return (int) x == x;
  }

  /**
   * Returns the arithmetic mean of {@code x} and {@code y}, rounded toward negative infinity. This
   * method is resilient to overflow.
   *
   * @since 14.0
   */
  public static long mean(long x, long y) {
    // Efficient method for computing the arithmetic mean.
    // The alternative (x + y) / 2 fails for large values.

import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import java.math.BigDecimal;
import java.math.RoundingMode;

/**
 * A class for arithmetic on {@link BigDecimal} that is not covered by its built-in methods.
 *
 * @author Louis Wasserman
 * @since 30.0
 */
@J2ktIncompatible
@GwtIncompatible
public class BigDecimalMath {
  private BigDecimalMath() {}

 *
 * <p>Its speed is comparable to CityHash64, and its quality of hashing is at least as good.
 *
 * <p>Note to maintainers: This implementation relies on signed arithmetic being bit-wise equivalent
 * to unsigned arithmetic in all cases except:
 *
 * <ul>
 *   <li>comparisons (signed values can be negative)
 *   <li>division (avoided here)
 *   <li>shifting (right shift must be unsigned)
 * </ul>
 *

  /** Helper method that asserts the arithmetic mean of x and y is equal to the expectedMean. */
  private static void assertMean(int expectedMean, int x, int y) {
    assertEquals(
        "The expectedMean should be the same as computeMeanSafely",
        expectedMean,
        computeMeanSafely(x, y));
    assertMean(x, y);
  }

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

        if (!VALID_SHARE.matcher(share).matches()) {
            throw new IllegalArgumentException("Share name contains invalid characters: " + share);
        }
    }

    /**
     * Validates integer for safe arithmetic operations
     *
     * @param a first operand
     * @param b second operand
     * @param operation the operation name
     * @throws ArithmeticException if operation would overflow
     */

     *
     * a) every iteration (except potentially the first) has guess >= floor(sqrt(x)). This is
     * because guess' is the arithmetic mean of guess and x / guess, sqrt(x) is the geometric mean,
     * and the arithmetic mean is always higher than the geometric mean.
     *
     * b) this iteration converges to floor(sqrt(x)). In fact, the number of correct digits doubles

  /** Helper method that asserts the arithmetic mean of x and y is equal to the expectedMean. */
  private static void assertMean(int expectedMean, int x, int y) {
    assertEquals(
        "The expectedMean should be the same as computeMeanSafely",
        expectedMean,
        computeMeanSafely(x, y));
    assertMean(x, y);
  }

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

  static final double INTEGER_MANY_VALUES_MAX = 555555.0;
  static final double INTEGER_MANY_VALUES_MIN = -4444.0;

  // Integers which will overflow if summed (using integer arithmetic):
  static final int[] LARGE_INTEGER_VALUES = {Integer.MAX_VALUE, Integer.MAX_VALUE / 2};
  static final double LARGE_INTEGER_VALUES_MEAN =
      BigInteger.valueOf(Integer.MAX_VALUE)

    return count;
  }

  /**
   * Returns the <a href="http://en.wikipedia.org/wiki/Arithmetic_mean">arithmetic mean</a> of the
   * values. The count must be non-zero.
   *
   * <p>If these values are a sample drawn from a population, this is also an unbiased estimator of
   * the arithmetic mean of the population.
   *
   * <h3>Non-finite values</h3>
   *

    // 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. */
  private static void assertMean(long expectedMean, long x, long y) {
    assertEquals(
        "The expectedMean should be the same as computeMeanSafely",