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  ANSI Common Lisp   12 Numbers   12.2 Dictionary of Numbers

12.2.15 =, /=, <, >, <=, >= Function

Syntax:
= &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 the next figure.

Uses of /=, =, <, >, <=, and >=
(= 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

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.

Allegro CL Implementation Details:
None.

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