Trait malachite_base::num::arithmetic::traits::DivRound

pub trait DivRound<RHS = Self> {
    type Output;

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

Divides a number by another number and rounds 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.

Required Associated Types

type Output

Required Methods

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

Implementations on Foreign Types

impl DivRound for i8

fn div_round(self, other: i8, rm: RoundingMode) -> (i8, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = i8

impl DivRound for i16

fn div_round(self, other: i16, rm: RoundingMode) -> (i16, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = i16

impl DivRound for i32

fn div_round(self, other: i32, rm: RoundingMode) -> (i32, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = i32

impl DivRound for i64

fn div_round(self, other: i64, rm: RoundingMode) -> (i64, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = i64

impl DivRound for i128

fn div_round(self, other: i128, rm: RoundingMode) -> (i128, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = i128

impl DivRound for isize

fn div_round(self, other: isize, rm: RoundingMode) -> (isize, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, if self is Self::MIN and other is -1, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = isize

impl DivRound for u8

fn div_round(self, other: u8, rm: RoundingMode) -> (u8, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = u8

impl DivRound for u16

fn div_round(self, other: u16, rm: RoundingMode) -> (u16, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = u16

impl DivRound for u32

fn div_round(self, other: u32, rm: RoundingMode) -> (u32, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = u32

impl DivRound for u64

fn div_round(self, other: u64, rm: RoundingMode) -> (u64, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = u64

impl DivRound for u128

fn div_round(self, other: u128, rm: RoundingMode) -> (u128, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = u128

impl DivRound for usize

fn div_round(self, other: usize, rm: RoundingMode) -> (usize, Ordering)

Divides a value by another value and rounds 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.

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

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

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

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

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

Then

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

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is zero, or if rm is Exact but self is not divisible by other.

Examples

See here.

type Output = usize

Implementors