Struct verified::NInt

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

Type-level signed integers with negative sign.

Implementations

impl<U> NInt<U> where
    U: NonZero + Unsigned, 

pub fn new() -> NInt<U>

Instantiates a singleton representing this strictly negative integer.

Trait Implementations

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

type Output = PInt<U>

The absolute value.

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

Performs the + operation.

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

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>) -> <PInt<Ul> as Add<NInt<Ur>>>::Output

Performs the + operation.

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

Performs the + operation.

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

NInt + Z0 = NInt

type Output = NInt<U>

The resulting type after applying the + operator.

fn add(self, Z0) -> <NInt<U> as Add<Z0>>::Output

Performs the + operation.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

X > - Y

type Output = Greater

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

fn compare<IM>(&self, &NInt<N>) -> <PInt<P> as Cmp<NInt<N>>>::Output where
    IM: InternalMarker, 

impl<Nl, Nr> Cmp<NInt<Nr>> for NInt<Nl> where
    Nl: NonZero + Unsigned,
    Nr: NonZero + Unsigned + Cmp<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>(&self, rhs: &NInt<Nr>) -> <NInt<Nl> as Cmp<NInt<Nr>>>::Output where
    IM: InternalMarker, 

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

0 > -X

type Output = Greater

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

fn compare<IM>(&self, &NInt<U>) -> <Z0 as Cmp<NInt<U>>>::Output where
    IM: InternalMarker, 

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

-X < Y

type Output = Less

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

fn compare<IM>(&self, &PInt<P>) -> <NInt<N> as Cmp<PInt<P>>>::Output where
    IM: InternalMarker, 

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

-X < 0

type Output = Less

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

fn compare<IM>(&self, &Z0) -> <NInt<U> as Cmp<Z0>>::Output where
    IM: InternalMarker, 

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

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

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

Formats the value using the given formatter.

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

fn default() -> NInt<U>

Returns the "default value" for a type.

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

Performs the / operation.

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

Performs the / operation.

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

Performs the / operation.

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

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

type Output = PInt<U>

The greatest common divisor.

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

type Output = PInt<<U1 as Gcd<U2>>::Output>

The greatest common divisor.

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

type Output = PInt<<U1 as Gcd<U2>>::Output>

The greatest common divisor.

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

type Output = PInt<<U1 as Gcd<U2>>::Output>

The greatest common divisor.

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

type Output = PInt<U>

The greatest common divisor.

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

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

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> Integer for NInt<U> where
    U: NonZero + Unsigned, 

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> 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>) -> <Z0 as Max<NInt<U>>>::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>) -> <PInt<Ul> as Max<NInt<Ur>>>::Output

Method returning the maximum

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

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

The type of the maximum of Self and Rhs

fn max(self, rhs: NInt<Ur>) -> <NInt<Ul> as Max<NInt<Ur>>>::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>) -> <NInt<Ul> as Max<PInt<Ur>>>::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) -> <NInt<U> as Max<Z0>>::Output

Method returning the maximum

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>) -> <Z0 as Min<NInt<U>>>::Output

Method returning the minimum

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

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

The type of the minimum of Self and Rhs

fn min(self, rhs: NInt<Ur>) -> <NInt<Ul> as Min<NInt<Ur>>>::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>) -> <PInt<Ul> as Min<NInt<Ur>>>::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>) -> <NInt<Ul> as Min<PInt<Ur>>>::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) -> <NInt<U> as Min<Z0>>::Output

Method returning the minimum

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) -> <NInt<U> as Mul<ATerm>>::Output

Performs the * operation.

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

Performs the * operation.

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

Performs the * operation.

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

Performs the * operation.

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

type Output = TArr<<NInt<U> as Mul<V>>::Output, <NInt<U> as Mul<A>>::Output>

The resulting type after applying the * operator.

fn mul(self, rhs: TArr<V, A>) -> <NInt<U> as Mul<TArr<V, A>>>::Output

Performs the * operation.

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

N * Z0 = Z0

type Output = Z0

The resulting type after applying the * operator.

fn mul(self, Z0) -> <NInt<U> as Mul<Z0>>::Output

Performs the * operation.

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

-NInt = PInt

type Output = PInt<U>

The resulting type after applying the - operator.

fn neg(self) -> <NInt<U> as Neg>::Output

Performs the unary - operation.

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

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

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

This method returns an [Ordering] between self and other.

#[must_use]fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

#[must_use]fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

#[must_use]fn clamp(self, min: Self, max: Self) -> Self

🔬 This is a nightly-only experimental API. (clamp)

Restrict a value to a certain interval.

impl<U> PartialEq<NInt<U>> for NInt<U> where
    U: NonZero + Unsigned + PartialEq<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> PartialOrd<NInt<U>> for NInt<U> where
    U: NonZero + Unsigned + PartialOrd<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> Pow<NInt<U>> for Z0 where
    U: NonZero + Unsigned, 

0^N = 0

type Output = Z0

The result of the exponentiation.

fn powi(self, NInt<U>) -> <Z0 as Pow<NInt<U>>>::Output

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

impl<U> Pow<NInt<U>> for PInt<UInt<UTerm, B1>> where
    U: NonZero + Unsigned, 

1^N = 1

type Output = PInt<UInt<UTerm, B1>>

The result of the exponentiation.

fn powi(self, NInt<U>) -> <PInt<UInt<UTerm, B1>> as Pow<NInt<U>>>::Output

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

impl<U> Pow<NInt<UInt<U, B0>>> for NInt<UInt<UTerm, B1>> where
    U: Unsigned, 

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

type Output = PInt<UInt<UTerm, B1>>

The result of the exponentiation.

fn powi(
    self,
    NInt<UInt<U, B0>>
) -> <NInt<UInt<UTerm, B1>> as Pow<NInt<UInt<U, B0>>>>::Output

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

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

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

type Output = NInt<UInt<UTerm, B1>>

The result of the exponentiation.

fn powi(
    self,
    NInt<UInt<U, B1>>
) -> <NInt<UInt<UTerm, B1>> as Pow<NInt<UInt<U, B1>>>>::Output

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

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

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

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

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

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

N^0 = 1

type Output = PInt<UInt<UTerm, B1>>

The result of the exponentiation.

fn powi(self, Z0) -> <NInt<U> as Pow<Z0>>::Output

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

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

Performs the % operation.

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

Performs the % operation.

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

Performs the % operation.

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

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

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

Z0 - N = P

type Output = PInt<U>

The resulting type after applying the - operator.

fn sub(self, NInt<U>) -> <Z0 as Sub<NInt<U>>>::Output

Performs the - operation.

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

Performs the - operation.

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

Performs the - operation.

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

Performs the - operation.

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

NInt - Z0 = NInt

type Output = NInt<U>

The resulting type after applying the - operator.

fn sub(self, Z0) -> <NInt<U> as Sub<Z0>>::Output

Performs the - operation.