Round

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⟩

Works in: TinyAPL

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⟩

Works in: TinyAPL

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]

Works in: Uiua

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

Works in: Kap

External links

Documentation

References

↑ Wikipedia: Rounding half to even

APL built-ins [edit]
Primitives (Timeline)	Functions
Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
		Dyadic	Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
		Structural	Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
		Selection	First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Operators	Dyadic	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)
Quad names	Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector

[1] Wikipedia: Rounding half to even

[1]

Round

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