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() {

        .roundUnnecessaryShouldThrow()
        .test();
  }

  public void testRoundToDouble_negativeTwoToThe54MinusOne() {
    new RoundToDoubleTester(BigDecimal.valueOf((-1L << 54) - 1))
        .setExpectation(-Math.pow(2, 54), DOWN, CEILING, HALF_DOWN, HALF_UP, HALF_EVEN)
        .setExpectation(DoubleUtils.nextDown(-Math.pow(2, 54)), FLOOR, UP)

      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

   * infinite {@code double} values are considered infinitely far away. For example, 2^2000 is not
   * representable as a double, but {@code roundToDouble(BigDecimal.valueOf(2).pow(2000), HALF_UP)}
   * will return {@code Double.MAX_VALUE}, not {@code Double.POSITIVE_INFINITY}.
   *
   * <p>For the case of {@link RoundingMode#HALF_EVEN}, this implementation uses the IEEE 754

   * infinite {@code double} values are considered infinitely far away. For example, 2^2000 is not
   * representable as a double, but {@code roundToDouble(BigDecimal.valueOf(2).pow(2000), HALF_UP)}
   * will return {@code Double.MAX_VALUE}, not {@code Double.POSITIVE_INFINITY}.
   *
   * <p>For the case of {@link RoundingMode#HALF_EVEN}, this implementation uses the IEEE 754

  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. */