// supports float types. tf.round with integer input type will become an
// identity op, so we will never face an mhlo.floor with an integer input type.
// The pattern matched executes the following computation:
// frac = x - floor(x)
// to_even = (floor(x) - 2 * floor(0.5 * x)) == 1
// if frac > 0.5 || (frac == 0.5 && to_even)
//   return floor(x) + 1
// else
//   return floor(x)

     * can narrow the possible floor(log10(x)) values to two. For example, if floor(log2(x)) is 6,
     * then 64 <= x < 128, so floor(log10(x)) is either 1 or 2.
     */
    int y = maxLog10ForLeadingZeros[Long.numberOfLeadingZeros(x)];
    /*
     * y is the higher of the two possible values of floor(log10(x)). If x < 10^y, then we want the

    /*
     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
     * guaranteed to be either exact or one less than the correct value. This follows from fact that
     * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
     * trivial.
     */
    long quotient = ((dividend >>> 1) / divisor) << 1;
    long rem = dividend - quotient * divisor;

    /*
     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
     * guaranteed to be either exact or one less than the correct value. This follows from fact that
     * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
     * trivial.
     */
    long quotient = ((dividend >>> 1) / divisor) << 1;
    long rem = dividend - quotient * divisor;

	if config.MaxPerCore != nil && *config.MaxPerCore > 0 {
		floor := 0
		if config.Min != nil {
			floor = int(*config.Min)
		}
		scaled := int(*config.MaxPerCore) * detectNumCPU()
		if scaled > floor {
			logger.V(3).Info("GetConntrackMax: using scaled conntrack-max-per-core")
			return scaled, nil
		}
		logger.V(3).Info("GetConntrackMax: using conntrack-min")
		return floor, nil
	}
	return 0, nil
}

			// `memory.high=floor[(requests.memory + memory throttling factor * (limits.memory or node allocatable memory - requests.memory))/pageSize] * pageSize`
			// where default value of memory throttling factor is set to 0.9
			// More info: https://git.k8s.io/enhancements/keps/sig-node/2570-memory-qos
			memoryHigh := int64(0)
			if memoryLimit != 0 {
				memoryHigh = int64(math.Floor(
					float64(memoryRequest)+

import static com.google.common.math.MathTesting.POSITIVE_FINITE_DOUBLE_CANDIDATES;
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;
import static java.math.RoundingMode.HALF_UP;
import static java.math.RoundingMode.UNNECESSARY;

    // is an integer 199*index/2. If index is odd, that is halfway between floor(199*index/2) and
    // ceil(199*index/2).
    if (index % 2 == 0) {
      int position = IntMath.divide(199 * index, 2, UNNECESSARY);
      return PSEUDORANDOM_DATASET_SORTED.get(position);
    } else {
      int positionFloor = IntMath.divide(199 * index, 2, FLOOR);
      int positionCeil = IntMath.divide(199 * index, 2, CEILING);

    @CheckForNull
    private AvlNode<E> floor(Comparator<? super E> comparator, @ParametricNullness E e) {
      int cmp = comparator.compare(e, getElement());
      if (cmp > 0) {
        return (right == null) ? this : MoreObjects.firstNonNull(right.floor(comparator, e), this);
      } else if (cmp == 0) {
        return this;
      } else {
        return (left == null) ? null : left.floor(comparator, e);
      }
    }

def LowerTruncateDivOpOnIntTensors : Pat<
  (TF_TruncateDivOp TF_IntTensor:$lhs, $rhs),
  (TF_DivOp $lhs, $rhs)>;

// Note: truncation could also be implemented as sign(x) * floor(abs(x)) or
//       (-1 & x) || floor(abs(x)), based on performance benchmarks.
def LowerTruncateDivOpOnFloatTensors : Pat<
  (TF_TruncateDivOp TF_FloatTensor:$lhs, $rhs),
  (TF_SelectV2Op
    (TF_LessOp
      (TF_DivOp:$div $lhs, $rhs),