, V>): boolean;
  public add(key: K, value: V, opts?: { size?: number; age?: number; }, victim?: Entry<K, V>): boolean {
    const { size = 1, age = this.age } = opts ?? {};
    if (opts !== undefined && !this.validate(size, age)) {
      this.disposer?.(value, key);
      return false;
    }

    assert(!this.dict.has(key));
    const { LRU } = this;
    const expiration = age === Infinity
      ? age
      : now() + age;
    victim = this.ensure(size, victim, true);
    // Note that the key will be duplicate if the key is evicted and added again in disposing.
    if (victim !== undefined) {
      assert(victim === LRU.head!.prev);
      victim.affiliation === 'LFU' && --this.overlapLFU;
      assert(this.overlapLFU >= 0);
      this.dict.delete(victim.key);
      this.dict.set(key, victim);
      assert(this.LRU.length + this.LFU.length === this.dict.size);
      assert(this.dict.size <= this.capacity);
      victim.affiliation = 'LRU';
      LRU.head = victim;
      this.update(victim, key, value, size, expiration);
      return true;
    }

    assert(!this.dict.has(key));
    assert(LRU.length !== this.capacity);
    this.$size += size;
    assert(0 < this.size && this.size <= this.resource);
    const entry = new Entry(key, value, size, expiration);
    LRU.unshift(entry);
    this.dict.set(key, entry);
    assert(this.LRU.length + this.LFU.length === this.dict.size);
    assert(this.dict.size <= this.capacity);
    if (this.expiration && this.expirations !== undefined && expiration !== Infinity) {
      entry.enode = this.expirations.insert(entry, segment(expiration));
      assert(this.expirations.length <= this.length);
    }
    return true;
  }
  public put(key: K, value: V, opts?: { size?: number; age?: number; }): boolean;
  public put(this: Cache<K, undefined>, key: K, value?: V, opts?: { size?: number; age?: number; }): boolean;
  public put(key: K, value: V, opts?: { size?: number; age?: number; }): boolean {
    const { size = 1, age = this.age } = opts ?? {};
    if (opts !== undefined && !this.validate(size, age)) {
      this.disposer?.(value, key);
      return false;
    }

    const entry = this.dict.get(key);
    const match = entry !== undefined;
    const victim = this.ensure(size, entry, true);
    // Note that the key of entry or victim may be changed if the new key is set in disposing.
    if (match && entry === victim) {
      const expiration = age === Infinity
        ? age
        : now() + age;
      this.update(entry, key, value, size, expiration);
      return match;
    }

    this.add(key, value, { size, age }, victim);
    return match;
  }
  public set(key: K, value: V, opts?: { size?: number; age?: number; }): this;
  public set(this: Cache<K, undefined>, key: K, value?: V, opts?: { size?: number; age?: number; }): this;
  public set(key: K, value: V, opts?: { size?: number; age?: number; }): this {
    this.put(key, value, opts);
    return this;
  }
  public get(key: K): V | undefined {
    const entry = this.dict.get(key);
    if (entry === undefined) {
      this.sweeper?.miss();
      return;
    }
    if (this.expiration && entry.expiration !== Infinity && entry.expiration < now()) {
      this.sweeper?.miss();
      this.evict$(entry, true);
      return;
    }
    this.sweeper?.hit();
    this.replace(entry);
    return entry.value;
  }
  public has(key: K): boolean {
    const entry = this.dict.get(key);
    if (entry === undefined) return false;
    if (this.expiration && entry.expiration !== Infinity && entry.expiration < now()) {
      this.evict$(entry, true);
      return false;
    }
    return true;
  }
  public delete(key: K): boolean {
    const entry = this.dict.get(key);
    if (entry === undefined) return false;
    this.evict$(entry, this.settings.capture!.delete === true);
    return true;
  }
  public *[Symbol.iterator](): Iterator<[K, V], undefined, undefined> {
    for (const { key, value } of this.LRU) {
      yield [key, value];
    }
    for (const { key, value } of this.LFU) {
      yield [key, value];
    }
  }
}

// Transitive Wide MRU with Cyclic Replacement
class Sweeper<T extends List<Entry<unknown, unknown>>> {
  constructor(
    private target: T,
    private readonly context: {
      readonly capacity: number;
      readonly partition: number;
    },
    private readonly config: {
      readonly threshold: number;
      readonly ground: number;
      readonly window: number;
      readonly room: number;
      readonly interval: number;
      readonly slide: number;
    },
  ) {
  }
  private get window(): number {
    const window = this.context.capacity * this.config.window / 100 >>> 0 || 1;
    return max(window, min(this.target.length >>> 2, window << 3));
  }
  private get interval(): number {
    const interval = this.context.capacity * this.config.interval / 100;
    return max(interval, min(this.window >>> 1, this.target.length >>> 2));
  }
  private get room(): number {
    return this.context.capacity * this.config.room / 100 >>> 0 || 1;
  }
  public resize(): void {
    this.currWindowHits + this.currWindowMisses >= this.window && this.slideWindow();
    this.currRoomHits + this.currRoomMisses >= this.room && this.slideRoom();
    this.update();
  }
  public clear(): void {
    this.active = true;
    this.processing = true;
    this.reset();
    assert(!this.processing);
    this.slideWindow();
    this.slideWindow();
    this.slideRoom();
    this.slideRoom();
    assert(!this.isActive());
  }
  public replace(target: T): void {
    this.target = target;
  }
  private currWindowHits = 0;
  private currWindowMisses = 0;
  private prevWindowHits = 0;
  private prevWindowMisses = 0;
  private slideWindow(): void {
    this.prevWindowHits = this.currWindowHits;
    this.prevWindowMisses = this.currWindowMisses;
    this.currWindowHits = 0;
    this.currWindowMisses = 0;
  }
  private currRoomHits = 0;
  private currRoomMisses = 0;
  private prevRoomHits = 0;
  private prevRoomMisses = 0;
  private slideRoom(): void {
    this.prevRoomHits = this.currRoomHits;
    this.prevRoomMisses = this.currRoomMisses;
    this.currRoomHits = 0;
    this.currRoomMisses = 0;
  }
  public hit(): void {
    ++this.currWindowHits + this.currWindowMisses >= this.window && this.slideWindow();
    !this.active && ++this.currRoomHits + this.currRoomMisses >= this.room && this.slideRoom();
    this.update();
    this.processing && !this.active && this.reset();
  }
  public miss(): void {
    this.currWindowHits + ++this.currWindowMisses >= this.window && this.slideWindow();
    !this.active && this.currRoomHits + ++this.currRoomMisses >= this.room && this.slideRoom();
    this.update();
  }
  private active = true;
  private update(): void {
    const ratio = this.ratioWindow();
    this.active =
      ratio < this.config.threshold * 100 ||
      ratio < this.ratioRoom() * this.context.partition / this.context.capacity * this.config.ground / 100;
  }
  public isActive(): boolean {
    return this.active;
  }
  private ratioWindow(): number {
    return ratio(
      this.window,
      this.currWindowHits,
      this.prevWindowHits,
      this.currWindowMisses,
      this.prevWindowMisses,
      0);
  }
  private ratioRoom(): number {
    return ratio(
      this.room,
      this.currRoomHits,
      this.prevRoomHits,
      this.currRoomMisses,
      this.prevRoomMisses,
      0);
  }
  private processing = false;
  private direction = true;
  private initiation = true;
  private back = 0;
  private advance = 0;
  public sweep(): -1 | 0 | 1 {
    const { target } = this;
    if (target.length === 0) return 1;
    this.processing ||= true;
    if (this.direction) {
      if (this.back < 1) {
        this.back += this.interval;
      }
    }
    else {
      if (this.advance < 1) {
        this.advance += this.interval * (100 - this.config.slide) / 100;
      }
    }
    assert(this.back > 0 || this.advance > 0);
    if (this.back >= 1) {
      assert(this.direction === true);
      if (--this.back < 1) {
        this.direction = false;
      }
      if (this.initiation) {
        this.initiation = false;
        target.head = target.head!.next;
        return 0;
      }
      else {
        target.head = target.head!.next!.next;
        return -1;
      }
    }
    else if (this.advance >= 1) {
      assert(this.direction === false);
      assert(!this.initiation);
      if (--this.advance < 1) {
        this.direction = true;
      }
      return 1;
    }
    else {
      this.direction = !this.direction;
      target.head = target.head!.next;
      return 0;
    }
  }
  private reset(): void {
    assert(this.processing);
    assert(!this.active);
    this.processing = false;
    this.direction = true;
    this.initiation = true;
    this.back = 0;
    this.advance = 0;
  }
}

function ratio(
  window: number,
  currHits: number,
  prevHits: number,
  currMisses: number,
  prevMisses: number,
  offset: number,
): number {
  const currTotal = currHits + currMisses;
  const prevTotal = prevHits + prevMisses;
  assert(currTotal <= window);
  const prevRate = prevHits && prevHits * 100 / prevTotal;
  const currRatio = currTotal * 100 / window - offset;
  if (currRatio <= 0) return prevRate * 100 | 0;
  const currRate = currHits && currHits * 100 / currTotal;
  if (prevTotal === 0) return currRate * 100 | 0;
  const prevRatio = 100 - currRatio;
  return currRate * currRatio + prevRate * prevRatio | 0;
}
function ratio2(
  window: number,
  targets: readonly number[],
  remains: readonly number[],
  offset: number,
): number {
  assert(targets.length >= 2);
  assert(targets.length === remains.length);
  let total = 0;
  let hits = 0;
  let ratio = 100;
  for (let len = targets.length, i = 0; i < len; ++i) {
    const subtotal = targets[i] + remains[i];
    if (subtotal === 0) continue;
    offset = i + 1 === len ? 0 : offset;
    const subratio = min(subtotal * 100 / window, ratio) - offset;
    offset = offset && subratio < 0 ? -subratio : 0;
    if (subratio <= 0) continue;
    const r = window * subratio / subtotal;
    total += subtotal * r;
    hits += targets[i] * r;
    ratio -= subratio;
    if (ratio <= 0) break;
  }
  return hits * 10000 / total | 0;
}
assert(ratio(10, 4, 0, 6, 0, 0) === 4000);
assert(ratio(10, 0, 4, 0, 6, 0) === 4000);
assert(ratio(10, 1, 4, 4, 6, 0) === 3000);
assert(ratio(10, 0, 4, 0, 6, 5) === 4000);
assert(ratio(10, 1, 2, 4, 8, 5) === 2000);
assert(ratio(10, 2, 2, 3, 8, 5) === 2900);
assert(ratio(10, 2, 0, 3, 0, 0) === 4000);
assert(ratio2(10, [4, 0], [6, 0], 0) === 4000);
assert(ratio2(10, [0, 4], [0, 6], 0) === 4000);
assert(ratio2(10, [1, 4], [4, 6], 0) === 3000);
assert(ratio2(10, [0, 4], [0, 6], 5) === 4000);
assert(ratio2(10, [1, 2], [4, 8], 5) === 2000);
assert(ratio2(10, [2, 2], [3, 8], 5) === 2900);
assert(ratio2(10, [2, 0], [3, 0], 0) === 4000);

// OLTPのような流出の多いワークロードで1%未満上がる効果しかない。
// 流出軽減以外の効果はないと思われる。
// 速度も落ちるので不採用。
// @ts-ignore
class TLRU<T extends Entry<K, V>> {
  constructor(
    private readonly demotion: number = 2,
    private readonly window: number = 0,
    private readonly retrial: boolean = true,
  ) {
  }
  public get head(): T | undefined {
    return this.list.head;
  }
  public set head(entry: T | undefined) {
    this.list.head = entry;
  }
  public get victim(): T | undefined {
    return this.handV ?? this.list.last;
  }
  private readonly list = new List<T>();
  private handV?: T = undefined;
  private handG?: T = undefined;
  private count = 0;
  public get length(): number {
    return this.list.length;
  }
  public get size(): number {
    return this.list.length;
  }
  private extend(): void {
    const { list } = this;
    this.count = -max(
      //list.length * this.demotion / 100 / max(this.count / list.length * this.demotion, 1) | 0,
      (list.length - this.count) * this.demotion / 100 | 0,
      list.length * this.window / 100 - this.count | 0,
      this.demotion && 1);
    assert(this.count <= 0);
  }
  public unshift(entry: T): void {
    const { list } = this;
    this.handV ??= list.last;
    if (this.handV === this.handG && this.count >= 0) {
      this.extend();
    }
    list.unshift(entry);
    this.hit(entry);
  }
  public hit(entry: T): void {
    this.handG ??= entry;
  }
  public add(entry: T): boolean {
    const { list } = this;
    this.handV ??= list.last;
    if (this.handV === this.handG && this.count >= 0) {
      this.extend();
    }
    // 非延命
    if (this.count >= 0 || this.handV === list.last || !this.retrial) {
      list.insert(entry, this.handV?.next);
      this.handV ??= list.last!;
    }
    // 延命
    else {
      assert(this.count < 0);
      assert(this.handG !== undefined);
      if (this.handG !== list.head) {
        list.insert(entry, this.handG);
      }
      else {
        list.unshift(entry);
      }
      this.handV = entry;
      this.handG = entry;
    }
    if (this.count < 0) {
      assert(this.handV === this.handG);
      assert(this.handG = this.handG!);
      this.handG = this.handG !== list.head
        ? this.handG.prev
        : undefined;
    }
    if (this.handV !== this.handG) {
      this.handV = this.handV.prev;
    }
    if (this.handV === list.last || this.count === -1) {
      this.handV = list.last;
      this.count = 0;
    }
    else {
      ++this.count;
    }
    assert(this.count >= 0 || this.handV === this.handG);
    return true;
  }
  private escape(entry: T): void {
    const { list } = this;
    assert(list.length !== 0);
    if (list.length === 1) {
      this.handV = undefined;
      this.handG = undefined;
      this.count = 0;
      return;
    }
    if (entry === this.handV) {
      this.handV = this.handV.prev;
    }
    if (entry === this.handG) {
      this.handG = this.handG.prev;
    }
  }
  public delete(entry: T): void {
    const { list } = this;
    if (entry === undefined) return;
    this.escape(entry);
    list.delete(entry);
    assert(entry !== this.handV);
    assert(entry !== this.handG);
  }
  public clear(): void {
    this.list.clear();
    this.handV = undefined;
    this.handG = undefined;
    this.count = 0;
  }
  public *[Symbol.iterator](): Iterator<T, undefined, undefined> {
    for (const entry of this.list) {
      yield entry;
    }
  }
}