Fastest way to determine if an integer's square root is an integer

Question

I\'m looking for the fastest way to determine if a long value is a perfect square (i.e. its square root is another integer):

1. I\'ve done it the ea

Answer 1

Regarding the Carmac method, it seems like it would be quite easy just to iterate once more, which should double the number of digits of accuracy. It is, after all, an extremely truncated iterative method -- Newton's, with a very good first guess.

Regarding your current best, I see two micro-optimizations:

• move the check vs. 0 after the check using mod255
• rearrange the dividing out powers of four to skip all the checks for the usual (75%) case.

I.e:

// Divide out powers of 4 using binary search

if((n & 0x3L) == 0) {
  n >>=2;

  if((n & 0xffffffffL) == 0)
    n >>= 32;
  if((n & 0xffffL) == 0)
      n >>= 16;
  if((n & 0xffL) == 0)
      n >>= 8;
  if((n & 0xfL) == 0)
      n >>= 4;
  if((n & 0x3L) == 0)
      n >>= 2;
}

Even better might be a simple

while ((n & 0x03L) == 0) n >>= 2;

Obviously, it would be interesting to know how many numbers get culled at each checkpoint -- I rather doubt the checks are truly independent, which makes things tricky.