* values, see {@link com.google.common.primitives.Longs}.
 *
 * @author Louis Wasserman
 * @since 11.0
 */
@GwtCompatible
public final class LongMath {
  @VisibleForTesting static final long MAX_SIGNED_POWER_OF_TWO = 1L << (Long.SIZE - 2);

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to

    int startingNumber = LongMath.factorials.length;
    long product = LongMath.factorials[startingNumber - 1];
    // Strip off 2s from this value.
    int shift = Long.numberOfTrailingZeros(product);
    product >>= shift;

    // Use floor(log2(num)) + 1 to prevent overflow of multiplication.
    int productBits = LongMath.log2(product, FLOOR) + 1;
    int bits = LongMath.log2(startingNumber, FLOOR) + 1;

import static java.lang.Math.min;
import static java.util.Objects.requireNonNull;

import com.google.common.annotations.Beta;
import com.google.common.annotations.GwtCompatible;
import com.google.common.math.LongMath;
import com.google.errorprone.annotations.InlineMe;
import com.google.errorprone.annotations.InlineMeValidationDisabled;
import java.util.ArrayDeque;
import java.util.Collection;
import java.util.Deque;

import static java.lang.Math.min;
import static java.util.Objects.requireNonNull;

import com.google.common.annotations.Beta;
import com.google.common.annotations.GwtCompatible;
import com.google.common.math.LongMath;
import com.google.errorprone.annotations.InlineMe;
import com.google.errorprone.annotations.InlineMeValidationDisabled;
import java.util.ArrayDeque;
import java.util.Collection;
import java.util.Deque;

 * the License.
 */

package com.google.common.cache;

import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.math.LongMath.saturatedAdd;
import static com.google.common.math.LongMath.saturatedSubtract;
import static java.lang.Math.max;

import com.google.common.annotations.GwtCompatible;
import com.google.common.base.MoreObjects;
import java.util.Objects;

 * the License.
 */

package com.google.common.cache;

import static com.google.common.base.Preconditions.checkArgument;
import static com.google.common.math.LongMath.saturatedAdd;
import static com.google.common.math.LongMath.saturatedSubtract;
import static java.lang.Math.max;

import com.google.common.annotations.GwtCompatible;
import com.google.common.base.MoreObjects;
import java.util.Objects;

 * the License.
 */

package com.google.common.hash;

import static com.google.common.base.Preconditions.checkArgument;

import com.google.common.math.LongMath;
import com.google.common.primitives.Ints;
import com.google.common.primitives.Longs;
import java.math.RoundingMode;
import java.util.Arrays;
import java.util.concurrent.atomic.AtomicLongArray;

    for (int i = 0; i < 100000; i++) {
      assertEquals(LongMath.isPrime(i), IntMath.isPrime(i));
    }

    // Then check 1000 deterministic pseudo-random int values.
    Random rand = new Random(1);
    for (int i = 0; i < 1000; i++) {
      int n = rand.nextInt(Integer.MAX_VALUE);
      assertEquals(LongMath.isPrime(n), IntMath.isPrime(n));
    }
  }

  public void testSaturatedAbs() {

import static java.lang.Math.min;
import static java.util.concurrent.TimeUnit.SECONDS;

import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import com.google.common.math.LongMath;
import java.util.concurrent.TimeUnit;

@J2ktIncompatible
@GwtIncompatible
abstract class SmoothRateLimiter extends RateLimiter {
  /*
   * How is the RateLimiter designed, and why?
   *

import com.google.common.base.Stopwatch;
import com.google.common.collect.ImmutableSet;
import com.google.common.hash.BloomFilterStrategies.LockFreeBitArray;
import com.google.common.math.LongMath;
import com.google.common.primitives.Ints;
import com.google.common.testing.EqualsTester;
import com.google.common.testing.NullPointerTester;
import com.google.common.testing.SerializableTester;