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Ceiling: Difference between revisions
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{{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]] < | {{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]] <syntaxhighlight lang=apl inline>⌈</syntaxhighlight> 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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Ceiling rounds up the given numbers to the nearest integers. | Ceiling rounds up the given numbers to the nearest integers. | ||
< | <syntaxhighlight lang=apl> | ||
⌈2 2.8 ¯2 ¯2.8 | ⌈2 2.8 ¯2 ¯2.8 | ||
2 3 ¯2 ¯2 | 2 3 ¯2 ¯2 | ||
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Ceiling is affected by [[comparison tolerance]]. If the given number is [[tolerant comparison|tolerantly equal]] to its [[floor]], it is rounded to that number instead. | Ceiling is affected by [[comparison tolerance]]. If the given number is [[tolerant comparison|tolerantly equal]] to its [[floor]], it is rounded to that number instead. | ||
< | <syntaxhighlight lang=apl> | ||
⎕PP←16 | ⎕PP←16 | ||
⎕←v←1+0.6×⎕CT×0 1 2 | ⎕←v←1+0.6×⎕CT×0 1 2 | ||
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Ceiling is the dual to [[Floor]] by [[negate|negation]]. | Ceiling is the dual to [[Floor]] by [[negate|negation]]. | ||
< | <syntaxhighlight lang=apl> | ||
v←2 2.8 ¯2 ¯2.8 | v←2 2.8 ¯2 ¯2.8 | ||
(⌈v)≡-⌊-v | (⌈v)≡-⌊-v | ||
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The extension for [[complex number|complex numbers]] is derived from [[complex Floor]] via this property. | The extension for [[complex number|complex numbers]] is derived from [[complex Floor]] via this property. | ||
< | <syntaxhighlight lang=apl> | ||
v←1.8J2.5 2.5J2.2 1.7J2.2 | v←1.8J2.5 2.5J2.2 1.7J2.2 | ||
⌈v | ⌈v | ||