Trait BalancedModPowerOf2 

pub trait BalancedModPowerOf2 {
    type Output;

    // Required method
    fn balanced_mod_power_of_2(self, pow: u64) -> Self::Output;
}

Divides a number by $2^k$, returning the balanced remainder: the representative of the number modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$, so a remainder of exactly $2^{k-1}$ is positive, as with BalancedMod; for $k = 0$ it is 0. It is congruent to $x$ modulo $2^k$, and those two properties determine it uniquely.

Required Associated Types

type Output

Required Methods

fn balanced_mod_power_of_2(self, pow: u64) -> 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 BalancedModPowerOf2 for i8

fn balanced_mod_power_of_2(self, pow: u64) -> i8

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive. When pow is greater than Self::WIDTH, every value is its own balanced remainder.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if pow is Self::WIDTH and self is Self::MIN, whose balanced remainder $2^{W-1}$ does not fit in the type.

Examples

See here.

type Output = i8

impl BalancedModPowerOf2 for i16

fn balanced_mod_power_of_2(self, pow: u64) -> i16

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive. When pow is greater than Self::WIDTH, every value is its own balanced remainder.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if pow is Self::WIDTH and self is Self::MIN, whose balanced remainder $2^{W-1}$ does not fit in the type.

Examples

See here.

type Output = i16

impl BalancedModPowerOf2 for i32

fn balanced_mod_power_of_2(self, pow: u64) -> i32

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive. When pow is greater than Self::WIDTH, every value is its own balanced remainder.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if pow is Self::WIDTH and self is Self::MIN, whose balanced remainder $2^{W-1}$ does not fit in the type.

Examples

See here.

type Output = i32

impl BalancedModPowerOf2 for i64

fn balanced_mod_power_of_2(self, pow: u64) -> i64

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive. When pow is greater than Self::WIDTH, every value is its own balanced remainder.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if pow is Self::WIDTH and self is Self::MIN, whose balanced remainder $2^{W-1}$ does not fit in the type.

Examples

See here.

type Output = i64

impl BalancedModPowerOf2 for i128

fn balanced_mod_power_of_2(self, pow: u64) -> i128

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive. When pow is greater than Self::WIDTH, every value is its own balanced remainder.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if pow is Self::WIDTH and self is Self::MIN, whose balanced remainder $2^{W-1}$ does not fit in the type.

Examples

See here.

type Output = i128

impl BalancedModPowerOf2 for isize

fn balanced_mod_power_of_2(self, pow: u64) -> isize

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive. When pow is greater than Self::WIDTH, every value is its own balanced remainder.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if pow is Self::WIDTH and self is Self::MIN, whose balanced remainder $2^{W-1}$ does not fit in the type.

Examples

See here.

type Output = isize

impl BalancedModPowerOf2 for u8

fn balanced_mod_power_of_2(self, pow: u64) -> i8

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so the result may be negative and is returned as the signed type of the same width. This is the same as balanced_mod with modulus $2^k$, when $2^k$ fits in the type.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the result does not fit in the signed type: if pow is Self::WIDTH and self is $2^{W-1}$, or if pow is greater than Self::WIDTH and self is at least $2^{W-1}$, where $W$ is Self::WIDTH.

Examples

See here.

type Output = i8

impl BalancedModPowerOf2 for u16

fn balanced_mod_power_of_2(self, pow: u64) -> i16

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so the result may be negative and is returned as the signed type of the same width. This is the same as balanced_mod with modulus $2^k$, when $2^k$ fits in the type.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the result does not fit in the signed type: if pow is Self::WIDTH and self is $2^{W-1}$, or if pow is greater than Self::WIDTH and self is at least $2^{W-1}$, where $W$ is Self::WIDTH.

Examples

See here.

type Output = i16

impl BalancedModPowerOf2 for u32

fn balanced_mod_power_of_2(self, pow: u64) -> i32

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so the result may be negative and is returned as the signed type of the same width. This is the same as balanced_mod with modulus $2^k$, when $2^k$ fits in the type.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the result does not fit in the signed type: if pow is Self::WIDTH and self is $2^{W-1}$, or if pow is greater than Self::WIDTH and self is at least $2^{W-1}$, where $W$ is Self::WIDTH.

Examples

See here.

type Output = i32

impl BalancedModPowerOf2 for u64

fn balanced_mod_power_of_2(self, pow: u64) -> i64

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so the result may be negative and is returned as the signed type of the same width. This is the same as balanced_mod with modulus $2^k$, when $2^k$ fits in the type.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the result does not fit in the signed type: if pow is Self::WIDTH and self is $2^{W-1}$, or if pow is greater than Self::WIDTH and self is at least $2^{W-1}$, where $W$ is Self::WIDTH.

Examples

See here.

type Output = i64

impl BalancedModPowerOf2 for u128

fn balanced_mod_power_of_2(self, pow: u64) -> i128

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so the result may be negative and is returned as the signed type of the same width. This is the same as balanced_mod with modulus $2^k$, when $2^k$ fits in the type.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the result does not fit in the signed type: if pow is Self::WIDTH and self is $2^{W-1}$, or if pow is greater than Self::WIDTH and self is at least $2^{W-1}$, where $W$ is Self::WIDTH.

Examples

See here.

type Output = i128

impl BalancedModPowerOf2 for usize

fn balanced_mod_power_of_2(self, pow: u64) -> isize

Divides a number by $2^k$, returning the balanced remainder: the representative of self modulo $2^k$ that is closest to zero.

The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive, so the result may be negative and is returned as the signed type of the same width. This is the same as balanced_mod with modulus $2^k$, when $2^k$ fits in the type.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if the result does not fit in the signed type: if pow is Self::WIDTH and self is $2^{W-1}$, or if pow is greater than Self::WIDTH and self is at least $2^{W-1}$, where $W$ is Self::WIDTH.

Examples

See here.

type Output = isize

Implementors