chickadee » scheme » ceiling

These procedures return integers. Floor returns the largest integer not larger than x. Ceiling 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. Round returns the closest integer to x, rounding to even when x is halfway between two integers.

Rationale: Round rounds to even for consistency with the default rounding mode specified by the 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 should be passed to the inexact->exact procedure.

(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