reversible modulo equation

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I came across an equation regarding some cryptography article that said for each $i$ $z_i= \mod( \lfloor(s_i*f)\rfloor+p_i, f)$ is reversible, i.e given $f, z,s$ we can get back $p$. My question is I doubt that this equation is invertible, but if at all this equation is invertible what makes it invertible, because there is a modulo operation involved and a flooring function which are not one-one