return Long.MAX_VALUE;
      }
      if (end < start && result > 0) { // underflow
        return Long.MIN_VALUE;
      }
      return result;
    }

    @Override
    public Long minValue() {
      return Long.MIN_VALUE;
    }

    @Override
    public Long maxValue() {
      return Long.MAX_VALUE;
    }

    private Object readResolve() {

        "byte[]"                             | "[Byte.MIN_VALUE, Byte.MAX_VALUE]"        | "[-128, 127]"
        "short[]"                            | "[Short.MIN_VALUE, Short.MAX_VALUE]"      | "[-32768, 32767]"
        "int[]"                              | integerArray()                            | "[-2147483648, 2147483647]"
        "long[]"                             | "[Long.MIN_VALUE, Long.MAX_VALUE]"        | "[-9223372036854775808, 9223372036854775807]"

// number of bins might be smaller than the given `num_bins`.
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

   * Returns the number of nanoseconds of the given duration without throwing or overflowing.
   *
   * <p>Instead of throwing {@link ArithmeticException}, this method silently saturates to either
   * {@link Long#MAX_VALUE} or {@link Long#MIN_VALUE}. This behavior can be useful when decomposing
   * a duration in order to call a legacy API which requires a {@code long, TimeUnit} pair.
   */
  @SuppressWarnings({

    Double.NEGATIVE_INFINITY,
    -Double.MAX_VALUE,
    (double) Long.MIN_VALUE,
    (double) Integer.MIN_VALUE,
    -Math.PI,
    -1.0,
    -Double.MIN_VALUE,
    -0.0,
    +0.0,
    Double.MIN_VALUE,
    1.0,
    Math.PI,
    (double) Integer.MAX_VALUE,
    (double) Long.MAX_VALUE,
    Double.MAX_VALUE,
    Double.POSITIVE_INFINITY,
    Double.NaN,
    Float.MAX_VALUE,
  };

   * Returns the number of nanoseconds of the given duration without throwing or overflowing.
   *
   * <p>Instead of throwing {@link ArithmeticException}, this method silently saturates to either
   * {@link Long#MAX_VALUE} or {@link Long#MIN_VALUE}. This behavior can be useful when decomposing
   * a duration in order to call a legacy API which requires a {@code long, TimeUnit} pair.
   */
  static long toNanosSaturated(Duration duration) {

    assertMean(-1, -1, -1);
    assertMean(Long.MIN_VALUE, Long.MIN_VALUE, Long.MIN_VALUE);
    assertMean(Long.MAX_VALUE, Long.MAX_VALUE, Long.MAX_VALUE);

    // Exhaustive checks
    for (long x : ALL_LONG_CANDIDATES) {
      for (long y : ALL_LONG_CANDIDATES) {
        assertMean(x, y);
      }
    }
  }

  /** Helper method that asserts the arithmetic mean of x and y is equal to the expectedMean. */

   *     {@link Byte#MAX_VALUE} if it is too large, or {@link Byte#MIN_VALUE} if it is too small
   */
  public static byte saturatedCast(long value) {
    if (value > Byte.MAX_VALUE) {
      return Byte.MAX_VALUE;
    }
    if (value < Byte.MIN_VALUE) {
      return Byte.MIN_VALUE;
    }
    return (byte) value;
  }

  /**

   * Returns the number of nanoseconds of the given duration without throwing or overflowing.
   *
   * <p>Instead of throwing {@link ArithmeticException}, this method silently saturates to either
   * {@link Long#MAX_VALUE} or {@link Long#MIN_VALUE}. This behavior can be useful when decomposing
   * a duration in order to call a legacy API which requires a {@code long, TimeUnit} pair.
   */
  @SuppressWarnings({

    (TF_CastOp:$i8_cast
      (TF_ClipByValueOp:$clip $input, $min_value, $max_value),
      ConstBoolAttrFalse:$truncate2),
    ConstBoolAttrFalse:$truncate1),
  (TF_CastOp $clip, ConstBoolAttrFalse),
  [(TensorOf<[I8]> $i8_cast),
   (TensorOf<[I32]> $clip),
   (IsIntSplatValueEqual<"int32_t", "-128"> $min_value),
   (IsIntSplatValueEqual<"int32_t", "127"> $max_value)]>;

// This pattern optimizes:
//   (x + cst1) + cst2 -> x + cst