Trait malachite_base::num::arithmetic::traits::CheckedRoot

pub trait CheckedRoot<POW> {
    type Output;

    // Required method
    fn checked_root(self, pow: POW) -> Option<Self::Output>;
}

Finds the $n$th root of a number, returning None if it is not a perfect $n$th power.

Required Associated Types

type Output

Required Methods

fn checked_root(self, pow: POW) -> Option<Self::Output>

Implementations on Foreign Types

impl CheckedRoot<u64> for i8

fn checked_root(self, exp: u64) -> Option<i8>

Returns the the $n$th root of an integer, or None if the integer is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero, or if self is negative and exp is even.

Examples

See here.

type Output = i8

impl CheckedRoot<u64> for i16

fn checked_root(self, exp: u64) -> Option<i16>

Returns the the $n$th root of an integer, or None if the integer is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero, or if self is negative and exp is even.

Examples

See here.

type Output = i16

impl CheckedRoot<u64> for i32

fn checked_root(self, exp: u64) -> Option<i32>

Returns the the $n$th root of an integer, or None if the integer is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero, or if self is negative and exp is even.

Examples

See here.

type Output = i32

impl CheckedRoot<u64> for i64

fn checked_root(self, exp: u64) -> Option<i64>

Returns the the $n$th root of an integer, or None if the integer is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero, or if self is negative and exp is even.

Examples

See here.

type Output = i64

impl CheckedRoot<u64> for i128

fn checked_root(self, exp: u64) -> Option<i128>

Returns the the $n$th root of an integer, or None if the integer is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero, or if self is negative and exp is even.

Examples

See here.

type Output = i128

impl CheckedRoot<u64> for isize

fn checked_root(self, exp: u64) -> Option<isize>

Returns the the $n$th root of an integer, or None if the integer is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero, or if self is negative and exp is even.

Examples

See here.

type Output = isize

impl CheckedRoot<u64> for u8

fn checked_root(self, exp: u64) -> Option<u8>

Returns the the $n$th root of a u8, or None if the u8 is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

The u8 implementation uses lookup tables.

type Output = u8

impl CheckedRoot<u64> for u16

fn checked_root(self, exp: u64) -> Option<u16>

Returns the the $n$th root of a u16, or None if the u16 is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

The u16 implementation calls the implementation for u32s.

type Output = u16

impl CheckedRoot<u64> for u32

fn checked_root(self, exp: u64) -> Option<u32>

Returns the the $n$th root of a u32, or None if the u32 is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

For cube roots, the u32 implementation uses a piecewise Chebyshev approximation. For other roots, it uses Newton’s method. In both implementations, the result of these approximations is adjusted afterwards to account for error.

type Output = u32

impl CheckedRoot<u64> for u64

fn checked_root(self, exp: u64) -> Option<u64>

Returns the the $n$th root of a u64, or None if the u64 is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

For cube roots, the u64 implementation uses a piecewise Chebyshev approximation. For other roots, it uses Newton’s method. In both implementations, the result of these approximations is adjusted afterwards to account for error.

type Output = u64

impl CheckedRoot<u64> for u128

fn checked_root(self, exp: u64) -> Option<u128>

Returns the the $n$th root of a u128, or None if the u128 is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

The u128 implementation computes the root using floating-point arithmetic. The approximate result is adjusted afterwards to account for error.

type Output = u128

impl CheckedRoot<u64> for usize

fn checked_root(self, exp: u64) -> Option<usize>

Returns the the $n$th root of a usize, or None if the usize is not a perfect $n$th power.

$$ f(x, n) = \begin{cases} \operatorname{Some}(sqrt[n]{x}) & \text{if} \quad \sqrt[n]{x} \in \Z, \\ \operatorname{None} & \textrm{otherwise}. \end{cases} $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if exp is zero.

Examples

See here.

Notes

The usize implementation calls the u32 or u64 implementations.

type Output = usize

Implementors