Ceiling

Ceiling (⌈) is a monadic scalar function which gives the ceiling of a real number, i.e. the least integer greater than or equal to the given value. This operation is also known as round up. Ceiling shares the glyph ⌈ with the dyadic arithmetic function Maximum.

Examples

Ceiling rounds up the given numbers to the nearest integers.

      ⌈2 2.8 ¯2 ¯2.8
2 3 ¯2 ¯2

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.

      ⎕PP←16
      ⊢v←1+0.6×⎕CT×0 1 2
1 1.000000000000006 1.000000000000012
      ⌈v
1 1 2

Ceiling is the dual to Floor by negation.

      v←2 2.8 ¯2 ¯2.8
      (⌈v)≡-⌊-v
1

The extension for complex numbers is derived from complex Floor via this property.

      v←1.8J2.5 2.5J2.2 1.7J2.2
      ⌈v
2J3 3J2 2J2
      (⌈v)≡-⌊-v
1

Works in: Dyalog APL

External links

Documentation

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

Ceiling

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Examples

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Ceiling

Examples

Properties

External links

Documentation

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