# Floors and Ceilings and Cosines, Oh My!

Geometry Level 5

$\begin{eqnarray} f\left( x \right) &=&\cos { \left( \pi \left\lfloor x \right\rfloor \right) } \left( { 2 }^{ x-\left\lfloor x \right\rfloor }-1 \right) \\\ g\left( x \right) &=&\cos { \left( \frac { \pi }{ 2 } \left\lfloor x \right\rfloor \right) } \left( { 2 }^{ \left\lceil x \right\rceil -x }-1 \right) \end{eqnarray}$

The set of all real $$x$$ such that $$0 \leq x \leq 2015$$ and $$f(x) > g(x)$$ is a union of disjoint intervals. What is the sum of the lengths of those intervals?

Notations:

-$$\left\lfloor x \right\rfloor$$ denotes the greatest integer not exceeding $$x$$. For example, $$\left\lfloor 2.123 \right\rfloor = 2$$ and $$\left\lfloor 7 \right\rfloor = 7$$

-$$\left\lceil x \right\rceil$$ denotes the smallest integer greater than or equal to $$x$$. For example, $$\left\lceil 2.123 \right\rceil =3$$ and $$\left\lceil 7 \right\rceil =7$$

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