The distribution of the values sampled by the Gaussian sampler when using large norm (when $\sigma > 2^{53}$ or when $\mathcal{B} > 2^{64}-1$) does not look like a smooth Gaussian:
In orange the expected PDF, in blue the actual PDF for $\sigma = 2^{128}$.
The distribution of the values sampled by the Gaussian sampler when using large norm (when $\sigma > 2^{53}$ or when $\mathcal{B} > 2^{64}-1$) does not look like a smooth Gaussian:
In orange the expected PDF, in blue the actual PDF for $\sigma = 2^{128}$.