Ceil

A function common to many programming languages that returns the next integer value by rounding the value up if necessary.

Floor

A function common to many programming languages that returns the next lowest integer value by rounding the value down if necessary.

Fractions direction higher

Quality | Example |
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Idx lower element |
"So floor idx is the lower element and ceil idx is the higher" from question "To find an element with nearest lower and greater value in MATLAB" |

Always higher |
"On the other hand if what you want to do is not rounding but elimination of fractions into one direction then you have std ceil that goes always higher and std floor that always goes lower" from question "How to round off the totalcost (double) to nearest inetegrs" |

Greater possible works

Quality | Example |
---|---|

Greater |
"The floor times the ceil are greater than the floor xy...that s very much possible" from question "Proving with floor and ceiling functions formally for computer scientists" "Works because ceil a b is always one greater than floor a b except when a b is a whole number" from question "Java rounding up to an int using Math.ceil" |

Others

Quality | Example |
---|---|

Higher |
"Now if floor is higher than 0 or ceil is lower than 0 on any axis it means that there just as many tiles outside of the camera scoop" from question "Optimizing a simple 2D Tile engine (+potential bugfix)" |