Negative number outputs that should be positive

Question

I am working on a java project and I have a loop that is driving me crazy.

The program takes an input, N, which is a positive integer. What I want my loop to do is this:

Lets say that N = 10. The loop will take all numbers from 1 to 10, raise it to the fifth power, and store each value in an array of length N.

It works (seemingly) correctly up until N = 73, I think. Once N hits 74 or above it starts to randomly give me negative numbers for 74^5. Which obviously is incorrect. The higher the number, the more negatives it gives me.

private static int _theLimit = EquationSolver.getLimit(); //input "N"
private static int length = (int) (_theLimit); //length of possible solutions array = N
static int[] _solutions = new int[length]; 

public static void solutionRun() {
    for(int i = 1; i <=_theLimit ;) { 
        //theLimit refers to the input N; for numbers from 1 until N
        for (int p = 0; p <= _solutions.length-1; p++) { 
            //solutions is an array that stores all possible solutions to ^5 from 1 to N; 
            _solutions[p] = i*i*i*i*i; 
            //p refers to the array location, increments with each new i
            i++;
        }           
    }
    for(int q = 0; q<=_solutions.length-1; q++){ //outputs solutions for debugging purposes
        System.out.println(_solutions[q]);
    }
}

Answer 1

The problem is that you just passed the range that integer allows.

Int allow numbers from -2,147,483,648 to a maximum value of 2,147,483,647 (inclusive) (source), since 74^5 = 2,219,006,624. Thus, more that the Int can handle.

If you want a bigger range you can use java BigInteger Class. A code example:

BigInteger pow(BigInteger base, BigInteger exponent) {
  BigInteger result = BigInteger.ONE;
  while (exponent.signum() > 0) {
    if (exponent.testBit(0)) result = result.multiply(base);
    base = base.multiply(base);
    exponent = exponent.shiftRight(1);
  }
  return result;
}

Considerations: This may not be very efficient and might not work for negative bases or exponents. Use it as an example on how to use BigIntegers.

Instead of BigInteger, you can also use the long type that vary from -9,223,372,036,854,775,808 to 9,223,372,036,854,775,807 (inclusive) (source).

Do not use double for this purpose, since you can have precision problems.