*
   * @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 // need BigIntegerMath to adequately test
  @SuppressWarnings("fallthrough")
  public static int log10(int x, RoundingMode mode) {
    checkPositive("x", x);
    int logFloor = log10Floor(x);

            "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 < 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);
  }

walup?zutrak??z&am-awar?c&aprak?iwol?zsogdyb??dalezc?ib?s&i&lak?p??uklo????l??r&as?f?s??s!.&gro?moc?ten?ude?vog???t!.vog??ubnatsi?x3b689qq6--nx?yc5rb54--nx??m&00tsb3--nx?1qtxm--nx?981rvj--nx?a!.&aayn,enummoc?gro?moc?o&c?idar,ken,?t&en?opsgolb,??c!bew??dretsma?e&rts?t!.&citsalej,esruocsid,???fma?xq--nx??b!.&gro?moc?ten?ude?vog??i??c!.&moc?oc?ten?vog???d!.&gro?moc?ten?ude?vog???f!.&gro?moc?oidar,ten?ude??i??g!vu96d8syzf--nx??h?i!.&ca?gro?moc?o&c!.&clp?dtl???r,?t&en?t??vt??k?rbg4--nx??k!.&drp?e&ria...

        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);
  }

    for (int i = 0; i < IntMath.halfPowersOf10.length; i++) {
      assertEquals(
          IntMath.halfPowersOf10[i],
          Math.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++) {

looked round, eager to see the Queen.

  First came ten soldiers carrying clubs; these were all shaped
like the three gardeners, oblong and flat, with their hands and
feet at the corners:  next the ten courtiers; these were
ornamented all over with diamonds, and walked two and two, as the
soldiers did.  After these came the royal children; there were
ten of them, and the little dears came jumping merrily along hand

            "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);
  }