}

  /* Relies on the correctness of sqrt(int, FLOOR). */
  @GwtIncompatible // sqrt
  public void testSqrtExactMatchesFloorOrThrows() {
    for (int x : POSITIVE_INTEGER_CANDIDATES) {
      int floor = IntMath.sqrt(x, FLOOR);
      // We only expect an exception if x was not a perfect square.
      boolean isPerfectSquare = floor * floor == x;
      try {
        assertEquals(floor, IntMath.sqrt(x, UNNECESSARY));

      return LongMath.log10(x.longValue(), mode);
    }

    int approxLog10 = (int) (log2(x, FLOOR) * LN_2 / LN_10);
    BigInteger approxPow = BigInteger.TEN.pow(approxLog10);
    int approxCmp = approxPow.compareTo(x);

    /*
     * We adjust approxLog10 and approxPow until they're equal to floor(log10(x)) and
     * 10^floor(log10(x)).
     */

    if (approxCmp > 0) {
      /*

      }
    }
  }

  // Relies on the correctness of log10(long, FLOOR) and of pow(long, int).
  @GwtIncompatible // TODO
  public void testLog10Exact() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      int floor = LongMath.log10(x, FLOOR);
      boolean expectedSuccess = LongMath.pow(10, floor) == x;
      try {
        assertEquals(floor, LongMath.log10(x, UNNECESSARY));
        assertTrue(expectedSuccess);

  // Relies on the correctness of sqrt(BigInteger, FLOOR).
  @GwtIncompatible // TODO
  public void testSqrtExact() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      BigInteger floor = BigIntegerMath.sqrt(x, FLOOR);
      // We only expect an exception if x was not a perfect square.
      boolean isPerfectSquare = floor.pow(2).equals(x);
      try {
        assertEquals(floor, BigIntegerMath.sqrt(x, UNNECESSARY));

        .roundUnnecessaryShouldThrow()
        .test();
  }

  public void testRoundToDouble_negativeTwoToThe54MinusThree() {
    new RoundToDoubleTester(BigDecimal.valueOf((-1L << 54) - 3))
        .setExpectation(-Math.pow(2, 54), DOWN, CEILING)
        .setExpectation(
            DoubleUtils.nextDown(-Math.pow(2, 54)), FLOOR, UP, HALF_DOWN, HALF_UP, HALF_EVEN)

     * can narrow the possible floor(log10(x)) values to two. For example, if floor(log2(x)) is 6,
     * then 64 <= x < 128, so floor(log10(x)) is either 1 or 2.
     */
    int y = maxLog10ForLeadingZeros[Long.numberOfLeadingZeros(x)];
    /*
     * y is the higher of the two possible values of floor(log10(x)). If x < 10^y, then we want the

    do {
      result = randomNonNegativeBigInteger(numBits);
    } while (result.signum() == 0);
    return result;
  }

  /**
   * Generates a number in [0, 2^numBits) with an exponential distribution. The floor of the log2 of
   * the result is chosen uniformly at random in [0, numBits), and then the result is chosen in that
   * range uniformly at random. Zero is treated as having log2 == 0.
   */

    /*
     * Otherwise, approximate the quotient, check, and correct if necessary. Our approximation is
     * guaranteed to be either exact or one less than the correct value. This follows from fact that
     * floor(floor(x)/i) == floor(x/i) for any real x and integer i != 0. The proof is not quite
     * trivial.
     */
    long quotient = ((dividend >>> 1) / divisor) << 1;
    long rem = dividend - quotient * divisor;

import static java.math.BigInteger.ONE;
import static java.math.BigInteger.ZERO;
import static java.math.RoundingMode.CEILING;
import static java.math.RoundingMode.DOWN;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.HALF_DOWN;
import static java.math.RoundingMode.HALF_EVEN;
import static java.math.RoundingMode.HALF_UP;
import static java.math.RoundingMode.UP;
import static java.util.Arrays.asList;

    do {
      result = randomNonNegativeBigInteger(numBits);
    } while (result.signum() == 0);
    return result;
  }

  /**
   * Generates a number in [0, 2^numBits) with an exponential distribution. The floor of the log2 of
   * the result is chosen uniformly at random in [0, numBits), and then the result is chosen in that
   * range uniformly at random. Zero is treated as having log2 == 0.
   */