Trait malachite_base::num::arithmetic::traits::DivRem

pub trait DivRem<RHS = Self> {
    type DivOutput;
    type RemOutput;

    // Required method
    fn div_rem(self, other: RHS) -> (Self::DivOutput, Self::RemOutput);
}

Divides two numbers, returning the quotient and remainder. The quotient is rounded towards zero, and the remainder has the same sign as the dividend (first input).

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

Required Associated Types

type DivOutput

type RemOutput

Required Methods

fn div_rem(self, other: RHS) -> (Self::DivOutput, Self::RemOutput)

Implementations on Foreign Types

impl DivRem for i8

fn div_rem(self, other: i8) -> (i8, i8)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero and the remainder has the same sign as the dividend.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

$$ f(x, y) = \left ( \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor, \space x - y \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor \right ). $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0, or if self is $t::MIN and other is -1.

Examples

See here.

type DivOutput = i8

type RemOutput = i8

impl DivRem for i16

fn div_rem(self, other: i16) -> (i16, i16)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero and the remainder has the same sign as the dividend.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

$$ f(x, y) = \left ( \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor, \space x - y \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor \right ). $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0, or if self is $t::MIN and other is -1.

Examples

See here.

type DivOutput = i16

type RemOutput = i16

impl DivRem for i32

fn div_rem(self, other: i32) -> (i32, i32)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero and the remainder has the same sign as the dividend.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

$$ f(x, y) = \left ( \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor, \space x - y \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor \right ). $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0, or if self is $t::MIN and other is -1.

Examples

See here.

type DivOutput = i32

type RemOutput = i32

impl DivRem for i64

fn div_rem(self, other: i64) -> (i64, i64)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero and the remainder has the same sign as the dividend.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

$$ f(x, y) = \left ( \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor, \space x - y \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor \right ). $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0, or if self is $t::MIN and other is -1.

Examples

See here.

type DivOutput = i64

type RemOutput = i64

impl DivRem for i128

fn div_rem(self, other: i128) -> (i128, i128)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero and the remainder has the same sign as the dividend.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

$$ f(x, y) = \left ( \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor, \space x - y \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor \right ). $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0, or if self is $t::MIN and other is -1.

Examples

See here.

type DivOutput = i128

type RemOutput = i128

impl DivRem for isize

fn div_rem(self, other: isize) -> (isize, isize)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero and the remainder has the same sign as the dividend.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq |r| < |y|$.

$$ f(x, y) = \left ( \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor, \space x - y \operatorname{sgn}(xy) \left \lfloor \left | \frac{x}{y} \right | \right \rfloor \right ). $$

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0, or if self is $t::MIN and other is -1.

Examples

See here.

type DivOutput = isize

type RemOutput = isize

impl DivRem for u8

fn div_rem(self, other: u8) -> (u8, u8)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq r < y$.

$$ f(x, y) = \left ( \left \lfloor \frac{x}{y} \right \rfloor, \space x - y\left \lfloor \frac{x}{y} \right \rfloor \right ). $$

For unsigned integers, div_rem is equivalent to div_mod.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0.

Examples

See here.

type DivOutput = u8

type RemOutput = u8

impl DivRem for u16

fn div_rem(self, other: u16) -> (u16, u16)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq r < y$.

$$ f(x, y) = \left ( \left \lfloor \frac{x}{y} \right \rfloor, \space x - y\left \lfloor \frac{x}{y} \right \rfloor \right ). $$

For unsigned integers, div_rem is equivalent to div_mod.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0.

Examples

See here.

type DivOutput = u16

type RemOutput = u16

impl DivRem for u32

fn div_rem(self, other: u32) -> (u32, u32)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq r < y$.

$$ f(x, y) = \left ( \left \lfloor \frac{x}{y} \right \rfloor, \space x - y\left \lfloor \frac{x}{y} \right \rfloor \right ). $$

For unsigned integers, div_rem is equivalent to div_mod.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0.

Examples

See here.

type DivOutput = u32

type RemOutput = u32

impl DivRem for u64

fn div_rem(self, other: u64) -> (u64, u64)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq r < y$.

$$ f(x, y) = \left ( \left \lfloor \frac{x}{y} \right \rfloor, \space x - y\left \lfloor \frac{x}{y} \right \rfloor \right ). $$

For unsigned integers, div_rem is equivalent to div_mod.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0.

Examples

See here.

type DivOutput = u64

type RemOutput = u64

impl DivRem for u128

fn div_rem(self, other: u128) -> (u128, u128)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq r < y$.

$$ f(x, y) = \left ( \left \lfloor \frac{x}{y} \right \rfloor, \space x - y\left \lfloor \frac{x}{y} \right \rfloor \right ). $$

For unsigned integers, div_rem is equivalent to div_mod.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0.

Examples

See here.

type DivOutput = u128

type RemOutput = u128

impl DivRem for usize

fn div_rem(self, other: usize) -> (usize, usize)

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards zero.

The quotient and remainder satisfy $x = qy + r$ and $0 \leq r < y$.

$$ f(x, y) = \left ( \left \lfloor \frac{x}{y} \right \rfloor, \space x - y\left \lfloor \frac{x}{y} \right \rfloor \right ). $$

For unsigned integers, div_rem is equivalent to div_mod.

Worst-case complexity

Constant time and additional memory.

Panics

Panics if other is 0.

Examples

See here.

type DivOutput = usize

type RemOutput = usize

Implementors