Ceiling: Difference between revisions
(→Documentation: BQN) 
m (Text replacement  "</source>" to "</syntaxhighlight>") 

Line 1:  Line 1:  
{{BuiltinCeiling⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikipedia:floor and ceiling functionsceiling]] of a real number, that is, the least integer [[Comparison tolerancetolerantly]] [[greater than or equal to]] the given value. This operation is also known as '''round up'''. Ceiling shares the [[glyph]] <source lang=apl inline>⌈</  {{BuiltinCeiling⌈}} is a [[monadic]] [[scalar function]] that gives the [[wikipedia:floor and ceiling functionsceiling]] of a real number, that is, the least integer [[Comparison tolerancetolerantly]] [[greater than or equal to]] the given value. This operation is also known as '''round up'''. Ceiling shares the [[glyph]] <source lang=apl inline>⌈</syntaxhighlight> with the dyadic arithmetic function [[Maximum]]. [[Comparison_with_traditional_mathematics#PrefixTraditional mathematics]] derives [[Ken_Iverson#Floor_and_Ceilingits notation]] and name for ceiling from APL.  
== Examples ==  == Examples ==  
Line 8:  Line 8:  
⌈2 2.8 ¯2 ¯2.8  ⌈2 2.8 ¯2 ¯2.8  
2 3 ¯2 ¯2  2 3 ¯2 ¯2  
</  </syntaxhighlight>  
== Properties ==  == Properties ==  
Line 22:  Line 22:  
⌈v  ⌈v  
1 1 2  1 1 2  
</  </syntaxhighlight>  
Ceiling is the dual to [[Floor]] by [[negatenegation]].  Ceiling is the dual to [[Floor]] by [[negatenegation]].  
Line 30:  Line 30:  
(⌈v)≡⌊v  (⌈v)≡⌊v  
1  1  
</  </syntaxhighlight>  
The extension for [[complex numbercomplex numbers]] is derived from [[complex Floor]] via this property.  The extension for [[complex numbercomplex numbers]] is derived from [[complex Floor]] via this property.  
Line 40:  Line 40:  
(⌈v)≡⌊v  (⌈v)≡⌊v  
1  1  
</  </syntaxhighlight>{{Works in[[Dyalog APL]]}}  
== External links ==  == External links == 
Revision as of 21:51, 10 September 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 <source lang=apl inline>⌈</syntaxhighlight> 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.
<source lang=apl>
⌈2 2.8 ¯2 ¯2.8
2 3 ¯2 ¯2 </syntaxhighlight>
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.
<source lang=apl>
⎕PP←16 ⎕←v←1+0.6×⎕CT×0 1 2
1 1.000000000000006 1.000000000000012
⌈v
1 1 2 </syntaxhighlight>
Ceiling is the dual to Floor by negation.
<source lang=apl>
v←2 2.8 ¯2 ¯2.8 (⌈v)≡⌊v
1 </syntaxhighlight>
The extension for complex numbers is derived from complex Floor via this property.
<source lang=apl>
v←1.8J2.5 2.5J2.2 1.7J2.2 ⌈v
2J3 3J2 2J2
(⌈v)≡⌊v
1
</syntaxhighlight>