* 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

    for (int exp : asList(-1022, -50, -1, 0, 1, 2, 3, 4, 100, 1022, 1023)) {
      for (RoundingMode mode : asList(HALF_EVEN, HALF_UP, HALF_DOWN)) {
        double x = Math.scalb(Math.sqrt(2) + 0.001, exp);
        double y = Math.scalb(Math.sqrt(2) - 0.001, exp);
        assertEquals(exp + 1, DoubleMath.log2(x, mode));
        assertEquals(exp, DoubleMath.log2(y, mode));
      }
    }
  }

   *
   * @throws IllegalStateException if the dataset is empty
   */
  public final double populationStandardDeviation() {
    return Math.sqrt(populationVariance());
  }

  /**
   * Returns the <a href="http://en.wikipedia.org/wiki/Variance#Sample_variance">unbiased sample

    for (int exp : asList(-1022, -50, -1, 0, 1, 2, 3, 4, 100, 1022, 1023)) {
      for (RoundingMode mode : asList(HALF_EVEN, HALF_UP, HALF_DOWN)) {
        double x = Math.scalb(Math.sqrt(2) + 0.001, exp);
        double y = Math.scalb(Math.sqrt(2) - 0.001, exp);
        assertEquals(exp + 1, DoubleMath.log2(x, mode));
        assertEquals(exp, DoubleMath.log2(y, mode));
      }
    }
  }

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;

   *
   * {@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}}.
   *

   *
   * @throws IllegalStateException if the dataset is empty
   */
  public double populationStandardDeviation() {
    return Math.sqrt(populationVariance());
  }

  /**
   * Returns the <a href="http://en.wikipedia.org/wiki/Variance#Sample_variance">unbiased sample

pkg go/doc, func IsPredeclared(string) bool
pkg go/types, func Default(Type) Type
pkg go/types, func IdenticalIgnoreTags(Type, Type) bool
pkg math/big, method (*Float) Scan(fmt.ScanState, int32) error
pkg math/big, method (*Int) Sqrt(*Int) *Int
pkg math/rand, func Uint64() uint64
pkg math/rand, method (*Rand) Uint64() uint64
pkg math/rand, type Source64 interface, Int63() int64
pkg math/rand, type Source64 interface { Int63, Seed, Uint64 }