Function malachite_nz::natural::random::random_naturals
source · pub fn random_naturals(
seed: Seed,
mean_bits_numerator: u64,
mean_bits_denominator: u64
) -> RandomNaturals<GeometricRandomNaturalValues<u64>> ⓘ
Expand description
Generates random Natural
s with a specified mean bit length.
The actual bit length is chosen from a geometric distribution with mean $m$, where $m$ is
mean_bits_numerator / mean_bits_denominator
; $m$ must be greater than 0. Then a Natural
is
chosen uniformly among all Natural
s with that bit length. The resulting distribution
resembles a Pareto distribution. It has no mean or higher-order statistics (unless $m < 1$,
which is not typical).
$$ P(n) = \begin{cases} \frac{1}{m + 1} & \text{if} \quad n = 0, \\ \frac{2}{m+1} \left ( \frac{m}{2(m+1)} \right ) ^ {\lfloor \log_2 n \rfloor + 1} & \text{if} \quad \text{otherwise}. \end{cases} $$
The output length is infinite.
§Expected complexity per iteration
$T(n, m) = O(n + m)$
$M(n, m) = O(n / m)$
where $T$ is time, $M$ is additional memory, $n$ is mean_precision_numerator
, and $m$ is
mean_precision_denominator
.
§Panics
Panics if mean_bits_numerator
or mean_bits_denominator
are zero, or, if after being reduced
to lowest terms, their sum is greater than or equal to $2^{64}$.
§Examples
use malachite_base::iterators::prefix_to_string;
use malachite_base::random::EXAMPLE_SEED;
use malachite_nz::natural::random::random_naturals;
use malachite_nz::natural::Natural;
assert_eq!(
prefix_to_string(random_naturals(EXAMPLE_SEED, 32, 1), 10),
"[20431208470830262, 2777240, 114, 12184833305054, 1121025855008623490210, \
13478874522577592, 115311695, 7, 18, 54522366353, ...]"
)