};

  @VisibleForTesting
  static final int[] powersOf10 = {
    1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000
  };

  // halfPowersOf10[i] = largest int less than 10^(i + 0.5)
  @VisibleForTesting
  static final int[] halfPowersOf10 = {
    3, 31, 316, 3162, 31622, 316227, 3162277, 31622776, 316227766, Integer.MAX_VALUE
  };

  /**

    100000000000000L,
    1000000000000000L,
    10000000000000000L,
    100000000000000000L,
    1000000000000000000L
  };

  // halfPowersOf10[i] = largest long less than 10^(i + 0.5)
  @GwtIncompatible // TODO
  @VisibleForTesting
  static final long[] halfPowersOf10 = {
    3L,
    31L,
    316L,
    3162L,
    31622L,
    316227L,
    3162277L,
    31622776L,
    316227766L,

    }
  }

  @GwtIncompatible // BigIntegerMath // TODO(cpovirk): GWT-enable BigIntegerMath
  public void testConstantsHalfPowersOf10() {
    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 testConstantsHalfPowersOf10() {
    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);

    }
  }

  @GwtIncompatible // BigIntegerMath // TODO(cpovirk): GWT-enable BigIntegerMath
  public void testConstantsHalfPowersOf10() {
    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()));
    }
  }