Trait 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>

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so 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