12.2.15 =, /=, <, >, <=, >= [Function]

= &rest numbers^+ ⇒ generalized-boolean

/= &rest numbers^+ ⇒ generalized-boolean

< &rest numbers^+ ⇒ generalized-boolean

> &rest numbers^+ ⇒ generalized-boolean

<= &rest numbers^+ ⇒ generalized-boolean

>= &rest numbers^+ ⇒ generalized-boolean

Arguments and Values::

number—for <, >, <=, >=: a real; for =, /=: a number.

generalized-boolean—a generalized boolean.

Description::

=, /=, <, >, <=, and >= perform arithmetic comparisons on their arguments as follows:

=

The value of = is true if all numbers are the same in value; otherwise it is false. Two complexes are considered equal by = if their real and imaginary parts are equal according to =.

/=

The value of /= is true if no two numbers are the same in value; otherwise it is false.

<

The value of < is true if the numbers are in monotonically increasing order; otherwise it is false.

>

The value of > is true if the numbers are in monotonically decreasing order; otherwise it is false.

<=

The value of <= is true if the numbers are in monotonically nondecreasing order; otherwise it is false.

>=

The value of >= is true if the numbers are in monotonically nonincreasing order; otherwise it is false.

=, /=, <, >, <=, and >= perform necessary type conversions.

Examples::

The uses of these functions are illustrated in Figure 12–12.

  (= 3 3) is true.              (/= 3 3) is false.             
  (= 3 5) is false.             (/= 3 5) is true.              
  (= 3 3 3 3) is true.          (/= 3 3 3 3) is false.         
  (= 3 3 5 3) is false.         (/= 3 3 5 3) is false.         
  (= 3 6 5 2) is false.         (/= 3 6 5 2) is true.          
  (= 3 2 3) is false.           (/= 3 2 3) is false.           
  (< 3 5) is true.              (<= 3 5) is true.              
  (< 3 -5) is false.            (<= 3 -5) is false.            
  (< 3 3) is false.             (<= 3 3) is true.              
  (< 0 3 4 6 7) is true.        (<= 0 3 4 6 7) is true.        
  (< 0 3 4 4 6) is false.       (<= 0 3 4 4 6) is true.        
  (> 4 3) is true.              (>= 4 3) is true.              
  (> 4 3 2 1 0) is true.        (>= 4 3 2 1 0) is true.        
  (> 4 3 3 2 0) is false.       (>= 4 3 3 2 0) is true.        
  (> 4 3 1 2 0) is false.       (>= 4 3 1 2 0) is false.       
  (= 3) is true.                (/= 3) is true.                
  (< 3) is true.                (<= 3) is true.                
  (= 3.0 #c(3.0 0.0)) is true.  (/= 3.0 #c(3.0 1.0)) is true.  
  (= 3 3.0) is true.            (= 3.0s0 3.0d0) is true.       
  (= 0.0 -0.0) is true.         (= 5/2 2.5) is true.           
  (> 0.0 -0.0) is false.        (= 0 -0.0) is true.            
  (<= 0 x 9) is true if x is between 0 and 9, inclusive
  (< 0.0 x 1.0) is true if x is between 0.0 and 1.0, exclusive
  (< -1 j (length v)) is true if j is a valid array index for a vector v

         Figure 12–12: Uses of /=, =, <, >, <=, and >=        

Exceptional Situations::

Might signal type-error if some argument is not a real. Might signal arithmetic-error if otherwise unable to fulfill its contract.

Notes::

= differs from eql in that (= 0.0 -0.0) is always true, because = compares the mathematical values of its operands, whereas eql compares the representational values, so to speak.