[−][src]Trait maths_traits::algebra::integer::IntegerSubset

pub trait IntegerSubset: Ord + Eq + Clone + CastPrimInt + ToPrimitive + FromPrimitive + EuclideanSemidomain + Primality + ArchSemiring + ArchimedeanDiv + Sign + Sub<Self, Output = Self> + Div<Self, Output = Self> + Rem<Self, Output = Self> + SubAssign<Self> + DivAssign<Self> + RemAssign<Self> {
    type Signed: Integer + IntegerSubset<Signed = Self::Signed, Unsigned = Self::Unsigned>;
    type Unsigned: Natural + IntegerSubset<Signed = Self::Signed, Unsigned = Self::Unsigned>;
    fn as_signed(self) -> Self::Signed;
    fn as_unsigned(self) -> Self::Unsigned;

    fn abs_unsigned(self) -> Self::Unsigned { ... }
    fn two() -> Self { ... }
    fn mul_two(self) -> Self { ... }
    fn div_two(self) -> Self { ... }
    fn even(&self) -> bool { ... }
    fn odd(&self) -> bool { ... }
}

A subset of the Integers that has all of the major integer operations

This includes:

Basic ring operations
Euclidean division any everything implied by having it
Algebraic ordering properties and archimedian division
Additional operations conventionally implemented on integer types

In practice, this means that a type implementing this trait must be either a representation of the natural numbers or the integers as a whole.

Furthermore, this trait contains associated types referring to an unsigned and signed type of similar precision to make it easier to manage the broader system of types used in integer algorithms

Associated Types

`type Signed: Integer + IntegerSubset<Signed = Self::Signed, Unsigned = Self::Unsigned>`

This type's corresponding signed Integer representation

Implementors should guarantee that this type has the same theoretical bit precision as the Unsigned type

`type Unsigned: Natural + IntegerSubset<Signed = Self::Signed, Unsigned = Self::Unsigned>`

This type's corresponding unsigned Integer representation

Implementors should guarantee that this type has the same theoretical bit precision as the Signed type

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Required methods

`fn as_signed(self) -> Self::Signed`

Converts self to a signed integer representation

Note that this has the same guarantees as the primitive as operation and can thus panic on overflow

`fn as_unsigned(self) -> Self::Unsigned`

Converts self into an unsigned integer representation

Note that this has the same guarantees as the primitive as operation and can thus panic on underflow

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Provided methods

`fn abs_unsigned(self) -> Self::Unsigned`

Takes the absolute value and converts into an unsigned integer representation

Implementors should guarantee that this conversion never fails or panics since the unsigned and signed types are assumed to be of the same theoretical bit precision

`fn two() -> Self`

A shorthand for 1+1

`fn mul_two(self) -> Self`

Multiplies by two

This is meant both as convenience and to expose the << operator for representations that support it. As such, this method has the potential to be faster than normal multiplication

`fn div_two(self) -> Self`

Divides by two

This is meant both as convenience and to expose the >> operator for representations that support it. As such, this method has the potential to be faster than normal division