Trait malachite_base::num::arithmetic::traits::ShrRound

pub trait ShrRound<RHS> {
    type Output;

    // Required method
    fn shr_round(self, other: RHS, rm: RoundingMode) -> (Self::Output, Ordering);
}

Right-shifts a number (divides it by a power of 2), rounding the result according to a specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Rounding might only be necessary if other is positive.

Required Associated Types

type Output

Required Methods

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

Implementations on Foreign Types

impl ShrRound<i8> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i8

impl ShrRound<i8> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i16

impl ShrRound<i8> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i32

impl ShrRound<i8> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i64

impl ShrRound<i8> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i128

impl ShrRound<i8> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = isize

impl ShrRound<i8> for u8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u8

impl ShrRound<i8> for u16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u16

impl ShrRound<i8> for u32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u32

impl ShrRound<i8> for u64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u64

impl ShrRound<i8> for u128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u128

impl ShrRound<i8> for usize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = usize

impl ShrRound<i16> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i8

impl ShrRound<i16> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i16

impl ShrRound<i16> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i32

impl ShrRound<i16> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i64

impl ShrRound<i16> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i128

impl ShrRound<i16> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = isize

impl ShrRound<i16> for u8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u8

impl ShrRound<i16> for u16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u16

impl ShrRound<i16> for u32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u32

impl ShrRound<i16> for u64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u64

impl ShrRound<i16> for u128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u128

impl ShrRound<i16> for usize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = usize

impl ShrRound<i32> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i8

impl ShrRound<i32> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i16

impl ShrRound<i32> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i32

impl ShrRound<i32> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i64

impl ShrRound<i32> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i128

impl ShrRound<i32> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = isize

impl ShrRound<i32> for u8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u8

impl ShrRound<i32> for u16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u16

impl ShrRound<i32> for u32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u32

impl ShrRound<i32> for u64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u64

impl ShrRound<i32> for u128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u128

impl ShrRound<i32> for usize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = usize

impl ShrRound<i64> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i8

impl ShrRound<i64> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i16

impl ShrRound<i64> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i32

impl ShrRound<i64> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i64

impl ShrRound<i64> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i128

impl ShrRound<i64> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = isize

impl ShrRound<i64> for u8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u8

impl ShrRound<i64> for u16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u16

impl ShrRound<i64> for u32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u32

impl ShrRound<i64> for u64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u64

impl ShrRound<i64> for u128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u128

impl ShrRound<i64> for usize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = usize

impl ShrRound<i128> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i8

impl ShrRound<i128> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i16

impl ShrRound<i128> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i32

impl ShrRound<i128> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i64

impl ShrRound<i128> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i128

impl ShrRound<i128> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = isize

impl ShrRound<i128> for u8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u8

impl ShrRound<i128> for u16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u16

impl ShrRound<i128> for u32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u32

impl ShrRound<i128> for u64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u64

impl ShrRound<i128> for u128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u128

impl ShrRound<i128> for usize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = usize

impl ShrRound<isize> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i8

impl ShrRound<isize> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i16

impl ShrRound<isize> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i32

impl ShrRound<isize> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i64

impl ShrRound<isize> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = i128

impl ShrRound<isize> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = isize

impl ShrRound<isize> for u8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u8

impl ShrRound<isize> for u16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u16

impl ShrRound<isize> for u32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u32

impl ShrRound<isize> for u64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u64

impl ShrRound<isize> for u128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = u128

impl ShrRound<isize> for usize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value. If bits is negative, then the returned Ordering is always Equal, even if the higher bits of the result are lost.

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

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = \operatorname{sgn}(q) \lfloor |q| \rfloor.$

$g(x, k, \mathrm{Up}) = \operatorname{sgn}(q) \lceil |q| \rceil.$

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

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

Examples

See here.

type Output = usize

impl ShrRound<u8> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShrRound<u8> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShrRound<u8> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShrRound<u8> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShrRound<u8> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShrRound<u8> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShrRound<u8> for u8

fn shr_round(self, bits: u8, rm: RoundingMode) -> (u8, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShrRound<u8> for u16

fn shr_round(self, bits: u8, rm: RoundingMode) -> (u16, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShrRound<u8> for u32

fn shr_round(self, bits: u8, rm: RoundingMode) -> (u32, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShrRound<u8> for u64

fn shr_round(self, bits: u8, rm: RoundingMode) -> (u64, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShrRound<u8> for u128

fn shr_round(self, bits: u8, rm: RoundingMode) -> (u128, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShrRound<u8> for usize

fn shr_round(self, bits: u8, rm: RoundingMode) -> (usize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShrRound<u16> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShrRound<u16> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShrRound<u16> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShrRound<u16> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShrRound<u16> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShrRound<u16> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShrRound<u16> for u8

fn shr_round(self, bits: u16, rm: RoundingMode) -> (u8, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShrRound<u16> for u16

fn shr_round(self, bits: u16, rm: RoundingMode) -> (u16, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShrRound<u16> for u32

fn shr_round(self, bits: u16, rm: RoundingMode) -> (u32, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShrRound<u16> for u64

fn shr_round(self, bits: u16, rm: RoundingMode) -> (u64, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShrRound<u16> for u128

fn shr_round(self, bits: u16, rm: RoundingMode) -> (u128, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShrRound<u16> for usize

fn shr_round(self, bits: u16, rm: RoundingMode) -> (usize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShrRound<u32> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShrRound<u32> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShrRound<u32> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShrRound<u32> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShrRound<u32> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShrRound<u32> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShrRound<u32> for u8

fn shr_round(self, bits: u32, rm: RoundingMode) -> (u8, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShrRound<u32> for u16

fn shr_round(self, bits: u32, rm: RoundingMode) -> (u16, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShrRound<u32> for u32

fn shr_round(self, bits: u32, rm: RoundingMode) -> (u32, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShrRound<u32> for u64

fn shr_round(self, bits: u32, rm: RoundingMode) -> (u64, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShrRound<u32> for u128

fn shr_round(self, bits: u32, rm: RoundingMode) -> (u128, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShrRound<u32> for usize

fn shr_round(self, bits: u32, rm: RoundingMode) -> (usize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShrRound<u64> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShrRound<u64> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShrRound<u64> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShrRound<u64> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShrRound<u64> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShrRound<u64> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShrRound<u64> for u8

fn shr_round(self, bits: u64, rm: RoundingMode) -> (u8, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShrRound<u64> for u16

fn shr_round(self, bits: u64, rm: RoundingMode) -> (u16, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShrRound<u64> for u32

fn shr_round(self, bits: u64, rm: RoundingMode) -> (u32, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShrRound<u64> for u64

fn shr_round(self, bits: u64, rm: RoundingMode) -> (u64, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShrRound<u64> for u128

fn shr_round(self, bits: u64, rm: RoundingMode) -> (u128, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShrRound<u64> for usize

fn shr_round(self, bits: u64, rm: RoundingMode) -> (usize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShrRound<u128> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShrRound<u128> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShrRound<u128> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShrRound<u128> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShrRound<u128> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShrRound<u128> for isize

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShrRound<u128> for u8

fn shr_round(self, bits: u128, rm: RoundingMode) -> (u8, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShrRound<u128> for u16

fn shr_round(self, bits: u128, rm: RoundingMode) -> (u16, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShrRound<u128> for u32

fn shr_round(self, bits: u128, rm: RoundingMode) -> (u32, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShrRound<u128> for u64

fn shr_round(self, bits: u128, rm: RoundingMode) -> (u64, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShrRound<u128> for u128

fn shr_round(self, bits: u128, rm: RoundingMode) -> (u128, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShrRound<u128> for usize

fn shr_round(self, bits: u128, rm: RoundingMode) -> (usize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

impl ShrRound<usize> for i8

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i8

impl ShrRound<usize> for i16

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i16

impl ShrRound<usize> for i32

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i32

impl ShrRound<usize> for i64

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i64

impl ShrRound<usize> for i128

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

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

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

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

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

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

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = i128

impl ShrRound<usize> for isize

fn shr_round(self, bits: usize, rm: RoundingMode) -> (isize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = isize

impl ShrRound<usize> for u8

fn shr_round(self, bits: usize, rm: RoundingMode) -> (u8, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u8

impl ShrRound<usize> for u16

fn shr_round(self, bits: usize, rm: RoundingMode) -> (u16, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u16

impl ShrRound<usize> for u32

fn shr_round(self, bits: usize, rm: RoundingMode) -> (u32, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u32

impl ShrRound<usize> for u64

fn shr_round(self, bits: usize, rm: RoundingMode) -> (u64, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u64

impl ShrRound<usize> for u128

fn shr_round(self, bits: usize, rm: RoundingMode) -> (u128, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = u128

impl ShrRound<usize> for usize

fn shr_round(self, bits: usize, rm: RoundingMode) -> (usize, Ordering)

Shifts a number right (divides it by a power of 2) and rounds according to the specified rounding mode. An Ordering is also returned, indicating whether the returned value is less than, equal to, or greater than the exact value.

Passing Floor or Down is equivalent to using >>. To test whether Exact can be passed, use self.divisible_by_power_of_2(bits).

Let $q = \frac{x}{2^k}$, and let $g$ be the function that just returns the first element of the pair, without the Ordering:

$g(x, k, \mathrm{Down}) = g(x, y, \mathrm{Floor}) = \lfloor q \rfloor.$

$g(x, k, \mathrm{Up}) = g(x, y, \mathrm{Ceiling}) = \lceil q \rceil.$

$$ g(x, k, \mathrm{Nearest}) = \begin{cases} \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor < \frac{1}{2}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor > \frac{1}{2}, \\ \lfloor q \rfloor & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is even}, \\ \lceil q \rceil & \text{if} \quad q - \lfloor q \rfloor = \frac{1}{2} \ \text{and} \ \lfloor q \rfloor \ \text{is odd}. \end{cases} $$

$g(x, k, \mathrm{Exact}) = q$, but panics if $q \notin \N$.

Then

$f(x, k, r) = (g(x, k, r), \operatorname{cmp}(g(x, k, r), q))$.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if rm is Exact but self is not divisible by $2^b$.

Examples

See here.

type Output = usize

Implementors