大输入的阶乘函数返回负数 [英] Factorial function returning negative number for large input

问题描述

我的阶乘函数似乎适用于1到6之间的数字，但不适用于比6大得多的数字，例如以21开头！结果是否定的.

My factorial function seems to work for numbers between 1 and 6, but not for numbers much bigger than 6, for example starting with 21! the results are negative.

我不知道为什么.这是我的功能:

I cannot figure out why. Here's my function:

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，它调用了我的阶乘函数(也许问题出在这个函数上?):

And here's my binomial coefficient function that calls my factorial function (maybe the problem comes from this one ?):

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

推荐答案

(…)意识到我的阶乘函数从21！开始返回负数，我不知道为什么.

(…) realized my factorial function returns negative numbers starting at 21!, and I can't figure out why.

因为 Int 具有固定的位数. Int 至少应表示-2 ^-29 和2 ²⁹ -1之间的所有数字，在64位系统上，通常将表示介于-2 ^-63 和2 ⁶³ -1之间的数字，但是无论其表示什么边界，它最终都将用完表示该数字的位.

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.

您可以使用 整数 代表任意大数字:

You can work with Integer to represent arbitrary large numbers:

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

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