Trait malachite_base::num::arithmetic::traits::DoubleFactorial

pub trait DoubleFactorial {
    // Required method
    fn double_factorial(n: u64) -> Self;
}

Computes the double factorial of a u64. 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 double_factorial(n: u64) -> Self

Object Safety

This trait is not object safe.

Implementations on Foreign Types

impl DoubleFactorial for u8

fn double_factorial(n: u64) -> u8

Computes the double factorial of a number.

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

$$ f(n) = n!! = n \times (n - 2) \times (n - 4) \times \cdots \times i, $$ where $i$ is 1 if $n$ is odd and $2$ if $n$ is even.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl DoubleFactorial for u16

fn double_factorial(n: u64) -> u16

Computes the double factorial of a number.

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

$$ f(n) = n!! = n \times (n - 2) \times (n - 4) \times \cdots \times i, $$ where $i$ is 1 if $n$ is odd and $2$ if $n$ is even.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl DoubleFactorial for u32

fn double_factorial(n: u64) -> u32

Computes the double factorial of a number.

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

$$ f(n) = n!! = n \times (n - 2) \times (n - 4) \times \cdots \times i, $$ where $i$ is 1 if $n$ is odd and $2$ if $n$ is even.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl DoubleFactorial for u64

fn double_factorial(n: u64) -> u64

Computes the double factorial of a number.

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

$$ f(n) = n!! = n \times (n - 2) \times (n - 4) \times \cdots \times i, $$ where $i$ is 1 if $n$ is odd and $2$ if $n$ is even.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl DoubleFactorial for u128

fn double_factorial(n: u64) -> u128

Computes the double factorial of a number.

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

$$ f(n) = n!! = n \times (n - 2) \times (n - 4) \times \cdots \times i, $$ where $i$ is 1 if $n$ is odd and $2$ if $n$ is even.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

impl DoubleFactorial for usize

fn double_factorial(n: u64) -> usize

Computes the double factorial of a number.

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

$$ f(n) = n!! = n \times (n - 2) \times (n - 4) \times \cdots \times i, $$ where $i$ is 1 if $n$ is odd and $2$ if $n$ is even.

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the output is too large to be represented.

Examples

See here.

Implementors