Trait malachite_base::num::arithmetic::traits::ModPowPrecomputed

pub trait ModPowPrecomputed<RHS = Self, M = Self>where
    Self: Sized,{
    type Output;
    type Data;

    fn precompute_mod_pow_data(m: &M) -> Self::Data;
    fn mod_pow_precomputed(self, exp: RHS, m: M, data: &Self::Data) -> Self::Output;
}

Expand description

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

If multiple modular exponentiations with the same modulus are necessary, it can be quicker to precompute some piece of data and reuse it in the exponentiation calls. This trait provides a function for precomputing the data and a function for using it during exponentiation.

Required Associated Types§

type Output

type Data

Required Methods§

fn precompute_mod_pow_data(m: &M) -> Self::Data

Precomputes some data to use for modular exponentiation.

fn mod_pow_precomputed(self, exp: RHS, m: M, data: &Self::Data) -> Self::Output

Implementations on Foreign Types§

impl ModPowPrecomputed<u64, u32> for u32

fn precompute_mod_pow_data(m: &u32) -> (u32, u64)

Precomputes data for modular exponentiation.

See mod_pow_precomputed and mod_pow_precomputed_assign.

Worst-case complexity

Constant time and additional memory.

fn mod_pow_precomputed(self, exp: u64, m: u32, data: &(u32, u64)) -> u32

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

Some precomputed data is provided; this speeds up computations involving several modular exponentiations with the same modulus. The precomputed data should be obtained using precompute_mod_pow_data.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is exp.significant_bits().

Examples

See here.

type Output = u32

type Data = (u32, u64)

impl ModPowPrecomputed<u64, u64> for u64

fn precompute_mod_pow_data(m: &u64) -> (u64, u64)

Precomputes data for modular exponentiation.

See mod_pow_precomputed and mod_pow_precomputed_assign.

Worst-case complexity

Constant time and additional memory.

fn mod_pow_precomputed(self, exp: u64, m: u64, data: &(u64, u64)) -> u64

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

Some precomputed data is provided; this speeds up computations involving several modular exponentiations with the same modulus. The precomputed data should be obtained using precompute_mod_pow_data.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is exp.significant_bits().

Examples

See here.

type Output = u64

type Data = (u64, u64)

impl ModPowPrecomputed<u64, u8> for u8

fn precompute_mod_pow_data(m: &u8) -> (u32, u64)

Precomputes data for modular exponentiation.

See mod_pow_precomputed and mod_pow_precomputed_assign.

Worst-case complexity

Constant time and additional memory.

fn mod_pow_precomputed(self, exp: u64, m: u8, data: &(u32, u64)) -> u8

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

Some precomputed data is provided; this speeds up computations involving several modular exponentiations with the same modulus. The precomputed data should be obtained using precompute_mod_pow_data.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is exp.significant_bits().

Examples

See here.

type Output = u8

type Data = (u32, u64)

impl ModPowPrecomputed<u64, u16> for u16

fn precompute_mod_pow_data(m: &u16) -> (u32, u64)

Precomputes data for modular exponentiation.

See mod_pow_precomputed and mod_pow_precomputed_assign.

Worst-case complexity

Constant time and additional memory.

fn mod_pow_precomputed(self, exp: u64, m: u16, data: &(u32, u64)) -> u16

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

Some precomputed data is provided; this speeds up computations involving several modular exponentiations with the same modulus. The precomputed data should be obtained using precompute_mod_pow_data.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is exp.significant_bits().

Examples

See here.

type Output = u16

type Data = (u32, u64)

impl ModPowPrecomputed<u64, u128> for u128

fn precompute_mod_pow_data(_m: &u128)

Precomputes data for modular exponentiation.

See mod_pow_precomputed and mod_pow_precomputed_assign.

Worst-case complexity

Constant time and additional memory.

fn mod_pow_precomputed(self, exp: u64, m: u128, _data: &()) -> u128

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

Some precomputed data is provided; this speeds up computations involving several modular exponentiations with the same modulus. The precomputed data should be obtained using precompute_mod_pow_data.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is exp.significant_bits().

Examples

See here.

type Output = u128

type Data = ()

impl ModPowPrecomputed<u64, usize> for usize

fn precompute_mod_pow_data(m: &usize) -> (usize, u64)

Precomputes data for modular exponentiation.

See mod_pow_precomputed and mod_pow_precomputed_assign.

Worst-case complexity

Constant time and additional memory.

fn mod_pow_precomputed(self, exp: u64, m: usize, data: &(usize, u64)) -> usize

Raises a number to a power modulo another number $m$. Assumes the input is already reduced modulo $m$.

Some precomputed data is provided; this speeds up computations involving several modular exponentiations with the same modulus. The precomputed data should be obtained using precompute_mod_pow_data.

Worst-case complexity

$T(n) = O(n)$

$M(n) = O(1)$

where $T$ is time, $M$ is additional memory, and $n$ is exp.significant_bits().

Examples

See here.

type Output = usize

type Data = (usize, u64)

Implementors§