int log2 = DoubleMath.log2(d, FLOOR);
      assertTrue(StrictMath.pow(2.0, log2) <= d);
      assertTrue(StrictMath.pow(2.0, log2 + 1) > d);
    }
  }

  @GwtIncompatible // DoubleMath.log2(double, RoundingMode), StrictMath
  public void testRoundLog2Ceiling() {
    for (double d : POSITIVE_FINITE_DOUBLE_CANDIDATES) {
      int log2 = DoubleMath.log2(d, CEILING);

      int log2 = DoubleMath.log2(d, FLOOR);
      assertTrue(StrictMath.pow(2.0, log2) <= d);
      assertTrue(StrictMath.pow(2.0, log2 + 1) > d);
    }
  }

  @GwtIncompatible // DoubleMath.log2(double, RoundingMode), StrictMath
  public void testRoundLog2Ceiling() {
    for (double d : POSITIVE_FINITE_DOUBLE_CANDIDATES) {
      int log2 = DoubleMath.log2(d, CEILING);

    return result;
  }

  /**
   * Generates a number in [0, 2^numBits) with an exponential distribution. The floor of the log2 of
   * the result is chosen uniformly at random in [0, numBits), and then the result is chosen in that
   * range uniformly at random. Zero is treated as having log2 == 0.
   */
  static BigInteger randomNonNegativeBigInteger(int numBits) {
    int digits = RANDOM_SOURCE.nextInt(numBits);

    return result;
  }

  /**
   * Generates a number in [0, 2^numBits) with an exponential distribution. The floor of the log2 of
   * the result is chosen uniformly at random in [0, numBits), and then the result is chosen in that
   * range uniformly at random. Zero is treated as having log2 == 0.
   */
  static BigInteger randomNonNegativeBigInteger(int numBits) {
    int digits = RANDOM_SOURCE.nextInt(numBits);

     * definitely >= floor(sqrt(x)), and then continue the iteration until we reach a fixed point.
     */
    BigInteger sqrt0;
    int log2 = log2(x, FLOOR);
    if (log2 < Double.MAX_EXPONENT) {
      sqrt0 = sqrtApproxWithDoubles(x);
    } else {
      int shift = (log2 - DoubleUtils.SIGNIFICAND_BITS) & ~1; // even!
      /*
       * We have that x / 2^shift < 2^54. Our initial approximation to sqrtFloor(x) will be

   * </ul>
   *
   * <p>The computed result is within 1 ulp of the exact result.
   *
   * <p>If the result of this method will be immediately rounded to an {@code int}, {@link
   * #log2(double, RoundingMode)} is faster.
   */
  public static double log2(double x) {
    return log(x) / LN_2; // surprisingly within 1 ulp according to tests
  }

  /**

      nonzero1[i] = randomNonZeroBigInteger(1024);
      nonzero2[i] = randomNonZeroBigInteger(1024);
    }
  }

  @Benchmark
  int log2(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += BigIntegerMath.log2(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int log10(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {

      doubles[i] = randomDouble(Long.SIZE);
      factorials[i] = RANDOM_SOURCE.nextInt(100);
    }
  }

  @Benchmark
  long log2(int reps) {
    long tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += Double.doubleToRawLongBits(DoubleMath.log2(positiveDoubles[j]));
    }
    return tmp;
  }

  @Benchmark
  long factorial(int reps) {
    long tmp = 0;

      nonzero[i] = randomNonZeroBigInteger(Long.SIZE - 2).longValue();
      longs[i] = RANDOM_SOURCE.nextLong();
    }
  }

  @Benchmark
  int log2(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += LongMath.log2(positive[j], mode);
    }
    return tmp;
  }

  @Benchmark
  int log10(int reps) {
    int tmp = 0;
    for (int i = 0; i < reps; i++) {

      doubles[i] = randomDouble(Long.SIZE);
      factorials[i] = RANDOM_SOURCE.nextInt(100);
    }
  }

  @Benchmark
  long log2(int reps) {
    long tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += Double.doubleToRawLongBits(DoubleMath.log2(positiveDoubles[j]));
    }
    return tmp;
  }

  @Benchmark
  long factorial(int reps) {
    long tmp = 0;