*     throw new IllegalArgumentException("input is negative: " + value);
 *   }
 *   // calculate square root
 * }
 * }</pre>
 *
 * <p>to be replaced with the more compact
 *
 * <pre>{@code
 * public static double sqrt(double value) {
 *   checkArgument(value >= 0, "input is negative: %s", value);
 *   // calculate square root
 * }
 * }</pre>
 *
 * <p>so that a hypothetical bad caller of this method, such as:
 *

 *     throw new IllegalArgumentException("input is negative: " + value);
 *   }
 *   // calculate square root
 * }
 * }</pre>
 *
 * <p>to be replaced with the more compact
 *
 * <pre>{@code
 * public static double sqrt(double value) {
 *   checkArgument(value >= 0, "input is negative: %s", value);
 *   // calculate square root
 * }
 * }</pre>
 *
 * <p>so that a hypothetical bad caller of this method, such as:
 *

  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));
        assertTrue(isPerfectSquare);
      } catch (ArithmeticException e) {

  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));
        assertTrue(isPerfectSquare);
      } catch (ArithmeticException e) {

        return (logX2Floor < 2 * logFloor + 1) ? logFloor : logFloor + 1;

      default:
        throw new AssertionError();
    }
  }

  /*
   * The maximum number of bits in a square root for which we'll precompute an explicit half power
   * of two. This can be any value, but higher values incur more class load time and linearly
   * increasing memory consumption.
   */

   *
   * <p>For IPv4 addresses, this is identical to {@link InetAddress#getHostAddress()}, but for IPv6
   * addresses it compresses zeroes and surrounds the text with square brackets; for example {@code
   * "[2001:db8::1]"}.
   *
   * <p>Per section 3.2.2 of <a target="_parent"
   * href="http://tools.ietf.org/html/rfc3986#section-3.2.2">RFC 3986</a>, a URI containing an IPv6

    Function<Integer, Integer> square =
        new Function<Integer, Integer>() {
          @Override
          public Integer apply(Integer in) {
            return in * in;
          }
        };
    Multimap<String, Integer> transformed = Multimaps.transformValues(multimap, square);
    assertThat(transformed.entries())
        .containsExactly(

  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));
        assertTrue(isPerfectSquare);
      } catch (ArithmeticException e) {

          return accum;
        case 1:
          return accum * b;
        default:
          accum *= ((k & 1) == 0) ? 1 : b;
          b *= b;
      }
    }
  }

  /**
   * Returns the square root of {@code x}, rounded with the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x < 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code

          return accum;
        case 1:
          return b * accum;
        default:
          accum *= ((k & 1) == 0) ? 1 : b;
          b *= b;
      }
    }
  }

  /**
   * Returns the square root of {@code x}, rounded with the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x < 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code