Trait Euclid

pub trait Euclid: Sized + Div<Self, Output = Self> + Rem<Self, Output = 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

# use num_traits::Euclid;
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));

Implementors