import static java.lang.Double.isNaN;
import static java.lang.Double.longBitsToDouble;
import static java.lang.Math.getExponent;
import static java.lang.Math.max;

import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.VisibleForTesting;
import java.math.BigInteger;

/**
 * Utilities for {@code double} primitives.
 *
 * @author Louis Wasserman
 */
@GwtIncompatible
final class DoubleUtils {

import static com.google.common.math.ReflectionFreeAssertThrows.assertThrows;
import static com.google.common.truth.Truth.assertThat;

import com.google.common.annotations.GwtCompatible;
import java.math.BigInteger;
import java.math.RoundingMode;
import junit.framework.TestCase;
import org.jspecify.annotations.NullUnmarked;

/**
 * Unit tests for {@link MathPreconditions}.
 *
 * @author Ben Yu
 */
@GwtCompatible
@NullUnmarked

import static com.google.common.collect.Iterables.unmodifiableIterable;
import static com.google.common.reflect.Reflection.newProxy;
import static java.util.Arrays.asList;

import com.google.common.annotations.GwtIncompatible;
import java.lang.reflect.InvocationHandler;
import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;
import java.util.Collection;
import java.util.HashSet;

    private Scope excludeScope;

    /** Specify pattern for types to ignore. */
    private Pattern ignorePattern = Pattern.compile("^$");

    /**
     * Specify the list of annotations that allow missed documentation.
     * Only short names are allowed, e.g. {@code Generated}.
     */
    private List<String> skipAnnotations = Collections.singletonList("Generated");

    /**

import static java.util.Collections.frequency;
import static junit.framework.Assert.assertEquals;
import static junit.framework.Assert.fail;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Iterator;
import java.util.List;

import static com.google.common.truth.Truth.assertThat;
import static java.util.Arrays.asList;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import com.google.common.collect.testing.ListTestSuiteBuilder;
import com.google.common.collect.testing.MinimalCollection;

import static java.util.concurrent.TimeUnit.NANOSECONDS;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import com.google.common.base.Preconditions;
import com.google.errorprone.annotations.CanIgnoreReturnValue;
import java.time.Duration;
import java.util.ArrayDeque;
import java.util.Collection;

¿Recuerdas que te dije antes que `Annotated` puede usarse para agregar metadatos a tus parámetros en la [Introducción a Tipos de Python](../python-types.md#type-hints-with-metadata-annotations)?

Ahora es el momento de usarlo con FastAPI. 🚀

Teníamos esta anotación de tipo:

```Python
q: str | None = None
```

Lo que haremos es envolver eso con `Annotated`, para que se convierta en:

```Python
q: Annotated[str | None] = None

import static com.google.common.base.Preconditions.checkNotNull;

import com.google.common.annotations.GwtCompatible;
import com.google.common.base.Function;
import com.google.common.collect.Maps;
import com.google.errorprone.annotations.CanIgnoreReturnValue;
import com.google.errorprone.annotations.concurrent.LazyInit;
import java.io.Serializable;
import java.util.Collections;
import java.util.Iterator;

# Python Types Intro { #python-types-intro }

Python has support for optional "type hints" (also called "type annotations").

These **"type hints"** or annotations are a special syntax that allow declaring the <dfn title="for example: str, int, float, bool">type</dfn> of a variable.

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