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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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| Scalar
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| Monadic
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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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| Dyadic
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Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
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| Non-Scalar
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| Structural
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Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
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| Selection
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First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
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| Selector
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Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
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| Computational
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Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
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| Operators |
Monadic
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Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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| Dyadic
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Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
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| Quad names
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Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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