Struct typenum::int::NInt

pub struct NInt<U: Unsigned + NonZero> { /* fields omitted */ }

Type-level signed integers with negative sign.

Methods

impl<U: Unsigned + NonZero> NInt<U>

pub fn new() -> NInt<U>

Instantiates a singleton representing this strictly negative integer.

Trait Implementations

impl<U: Unsigned + NonZero> NonZero for NInt<U>

impl<U: Unsigned + NonZero> Integer for NInt<U>

const I8: i8

const I16: i16

const I32: i32

const I64: i64

const ISIZE: isize

fn to_i8() -> i8

fn to_i16() -> i16

fn to_i32() -> i32

fn to_i64() -> i64

fn to_isize() -> isize

impl<U: Unsigned + NonZero> Abs for NInt<U>

type Output = PInt<U>

The absolute value.

impl<U: Unsigned + NonZero> Pow<NInt<U>> for Z0

0^N = 0

type Output = Z0

The result of the exponentiation.

fn powi(self, _: NInt<U>) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<U: Unsigned + NonZero> Pow<NInt<U>> for P1

1^N = 1

type Output = P1

The result of the exponentiation.

fn powi(self, _: NInt<U>) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<U: Unsigned> Pow<NInt<UInt<U, B0>>> for N1

(-1)^N = 1 if N is even

type Output = P1

The result of the exponentiation.

fn powi(self, _: NInt<UInt<U, B0>>) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<U: Unsigned> Pow<NInt<UInt<U, B1>>> for N1

(-1)^N = -1 if N is odd

type Output = N1

The result of the exponentiation.

fn powi(self, _: NInt<UInt<U, B1>>) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<U: Unsigned + NonZero> Pow<Z0> for NInt<U>

N^0 = 1

type Output = P1

The result of the exponentiation.

fn powi(self, _: Z0) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<Ul: Unsigned + NonZero, Ur: Unsigned> Pow<PInt<UInt<Ur, B0>>> for NInt<Ul> where     Ul: Pow<UInt<Ur, B0>>,     <Ul as Pow<UInt<Ur, B0>>>::Output: Unsigned + NonZero,

N(Ul)^P(Ur) = P(Ul^Ur) if Ur is even

type Output = PInt<<Ul as Pow<UInt<Ur, B0>>>::Output>

The result of the exponentiation.

fn powi(self, _: PInt<UInt<Ur, B0>>) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<Ul: Unsigned + NonZero, Ur: Unsigned> Pow<PInt<UInt<Ur, B1>>> for NInt<Ul> where     Ul: Pow<UInt<Ur, B1>>,     <Ul as Pow<UInt<Ur, B1>>>::Output: Unsigned + NonZero,

N(Ul)^P(Ur) = N(Ul^Ur) if Ur is odd

type Output = NInt<<Ul as Pow<UInt<Ur, B1>>>::Output>

The result of the exponentiation.

fn powi(self, _: PInt<UInt<Ur, B1>>) -> Self::Output

This function isn't used in this crate, but may be useful for others. It is implemented for primitives.

impl<U: Unsigned + NonZero> Cmp<NInt<U>> for Z0

0 > -X

type Output = Greater

The result of the comparison. It should only ever be one of Greater, Less, or Equal.

fn compare<IM: InternalMarker>(&self, _: &NInt<U>) -> Self::Output

impl<U: Unsigned + NonZero> Cmp<Z0> for NInt<U>

-X < 0

type Output = Less

The result of the comparison. It should only ever be one of Greater, Less, or Equal.

fn compare<IM: InternalMarker>(&self, _: &Z0) -> Self::Output

impl<P: Unsigned + NonZero, N: Unsigned + NonZero> Cmp<PInt<P>> for NInt<N>

-X < Y

type Output = Less

The result of the comparison. It should only ever be one of Greater, Less, or Equal.

fn compare<IM: InternalMarker>(&self, _: &PInt<P>) -> Self::Output

impl<P: Unsigned + NonZero, N: Unsigned + NonZero> Cmp<NInt<N>> for PInt<P>

X > - Y

type Output = Greater

The result of the comparison. It should only ever be one of Greater, Less, or Equal.

fn compare<IM: InternalMarker>(&self, _: &NInt<N>) -> Self::Output

impl<Nl: Unsigned + NonZero, Nr: Cmp<Nl> + Unsigned + NonZero> Cmp<NInt<Nr>> for NInt<Nl>

-X <==> -Y

type Output = <Nr as Cmp<Nl>>::Output

The result of the comparison. It should only ever be one of Greater, Less, or Equal.

fn compare<IM: InternalMarker>(&self, rhs: &NInt<Nr>) -> Self::Output

impl<U> Min<NInt<U>> for Z0 where     U: Unsigned + NonZero,

type Output = NInt<U>

The type of the minimum of Self and Rhs

fn min(self, rhs: NInt<U>) -> Self::Output

Method returning the minimum

impl<U> Min<Z0> for NInt<U> where     U: Unsigned + NonZero,

type Output = NInt<U>

The type of the minimum of Self and Rhs

fn min(self, _: Z0) -> Self::Output

Method returning the minimum

impl<Ul, Ur> Min<PInt<Ur>> for NInt<Ul> where     Ul: Unsigned + NonZero,     Ur: Unsigned + NonZero,

type Output = NInt<Ul>

The type of the minimum of Self and Rhs

fn min(self, _: PInt<Ur>) -> Self::Output

Method returning the minimum

impl<Ul, Ur> Min<NInt<Ur>> for PInt<Ul> where     Ul: Unsigned + NonZero,     Ur: Unsigned + NonZero,

type Output = NInt<Ur>

The type of the minimum of Self and Rhs

fn min(self, rhs: NInt<Ur>) -> Self::Output

Method returning the minimum

impl<Ul, Ur> Min<NInt<Ur>> for NInt<Ul> where     Ul: Unsigned + NonZero + Max<Ur>,     Ur: Unsigned + NonZero,     Maximum<Ul, Ur>: Unsigned + NonZero,

type Output = NInt<Maximum<Ul, Ur>>

The type of the minimum of Self and Rhs

fn min(self, rhs: NInt<Ur>) -> Self::Output

Method returning the minimum

impl<U> Max<NInt<U>> for Z0 where     U: Unsigned + NonZero,

type Output = Z0

The type of the maximum of Self and Rhs

fn max(self, _: NInt<U>) -> Self::Output

Method returning the maximum

impl<U> Max<Z0> for NInt<U> where     U: Unsigned + NonZero,

type Output = Z0

The type of the maximum of Self and Rhs

fn max(self, rhs: Z0) -> Self::Output

Method returning the maximum

impl<Ul, Ur> Max<PInt<Ur>> for NInt<Ul> where     Ul: Unsigned + NonZero,     Ur: Unsigned + NonZero,

type Output = PInt<Ur>

The type of the maximum of Self and Rhs

fn max(self, rhs: PInt<Ur>) -> Self::Output

Method returning the maximum

impl<Ul, Ur> Max<NInt<Ur>> for PInt<Ul> where     Ul: Unsigned + NonZero,     Ur: Unsigned + NonZero,

type Output = PInt<Ul>

The type of the maximum of Self and Rhs

fn max(self, _: NInt<Ur>) -> Self::Output

Method returning the maximum

impl<Ul, Ur> Max<NInt<Ur>> for NInt<Ul> where     Ul: Unsigned + NonZero + Min<Ur>,     Ur: Unsigned + NonZero,     Minimum<Ul, Ur>: Unsigned + NonZero,

type Output = NInt<Minimum<Ul, Ur>>

The type of the maximum of Self and Rhs

fn max(self, rhs: NInt<Ur>) -> Self::Output

Method returning the maximum

impl<U> Gcd<NInt<U>> for Z0 where     U: Unsigned + NonZero,

type Output = PInt<U>

The greatest common divisor.

impl<U> Gcd<Z0> for NInt<U> where     U: Unsigned + NonZero,

type Output = PInt<U>

The greatest common divisor.

impl<U1, U2> Gcd<PInt<U2>> for NInt<U1> where     U1: Unsigned + NonZero + Gcd<U2>,     U2: Unsigned + NonZero,     Gcf<U1, U2>: Unsigned + NonZero,

type Output = PInt<Gcf<U1, U2>>

The greatest common divisor.

impl<U1, U2> Gcd<NInt<U2>> for PInt<U1> where     U1: Unsigned + NonZero + Gcd<U2>,     U2: Unsigned + NonZero,     Gcf<U1, U2>: Unsigned + NonZero,

type Output = PInt<Gcf<U1, U2>>

The greatest common divisor.

impl<U1, U2> Gcd<NInt<U2>> for NInt<U1> where     U1: Unsigned + NonZero + Gcd<U2>,     U2: Unsigned + NonZero,     Gcf<U1, U2>: Unsigned + NonZero,

type Output = PInt<Gcf<U1, U2>>

The greatest common divisor.

impl<U: Debug + Unsigned + NonZero> Debug for NInt<U>

fn fmt(&self, f: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<U: PartialEq + Unsigned + NonZero> PartialEq<NInt<U>> for NInt<U>

fn eq(&self, other: &NInt<U>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &NInt<U>) -> bool

This method tests for !=.

impl<U: Eq + Unsigned + NonZero> Eq for NInt<U>

impl<U: Ord + Unsigned + NonZero> Ord for NInt<U>

fn cmp(&self, other: &NInt<U>) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

impl<U: PartialOrd + Unsigned + NonZero> PartialOrd<NInt<U>> for NInt<U>

fn partial_cmp(&self, other: &NInt<U>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &NInt<U>) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &NInt<U>) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &NInt<U>) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &NInt<U>) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<U: Unsigned + NonZero> Add<Z0> for NInt<U>

NInt + Z0 = NInt

type Output = NInt<U>

The resulting type after applying the + operator.

fn add(self, _: Z0) -> Self::Output

Performs the + operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<NInt<Ur>> for NInt<Ul> where     Ul: Add<Ur>,     <Ul as Add<Ur>>::Output: Unsigned + NonZero,

N(Ul) + N(Ur) = N(Ul + Ur)

type Output = NInt<<Ul as Add<Ur>>::Output>

The resulting type after applying the + operator.

fn add(self, _: NInt<Ur>) -> Self::Output

Performs the + operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<NInt<Ur>> for PInt<Ul> where     Ul: Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>,

P(Ul) + N(Ur): We resolve this with our PrivateAdd

type Output = <Ul as PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: NInt<Ur>) -> Self::Output

Performs the + operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<PInt<Ur>> for NInt<Ul> where     Ur: Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,

N(Ul) + P(Ur): We resolve this with our PrivateAdd

type Output = <Ur as PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>>::Output

The resulting type after applying the + operator.

fn add(self, rhs: PInt<Ur>) -> Self::Output

Performs the + operation.

impl<U: Unsigned + NonZero> Sub<NInt<U>> for Z0

Z0 - N = P

type Output = PInt<U>

The resulting type after applying the - operator.

fn sub(self, _: NInt<U>) -> Self::Output

Performs the - operation.

impl<U: Unsigned + NonZero> Sub<Z0> for NInt<U>

NInt - Z0 = NInt

type Output = NInt<U>

The resulting type after applying the - operator.

fn sub(self, _: Z0) -> Self::Output

Performs the - operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<NInt<Ur>> for PInt<Ul> where     Ul: Add<Ur>,     <Ul as Add<Ur>>::Output: Unsigned + NonZero,

P(Ul) - N(Ur) = P(Ul + Ur)

type Output = PInt<<Ul as Add<Ur>>::Output>

The resulting type after applying the - operator.

fn sub(self, _: NInt<Ur>) -> Self::Output

Performs the - operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<PInt<Ur>> for NInt<Ul> where     Ul: Add<Ur>,     <Ul as Add<Ur>>::Output: Unsigned + NonZero,

N(Ul) - P(Ur) = N(Ul + Ur)

type Output = NInt<<Ul as Add<Ur>>::Output>

The resulting type after applying the - operator.

fn sub(self, _: PInt<Ur>) -> Self::Output

Performs the - operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<NInt<Ur>> for NInt<Ul> where     Ur: Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,

N(Ul) - N(Ur): We resolve this with our PrivateAdd

type Output = <Ur as PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>>::Output

The resulting type after applying the - operator.

fn sub(self, rhs: NInt<Ur>) -> Self::Output

Performs the - operation.

impl<U: Unsigned + NonZero> Mul<Z0> for NInt<U>

N * Z0 = Z0

type Output = Z0

The resulting type after applying the * operator.

fn mul(self, _: Z0) -> Self::Output

Performs the * operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<NInt<Ur>> for NInt<Ul> where     Ul: Mul<Ur>,     <Ul as Mul<Ur>>::Output: Unsigned + NonZero,

N(Ul) * N(Ur) = P(Ul * Ur)

type Output = PInt<<Ul as Mul<Ur>>::Output>

The resulting type after applying the * operator.

fn mul(self, _: NInt<Ur>) -> Self::Output

Performs the * operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<NInt<Ur>> for PInt<Ul> where     Ul: Mul<Ur>,     <Ul as Mul<Ur>>::Output: Unsigned + NonZero,

P(Ul) * N(Ur) = N(Ul * Ur)

type Output = NInt<<Ul as Mul<Ur>>::Output>

The resulting type after applying the * operator.

fn mul(self, _: NInt<Ur>) -> Self::Output

Performs the * operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<PInt<Ur>> for NInt<Ul> where     Ul: Mul<Ur>,     <Ul as Mul<Ur>>::Output: Unsigned + NonZero,

N(Ul) * P(Ur) = N(Ul * Ur)

type Output = NInt<<Ul as Mul<Ur>>::Output>

The resulting type after applying the * operator.

fn mul(self, _: PInt<Ur>) -> Self::Output

Performs the * operation.

impl<U> Mul<ATerm> for NInt<U> where     U: Unsigned + NonZero,

type Output = ATerm

The resulting type after applying the * operator.

fn mul(self, _: ATerm) -> Self::Output

Performs the * operation.

impl<V, A, U> Mul<TArr<V, A>> for NInt<U> where     U: Unsigned + NonZero,     NInt<U>: Mul<A> + Mul<V>,

type Output = TArr<Prod<NInt<U>, V>, Prod<NInt<U>, A>>

The resulting type after applying the * operator.

fn mul(self, rhs: TArr<V, A>) -> Self::Output

Performs the * operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Div<NInt<Ur>> for PInt<Ul> where     Ul: Cmp<Ur>,     PInt<Ul>: PrivateDivInt<<Ul as Cmp<Ur>>::Output, NInt<Ur>>,

$A<Ul> / $B<Ur> = $R<Ul / Ur>

type Output = <PInt<Ul> as PrivateDivInt<<Ul as Cmp<Ur>>::Output, NInt<Ur>>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: NInt<Ur>) -> Self::Output

Performs the / operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Div<PInt<Ur>> for NInt<Ul> where     Ul: Cmp<Ur>,     NInt<Ul>: PrivateDivInt<<Ul as Cmp<Ur>>::Output, PInt<Ur>>,

$A<Ul> / $B<Ur> = $R<Ul / Ur>

type Output = <NInt<Ul> as PrivateDivInt<<Ul as Cmp<Ur>>::Output, PInt<Ur>>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: PInt<Ur>) -> Self::Output

Performs the / operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Div<NInt<Ur>> for NInt<Ul> where     Ul: Cmp<Ur>,     NInt<Ul>: PrivateDivInt<<Ul as Cmp<Ur>>::Output, NInt<Ur>>,

$A<Ul> / $B<Ur> = $R<Ul / Ur>

type Output = <NInt<Ul> as PrivateDivInt<<Ul as Cmp<Ur>>::Output, NInt<Ur>>>::Output

The resulting type after applying the / operator.

fn div(self, rhs: NInt<Ur>) -> Self::Output

Performs the / operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Rem<NInt<Ur>> for PInt<Ul> where     Ul: Rem<Ur>,     PInt<Ul>: PrivateRem<<Ul as Rem<Ur>>::Output, NInt<Ur>>,

$A<Ul> % $B<Ur> = $R<Ul % Ur>

type Output = <PInt<Ul> as PrivateRem<<Ul as Rem<Ur>>::Output, NInt<Ur>>>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: NInt<Ur>) -> Self::Output

Performs the % operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Rem<PInt<Ur>> for NInt<Ul> where     Ul: Rem<Ur>,     NInt<Ul>: PrivateRem<<Ul as Rem<Ur>>::Output, PInt<Ur>>,

$A<Ul> % $B<Ur> = $R<Ul % Ur>

type Output = <NInt<Ul> as PrivateRem<<Ul as Rem<Ur>>::Output, PInt<Ur>>>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: PInt<Ur>) -> Self::Output

Performs the % operation.

impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Rem<NInt<Ur>> for NInt<Ul> where     Ul: Rem<Ur>,     NInt<Ul>: PrivateRem<<Ul as Rem<Ur>>::Output, NInt<Ur>>,

$A<Ul> % $B<Ur> = $R<Ul % Ur>

type Output = <NInt<Ul> as PrivateRem<<Ul as Rem<Ur>>::Output, NInt<Ur>>>::Output

The resulting type after applying the % operator.

fn rem(self, rhs: NInt<Ur>) -> Self::Output

Performs the % operation.

impl<U: Unsigned + NonZero> Neg for NInt<U>

-NInt = PInt

type Output = PInt<U>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<U: Hash + Unsigned + NonZero> Hash for NInt<U>

fn hash<__HU: Hasher>(&self, state: &mut __HU)

Feeds this value into the given [Hasher].

fn hash_slice<H>(data: &[Self], state: &mut H) where     H: Hasher,

Feeds a slice of this type into the given [Hasher].

impl<U: Copy + Unsigned + NonZero> Copy for NInt<U>

impl<U: Clone + Unsigned + NonZero> Clone for NInt<U>

fn clone(&self) -> NInt<U>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<U: Default + Unsigned + NonZero> Default for NInt<U>

fn default() -> NInt<U>

Returns the "default value" for a type.