How to imagine Float in the form of Integer without loss of information?

Important

it is necessary that the order and sum,
i.e. For any a, b: float should be performed:

  to_float (to_int (a) + to_int (b)) == a + bto_int (a) & lt; to_int (b) at a & lt; b, etc.    
 found on the English -speaking SO, where the structure of the  float  values ​​is represented, but I can’t imagine how it can be applied to its task. 
  
 Note:  nan  and  Inf  You do not need to transform into my task. 
  
  
 attempts to solve 
  
 The production of serialization using  pickle.dumps , and then getting  into  from these baites, from these baites. But this is not at all a rational decision and it does not satisfy the requirements at all. 
  
 there were attempts to realize this through byte representations of numbers (), the amount is not preserved in this option.