64-bit floats are a finite set. The solution of problems where the real numbers are replaced by the finite set is sometimes easier, but often much more difficul

64-bit floats are a finite set. The solution of problems where the real numbers are replaced by the finite set is sometimes easier, but often much more difficult. The reason is that you can't do calculus over finite fields. For instance, taking the inverse of the natural log is efficient, but the inverse of the discrete log is a hard problem, and hence is used in cryptographic algorithms. Complexity theory is a very subtle science.