Given some random number function rand
, and some numbers $x$ and $y$, how do you find a random number $r$ such that $r\geq x \wedge r \leq y$?
Previously i've tried (and somewhat failed) with formulas like $$ r = \text{rand()}\bmod \frac{x}{y} $$ or $$ r = \text{rand()}\bmod x + 1 $$ or, given that $y>x$, $$ r = (\text{rand()}\bmod (y-x))+x $$ Is there a better or truer way to do this?