abstract boolean noAddOverflow(long a, long b);

    abstract boolean noMulOverflow(int a, int b);

    abstract boolean noMulOverflow(long a, long b);
  }

  private final int[] factorials = new int[ARRAY_SIZE];
  private final int[][] binomials = new int[ARRAY_SIZE][2];
  private final int[][] nonnegInt = new int[ARRAY_SIZE][2];
  private final long[][] nonnegLong = new long[ARRAY_SIZE][2];

      return BigInteger.valueOf(LongMath.factorials[n]);
    }

    // Pre-allocate space for our list of intermediate BigIntegers.
    int approxSize = IntMath.divide(n * IntMath.log2(n, CEILING), Long.SIZE, CEILING);
    ArrayList<BigInteger> bignums = new ArrayList<>(approxSize);

    // Start from the pre-computed maximum long factorial.
    int startingNumber = LongMath.factorials.length;

    long expected = 1;
    for (int i = 0; i < LongMath.factorials.length; i++, expected *= i) {
      assertEquals(expected, LongMath.factorials[i]);
    }
    assertThrows(
        ArithmeticException.class,
        () ->
            LongMath.checkedMultiply(
                LongMath.factorials[LongMath.factorials.length - 1], LongMath.factorials.length));
  }

  @GwtIncompatible // TODO

    if (k > (n >> 1)) {
      k = n - k;
    }
    switch (k) {
      case 0:
        return 1;
      case 1:
        return n;
      default:
        if (n < factorials.length) {
          return factorials[n] / (factorials[k] * factorials[n - k]);
        } else if (k >= biggestBinomials.length || n > biggestBinomials[k]) {
          return Long.MAX_VALUE;

      double actual = BigIntegerMath.factorial(i).doubleValue();
      double result = DoubleMath.factorial(i);
      assertThat(result).isWithin(Math.ulp(actual)).of(actual);
    }
  }

  public void testFactorialTooHigh() {
    assertThat(DoubleMath.factorial(DoubleMath.MAX_FACTORIAL + 1)).isPositiveInfinity();
    assertThat(DoubleMath.factorial(DoubleMath.MAX_FACTORIAL + 20)).isPositiveInfinity();
  }

  }

  // Depends on the correctness of BigIntegerMath.factorial
  private static void runBinomialTest(int firstN, int lastN) {
    for (int n = firstN; n <= lastN; n++) {
      for (int k = 0; k <= n; k++) {
        BigInteger expected =
            BigIntegerMath.factorial(n)
                .divide(BigIntegerMath.factorial(k))
                .divide(BigIntegerMath.factorial(n - k));

          FactoryMethodReturnsNullException {
    if (cls.isEnum()) {
      return;
    }
    List<? extends Invokable<?, ?>> factories = Lists.reverse(getFactories(TypeToken.of(cls)));
    if (factories.isEmpty()) {
      return;
    }
    int numberOfParameters = factories.get(0).getParameters().size();
    List<ParameterNotInstantiableException> paramErrors = new ArrayList<>();

          FactoryMethodReturnsNullException {
    if (cls.isEnum()) {
      return;
    }
    List<? extends Invokable<?, ?>> factories = Lists.reverse(getFactories(TypeToken.of(cls)));
    if (factories.isEmpty()) {
      return;
    }
    int numberOfParameters = factories.get(0).getParameters().size();
    List<ParameterNotInstantiableException> paramErrors = new ArrayList<>();

/**
 * Creates and manages crawler clients for web crawling operations.
 * This class handles the registration and loading of crawler client factories and their associated clients.
 * <p>
 * The class maintains a mapping between regular expressions and component names, and manages a list
 * of crawler client factories with a configurable maximum size.
 * </p>
 *
 */
public class CrawlerClientCreator {
    /**

    }
  }

  // Depends on the correctness of BigIntegerMath.factorial.
  public void testFactorial() {
    for (int n = 0; n <= 50; n++) {
      BigInteger expectedBig = BigIntegerMath.factorial(n);
      int expectedInt = fitsInInt(expectedBig) ? expectedBig.intValue() : Integer.MAX_VALUE;
      assertEquals(expectedInt, IntMath.factorial(n));
    }
  }

  public void testFactorialNegative() {