Base64 can encode binary data in strings, but to do it, it needs to use more characters than the original binary data, so it would normally be less efficient than regular files.

Use base64 only if you definitely need to include binary data in JSON, and you can't use files for that.

## Pydantic `bytes` { #pydantic-bytes }

 * with one-sided error: if it claims that an element is contained in it, this might be in error,
 * but if it claims that an element is <i>not</i> contained in it, then this is definitely true.
 *
 * <p>If you are unfamiliar with Bloom filters, this nice <a
 * href="http://llimllib.github.io/bloomfilter-tutorial/">tutorial</a> may help you understand how
 * they work.
 *

    // all values are lower or higher than centerFloor, in which case we find the two highest or
    // lowest respectively). If centerFloor is in allRequired, we will definitely find it. If not,
    // but centerFloor + 1 is, we'll definitely find that. The closest value to the true (unrounded)
    // center will be at either low or high.
    int low = requiredFrom;
    int high = requiredTo;
    while (high > low + 1) {

    return file(new File(first), more);
  }

  /** Returns a {@code File} object for the given path parts. */
  private static File file(File first, String... more) {
    // not very efficient, but should definitely be correct
    File file = first;
    for (String name : more) {
      file = new File(file, name);
    }
    return file;
  }

   * isn't guaranteed to expose the issue, but it is at least likely to become flaky if the race
   * sneaks back in, and in this case flaky means something is definitely wrong.
   *
   * <p>Before the bug was fixed this test would fail at least 30% of the time.
   */
  public void testTransitionRace() throws TimeoutException {
    for (int k = 0; k < 1000; k++) {

        return false;
      }
    }

    @Override
    int indexOf(@Nullable Object target) {
      if (contains(target)) {
        @SuppressWarnings("unchecked") // if it's contained, it's definitely a C
        C c = (C) requireNonNull(target);
        long total = 0;
        for (Range<C> range : ranges) {
          if (range.contains(c)) {

   * isn't guaranteed to expose the issue, but it is at least likely to become flaky if the race
   * sneaks back in, and in this case flaky means something is definitely wrong.
   *
   * <p>Before the bug was fixed this test would fail at least 30% of the time.
   */
  public void testTransitionRace() throws TimeoutException {
    for (int k = 0; k < 1000; k++) {

        return false;
      }
    }

    @Override
    int indexOf(@Nullable Object target) {
      if (contains(target)) {
        @SuppressWarnings("unchecked") // if it's contained, it's definitely a C
        C c = (C) requireNonNull(target);
        long total = 0;
        for (Range<C> range : ranges) {
          if (range.contains(c)) {

           */
          for (int i = 2; i <= k; i++, n--) {
            if (numeratorBits + nBits < Long.SIZE - 1) {
              // It's definitely safe to multiply into numerator and denominator.
              numerator *= n;
              denominator *= i;
              numeratorBits += nBits;
            } else {

  //    (hypothetical) unsafe read by our caller. Note: adding 'volatile' does not fix this issue,
  //    it would just add an edge such that if done() observed non-null, then it would also
  //    definitely observe all earlier writes, but we still have no guarantee that done() would see
  //    the initial write (just stronger guarantees if it does).
  //