Modular arithmetic with decimals

Is there any way to find $\lfloor xy\rfloor$ mod $m$ if $x$ is something large (like a big factorial where it is normal to calculate it stepwise, taking the modulus each step) and $y$ is irrational?

It does not appear that $\lfloor$(($x$ mod $m$) times $y$)$\rfloor$ mod $m$ is the same as $\lfloor$($x$ times $y$)$\rfloor$ mod $m$ even if it may work for integers.

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this might help, at least for a lack luster answer, think about x being $10^{10}$. Then the value of this would be $y$ to the first 10 decimal places. It really seems to depend on $x$ –  DanZimm May 9 '13 at 2:45
$\lfloor xy\rfloor \pmod{m}=\lfloor \left(x \pmod{\frac{m}{y}}\right)y\rfloor \pmod{m}$. You may subtract as many integer multiples of $\frac my$ as you want from $x$ without changing the final result.