  We present a modified Ziggurat algorithm that could generate a random number
from all unimodal and unbounded PDFs. For PDFs that have unbounded density
and/or unbounded support we use a combination of nonlinear mapping function and
rejection sampling to generate a random number from the peak and/or the tail
distribution. A family of mapping functions and their corresponding acceptance
probability functions are presented (along with the criteria for their use and
their efficiency) that could be used to generate random numbers from infinite
tails and unbounded densities.
  The Zest library which is a C++ implementation of this algorithm is also
presented. Zest can efficiently generate normal, exponential, cauchy, gamma,
Weibull, log-normal, chi-squared, student's t and Fisher's f variates. The user
can also define their custom PDF as a class and supply it as a template
argument to our library's class without modifying any part of the library.
Performance of Zest is compared against performance of random modules of (GCC's
implementation of) Standard Template Library (STL) and Boost. The presented
results show that Zest is faster than both in most cases, sometimes by a factor
of more than 10.
  We also present a C++ implementation of a uniform floating-point random
number generator (RNG) which is capable of producing all representable
floating-point numbers in $[0,1)$ which will be used in the Ziggurat algorithm
near unbounded peaks and tails. The common method of dividing a random integer
by the range of the RNG can not produce random floating-point numbers with
fully random fraction bits and very small random numbers. The presented uniform
floating-point RNG is very efficient and in the case of producing double
precision floating-point numbers it's even faster than simply multiplying a
64-bit integer by $2^{-64}$.
