Javadoc
The Laplace distribution is a continuous probability distribution with probability density function
$$
\begin{align*}
f(x)=\frac{1}{2b}e^{-\frac{|x-\mu|}{b}}
\end{align*}
$$
where $\mu$ is the location parameter and $b$ is the scale parameter. The
cumulative distribution function and its inverse are defined as:
$$
\begin{align*}
F(x)&=
\begin{cases}
\frac{1}{2}e^{\frac{x-\mu}{b}} & \text{if } x < \mu\\
1-\frac{1}{2}e^{-\frac{x-\mu}{b}} & \text{if } x\geq \mu
\end{cases}\\
F^{-1}(p)&=\mu-b\text{ sgn}(p-0.5)\ln(1-2|p-0.5|)
\end{align*}
$$
Given a uniform random variable $U$ drawn from the interval $(-\frac{1}{2}, \frac{1}{2}]$,
a Laplace-distributed random variable with parameters $\mu$ and $b$ is given by:
$$
\begin{align*}
X=\mu-b\text{ sgn}(U)\ln(1-2|U|)
\end{align*}
$$