In computer programming, I often encounter the need to give the binary operations:
- The greatest multiple of $y$ that is not greater than $x$
- $41 \circ_1 6 = 36$
- $3.2 \circ_1 0.5 = 3$
- The least multiple of $y$ that is not less than $x$
- $41 \circ_2 7 = 42$
- $3.2 \circ_2 0.5 = 3.5$
where $x$ and $y$ belong to the same class (such integer or float). Mathematically, it can be considered that they are both integers or both real numbers. They are somewhat reminiscent of floor and ceiling functions.
Is there such notion (and perhaps names and/or notations) like these binary operations?