exp函数使用c ++

Question

我无法弄清楚为什么我一直得到结果1.#INF从my_exp()我给它1作为输入时.这是代码:

double factorial(const int k)
{
    int prod = 1;
    for(int i=1; i<=k; i++)
        prod = i * prod;
    return prod;
}

double power(const double base, const int exponent)
{
    double result = 1;
    for(int i=1; i<=exponent; i++)
        result = result * base;
    return result;
}

double my_exp(double x)
{
    double sum = 1 + x;
    for(int k=2; k<50; k++)
        sum = sum + power(x,k) / factorial(k);
    return sum;
}

Answer 1

您的factorial函数中有整数溢出.这导致它输出零.49!可以被整除2^32,所以你的factorial函数将返回零.

然后你除以它导致它无限.所以解决方案是prod改为double:

double prod = 1;

Answer 2

您不应该完全评估扩展中每个术语的权力和因子术语,而应该考虑第k个术语与第k-1个术语的关系,并根据这种关系更新每个术语.这样可以避免功率和阶乘函数(你将不再需要)中令人讨厌的溢出.例如

double my_exp(double x)
{
    double sum = 1.0 + x;
    double term = x;                 // term for k = 1 is just x
    for (int k = 2; k < 50; k++)
    {
        term = term * x / (double)k; // term[k] = term[k-1] * x / k
        sum = sum + term;
    }
    return sum;
}