* 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 :
   * Map<String, Integer> map = ImmutableMap.of("a", 4, "b", 9);
   * Function<Integer, Double> sqrt = (Integer in) -> Math.sqrt((int) in);
   * Map<String, Double> transformed = Maps.transformValues(map, sqrt);
   * System.out.println(transformed);
   * }
   *
   * ... prints {@code {a=2.0, b=3.0}}.
   *

   *
   * {@snippet :
   * Map<String, Integer> map = ImmutableMap.of("a", 4, "b", 9);
   * Function<Integer, Double> sqrt = (Integer in) -> Math.sqrt((int) in);
   * Map<String, Double> transformed = Maps.transformValues(map, sqrt);
   * System.out.println(transformed);
   * }
   *
   * ... prints {@code {a=2.0, b=3.0}}.
   *

pkg runtime, func SetMutexProfileFraction(int) int
pkg runtime, type MemStats struct, NumForcedGC uint32
pkg sort, func Slice(interface{}, func(int, int) bool)
pkg sort, func SliceIsSorted(interface{}, func(int, int) bool) bool
pkg sort, func SliceStable(interface{}, func(int, int) bool)
pkg syscall (linux-arm-cgo), func TimevalToNsec(Timeval) int64

      case UP:
        increment = exponent >= 0 & !isPowerOfTwo(x);
        break;
      case HALF_DOWN:
      case HALF_EVEN:
      case HALF_UP:
        double xScaled = scaleNormalize(x);
        // sqrt(2) is irrational, and the spec is relative to the "exact numerical result,"
        // so log2(x) is never exactly exponent + 0.5.
        increment = (xScaled * xScaled) > 2.0;
        break;
      default:

import static com.google.common.collect.CollectPreconditions.checkNonnegative;
import static com.google.common.collect.ImmutableList.asImmutableList;
import static com.google.common.math.IntMath.sqrt;
import static java.lang.Math.max;
import static java.util.Objects.requireNonNull;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;