为什么下面的代码跑出的结果不对

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#include<iostream>
#include<cmath>
using namespace std;
int main()
{
    float e(float x);
    float x;
    cout << "请输入x" << endl;
    cin >> x;
    float sinh;
    sinh = (e(x) - e(-x)) / 2;
    cout << sinh;
    return 0;

}
float e(float x)
{
    int  fac(int x);
    float s;
    float m;
    int n;
    s = 1;
    for (n = 1; n <= 1000; n++)
    {
        m = x / fac(n);
        s = s + m;
            x *= x;
    }
    return s;
}
int fac(int x)
{    int s = 1;
    if (x == 0)
        return s;
    else
    {
    
        for (; x >= 1; x--)
            s *= x;
        return s;

    }
}

中间溢出了。int只能存下12的阶乘，double只能存下170的阶乘。换个算法吧。

#include <iostream>
#include <limits>

double factorial(int n) {
    double ret = 1;
    bool int_fl = false;
    for (int i = 1; i <= n; i++) {
        ret *= i;
        if (ret > std::numeric_limits<int>::max() && !int_fl) {
            std::cout << "max factorial that int can store: " << i-1 << "\n";
            int_fl = true;
        }
        if (ret > std::numeric_limits<double>::max()) {
            std::cout << "max factorial that double can store: " << i-1 << "\n";
            break;
        }
    }
    return ret;
}

int main() {
    int imax = std::numeric_limits<int>::max();
    std::cout << imax << '\n';
    double dmax = std::numeric_limits<double>::max();
    std::cout << dmax << '\n';
    std::cout << factorial(1000) << '\n';
    return 0;
}

结果：

2147483647
1.79769e+308
max factorial that int can store: 12    
max factorial that double can store: 170
inf
PS D:\src\cpp_back_to_basics> py -c 'import math; print(math.factorial(13)>2147483647)'
True
PS D:\src\cpp_back_to_basics> py -c 'import math; print(math.factorial(171)>1.79769e+308)'
True