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{{Built-in|Ceiling|⌈}} is a [[monadic]] [[scalar function]] which gives the [[wikipedia:floor and ceiling functions|ceiling]] of a real number, i.e. the least integer greater than or equal to the given value. This operation is also known as '''round up'''. Ceiling shares the [[glyph]] <source lang=apl inline>⌈</source> with the dyadic arithmetic function [[Maximum]]. [[Comparison_with_traditional_mathematics#Prefix|Traditional mathematics]] derives [[Ken_Iverson#Floor_and_Ceiling|its notation]] and name for ceiling from APL.
{{Built-in|Ceiling|⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikipedia:floor and ceiling functions|ceiling]] of a real number, that is, the least integer [[Comparison tolerance|tolerantly]] [[greater than or equal to]] the given value. This operation is also known as '''round up'''. Ceiling shares the [[glyph]] <source lang=apl inline>⌈</source> with the dyadic arithmetic function [[Maximum]]. [[Comparison_with_traditional_mathematics#Prefix|Traditional mathematics]] derives [[Ken_Iverson#Floor_and_Ceiling|its notation]] and name for ceiling from APL.


== Examples ==
== Examples ==
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<source lang=apl>
<source lang=apl>
       ⎕PP←16
       ⎕PP←16
       ⊢v←1+0.6×⎕CT×0 1 2
       ⎕←v←1+0.6×⎕CT×0 1 2
1 1.000000000000006 1.000000000000012
1 1.000000000000006 1.000000000000012
       ⌈v
       ⌈v
Line 46: Line 46:
=== Documentation ===
=== Documentation ===


* [http://help.dyalog.com/latest/#Language/Primitive%20Functions/Ceiling.htm Dyalog]
* [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Ceiling.htm Dyalog]
* [http://microapl.com/apl_help/ch_020_020_090.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_090.htm APLX]
* [https://www.jsoftware.com/help/dictionary/d021.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/gtdot NuVoc]
* [https://www.jsoftware.com/help/dictionary/d021.htm J Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/gtdot NuVoc]
* [https://mlochbaum.github.io/BQN/doc/arithmetic.html#additional-arithmetic BQN]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]
{{APL built-ins}}[[Category:Primitive functions]][[Category:Scalar monadic functions]]

Revision as of 02:16, 28 May 2022

Ceiling () is a monadic scalar function that gives the ceiling of a real number, that is, the least integer tolerantly greater than or equal to the given value. This operation is also known as round up. Ceiling shares the glyph with the dyadic arithmetic function Maximum. Traditional mathematics derives its notation and name for ceiling from APL.

Examples

Ceiling rounds up the given numbers to the nearest integers.

      2 2.8 ¯2 ¯2.8
2 3 ¯2 ¯2

Properties

The ceiling of any real number is an integer.

Ceiling is affected by comparison tolerance. If the given number is tolerantly equal to its floor, it is rounded to that number instead.

      ⎕PP16
      v1+0.6×⎕CT×0 1 2
1 1.000000000000006 1.000000000000012
      v
1 1 2

Ceiling is the dual to Floor by negation.

      v2 2.8 ¯2 ¯2.8
      (v)≡-⌊-v
1

The extension for complex numbers is derived from complex Floor via this property.

      v1.8J2.5 2.5J2.2 1.7J2.2
      v
2J3 3J2 2J2
      (v)≡-⌊-v
1
Works in: Dyalog APL

External links

Documentation

APL built-ins [edit]
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Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
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