assertThat(INTEGER_MANY_VALUES_STATS_ITERABLE.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT));
    assertThat(LONG_MANY_VALUES_STATS_ITERATOR.populationStandardDeviation())

          fractionalBuilder.add(x);
        }
      }
    }
    INTEGRAL_DOUBLE_CANDIDATES = integralBuilder.build();
    fractionalBuilder.add(1.414).add(1.415).add(Math.sqrt(2));
    fractionalBuilder.add(5.656).add(5.657).add(4 * Math.sqrt(2));
    for (double d : INTEGRAL_DOUBLE_CANDIDATES) {
      double x = 1 / d;
      if (x != Math.rint(x)) {
        fractionalBuilder.add(x);
      }
    }

          fractionalBuilder.add(x);
        }
      }
    }
    INTEGRAL_DOUBLE_CANDIDATES = integralBuilder.build();
    fractionalBuilder.add(1.414).add(1.415).add(Math.sqrt(2));
    fractionalBuilder.add(5.656).add(5.657).add(4 * Math.sqrt(2));
    for (double d : INTEGRAL_DOUBLE_CANDIDATES) {
      double x = 1 / d;
      if (x != Math.rint(x)) {
        fractionalBuilder.add(x);
      }
    }

        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));
    assertThat(longManyValuesAccumulatorByAddAllVarargs.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));

        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));
    assertThat(longManyValuesAccumulatorByAddAllVarargs.populationStandardDeviation())
        .isWithin(ALLOWED_ERROR * sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS))
        .of(sqrt(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT));

       */
      sqrt0 = sqrtApproxWithDoubles(x.shiftRight(shift)).shiftLeft(shift >> 1);
    }
    BigInteger sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    if (sqrt0.equals(sqrt1)) {
      return sqrt0;
    }
    do {
      sqrt0 = sqrt1;
      sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    } while (sqrt1.compareTo(sqrt0) < 0);
    return sqrt0;
  }

  @GwtIncompatible // TODO

      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;

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

  /* Relies on the correctness of sqrt(int, FLOOR). */
  @GwtIncompatible // sqrt
  public void testSqrtExactMatchesFloorOrThrows() {
    for (int x : POSITIVE_INTEGER_CANDIDATES) {
      int floor = IntMath.sqrt(x, FLOOR);

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

  /* Relies on the correctness of sqrt(int, FLOOR). */
  @GwtIncompatible // sqrt
  public void testSqrtExactMatchesFloorOrThrows() {
    for (int x : POSITIVE_INTEGER_CANDIDATES) {
      int floor = IntMath.sqrt(x, FLOOR);

      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++) {