Testing if given number is integer

#include <cmath>

bool is_integer(float k)
{
  return std::floor(k) == k;
}

This solution should work for all possible values of k. I am pretty sure this is a case where you can safely compare floats using ==.

Try to thoughtfully name functions. integer does not give any clue what it actually does, so I changed the function name to something more meaningful.

For the future, testing if a number is integer should feel like a very simple operation, so you should have a strong feeling that the best solution will be very simple. I hope you realize your original solution is absurd for many reasons (biggest reason: it will cause a stack overflow for the vast majority of cases).

This is not going to work, as for sufficiently large floats, x-1 == x.

You should test the bit pattern of the float to check whether the fractional part is 0.

Why not just do something like this:

bool integer(float k)
{
    return k == (float)(int)k;
}

?

(Feel free to use proper C++ type casts of course.)