assertEquals(expected, BigIntegerMath.binomial(n, k));
      }
    }
  }

  public void testBinomialOutside() {
    for (int n = 0; n <= 50; n++) {
      try {
        BigIntegerMath.binomial(n, -1);
        fail("Expected IllegalArgumentException");
      } catch (IllegalArgumentException expected) {
      }
      try {
        BigIntegerMath.binomial(n, n + 1);

          permutations = IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
          r = 0;
          if (permutations == Integer.MAX_VALUE) {
            return Integer.MAX_VALUE;
          }
        }
        n++;
        r++;
      }
      return IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
    }

    @Override
    public int size() {
      return size;

          permutations = IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
          r = 0;
          if (permutations == Integer.MAX_VALUE) {
            return Integer.MAX_VALUE;
          }
        }
        n++;
        r++;
      }
      return IntMath.saturatedMultiply(permutations, IntMath.binomial(n, r));
    }

    @Override
    public int size() {
      return size;

		{1000, 990, "263409560461970212832400"},
	} {
		if got := z.Binomial(test.n, test.k).String(); got != test.want {
			t.Errorf("Binomial(%d, %d) = %s; want %s", test.n, test.k, got, test.want)
		}
	}
}

func BenchmarkBinomial(b *testing.B) {
	var z Int
	for i := 0; i < b.N; i++ {
		z.Binomial(1000, 990)
	}
}

// Examples from the Go Language Spec, section "Arithmetic operators"

	neg := false
	if a < 0 {
		neg = (b-a)&1 == 0
		a, b = -b, -a
	}

	z.abs = z.abs.mulRange(uint64(a), uint64(b))
	z.neg = neg
	return z
}

// Binomial sets z to the binomial coefficient C(n, k) and returns z.
func (z *Int) Binomial(n, k int64) *Int {
	if k > n {
		return z.SetInt64(0)
	}
	// reduce the number of multiplications by reducing k
	if k > n-k {
		k = n - k // C(n, k) == C(n, n-k)
	}

			// With 100 trials and profile fraction of 2, we expect to capture
			// 50 samples. Allow the test to pass if we get at least 20 samples;
			// the CDF of the binomial distribution says there's less than a
			// 1e-9 chance of that, which is an acceptably low flakiness rate.
			const samplingSlop = 2.5

                return size;
              }
            };
          }
        };
      }

      @Override
      public int size() {
        return IntMath.binomial(index.size(), size);
      }

      @Override
      public String toString() {
        return "Sets.combinations(" + index.keySet() + ", " + size + ")";
      }
    };
  }

                return size;
              }
            };
          }
        };
      }

      @Override
      public int size() {
        return IntMath.binomial(index.size(), size);
      }

      @Override
      public String toString() {
        return "Sets.combinations(" + index.keySet() + ", " + size + ")";
      }
    };
  }

		g.p("\tprintln(")
		for j := 0; j < n; j++ {
			if j > 0 {
				g.p(", ")
			}
			g.p("p%d_%d", i, j)
		}
		g.p(")\n")
	}
	g.p("}\n\n")
}

func (g *gen) binomials(n int) {
	g.p(`// Binomials
const (
`)
	for j := 0; j <= n; j++ {
		if j > 0 {
			g.p("\n")
		}
		for k := 0; k <= j; k++ {
			g.p("\tb%d_%d = f%d / (f%d*f%d)\n", j, k, j, k, j-k)
		}
	}
	g.p(")\n\n")

def TF_StatelessRandomBinomialOp : TF_Op<"StatelessRandomBinomial", [Pure, TF_NoConstantFold]> {
  let summary = [{
Outputs deterministic pseudorandom random numbers from a binomial distribution.
  }];

  let description = [{
Outputs random values from a binomial distribution.

The outputs are a deterministic function of `shape`, `seed`, `counts`, and `probs`.
  }];

  let arguments = (ins