Overview
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Discrete Gaussians over the Integers
A discrete Gaussian distribution on the Integers is a distribution where the
integer $x$ is sampled with probability proportional to $exp((xc)²/(2σ²))$.
It is denoted by $D_{σ,c}$ where σ
is the width parameter (close to the
standard deviation) and $c$ is the center.
This library samples from this distributions.
Installation
You can either clone this repository or download a
release tarball. The latter
includes a configure
script.
Hence, if you cloned the repository do
mkdir m4 autoreconf i mkdir m4 autoreconf i ./configure make make check
If you downloaded the release tarball then the following will suffice:
./configure make make check
Algorithms

DGS_DISC_GAUSS_UNIFORM_TABLE
 classical rejection sampling, sampling from the uniform distribution and accepted with probability proportional to $\exp((xc)²/(2σ²))$ where $\exp((xc)²/(2σ²))$ is precomputed and stored in a table. Any realvaluedc
is supported. 
DGS_DISC_GAUSS_UNIFORM_LOGTABLE
 samples are drawn from a uniform distribution and accepted with probability proportional to $\exp((xc)²/(2σ²))$ where $\exp((xc)²/(2σ²))$ is computed using logarithmically many calls to Bernoulli distributions. Only integervalued $c$ are supported. 
DGS_DISC_GAUSS_UNIFORM_ONLINE
 samples are drawn from a uniform distribution and accepted with probability proportional to $\exp((xc)²/(2σ²))$ where $\exp((xc)²/(2σ²))$ is computed in each invocation. Typically this is very slow. Any realvalued $c$ is accepted. 
DGS_DISC_SIGMA2_LOGTABLE
 samples are drawn from an easily samplable distribution with $σ = k·σ₂$ where $σ₂ := \sqrt{1/(2\log 2)}$ and accepted with probability proportional to $\exp((xc)²/(2σ²))$ where $\exp((xc)²/(2σ²))$ is computed using logarithmically many calls to Bernoulli distributions (but no calls to $\exp$). Note that this sampler adjusts sigma to match $σ₂·k$ for some integer $k$. Only integervalued $c$ are supported.
Algorithm 24 are described in:
Léo Ducas, Alain Durmus, Tancrède Lepoint and Vadim Lyubashevsky. Lattice Signatures and Bimodal Gaussians; in Advances in Cryptology – CRYPTO 2013; Lecture Notes in Computer Science Volume 8042, 2013, pp 4056 (PDF)
Precisions

mp
 multiprecision using MPFR, cf.dgs_gauss_mp.c

dp
 double precision using machine doubles, cf.dgs_gauss_dp.c
.
For readers unfamiliar with the implemented algorithms it makes sense to start
with dgs_gauss_dp.c
which implements the same algorithms as
dgs_gauss_mp.c
but should be easier to read.
Typical Usage
dgs_disc_gauss_dp_t *D = dgs_disc_gauss_dp_init(<sigma>, <c>, <tau>, <algorithm>); D>call(D); // as often as needed dgs_disc_gauss_dp_clear(D);