wren/val Public Public: anyone can read this; nobody can change it.

/**

 * The whole feel, measured.

 *

 * A wire between the real match and the real client modules: snapshots leave

 * on the server's ticks, arrive a little late and a little unevenly, and the

 * browser side draws sixty frames a second from them exactly the way val.js

 * does. What comes out is a set of numbers a person's "it stutters" can be

 * held against — how even the per-frame steps are, how often a correction

 * jumps, how large the largest jump is — and every one of them is a rule

 * this file enforces from here on.

 */

import { expect, test } from "bun:test";

import { mkdtempSync } from "node:fs";

import { tmpdir } from "node:os";

import { join } from "node:path";

import { BODY_R, RUN } from "./engine/glide.ts";

import { solidTile, TILE } from "./map.ts";

import { newMatch, setInput, speedOf, startRound, tick } from "./match.ts";

import { runBots } from "./bots.ts";

import { arrive, bodyAt, delay, feed, makeTimeline, renderTime } from "../static/engine/interp.js";

import { makeLocal, stepLocal } from "../static/engine/predict.js";

import { makeYaw, settle, told } from "../static/engine/yaw.js";

// The arena records finished matches under FORGE_APP_DATA the moment it is imported.

process.env.FORGE_APP_DATA ??= mkdtempSync(join(tmpdir(), "app-"));

const { broadcastEvery, makeValArena } = await import("./arena.ts");

const round2 = (n: number) => Math.round(n * 10) / 10;

const world = { solid: solidTile, tile: TILE, r: BODY_R };

/** A seeded wobble, so the run is the same every time. */

function rng(seed: number) {

  let s = seed | 0;

  return () => {

    s = (s + 0x6d2b79f5) | 0;

    let t = Math.imul(s ^ (s >>> 15), s | 1);

    t ^= t + Math.imul(t ^ (t >>> 7), t | 61);

    return ((t ^ (t >>> 14)) >>> 0) / 4294967296;

  };

}

/**

 * The wire as it was measured: 30 a second, p50 gap 33ms, p99 41–48ms, no

 * gap over 100ms. Each packet takes a base latency plus a wobble, and now

 * and then one is held a dozen milliseconds longer.

 */

function jitter(random: () => number): number {

  const u = random();

  const v = random();

  const gauss = Math.sqrt(-2 * Math.log(1 - u)) * Math.cos(2 * Math.PI * v);

  return Math.abs(gauss) * 0.004 + (random() < 0.03 ? 0.012 : 0);

}

const spreadOf = (steps: number[]) => {

  const mean = steps.reduce((s, x) => s + x, 0) / steps.length;

  const sd = Math.sqrt(steps.reduce((s, x) => s + (x - mean) ** 2, 0) / steps.length);

  return { mean, spread: sd / mean };

};

type Body = { id: string; x: number; y: number; angle: number };

type Packet = { at: number; stamp: number; me: Body & { alive: boolean; phase: string; speed: number }; bodies: Body[] };

/**

 * A person walking east across open ground for two seconds, sending intent

 * every 50ms, hearing back thirty times a second over a jittery wire, and

 * drawn at sixty frames — with the input reaching the server one way late.

 *

 * The packet carries `speed` the way the arena's snapshot does — the match's

 * own answer, to a tenth — and the drawing uses that and nothing else, which

 * is what val.js does. `on` is whatever the walk is carrying: a haste, an

 * operator, the states whose speed is not the plain run.

 */

function walkOwnBody(base = 0.02, on: Partial<{ haste: number; slow: number; weapon: string }> = {}) {

  const random = rng(7);

  const state = newMatch(11);

  const me = state.players[0]!;

  me.bot = false;

  for (let i = 0; i < 30 * 40 && state.phase !== "live"; i++) {

    runBots(state, 1 / 30);

    tick(state, 1 / 30);

  }

  // Somewhere open: the middle of the map, facing east.

  me.x = 1000;

  me.y = 640;

  me.hp = 100;

  me.alive = true;

  me.haste = 0;

  me.slow = 0;

  me.weapon = "classic";

  Object.assign(me, on);

  const packets: Packet[] = [];

  const inputs: { at: number; mx: number; my: number }[] = [];

  const held = { mx: 0, my: 0 };

  const walkFrom = 0.3;

  const walkUntil = 1.6;

  // The server's clock: one tick every 33ms; snapshots leave right after.

  for (let k = 0; k * (1 / 30) < 2.2; k++) {

    const t = k / 30;

    while (inputs.length && inputs[0]!.at <= t) {

      const input = inputs.shift()!;

      setInput(me, { mx: input.mx, my: input.my, angle: 0 });

    }

    // The browser's send timer is on its own clock: every 50ms, arriving one

    // way of latency later.

    for (let s = Math.ceil((t - 1 / 30) / 0.05); s * 0.05 < t; s++) {

      if (s * 0.05 < t - 1 / 30) continue;

      const sentAt = s * 0.05;

      const moving = sentAt >= walkFrom && sentAt < walkUntil;

      inputs.push({ at: sentAt + base, mx: moving ? 1 : 0, my: 0 });

    }

    inputs.sort((a, b) => a.at - b.at);

    tick(state, 1 / 30);

    packets.push({

      at: t + base + jitter(random),

      stamp: 0,

      me: {

        id: me.id,

        x: round2(me.x),

        y: round2(me.y),

        angle: round2(me.angle),

        alive: me.alive,

        phase: state.phase,

        speed: round2(speedOf(state, me)),

      },

      bodies: [],

    });

  }

  packets.sort((a, b) => a.at - b.at);

  const timeline = makeTimeline();

  const local = makeLocal();

  let snap: Packet | null = null;

  let next = 0;

  let previous = 0;

  const steps: number[] = [];

  let back = 0;

  let anchors = 0;

  for (let f = 0; f / 60 < 2.2; f++) {

    const now = f / 60;

    while (next < packets.length && packets[next]!.at <= now) {

      snap = packets[next]!;

      snap.stamp = arrive(timeline, snap.at);

      next += 1;

    }

    if (!snap) continue;

    held.mx = now >= walkFrom && now < walkUntil ? 1 : 0;

    const before = local.anchored;

    // The speed the server sent, exactly as val.js passes it: no rule about

    // movement is re-derived on this side of the wire.

    stepLocal(local, snap.me, held, snap.me.speed, now - snap.stamp, 1 / 60, world, null);

    // The first word about where you are is taken outright: that one is not a jump.

    if (before > 0) anchors += local.anchored - before;

    if (f > 0 && previous !== 0 && now > walkFrom + 0.2 && now < walkUntil - 0.05) {

      const step = local.x - previous;

      steps.push(step);

      back = Math.min(back, step);

    }

    previous = local.x;

  }

  return { steps, back, anchors, local, server: me };

}

test("your own body, walking, takes even steps and never a backward one", () => {

  const { steps, back, anchors } = walkOwnBody();

  const { mean, spread } = spreadOf(steps);

  console.log(

    `own body: ${steps.length} steps, mean ${mean.toFixed(2)}/frame, spread ${(spread * 100).toFixed(1)}%, ` +

      `largest backward step ${back.toFixed(2)}, anchors ${anchors}`,

  );

  // Running east at 250 a second is 4.17 a frame.

  expect(mean * 60).toBeGreaterThan(RUN * 0.9);

  expect(mean * 60).toBeLessThan(RUN * 1.1);

  // Even: the per-frame step does not beat against the wire's jitter.

  expect(spread).toBeLessThan(0.05);

  // And a step backwards is a stutter by definition.

  expect(back).toBeGreaterThan(-0.01);

  expect(anchors).toBe(0);

});

test("a hasted walk is drawn at the speed the wire carried, rounding and all", () => {

  // Haste is the case where the match's own answer is not a whole number:

  // 250 × 1.35 is 337.5, and the wire carries it to a tenth, like every other

  // number in the snapshot. What is checked is that the drawing runs at the

  // speed the server will use — no correction, no backward step, and no body

  // drawn out past where the server is about to put it.

  const { steps, back, anchors, local, server } = walkOwnBody(0.02, { haste: 10 });

  const { mean, spread } = spreadOf(steps);

  console.log(

    `hasted body: ${steps.length} steps, mean ${mean.toFixed(2)}/frame, spread ${(spread * 100).toFixed(1)}%, ` +

      `largest backward step ${back.toFixed(2)}, anchors ${anchors}, drawn ${(local.x - server.x).toFixed(1)} past the server`,

  );

  expect(mean * 60).toBeGreaterThan(RUN * 1.35 * 0.9);

  expect(mean * 60).toBeLessThan(RUN * 1.35 * 1.1);

  expect(spread).toBeLessThan(0.05);

  expect(back).toBeGreaterThan(-0.01);

  expect(anchors).toBe(0);

});

test("starting and stopping never pulls you back, and the speed never dips a third", () => {

  // The first tenth of a second after the key goes down the server has not

  // heard yet, and the guess used to be yanked back to the server's still

  // body on each of the first two snapshots. Letting go, the server runs on

  // for the same lag and the guess must not be dragged back to meet it.

  const random = rng(3);

  const timeline = makeTimeline();

  const local = makeLocal();

  const me = { x: 1000, y: 640, angle: 0, alive: true };

  const held = { mx: 0, my: 0 };

  const hop = 0.03; // one way, plus the send timer's own phase

  let serverX = 1000;

  const packets: { at: number; x: number }[] = [];

  for (let k = 0; k / 30 < 2; k++) {

    const t = k / 30;

    // The server hears the key a hop after the next 50ms send.

    const heardDown = Math.ceil(0.3 / 0.05) * 0.05 + hop;

    const heardUp = Math.ceil(1.2 / 0.05) * 0.05 + hop;

    if (t > heardDown && t <= heardUp) serverX += RUN / 30;

    packets.push({ at: t + hop + jitter(random), x: round2(serverX) });

  }

  let next = 0;

  let previous = 0;

  let back = 0;

  let slowest = Infinity;

  for (let f = 0; f / 60 < 2; f++) {

    const now = f / 60;

    while (next < packets.length && packets[next]!.at <= now) {

      me.x = packets[next]!.x;

      arrive(timeline, packets[next]!.at);

      next += 1;

    }

    if (next === 0) continue;

    held.mx = now >= 0.3 && now < 1.2 ? 1 : 0;

    stepLocal(local, me, held, RUN, now - timeline.stamp, 1 / 60, world, null);

    const step = local.x - previous;

    if (now > 0.3 + 1 / 60) back = Math.min(back, step);

    if (now > 0.3 + 1 / 60 && now < 1.2) slowest = Math.min(slowest, step);

    previous = local.x;

  }

  console.log(

    `walk start and stop: largest backward step ${back.toFixed(2)}, slowest frame while walking ${slowest.toFixed(2)} of ${(RUN / 60).toFixed(2)}, ` +

      `settled ${(local.x - serverX).toFixed(1)} from the server`,

  );

  expect(back).toBeGreaterThan(-0.01);

  expect(slowest).toBeGreaterThan((RUN / 60) * 0.67);

  // Where you stopped is where the server stops: the guess settles onto it.

  expect(Math.abs(local.x - serverX)).toBeLessThan(1);

});

/**

 * Everybody else: a bot walking, heard about thirty times a second over the

 * same wire, drawn a little in the past between the samples on hand.

 */

function watchBots() {

  const random = rng(5);

  const state = newMatch(23);

  const step = () => {

    runBots(state, 1 / 30);

    tick(state, 1 / 30);

  };

  for (let i = 0; i < 30 * 40 && state.phase !== "live"; i++) step();

  const packets: { at: number; bodies: Body[] }[] = [];

  for (let k = 0; k < 90; k++) {

    step();

    packets.push({

      at: k / 30 + 0.02 + jitter(random),

      bodies: state.players.map((p) => ({ id: p.id, x: round2(p.x), y: round2(p.y), angle: round2(p.angle) })),

    });

  }

  const timeline = makeTimeline();

  const paths = new Map<string, { x: number; y: number }[]>();

  const delays: number[] = [];

  let ahead = 0;

  let frames = 0;

  let next = 0;

  for (let f = 0; f / 60 < 2.8; f++) {

    const now = f / 60;

    while (next < packets.length && packets[next]!.at <= now) {

      const stamp = arrive(timeline, packets[next]!.at);

      for (const p of packets[next]!.bodies) feed(timeline, p.id, p, stamp);

      next += 1;

    }

    if (next < 4) continue;

    const drawAt = renderTime(timeline, now);

    delays.push(now - drawAt);

    frames += 1;

    if (drawAt > timeline.stamp) ahead += 1;

    for (const p of packets[next - 1]!.bodies) {

      const at = bodyAt(timeline, p, drawAt);

      paths.set(p.id, [...(paths.get(p.id) ?? []), { x: at.x, y: at.y }]);

    }

  }

  const walked = [...paths.values()]

    .map((path) => path.slice(1).map((at, i) => Math.hypot(at.x - path[i]!.x, at.y - path[i]!.y)))

    .map((steps) => steps.filter((s) => s > 0.001))

    .sort((a, b) => b.reduce((s, x) => s + x, 0) - a.reduce((s, x) => s + x, 0))[0]!;

  return { walked, restarts: timeline.restarts, delays, ahead, frames, timeline };

}

test("everybody else walks at an even speed over a jittery wire, and nobody restarts", () => {

  const { walked, restarts, delays, ahead, frames } = watchBots();

  const { mean, spread } = spreadOf(walked);

  const dmin = Math.min(...delays);

  const dmax = Math.max(...delays);

  console.log(

    `others: ${walked.length} steps, mean ${mean.toFixed(2)}/frame, spread ${(spread * 100).toFixed(1)}%, ` +

      `restarts ${restarts}, delay ${(dmin * 1000).toFixed(1)}–${(dmax * 1000).toFixed(1)}ms, ` +

      `drawn past the newest sample ${ahead}/${frames} frames`,

  );

  expect(walked.length).toBeGreaterThan(40);

  expect(mean * 60).toBeGreaterThan(150);

  expect(spread).toBeLessThan(0.08);

  // A body that was in sight all along never jumps to start again.

  expect(restarts).toBe(0);

  // The moment drawn is never later than the newest word: no guessing ahead.

  expect(ahead).toBe(0);

});

test("the render clock never steps backwards or stalls, whatever the wire does", () => {

  const random = rng(9);

  const timeline = makeTimeline();

  let arrival = 0.02;

  let drawn = 0;

  let worstShort = Infinity;

  let worstLong = 0;

  for (let f = 0; f / 60 < 5; f++) {

    const now = f / 60;

    while (arrival <= now) {

      arrive(timeline, arrival);

      arrival += 1 / 30 + jitter(random) - 0.002;

    }

    const at = renderTime(timeline, now);

    if (f > 30 && drawn > 0) {

      worstShort = Math.min(worstShort, at - drawn);

      worstLong = Math.max(worstLong, at - drawn);

    }

    drawn = at;

  }

  console.log(`render clock: frame advance ${(worstShort * 1000).toFixed(2)}–${(worstLong * 1000).toFixed(2)}ms of 16.67`);

  // Within a few percent of real time, every frame: 16.67ms give or take.

  expect(worstShort * 60).toBeGreaterThan(0.97);

  expect(worstLong * 60).toBeLessThan(1.03);

});

test("a burst of snapshots does not walk the even clock into the future", () => {

  // A tab back from the background is handed everything it missed at once.

  // The clock those samples are filed on may lead the arrivals by half a

  // beat and no more, or the sent angles age out and every echo of your own

  // view comes back as a correction.

  const timeline = makeTimeline();

  let at = 10;

  for (let i = 0; i < 40; i++) arrive(timeline, (at += 1 / 30));

  const before = timeline.stamp;

  for (let i = 0; i < 150; i++) {

    const stamp = arrive(timeline, (at += 0.0002));

    expect(stamp - at).toBeLessThanOrEqual(timeline.interval / 2 + 1e-9);

    expect(stamp).toBeGreaterThanOrEqual(before);

  }

  // And once the wire is itself again, the beat is back on it.

  for (let i = 0; i < 40; i++) arrive(timeline, (at += 1 / 30));

  expect(Math.abs(timeline.stamp - at)).toBeLessThan(0.01);

});

test("a round start points you at the site once, and nothing stomps it a tick later", () => {

  const state = newMatch(31);

  const me = state.players[0]!;

  me.bot = false;

  const yaw = makeYaw();

  let corrections = 0;

  let worstRound = 0;

  let at = 0;

  const hear = () => {

    const before = yaw.angle;

    settle(yaw, { id: me.id, angle: round2(me.angle), alive: me.alive }, at);

    if (yaw.angle !== before) corrections += 1;

  };

  hear();

  // A dozen round starts, each followed by a second of ticks with the client

  // echoing back exactly what it was pointed at, the way the input timer

  // does — and each echo reaching the server a tick after it was sent.

  const inFlight: number[] = [];

  for (let round = 0; round < 12; round++) {

    const were = corrections;

    startRound(state);

    hear(); // the snapshot that follows the tick which started the round

    for (let k = 0; k < 30; k++) {

      at += 1 / 30;

      if (inFlight.length) setInput(me, { angle: inFlight.shift()! });

      if (k % 2 === 0) {

        told(yaw, yaw.angle, at);

        inFlight.push(yaw.angle);

      }

      tick(state, 1 / 30);

      hear();

    }

    // Facing the site the server put us at, still, a second later.

    const centre = me.side === "atk" ? { x: 1200, y: 400 } : { x: 1200, y: 1200 };

    const want = Math.atan2(centre.y - me.y, centre.x - me.x);

    expect(Math.abs(((yaw.angle - want + Math.PI * 3) % (Math.PI * 2)) - Math.PI)).toBeLessThan(0.11);

    worstRound = Math.max(worstRound, corrections - were);

  }

  console.log(`round starts: ${corrections} camera corrections over 12 rounds, at most ${worstRound} in one`);

  // At most one a round — the spawn — and never a second one to angle zero.

  expect(worstRound).toBeLessThanOrEqual(1);

});

/**

 * The match's own motion, sampled at the rate the server broadcasts it and

 * drawn at the rate a browser draws: what a bot walking across the map

 * actually looks like. The samples carry exactly what a snapshot carries —

 * a position rounded to a tenth, thirty times a second.

 *

 * The measure is the spread of the per-frame steps. A body drawn at the

 * server's speed takes even steps; the exponential chase this replaced took

 * a long step just after each snapshot and shorter ones after it, which is

 * choppiness with a number on it — twice this spread, measured the same way.

 */

test("the simulation's own motion is drawn at an even speed", async () => {

  const { runBots } = await import("./bots.ts");

  const { newMatch, tick } = await import("./match.ts");

  const round2 = (n: number) => Math.round(n * 10) / 10;

  // A match of its own: nothing here touches the arena everybody shares.

  const state = newMatch();

  const step = () => {

    runBots(state, 1 / 30);

    tick(state, 1 / 30);

  };

  for (let i = 0; i < 30 * 40 && state.phase !== "live"; i++) step();

  const stream: { t: number; bodies: { id: string; x: number; y: number; angle: number }[] }[] = [];

  for (let i = 0; i < 60; i++) {

    step();

    stream.push({

      t: i / 30,

      bodies: state.players.map((p) => ({ id: p.id, x: round2(p.x), y: round2(p.y), angle: round2(p.angle) })),

    });

  }

  const timeline = makeTimeline();

  const paths = new Map<string, { x: number; y: number }[]>();

  let next = 0;

  for (let f = 0; f / 60 < 1.8; f++) {

    const now = f / 60;

    while (next < stream.length && stream[next]!.t <= now) {

      arrive(timeline, stream[next]!.t);

      for (const p of stream[next]!.bodies) feed(timeline, p.id, p, stream[next]!.t);

      next += 1;

    }

    for (const p of stream[Math.max(0, next - 1)]!.bodies) {

      const at = bodyAt(timeline, p, now - delay(timeline));

      paths.set(p.id, [...(paths.get(p.id) ?? []), { x: at.x, y: at.y }]);

    }

  }

  // Whoever walked furthest in that second and a half.

  const walked = [...paths.values()]

    .filter((path) => path.length > 80)

    .map((path) => path.slice(1).map((at, i) => Math.hypot(at.x - path[i]!.x, at.y - path[i]!.y)))

    .map((steps) => steps.filter((step) => step > 0.001))

    .sort((a, b) => b.reduce((s, x) => s + x, 0) - a.reduce((s, x) => s + x, 0))[0]!;

  expect(walked.length).toBeGreaterThan(30);

  const mean = walked.reduce((s, x) => s + x, 0) / walked.length;

  const spread = Math.sqrt(walked.reduce((s, x) => s + (x - mean) ** 2, 0) / walked.length) / mean;

  // A body moving at the server's own speed: about four units every sixtieth

  // of a second, which is the run speed.

  expect(mean * 60).toBeGreaterThan(150);

  expect(spread).toBeLessThan(0.15);

});

/**

 * Everybody else, as the real arena sends them to a real seat in a room of

 * `seats` people: the cadence the arena picks for that room, the vision

 * filter, the sticky board, all of it — over the same jittery wire as

 * `watchBots`, drawn the same way. The room is what is being measured, so

 * the seats sit idle and the bots do the walking.

 *

 * The wire opens three seconds before the round goes live and the first

 * three seconds of the rush are measured: the render delay creeps toward

 * its mark at two percent of real time, so a timeline that has just met a

 * 15Hz stream spends two seconds drawing bodies past the newest sample

 * while it gets there. That is what a room felt at the moment its third

 * seat filled; here each cadence is measured settled, and `cold` says how

 * many frames the buy phase spent guessing ahead.

 */

function watchRoom(seats: number, cadence: (filled: number) => number) {

  const random = rng(5);

  const arena = makeValArena(newMatch(23), () => {}, cadence);

  const packets: { at: number; bodies: Body[] }[] = [];

  let t = 0;

  let viewer = "";

  for (let i = 0; i < seats; i++) {

    const seat = arena.takeSeat(`10.9.0.${i + 1}`, `feel-${i}`, `Seat ${i}`)!;

    if (i === 0) viewer = seat.id;

    arena.attach(`feel-${i}`, seat.id, `10.9.0.${i + 1}`, `t${i}`, (data) => {

      if (i !== 0) return;

      const snap = JSON.parse(data) as { players: Body[] };

      packets.push({ at: t + 0.02 + jitter(random), bodies: snap.players.filter((p) => p.id !== viewer) });

    });

  }

  const tickOnce = () => {

    t += 1 / 30;

    arena.advance(1 / 30);

  };

  // The last three seconds of the buy phase, then the first three of the round.

  const state = arena.match();

  while (!(state.phase === "buy" && state.clock <= 3)) tickOnce();

  packets.length = 0;

  t = 0;

  let warm = 0;

  while (state.phase !== "live") {

    tickOnce();

    warm = t;

  }

  for (let k = 0; k < 90; k++) tickOnce();

  packets.sort((a, b) => a.at - b.at);

  const timeline = makeTimeline();

  const paths = new Map<string, { x: number; y: number }[]>();

  const delays: number[] = [];

  let ahead = 0;

  let cold = 0;

  let frames = 0;

  let next = 0;

  let restartsWarm = 0;

  for (let f = 0; f / 60 < warm + 2.8; f++) {

    const now = f / 60;

    while (next < packets.length && packets[next]!.at <= now) {

      const stamp = arrive(timeline, packets[next]!.at);

      for (const p of packets[next]!.bodies) feed(timeline, p.id, p, stamp);

      next += 1;

    }

    if (next < 4) continue;

    const drawAt = renderTime(timeline, now);

    if (now < warm) {

      if (drawAt > timeline.stamp) cold += 1;

      restartsWarm = timeline.restarts;

      continue;

    }

    delays.push(now - drawAt);

    frames += 1;

    if (drawAt > timeline.stamp) ahead += 1;

    for (const p of packets[next - 1]!.bodies) {

      const at = bodyAt(timeline, p, drawAt);

      paths.set(p.id, [...(paths.get(p.id) ?? []), { x: at.x, y: at.y }]);

    }

  }

  const walked = [...paths.values()]

    .map((path) => path.slice(1).map((at, i) => Math.hypot(at.x - path[i]!.x, at.y - path[i]!.y)))

    .map((steps) => steps.filter((s) => s > 0.001))

    .sort((a, b) => b.reduce((s, x) => s + x, 0) - a.reduce((s, x) => s + x, 0))[0]!;

  const { mean, spread } = spreadOf(walked);

  return {

    packets: packets.filter((p) => p.at >= warm).length,

    steps: walked.length,

    mean,

    spread,

    restarts: timeline.restarts - restartsWarm,

    delay: { min: Math.min(...delays), max: Math.max(...delays), now: delay(timeline) },

    ahead,

    cold,

    frames,

  };

}

/** The rule as it stood before: every other tick from the third seat. */

const halvedAtThree = (filled: number): number => (filled <= 2 ? 1 : 2);

test("in a room of four or eight, everybody else is drawn 45ms behind, not 87, with no new jitter", () => {

  for (const seats of [4, 8]) {

    const before = watchRoom(seats, halvedAtThree);

    const after = watchRoom(seats, broadcastEvery);

    for (const [label, r] of [

      ["before", before],

      [" after", after],

    ] as const) {

      console.log(

        `room of ${seats}, ${label}: ${r.packets} snapshots in 3s, ${r.steps} steps, mean ${r.mean.toFixed(2)}/frame, ` +

          `spread ${(r.spread * 100).toFixed(1)}%, restarts ${r.restarts}, ` +

          `delay ${(r.delay.min * 1000).toFixed(1)}–${(r.delay.max * 1000).toFixed(1)}ms (${(r.delay.now * 1000).toFixed(1)} in force), ` +

          `drawn past the newest sample ${r.ahead}/${r.frames} frames, ${r.cold} while the delay settled`,

      );

    }

    // Thirty a second reach this seat, not fifteen.

    expect(after.packets).toBeGreaterThanOrEqual(85);

    expect(before.packets).toBeLessThanOrEqual(46);

    // And so every other body is drawn at the floor of the render delay, not

    // 1.3 intervals of a halved rate: 45ms behind the present, not 87.

    expect(after.delay.max).toBeLessThan(0.05);

    expect(before.delay.max).toBeGreaterThan(0.08);

    // Closer to the present buys no jitter: the steps are never less even

    // than they were at the halved rate, and no body in sight all along

    // started again. In the room of four the body measured runs clean and

    // holds the small room's 8% (`watchBots`); in the room of eight the two

    // bots left thread past the idle bodies at spawn, and those stops are the

    // server's, the same in both columns, so only the comparison is held.

    expect(after.steps).toBeGreaterThan(40);

    expect(after.mean * 60).toBeGreaterThan(150);

    if (seats === 4) expect(after.spread).toBeLessThan(0.08);

    expect(after.spread).toBeLessThanOrEqual(before.spread + 0.01);

    expect(after.restarts).toBeLessThanOrEqual(before.restarts);

    // A 45ms delay over a 33ms beat leaves 12ms for a packet to be late, and

    // the wire holds one in thirty by about that: the odd frame is drawn on

    // the newest pair's velocity, one interval at most, which a room of two

    // gets today. What must not appear is the run of guessed frames a

    // timeline spends settling on a halved rate.

    expect(after.ahead).toBeLessThanOrEqual(Math.ceil(after.frames * 0.03));

    expect(before.cold).toBeGreaterThan(10);

    expect(after.cold).toBeLessThanOrEqual(2);

  }

});