对于大输入返回负数的阶乘函数

我的阶乘函数似乎适用于 1 到 6 之间的数字，但不适用于大于 6 的数字，例如从 21 开始！结果是否定的。

我不明白为什么。这是我的功能：

factorial :: Int -> Int
factorial 0 = 1
factorial 1 = 1
factorial num = num * factorial( num - 1)

这是我的二项式系数函数，它调用我的阶乘函数（也许问题来自于此？）：

binomialCoef :: Int -> Int -> Int
binomialCoef n 1 = n
binomialCoef n k = factorial n `div` 
                        ((factorial k) * factorial (n - k))

(…) 意识到我的阶乘函数返回从 21 开始的负数！，我不明白为什么。

Because an Int has a fixed number of bits. An Int should at least represent all numbers between -2^-29 and 2²⁹-1, and on a 64-bit system, typically it will represent numbers between -2^-63 and 2⁶³-1, but regardless what bounds it represents, it will eventually run out of bits to represent such number.

您可以与Integer https://hackage.haskell.org/package/base-4.14.1.0/docs/Prelude.html#t:Integer表示任意大数：

factorial :: Integer -> Integer
factorial 0 = 1
factorial 1 = 1
factorial num = num * factorial (num-1)

例如：

Prelude> factorial 21
51090942171709440000
Prelude> factorial 22
1124000727777607680000