* whose keys and values are the result of applying the provided mapping functions to the input
   * elements.
   *
   * <p>For streams with defined encounter order (as defined in the Ordering section of the {@link
   * java.util.stream} Javadoc), that order is preserved, but entries are <a
   * href="ImmutableMultimap.html#iteration">grouped by key</a>.
   *
   * <p>Example:
   *
   * <pre>{@code

 *
 * <p>A discrete domain always represents the <i>entire</i> set of values of its type; it cannot
 * represent partial domains such as "prime integers" or "strings of length 5."
 *
 * <p>See the Guava User Guide section on <a href=
 * "https://github.com/google/guava/wiki/RangesExplained#discrete-domains">{@code
 * DiscreteDomain}</a>.
 *
 * @author Kevin Bourrillion
 * @since 10.0
 */

import com.google.common.annotations.GwtCompatible;

/**
 * Low-level, high-performance utility methods related to the {@linkplain Charsets#UTF_8 UTF-8}
 * character encoding. UTF-8 is defined in section D92 of <a
 * href="http://www.unicode.org/versions/Unicode6.2.0/ch03.pdf">The Unicode Standard Core
 * Specification, Chapter 3</a>.
 *
 * <p>The variant of UTF-8 implemented by this class is the restricted definition of UTF-8

    // places left to rotate.
    int m = -distance % length;
    m = (m < 0) ? m + length : m;
    // The current index of what will become the first element of the rotated section.
    int newFirstIndex = m + fromIndex;
    if (newFirstIndex == fromIndex) {
      return;
    }

    reverse(array, fromIndex, newFirstIndex);
    reverse(array, newFirstIndex, toIndex);

   * @throws ArithmeticException if {@code a * b} overflows in signed {@code long} arithmetic
   */
  @SuppressWarnings("ShortCircuitBoolean")
  public static long checkedMultiply(long a, long b) {
    // Hacker's Delight, Section 2-12
    int leadingZeros =
        Long.numberOfLeadingZeros(a)
            + Long.numberOfLeadingZeros(~a)
            + Long.numberOfLeadingZeros(b)
            + Long.numberOfLeadingZeros(~b);
    /*

   * whose keys and values are the result of applying the provided mapping functions to the input
   * elements.
   *
   * <p>For streams with defined encounter order (as defined in the Ordering section of the {@link
   * java.util.stream} Javadoc), that order is preserved, but entries are <a
   * href="ImmutableMultimap.html#iteration">grouped by key</a>.
   *
   * <p>Example:
   *
   * <pre>{@code

 * prefer the simplest interface that satisfies your use case. See the <a
 * href="https://github.com/google/guava/wiki/GraphsExplained#choosing-the-right-graph-type">
 * "Choosing the right graph type"</a> section of the Guava User Guide for more details.
 *
 * <h3>Capabilities</h3>
 *
 * <p>{@code ValueGraph} supports the following use cases (<a
 * href="https://github.com/google/guava/wiki/GraphsExplained#definitions">definitions of

   *   <li>Underscores ('_') are permitted wherever dashes ('-') are permitted.
   *   <li>Parts other than the final part may start with a digit, as mandated by <a
   *       href="https://tools.ietf.org/html/rfc1123#section-2">RFC 1123</a>.
   * </ul>
   *
   * @param domain A domain name (not IP address)
   * @throws IllegalArgumentException if {@code domain} is not syntactically valid according to
   *     {@link #isValid}

   * whose keys and values are the result of applying the provided mapping functions to the input
   * elements.
   *
   * <p>For streams with defined encounter order (as defined in the Ordering section of the {@link
   * java.util.stream} Javadoc), that order is preserved, but entries are <a
   * href="ImmutableMultimap.html#iteration">grouped by key</a>.
   *
   * <p>Example:
   *
   * <pre>{@code

    // places left to rotate.
    int m = -distance % length;
    m = (m < 0) ? m + length : m;
    // The current index of what will become the first element of the rotated section.
    int newFirstIndex = m + fromIndex;
    if (newFirstIndex == fromIndex) {
      return;
    }

    reverse(array, fromIndex, newFirstIndex);
    reverse(array, newFirstIndex, toIndex);