async tests [nfc]: Put BackoffMachine tests where they belong.

Follow the suggestion in the comment (deleted in this commit) at the
top of `backoffMachine-test`, and move these tests. Observe that
there are no errors.

src/utils/__tests__/async-test.js

@@ -1,7 +1,55 @@
 /* @flow strict-local */
-import { sleep } from '../async';
+import { sleep, BackoffMachine } from '../async';
 import { assertUsingModernFakeTimers } from '../../__tests__/lib/fakeTimers';
 
+describe('BackoffMachine', () => {
+  beforeAll(() => {
+    assertUsingModernFakeTimers();
+  });
+
+  afterEach(() => {
+    expect(jest.getTimerCount()).toBe(0);
+    jest.clearAllTimers();
+  });
+
+  const measureWait = async (promise: Promise<void>) => {
+    const start = Date.now();
+    jest.runOnlyPendingTimers();
+    await promise;
+    return Date.now() - start;
+  };
+
+  test('timeouts are random from zero to 100ms, 200ms, 400ms, 800ms...', async () => {
+    // This is a randomized test. NUM_TRIALS is chosen so that the failure
+    // probability < 1e-9. There are 2 * 11 assertions, and each one has a
+    // failure probability < 1e-12; see below.
+    const NUM_TRIALS = 100;
+    const expectedMaxDurations = [100, 200, 400, 800, 1600, 3200, 6400, 10000, 10000, 10000, 10000];
+
+    const trialResults: Array<number[]> = [];
+
+    for (let i = 0; i < NUM_TRIALS; i++) {
+      const resultsForThisTrial = [];
+      const backoffMachine = new BackoffMachine();
+      for (let j = 0; j < expectedMaxDurations.length; j++) {
+        const duration = await measureWait(backoffMachine.wait());
+        resultsForThisTrial.push(duration);
+      }
+      trialResults.push(resultsForThisTrial);
+    }
+
+    expectedMaxDurations.forEach((expectedMax, i) => {
+      const maxFromAllTrials = Math.max(...trialResults.map(r => r[i]));
+      const minFromAllTrials = Math.min(...trialResults.map(r => r[i]));
+
+      // Each of these assertions has a failure probability of:
+      //     0.75 ** NUM_TRIALS = 0.75 ** 100 < 1e-12
+      expect(minFromAllTrials).toBeLessThan(expectedMax * 0.25);
+      expect(maxFromAllTrials).toBeGreaterThan(expectedMax * 0.75);
+    });
+  });
+});
+
 const sleepMeasure = async (expectedMs: number) => {
   const start = Date.now();
   await sleep(expectedMs);