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;

    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

      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<>();

      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();
  }

          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<>();

        buildFactories(new AggregatorFactories.Builder().addAggregator(b));
    }

    private void buildFactories(AggregatorFactories.Builder factories) throws IOException {
        try (DummyAggregationContext context = new DummyAggregationContext(factories.bytesToPreallocate())) {
            factories.build(context, null).createTopLevelAggregators();
        }
    }

    private class DummyAggregationContext extends AggregationContext {

        MockitoAnnotations.initMocks(this);

        Map<String, ToolchainFactory> factories = new HashMap<>();
        factories.put("basic", toolchainFactoryBasicType);
        factories.put("rare", toolchainFactoryRareType);

        when(lookup.lookupMap(ToolchainFactory.class)).thenReturn(factories);
        when(lookup.lookupMap(org.apache.maven.toolchain.ToolchainFactory.class))
                .thenReturn(Map.of());

    }
  }

  // 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() {