Algebra Level 4

Is $$f(x)$$$$=$$$$(-1)^{\lfloor x \rfloor} \sqrt{\frac{1}{4}-(x-\frac{1}{2}-\lfloor x \rfloor)^2}$$ an odd or even function?

Try not to use graph!

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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