int j = i & ARRAY_MASK;
      tmp += BigIntegerMath.log10(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int sqrt(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += BigIntegerMath.sqrt(positive[j], mode).intValue();
    }
    return tmp;
  }

  @Benchmark
  int divide(int reps) {
    int tmp = 0;

      int j = i & ARRAY_MASK;
      tmp += LongMath.log10(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int sqrt(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += LongMath.sqrt(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int divide(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {

      int j = i & ARRAY_MASK;
      tmp += IntMath.log10(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int sqrt(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += IntMath.sqrt(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int divide(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {

   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code
   *     sqrt(x)} is not an integer
   */
  @GwtIncompatible // need BigIntegerMath to adequately test
  @SuppressWarnings("fallthrough")
  public static int sqrt(int x, RoundingMode mode) {
    checkNonNegative("x", x);
    int sqrtFloor = sqrtFloor(x);
    switch (mode) {
      case UNNECESSARY:

   * R*R)} of the population standard deviation of {@code y}, where {@code R} is the Pearson's
   * correlation coefficient (as given by {@link #pearsonsCorrelationCoefficient()}).
   *
   * <p>The corresponding root-mean-square error in {@code x} as a function of {@code y} is a
   * fraction {@code sqrt(1/(R*R) - 1)} of the population standard deviation of {@code x}. This fit

   * R*R)} of the population standard deviation of {@code y}, where {@code R} is the Pearson's
   * correlation coefficient (as given by {@link #pearsonsCorrelationCoefficient()}).
   *
   * <p>The corresponding root-mean-square error in {@code x} as a function of {@code y} is a
   * fraction {@code sqrt(1/(R*R) - 1)} of the population standard deviation of {@code x}. This fit

     * Math.sqrt(k * k) <= Math.sqrt(x) <= Math.sqrt((k + 1) * (k + 1))
     *          since Math.sqrt is monotonic.
     * (long) Math.sqrt(k * k) <= (long) Math.sqrt(x) <= (long) Math.sqrt((k + 1) * (k + 1))
     *          since casting to long is monotonic
     * k <= (long) Math.sqrt(x) <= k + 1
     *          since (long) Math.sqrt(k * k) == k, as checked exhaustively in

 *
 * {@snippet :
 * public static double sqrt(double value) {
 *   if (value < 0) {
 *     throw new IllegalArgumentException("input is negative: " + value);
 *   }
 *   // calculate square root
 * }
 * }
 *
 * <p>to be replaced with the more compact
 *
 * {@snippet :
 * public static double sqrt(double value) {
 *   checkArgument(value >= 0, "input is negative: %s", value);

        assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(long, FLOOR). */
  @GwtIncompatible // TODO
  public void testSqrtExactMatchesFloorOrThrows() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      long sqrtFloor = LongMath.sqrt(x, FLOOR);

 *
 * {@snippet :
 * public static double sqrt(double value) {
 *   if (value < 0) {
 *     throw new IllegalArgumentException("input is negative: " + value);
 *   }
 *   // calculate square root
 * }
 * }
 *
 * <p>to be replaced with the more compact
 *
 * {@snippet :
 * public static double sqrt(double value) {
 *   checkArgument(value >= 0, "input is negative: %s", value);