Trait malachite_base::num::arithmetic::traits::CheckedSubMul

pub trait CheckedSubMul<Y = Self, Z = Self> {
    type Output;

    // Required method
    fn checked_sub_mul(self, y: Y, z: Z) -> Option<Self::Output>;
}

Subtracts a number by the product of two other numbers, returning None if the result is not representable.

Required Associated Types

type Output

Required Methods

fn checked_sub_mul(self, y: Y, z: Z) -> Option<Self::Output>

Implementations on Foreign Types

impl CheckedSubMul for i8

fn checked_sub_mul(self, y: i8, z: i8) -> Option<i8>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad -2^{W-1} \leq x - yz < 2^{W-1}, \\ \operatorname{None} & \text{if} \quad x - yz < -2^{W-1} \ \mathrm{or} \ xy - z \geq 2^{W-1}, \\ \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = i8

impl CheckedSubMul for i16

fn checked_sub_mul(self, y: i16, z: i16) -> Option<i16>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad -2^{W-1} \leq x - yz < 2^{W-1}, \\ \operatorname{None} & \text{if} \quad x - yz < -2^{W-1} \ \mathrm{or} \ xy - z \geq 2^{W-1}, \\ \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = i16

impl CheckedSubMul for i32

fn checked_sub_mul(self, y: i32, z: i32) -> Option<i32>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad -2^{W-1} \leq x - yz < 2^{W-1}, \\ \operatorname{None} & \text{if} \quad x - yz < -2^{W-1} \ \mathrm{or} \ xy - z \geq 2^{W-1}, \\ \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = i32

impl CheckedSubMul for i64

fn checked_sub_mul(self, y: i64, z: i64) -> Option<i64>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad -2^{W-1} \leq x - yz < 2^{W-1}, \\ \operatorname{None} & \text{if} \quad x - yz < -2^{W-1} \ \mathrm{or} \ xy - z \geq 2^{W-1}, \\ \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = i64

impl CheckedSubMul for i128

fn checked_sub_mul(self, y: i128, z: i128) -> Option<i128>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad -2^{W-1} \leq x - yz < 2^{W-1}, \\ \operatorname{None} & \text{if} \quad x - yz < -2^{W-1} \ \mathrm{or} \ xy - z \geq 2^{W-1}, \\ \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = i128

impl CheckedSubMul for isize

fn checked_sub_mul(self, y: isize, z: isize) -> Option<isize>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad -2^{W-1} \leq x - yz < 2^{W-1}, \\ \operatorname{None} & \text{if} \quad x - yz < -2^{W-1} \ \mathrm{or} \ xy - z \geq 2^{W-1}, \\ \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = isize

impl CheckedSubMul for u8

fn checked_sub_mul(self, y: u8, z: u8) -> Option<u8>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad x \geq yz, \\ \operatorname{None} & \text{if} \quad x < yz, \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = u8

impl CheckedSubMul for u16

fn checked_sub_mul(self, y: u16, z: u16) -> Option<u16>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad x \geq yz, \\ \operatorname{None} & \text{if} \quad x < yz, \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = u16

impl CheckedSubMul for u32

fn checked_sub_mul(self, y: u32, z: u32) -> Option<u32>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad x \geq yz, \\ \operatorname{None} & \text{if} \quad x < yz, \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = u32

impl CheckedSubMul for u64

fn checked_sub_mul(self, y: u64, z: u64) -> Option<u64>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad x \geq yz, \\ \operatorname{None} & \text{if} \quad x < yz, \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = u64

impl CheckedSubMul for u128

fn checked_sub_mul(self, y: u128, z: u128) -> Option<u128>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad x \geq yz, \\ \operatorname{None} & \text{if} \quad x < yz, \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = u128

impl CheckedSubMul for usize

fn checked_sub_mul(self, y: usize, z: usize) -> Option<usize>

Subtracts a number by the product of two other numbers, returning None if the result cannot be represented.

$$ f(x, y, z) = \begin{cases} \operatorname{Some}(x - yz) & \text{if} \quad x \geq yz, \\ \operatorname{None} & \text{if} \quad x < yz, \end{cases} $$ where $W$ is Self::WIDTH.

Worst-case complexity

Constant time and additional memory.

Examples

See here.

type Output = usize

Implementors