Trait malachite_base::num::arithmetic::traits::ModPowerOf2Inverse

source · 
pub trait ModPowerOf2Inverse {
    type Output;

    fn mod_power_of_2_inverse(self, pow: u64) -> Option<Self::Output>;
}
Expand description

Finds the multiplicative inverse of a number modulo $2^k$. Assumes the input is already reduced modulo $2^k$.

Required Associated Types§

Required Methods§

Implementations on Foreign Types§

Computes the multiplicative inverse of a number modulo $2^k$. Assumes the number is already reduced modulo $2^k$.

Returns None if $x$ is even.

$f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is pow.

Examples

See here.

Computes the multiplicative inverse of a number modulo $2^k$. Assumes the number is already reduced modulo $2^k$.

Returns None if $x$ is even.

$f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is pow.

Examples

See here.

Computes the multiplicative inverse of a number modulo $2^k$. Assumes the number is already reduced modulo $2^k$.

Returns None if $x$ is even.

$f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is pow.

Examples

See here.

Computes the multiplicative inverse of a number modulo $2^k$. Assumes the number is already reduced modulo $2^k$.

Returns None if $x$ is even.

$f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is pow.

Examples

See here.

Computes the multiplicative inverse of a number modulo $2^k$. Assumes the number is already reduced modulo $2^k$.

Returns None if $x$ is even.

$f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is pow.

Examples

See here.

Computes the multiplicative inverse of a number modulo $2^k$. Assumes the number is already reduced modulo $2^k$.

Returns None if $x$ is even.

$f(x, k) = y$, where $x, y < 2^k$, $x$ is odd, and $xy \equiv 1 \mod 2^k$.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is pow.

Examples

See here.

Implementors§