Struct PInt 

pub struct PInt<U: Unsigned + NonZero> { /* private fields */ }

Type-level signed integers with positive sign.

Implementations

impl<U: Unsigned + NonZero> PInt<U>

pub fn new() -> PInt<U>

Instantiates a singleton representing this strictly positive integer.

Trait Implementations

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

type Output = PInt<U>

The absolute value.

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

where Ul: Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur> + Unsigned + NonZero,

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> Add<PInt<Ur>> for NInt<Ul>

where Ur: Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul> + Unsigned + NonZero,

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<Ul, Ur: Unsigned + NonZero> Add<PInt<Ur>> for PInt<Ul>

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

P(Ul) + P(Ur) = P(Ul + Ur)

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

The resulting type after applying the + operator.

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

Performs the + operation.

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

PInt + Z0 = PInt

type Output = PInt<U>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

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.

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.

impl<Pl: Cmp<Pr> + Unsigned + NonZero, Pr: Unsigned + NonZero> Cmp<PInt<Pr>> for PInt<Pl>

X <==> Y

type Output = <Pl as Cmp<Pr>>::Output

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

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

0 < X

type Output = Less

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

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

X > 0

type Output = Greater

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

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

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

Formats the value using the given formatter.

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

fn default() -> PInt<U>

Returns the “default value” for a type.

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

where Ul: Cmp<Ur> + Unsigned + NonZero, 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, Ur: Unsigned + NonZero> Div<PInt<Ur>> for NInt<Ul>

where Ul: Cmp<Ur> + Unsigned + NonZero, 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, Ur: Unsigned + NonZero> Div<PInt<Ur>> for PInt<Ul>

where Ul: Cmp<Ur> + Unsigned + NonZero, PInt<Ul>: PrivateDivInt<<Ul as Cmp<Ur>>::Output, PInt<Ur>>,

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

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

The greatest common divisor.

impl<U> Gcd<PInt<U>> for Z0

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<<U1 as Gcd<U2>>::Output>

The greatest common divisor.

impl<U1, U2> Gcd<PInt<U2>> for PInt<U1>

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

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

The greatest common divisor.

impl<U> Gcd<Z0> for PInt<U>

where U: Unsigned + NonZero,

type Output = PInt<U>

The greatest common divisor.

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

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

Feeds this value into the given Hasher.

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

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

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

const I8: i8 = U::I8

const I16: i16 = U::I16

const I32: i32 = U::I32

const I64: i64 = U::I64

const ISIZE: isize = U::ISIZE

fn to_i8() -> i8

fn to_i16() -> i16

fn to_i32() -> i32

fn to_i64() -> i64

fn to_isize() -> isize

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<U> Max<PInt<U>> for Z0

where U: Unsigned + NonZero,

type Output = PInt<U>

The type of the maximum of Self and Rhs

fn max(self, rhs: PInt<U>) -> 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<PInt<Ur>> for PInt<Ul>

where Ul: Unsigned + NonZero + Max<Ur>, Ur: Unsigned + NonZero, Maximum<Ul, Ur>: Unsigned + NonZero,

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

The type of the maximum of Self and Rhs

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

Method returning the maximum

impl<U> Max<Z0> for PInt<U>

where U: Unsigned + NonZero,

type Output = PInt<U>

The type of the maximum of Self and Rhs

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

Method returning the maximum

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<U> Min<PInt<U>> for Z0

where U: Unsigned + NonZero,

type Output = Z0

The type of the minimum of Self and Rhs

fn min(self, _: PInt<U>) -> 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<PInt<Ur>> for PInt<Ul>

where Ul: Unsigned + NonZero + Min<Ur>, Ur: Unsigned + NonZero, Minimum<Ul, Ur>: Unsigned + NonZero,

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

The type of the minimum of Self and Rhs

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

Method returning the minimum

impl<U> Min<Z0> for PInt<U>

where U: Unsigned + NonZero,

type Output = Z0

The type of the minimum of Self and Rhs

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

Method returning the minimum

impl<U> Mul<ATerm> for PInt<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<Ul, Ur: Unsigned + NonZero> Mul<NInt<Ur>> for PInt<Ul>

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

where Ul: Mul<Ur> + Unsigned + NonZero, <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<Ul, Ur: Unsigned + NonZero> Mul<PInt<Ur>> for PInt<Ul>

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

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<V, A, U> Mul<TArr<V, A>> for PInt<U>

where U: Unsigned + NonZero, PInt<U>: Mul<A> + Mul<V>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

P * Z0 = Z0

type Output = Z0

The resulting type after applying the * operator.

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

Performs the * operation.

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

-PInt = NInt

type Output = NInt<U>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

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

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

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

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

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

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

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

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

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

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

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

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

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

0^P = 0

type Output = Z0

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for f32

type Output = f32

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for f64

type Output = f64

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for i16

type Output = i16

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for i32

type Output = i32

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for i64

type Output = i64

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for i8

type Output = i8

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for isize

type Output = isize

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for u16

type Output = u16

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for u32

type Output = u32

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for u64

type Output = u64

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for u8

type Output = u8

The result of the exponentiation.

fn powi(self, _: PInt<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<PInt<U>> for usize

type Output = usize

The result of the exponentiation.

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

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

impl<Ul, Ur: Unsigned> Pow<PInt<UInt<Ur, B0>>> for NInt<Ul>

where Ul: Pow<UInt<Ur, B0>> + Unsigned + NonZero, <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, Ur: Unsigned> Pow<PInt<UInt<Ur, B1>>> for NInt<Ul>

where Ul: Pow<UInt<Ur, B1>> + Unsigned + NonZero, <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<Ul, Ur: Unsigned + NonZero> Pow<PInt<Ur>> for PInt<Ul>

where Ul: Pow<Ur> + Unsigned + NonZero, <Ul as Pow<Ur>>::Output: Unsigned + NonZero,

P(Ul)^P(Ur) = P(Ul^Ur)

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

The result of the exponentiation.

fn powi(self, _: PInt<Ur>) -> 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 PInt<U>

P^0 = 1

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

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, Ur: Unsigned + NonZero> Rem<NInt<Ur>> for PInt<Ul>

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

where Ul: Rem<Ur> + Unsigned + NonZero, 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, Ur: Unsigned + NonZero> Rem<PInt<Ur>> for PInt<Ul>

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

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

type Output = <PInt<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, Ur: Unsigned + NonZero> Sub<NInt<Ur>> for PInt<Ul>

where Ul: Add<Ur> + Unsigned + NonZero, <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<U: Unsigned + NonZero> Sub<PInt<U>> for Z0

Z0 - P = N

type Output = NInt<U>

The resulting type after applying the - operator.

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

Performs the - operation.

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

where Ul: Add<Ur> + Unsigned + NonZero, <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, Ur: Unsigned + NonZero> Sub<PInt<Ur>> for PInt<Ul>

where Ul: Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur> + Unsigned + NonZero,

P(Ul) - P(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 sub(self, rhs: PInt<Ur>) -> Self::Output

Performs the - operation.

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

PInt - Z0 = PInt

type Output = PInt<U>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<U> ToInt<i16> for PInt<U>

where U: Unsigned + NonZero,

fn to_int() -> i16

Method returning the concrete value for the type.

impl<U> ToInt<i32> for PInt<U>

where U: Unsigned + NonZero,

fn to_int() -> i32

Method returning the concrete value for the type.

impl<U> ToInt<i64> for PInt<U>

where U: Unsigned + NonZero,

fn to_int() -> i64

Method returning the concrete value for the type.

impl<U> ToInt<i8> for PInt<U>

where U: Unsigned + NonZero,

fn to_int() -> i8

Method returning the concrete value for the type.

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

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

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

impl<U: Unsigned + NonZero + PowerOfTwo> PowerOfTwo for PInt<U>

impl<U: Unsigned + NonZero> StructuralPartialEq for PInt<U>