Trait Euclid 

pub trait Euclid:
    Sized
    + Div<Self, Output = Self>
    + Rem<Self, Output = Self> {
    // Required methods
    fn div_euclid(&self, v: &Self) -> Self;
    fn rem_euclid(&self, v: &Self) -> Self;

    // Provided method
    fn div_rem_euclid(&self, v: &Self) -> (Self, Self) { ... }
}

Required Methods

fn div_euclid(&self, v: &Self) -> Self

Calculates Euclidean division, the matching method for rem_euclid.

This computes the integer n such that self = n * v + self.rem_euclid(v). In other words, the result is self / v rounded to the integer n such that self >= n * v.

Examples

use num_traits::Euclid;

let a: i32 = 7;
let b: i32 = 4;
assert_eq!(Euclid::div_euclid(&a, &b), 1); // 7 > 4 * 1
assert_eq!(Euclid::div_euclid(&-a, &b), -2); // -7 >= 4 * -2
assert_eq!(Euclid::div_euclid(&a, &-b), -1); // 7 >= -4 * -1
assert_eq!(Euclid::div_euclid(&-a, &-b), 2); // -7 >= -4 * 2

fn rem_euclid(&self, v: &Self) -> Self

Calculates the least nonnegative remainder of self (mod v).

In particular, the return value r satisfies 0.0 <= r < v.abs() in most cases. However, due to a floating point round-off error it can result in r == v.abs(), violating the mathematical definition, if self is much smaller than v.abs() in magnitude and self < 0.0. This result is not an element of the function’s codomain, but it is the closest floating point number in the real numbers and thus fulfills the property self == self.div_euclid(v) * v + self.rem_euclid(v) approximatively.

Examples

use num_traits::Euclid;

let a: i32 = 7;
let b: i32 = 4;
assert_eq!(Euclid::rem_euclid(&a, &b), 3);
assert_eq!(Euclid::rem_euclid(&-a, &b), 1);
assert_eq!(Euclid::rem_euclid(&a, &-b), 3);
assert_eq!(Euclid::rem_euclid(&-a, &-b), 1);

Provided Methods

fn div_rem_euclid(&self, v: &Self) -> (Self, Self)

Returns both the quotient and remainder from Euclidean division.

By default, it internally calls both Euclid::div_euclid and Euclid::rem_euclid, but it can be overridden in order to implement some optimization.

Examples

let x = 5u8;
let y = 3u8;

let div = Euclid::div_euclid(&x, &y);
let rem = Euclid::rem_euclid(&x, &y);

assert_eq!((div, rem), Euclid::div_rem_euclid(&x, &y));

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl Euclid for f32

Available on non-crate feature std only.

fn div_euclid(&self, v: &f32) -> f32

fn rem_euclid(&self, v: &f32) -> f32

impl Euclid for f64

Available on non-crate feature std only.

fn div_euclid(&self, v: &f64) -> f64

fn rem_euclid(&self, v: &f64) -> f64

impl Euclid for i8

fn div_euclid(&self, v: &i8) -> Self

fn rem_euclid(&self, v: &i8) -> Self

impl Euclid for i16

fn div_euclid(&self, v: &i16) -> Self

fn rem_euclid(&self, v: &i16) -> Self

impl Euclid for i32

fn div_euclid(&self, v: &i32) -> Self

fn rem_euclid(&self, v: &i32) -> Self

impl Euclid for i64

fn div_euclid(&self, v: &i64) -> Self

fn rem_euclid(&self, v: &i64) -> Self

impl Euclid for i128

fn div_euclid(&self, v: &i128) -> Self

fn rem_euclid(&self, v: &i128) -> Self

impl Euclid for isize

fn div_euclid(&self, v: &isize) -> Self

fn rem_euclid(&self, v: &isize) -> Self

impl Euclid for u8

fn div_euclid(&self, v: &u8) -> Self

fn rem_euclid(&self, v: &u8) -> Self

impl Euclid for u16

fn div_euclid(&self, v: &u16) -> Self

fn rem_euclid(&self, v: &u16) -> Self

impl Euclid for u32

fn div_euclid(&self, v: &u32) -> Self

fn rem_euclid(&self, v: &u32) -> Self

impl Euclid for u64

fn div_euclid(&self, v: &u64) -> Self

fn rem_euclid(&self, v: &u64) -> Self

impl Euclid for u128

fn div_euclid(&self, v: &u128) -> Self

fn rem_euclid(&self, v: &u128) -> Self

impl Euclid for usize

fn div_euclid(&self, v: &usize) -> Self

fn rem_euclid(&self, v: &usize) -> Self

Implementors