static final double INTEGER_MANY_VALUES_MIN = -4444.0;

  // Integers which will overflow if summed (using integer arithmetic):
  static final int[] LARGE_INTEGER_VALUES = {Integer.MAX_VALUE, Integer.MAX_VALUE / 2};
  static final double LARGE_INTEGER_VALUES_MEAN =
      BigInteger.valueOf(Integer.MAX_VALUE)
          .multiply(BigInteger.valueOf(3L))
          .divide(BigInteger.valueOf(4L))

  static final double INTEGER_MANY_VALUES_MIN = -4444.0;

  // Integers which will overflow if summed (using integer arithmetic):
  static final int[] LARGE_INTEGER_VALUES = {Integer.MAX_VALUE, Integer.MAX_VALUE / 2};
  static final double LARGE_INTEGER_VALUES_MEAN =
      BigInteger.valueOf(Integer.MAX_VALUE)
          .multiply(BigInteger.valueOf(3L))
          .divide(BigInteger.valueOf(4L))

   *     <ul>
   *       <li>{@code x} is infinite or NaN
   *       <li>{@code x}, after being rounded to a mathematical integer using the specified rounding
   *           mode, is either less than {@code Integer.MIN_VALUE} or greater than {@code
   *           Integer.MAX_VALUE}
   *       <li>{@code x} is not a mathematical integer and {@code mode} is {@link
   *           RoundingMode#UNNECESSARY}
   *     </ul>
   */

You can use **type annotations** the same way you would for input data in function **parameters**, you can use Pydantic models, lists, dictionaries, scalar values like integers, booleans, etc.

{* ../../docs_src/response_model/tutorial001_01_py310.py hl[16,21] *}

FastAPI will use this return type to:

* **Validate** the returned data.

    assertMean(0, 0, 0);
    assertMean(-1, -1, -1);
    assertMean(Integer.MIN_VALUE, Integer.MIN_VALUE, Integer.MIN_VALUE);
    assertMean(Integer.MAX_VALUE, Integer.MAX_VALUE, Integer.MAX_VALUE);

    // Exhaustive checks
    for (int x : ALL_INTEGER_CANDIDATES) {
      for (int y : ALL_INTEGER_CANDIDATES) {
        assertMean(x, y);
      }
    }
  }

    int scale = Integer.MAX_VALUE;
    int otherIndex = (Integer.MAX_VALUE - 1) / 3; // this divides exactly
    // For the otherIndex calculation, we have q=Integer.MAX_VALUE, k=(Integer.MAX_VALUE-1)/3, and
    // N=16. Therefore k*(N-1)/q = 5-5/Integer.MAX_VALUE, which has floor 4 and fractional part
    // (1-5/Integer.MAX_VALUE).
    double otherValue = 16.0 * 5.0 / Integer.MAX_VALUE + 25.0 * (1.0 - 5.0 / Integer.MAX_VALUE);

    int scale = Integer.MAX_VALUE;
    int otherIndex = (Integer.MAX_VALUE - 1) / 3; // this divides exactly
    // For the otherIndex calculation, we have q=Integer.MAX_VALUE, k=(Integer.MAX_VALUE-1)/3, and
    // N=16. Therefore k*(N-1)/q = 5-5/Integer.MAX_VALUE, which has floor 4 and fractional part
    // (1-5/Integer.MAX_VALUE).
    double otherValue = 16.0 * 5.0 / Integer.MAX_VALUE + 25.0 * (1.0 - 5.0 / Integer.MAX_VALUE);

/// note

Keep in mind that in this case, FastAPI won't check the contents of the list.

For example, `list[int]` would check (and document) that the contents of the list are integers. But `list` alone wouldn't.

///

## Declare more metadata { #declare-more-metadata }

You can add more information about the parameter.

    assertMean(0, 0, 0);
    assertMean(-1, -1, -1);
    assertMean(Integer.MIN_VALUE, Integer.MIN_VALUE, Integer.MIN_VALUE);
    assertMean(Integer.MAX_VALUE, Integer.MAX_VALUE, Integer.MAX_VALUE);

    // Exhaustive checks
    for (int x : ALL_INTEGER_CANDIDATES) {
      for (int y : ALL_INTEGER_CANDIDATES) {
        assertMean(x, y);
      }
    }
  }

  }

  private static final class MyIntegerDomain extends DiscreteDomain<Integer> {
    static final DiscreteDomain<Integer> DELEGATE = DiscreteDomain.integers();

    @Override
    public Integer next(Integer value) {
      return DELEGATE.next(value);
    }

    @Override
    public Integer previous(Integer value) {
      return DELEGATE.previous(value);