Ceiling Function

$\begin{figure}\begin{center}\BoxedEPSF{CeilingFloorNint.epsf}\end{center}\end{figure}$

The function $\left\lceil{x}\right\rceil$ which gives the smallest Integer $\geq x$ , shown as the thick curve in the above plot. Schroeder (1991) calls the ceiling function symbols the ``Gallows'' because of the similarity in appearance to the structure used for hangings. The name and symbol for the ceiling function were coined by K. E. Iverson (Graham et al. 1990). It can be implemented as ceil(x)=-int(-x), where int(x) is the Integer Part of .

See also Floor Function, Integer Part, Nint

References

Graham, R. L.; Knuth, D. E.; and Patashnik, O. ``Integer Functions.'' Ch. 3 in Concrete Mathematics: A Foundation for Computer Science. Reading, MA: Addison-Wesley, pp. 67-101, 1990.

Iverson, K. E. A Programming Language. New York: Wiley, p. 12, 1962.

Schroeder, M. Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, p. 57, 1991.