Rounding methods

Question

I have a question regarding the rounding methods to nearest -infinty and +infinity.

In the lecture videos for the case "nearest -infinity", we say at the corner cases .5 it get rounded down, but the formula is with ⌈x − 0.5⌉. I would interprete this as if you have x=2 then we get such a corner case 1.5. With the positive gauss brackets we are supposed to round up to 2. This would conflict to the video, where we would round down at those corner cases.

For "round to nearest +infinity" its just the other way around.

Did i misunderstand something in the lecture videos or is this a mistake?

Thank you in Advance.

Answer 1

I don't see a mistake in the slides, let's check some examples:

• ceil(1.0-0.5) = ceil(0.5) = 1.0
• ceil(1.4-0.5) = ceil(0.9) = 1.0
• ceil(1.5-0.5) = ceil(1.0) = 1.0
• ceil(1.6-0.5) = ceil(1.1) = 2.0
• ceil(2.0-0.5) = ceil(1.5) = 2.0

About cornercases: these are the numbers which are exactly in between two integers like x=1.5 (and not x=2.0). For those numbers n+0.5, we obtain ceil(n+0.5-0.5) = ceil(n) = n which means that we are rounding downwards, right?