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    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      for (RoundingMode mode : asList(FLOOR, DOWN)) {
        int result = BigIntegerMath.log10(x, mode);
        assertTrue(TEN.pow(result).compareTo(x) <= 0);
        assertTrue(TEN.pow(result + 1).compareTo(x) > 0);
      }
    }
  }

  @GwtIncompatible // TODO
  public void testLog10Ceiling() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {

        approxPow = approxPow.divide(BigInteger.TEN);
        approxCmp = approxPow.compareTo(x);
      } while (approxCmp > 0);
    } else {
      BigInteger nextPow = BigInteger.TEN.multiply(approxPow);
      int nextCmp = nextPow.compareTo(x);
      while (nextCmp <= 0) {
        approxLog10++;
        approxPow = nextPow;
        approxCmp = nextCmp;
        nextPow = BigInteger.TEN.multiply(approxPow);

            "nine", 9,
            "ten", 10),
        "one",
        1,
        "two",
        2,
        "three",
        3,
        "four",
        4,
        "five",
        5,
        "six",
        6,
        "seven",
        7,
        "eight",
        8,
        "nine",
        9,
        "ten",
        10);
  }

            "seven", 7,
            "eight", 8,
            "nine", 9,
            "ten", 10),
        "eight",
        8,
        "five",
        5,
        "four",
        4,
        "nine",
        9,
        "one",
        1,
        "seven",
        7,
        "six",
        6,
        "ten",
        10,
        "three",
        3,
        "two",
        2);
  }

    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);
  }

        .that(Longs.tryParse(BigInteger.valueOf(MAX_VALUE).multiply(BigInteger.TEN).toString()))
        .isNull();
    assertWithMessage("Min long - 1")
        .that(Longs.tryParse(BigInteger.valueOf(MIN_VALUE).subtract(BigInteger.ONE).toString()))
        .isNull();
    assertWithMessage("Min long * 10")
        .that(Longs.tryParse(BigInteger.valueOf(MIN_VALUE).multiply(BigInteger.TEN).toString()))
        .isNull();

            "nine", 9,
            "ten", 10),
        "one",
        1,
        "two",
        2,
        "three",
        3,
        "four",
        4,
        "five",
        5,
        "six",
        6,
        "seven",
        7,
        "eight",
        8,
        "nine",
        9,
        "ten",
        10);
  }

    for (int i = 0; i < IntMath.halfPowersOf10.length; i++) {
      assertEquals(
          IntMath.halfPowersOf10[i],
          min(
              Integer.MAX_VALUE,
              BigIntegerMath.sqrt(BigInteger.TEN.pow(2 * i + 1), FLOOR).longValue()));
    }
  }

  public void testConstantsBiggestBinomials() {
    for (int k = 0; k < IntMath.biggestBinomials.length; k++) {

   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}
   *     is not a power of ten
   */
  @GwtIncompatible // TODO
  @SuppressWarnings("fallthrough")
  // TODO(kevinb): remove after this warning is disabled globally
  public static int log10(long x, RoundingMode mode) {
    checkPositive("x", x);