Function malachite_nz::integer::random::random_nonzero_integers
source · pub fn random_nonzero_integers(
seed: Seed,
mean_bits_numerator: u64,
mean_bits_denominator: u64
) -> RandomIntegers<GeometricRandomNonzeroSigneds<i64>> ⓘ
Expand description
Generates random nonzero Integer
s whose absolute values have a specified mean bit length.
The actual signed bit length is chosen from a distribution that produces values whose mean
absolute values are $m$, where $m$ is mean_bits_numerator / mean_bits_denominator
(see
geometric_random_nonzero_signeds
); $m$ must be greater than 1. Then an Integer
is chosen
uniformly among all positive Integer
s with that bit length, and its sign is set to the sign
of the signed bit length. The resulting distribution has no mean or higher-order statistics
(unless $m < 2$, which is not typical).
$$ P(n) = \begin{cases} 0 & \text{if} \quad n = 0, \\ \frac{1}{2m} \left ( \frac{m-1}{2m} \right ) ^ {\lfloor \log_2 |n| \rfloor} & \text{otherwise}. \end{cases} $$
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 mean_bits_numerator <= mean_bits_denominator
.
§Examples
use malachite_base::iterators::prefix_to_string;
use malachite_base::random::EXAMPLE_SEED;
use malachite_nz::integer::random::random_nonzero_integers;
assert_eq!(
prefix_to_string(random_nonzero_integers(EXAMPLE_SEED, 32, 1), 10),
"[6, 373973144, 46887963477285686350042496363292819122, -93254818, -126908, \
-4471675267836600, 1860142159, -118004986915853475, -98, 346513, ...]"
)