*
   * <p>This fit minimizes the root-mean-square error in {@code y} as a function of {@code x}. This
   * error is defined as the square root of the mean of the squares of the differences between the
   * actual {@code y} values of the data and the values predicted by the fit for the {@code x}
   * values (i.e. it is the square root of the mean of the squares of the vertical distances between

 *     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:
 *

      builder.append(args[i++]);
      templateStart = placeholderStart + 2;
    }
    builder.append(template, templateStart, template.length());

    // if we run out of placeholders, append the extra args in square braces
    if (i < args.length) {
      builder.append(" [");
      builder.append(args[i++]);
      while (i < args.length) {
        builder.append(", ");
        builder.append(args[i++]);
      }

    }
    requests.addAndGet(reps);
    return dummy;
  }

  private int nextRandomKey() {
    int a = random.nextInt(max);

    /*
     * For example, if concentration=2.0, the following takes the square root of
     * the uniformly-distributed random integer, then truncates any fractional
     * part, so higher integers would appear (in this case linearly) more often
     * than lower ones.
     */

  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) {

   *     argument. These are matched by position - the first {@code %s} gets {@code
   *     errorMessageArgs[0]}, etc. Unmatched arguments will be appended to the formatted message in
   *     square braces. Unmatched placeholders will be left as-is.
   * @param errorMessageArgs the arguments to be substituted into the message template. Arguments
   *     are converted to strings using {@link String#valueOf(Object)}.

      builder.append(args[i++]);
      templateStart = placeholderStart + 2;
    }
    builder.append(template.substring(templateStart));

    // if we run out of placeholders, append the extra args in square braces
    if (i < args.length) {
      builder.append(" [");
      builder.append(args[i++]);
      while (i < args.length) {
        builder.append(", ");
        builder.append(args[i++]);
      }

    // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31).
    intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE);
    // Add values up to 40. This covers cases like "square of a prime" and such.
    for (int i = 1; i <= 40; i++) {
      intValues.add(i);
    }
    // Now add values near 2^N for lots of values of N.
    for (int exponent : asList(2, 3, 4, 9, 15, 16, 17, 24, 25, 30)) {

   *
   * <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