root functions?

This forum is endlessly full of people screaming about how to make a wicked awesome tubular crazy fast square root function. Go back a few days, I think there just was one a day or two ago.

Returning NaN or throwing a std::domain_error would be much more appropriate than returning -1

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pow(number, 1/exp);

exp = 2 for square root, 3 for cube, etc.

The classical method of calculating sqrt() is to use Newton's method. There is a good concise explanation here.

For calculating the square root we use the equation x^2 - n, with the derivative 2x in Newton's method.

The following code is a working sqrt() implemenation using Newton's method:

#include <iostream>
#include <limits>
using namespace std;

double mysqrt(double n) {
	const double TOL = 1e-12;
	const double N = 100;

	if (n < 0) return std::numeric_limits<double>::quiet_NaN();

	double guess = n / 2.0;
	for (int i=0; i<N; i++) {
		double f = guess * guess - n;
		double df = 2 * guess;
		if (fabs(f) < TOL) return guess;
		double tmp = guess - f/df;
		if (fabs(guess - tmp) < TOL) return guess;
		guess = tmp;
	}
	return std::numeric_limits<double>::quiet_NaN();
}

int main() {
	cout << mysqrt(0) << endl;
}

Edit: Correction in algorithm for n = 0, fixed another bug with df being very close to zero.

[edited by - premandrake on October 16, 2003 1:06:42 PM]

I am afraid it works.

pow(number, 1/(float) exp);

a small notice (1/3 is 0 in C )

It works when you put it into a function of its own as any sane person plus me would do:
inline double root(double num, double exp)
{
return pow(num, 1/exp);
}