continuous_gaussian

Module for sampling from a continuous Gaussian distribution.

Functions

gaussian_inverse_cdf()	Returns inverse CDF for N(u,sigma_squared) at p.
gaussian()	Samples a float from the Gaussian distribution.

gaussian_inverse_cdf(u, sigma_squared, p, prec)

Returns inverse CDF for N(u,sigma_squared) at p.

Parameters:

• u (Union[int, float, tmlt.core.utils.arb.Arb]) – The mean of the distribution. Must be finite and non-nan.

• sigma_squared (Union[int, float, tmlt.core.utils.arb.Arb]) – The variance of the distribution. Must be finite, non-nan and non-negative.

• p (tmlt.core.utils.arb.Arb) – Probability to compute the CDF at.

• prec (int) – Precision to use for computing CDF.

Return type:

tmlt.core.utils.arb.Arb

gaussian(sigma_squared, u=0, step_size=63)

Samples a float from the Gaussian distribution.

In particular, this returns a sample from the Gaussian

\(\mathcal{N}_{\mathbb{Z}}(u, sigma\_squared)\)

Parameters:

• sigma_squared (Union[tmlt.core.utils.arb.Arb, float]) – The variance of the distribution. Must be positive, finite and non-nan.

• u (Union[tmlt.core.utils.arb.Arb, float]) – The mean of the distribution. Must be finite and non-nan. Defaults to 0

• step_size (int) – How many bits of probability to sample at a time.

Return type:

float