= -- r7rs Definition

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Kind

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comparator;

Extended by

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• = (from vonuvoli);

Procedure signature

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Procedure variants:

• ((number-not-nan |2...|) -> (boolean))
  • inputs:
    • a value of type number-not-nan;
    • ... -- at least 2 times;
  • output: a value of type boolean;
• ((number |2...|) -> (false))
  • inputs:
    • a value of type number;
    • ... -- at least 2 times;
  • output: a value of type false;

Exports

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• scheme:base -- (scheme base);

Exports recursive

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• scheme -- (scheme);

Description

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(= z_1 z_2 z_3 ...)
(< x_1 x_2 x_3 ...)
(> x_1 x_2 x_3 ...)
(<= x_1 x_2 x_3 ...)
(>= x_1 x_2 x_3 ...)

These procedures return #t if their arguments are (respectively): equal, monotonically increasing, monotonically decreasing, monotonically non-decreasing, or monotonically non-increasing, and #f otherwise. If any of the arguments are +nan.0, all the predicates return #f. They do not distinguish between inexact zero and inexact negative zero.

These predicates are required to be transitive.

Note: The implementation approach of converting all arguments to inexact numbers if any argument is inexact is not transitive. For example, let big be (expt 2 1000), and assume that big is exact and that inexact numbers are represented by 64-bit IEEE binary floating point numbers. Then (= (- big 1) (inexact big)) and (= (inexact big) (+ big 1)) would both be true with this approach, because of the limitations of IEEE representations of large integers, whereas (= (- big 1) (+ big 1)) is false. Converting inexact values to exact numbers that are the same (in the sense of =) to them will avoid this problem, though special care must be taken with infinities.

Note: While it is not an error to compare inexact numbers using these predicates, the results are unreliable because a small inaccuracy can affect the result; this is especially true of = and zero?. When in doubt, consult a numerical analyst.

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The text herein was sourced and adapted as described in the "R7RS attribution of various text snippets" appendix.

Referenced-types

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• number-not-nan;
• boolean;
• number;
• false;