BigInteger x2 = x.pow(2);
      // x^2 < 10^(2 * result + 1), or else we would have rounded up
      assertTrue(TEN.pow(2 * result + 1).compareTo(x2) > 0);
      // x^2 >= 10^(2 * result - 1), or else we would have rounded down
      assertTrue(result == 0 || TEN.pow(2 * result - 1).compareTo(x2) <= 0);
    }
  }

  @GwtIncompatible // TODO
  public void testLog10HalfDown() {

      if (d >= 1.0) {
        assertTrue(log2 >= 0);
        assertTrue(StrictMath.pow(2.0, log2) <= d);
        assertTrue(StrictMath.pow(2.0, log2 + 1) > d);
      } else {
        assertTrue(log2 <= 0);
        assertTrue(StrictMath.pow(2.0, log2) >= d);
        assertTrue(StrictMath.pow(2.0, log2 - 1) < d);
      }
    }
  }

      case HALF_DOWN:
      case HALF_UP:
      case HALF_EVEN:
        // Since sqrt(10) is irrational, log10(x) - floorLog can never be exactly 0.5
        BigInteger x2 = x.pow(2);
        BigInteger halfPowerSquared = floorPow.pow(2).multiply(BigInteger.TEN);
        return (x2.compareTo(halfPowerSquared) <= 0) ? floorLog : floorLog + 1;
    }
    throw new AssertionError();
  }

      }
    }
  }

  @GwtIncompatible // 2147483646^2 expected=4
  public void testPow() {
    for (int i : ALL_INTEGER_CANDIDATES) {
      for (int pow : EXPONENTS) {
        assertEquals(i + "^" + pow, BigInteger.valueOf(i).pow(pow).intValue(), IntMath.pow(i, pow));
      }
    }
  }

  @AndroidIncompatible // slow
  @GwtIncompatible // Math.floorDiv gets wrong answers for negative divisors

    for (int i = 0; i < LongMath.halfPowersOf10.length; i++) {
      assertEquals(
          BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * i + 1), FLOOR),
          BigInteger.valueOf(LongMath.halfPowersOf10[i]));
    }
    BigInteger nextBigger =
        BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * LongMath.halfPowersOf10.length + 1), FLOOR);
    assertTrue(nextBigger.compareTo(BigInteger.valueOf(Long.MAX_VALUE)) > 0);
  }

  // 18,304
  private static final long EXPECTED_TWO_BYTE_ROUNDTRIPPABLE_COUNT =
      // Both bytes are one byte characters
      (long) Math.pow(EXPECTED_ONE_BYTE_ROUNDTRIPPABLE_COUNT, 2)
          +
          // The possible number of two byte characters
          TWO_BYTE_ROUNDTRIPPABLE_CHARACTERS;

  // 2048

  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.
  static final ImmutableList<Integer> EXPONENTS =
      ImmutableList.of(0, 1, 2, 3, 4, 7, 10, 15, 20, 25, 40, 70);

  /* Helper function to make a Long value from an Integer. */

   * Returns {@code b} to the {@code k}th power. Even if the result overflows, it will be equal to
   * {@code BigInteger.valueOf(b).pow(k).longValue()}. This implementation runs in {@code O(log k)}
   * time.
   *
   * @throws IllegalArgumentException if {@code k < 0}
   */
  @GwtIncompatible // TODO
  public static long pow(long b, int k) {
    checkNonNegative("exponent", k);
    if (-2 <= b && b <= 2) {
      switch ((int) b) {

   * degenerating it.
   *
   * @since 14.0 (since 11.0 as expectedFalsePositiveProbability())
   */
  public double expectedFpp() {
    return Math.pow((double) bits.bitCount() / bitSize(), numHashFunctions);
  }

  /**
   * Returns an estimate for the total number of distinct elements that have been added to this

    *   gRPC: Propagate truncated errors (instead of returning gRPC internal
        error).
    *   Augment `parallel_interleave` to support 2 kinds of prefetching.
    *   Improved XLA support for C64-related ops log, pow, atan2, tanh.
    *   Add probabilistic convolutional layers.

## API Changes

*   Introducing `prepare_variance` boolean with default setting to False for
    backward compatibility.