牛顿迭代开平方

sqrt.cpp

#include<cstdio>

double sqr(double x){
	return x*x;
}

double sqrt(int v,double t){
	double ans=v;
	while(1){
		if(sqr(ans-t)<=v&&sqr(ans+t)>=v)break;
		ans=(ans+v/ans)/2;
	}
	return ans;
}

int main(){
	printf("%.16f",sqrt(123456789,0.000000001));
	return 0;
}

/*
output:  
11111.1110605555550137

python:  
>>> 123456789**0.5
11111.111060555555
*/