*  Fix: Recover gracefully when a cache entry's certificate is corrupted.

 *  Fix: Fail permanently when there's a failure loading the bundled public suffix database.
    This is the dataset that powers `HttpUrl.topPrivateDomain()`.

 *  Fix: Immediately update the connection's flow control window instead of waiting for the
    receiving stream to process it.

  }

  private static final int EVEN_POWERS_OF_TWO = 0x55555555;
  private static final int ODD_POWERS_OF_TWO = 0xaaaaaaaa;

  @VisibleForTesting
  static boolean isEvenLevel(int index) {
    int oneBased = ~~(index + 1); // for GWT
    checkState(oneBased > 0, "negative index");
    return (oneBased & EVEN_POWERS_OF_TWO) > (oneBased & ODD_POWERS_OF_TWO);
  }

  /**

  static {
    ImmutableSet.Builder<Integer> intValues = ImmutableSet.builder();
    // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31).
    intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE);
    // Add values up to 40. This covers cases like "square of a prime" and such.
    for (int i = 1; i <= 40; i++) {
      intValues.add(i);
    }

                        "content": {
                            "application/json": {



...
```

#### What is OpenAPI for

The OpenAPI schema is what powers the two interactive documentation systems included.

And there are dozens of alternatives, all based on OpenAPI. You could easily add any of those alternatives to your application built with **FastAPI**.

  static {
    ImmutableSet.Builder<Integer> intValues = ImmutableSet.builder();
    // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31).
    intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE);
    // Add values up to 40. This covers cases like "square of a prime" and such.
    for (int i = 1; i <= 40; i++) {
      intValues.add(i);
    }

  @VisibleForTesting static final long MAX_SIGNED_POWER_OF_TWO = 1L << (Long.SIZE - 2);

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code checkedPow(2, log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as a {@code

  @VisibleForTesting static final int MAX_SIGNED_POWER_OF_TWO = 1 << (Integer.SIZE - 2);

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code checkedPow(2, log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as an {@code

> Modern versions of Python have support for **"asynchronous code"** using something called **"coroutines"**, with **`async` and `await`** syntax.

That should make more sense now. ✨

All that is what powers FastAPI (through Starlette) and what makes it have such an impressive performance.

## Very Technical Details

!!! warning
    You can probably skip this.

!!! tip
    This will just make Peewee behave correctly when used with FastAPI. Not randomly opening or closing connections that are being used, creating errors, etc.

    But it doesn't give Peewee async super-powers. You should still use normal `def` functions and not `async def`.

### Use the custom `PeeweeConnectionState` class

        Prefer to use the `Annotated` version if possible.

    ```Python hl_lines="9"
    {!> ../../../docs_src/query_params_str_validations/tutorial006c.py!}
    ```

!!! tip