ClickHouse/src/Functions/factorial.cpp

#include <Functions/FunctionFactory.h>
#include <Functions/FunctionUnaryArithmetic.h>
#include <DataTypes/NumberTraits.h>

namespace DB
{

namespace ErrorCodes
{
    extern const int ILLEGAL_TYPE_OF_ARGUMENT;
    extern const int BAD_ARGUMENTS;
}

template <typename A>
struct FactorialImpl
{
    using ResultType = Int64;
    static const constexpr bool allow_decimal = false;
    static const constexpr bool allow_fixed_string = false;
    static const constexpr bool allow_string_integer = false;

    static inline NO_SANITIZE_UNDEFINED ResultType apply(A a)
    {
        if constexpr (std::is_floating_point_v<A> || is_over_big_int<A>)
            throw Exception(
                ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT,
                "Illegal type of argument of function factorial, should not be floating point or big int");

        if constexpr (is_integer<A>)
        {
            if (a > 20)
                throw Exception(ErrorCodes::BAD_ARGUMENTS, "The maximum value for the input argument of function factorial is 20");

            if constexpr (is_unsigned_v<A>)
                return factorials[a];
            else if constexpr (is_signed_v<A>)
                return a >= 0 ? factorials[a] : 1;
        }
    }

#if USE_EMBEDDED_COMPILER
    static constexpr bool compilable = false; /// special type handling, some other time
#endif

private:
    static const constexpr ResultType factorials[21]
        = {1,
           1,
           2,
           6,
           24,
           120,
           720,
           5040,
           40320,
           362880,
           3628800,
           39916800,
           479001600,
           6227020800L,
           87178291200L,
           1307674368000L,
           20922789888000L,
           355687428096000L,
           6402373705728000L,
           121645100408832000L,
           2432902008176640000L};
};

struct NameFactorial { static constexpr auto name = "factorial"; };
using FunctionFactorial = FunctionUnaryArithmetic<FactorialImpl, NameFactorial, false>;

template <> struct FunctionUnaryArithmeticMonotonicity<NameFactorial>
{
    static bool has() { return true; }

    static IFunction::Monotonicity get(const Field & /*left*/, const Field & /*right*/)
    {
        return {
            .is_monotonic = true,
            .is_positive = true,
            .is_always_monotonic = true,
            .is_strict = false,
        };
    }
};


REGISTER_FUNCTION(Factorial)
{
    factory.registerFunction<FunctionFactorial>(
        {
            R"(
Computes the factorial of an integer value. It works with any native integer type. The return type is Int64.

The factorial of 0 is 1. Likewise, the factorial() function returns 1 for any negative value. The maximum positive value for the input argument is 20; a value of 21 or greater overflows the range for Int64 and will causes an throw exception.
)",
            Documentation::Examples{{"factorial", "SELECT factorial(10)"}},
            Documentation::Categories{"Mathematical"}},
        FunctionFactory::CaseInsensitive);
}

}