Trait malachite_base::num::arithmetic::traits::CheckedDoubleFactorial

pub trait CheckedDoubleFactorial: Sized {
    // Required method
    fn checked_double_factorial(n: u64) -> Option<Self>;
}

Computes the double factorial of a u64, returning None if the result is too large to be represented. The double factorial of a non-negative integer is the product of all the positive integers that are less than or equal to it and have the same parity as it.

Required Methods

fn checked_double_factorial(n: u64) -> Option<Self>

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl CheckedDoubleFactorial for u8

fn checked_double_factorial(n: u64) -> Option<u8>

Computes the double factorial of a number.

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

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

$n!! = O(\sqrt{n}(n/e)^{n/2})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedDoubleFactorial for u16

fn checked_double_factorial(n: u64) -> Option<u16>

Computes the double factorial of a number.

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

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

$n!! = O(\sqrt{n}(n/e)^{n/2})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedDoubleFactorial for u32

fn checked_double_factorial(n: u64) -> Option<u32>

Computes the double factorial of a number.

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

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

$n!! = O(\sqrt{n}(n/e)^{n/2})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedDoubleFactorial for u64

fn checked_double_factorial(n: u64) -> Option<u64>

Computes the double factorial of a number.

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

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

$n!! = O(\sqrt{n}(n/e)^{n/2})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedDoubleFactorial for u128

fn checked_double_factorial(n: u64) -> Option<u128>

Computes the double factorial of a number.

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

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

$n!! = O(\sqrt{n}(n/e)^{n/2})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

impl CheckedDoubleFactorial for usize

fn checked_double_factorial(n: u64) -> Option<usize>

Computes the double factorial of a usize.

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

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

$n!! = O(\sqrt{n}(n/e)^{n/2})$.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

Implementors