int result = BigIntegerMath.log2(x, HALF_UP);
      BigInteger x2 = x.pow(2);
      // x^2 < 2^(2 * result + 1), or else we would have rounded up
      assertTrue(ZERO.setBit(2 * result + 1).compareTo(x2) > 0);
      // x^2 >= 2^(2 * result - 1), or else we would have rounded down
      assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) <= 0);
    }
  }

  public void testLog2HalfDown() {

### Use cases: external service { #use-cases-external-service }

An example could be that you have an external authentication provider that you need to call.

You send it a token and it returns an authenticated user.

# This env is only valid when RBE is available on the selected platform, since
# it enables a derived --config setting.  If RBE is not available (i.e. there
# is no --config setting), bazel would fail and quit. This script does a quick
# check This script checks for such errors early
if ! grep "rbe_$TFCI_BAZEL_TARGET_SELECTING_CONFIG_PREFIX" .bazelrc; then
  cat <<EOF

      description: "Is the goal of this change a performance improvement? If so, what quantifiable improvement should we expect? How would we measure it?"
    validations:
      required: false

  - type: textarea
    id: learning-curve
    attributes:
      label: "Would this change make Go easier or harder to learn, and why?"

  - type: textarea
    id: cost-description
    attributes:

The following self-signed certificate is issued for `consoleAdmin`. So, MinIO would associate it with the pre-defined `consoleAdmin` policy.

```
Certificate:
    Data:
        Version: 3 (0x2)
        Serial Number:
            35:ac:60:46:ad:8d:de:18:dc:0b:f6:98:14:ee:89:e8

    LockFreeBitArray bitArray = new LockFreeBitArray(numBits);
    assertTrue(
        "BitArray.bitSize() must return a positive number, but was " + bitArray.bitSize(),
        bitArray.bitSize() > 0);

    // Ideally we would also test the bitSize() overflow of this BF, but it runs out of heap space
    // BloomFilter.create(Funnels.unencodedCharsFunnel(), 244412641, 1e-11);
  }

  /**

 * </dl>
 *
 * <p>A few notes about IPv6 "IPv4 mapped" addresses and their observed use in Java.
 *
 * <p>"IPv4 mapped" addresses were originally a representation of IPv4 addresses for use on an IPv6
 * socket that could receive both IPv4 and IPv6 connections (by disabling the {@code IPV6_V6ONLY}
 * socket option on an IPv6 socket). Yes, it's confusing. Nevertheless, these "mapped" addresses

            throw new FessSystemException("Could not find extractorFactory.");
        }
        Extractor extractor = extractorFactory.getExtractor(responseData.getMimeType());
        if (extractor == null) {
            extractor = ComponentUtil.getComponent("tikaExtractor");
            if (extractor == null) {
                throw new FessSystemException("Could not find tikaExtractor.");
            }
        }

* `fastapi-people.md`
* `external-links.md`
* `newsletter.md`
* `management-tasks.md`
* `management.md`
* `contributing.md`

Some of these files are updated very frequently and a translation would always be behind, or they include the main content from English source files, etc.

#### Request a New Language

                        logger.warn("Could not close a process input stream.", e);
                    }
                });
                CommonPoolUtil.execute(() -> {
                    try {
                        CloseableUtil.closeQuietly(p.getErrorStream());
                    } catch (final Exception e) {
                        logger.warn("Could not close a process error stream.", e);
                    }