Trait malachite_base::num::arithmetic::traits::NegModPowerOf2

pub trait NegModPowerOf2 {
    type Output;

    // Required method
    fn neg_mod_power_of_2(self, other: u64) -> Self::Output;
}

Divides the negative of a number by $2^k$, returning the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

Required Associated Types

type Output

Required Methods

fn neg_mod_power_of_2(self, other: u64) -> Self::Output

Implementations on Foreign Types

impl NegModPowerOf2 for u8

fn neg_mod_power_of_2(self, pow: u64) -> u8

Divides the negative of a number by a $2^k$, returning just the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

$$ f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if self is nonzero and pow is greater than Self::WIDTH.

Examples

See here.

type Output = u8

impl NegModPowerOf2 for u16

fn neg_mod_power_of_2(self, pow: u64) -> u16

Divides the negative of a number by a $2^k$, returning just the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

$$ f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if self is nonzero and pow is greater than Self::WIDTH.

Examples

See here.

type Output = u16

impl NegModPowerOf2 for u32

fn neg_mod_power_of_2(self, pow: u64) -> u32

Divides the negative of a number by a $2^k$, returning just the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

$$ f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if self is nonzero and pow is greater than Self::WIDTH.

Examples

See here.

type Output = u32

impl NegModPowerOf2 for u64

fn neg_mod_power_of_2(self, pow: u64) -> u64

Divides the negative of a number by a $2^k$, returning just the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

$$ f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if self is nonzero and pow is greater than Self::WIDTH.

Examples

See here.

type Output = u64

impl NegModPowerOf2 for u128

fn neg_mod_power_of_2(self, pow: u64) -> u128

Divides the negative of a number by a $2^k$, returning just the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

$$ f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if self is nonzero and pow is greater than Self::WIDTH.

Examples

See here.

type Output = u128

impl NegModPowerOf2 for usize

fn neg_mod_power_of_2(self, pow: u64) -> usize

Divides the negative of a number by a $2^k$, returning just the remainder.

If the quotient were computed, the quotient and remainder would satisfy $x = q2^k - r$ and $0 \leq r < 2^k$.

$$ f(x, k) = 2^k\left \lceil \frac{x}{2^k} \right \rceil - x. $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if self is nonzero and pow is greater than Self::WIDTH.

Examples

See here.

type Output = usize

Implementors