Trait malachite_base::num::arithmetic::traits::Multifactorial

pub trait Multifactorial {
    // Required method
    fn multifactorial(n: u64, m: u64) -> Self;
}

Computes the $m$-multifactorial of a u64. 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 multifactorial(n: u64, m: u64) -> Self

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl Multifactorial for u8

fn multifactorial(n: u64, m: u64) -> u8

Computes a multifactorial of a number.

If the input is too large, the function panics. For a function that returns None instead, try checked_multifactorial.

$$ f(n, m) = n!^{(m)} = n \times (n - m) \times (n - 2m) \times \cdots \times i. $$ If $n$ is divisible by $m$, then $i$ is $m$; otherwise, $i$ is the remainder when $n$ is divided by $m$.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Multifactorial for u16

fn multifactorial(n: u64, m: u64) -> u16

Computes a multifactorial of a number.

If the input is too large, the function panics. For a function that returns None instead, try checked_multifactorial.

$$ f(n, m) = n!^{(m)} = n \times (n - m) \times (n - 2m) \times \cdots \times i. $$ If $n$ is divisible by $m$, then $i$ is $m$; otherwise, $i$ is the remainder when $n$ is divided by $m$.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Multifactorial for u32

fn multifactorial(n: u64, m: u64) -> u32

Computes a multifactorial of a number.

If the input is too large, the function panics. For a function that returns None instead, try checked_multifactorial.

$$ f(n, m) = n!^{(m)} = n \times (n - m) \times (n - 2m) \times \cdots \times i. $$ If $n$ is divisible by $m$, then $i$ is $m$; otherwise, $i$ is the remainder when $n$ is divided by $m$.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Multifactorial for u64

fn multifactorial(n: u64, m: u64) -> u64

Computes a multifactorial of a number.

If the input is too large, the function panics. For a function that returns None instead, try checked_multifactorial.

$$ f(n, m) = n!^{(m)} = n \times (n - m) \times (n - 2m) \times \cdots \times i. $$ If $n$ is divisible by $m$, then $i$ is $m$; otherwise, $i$ is the remainder when $n$ is divided by $m$.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Multifactorial for u128

fn multifactorial(n: u64, m: u64) -> u128

Computes a multifactorial of a number.

If the input is too large, the function panics. For a function that returns None instead, try checked_multifactorial.

$$ f(n, m) = n!^{(m)} = n \times (n - m) \times (n - 2m) \times \cdots \times i. $$ If $n$ is divisible by $m$, then $i$ is $m$; otherwise, $i$ is the remainder when $n$ is divided by $m$.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl Multifactorial for usize

fn multifactorial(n: u64, m: u64) -> usize

Computes a multifactorial of a number.

If the input is too large, the function panics. For a function that returns None instead, try checked_multifactorial.

$$ f(n, m) = n!^{(m)} = n \times (n - m) \times (n - 2m) \times \cdots \times i. $$ If $n$ is divisible by $m$, then $i$ is $m$; otherwise, $i$ is the remainder when $n$ is divided by $m$.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

Implementors