K

$\varphi <0$

$\varphi \in \left[\mathrm{0,}\alpha \right]$

$\varphi >\alpha$

condition

$-\frac{\varphi }{\alpha }$

0

$\frac{\varphi }{\alpha }-1$

$\frac{\varphi }{\alpha }$ is an integer

$\lfloor -\frac{\varphi }{\alpha }\rfloor +1$

0

$\lfloor \frac{\varphi }{\alpha }\rfloor$

$\frac{\varphi }{\alpha }$ is not an integer