floor -- r7rs Definition

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Kind

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procedure;

Implemented by

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• floor (from vonuvoli);

Procedure signature

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Procedure variants:

• (((n integer)) -> ((n integer)))
  • input: n of type integer;
  • output: n of type integer;
• ((real-not-inf-not-nan) -> (integer))
  • input: a value of type real-not-inf-not-nan;
  • output: a value of type integer;
• ((real-inf) -> (real-inf))
  • input: a value of type real-inf;
  • output: a value of type real-inf;
• ((real-nan) -> (real-nan))
  • input: a value of type real-nan;
  • output: a value of type real-nan;

Exports

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• scheme:base -- (scheme base);

Exports recursive

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• scheme -- (scheme);

Description

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(floor x)
(ceiling x)
(truncate x)
(round x)

These procedures return integers.

The floor procedure returns the largest integer not larger than x. The ceiling procedure returns the smallest integer not smaller than x, truncate returns the integer closest to x whose absolute value is not larger than the absolute value of x, and round returns the closest integer to x, rounding to even when x is halfway between two integers.

Rationale: The round procedure rounds to even for consistency with the default rounding mode specified by the IEEE 754 IEEE floating-point standard.

Note: If the argument to one of these procedures is inexact, then the result will also be inexact. If an exact value is needed, the result can be passed to the exact procedure. If the argument is infinite or a NaN, then it is returned.

(floor -4.3)          ===>  -5.0
(ceiling -4.3)        ===>  -4.0
(truncate -4.3)       ===>  -4.0
(round -4.3)          ===>  -4.0

(floor 3.5)           ===>   3.0
(ceiling 3.5)         ===>   4.0
(truncate 3.5)        ===>   3.0
(round 3.5)           ===>   4.0  ; inexact

(round 7/2)           ===>   4    ; exact
(round 7)             ===>   7

---

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

Referenced-types

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• integer;
• real-not-inf-not-nan;
• real-inf;
• real-nan;