return x > 0 & (x & (x - 1)) == 0;
  }

  /**
   * Returns 1 if {@code x < y} as unsigned longs, and 0 otherwise. Assumes that x - y fits into a
   * signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster
   * than the straightforward ternary expression.
   */
  @VisibleForTesting
  static int lessThanBranchFree(long x, long y) {
    // Returns the sign bit of x - y.

But then, when you open the integrated docs UI (the frontend), it would expect to get the OpenAPI schema at `/openapi.json`, instead of `/api/v1/openapi.json`.

So, the frontend (that runs in the browser) would try to reach `/openapi.json` and wouldn't be able to get the OpenAPI schema.

Because we have a proxy with a path prefix of `/api/v1` for our app, the frontend needs to fetch the OpenAPI schema at `/api/v1/openapi.json`.

```mermaid

## Sponsor the author { #sponsor-the-author }

If your **product/company** depends on or is related to **FastAPI** and you want to reach its users, you can sponsor the author (me) through <a href="https://github.com/sponsors/tiangolo" class="external-link" target="_blank">GitHub sponsors</a>. Depending on the tier, you could get some extra benefits, like a badge in the docs. 🎁

    if (waiter.isAlive()) {
      waiter.interrupt();
      fail("awaitTermination failed to trigger after shutdown()");
    }
  }

  /** Wait for the given thread to reach the {@link State#TIMED_WAITING} thread state. */
  @SuppressWarnings("ThreadPriorityCheck") // TODO: b/175898629 - Consider onSpinWait.
  void awaitTimedWaiting(Thread thread) {
    while (true) {

            V entryValue = e.getValue();

            if (entryValue != null) {
              // TODO(kak): Remove this branch
            } else if (isCollected(e)) {
              // TODO(kak): Remove this branch
            } else {
              return null;
            }

            ++modCount;
            E newFirst = removeFromChain(first, e);

			r:            metadataResolutionParams{dirQuorum: 2, objQuorum: 2, strict: false},
			wantSelected: &inputSerialized[6],
			wantOk:       true,
		},
		{
			// When ID is zero, do not allow non-strict matches to reach quorum.
			name:         "zeroid-belowq",
			m:            metaCacheEntries{inputSerialized[5], inputSerialized[5], inputSerialized[6], inputSerialized[6]},

			rp = &r.buf[len(r.buf)-1]
		} else {
			rp.n++
		}
	}
	return len(p), nil
}

func memset(a []byte, b byte) {
	if len(a) == 0 {
		return
	}
	// Double, until we reach power of 2 >= len(a), same as bytes.Repeat,
	// but without allocation.
	a[0] = b
	for i, l := 1, len(a); i < l; i *= 2 {
		copy(a[i:], a[:i])
	}
}

            .put(key1, 1)
            .put(key2, 2)
            .put(key1, 3)
            .put(key2, 4)
            .buildKeepingLast();
    assertMapEquals(map, key1, 3, key2, 4);
  }

  // The java7 branch has different code depending on whether the entry indexes fit in a byte,
  // short, or int. The small table in testBuildKeepingLast_allowsOverwrite will test the byte
  // case. This method tests the short case.

            currentWeight += channel.getScore();
            if (random < currentWeight) {
                return channel;
            }
        }
        
        // Should not reach here
        return channels.iterator().next();
    }
    
    private ChannelInfo selectWithAffinity(SMBMessage message, Collection<ChannelInfo> channels) {
        // Use file handle or tree ID for affinity

			continue
		}
	}

	// Return dir entries, if enough...
	if selected != nil && selected.isDir() && dirExists >= r.dirQuorum {
		return selected, true
	}

	// If we would never be able to reach read quorum.
	if objsValid < r.objQuorum {
		return nil, false
	}

	// If all objects agree.
	if selected != nil && objsAgree == objsValid {
		return selected, true
	}