Power to n implementation that produces wrong results for negative exponent

Question

In the following (naive) implementation of a pow(x, n) method, ignoring completely any optimized approach, I find the following problem:

public double pow(double x, int n) {  
  boolean negative = n < 0;  
  long power = Math.abs(n);  
  double ans = 1.0;  
  for(long i = 0; i < power; i++) {  
    ans = ans * x;  
  }    
  return negative ? 1.0/ans: ans;  
}  

Here I have made the assumption that for the case of negative exponent I simply calculate the x^n and then return 1/(x^n) since eg 2^(-3) = 1/(2^3)

Problem:
The code fails in the following case:
pow(2.00000, -2147483648)
The output is 1.00000 while the expected correct result is 0.00000

If I change the code as follows:

public double pow(double x, int n) {  
  long power = n;  
  if(power < 0) {  
    x = 1 / x;  
    power = -power;
  }  
  double ans = 1.0;  
  for(long i = 0; i < power; i++) {  
    ans = ans * x;  
  }    
  return ans;  
}  

The result is correct!

So what is the difference between doing the approaches? I was expecting them to be equivalent but they are not

Answer 1

Math.abs(n) is still an int , and only afterwards it is assigned to a long , Therefore, the absolute value of -2147483648 was -2147483648 again (this is noted in the documentation of Math.abs(int) ). With the negative bound, the loop performed no iterations.

Math.abs((long)n) would work around that issue.