题目描述

求base的exponent次方

考虑：当次方为负，base不能为0

bool equal(double a, double b)
{
    if((a-b<0.0000001) && (b-a<0.0000001))
    return true;
    else
    return false;
}

double PowerCore(double base, unsigned int e)
{
    double res = 1.0;
    for(int i=0; i<=e; i++)
    {
        res *= base;
    }
    return res;
}

double Power(double base, int exponent)
{
    /*
    enponent小于0， base！=0
     */
    
    if(exponent <=0 && equal(base, 0.0))
    {
        throw "Wrong Valid";
    }
    
    unsigned int absExponent = abs(exponent);
    
    if(exponent<0)
    {
        absExponent = (unsigned int)(-exponent);
    }
    
    double res = PowerCore(base, absExponent);
    
    if(exponent<0)
    {
        res = 1.0/res;
    }
    
    return res;

}

注意：由于精度问题，double和float不能直接用==相比

高效算法

知道16次方，*当前的数即可得到32次方

$a^n = a^{n/2} * a^{n/2} (奇数)*a$

double PowerCore(double base, unsigned int exponent)
{
	if(exponent == 0)
		return 1;
	if(exponent == 1)
		return base;
	double res = PowerCore(base, exponent>>1);
	res *= res;
	if(exponent & 0x01 == 1)
		return res * base;
	return res;

}