* Audit logging with buffering enabled can increase apiserver memory usage (e.g. up to 200MB in 100-node cluster). The increase is bounded by the buffer size (configurable). Ref: issue [#60500](https://github.com/kubernetes/kubernetes/pull/60500) ([#61118](https://github.com/kubernetes/kubernetes/pull/61118), [@shyamjvs](https://github.com/shyamjvs))

This is different from using an `APIRouter` as a mounted application is completely independent. The OpenAPI and docs from your main application won't include anything from the mounted application, etc.

You can read more about this in the [Advanced User Guide](../advanced/index.md){.internal-link target=_blank}.

## Details

This sub-application is just another standard FastAPI application, but this is the one that will be "mounted":

```Python hl_lines="11  14-16"
{!../../docs_src/sub_applications/tutorial001.py!}
```

### Mount the sub-application

In your top-level application, `app`, mount the sub-application, `subapi`.

In this case, it will be mounted at the path `/subapi`:

```Python hl_lines="11  19"

      int x = 1 << exponent;
      intValues.add(x, x + 1, x - 1);
    }
    intValues.add(9999).add(10000).add(10001).add(1000000); // near powers of 10
    intValues.add(5792).add(5793); // sqrt(2^25) rounded up and down
    POSITIVE_INTEGER_CANDIDATES = intValues.build();
    NEGATIVE_INTEGER_CANDIDATES =
        ImmutableList.copyOf(
            Iterables.concat(

      int x = 1 << exponent;
      intValues.add(x, x + 1, x - 1);
    }
    intValues.add(9999).add(10000).add(10001).add(1000000); // near powers of 10
    intValues.add(5792).add(5793); // sqrt(2^25) rounded up and down
    POSITIVE_INTEGER_CANDIDATES = intValues.build();
    NEGATIVE_INTEGER_CANDIDATES =
        ImmutableList.copyOf(
            Iterables.concat(

  public static boolean isPowerOfTwo(BigInteger x) {
    checkNotNull(x);
    return x.signum() > 0 && x.getLowestSetBit() == x.bitLength() - 1;
  }

  /**
   * Returns the base-2 logarithm of {@code x}, rounded according to the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}

  /**
   * Returns x rounded to either the greatest double less than or equal to the precise value of x,
   * or the least double greater than or equal to the precise value of x.
   */
  abstract double roundToDoubleArbitrarily(X x);

  /** Returns the sign of x: either -1, 0, or 1. */
  abstract int sign(X x);

  /** Returns d's value as an X, rounded with the specified mode. */

   * primitive conversion from {@code int} to {@code float}, and correctly rounded.
   */
  @Override
  public float floatValue() {
    return longValue();
  }

  /**
   * Returns the value of this {@code UnsignedInteger} as a {@code float}, analogous to a widening
   * primitive conversion from {@code int} to {@code double}, and correctly rounded.
   */
  @Override
  public double doubleValue() {

   * primitive conversion from {@code int} to {@code float}, and correctly rounded.
   */
  @Override
  public float floatValue() {
    return longValue();
  }

  /**
   * Returns the value of this {@code UnsignedInteger} as a {@code float}, analogous to a widening
   * primitive conversion from {@code int} to {@code double}, and correctly rounded.
   */
  @Override
  public double doubleValue() {

 * @author Louis Wasserman
 * @since 30.0
 */
@J2ktIncompatible
@GwtIncompatible
@ElementTypesAreNonnullByDefault
public class BigDecimalMath {
  private BigDecimalMath() {}

  /**
   * Returns {@code x}, rounded to a {@code double} with the specified rounding mode. If {@code x}
   * is precisely representable as a {@code double}, its {@code double} value will be returned;