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