# ceiling function

The**ceiling function**of

*x*, historically called the

**least integer function**, is the least integer greater than or equal to

*x*. This function is usually written (a notation first suggested by Iverson in 1962), but on these web pages we will usually write ceiling(

*x*) (for those with non-graphical browsers).

Examples: ceiling(3.14159)=4, ceiling(-3.14159)=-3,
and ceiling(*n*)=*n* for all integers *n*.

As a more complicated example, we note that Lame's
Theorem implies that the Euclidean algorithm takes at most
ceiling(*x*) "division steps" where *x* is the number of digits in the smaller of the two numbers,

**See Also:** FloorFunction

**References:**

- Iverson62
K. E. Iverson,A programming language, John Wiley \& Sons, 1962.MR 26:913

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