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§
sourcefn div_euclid(&self, v: &Self) -> Self
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 * 2sourcefn rem_euclid(&self, v: &Self) -> Self
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§
sourcefn div_rem_euclid(&self, v: &Self) -> (Self, Self)
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));