Brute-force, single-threaded prime factorization

Question

Up for consideration is the following function which can be used to (relatively quickly) factor a 64-bit unsigned integer into its prime factors. Note that the factoring is

Answer 1

Incorporating some ideas from Omnifarious, plus other improvements:

// system specific typedef for ulong should go here (or use boost::uint64_t)
typedef unsigned __int64 ulong;
typedef std::vector ULongVector;

// Caller needs to pass in an empty factors vector
void GetFactors(ULongVector &factors, ulong num)
{
  if (num<2)
    return;

  ulong workingNum=num;

  // Factor out factors of 2
  while (workingNum%2==0)
  {
    factors.push_back(2);
    workingNum/=2;
  }

  // Factor out factors of 3
  while (workingNum%3==0)
  {
    factors.push_back(3);
    workingNum/=3;
  }

  if (workingNum==1)
    return;

  // Factor out factors >=5
  ulong nextOffset=2;
  char nextShift = 1;
  ulong n = 5;
  ulong nn = 25;
  do {
    // Is workingNum divisible by n?
    if (workingNum%n==0)
    {
      // n is a factor!
      // so is the number multiplied by n to get workingNum

      // Insert n into the list of factors
      factors.push_back(n);

      // Divide working number by n
      workingNum/=n;

      // Test for done...
      if (workingNum==1)
        return;

      // Try n again
    }  
    else {
      nn += (n << (nextShift+1)) + (1<<(nextShift*2)); // (n+b)^2 = n^2 + 2*n*b + b*2
      n += nextOffset;
      nextOffset ^= 6;
      nextShift ^= 3;
      // invariant: nn == n*n
      if (n & 0x100000000LL) break; // careful of integer wraparound in n^2
    }
  } while (nn <= workingNum);

  // workingNum is prime, add it to the list of factors        
  factors.push_back(workingNum);
}