Trait ModDivList 

pub trait ModDivList<RHS = Self, M = Self> {
    type Output;

    // Required method
    fn mod_div_list(
        self,
        other: RHS,
        m: M,
    ) -> Option<(Self::Output, Self::Output, Self::Output)>;
}

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

The quotients form an arithmetic progression: Some((start, stride, length)) means that the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where start is the smallest quotient.

Required Associated Types

type Output

Required Methods

fn mod_div_list( self, other: RHS, m: M, ) -> Option<(Self::Output, Self::Output, Self::Output)>

Dyn Compatibility

This trait is dyn compatible.

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

Implementations on Foreign Types

impl ModDivList for u8

fn mod_div_list(self, other: u8, m: u8) -> Option<(u8, u8, u8)>

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

A quotient exists if and only if $g = \gcd(y, m)$ divides $x$. In that case the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where $\text{start}$ is the smallest quotient, $\text{stride} = m/g$, and $\text{length} = g$. Unlike the quotient returned by ModDiv, the result is canonical.

$f(x, y, m) = \operatorname{Some}((s, t, \ell))$, where $qy \equiv x \mod m$ if and only if $q = s + ti$ for some $0 \leq i < \ell$, if such $q$ exist.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is m.significant_bits(): the extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost word operations, with no allocation.

Panics

Panics if self or other are greater than or equal to m.

Examples

See here.

type Output = u8

impl ModDivList for u16

fn mod_div_list(self, other: u16, m: u16) -> Option<(u16, u16, u16)>

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

A quotient exists if and only if $g = \gcd(y, m)$ divides $x$. In that case the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where $\text{start}$ is the smallest quotient, $\text{stride} = m/g$, and $\text{length} = g$. Unlike the quotient returned by ModDiv, the result is canonical.

$f(x, y, m) = \operatorname{Some}((s, t, \ell))$, where $qy \equiv x \mod m$ if and only if $q = s + ti$ for some $0 \leq i < \ell$, if such $q$ exist.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is m.significant_bits(): the extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost word operations, with no allocation.

Panics

Panics if self or other are greater than or equal to m.

Examples

See here.

type Output = u16

impl ModDivList for u32

fn mod_div_list(self, other: u32, m: u32) -> Option<(u32, u32, u32)>

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

A quotient exists if and only if $g = \gcd(y, m)$ divides $x$. In that case the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where $\text{start}$ is the smallest quotient, $\text{stride} = m/g$, and $\text{length} = g$. Unlike the quotient returned by ModDiv, the result is canonical.

$f(x, y, m) = \operatorname{Some}((s, t, \ell))$, where $qy \equiv x \mod m$ if and only if $q = s + ti$ for some $0 \leq i < \ell$, if such $q$ exist.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is m.significant_bits(): the extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost word operations, with no allocation.

Panics

Panics if self or other are greater than or equal to m.

Examples

See here.

type Output = u32

impl ModDivList for u64

fn mod_div_list(self, other: u64, m: u64) -> Option<(u64, u64, u64)>

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

A quotient exists if and only if $g = \gcd(y, m)$ divides $x$. In that case the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where $\text{start}$ is the smallest quotient, $\text{stride} = m/g$, and $\text{length} = g$. Unlike the quotient returned by ModDiv, the result is canonical.

$f(x, y, m) = \operatorname{Some}((s, t, \ell))$, where $qy \equiv x \mod m$ if and only if $q = s + ti$ for some $0 \leq i < \ell$, if such $q$ exist.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is m.significant_bits(): the extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost word operations, with no allocation.

Panics

Panics if self or other are greater than or equal to m.

Examples

See here.

type Output = u64

impl ModDivList for u128

fn mod_div_list(self, other: u128, m: u128) -> Option<(u128, u128, u128)>

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

A quotient exists if and only if $g = \gcd(y, m)$ divides $x$. In that case the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where $\text{start}$ is the smallest quotient, $\text{stride} = m/g$, and $\text{length} = g$. Unlike the quotient returned by ModDiv, the result is canonical.

$f(x, y, m) = \operatorname{Some}((s, t, \ell))$, where $qy \equiv x \mod m$ if and only if $q = s + ti$ for some $0 \leq i < \ell$, if such $q$ exist.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is m.significant_bits(): the extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost word operations, with no allocation.

Panics

Panics if self or other are greater than or equal to m.

Examples

See here.

type Output = u128

impl ModDivList for usize

fn mod_div_list(self, other: usize, m: usize) -> Option<(usize, usize, usize)>

Finds all quotients of a number and another number modulo a third number $m$, returning None if no quotient exists. The inputs must be already reduced modulo $m$.

A quotient exists if and only if $g = \gcd(y, m)$ divides $x$. In that case the quotients are exactly the numbers $\text{start} + \text{stride} \cdot i$ for $0 \leq i < \text{length}$, where $\text{start}$ is the smallest quotient, $\text{stride} = m/g$, and $\text{length} = g$. Unlike the quotient returned by ModDiv, the result is canonical.

$f(x, y, m) = \operatorname{Some}((s, t, \ell))$, where $qy \equiv x \mod m$ if and only if $q = s + ti$ for some $0 \leq i < \ell$, if such $q$ exist.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is m.significant_bits(): the extended Euclidean algorithm on words performs $O(n)$ iterations of constant-cost word operations, with no allocation.

Panics

Panics if self or other are greater than or equal to m.

Examples

See here.

type Output = usize

Implementors