case "url", "lowerAscii", "upperAscii", "substring", "trim":
		if len(args) >= 1 {
			cost := uint64(math.Ceil(float64(actualSize(args[0])) * common.StringTraversalCostFactor))
			return &cost
		}
	case "replace", "split":
		if len(args) >= 1 {
			// cost is the traversal plus the construction of the result
			cost := uint64(math.Ceil(float64(actualSize(args[0])) * 2 * common.StringTraversalCostFactor))
			return &cost
		}
	case "join":

  int sh;  // Stride on "height" dimension.
  int sw;  // Stride on "width" dimension.

  bool ceil_mode;  // Rounding strategy (ceil or floor).
};

// Rounds the dimension based on the ceil mode.
int RoundDim(float dim, bool ceil_mode) {
  if (ceil_mode) {
    return std::ceil(dim);
  }
  return std::floor(dim);
}

// For H or W, calculate the output dimension for average pool.

		if err != nil {
			return 0, time.Time{}, fmt.Errorf("unable to calculate ready pods: %s", err)
		}
		replicaCount = int32(math.Ceil(usageRatio * float64(readyPodCount)))
	} else {
		// Scale to zero or n pods depending on usageRatio
		replicaCount = int32(math.Ceil(usageRatio))
	}

	return replicaCount, timestamp, err
}

                    (IsBoolCompositeAttribute<"count_include_pad", "true"> $attrs)]>;

// Replaces aten.avg_pool2d with ceil mode with (T -> tfl.pad -> tfl.average_pool_2d -> mul -> T). Multiplies by a constant
// which corrects the overcounting of divisors that would occur if doing this computation on a padded tensor with ceil mode off.
def LegalizeAvgPoolCeilModeTrue: Pat<
                    (MHLO_CompositeOp:$old_val

#include <cmath>

#include "absl/container/flat_hash_set.h"
#include "tensorflow/core/framework/types.pb.h"

namespace mlir {
namespace TFL {

double PowerOfTwoBound(double value) {
  return std::pow(2, std::ceil(std::log2(value)));
}

tensorflow::DataType GetQuantizedInferenceType(bool is_signed,
                                               int number_of_bits) {
  if (is_signed && number_of_bits == 8) {

// See: https://github.com/kubernetes/kubernetes/pull/102884#discussion_r662552642
func sharesToMilliCPU(shares int64) int64 {
	milliCPU := int64(0)
	if shares >= int64(cm.MinShares) {
		milliCPU = int64(math.Ceil(float64(shares*milliCPUToCPU) / float64(cm.SharesPerCPU)))
	}
	return milliCPU
}

// quotaToMilliCPU converts cpu.cfs_quota_us and cpu.cfs_period_us to milli-CPU value

	c := int64(math.Ceil(float64(cpu.MilliValue()) / float64(divisor.MilliValue())))
	return strconv.FormatInt(c, 10), nil
}

// convertResourceMemoryToString converts memory value to the format of divisor and returns
// ceiling of the value.
func convertResourceMemoryToString(memory *resource.Quantity, divisor resource.Quantity) (string, error) {
	m := int64(math.Ceil(float64(memory.Value()) / float64(divisor.Value())))

StringAttr GetAvgPoolOpPadAttr(Builder& builder, mhlo::CompositeOp op);

// Get dense attr for a matrix that corrects the over counting of divisors when
// casting an average pool with ceil mode on in terms of average pool with it
// off.
DenseFPElementsAttr GetCorrectionMatrix(Builder& builder, mhlo::CompositeOp op);

}  // namespace odml
}  // namespace mlir

func (d IP) Value() any {
	return d.Addr
}

// Size returns the size of the IP address in bytes.
// Used in the size estimation of the runtime cost.
func (d IP) Size() ref.Val {
	return types.Int(int(math.Ceil(float64(d.Addr.BitLen()) / 8)))

inline float CalculateBinWidth(const float min_value, const float max_value,
                               const int32_t num_bins) {
  const float raw_bin_width = (max_value - min_value) / num_bins;
  return std::pow(2, std::ceil(std::log2(raw_bin_width)));
}

// Calculates the lower bound of the histogram. The lower bound is in form of
// `N * bin_width`.
inline float CalculateLowerBound(const float min_value, const float bin_width) {