Round (⸠, ⁅) (respectively in TinyAPL and Uiua) is a monadic scalar function that rounds a number. While it doesn't appear in most APLs, its behavior is most commonly replicated with the idiom ⌊0.5+y.
Examples
⸠0.1‿2.9
⟨0 ⋄ 3⟩
Variants
In traditional mathematics and programming, there are multiple definitions of rounding a number when its fractional part is one half.
The traditional APL expression always rounds halves up, and TinyAPL also chooses this behavior:
⸠0.5‿1.5‿¯0.5‿¯1.5
⟨1 ⋄ 2 ⋄ 0 ⋄ ¯1⟩
Another way is to round away from zero, which is equivalent to rounding positive numbers above and negative numbers below. This is chosen by Uiua:
⁅0.5_1.5_¯0.5_¯1.5
## [1 2 ¯1 ¯2]
A third way is rounding to the nearest even integer. This might be preferred because it reduces bias and accumulation of error in subsequent rounding[1]. This is the behavior used by Kap:
math:round 0.5 1.5 ¯0.5 ¯1.5
0 2 0 -2
External links
Documentation
References
| APL built-ins [edit]
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| Primitives (Timeline) |
Functions
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Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
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