Numeric Comparisons

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.

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