# Ceiling

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**Ceiling** (`⌈`

) is a monadic scalar function that gives the ceiling of a real number, that is, the least integer tolerantly^{[1]} 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. Traditional mathematics derives its notation and name for ceiling from APL.

## 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

## References

- ↑ Bernecky, Robert. "Comparison Tolerance". Sharp APL Technical Notes. 1977-06-10;.