Floor and Ceiling

Floor and ceiling are two functions. The floor function, R→Z, maps a real number, x, to the greatest integer that is less than or equal to x. This is written ⌊x⌋. The ceiling function, R→Z, maps a real number, x, to the least integer that is greater than or equal to x. This is written ⌈x⌉.

Examples

• ⌈99.9⌉=100
• ⌊99.9⌋=99
• ⌈-99.9⌉=-99
• ⌊-99.9⌋=-100

References

T. H. Cormen, C. E. Leiserson, R. L. Rivest, Introduction to Algorithms. MIT Press, 1990.