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//! Type-level signed integers.
//!
//!
//! Type **operators** implemented:
//!
//! From `core::ops`: `Add`, `Sub`, `Mul`, `Div`, and `Rem`.
//! From `typenum`: `Same`, `Cmp`, and `Pow`.
//!
//! Rather than directly using the structs defined in this module, it is recommended that
//! you import and use the relevant aliases from the [consts](../consts/index.html) module.
//!
//! Note that operators that work on the underlying structure of the number are
//! intentionally not implemented. This is because this implementation of signed integers
//! does *not* use twos-complement, and implementing them would require making arbitrary
//! choices, causing the results of such operators to be difficult to reason about.
//!
//! # Example
//! ```rust
//! use std::ops::{Add, Div, Mul, Rem, Sub};
//! use typenum::{Integer, N3, P2};
//!
//! assert_eq!(<N3 as Add<P2>>::Output::to_i32(), -1);
//! assert_eq!(<N3 as Sub<P2>>::Output::to_i32(), -5);
//! assert_eq!(<N3 as Mul<P2>>::Output::to_i32(), -6);
//! assert_eq!(<N3 as Div<P2>>::Output::to_i32(), -1);
//! assert_eq!(<N3 as Rem<P2>>::Output::to_i32(), -1);
//! ```
pub use crate::marker_traits::Integer;
use crate::{
bit::{Bit, B0, B1},
consts::{N1, P1, U0, U1},
private::{Internal, InternalMarker, PrivateDivInt, PrivateIntegerAdd, PrivateRem},
uint::{UInt, Unsigned},
Cmp, Equal, Greater, Less, NonZero, Pow, PowerOfTwo, ToInt, Zero,
};
use core::ops::{Add, Div, Mul, Neg, Rem, Sub};
/// Type-level signed integers with positive sign.
#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
pub struct PInt<U: Unsigned + NonZero> {
pub(crate) n: U,
}
/// Type-level signed integers with negative sign.
#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
pub struct NInt<U: Unsigned + NonZero> {
pub(crate) n: U,
}
impl<U: Unsigned + NonZero> PInt<U> {
/// Instantiates a singleton representing this strictly positive integer.
#[inline]
pub fn new() -> PInt<U> {
PInt::default()
}
}
impl<U: Unsigned + NonZero> NInt<U> {
/// Instantiates a singleton representing this strictly negative integer.
#[inline]
pub fn new() -> NInt<U> {
NInt::default()
}
}
/// The type-level signed integer 0.
#[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)]
#[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))]
pub struct Z0;
impl Z0 {
/// Instantiates a singleton representing the integer 0.
#[inline]
pub fn new() -> Z0 {
Z0
}
}
impl<U: Unsigned + NonZero> NonZero for PInt<U> {}
impl<U: Unsigned + NonZero> NonZero for NInt<U> {}
impl Zero for Z0 {}
impl<U: Unsigned + NonZero + PowerOfTwo> PowerOfTwo for PInt<U> {}
impl Integer for Z0 {
const I8: i8 = 0;
const I16: i16 = 0;
const I32: i32 = 0;
const I64: i64 = 0;
#[cfg(feature = "i128")]
const I128: i128 = 0;
const ISIZE: isize = 0;
#[inline]
fn to_i8() -> i8 {
0
}
#[inline]
fn to_i16() -> i16 {
0
}
#[inline]
fn to_i32() -> i32 {
0
}
#[inline]
fn to_i64() -> i64 {
0
}
#[cfg(feature = "i128")]
#[inline]
fn to_i128() -> i128 {
0
}
#[inline]
fn to_isize() -> isize {
0
}
}
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;
#[cfg(feature = "i128")]
const I128: i128 = U::I128;
const ISIZE: isize = U::ISIZE;
#[inline]
fn to_i8() -> i8 {
<U as Unsigned>::to_i8()
}
#[inline]
fn to_i16() -> i16 {
<U as Unsigned>::to_i16()
}
#[inline]
fn to_i32() -> i32 {
<U as Unsigned>::to_i32()
}
#[inline]
fn to_i64() -> i64 {
<U as Unsigned>::to_i64()
}
#[cfg(feature = "i128")]
#[inline]
fn to_i128() -> i128 {
<U as Unsigned>::to_i128()
}
#[inline]
fn to_isize() -> isize {
<U as Unsigned>::to_isize()
}
}
// Simply negating the result of e.g. `U::I8` will result in overflow for `std::i8::MIN`. Instead,
// we use the fact that `U: NonZero` by subtracting one from the `U::U8` before negating.
impl<U: Unsigned + NonZero> Integer for NInt<U> {
const I8: i8 = -((U::U8 - 1) as i8) - 1;
const I16: i16 = -((U::U16 - 1) as i16) - 1;
const I32: i32 = -((U::U32 - 1) as i32) - 1;
const I64: i64 = -((U::U64 - 1) as i64) - 1;
#[cfg(feature = "i128")]
const I128: i128 = -((U::U128 - 1) as i128) - 1;
const ISIZE: isize = -((U::USIZE - 1) as isize) - 1;
#[inline]
fn to_i8() -> i8 {
Self::I8
}
#[inline]
fn to_i16() -> i16 {
Self::I16
}
#[inline]
fn to_i32() -> i32 {
Self::I32
}
#[inline]
fn to_i64() -> i64 {
Self::I64
}
#[cfg(feature = "i128")]
#[inline]
fn to_i128() -> i128 {
Self::I128
}
#[inline]
fn to_isize() -> isize {
Self::ISIZE
}
}
// ---------------------------------------------------------------------------------------
// Neg
/// `-Z0 = Z0`
impl Neg for Z0 {
type Output = Z0;
#[inline]
fn neg(self) -> Self::Output {
Z0
}
}
/// `-PInt = NInt`
impl<U: Unsigned + NonZero> Neg for PInt<U> {
type Output = NInt<U>;
#[inline]
fn neg(self) -> Self::Output {
NInt::new()
}
}
/// `-NInt = PInt`
impl<U: Unsigned + NonZero> Neg for NInt<U> {
type Output = PInt<U>;
#[inline]
fn neg(self) -> Self::Output {
PInt::new()
}
}
// ---------------------------------------------------------------------------------------
// Add
/// `Z0 + I = I`
impl<I: Integer> Add<I> for Z0 {
type Output = I;
#[inline]
fn add(self, rhs: I) -> Self::Output {
rhs
}
}
/// `PInt + Z0 = PInt`
impl<U: Unsigned + NonZero> Add<Z0> for PInt<U> {
type Output = PInt<U>;
#[inline]
fn add(self, _: Z0) -> Self::Output {
PInt::new()
}
}
/// `NInt + Z0 = NInt`
impl<U: Unsigned + NonZero> Add<Z0> for NInt<U> {
type Output = NInt<U>;
#[inline]
fn add(self, _: Z0) -> Self::Output {
NInt::new()
}
}
/// `P(Ul) + P(Ur) = P(Ul + Ur)`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<PInt<Ur>> for PInt<Ul>
where
Ul: Add<Ur>,
<Ul as Add<Ur>>::Output: Unsigned + NonZero,
{
type Output = PInt<<Ul as Add<Ur>>::Output>;
#[inline]
fn add(self, _: PInt<Ur>) -> Self::Output {
PInt::new()
}
}
/// `N(Ul) + N(Ur) = N(Ul + Ur)`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<NInt<Ur>> for NInt<Ul>
where
Ul: Add<Ur>,
<Ul as Add<Ur>>::Output: Unsigned + NonZero,
{
type Output = NInt<<Ul as Add<Ur>>::Output>;
#[inline]
fn add(self, _: NInt<Ur>) -> Self::Output {
NInt::new()
}
}
/// `P(Ul) + N(Ur)`: We resolve this with our `PrivateAdd`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<NInt<Ur>> for PInt<Ul>
where
Ul: Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>,
{
type Output = <Ul as PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>>::Output;
#[inline]
fn add(self, rhs: NInt<Ur>) -> Self::Output {
let lhs = self.n;
let rhs = rhs.n;
let lhs_cmp_rhs = lhs.compare::<Internal>(&rhs);
lhs.private_integer_add(lhs_cmp_rhs, rhs)
}
}
/// `N(Ul) + P(Ur)`: We resolve this with our `PrivateAdd`
// We just do the same thing as above, swapping Lhs and Rhs
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Add<PInt<Ur>> for NInt<Ul>
where
Ur: Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,
{
type Output = <Ur as PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>>::Output;
#[inline]
fn add(self, rhs: PInt<Ur>) -> Self::Output {
let lhs = self.n;
let rhs = rhs.n;
let rhs_cmp_lhs = rhs.compare::<Internal>(&lhs);
rhs.private_integer_add(rhs_cmp_lhs, lhs)
}
}
/// `P + N = 0` where `P == N`
impl<N: Unsigned, P: Unsigned> PrivateIntegerAdd<Equal, N> for P {
type Output = Z0;
#[inline]
fn private_integer_add(self, _: Equal, _: N) -> Self::Output {
Z0
}
}
/// `P + N = Positive` where `P > N`
impl<N: Unsigned, P: Unsigned> PrivateIntegerAdd<Greater, N> for P
where
P: Sub<N>,
<P as Sub<N>>::Output: Unsigned + NonZero,
{
type Output = PInt<<P as Sub<N>>::Output>;
#[inline]
fn private_integer_add(self, _: Greater, n: N) -> Self::Output {
PInt { n: self - n }
}
}
/// `P + N = Negative` where `P < N`
impl<N: Unsigned, P: Unsigned> PrivateIntegerAdd<Less, N> for P
where
N: Sub<P>,
<N as Sub<P>>::Output: Unsigned + NonZero,
{
type Output = NInt<<N as Sub<P>>::Output>;
#[inline]
fn private_integer_add(self, _: Less, n: N) -> Self::Output {
NInt { n: n - self }
}
}
// ---------------------------------------------------------------------------------------
// Sub
/// `Z0 - Z0 = Z0`
impl Sub<Z0> for Z0 {
type Output = Z0;
#[inline]
fn sub(self, _: Z0) -> Self::Output {
Z0
}
}
/// `Z0 - P = N`
impl<U: Unsigned + NonZero> Sub<PInt<U>> for Z0 {
type Output = NInt<U>;
#[inline]
fn sub(self, _: PInt<U>) -> Self::Output {
NInt::new()
}
}
/// `Z0 - N = P`
impl<U: Unsigned + NonZero> Sub<NInt<U>> for Z0 {
type Output = PInt<U>;
#[inline]
fn sub(self, _: NInt<U>) -> Self::Output {
PInt::new()
}
}
/// `PInt - Z0 = PInt`
impl<U: Unsigned + NonZero> Sub<Z0> for PInt<U> {
type Output = PInt<U>;
#[inline]
fn sub(self, _: Z0) -> Self::Output {
PInt::new()
}
}
/// `NInt - Z0 = NInt`
impl<U: Unsigned + NonZero> Sub<Z0> for NInt<U> {
type Output = NInt<U>;
#[inline]
fn sub(self, _: Z0) -> Self::Output {
NInt::new()
}
}
/// `P(Ul) - N(Ur) = P(Ul + Ur)`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<NInt<Ur>> for PInt<Ul>
where
Ul: Add<Ur>,
<Ul as Add<Ur>>::Output: Unsigned + NonZero,
{
type Output = PInt<<Ul as Add<Ur>>::Output>;
#[inline]
fn sub(self, _: NInt<Ur>) -> Self::Output {
PInt::new()
}
}
/// `N(Ul) - P(Ur) = N(Ul + Ur)`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<PInt<Ur>> for NInt<Ul>
where
Ul: Add<Ur>,
<Ul as Add<Ur>>::Output: Unsigned + NonZero,
{
type Output = NInt<<Ul as Add<Ur>>::Output>;
#[inline]
fn sub(self, _: PInt<Ur>) -> Self::Output {
NInt::new()
}
}
/// `P(Ul) - P(Ur)`: We resolve this with our `PrivateAdd`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<PInt<Ur>> for PInt<Ul>
where
Ul: Cmp<Ur> + PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>,
{
type Output = <Ul as PrivateIntegerAdd<<Ul as Cmp<Ur>>::Output, Ur>>::Output;
#[inline]
fn sub(self, rhs: PInt<Ur>) -> Self::Output {
let lhs = self.n;
let rhs = rhs.n;
let lhs_cmp_rhs = lhs.compare::<Internal>(&rhs);
lhs.private_integer_add(lhs_cmp_rhs, rhs)
}
}
/// `N(Ul) - N(Ur)`: We resolve this with our `PrivateAdd`
// We just do the same thing as above, swapping Lhs and Rhs
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Sub<NInt<Ur>> for NInt<Ul>
where
Ur: Cmp<Ul> + PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>,
{
type Output = <Ur as PrivateIntegerAdd<<Ur as Cmp<Ul>>::Output, Ul>>::Output;
#[inline]
fn sub(self, rhs: NInt<Ur>) -> Self::Output {
let lhs = self.n;
let rhs = rhs.n;
let rhs_cmp_lhs = rhs.compare::<Internal>(&lhs);
rhs.private_integer_add(rhs_cmp_lhs, lhs)
}
}
// ---------------------------------------------------------------------------------------
// Mul
/// `Z0 * I = Z0`
impl<I: Integer> Mul<I> for Z0 {
type Output = Z0;
#[inline]
fn mul(self, _: I) -> Self::Output {
Z0
}
}
/// `P * Z0 = Z0`
impl<U: Unsigned + NonZero> Mul<Z0> for PInt<U> {
type Output = Z0;
#[inline]
fn mul(self, _: Z0) -> Self::Output {
Z0
}
}
/// `N * Z0 = Z0`
impl<U: Unsigned + NonZero> Mul<Z0> for NInt<U> {
type Output = Z0;
#[inline]
fn mul(self, _: Z0) -> Self::Output {
Z0
}
}
/// P(Ul) * P(Ur) = P(Ul * Ur)
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<PInt<Ur>> for PInt<Ul>
where
Ul: Mul<Ur>,
<Ul as Mul<Ur>>::Output: Unsigned + NonZero,
{
type Output = PInt<<Ul as Mul<Ur>>::Output>;
#[inline]
fn mul(self, _: PInt<Ur>) -> Self::Output {
PInt::new()
}
}
/// N(Ul) * N(Ur) = P(Ul * Ur)
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<NInt<Ur>> for NInt<Ul>
where
Ul: Mul<Ur>,
<Ul as Mul<Ur>>::Output: Unsigned + NonZero,
{
type Output = PInt<<Ul as Mul<Ur>>::Output>;
#[inline]
fn mul(self, _: NInt<Ur>) -> Self::Output {
PInt::new()
}
}
/// P(Ul) * N(Ur) = N(Ul * Ur)
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<NInt<Ur>> for PInt<Ul>
where
Ul: Mul<Ur>,
<Ul as Mul<Ur>>::Output: Unsigned + NonZero,
{
type Output = NInt<<Ul as Mul<Ur>>::Output>;
#[inline]
fn mul(self, _: NInt<Ur>) -> Self::Output {
NInt::new()
}
}
/// N(Ul) * P(Ur) = N(Ul * Ur)
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Mul<PInt<Ur>> for NInt<Ul>
where
Ul: Mul<Ur>,
<Ul as Mul<Ur>>::Output: Unsigned + NonZero,
{
type Output = NInt<<Ul as Mul<Ur>>::Output>;
#[inline]
fn mul(self, _: PInt<Ur>) -> Self::Output {
NInt::new()
}
}
// ---------------------------------------------------------------------------------------
// Div
/// `Z0 / I = Z0` where `I != 0`
impl<I: Integer + NonZero> Div<I> for Z0 {
type Output = Z0;
#[inline]
fn div(self, _: I) -> Self::Output {
Z0
}
}
macro_rules! impl_int_div {
($A:ident, $B:ident, $R:ident) => {
/// `$A<Ul> / $B<Ur> = $R<Ul / Ur>`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Div<$B<Ur>> for $A<Ul>
where
Ul: Cmp<Ur>,
$A<Ul>: PrivateDivInt<<Ul as Cmp<Ur>>::Output, $B<Ur>>,
{
type Output = <$A<Ul> as PrivateDivInt<<Ul as Cmp<Ur>>::Output, $B<Ur>>>::Output;
#[inline]
fn div(self, rhs: $B<Ur>) -> Self::Output {
let lhs_cmp_rhs = self.n.compare::<Internal>(&rhs.n);
self.private_div_int(lhs_cmp_rhs, rhs)
}
}
impl<Ul, Ur> PrivateDivInt<Less, $B<Ur>> for $A<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
{
type Output = Z0;
#[inline]
fn private_div_int(self, _: Less, _: $B<Ur>) -> Self::Output {
Z0
}
}
impl<Ul, Ur> PrivateDivInt<Equal, $B<Ur>> for $A<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
{
type Output = $R<U1>;
#[inline]
fn private_div_int(self, _: Equal, _: $B<Ur>) -> Self::Output {
$R { n: U1::new() }
}
}
impl<Ul, Ur> PrivateDivInt<Greater, $B<Ur>> for $A<Ul>
where
Ul: Unsigned + NonZero + Div<Ur>,
Ur: Unsigned + NonZero,
<Ul as Div<Ur>>::Output: Unsigned + NonZero,
{
type Output = $R<<Ul as Div<Ur>>::Output>;
#[inline]
fn private_div_int(self, _: Greater, d: $B<Ur>) -> Self::Output {
$R { n: self.n / d.n }
}
}
};
}
impl_int_div!(PInt, PInt, PInt);
impl_int_div!(PInt, NInt, NInt);
impl_int_div!(NInt, PInt, NInt);
impl_int_div!(NInt, NInt, PInt);
// ---------------------------------------------------------------------------------------
// PartialDiv
use crate::{PartialDiv, Quot};
impl<M, N> PartialDiv<N> for M
where
M: Integer + Div<N> + Rem<N, Output = Z0>,
{
type Output = Quot<M, N>;
#[inline]
fn partial_div(self, rhs: N) -> Self::Output {
self / rhs
}
}
// ---------------------------------------------------------------------------------------
// Cmp
/// 0 == 0
impl Cmp<Z0> for Z0 {
type Output = Equal;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &Z0) -> Self::Output {
Equal
}
}
/// 0 > -X
impl<U: Unsigned + NonZero> Cmp<NInt<U>> for Z0 {
type Output = Greater;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &NInt<U>) -> Self::Output {
Greater
}
}
/// 0 < X
impl<U: Unsigned + NonZero> Cmp<PInt<U>> for Z0 {
type Output = Less;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &PInt<U>) -> Self::Output {
Less
}
}
/// X > 0
impl<U: Unsigned + NonZero> Cmp<Z0> for PInt<U> {
type Output = Greater;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &Z0) -> Self::Output {
Greater
}
}
/// -X < 0
impl<U: Unsigned + NonZero> Cmp<Z0> for NInt<U> {
type Output = Less;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &Z0) -> Self::Output {
Less
}
}
/// -X < Y
impl<P: Unsigned + NonZero, N: Unsigned + NonZero> Cmp<PInt<P>> for NInt<N> {
type Output = Less;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &PInt<P>) -> Self::Output {
Less
}
}
/// X > - Y
impl<P: Unsigned + NonZero, N: Unsigned + NonZero> Cmp<NInt<N>> for PInt<P> {
type Output = Greater;
#[inline]
fn compare<IM: InternalMarker>(&self, _: &NInt<N>) -> Self::Output {
Greater
}
}
/// X <==> Y
impl<Pl: Cmp<Pr> + Unsigned + NonZero, Pr: Unsigned + NonZero> Cmp<PInt<Pr>> for PInt<Pl> {
type Output = <Pl as Cmp<Pr>>::Output;
#[inline]
fn compare<IM: InternalMarker>(&self, rhs: &PInt<Pr>) -> Self::Output {
self.n.compare::<Internal>(&rhs.n)
}
}
/// -X <==> -Y
impl<Nl: Unsigned + NonZero, Nr: Cmp<Nl> + Unsigned + NonZero> Cmp<NInt<Nr>> for NInt<Nl> {
type Output = <Nr as Cmp<Nl>>::Output;
#[inline]
fn compare<IM: InternalMarker>(&self, rhs: &NInt<Nr>) -> Self::Output {
rhs.n.compare::<Internal>(&self.n)
}
}
// ---------------------------------------------------------------------------------------
// Rem
/// `Z0 % I = Z0` where `I != 0`
impl<I: Integer + NonZero> Rem<I> for Z0 {
type Output = Z0;
#[inline]
fn rem(self, _: I) -> Self::Output {
Z0
}
}
macro_rules! impl_int_rem {
($A:ident, $B:ident, $R:ident) => {
/// `$A<Ul> % $B<Ur> = $R<Ul % Ur>`
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Rem<$B<Ur>> for $A<Ul>
where
Ul: Rem<Ur>,
$A<Ul>: PrivateRem<<Ul as Rem<Ur>>::Output, $B<Ur>>,
{
type Output = <$A<Ul> as PrivateRem<<Ul as Rem<Ur>>::Output, $B<Ur>>>::Output;
#[inline]
fn rem(self, rhs: $B<Ur>) -> Self::Output {
self.private_rem(self.n % rhs.n, rhs)
}
}
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> PrivateRem<U0, $B<Ur>> for $A<Ul> {
type Output = Z0;
#[inline]
fn private_rem(self, _: U0, _: $B<Ur>) -> Self::Output {
Z0
}
}
impl<Ul, Ur, U, B> PrivateRem<UInt<U, B>, $B<Ur>> for $A<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
U: Unsigned,
B: Bit,
{
type Output = $R<UInt<U, B>>;
#[inline]
fn private_rem(self, urem: UInt<U, B>, _: $B<Ur>) -> Self::Output {
$R { n: urem }
}
}
};
}
impl_int_rem!(PInt, PInt, PInt);
impl_int_rem!(PInt, NInt, PInt);
impl_int_rem!(NInt, PInt, NInt);
impl_int_rem!(NInt, NInt, NInt);
// ---------------------------------------------------------------------------------------
// Pow
/// 0^0 = 1
impl Pow<Z0> for Z0 {
type Output = P1;
#[inline]
fn powi(self, _: Z0) -> Self::Output {
P1::new()
}
}
/// 0^P = 0
impl<U: Unsigned + NonZero> Pow<PInt<U>> for Z0 {
type Output = Z0;
#[inline]
fn powi(self, _: PInt<U>) -> Self::Output {
Z0
}
}
/// 0^N = 0
impl<U: Unsigned + NonZero> Pow<NInt<U>> for Z0 {
type Output = Z0;
#[inline]
fn powi(self, _: NInt<U>) -> Self::Output {
Z0
}
}
/// 1^N = 1
impl<U: Unsigned + NonZero> Pow<NInt<U>> for P1 {
type Output = P1;
#[inline]
fn powi(self, _: NInt<U>) -> Self::Output {
P1::new()
}
}
/// (-1)^N = 1 if N is even
impl<U: Unsigned> Pow<NInt<UInt<U, B0>>> for N1 {
type Output = P1;
#[inline]
fn powi(self, _: NInt<UInt<U, B0>>) -> Self::Output {
P1::new()
}
}
/// (-1)^N = -1 if N is odd
impl<U: Unsigned> Pow<NInt<UInt<U, B1>>> for N1 {
type Output = N1;
#[inline]
fn powi(self, _: NInt<UInt<U, B1>>) -> Self::Output {
N1::new()
}
}
/// P^0 = 1
impl<U: Unsigned + NonZero> Pow<Z0> for PInt<U> {
type Output = P1;
#[inline]
fn powi(self, _: Z0) -> Self::Output {
P1::new()
}
}
/// N^0 = 1
impl<U: Unsigned + NonZero> Pow<Z0> for NInt<U> {
type Output = P1;
#[inline]
fn powi(self, _: Z0) -> Self::Output {
P1::new()
}
}
/// P(Ul)^P(Ur) = P(Ul^Ur)
impl<Ul: Unsigned + NonZero, Ur: Unsigned + NonZero> Pow<PInt<Ur>> for PInt<Ul>
where
Ul: Pow<Ur>,
<Ul as Pow<Ur>>::Output: Unsigned + NonZero,
{
type Output = PInt<<Ul as Pow<Ur>>::Output>;
#[inline]
fn powi(self, _: PInt<Ur>) -> Self::Output {
PInt::new()
}
}
/// N(Ul)^P(Ur) = P(Ul^Ur) if Ur is even
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,
{
type Output = PInt<<Ul as Pow<UInt<Ur, B0>>>::Output>;
#[inline]
fn powi(self, _: PInt<UInt<Ur, B0>>) -> Self::Output {
PInt::new()
}
}
/// N(Ul)^P(Ur) = N(Ul^Ur) if Ur is odd
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,
{
type Output = NInt<<Ul as Pow<UInt<Ur, B1>>>::Output>;
#[inline]
fn powi(self, _: PInt<UInt<Ur, B1>>) -> Self::Output {
NInt::new()
}
}
// ---------------------------------------------------------------------------------------
// Gcd
use crate::{Gcd, Gcf};
impl Gcd<Z0> for Z0 {
type Output = Z0;
}
impl<U> Gcd<PInt<U>> for Z0
where
U: Unsigned + NonZero,
{
type Output = PInt<U>;
}
impl<U> Gcd<Z0> for PInt<U>
where
U: Unsigned + NonZero,
{
type Output = PInt<U>;
}
impl<U> Gcd<NInt<U>> for Z0
where
U: Unsigned + NonZero,
{
type Output = PInt<U>;
}
impl<U> Gcd<Z0> for NInt<U>
where
U: Unsigned + NonZero,
{
type Output = PInt<U>;
}
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<Gcf<U1, U2>>;
}
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>>;
}
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>>;
}
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>>;
}
// ---------------------------------------------------------------------------------------
// Min
use crate::{Max, Maximum, Min, Minimum};
impl Min<Z0> for Z0 {
type Output = Z0;
#[inline]
fn min(self, _: Z0) -> Self::Output {
self
}
}
impl<U> Min<PInt<U>> for Z0
where
U: Unsigned + NonZero,
{
type Output = Z0;
#[inline]
fn min(self, _: PInt<U>) -> Self::Output {
self
}
}
impl<U> Min<NInt<U>> for Z0
where
U: Unsigned + NonZero,
{
type Output = NInt<U>;
#[inline]
fn min(self, rhs: NInt<U>) -> Self::Output {
rhs
}
}
impl<U> Min<Z0> for PInt<U>
where
U: Unsigned + NonZero,
{
type Output = Z0;
#[inline]
fn min(self, rhs: Z0) -> Self::Output {
rhs
}
}
impl<U> Min<Z0> for NInt<U>
where
U: Unsigned + NonZero,
{
type Output = NInt<U>;
#[inline]
fn min(self, _: Z0) -> Self::Output {
self
}
}
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<Minimum<Ul, Ur>>;
#[inline]
fn min(self, rhs: PInt<Ur>) -> Self::Output {
PInt {
n: self.n.min(rhs.n),
}
}
}
impl<Ul, Ur> Min<PInt<Ur>> for NInt<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
{
type Output = NInt<Ul>;
#[inline]
fn min(self, _: PInt<Ur>) -> Self::Output {
self
}
}
impl<Ul, Ur> Min<NInt<Ur>> for PInt<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
{
type Output = NInt<Ur>;
#[inline]
fn min(self, rhs: NInt<Ur>) -> Self::Output {
rhs
}
}
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>>;
#[inline]
fn min(self, rhs: NInt<Ur>) -> Self::Output {
NInt {
n: self.n.max(rhs.n),
}
}
}
// ---------------------------------------------------------------------------------------
// Max
impl Max<Z0> for Z0 {
type Output = Z0;
#[inline]
fn max(self, _: Z0) -> Self::Output {
self
}
}
impl<U> Max<PInt<U>> for Z0
where
U: Unsigned + NonZero,
{
type Output = PInt<U>;
#[inline]
fn max(self, rhs: PInt<U>) -> Self::Output {
rhs
}
}
impl<U> Max<NInt<U>> for Z0
where
U: Unsigned + NonZero,
{
type Output = Z0;
#[inline]
fn max(self, _: NInt<U>) -> Self::Output {
self
}
}
impl<U> Max<Z0> for PInt<U>
where
U: Unsigned + NonZero,
{
type Output = PInt<U>;
#[inline]
fn max(self, _: Z0) -> Self::Output {
self
}
}
impl<U> Max<Z0> for NInt<U>
where
U: Unsigned + NonZero,
{
type Output = Z0;
#[inline]
fn max(self, rhs: Z0) -> Self::Output {
rhs
}
}
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<Maximum<Ul, Ur>>;
#[inline]
fn max(self, rhs: PInt<Ur>) -> Self::Output {
PInt {
n: self.n.max(rhs.n),
}
}
}
impl<Ul, Ur> Max<PInt<Ur>> for NInt<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
{
type Output = PInt<Ur>;
#[inline]
fn max(self, rhs: PInt<Ur>) -> Self::Output {
rhs
}
}
impl<Ul, Ur> Max<NInt<Ur>> for PInt<Ul>
where
Ul: Unsigned + NonZero,
Ur: Unsigned + NonZero,
{
type Output = PInt<Ul>;
#[inline]
fn max(self, _: NInt<Ur>) -> Self::Output {
self
}
}
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>>;
#[inline]
fn max(self, rhs: NInt<Ur>) -> Self::Output {
NInt {
n: self.n.min(rhs.n),
}
}
}
// -----------------------------------------
// ToInt
impl ToInt<i8> for Z0 {
#[inline]
fn to_int() -> i8 {
Self::I8
}
const INT: i8 = Self::I8;
}
impl ToInt<i16> for Z0 {
#[inline]
fn to_int() -> i16 {
Self::I16
}
const INT: i16 = Self::I16;
}
impl ToInt<i32> for Z0 {
#[inline]
fn to_int() -> i32 {
Self::I32
}
const INT: i32 = Self::I32;
}
impl ToInt<i64> for Z0 {
#[inline]
fn to_int() -> i64 {
Self::I64
}
const INT: i64 = Self::I64;
}
// negative numbers
impl<U> ToInt<i8> for NInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i8 {
Self::I8
}
const INT: i8 = Self::I8;
}
impl<U> ToInt<i16> for NInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i16 {
Self::I16
}
const INT: i16 = Self::I16;
}
impl<U> ToInt<i32> for NInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i32 {
Self::I32
}
const INT: i32 = Self::I32;
}
impl<U> ToInt<i64> for NInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i64 {
Self::I64
}
const INT: i64 = Self::I64;
}
// positive numbers
impl<U> ToInt<i8> for PInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i8 {
Self::I8
}
const INT: i8 = Self::I8;
}
impl<U> ToInt<i16> for PInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i16 {
Self::I16
}
const INT: i16 = Self::I16;
}
impl<U> ToInt<i32> for PInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i32 {
Self::I32
}
const INT: i32 = Self::I32;
}
impl<U> ToInt<i64> for PInt<U>
where
U: Unsigned + NonZero,
{
#[inline]
fn to_int() -> i64 {
Self::I64
}
const INT: i64 = Self::I64;
}
#[cfg(test)]
mod tests {
use crate::{consts::*, Integer, ToInt};
#[test]
fn to_ix_min() {
assert_eq!(N128::to_i8(), ::core::i8::MIN);
assert_eq!(N32768::to_i16(), ::core::i16::MIN);
}
#[test]
fn int_toint_test() {
// i8
assert_eq!(0_i8, Z0::to_int());
assert_eq!(1_i8, P1::to_int());
assert_eq!(2_i8, P2::to_int());
assert_eq!(3_i8, P3::to_int());
assert_eq!(4_i8, P4::to_int());
assert_eq!(-1_i8, N1::to_int());
assert_eq!(-2_i8, N2::to_int());
assert_eq!(-3_i8, N3::to_int());
assert_eq!(-4_i8, N4::to_int());
assert_eq!(0_i8, Z0::INT);
assert_eq!(1_i8, P1::INT);
assert_eq!(2_i8, P2::INT);
assert_eq!(3_i8, P3::INT);
assert_eq!(4_i8, P4::INT);
assert_eq!(-1_i8, N1::INT);
assert_eq!(-2_i8, N2::INT);
assert_eq!(-3_i8, N3::INT);
assert_eq!(-4_i8, N4::INT);
// i16
assert_eq!(0_i16, Z0::to_int());
assert_eq!(1_i16, P1::to_int());
assert_eq!(2_i16, P2::to_int());
assert_eq!(3_i16, P3::to_int());
assert_eq!(4_i16, P4::to_int());
assert_eq!(-1_i16, N1::to_int());
assert_eq!(-2_i16, N2::to_int());
assert_eq!(-3_i16, N3::to_int());
assert_eq!(-4_i16, N4::to_int());
assert_eq!(0_i16, Z0::INT);
assert_eq!(1_i16, P1::INT);
assert_eq!(2_i16, P2::INT);
assert_eq!(3_i16, P3::INT);
assert_eq!(4_i16, P4::INT);
assert_eq!(-1_i16, N1::INT);
assert_eq!(-2_i16, N2::INT);
assert_eq!(-3_i16, N3::INT);
assert_eq!(-4_i16, N4::INT);
// i32
assert_eq!(0_i32, Z0::to_int());
assert_eq!(1_i32, P1::to_int());
assert_eq!(2_i32, P2::to_int());
assert_eq!(3_i32, P3::to_int());
assert_eq!(4_i32, P4::to_int());
assert_eq!(-1_i32, N1::to_int());
assert_eq!(-2_i32, N2::to_int());
assert_eq!(-3_i32, N3::to_int());
assert_eq!(-4_i32, N4::to_int());
assert_eq!(0_i32, Z0::INT);
assert_eq!(1_i32, P1::INT);
assert_eq!(2_i32, P2::INT);
assert_eq!(3_i32, P3::INT);
assert_eq!(4_i32, P4::INT);
assert_eq!(-1_i32, N1::INT);
assert_eq!(-2_i32, N2::INT);
assert_eq!(-3_i32, N3::INT);
assert_eq!(-4_i32, N4::INT);
// i64
assert_eq!(0_i64, Z0::to_int());
assert_eq!(1_i64, P1::to_int());
assert_eq!(2_i64, P2::to_int());
assert_eq!(3_i64, P3::to_int());
assert_eq!(4_i64, P4::to_int());
assert_eq!(-1_i64, N1::to_int());
assert_eq!(-2_i64, N2::to_int());
assert_eq!(-3_i64, N3::to_int());
assert_eq!(-4_i64, N4::to_int());
assert_eq!(0_i64, Z0::INT);
assert_eq!(1_i64, P1::INT);
assert_eq!(2_i64, P2::INT);
assert_eq!(3_i64, P3::INT);
assert_eq!(4_i64, P4::INT);
assert_eq!(-1_i64, N1::INT);
assert_eq!(-2_i64, N2::INT);
assert_eq!(-3_i64, N3::INT);
assert_eq!(-4_i64, N4::INT);
}
}