int x = 1000000;
    for (RoundingMode mode : ALL_ROUNDING_MODES) {
      assertEquals(6, IntMath.log10(x, mode));
    }
  }

  // Simple test to cover sqrt(0) for all types and all modes.
  @GwtIncompatible // sqrt
  public void testSqrtZeroAlwaysZero() {
    for (RoundingMode mode : ALL_ROUNDING_MODES) {
      assertEquals(0, IntMath.sqrt(0, mode));
    }
  }

  @GwtIncompatible // sqrt

      this.input = input;
    }

    @CanIgnoreReturnValue
    RoundToDoubleTester setExpectation(double expectedValue, RoundingMode... modes) {
      for (RoundingMode mode : modes) {
        Double previous = expectedValues.put(mode, expectedValue);
        if (previous != null) {
          throw new AssertionError();
        }
      }
      return this;
    }

      }
    }
  }

  // Relies on the correctness of BigIntegerMath.log10 for all modes except UNNECESSARY.
  @GwtIncompatible // TODO
  public void testLog10MatchesBigInteger() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
        assertEquals(BigIntegerMath.log10(valueOf(x), mode), LongMath.log10(x, mode));
      }
    }
  }

    /**
     * Verifies that the provided CRUD mode matches the expected mode.
     * Throws a validation error if the modes do not match.
     *
     * @param crudMode the actual CRUD mode
     * @param expectedMode the expected CRUD mode
     */
    protected void verifyCrudMode(final int crudMode, final int expectedMode) {
        if (crudMode != expectedMode) {

    //                                                                        ============
    /**
     * Verify that the CRUD mode matches the expected mode.
     * Throws validation error if modes don't match.
     *
     * @param crudMode The current CRUD mode
     * @param expectedMode The expected CRUD mode
     * @param dictId The dictionary ID for error context
     */

 * It manages the crawling lifecycle, including initialization, execution coordination,
 * monitoring, and cleanup operations.
 *
 * <p>The crawler can operate in different modes based on command-line options:
 * <ul>
 * <li>Web crawling - crawls web sites and web content</li>
 * <li>File system crawling - crawls file systems and documents</li>

- The nftables mode of kube-proxy is now GA. (The iptables mode remains the
  default; you can select the nftables mode by passing `--proxy-mode nftables`
  or using a config file with `mode: nftables`. See the kube-proxy documentation

  - [Changelog since v1.32.0](#changelog-since-v1320)
  - [Important Security Information](#important-security-information-3)
    - [CVE-2024-9042: Command Injection affecting Windows nodes via nodes/*/logs/query API](#cve-2024-9042-command-injection-affecting-windows-nodes-via-nodeslogsquery-api)
  - [Changes by Kind](#changes-by-kind-7)
    - [API Change](#api-change-1)
    - [Feature](#feature-4)
    - [Bug or Regression](#bug-or-regression-7)

  }

  /**
   * Returns a hash code, having the same bit length as each of the input hash codes, that combines
   * the information of these hash codes in an ordered fashion. That is, whenever two equal hash
   * codes are produced by two calls to this method, it is <i>as likely as possible</i> that each
   * was computed from the <i>same</i> input hash codes in the <i>same</i> order.
   *

   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}
   *     is not a power of two
   */
  @SuppressWarnings("fallthrough")
  // TODO(kevinb): remove after this warning is disabled globally
  public static int log2(BigInteger x, RoundingMode mode) {
    checkPositive("x", checkNotNull(x));