// copySign(x, 1.0) is a branch-free version of abs(x), but with different NaN semantics
        || (a == b) // needed to ensure that infinities equal themselves
        || (Double.isNaN(a) && Double.isNaN(b));
  }

  /**
   * Compares {@code a} and {@code b} "fuzzily," with a tolerance for nearly-equal values.
   *

package com.google.common.math;

import static com.google.common.base.Preconditions.checkState;
import static com.google.common.primitives.Doubles.isFinite;
import static java.lang.Double.NaN;
import static java.lang.Double.isNaN;

import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import com.google.common.primitives.Doubles;

/**

      if (values.hasAnyNonFinite()) {
        assertWithMessage("population covariance of " + values).that(populationCovariance).isNaN();
        assertWithMessage("population covariance by addAll(PairedStats) of " + values)
            .that(populationCovarianceByAddAllPartitionedPairedStats)
            .isNaN();
      } else {
        assertWithMessage("population covariance of " + values)
            .that(populationCovariance)

      if (values.hasAnyNonFinite()) {
        assertWithMessage("population covariance of " + values).that(populationCovariance).isNaN();
        assertWithMessage("population covariance by addAll(PairedStats) of " + values)
            .that(populationCovarianceByAddAllPartitionedPairedStats)
            .isNaN();
      } else {
        assertWithMessage("population covariance of " + values)
            .that(populationCovariance)

    assertThat(ONE_VALUE_STATS.populationVariance()).isWithin(0.0).of(0.0);
    assertThat(Stats.of(POSITIVE_INFINITY).populationVariance()).isNaN();
    assertThat(Stats.of(NEGATIVE_INFINITY).populationVariance()).isNaN();
    assertThat(Stats.of(NaN).populationVariance()).isNaN();
    assertThat(TWO_VALUES_STATS.populationVariance())
        .isWithin(ALLOWED_ERROR)
        .of(TWO_VALUES_SUM_OF_SQUARES_OF_DELTAS / 2);

    assertThat(ONE_VALUE_STATS.populationVariance()).isWithin(0.0).of(0.0);
    assertThat(Stats.of(POSITIVE_INFINITY).populationVariance()).isNaN();
    assertThat(Stats.of(NEGATIVE_INFINITY).populationVariance()).isNaN();
    assertThat(Stats.of(NaN).populationVariance()).isNaN();
    assertThat(TWO_VALUES_STATS.populationVariance())
        .isWithin(ALLOWED_ERROR)
        .of(TWO_VALUES_SUM_OF_SQUARES_OF_DELTAS / 2);

    assertThat(createSingleStats(Double.POSITIVE_INFINITY, 1.23).populationCovariance()).isNaN();
    assertThat(createSingleStats(Double.NEGATIVE_INFINITY, 1.23).populationCovariance()).isNaN();
    assertThat(createSingleStats(Double.NaN, 1.23).populationCovariance()).isNaN();
    assertThat(TWO_VALUES_PAIRED_STATS.populationCovariance())
        .isWithin(ALLOWED_ERROR)

    assertThat(createSingleStats(Double.POSITIVE_INFINITY, 1.23).populationCovariance()).isNaN();
    assertThat(createSingleStats(Double.NEGATIVE_INFINITY, 1.23).populationCovariance()).isNaN();
    assertThat(createSingleStats(Double.NaN, 1.23).populationCovariance()).isNaN();
    assertThat(TWO_VALUES_PAIRED_STATS.populationCovariance())
        .isWithin(ALLOWED_ERROR)

import static com.google.common.base.Preconditions.checkState;
import static java.lang.Double.NaN;
import static java.lang.Double.doubleToLongBits;
import static java.lang.Double.isNaN;

import com.google.common.annotations.GwtIncompatible;
import com.google.common.annotations.J2ktIncompatible;
import com.google.common.base.MoreObjects;
import com.google.common.base.Objects;
import java.io.Serializable;

        assertWithMessage("mean of " + values).that(mean).isNaN();
        assertWithMessage("mean by addAll(Stats) of " + values).that(meanByAddAllStats).isNaN();
      } else if (values.hasAnyPositiveInfinity() && values.hasAnyNegativeInfinity()) {
        assertWithMessage("mean of " + values).that(mean).isNaN();
        assertWithMessage("mean by addAll(Stats) of " + values).that(meanByAddAllStats).isNaN();
      } else if (values.hasAnyPositiveInfinity()) {