Numeric Comparisons

The function **=** is the numeric equality predicate. It compares numbers by mathematical value, ignoring differences in type. Thus, **=** will consider mathematically equivalent values of different types equivalent while the generic equality predicate **EQL** would consider them inequivalent because of the difference in type. (The generic equality predicate **EQUALP**, however, uses **=** to compare numbers.) If it’s called with more than two arguments, it returns true only if they all have the same value. Thus:

(= 1 1)                        ==> T
(= 10 20/2)                    ==> T
(= 1 1.0 #c(1.0 0.0) #c(1 0))  ==> T

The **/=** function, conversely, returns true only if all its arguments are different values.

(/= 1 1)        ==> NIL
(/= 1 2)        ==> T
(/= 1 2 3)      ==> T
(/= 1 2 3 1)    ==> NIL
(/= 1 2 3 1.0)  ==> NIL

The functions **<**, **>**, **<=**, and **>=** order rationals and floating-point numbers (in other words, the real numbers.) Like **=** and **/=**, these functions can be called with more than two arguments, in which case each argument is compared to the argument to its right.

(< 2 3)       ==> T
(> 2 3)       ==> NIL
(> 3 2)       ==> T
(< 2 3 4)     ==> T
(< 2 3 3)     ==> NIL
(<= 2 3 3)    ==> T
(<= 2 3 3 4)  ==> T
(<= 2 3 4 3)  ==> NIL

To pick out the smallest or largest of several numbers, you can use the function **MIN** or **MAX**, which takes any number of real number arguments and returns the minimum or maximum value.

(max 10 11)    ==> 11
(min -12 -10)  ==> -12
(max -1 2 -3)  ==> 2

Some other handy functions are **ZEROP**, **MINUSP**, and **PLUSP**, which test whether a single real number is equal to, less than, or greater than zero. Two other predicates, **EVENP** and **ODDP**, test whether a single integer argument is even or odd. The P suffix on the names of these functions is a standard naming convention for predicate functions, functions that test some condition and return a boolean.