Trait malachite_base::num::arithmetic::traits::CeilingDivMod

pub trait CeilingDivMod<RHS = Self> {
    type DivOutput;
    type ModOutput;

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the divisor (second input).

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

Required Associated Types

type DivOutput

type ModOutput

Required Methods

fn ceiling_div_mod(self, other: RHS) -> (Self::DivOutput, Self::ModOutput)

Implementations on Foreign Types

impl CeilingDivMod for i8

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the second number.

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

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

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 ModOutput = i8

impl CeilingDivMod for i16

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the second number.

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

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

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 ModOutput = i16

impl CeilingDivMod for i32

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the second number.

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

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

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 ModOutput = i32

impl CeilingDivMod for i64

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the second number.

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

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

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 ModOutput = i64

impl CeilingDivMod for i128

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the second number.

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

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

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 ModOutput = i128

impl CeilingDivMod for isize

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

Divides a number by another number, returning the quotient and remainder. The quotient is rounded towards positive infinity and the remainder has the opposite sign as the second number.

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

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

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 ModOutput = isize

Implementors