private /* static */ long upperEight(byte[] bytes) {
      return Longs.fromBytes(
          bytes[15], bytes[14], bytes[13], bytes[12], bytes[11], bytes[10], bytes[9], bytes[8]);
    }
  };

  /**
   * Models a lock-free array of bits.
   *
   * <p>We use this instead of java.util.BitSet because we need access to the array of longs and we
   * need compare-and-swap.
   */
  static final class LockFreeBitArray {

    int x = 1000000;
    for (RoundingMode mode : ALL_ROUNDING_MODES) {
      assertEquals(6, IntMath.log10(x, mode));
    }
  }

  // Simple test to cover sqrt(0) for all types and all modes.
  @GwtIncompatible // sqrt
  public void testSqrtZeroAlwaysZero() {
    for (RoundingMode mode : ALL_ROUNDING_MODES) {
      assertEquals(0, IntMath.sqrt(0, mode));
    }
  }

  @GwtIncompatible // sqrt

      for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
        BigDecimal expected = new BigDecimal(d).setScale(0, mode);
        boolean isInBounds =
            expected.compareTo(MAX_INT_AS_BIG_DECIMAL) <= 0
                & expected.compareTo(MIN_INT_AS_BIG_DECIMAL) >= 0;

        try {
          assertEquals(
              "Rounding " + d + " with mode " + mode,
              expected.intValue(),

 *
 * @author Louis Wasserman
 */
@GwtCompatible
public class MathTesting {
  static final ImmutableSet<RoundingMode> ALL_ROUNDING_MODES =
      ImmutableSet.copyOf(RoundingMode.values());

  static final ImmutableList<RoundingMode> ALL_SAFE_ROUNDING_MODES =
      ImmutableList.of(DOWN, UP, FLOOR, CEILING, HALF_EVEN, HALF_UP, HALF_DOWN);

  // Exponents to test for the pow() function.

import java.lang.annotation.RetentionPolicy;
import java.lang.annotation.Target;
import java.lang.reflect.Method;
import java.lang.reflect.Type;
import java.util.Arrays;
import java.util.Comparator;
import javax.lang.model.element.Modifier;
import org.checkerframework.checker.nullness.qual.Nullable;

/**
 * Tester of subtyping relationships between two types.
 *

   * require a (different in each case) function that translates storedPermits to throttling time.
   *
   * This role is played by storedPermitsToWaitTime(double storedPermits, double permitsToTake). The
   * underlying model is a continuous function mapping storedPermits (from 0.0 to maxStoredPermits)
   * onto the 1/rate (i.e. intervals) that is effective at the given storedPermits. "storedPermits"

     * be read without locking. Next fields of nodes are immutable (final). All list additions are
     * performed at the front of each bin. This makes it easy to check changes, and also fast to
     * traverse. When nodes would otherwise be changed, new nodes are created to replace them. This

      for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
        BigDecimal expected = new BigDecimal(d).setScale(0, mode);
        boolean isInBounds =
            expected.compareTo(MAX_INT_AS_BIG_DECIMAL) <= 0
                & expected.compareTo(MIN_INT_AS_BIG_DECIMAL) >= 0;

        try {
          assertEquals(
              "Rounding " + d + " with mode " + mode,
              expected.intValue(),

    long x = 1000000000000L;
    for (RoundingMode mode : ALL_ROUNDING_MODES) {
      assertEquals(12, LongMath.log10(x, mode));
    }
  }

  @GwtIncompatible // TODO
  public void testSqrtNegativeAlwaysThrows() {
    for (long x : NEGATIVE_LONG_CANDIDATES) {
      for (RoundingMode mode : ALL_ROUNDING_MODES) {
        try {
          LongMath.sqrt(x, mode);
          fail("Expected IllegalArgumentException");

    private final File file;
    private final ImmutableSet<FileWriteMode> modes;

    private FileByteSink(File file, FileWriteMode... modes) {
      this.file = checkNotNull(file);
      this.modes = ImmutableSet.copyOf(modes);
    }

    @Override
    public FileOutputStream openStream() throws IOException {
      return new FileOutputStream(file, modes.contains(APPEND));
    }

    @Override