// The key to the binary GCD algorithm is as follows:
      // Both a and b are odd. Assume a > b; then gcd(a - b, b) = gcd(a, b).
      // But in gcd(a - b, b), a - b is even and b is odd, so we can divide out powers of two.

      // We bend over backwards to avoid branching, adapting a technique from
      // http://graphics.stanford.edu/~seander/bithacks.html#IntegerMinOrMax

an application component, consists of the following steps: Acquire a reference to an instance of org.apache.commons.logging.Log, by calling the factory method LogFactory.getInstance(String name). Your application can contain references to multiple loggers that are used for different purposes. A typical scenario for a server application is to have each major component of the server use its own Log instance. Cause messages to be logged (if the corresponding detail level is enabled) by calling appropriate...

/**
 * Tests for {@link Quantiles}.
 *
 * @author Pete Gillin
 */
public class QuantilesTest extends TestCase {

  /*
   * Since Quantiles provides a fluent-style API, each test covers a chain of methods resulting in
   * the computation of one or more quantiles (or in an error) rather than individual methods. The
   * tests are divided into three sections:

/**
 * Tests for {@link Quantiles}.
 *
 * @author Pete Gillin
 */
public class QuantilesTest extends TestCase {

  /*
   * Since Quantiles provides a fluent-style API, each test covers a chain of methods resulting in
   * the computation of one or more quantiles (or in an error) rather than individual methods. The
   * tests are divided into three sections:

By declaring types for your variables, editors and tools can give you better support.

This is just a **quick tutorial / refresher** about Python type hints. It covers only the minimum necessary to use them with **FastAPI**... which is actually very little.

**FastAPI** is all based on these type hints, they give it many advantages and benefits.

> 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.

   * @throws NullPointerException if any of {@code elements} is null
   * @since 7.0 (source-compatible since 2.0)
   */
  // This the best we could do to get copyOfEnumSet to compile in the mainline.
  // The suppression also covers the cast to E[], discussed below.
  // In the backport, we don't have those cases and thus don't need this suppression.
  // We keep it to minimize diffs.
  @SuppressWarnings("unchecked")

!!! 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