Trait malachite_base::num::arithmetic::traits::ShlRound

pub trait ShlRound<RHS> {
    type Output;

    fn shl_round(self, other: RHS, rm: RoundingMode) -> Self::Output;
}

Left-shifts a number (multiplies it by a power of 2), rounding the result according to a specified rounding mode.

Rounding might only be necessary if other is negative.

Required Associated Types

type Output

Required Methods

fn shl_round(self, other: RHS, rm: RoundingMode) -> Self::Output

Implementations on Foreign Types

impl ShlRound<i8> for u8

fn shl_round(self, bits: i8, rm: RoundingMode) -> u8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShlRound<i16> for u8

fn shl_round(self, bits: i16, rm: RoundingMode) -> u8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShlRound<i32> for u8

fn shl_round(self, bits: i32, rm: RoundingMode) -> u8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShlRound<i64> for u8

fn shl_round(self, bits: i64, rm: RoundingMode) -> u8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShlRound<i128> for u8

fn shl_round(self, bits: i128, rm: RoundingMode) -> u8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShlRound<isize> for u8

fn shl_round(self, bits: isize, rm: RoundingMode) -> u8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShlRound<i8> for u16

fn shl_round(self, bits: i8, rm: RoundingMode) -> u16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShlRound<i16> for u16

fn shl_round(self, bits: i16, rm: RoundingMode) -> u16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShlRound<i32> for u16

fn shl_round(self, bits: i32, rm: RoundingMode) -> u16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShlRound<i64> for u16

fn shl_round(self, bits: i64, rm: RoundingMode) -> u16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShlRound<i128> for u16

fn shl_round(self, bits: i128, rm: RoundingMode) -> u16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShlRound<isize> for u16

fn shl_round(self, bits: isize, rm: RoundingMode) -> u16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShlRound<i8> for u32

fn shl_round(self, bits: i8, rm: RoundingMode) -> u32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShlRound<i16> for u32

fn shl_round(self, bits: i16, rm: RoundingMode) -> u32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShlRound<i32> for u32

fn shl_round(self, bits: i32, rm: RoundingMode) -> u32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShlRound<i64> for u32

fn shl_round(self, bits: i64, rm: RoundingMode) -> u32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShlRound<i128> for u32

fn shl_round(self, bits: i128, rm: RoundingMode) -> u32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShlRound<isize> for u32

fn shl_round(self, bits: isize, rm: RoundingMode) -> u32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShlRound<i8> for u64

fn shl_round(self, bits: i8, rm: RoundingMode) -> u64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShlRound<i16> for u64

fn shl_round(self, bits: i16, rm: RoundingMode) -> u64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShlRound<i32> for u64

fn shl_round(self, bits: i32, rm: RoundingMode) -> u64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShlRound<i64> for u64

fn shl_round(self, bits: i64, rm: RoundingMode) -> u64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShlRound<i128> for u64

fn shl_round(self, bits: i128, rm: RoundingMode) -> u64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShlRound<isize> for u64

fn shl_round(self, bits: isize, rm: RoundingMode) -> u64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShlRound<i8> for u128

fn shl_round(self, bits: i8, rm: RoundingMode) -> u128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShlRound<i16> for u128

fn shl_round(self, bits: i16, rm: RoundingMode) -> u128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShlRound<i32> for u128

fn shl_round(self, bits: i32, rm: RoundingMode) -> u128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShlRound<i64> for u128

fn shl_round(self, bits: i64, rm: RoundingMode) -> u128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShlRound<i128> for u128

fn shl_round(self, bits: i128, rm: RoundingMode) -> u128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShlRound<isize> for u128

fn shl_round(self, bits: isize, rm: RoundingMode) -> u128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShlRound<i8> for usize

fn shl_round(self, bits: i8, rm: RoundingMode) -> usize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShlRound<i16> for usize

fn shl_round(self, bits: i16, rm: RoundingMode) -> usize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShlRound<i32> for usize

fn shl_round(self, bits: i32, rm: RoundingMode) -> usize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShlRound<i64> for usize

fn shl_round(self, bits: i64, rm: RoundingMode) -> usize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShlRound<i128> for usize

fn shl_round(self, bits: i128, rm: RoundingMode) -> usize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShlRound<isize> for usize

fn shl_round(self, bits: isize, rm: RoundingMode) -> usize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShlRound<i8> for i8

fn shl_round(self, bits: i8, rm: RoundingMode) -> i8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShlRound<i16> for i8

fn shl_round(self, bits: i16, rm: RoundingMode) -> i8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShlRound<i32> for i8

fn shl_round(self, bits: i32, rm: RoundingMode) -> i8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShlRound<i64> for i8

fn shl_round(self, bits: i64, rm: RoundingMode) -> i8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShlRound<i128> for i8

fn shl_round(self, bits: i128, rm: RoundingMode) -> i8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShlRound<isize> for i8

fn shl_round(self, bits: isize, rm: RoundingMode) -> i8

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShlRound<i8> for i16

fn shl_round(self, bits: i8, rm: RoundingMode) -> i16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShlRound<i16> for i16

fn shl_round(self, bits: i16, rm: RoundingMode) -> i16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShlRound<i32> for i16

fn shl_round(self, bits: i32, rm: RoundingMode) -> i16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShlRound<i64> for i16

fn shl_round(self, bits: i64, rm: RoundingMode) -> i16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShlRound<i128> for i16

fn shl_round(self, bits: i128, rm: RoundingMode) -> i16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShlRound<isize> for i16

fn shl_round(self, bits: isize, rm: RoundingMode) -> i16

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShlRound<i8> for i32

fn shl_round(self, bits: i8, rm: RoundingMode) -> i32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShlRound<i16> for i32

fn shl_round(self, bits: i16, rm: RoundingMode) -> i32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShlRound<i32> for i32

fn shl_round(self, bits: i32, rm: RoundingMode) -> i32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShlRound<i64> for i32

fn shl_round(self, bits: i64, rm: RoundingMode) -> i32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShlRound<i128> for i32

fn shl_round(self, bits: i128, rm: RoundingMode) -> i32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShlRound<isize> for i32

fn shl_round(self, bits: isize, rm: RoundingMode) -> i32

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShlRound<i8> for i64

fn shl_round(self, bits: i8, rm: RoundingMode) -> i64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShlRound<i16> for i64

fn shl_round(self, bits: i16, rm: RoundingMode) -> i64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShlRound<i32> for i64

fn shl_round(self, bits: i32, rm: RoundingMode) -> i64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShlRound<i64> for i64

fn shl_round(self, bits: i64, rm: RoundingMode) -> i64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShlRound<i128> for i64

fn shl_round(self, bits: i128, rm: RoundingMode) -> i64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShlRound<isize> for i64

fn shl_round(self, bits: isize, rm: RoundingMode) -> i64

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShlRound<i8> for i128

fn shl_round(self, bits: i8, rm: RoundingMode) -> i128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShlRound<i16> for i128

fn shl_round(self, bits: i16, rm: RoundingMode) -> i128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShlRound<i32> for i128

fn shl_round(self, bits: i32, rm: RoundingMode) -> i128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShlRound<i64> for i128

fn shl_round(self, bits: i64, rm: RoundingMode) -> i128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShlRound<i128> for i128

fn shl_round(self, bits: i128, rm: RoundingMode) -> i128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShlRound<isize> for i128

fn shl_round(self, bits: isize, rm: RoundingMode) -> i128

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShlRound<i8> for isize

fn shl_round(self, bits: i8, rm: RoundingMode) -> isize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShlRound<i16> for isize

fn shl_round(self, bits: i16, rm: RoundingMode) -> isize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShlRound<i32> for isize

fn shl_round(self, bits: i32, rm: RoundingMode) -> isize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShlRound<i64> for isize

fn shl_round(self, bits: i64, rm: RoundingMode) -> isize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShlRound<i128> for isize

fn shl_round(self, bits: i128, rm: RoundingMode) -> isize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShlRound<isize> for isize

fn shl_round(self, bits: isize, rm: RoundingMode) -> isize

Left-shifts a number (multiplies it by a power of 2 or divides it by a power of 2 and takes the floor) and rounds according to the specified rounding mode.

Passing RoundingMode::Floor or RoundingMode::Down is equivalent to using >>. To test whether RoundingMode::Exact can be passed, use bits > 0 || self.divisible_by_power_of_2(bits). Rounding might only be necessary if bits is negative.

Let $q = x2^k$:

$f(x, k, \mathrm{Down}) = f(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$f(x, k, \mathrm{Up}) = f(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ f(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$f(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if bits is positive and rm is RoundingMode::Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

Implementors