Trait malachite_base::num::arithmetic::traits::CheckedMultifactorial

pub trait CheckedMultifactorial: Sized {
    // Required method
    fn checked_multifactorial(n: u64, m: u64) -> Option<Self>;
}

Computes the $m$-multifactorial of a u64, returning None if the result is too large to be represented. The $m$-multifactorial of a non-negative integer $n$ is the product of all integers $k$ such that $0<k\leq n$ and $k\equiv n \pmod m$.

Required Methods

fn checked_multifactorial(n: u64, m: u64) -> Option<Self>

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl CheckedMultifactorial for u8

fn checked_multifactorial(n: u64, m: u64) -> Option<u8>

Computes a multifactorial of a number.

If the input is too large, the function returns None.

$$ f(n, m) = \begin{cases} \operatorname{Some}(n!^{(m)}) & \text{if} \quad n!^{(m)} < 2^W, \\ \operatorname{None} & \text{if} \quad n!^{(m)} \geq 2^W, \end{cases} $$ where $W$ is Self::WIDTH.

$n!^{(m)} = O(\sqrt{n}(n/e)^{n/m})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedMultifactorial for u16

fn checked_multifactorial(n: u64, m: u64) -> Option<u16>

Computes a multifactorial of a number.

If the input is too large, the function returns None.

$$ f(n, m) = \begin{cases} \operatorname{Some}(n!^{(m)}) & \text{if} \quad n!^{(m)} < 2^W, \\ \operatorname{None} & \text{if} \quad n!^{(m)} \geq 2^W, \end{cases} $$ where $W$ is Self::WIDTH.

$n!^{(m)} = O(\sqrt{n}(n/e)^{n/m})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedMultifactorial for u32

fn checked_multifactorial(n: u64, m: u64) -> Option<u32>

Computes a multifactorial of a number.

If the input is too large, the function returns None.

$$ f(n, m) = \begin{cases} \operatorname{Some}(n!^{(m)}) & \text{if} \quad n!^{(m)} < 2^W, \\ \operatorname{None} & \text{if} \quad n!^{(m)} \geq 2^W, \end{cases} $$ where $W$ is Self::WIDTH.

$n!^{(m)} = O(\sqrt{n}(n/e)^{n/m})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedMultifactorial for u64

fn checked_multifactorial(n: u64, m: u64) -> Option<u64>

Computes a multifactorial of a number.

If the input is too large, the function returns None.

$$ f(n, m) = \begin{cases} \operatorname{Some}(n!^{(m)}) & \text{if} \quad n!^{(m)} < 2^W, \\ \operatorname{None} & \text{if} \quad n!^{(m)} \geq 2^W, \end{cases} $$ where $W$ is Self::WIDTH.

$n!^{(m)} = O(\sqrt{n}(n/e)^{n/m})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedMultifactorial for u128

fn checked_multifactorial(n: u64, m: u64) -> Option<u128>

Computes a multifactorial of a number.

If the input is too large, the function returns None.

$$ f(n, m) = \begin{cases} \operatorname{Some}(n!^{(m)}) & \text{if} \quad n!^{(m)} < 2^W, \\ \operatorname{None} & \text{if} \quad n!^{(m)} \geq 2^W, \end{cases} $$ where $W$ is Self::WIDTH.

$n!^{(m)} = O(\sqrt{n}(n/e)^{n/m})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedMultifactorial for usize

fn checked_multifactorial(n: u64, m: u64) -> Option<usize>

Computes a multifactorial of a number.

If the input is too large, the function returns None.

$$ f(n, m) = \begin{cases} \operatorname{Some}(n!^{(m)}) & \text{if} \quad n!^{(m)} < 2^W, \\ \operatorname{None} & \text{if} \quad n!^{(m)} \geq 2^W, \end{cases} $$ where $W$ is Self::WIDTH.

$n!^{(m)} = O(\sqrt{n}(n/e)^{n/m})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Implementors