In Common Lisp, in fact, no numbers are required to be eq! Even (eq 0 0) is not required by ANSI CL to return true. Why your Lisp implementation produces true

In Common Lisp, in fact, no numbers are required to be eq! Even (eq 0 0) is not required by ANSI CL to return true. Why your Lisp implementation produces true for (eq a b) is probably because of the following. Firstly, in Common Lisp there are single and double precision floats. Floating point tokens written with E or e are single. An implementation is allowed to map that to a 32 bit float. If the implementation has 64 bit values, it can easily arrange for single precision floats to be unboxed without any special tricks; they need only half the word. Try evaluating with 1D+20 to see what that does. But even 64 bit values can be unboxed with a trick called NAN tagging. I implemented NAN tagging in TXR Lisp (which has only double-precision floats), enabled on 64 bit targets: 64 bit machine: 1> (eq 1E20 1E20) t 2> (sizeof val) 8 32 bit machine: 1> (eq 1E20 1E20) nil 2> (sizeof val) 4 On 32 bits, floating-point objects are on the heap. It's pretty important to have unboxed floats for intense numerical work.