*
   * <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

   *
   * <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:
 *

    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(

      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++]);
      }