* may attempt to download and install SDK components (platforms, build-tools, platform-tools) simultaneously.
 * This can cause race conditions leading to:
 * - `FileAlreadyExistsException` when extracting files
 * - Corrupted installations (e.g., "Build-tool X has corrupt source.properties")
 * - Missing SDK components after installation
 *

    for (E e : collection) {
      checkValid(e);
    }
    return delegate.addAll(collection);
  }

  @Override
  public @Nullable E ceiling(E e) {
    return delegate.ceiling(checkValid(e));
  }

  @Override
  public void clear() {
    delegate.clear();
  }

  @Override
  public Comparator<? super E> comparator() {

import java.lang.annotation.Target;

/**
 * Signifies that a public API (public class, method or field) is subject to incompatible changes,
 * or even removal, in a future release. An API bearing this annotation is exempt from any
 * compatibility guarantees made by its containing library. Note that the presence of this
 * annotation implies nothing about the quality or performance of the API in question, only the fact

import java.lang.annotation.Target;

/**
 * Signifies that a public API (public class, method or field) is subject to incompatible changes,
 * or even removal, in a future release. An API bearing this annotation is exempt from any
 * compatibility guarantees made by its containing library. Note that the presence of this
 * annotation implies nothing about the quality or performance of the API in question, only the fact

 * limitations under the License.
 */

package com.google.common.math;

import static java.math.BigInteger.ONE;
import static java.math.BigInteger.ZERO;
import static java.math.RoundingMode.CEILING;
import static java.math.RoundingMode.DOWN;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.HALF_DOWN;
import static java.math.RoundingMode.HALF_EVEN;

### Grammar and tone

1) Use clear, concise technical Traditional Chinese consistent with existing docs.
2) Address the reader naturally (commonly using “你/你的”).

### Headings

1) Follow existing Traditional Chinese heading style (short and descriptive).
2) Do not add trailing punctuation to headings.

### Quotes and punctuation

  private static final double[] doubleInLongRange = new double[ARRAY_SIZE];
  private static final double[] positiveDoubles = new double[ARRAY_SIZE];

  @Param({"DOWN", "UP", "FLOOR", "CEILING", "HALF_EVEN", "HALF_UP", "HALF_DOWN"})
  RoundingMode mode;

  @BeforeExperiment
  void setUp() {
    for (int i = 0; i < ARRAY_SIZE; i++) {
      doubleInIntRange[i] = randomDouble(Integer.SIZE - 2);

Java serialization is inherently Java-centric and does not support cross-language scenarios well.

- **Type Safety:**
Java serialization does not enforce type safety as strictly as some alternatives, potentially leading to runtime errors.

## Decision

We do not use Java serialization.
Instead, we use custom serialization where we explicitly describe how data objects should be serialized and deserialized.

    page = context.new_page()
    page.goto("http://localhost:8000/docs")
    page.get_by_role("button", name="GET /items/ Read Items").click()
    page.get_by_role("button", name="Try it out").click()
    page.get_by_role("heading", name="Servers").click()
    # Manually add the screenshot
    page.screenshot(path="docs/en/docs/img/tutorial/query-param-models/image01.png")

    # ---------------------
    context.close()
    browser.close()

  private static final BigInteger[] nonzero2 = new BigInteger[ARRAY_SIZE];
  private static final BigInteger[] positive = new BigInteger[ARRAY_SIZE];

  @Param({"DOWN", "UP", "FLOOR", "CEILING", "HALF_EVEN", "HALF_UP", "HALF_DOWN"})
  RoundingMode mode;

  @BeforeExperiment
  void setUp() {
    for (int i = 0; i < ARRAY_SIZE; i++) {
      positive[i] = randomPositiveBigInteger(1024);