Unexpected output when summing reciprocals of squares

[Faltoup]

Hello everyone!
I'm new to C++ and have a problem with exercise 3.6 from Scheinerman's C++ for mathematicians. The exercise asks me to write a programm that, given a (strictly) positive integer N as input, computes the Sum 1 + 1/(2^2) + ... + 1/(N^2). (The exercise asks for more, but this is the part where I run into problems).
This is what I did:
The header of the programm sum1:

#ifndef SUM1_H
#define SUM1_H

/**
 * A programm to calculate the the sum of 1/(k^2) from 1 to N for a 
 * given integer N, starting with 1/N^2 and then going down to 1/1^2.
 * @param positive integer N
 * @return The sum named above as float
 */
 
 float sum1(int n);
  
 #endif  

The code of sum1:

#include <iostream>
#include "sum1.h"

using namespace std;
float sum1(int n) {
	float a = 0;
	if (n <= 0) a = a;
	else {//in case n > 0:
		int m;
		for(m = n; m >= 1; m--) {
			a += 1/(float(m^2));//a = a + 1/(float(m^2));
		}		 	
	return a;
	}
}

And this is the file for testing it:

#include <iostream>
#include "sum1.h"

using namespace std;

int main() {
	int n;
	cout << "An integer, please!" << endl;
	cin >> n;
	cout << "1 + 1/(2^2) + ... + 1/(" << n << "^2)"
	<< " = " << sum1(n) << "." << endl;
	return 0;
}

I do not get any errors when compiling (I use the GNU compiler, my OS is Linux), but this is the output of it:
If I run it with a nonpositive integer as input (in this case -13), the ouput is

1 + 1/(2^2) + ... + 1/(-13^2) = nan.

,
If the input is 1, the output is

1 + 1/(2^2) + ... + 1/(1^2) = 0.333333.

,
and if the input i strictly positive (in this case 12), the ouput is

1 + 1/(2^2) + ... + 1/(12^2) = inf.

.
I have no idea what might cause this.
Best regards, Faltoup

[hamsterman]

in c++ ^ is a xor operation, not power. you'll just have to m*m.

[ne555]

Also, if n is not positive you've got no return statement.

[Faltoup]

Thanks a bunch you two! Working like a dream now. I took the return a; out of the else loop and put it at the end of the code. Do you think this is a good idea from the point of clear arrangement? Or is it better to include a return a; in both the if-loop and the end-loop?
Best regards, Faltoup

[hamsterman]

it's fine either way. the silly thing in your code is if (n <= 0) a = a; it does nothing.

[Faltoup]

Okay, that's right. Thanks for pointing it out. I killed it and am left with one if-loop only now.