| //! Type-level unsigned integers. |
| //! |
| //! |
| //! **Type operators** implemented: |
| //! |
| //! From `::core::ops`: `BitAnd`, `BitOr`, `BitXor`, `Shl`, `Shr`, `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. |
| //! |
| //! # Example |
| //! ```rust |
| //! use std::ops::{Add, BitAnd, BitOr, BitXor, Div, Mul, Rem, Shl, Shr, Sub}; |
| //! use typenum::{Unsigned, U1, U2, U3, U4}; |
| //! |
| //! assert_eq!(<U3 as BitAnd<U2>>::Output::to_u32(), 2); |
| //! assert_eq!(<U3 as BitOr<U4>>::Output::to_u32(), 7); |
| //! assert_eq!(<U3 as BitXor<U2>>::Output::to_u32(), 1); |
| //! assert_eq!(<U3 as Shl<U1>>::Output::to_u32(), 6); |
| //! assert_eq!(<U3 as Shr<U1>>::Output::to_u32(), 1); |
| //! assert_eq!(<U3 as Add<U2>>::Output::to_u32(), 5); |
| //! assert_eq!(<U3 as Sub<U2>>::Output::to_u32(), 1); |
| //! assert_eq!(<U3 as Mul<U2>>::Output::to_u32(), 6); |
| //! assert_eq!(<U3 as Div<U2>>::Output::to_u32(), 1); |
| //! assert_eq!(<U3 as Rem<U2>>::Output::to_u32(), 1); |
| //! ``` |
| |
| use crate::{ |
| bit::{Bit, B0, B1}, |
| consts::{U0, U1}, |
| private::{ |
| BitDiff, BitDiffOut, Internal, InternalMarker, PrivateAnd, PrivateAndOut, PrivateCmp, |
| PrivateCmpOut, PrivateLogarithm2, PrivatePow, PrivatePowOut, PrivateSquareRoot, PrivateSub, |
| PrivateSubOut, PrivateXor, PrivateXorOut, Trim, TrimOut, |
| }, |
| Add1, Cmp, Double, Equal, Gcd, Gcf, GrEq, Greater, IsGreaterOrEqual, Len, Length, Less, Log2, |
| Logarithm2, Maximum, Minimum, NonZero, Or, Ord, Pow, Prod, Shleft, Shright, Sqrt, Square, |
| SquareRoot, Sub1, Sum, ToInt, Zero, |
| }; |
| use core::ops::{Add, BitAnd, BitOr, BitXor, Mul, Shl, Shr, Sub}; |
| |
| pub use crate::marker_traits::{PowerOfTwo, Unsigned}; |
| |
| /// The terminating type for `UInt`; it always comes after the most significant |
| /// bit. `UTerm` by itself represents zero, which is aliased to `U0`. |
| #[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)] |
| #[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))] |
| pub struct UTerm; |
| |
| impl UTerm { |
| /// Instantiates a singleton representing this unsigned integer. |
| #[inline] |
| pub fn new() -> UTerm { |
| UTerm |
| } |
| } |
| |
| impl Unsigned for UTerm { |
| const U8: u8 = 0; |
| const U16: u16 = 0; |
| const U32: u32 = 0; |
| const U64: u64 = 0; |
| #[cfg(feature = "i128")] |
| const U128: u128 = 0; |
| const USIZE: usize = 0; |
| |
| 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_u8() -> u8 { |
| 0 |
| } |
| #[inline] |
| fn to_u16() -> u16 { |
| 0 |
| } |
| #[inline] |
| fn to_u32() -> u32 { |
| 0 |
| } |
| #[inline] |
| fn to_u64() -> u64 { |
| 0 |
| } |
| #[cfg(feature = "i128")] |
| #[inline] |
| fn to_u128() -> u128 { |
| 0 |
| } |
| #[inline] |
| fn to_usize() -> usize { |
| 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 |
| } |
| } |
| |
| /// `UInt` is defined recursively, where `B` is the least significant bit and `U` is the rest |
| /// of the number. Conceptually, `U` should be bound by the trait `Unsigned` and `B` should |
| /// be bound by the trait `Bit`, but enforcing these bounds causes linear instead of |
| /// logrithmic scaling in some places, so they are left off for now. They may be enforced in |
| /// future. |
| /// |
| /// In order to keep numbers unique, leading zeros are not allowed, so `UInt<UTerm, B0>` is |
| /// forbidden. |
| /// |
| /// # Example |
| /// ```rust |
| /// use typenum::{UInt, UTerm, B0, B1}; |
| /// |
| /// # #[allow(dead_code)] |
| /// type U6 = UInt<UInt<UInt<UTerm, B1>, B1>, B0>; |
| /// ``` |
| #[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash, Debug, Default)] |
| #[cfg_attr(feature = "scale_info", derive(scale_info::TypeInfo))] |
| pub struct UInt<U, B> { |
| /// The more significant bits of `Self`. |
| pub(crate) msb: U, |
| /// The least significant bit of `Self`. |
| pub(crate) lsb: B, |
| } |
| |
| impl<U: Unsigned, B: Bit> UInt<U, B> { |
| /// Instantiates a singleton representing this unsigned integer. |
| #[inline] |
| pub fn new() -> UInt<U, B> { |
| UInt::default() |
| } |
| } |
| |
| impl<U: Unsigned, B: Bit> Unsigned for UInt<U, B> { |
| const U8: u8 = B::U8 | U::U8 << 1; |
| const U16: u16 = B::U8 as u16 | U::U16 << 1; |
| const U32: u32 = B::U8 as u32 | U::U32 << 1; |
| const U64: u64 = B::U8 as u64 | U::U64 << 1; |
| #[cfg(feature = "i128")] |
| const U128: u128 = B::U8 as u128 | U::U128 << 1; |
| const USIZE: usize = B::U8 as usize | U::USIZE << 1; |
| |
| const I8: i8 = B::U8 as i8 | U::I8 << 1; |
| const I16: i16 = B::U8 as i16 | U::I16 << 1; |
| const I32: i32 = B::U8 as i32 | U::I32 << 1; |
| const I64: i64 = B::U8 as i64 | U::I64 << 1; |
| #[cfg(feature = "i128")] |
| const I128: i128 = B::U8 as i128 | U::I128 << 1; |
| const ISIZE: isize = B::U8 as isize | U::ISIZE << 1; |
| |
| #[inline] |
| fn to_u8() -> u8 { |
| B::to_u8() | U::to_u8() << 1 |
| } |
| #[inline] |
| fn to_u16() -> u16 { |
| u16::from(B::to_u8()) | U::to_u16() << 1 |
| } |
| #[inline] |
| fn to_u32() -> u32 { |
| u32::from(B::to_u8()) | U::to_u32() << 1 |
| } |
| #[inline] |
| fn to_u64() -> u64 { |
| u64::from(B::to_u8()) | U::to_u64() << 1 |
| } |
| #[cfg(feature = "i128")] |
| #[inline] |
| fn to_u128() -> u128 { |
| u128::from(B::to_u8()) | U::to_u128() << 1 |
| } |
| #[inline] |
| fn to_usize() -> usize { |
| usize::from(B::to_u8()) | U::to_usize() << 1 |
| } |
| |
| #[inline] |
| fn to_i8() -> i8 { |
| B::to_u8() as i8 | U::to_i8() << 1 |
| } |
| #[inline] |
| fn to_i16() -> i16 { |
| i16::from(B::to_u8()) | U::to_i16() << 1 |
| } |
| #[inline] |
| fn to_i32() -> i32 { |
| i32::from(B::to_u8()) | U::to_i32() << 1 |
| } |
| #[inline] |
| fn to_i64() -> i64 { |
| i64::from(B::to_u8()) | U::to_i64() << 1 |
| } |
| #[cfg(feature = "i128")] |
| #[inline] |
| fn to_i128() -> i128 { |
| i128::from(B::to_u8()) | U::to_i128() << 1 |
| } |
| #[inline] |
| fn to_isize() -> isize { |
| B::to_u8() as isize | U::to_isize() << 1 |
| } |
| } |
| |
| impl<U: Unsigned, B: Bit> NonZero for UInt<U, B> {} |
| impl Zero for UTerm {} |
| |
| impl PowerOfTwo for UInt<UTerm, B1> {} |
| impl<U: Unsigned + PowerOfTwo> PowerOfTwo for UInt<U, B0> {} |
| |
| // --------------------------------------------------------------------------------------- |
| // Getting length of unsigned integers, which is defined as the number of bits before `UTerm` |
| |
| /// Length of `UTerm` by itself is 0 |
| impl Len for UTerm { |
| type Output = U0; |
| #[inline] |
| fn len(&self) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Length of a bit is 1 |
| impl<U: Unsigned, B: Bit> Len for UInt<U, B> |
| where |
| U: Len, |
| Length<U>: Add<B1>, |
| Add1<Length<U>>: Unsigned, |
| { |
| type Output = Add1<Length<U>>; |
| #[inline] |
| fn len(&self) -> Self::Output { |
| self.msb.len() + B1 |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Adding bits to unsigned integers |
| |
| /// `UTerm + B0 = UTerm` |
| impl Add<B0> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn add(self, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `U + B0 = U` |
| impl<U: Unsigned, B: Bit> Add<B0> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn add(self, _: B0) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UTerm + B1 = UInt<UTerm, B1>` |
| impl Add<B1> for UTerm { |
| type Output = UInt<UTerm, B1>; |
| #[inline] |
| fn add(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<U, B0> + B1 = UInt<U + B1>` |
| impl<U: Unsigned> Add<B1> for UInt<U, B0> { |
| type Output = UInt<U, B1>; |
| #[inline] |
| fn add(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<U, B1> + B1 = UInt<U + B1, B0>` |
| impl<U: Unsigned> Add<B1> for UInt<U, B1> |
| where |
| U: Add<B1>, |
| Add1<U>: Unsigned, |
| { |
| type Output = UInt<Add1<U>, B0>; |
| #[inline] |
| fn add(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Adding unsigned integers |
| |
| /// `UTerm + U = U` |
| impl<U: Unsigned> Add<U> for UTerm { |
| type Output = U; |
| #[inline] |
| fn add(self, rhs: U) -> Self::Output { |
| rhs |
| } |
| } |
| |
| /// `UInt<U, B> + UTerm = UInt<U, B>` |
| impl<U: Unsigned, B: Bit> Add<UTerm> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn add(self, _: UTerm) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<Ul, B0> + UInt<Ur, B0> = UInt<Ul + Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> Add<UInt<Ur, B0>> for UInt<Ul, B0> |
| where |
| Ul: Add<Ur>, |
| { |
| type Output = UInt<Sum<Ul, Ur>, B0>; |
| #[inline] |
| fn add(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb + rhs.msb, |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B0> + UInt<Ur, B1> = UInt<Ul + Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> Add<UInt<Ur, B1>> for UInt<Ul, B0> |
| where |
| Ul: Add<Ur>, |
| { |
| type Output = UInt<Sum<Ul, Ur>, B1>; |
| #[inline] |
| fn add(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb + rhs.msb, |
| lsb: B1, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> + UInt<Ur, B0> = UInt<Ul + Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> Add<UInt<Ur, B0>> for UInt<Ul, B1> |
| where |
| Ul: Add<Ur>, |
| { |
| type Output = UInt<Sum<Ul, Ur>, B1>; |
| #[inline] |
| fn add(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb + rhs.msb, |
| lsb: B1, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> + UInt<Ur, B1> = UInt<(Ul + Ur) + B1, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> Add<UInt<Ur, B1>> for UInt<Ul, B1> |
| where |
| Ul: Add<Ur>, |
| Sum<Ul, Ur>: Add<B1>, |
| { |
| type Output = UInt<Add1<Sum<Ul, Ur>>, B0>; |
| #[inline] |
| fn add(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb + rhs.msb + B1, |
| lsb: B0, |
| } |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Subtracting bits from unsigned integers |
| |
| /// `UTerm - B0 = Term` |
| impl Sub<B0> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn sub(self, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UInt - B0 = UInt` |
| impl<U: Unsigned, B: Bit> Sub<B0> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn sub(self, _: B0) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<U, B1> - B1 = UInt<U, B0>` |
| impl<U: Unsigned, B: Bit> Sub<B1> for UInt<UInt<U, B>, B1> { |
| type Output = UInt<UInt<U, B>, B0>; |
| #[inline] |
| fn sub(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<UTerm, B1> - B1 = UTerm` |
| impl Sub<B1> for UInt<UTerm, B1> { |
| type Output = UTerm; |
| #[inline] |
| fn sub(self, _: B1) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UInt<U, B0> - B1 = UInt<U - B1, B1>` |
| impl<U: Unsigned> Sub<B1> for UInt<U, B0> |
| where |
| U: Sub<B1>, |
| Sub1<U>: Unsigned, |
| { |
| type Output = UInt<Sub1<U>, B1>; |
| #[inline] |
| fn sub(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Subtracting unsigned integers |
| |
| /// `UTerm - UTerm = UTerm` |
| impl Sub<UTerm> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn sub(self, _: UTerm) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Subtracting unsigned integers. We just do our `PrivateSub` and then `Trim` the output. |
| impl<Ul: Unsigned, Bl: Bit, Ur: Unsigned> Sub<Ur> for UInt<Ul, Bl> |
| where |
| UInt<Ul, Bl>: PrivateSub<Ur>, |
| PrivateSubOut<UInt<Ul, Bl>, Ur>: Trim, |
| { |
| type Output = TrimOut<PrivateSubOut<UInt<Ul, Bl>, Ur>>; |
| #[inline] |
| fn sub(self, rhs: Ur) -> Self::Output { |
| self.private_sub(rhs).trim() |
| } |
| } |
| |
| /// `U - UTerm = U` |
| impl<U: Unsigned> PrivateSub<UTerm> for U { |
| type Output = U; |
| |
| #[inline] |
| fn private_sub(self, _: UTerm) -> Self::Output { |
| self |
| } |
| } |
| |
| /// `UInt<Ul, B0> - UInt<Ur, B0> = UInt<Ul - Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateSub<UInt<Ur, B0>> for UInt<Ul, B0> |
| where |
| Ul: PrivateSub<Ur>, |
| { |
| type Output = UInt<PrivateSubOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_sub(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_sub(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B0> - UInt<Ur, B1> = UInt<(Ul - Ur) - B1, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateSub<UInt<Ur, B1>> for UInt<Ul, B0> |
| where |
| Ul: PrivateSub<Ur>, |
| PrivateSubOut<Ul, Ur>: Sub<B1>, |
| { |
| type Output = UInt<Sub1<PrivateSubOut<Ul, Ur>>, B1>; |
| |
| #[inline] |
| fn private_sub(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_sub(rhs.msb) - B1, |
| lsb: B1, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> - UInt<Ur, B0> = UInt<Ul - Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateSub<UInt<Ur, B0>> for UInt<Ul, B1> |
| where |
| Ul: PrivateSub<Ur>, |
| { |
| type Output = UInt<PrivateSubOut<Ul, Ur>, B1>; |
| |
| #[inline] |
| fn private_sub(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_sub(rhs.msb), |
| lsb: B1, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> - UInt<Ur, B1> = UInt<Ul - Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateSub<UInt<Ur, B1>> for UInt<Ul, B1> |
| where |
| Ul: PrivateSub<Ur>, |
| { |
| type Output = UInt<PrivateSubOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_sub(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_sub(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // And unsigned integers |
| |
| /// 0 & X = 0 |
| impl<Ur: Unsigned> BitAnd<Ur> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn bitand(self, _: Ur) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Anding unsigned integers. |
| /// We use our `PrivateAnd` operator and then `Trim` the output. |
| impl<Ul: Unsigned, Bl: Bit, Ur: Unsigned> BitAnd<Ur> for UInt<Ul, Bl> |
| where |
| UInt<Ul, Bl>: PrivateAnd<Ur>, |
| PrivateAndOut<UInt<Ul, Bl>, Ur>: Trim, |
| { |
| type Output = TrimOut<PrivateAndOut<UInt<Ul, Bl>, Ur>>; |
| #[inline] |
| fn bitand(self, rhs: Ur) -> Self::Output { |
| self.private_and(rhs).trim() |
| } |
| } |
| |
| /// `UTerm & X = UTerm` |
| impl<U: Unsigned> PrivateAnd<U> for UTerm { |
| type Output = UTerm; |
| |
| #[inline] |
| fn private_and(self, _: U) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `X & UTerm = UTerm` |
| impl<B: Bit, U: Unsigned> PrivateAnd<UTerm> for UInt<U, B> { |
| type Output = UTerm; |
| |
| #[inline] |
| fn private_and(self, _: UTerm) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UInt<Ul, B0> & UInt<Ur, B0> = UInt<Ul & Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateAnd<UInt<Ur, B0>> for UInt<Ul, B0> |
| where |
| Ul: PrivateAnd<Ur>, |
| { |
| type Output = UInt<PrivateAndOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_and(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_and(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B0> & UInt<Ur, B1> = UInt<Ul & Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateAnd<UInt<Ur, B1>> for UInt<Ul, B0> |
| where |
| Ul: PrivateAnd<Ur>, |
| { |
| type Output = UInt<PrivateAndOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_and(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_and(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> & UInt<Ur, B0> = UInt<Ul & Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateAnd<UInt<Ur, B0>> for UInt<Ul, B1> |
| where |
| Ul: PrivateAnd<Ur>, |
| { |
| type Output = UInt<PrivateAndOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_and(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_and(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> & UInt<Ur, B1> = UInt<Ul & Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateAnd<UInt<Ur, B1>> for UInt<Ul, B1> |
| where |
| Ul: PrivateAnd<Ur>, |
| { |
| type Output = UInt<PrivateAndOut<Ul, Ur>, B1>; |
| |
| #[inline] |
| fn private_and(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_and(rhs.msb), |
| lsb: B1, |
| } |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Or unsigned integers |
| |
| /// `UTerm | X = X` |
| impl<U: Unsigned> BitOr<U> for UTerm { |
| type Output = U; |
| #[inline] |
| fn bitor(self, rhs: U) -> Self::Output { |
| rhs |
| } |
| } |
| |
| /// `X | UTerm = X` |
| impl<B: Bit, U: Unsigned> BitOr<UTerm> for UInt<U, B> { |
| type Output = Self; |
| #[inline] |
| fn bitor(self, _: UTerm) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<Ul, B0> | UInt<Ur, B0> = UInt<Ul | Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> BitOr<UInt<Ur, B0>> for UInt<Ul, B0> |
| where |
| Ul: BitOr<Ur>, |
| { |
| type Output = UInt<<Ul as BitOr<Ur>>::Output, B0>; |
| #[inline] |
| fn bitor(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.bitor(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B0> | UInt<Ur, B1> = UInt<Ul | Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> BitOr<UInt<Ur, B1>> for UInt<Ul, B0> |
| where |
| Ul: BitOr<Ur>, |
| { |
| type Output = UInt<Or<Ul, Ur>, B1>; |
| #[inline] |
| fn bitor(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.bitor(rhs.msb), |
| lsb: self.lsb.bitor(rhs.lsb), |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> | UInt<Ur, B0> = UInt<Ul | Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> BitOr<UInt<Ur, B0>> for UInt<Ul, B1> |
| where |
| Ul: BitOr<Ur>, |
| { |
| type Output = UInt<Or<Ul, Ur>, B1>; |
| #[inline] |
| fn bitor(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.bitor(rhs.msb), |
| lsb: self.lsb.bitor(rhs.lsb), |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> | UInt<Ur, B1> = UInt<Ul | Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> BitOr<UInt<Ur, B1>> for UInt<Ul, B1> |
| where |
| Ul: BitOr<Ur>, |
| { |
| type Output = UInt<Or<Ul, Ur>, B1>; |
| #[inline] |
| fn bitor(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.bitor(rhs.msb), |
| lsb: self.lsb.bitor(rhs.lsb), |
| } |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Xor unsigned integers |
| |
| /// 0 ^ X = X |
| impl<Ur: Unsigned> BitXor<Ur> for UTerm { |
| type Output = Ur; |
| #[inline] |
| fn bitxor(self, rhs: Ur) -> Self::Output { |
| rhs |
| } |
| } |
| |
| /// Xoring unsigned integers. |
| /// We use our `PrivateXor` operator and then `Trim` the output. |
| impl<Ul: Unsigned, Bl: Bit, Ur: Unsigned> BitXor<Ur> for UInt<Ul, Bl> |
| where |
| UInt<Ul, Bl>: PrivateXor<Ur>, |
| PrivateXorOut<UInt<Ul, Bl>, Ur>: Trim, |
| { |
| type Output = TrimOut<PrivateXorOut<UInt<Ul, Bl>, Ur>>; |
| #[inline] |
| fn bitxor(self, rhs: Ur) -> Self::Output { |
| self.private_xor(rhs).trim() |
| } |
| } |
| |
| /// `UTerm ^ X = X` |
| impl<U: Unsigned> PrivateXor<U> for UTerm { |
| type Output = U; |
| |
| #[inline] |
| fn private_xor(self, rhs: U) -> Self::Output { |
| rhs |
| } |
| } |
| |
| /// `X ^ UTerm = X` |
| impl<B: Bit, U: Unsigned> PrivateXor<UTerm> for UInt<U, B> { |
| type Output = Self; |
| |
| #[inline] |
| fn private_xor(self, _: UTerm) -> Self::Output { |
| self |
| } |
| } |
| |
| /// `UInt<Ul, B0> ^ UInt<Ur, B0> = UInt<Ul ^ Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateXor<UInt<Ur, B0>> for UInt<Ul, B0> |
| where |
| Ul: PrivateXor<Ur>, |
| { |
| type Output = UInt<PrivateXorOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_xor(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_xor(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B0> ^ UInt<Ur, B1> = UInt<Ul ^ Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateXor<UInt<Ur, B1>> for UInt<Ul, B0> |
| where |
| Ul: PrivateXor<Ur>, |
| { |
| type Output = UInt<PrivateXorOut<Ul, Ur>, B1>; |
| |
| #[inline] |
| fn private_xor(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_xor(rhs.msb), |
| lsb: B1, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> ^ UInt<Ur, B0> = UInt<Ul ^ Ur, B1>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateXor<UInt<Ur, B0>> for UInt<Ul, B1> |
| where |
| Ul: PrivateXor<Ur>, |
| { |
| type Output = UInt<PrivateXorOut<Ul, Ur>, B1>; |
| |
| #[inline] |
| fn private_xor(self, rhs: UInt<Ur, B0>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_xor(rhs.msb), |
| lsb: B1, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> ^ UInt<Ur, B1> = UInt<Ul ^ Ur, B0>` |
| impl<Ul: Unsigned, Ur: Unsigned> PrivateXor<UInt<Ur, B1>> for UInt<Ul, B1> |
| where |
| Ul: PrivateXor<Ur>, |
| { |
| type Output = UInt<PrivateXorOut<Ul, Ur>, B0>; |
| |
| #[inline] |
| fn private_xor(self, rhs: UInt<Ur, B1>) -> Self::Output { |
| UInt { |
| msb: self.msb.private_xor(rhs.msb), |
| lsb: B0, |
| } |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Shl unsigned integers |
| |
| /// Shifting `UTerm` by a 0 bit: `UTerm << B0 = UTerm` |
| impl Shl<B0> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn shl(self, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Shifting `UTerm` by a 1 bit: `UTerm << B1 = UTerm` |
| impl Shl<B1> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn shl(self, _: B1) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Shifting left any unsigned by a zero bit: `U << B0 = U` |
| impl<U: Unsigned, B: Bit> Shl<B0> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn shl(self, _: B0) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// Shifting left a `UInt` by a one bit: `UInt<U, B> << B1 = UInt<UInt<U, B>, B0>` |
| impl<U: Unsigned, B: Bit> Shl<B1> for UInt<U, B> { |
| type Output = UInt<UInt<U, B>, B0>; |
| #[inline] |
| fn shl(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// Shifting left `UInt` by `UTerm`: `UInt<U, B> << UTerm = UInt<U, B>` |
| impl<U: Unsigned, B: Bit> Shl<UTerm> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn shl(self, _: UTerm) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// Shifting left `UTerm` by an unsigned integer: `UTerm << U = UTerm` |
| impl<U: Unsigned> Shl<U> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn shl(self, _: U) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Shifting left `UInt` by `UInt`: `X << Y` = `UInt(X, B0) << (Y - 1)` |
| impl<U: Unsigned, B: Bit, Ur: Unsigned, Br: Bit> Shl<UInt<Ur, Br>> for UInt<U, B> |
| where |
| UInt<Ur, Br>: Sub<B1>, |
| UInt<UInt<U, B>, B0>: Shl<Sub1<UInt<Ur, Br>>>, |
| { |
| type Output = Shleft<UInt<UInt<U, B>, B0>, Sub1<UInt<Ur, Br>>>; |
| #[inline] |
| fn shl(self, rhs: UInt<Ur, Br>) -> Self::Output { |
| (UInt { msb: self, lsb: B0 }).shl(rhs - B1) |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Shr unsigned integers |
| |
| /// Shifting right a `UTerm` by an unsigned integer: `UTerm >> U = UTerm` |
| impl<U: Unsigned> Shr<U> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn shr(self, _: U) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Shifting right `UInt` by `UTerm`: `UInt<U, B> >> UTerm = UInt<U, B>` |
| impl<U: Unsigned, B: Bit> Shr<UTerm> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn shr(self, _: UTerm) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// Shifting right `UTerm` by a 0 bit: `UTerm >> B0 = UTerm` |
| impl Shr<B0> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn shr(self, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Shifting right `UTerm` by a 1 bit: `UTerm >> B1 = UTerm` |
| impl Shr<B1> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn shr(self, _: B1) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// Shifting right any unsigned by a zero bit: `U >> B0 = U` |
| impl<U: Unsigned, B: Bit> Shr<B0> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn shr(self, _: B0) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// Shifting right a `UInt` by a 1 bit: `UInt<U, B> >> B1 = U` |
| impl<U: Unsigned, B: Bit> Shr<B1> for UInt<U, B> { |
| type Output = U; |
| #[inline] |
| fn shr(self, _: B1) -> Self::Output { |
| self.msb |
| } |
| } |
| |
| /// Shifting right `UInt` by `UInt`: `UInt(U, B) >> Y` = `U >> (Y - 1)` |
| impl<U: Unsigned, B: Bit, Ur: Unsigned, Br: Bit> Shr<UInt<Ur, Br>> for UInt<U, B> |
| where |
| UInt<Ur, Br>: Sub<B1>, |
| U: Shr<Sub1<UInt<Ur, Br>>>, |
| { |
| type Output = Shright<U, Sub1<UInt<Ur, Br>>>; |
| #[inline] |
| fn shr(self, rhs: UInt<Ur, Br>) -> Self::Output { |
| self.msb.shr(rhs - B1) |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Multiply unsigned integers |
| |
| /// `UInt * B0 = UTerm` |
| impl<U: Unsigned, B: Bit> Mul<B0> for UInt<U, B> { |
| type Output = UTerm; |
| #[inline] |
| fn mul(self, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UTerm * B0 = UTerm` |
| impl Mul<B0> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn mul(self, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UTerm * B1 = UTerm` |
| impl Mul<B1> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn mul(self, _: B1) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UInt * B1 = UInt` |
| impl<U: Unsigned, B: Bit> Mul<B1> for UInt<U, B> { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn mul(self, _: B1) -> Self::Output { |
| UInt::new() |
| } |
| } |
| |
| /// `UInt<U, B> * UTerm = UTerm` |
| impl<U: Unsigned, B: Bit> Mul<UTerm> for UInt<U, B> { |
| type Output = UTerm; |
| #[inline] |
| fn mul(self, _: UTerm) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UTerm * U = UTerm` |
| impl<U: Unsigned> Mul<U> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn mul(self, _: U) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| /// `UInt<Ul, B0> * UInt<Ur, B> = UInt<(Ul * UInt<Ur, B>), B0>` |
| impl<Ul: Unsigned, B: Bit, Ur: Unsigned> Mul<UInt<Ur, B>> for UInt<Ul, B0> |
| where |
| Ul: Mul<UInt<Ur, B>>, |
| { |
| type Output = UInt<Prod<Ul, UInt<Ur, B>>, B0>; |
| #[inline] |
| fn mul(self, rhs: UInt<Ur, B>) -> Self::Output { |
| UInt { |
| msb: self.msb * rhs, |
| lsb: B0, |
| } |
| } |
| } |
| |
| /// `UInt<Ul, B1> * UInt<Ur, B> = UInt<(Ul * UInt<Ur, B>), B0> + UInt<Ur, B>` |
| impl<Ul: Unsigned, B: Bit, Ur: Unsigned> Mul<UInt<Ur, B>> for UInt<Ul, B1> |
| where |
| Ul: Mul<UInt<Ur, B>>, |
| UInt<Prod<Ul, UInt<Ur, B>>, B0>: Add<UInt<Ur, B>>, |
| { |
| type Output = Sum<UInt<Prod<Ul, UInt<Ur, B>>, B0>, UInt<Ur, B>>; |
| #[inline] |
| fn mul(self, rhs: UInt<Ur, B>) -> Self::Output { |
| UInt { |
| msb: self.msb * rhs, |
| lsb: B0, |
| } + rhs |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Compare unsigned integers |
| |
| /// Zero == Zero |
| impl Cmp<UTerm> for UTerm { |
| type Output = Equal; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, _: &UTerm) -> Self::Output { |
| Equal |
| } |
| } |
| |
| /// Nonzero > Zero |
| impl<U: Unsigned, B: Bit> Cmp<UTerm> for UInt<U, B> { |
| type Output = Greater; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, _: &UTerm) -> Self::Output { |
| Greater |
| } |
| } |
| |
| /// Zero < Nonzero |
| impl<U: Unsigned, B: Bit> Cmp<UInt<U, B>> for UTerm { |
| type Output = Less; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, _: &UInt<U, B>) -> Self::Output { |
| Less |
| } |
| } |
| |
| /// `UInt<Ul, B0>` cmp with `UInt<Ur, B0>`: `SoFar` is `Equal` |
| impl<Ul: Unsigned, Ur: Unsigned> Cmp<UInt<Ur, B0>> for UInt<Ul, B0> |
| where |
| Ul: PrivateCmp<Ur, Equal>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, Equal>; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, rhs: &UInt<Ur, B0>) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, Equal) |
| } |
| } |
| |
| /// `UInt<Ul, B1>` cmp with `UInt<Ur, B1>`: `SoFar` is `Equal` |
| impl<Ul: Unsigned, Ur: Unsigned> Cmp<UInt<Ur, B1>> for UInt<Ul, B1> |
| where |
| Ul: PrivateCmp<Ur, Equal>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, Equal>; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, rhs: &UInt<Ur, B1>) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, Equal) |
| } |
| } |
| |
| /// `UInt<Ul, B0>` cmp with `UInt<Ur, B1>`: `SoFar` is `Less` |
| impl<Ul: Unsigned, Ur: Unsigned> Cmp<UInt<Ur, B1>> for UInt<Ul, B0> |
| where |
| Ul: PrivateCmp<Ur, Less>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, Less>; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, rhs: &UInt<Ur, B1>) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, Less) |
| } |
| } |
| |
| /// `UInt<Ul, B1>` cmp with `UInt<Ur, B0>`: `SoFar` is `Greater` |
| impl<Ul: Unsigned, Ur: Unsigned> Cmp<UInt<Ur, B0>> for UInt<Ul, B1> |
| where |
| Ul: PrivateCmp<Ur, Greater>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, Greater>; |
| |
| #[inline] |
| fn compare<IM: InternalMarker>(&self, rhs: &UInt<Ur, B0>) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, Greater) |
| } |
| } |
| |
| /// Comparing non-terimal bits, with both having bit `B0`. |
| /// These are `Equal`, so we propogate `SoFar`. |
| impl<Ul, Ur, SoFar> PrivateCmp<UInt<Ur, B0>, SoFar> for UInt<Ul, B0> |
| where |
| Ul: Unsigned, |
| Ur: Unsigned, |
| SoFar: Ord, |
| Ul: PrivateCmp<Ur, SoFar>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, SoFar>; |
| |
| #[inline] |
| fn private_cmp(&self, rhs: &UInt<Ur, B0>, so_far: SoFar) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, so_far) |
| } |
| } |
| |
| /// Comparing non-terimal bits, with both having bit `B1`. |
| /// These are `Equal`, so we propogate `SoFar`. |
| impl<Ul, Ur, SoFar> PrivateCmp<UInt<Ur, B1>, SoFar> for UInt<Ul, B1> |
| where |
| Ul: Unsigned, |
| Ur: Unsigned, |
| SoFar: Ord, |
| Ul: PrivateCmp<Ur, SoFar>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, SoFar>; |
| |
| #[inline] |
| fn private_cmp(&self, rhs: &UInt<Ur, B1>, so_far: SoFar) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, so_far) |
| } |
| } |
| |
| /// Comparing non-terimal bits, with `Lhs` having bit `B0` and `Rhs` having bit `B1`. |
| /// `SoFar`, Lhs is `Less`. |
| impl<Ul, Ur, SoFar> PrivateCmp<UInt<Ur, B1>, SoFar> for UInt<Ul, B0> |
| where |
| Ul: Unsigned, |
| Ur: Unsigned, |
| SoFar: Ord, |
| Ul: PrivateCmp<Ur, Less>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, Less>; |
| |
| #[inline] |
| fn private_cmp(&self, rhs: &UInt<Ur, B1>, _: SoFar) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, Less) |
| } |
| } |
| |
| /// Comparing non-terimal bits, with `Lhs` having bit `B1` and `Rhs` having bit `B0`. |
| /// `SoFar`, Lhs is `Greater`. |
| impl<Ul, Ur, SoFar> PrivateCmp<UInt<Ur, B0>, SoFar> for UInt<Ul, B1> |
| where |
| Ul: Unsigned, |
| Ur: Unsigned, |
| SoFar: Ord, |
| Ul: PrivateCmp<Ur, Greater>, |
| { |
| type Output = PrivateCmpOut<Ul, Ur, Greater>; |
| |
| #[inline] |
| fn private_cmp(&self, rhs: &UInt<Ur, B0>, _: SoFar) -> Self::Output { |
| self.msb.private_cmp(&rhs.msb, Greater) |
| } |
| } |
| |
| /// Got to the end of just the `Lhs`. It's `Less`. |
| impl<U: Unsigned, B: Bit, SoFar: Ord> PrivateCmp<UInt<U, B>, SoFar> for UTerm { |
| type Output = Less; |
| |
| #[inline] |
| fn private_cmp(&self, _: &UInt<U, B>, _: SoFar) -> Self::Output { |
| Less |
| } |
| } |
| |
| /// Got to the end of just the `Rhs`. `Lhs` is `Greater`. |
| impl<U: Unsigned, B: Bit, SoFar: Ord> PrivateCmp<UTerm, SoFar> for UInt<U, B> { |
| type Output = Greater; |
| |
| #[inline] |
| fn private_cmp(&self, _: &UTerm, _: SoFar) -> Self::Output { |
| Greater |
| } |
| } |
| |
| /// Got to the end of both! Return `SoFar` |
| impl<SoFar: Ord> PrivateCmp<UTerm, SoFar> for UTerm { |
| type Output = SoFar; |
| |
| #[inline] |
| fn private_cmp(&self, _: &UTerm, so_far: SoFar) -> Self::Output { |
| so_far |
| } |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Getting difference in number of bits |
| |
| impl<Ul, Bl, Ur, Br> BitDiff<UInt<Ur, Br>> for UInt<Ul, Bl> |
| where |
| Ul: Unsigned, |
| Bl: Bit, |
| Ur: Unsigned, |
| Br: Bit, |
| Ul: BitDiff<Ur>, |
| { |
| type Output = BitDiffOut<Ul, Ur>; |
| } |
| |
| impl<Ul> BitDiff<UTerm> for Ul |
| where |
| Ul: Unsigned + Len, |
| { |
| type Output = Length<Ul>; |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Shifting one number until it's the size of another |
| use crate::private::ShiftDiff; |
| impl<Ul: Unsigned, Ur: Unsigned> ShiftDiff<Ur> for Ul |
| where |
| Ur: BitDiff<Ul>, |
| Ul: Shl<BitDiffOut<Ur, Ul>>, |
| { |
| type Output = Shleft<Ul, BitDiffOut<Ur, Ul>>; |
| } |
| |
| // --------------------------------------------------------------------------------------- |
| // Powers of unsigned integers |
| |
| /// X^N |
| impl<X: Unsigned, N: Unsigned> Pow<N> for X |
| where |
| X: PrivatePow<U1, N>, |
| { |
| type Output = PrivatePowOut<X, U1, N>; |
| #[inline] |
| fn powi(self, n: N) -> Self::Output { |
| self.private_pow(U1::new(), n) |
| } |
| } |
| |
| impl<Y: Unsigned, X: Unsigned> PrivatePow<Y, U0> for X { |
| type Output = Y; |
| |
| #[inline] |
| fn private_pow(self, y: Y, _: U0) -> Self::Output { |
| y |
| } |
| } |
| |
| impl<Y: Unsigned, X: Unsigned> PrivatePow<Y, U1> for X |
| where |
| X: Mul<Y>, |
| { |
| type Output = Prod<X, Y>; |
| |
| #[inline] |
| fn private_pow(self, y: Y, _: U1) -> Self::Output { |
| self * y |
| } |
| } |
| |
| /// N is even |
| impl<Y: Unsigned, U: Unsigned, B: Bit, X: Unsigned> PrivatePow<Y, UInt<UInt<U, B>, B0>> for X |
| where |
| X: Mul, |
| Square<X>: PrivatePow<Y, UInt<U, B>>, |
| { |
| type Output = PrivatePowOut<Square<X>, Y, UInt<U, B>>; |
| |
| #[inline] |
| fn private_pow(self, y: Y, n: UInt<UInt<U, B>, B0>) -> Self::Output { |
| (self * self).private_pow(y, n.msb) |
| } |
| } |
| |
| /// N is odd |
| impl<Y: Unsigned, U: Unsigned, B: Bit, X: Unsigned> PrivatePow<Y, UInt<UInt<U, B>, B1>> for X |
| where |
| X: Mul + Mul<Y>, |
| Square<X>: PrivatePow<Prod<X, Y>, UInt<U, B>>, |
| { |
| type Output = PrivatePowOut<Square<X>, Prod<X, Y>, UInt<U, B>>; |
| |
| #[inline] |
| fn private_pow(self, y: Y, n: UInt<UInt<U, B>, B1>) -> Self::Output { |
| (self * self).private_pow(self * y, n.msb) |
| } |
| } |
| |
| //------------------------------------------ |
| // Greatest Common Divisor |
| |
| /// The even number 2*N |
| #[allow(unused)] // Silence spurious warning on older versions of rust |
| type Even<N> = UInt<N, B0>; |
| |
| /// The odd number 2*N + 1 |
| type Odd<N> = UInt<N, B1>; |
| |
| /// gcd(0, 0) = 0 |
| impl Gcd<U0> for U0 { |
| type Output = U0; |
| } |
| |
| /// gcd(x, 0) = x |
| impl<X> Gcd<U0> for X |
| where |
| X: Unsigned + NonZero, |
| { |
| type Output = X; |
| } |
| |
| /// gcd(0, y) = y |
| impl<Y> Gcd<Y> for U0 |
| where |
| Y: Unsigned + NonZero, |
| { |
| type Output = Y; |
| } |
| |
| /// gcd(x, y) = 2*gcd(x/2, y/2) if both x and y even |
| impl<Xp, Yp> Gcd<Even<Yp>> for Even<Xp> |
| where |
| Xp: Gcd<Yp>, |
| Even<Xp>: NonZero, |
| Even<Yp>: NonZero, |
| { |
| type Output = UInt<Gcf<Xp, Yp>, B0>; |
| } |
| |
| /// gcd(x, y) = gcd(x, y/2) if x odd and y even |
| impl<Xp, Yp> Gcd<Even<Yp>> for Odd<Xp> |
| where |
| Odd<Xp>: Gcd<Yp>, |
| Even<Yp>: NonZero, |
| { |
| type Output = Gcf<Odd<Xp>, Yp>; |
| } |
| |
| /// gcd(x, y) = gcd(x/2, y) if x even and y odd |
| impl<Xp, Yp> Gcd<Odd<Yp>> for Even<Xp> |
| where |
| Xp: Gcd<Odd<Yp>>, |
| Even<Xp>: NonZero, |
| { |
| type Output = Gcf<Xp, Odd<Yp>>; |
| } |
| |
| /// gcd(x, y) = gcd([max(x, y) - min(x, y)], min(x, y)) if both x and y odd |
| /// |
| /// This will immediately invoke the case for x even and y odd because the difference of two odd |
| /// numbers is an even number. |
| impl<Xp, Yp> Gcd<Odd<Yp>> for Odd<Xp> |
| where |
| Odd<Xp>: Max<Odd<Yp>> + Min<Odd<Yp>>, |
| Odd<Yp>: Max<Odd<Xp>> + Min<Odd<Xp>>, |
| Maximum<Odd<Xp>, Odd<Yp>>: Sub<Minimum<Odd<Xp>, Odd<Yp>>>, |
| Diff<Maximum<Odd<Xp>, Odd<Yp>>, Minimum<Odd<Xp>, Odd<Yp>>>: Gcd<Minimum<Odd<Xp>, Odd<Yp>>>, |
| { |
| type Output = |
| Gcf<Diff<Maximum<Odd<Xp>, Odd<Yp>>, Minimum<Odd<Xp>, Odd<Yp>>>, Minimum<Odd<Xp>, Odd<Yp>>>; |
| } |
| |
| #[cfg(test)] |
| mod gcd_tests { |
| use super::*; |
| use crate::consts::*; |
| |
| macro_rules! gcd_test { |
| ( |
| $( $a:ident, $b:ident => $c:ident ),* $(,)* |
| ) => { |
| $( |
| assert_eq!(<Gcf<$a, $b> as Unsigned>::to_usize(), $c::to_usize()); |
| assert_eq!(<Gcf<$b, $a> as Unsigned>::to_usize(), $c::to_usize()); |
| )* |
| } |
| } |
| |
| #[test] |
| fn gcd() { |
| gcd_test! { |
| U0, U0 => U0, |
| U0, U42 => U42, |
| U12, U8 => U4, |
| U13, U1013 => U1, // Two primes |
| U9, U26 => U1, // Not prime but coprime |
| U143, U273 => U13, |
| U117, U273 => U39, |
| } |
| } |
| } |
| |
| // ----------------------------------------- |
| // GetBit |
| |
| #[allow(missing_docs)] |
| pub trait GetBit<I> { |
| #[allow(missing_docs)] |
| type Output; |
| |
| #[doc(hidden)] |
| fn get_bit<IM: InternalMarker>(&self, _: &I) -> Self::Output; |
| } |
| |
| #[allow(missing_docs)] |
| pub type GetBitOut<N, I> = <N as GetBit<I>>::Output; |
| |
| // Base case |
| impl<Un, Bn> GetBit<U0> for UInt<Un, Bn> |
| where |
| Bn: Copy, |
| { |
| type Output = Bn; |
| |
| #[inline] |
| fn get_bit<IM: InternalMarker>(&self, _: &U0) -> Self::Output { |
| self.lsb |
| } |
| } |
| |
| // Recursion case |
| impl<Un, Bn, Ui, Bi> GetBit<UInt<Ui, Bi>> for UInt<Un, Bn> |
| where |
| UInt<Ui, Bi>: Copy + Sub<B1>, |
| Un: GetBit<Sub1<UInt<Ui, Bi>>>, |
| { |
| type Output = GetBitOut<Un, Sub1<UInt<Ui, Bi>>>; |
| |
| #[inline] |
| fn get_bit<IM: InternalMarker>(&self, i: &UInt<Ui, Bi>) -> Self::Output { |
| self.msb.get_bit::<Internal>(&(*i - B1)) |
| } |
| } |
| |
| // Ran out of bits |
| impl<I> GetBit<I> for UTerm { |
| type Output = B0; |
| |
| #[inline] |
| fn get_bit<IM: InternalMarker>(&self, _: &I) -> Self::Output { |
| B0 |
| } |
| } |
| |
| #[test] |
| fn test_get_bit() { |
| use crate::consts::*; |
| use crate::Same; |
| type T1 = <GetBitOut<U2, U0> as Same<B0>>::Output; |
| type T2 = <GetBitOut<U2, U1> as Same<B1>>::Output; |
| type T3 = <GetBitOut<U2, U2> as Same<B0>>::Output; |
| |
| <T1 as Bit>::to_bool(); |
| <T2 as Bit>::to_bool(); |
| <T3 as Bit>::to_bool(); |
| } |
| |
| // ----------------------------------------- |
| // SetBit |
| |
| /// A **type operator** that, when implemented for unsigned integer `N`, sets the bit at position |
| /// `I` to `B`. |
| pub trait SetBit<I, B> { |
| #[allow(missing_docs)] |
| type Output; |
| |
| #[doc(hidden)] |
| fn set_bit<IM: InternalMarker>(self, _: I, _: B) -> Self::Output; |
| } |
| /// Alias for the result of calling `SetBit`: `SetBitOut<N, I, B> = <N as SetBit<I, B>>::Output`. |
| pub type SetBitOut<N, I, B> = <N as SetBit<I, B>>::Output; |
| |
| use crate::private::{PrivateSetBit, PrivateSetBitOut}; |
| |
| // Call private one then trim it |
| impl<N, I, B> SetBit<I, B> for N |
| where |
| N: PrivateSetBit<I, B>, |
| PrivateSetBitOut<N, I, B>: Trim, |
| { |
| type Output = TrimOut<PrivateSetBitOut<N, I, B>>; |
| |
| #[inline] |
| fn set_bit<IM: InternalMarker>(self, i: I, b: B) -> Self::Output { |
| self.private_set_bit(i, b).trim() |
| } |
| } |
| |
| // Base case |
| impl<Un, Bn, B> PrivateSetBit<U0, B> for UInt<Un, Bn> { |
| type Output = UInt<Un, B>; |
| |
| #[inline] |
| fn private_set_bit(self, _: U0, b: B) -> Self::Output { |
| UInt { |
| msb: self.msb, |
| lsb: b, |
| } |
| } |
| } |
| |
| // Recursion case |
| impl<Un, Bn, Ui, Bi, B> PrivateSetBit<UInt<Ui, Bi>, B> for UInt<Un, Bn> |
| where |
| UInt<Ui, Bi>: Sub<B1>, |
| Un: PrivateSetBit<Sub1<UInt<Ui, Bi>>, B>, |
| { |
| type Output = UInt<PrivateSetBitOut<Un, Sub1<UInt<Ui, Bi>>, B>, Bn>; |
| |
| #[inline] |
| fn private_set_bit(self, i: UInt<Ui, Bi>, b: B) -> Self::Output { |
| UInt { |
| msb: self.msb.private_set_bit(i - B1, b), |
| lsb: self.lsb, |
| } |
| } |
| } |
| |
| // Ran out of bits, setting B0 |
| impl<I> PrivateSetBit<I, B0> for UTerm { |
| type Output = UTerm; |
| |
| #[inline] |
| fn private_set_bit(self, _: I, _: B0) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| // Ran out of bits, setting B1 |
| impl<I> PrivateSetBit<I, B1> for UTerm |
| where |
| U1: Shl<I>, |
| { |
| type Output = Shleft<U1, I>; |
| |
| #[inline] |
| fn private_set_bit(self, i: I, _: B1) -> Self::Output { |
| <U1 as Shl<I>>::shl(U1::new(), i) |
| } |
| } |
| |
| #[test] |
| fn test_set_bit() { |
| use crate::consts::*; |
| use crate::Same; |
| type T1 = <SetBitOut<U2, U0, B0> as Same<U2>>::Output; |
| type T2 = <SetBitOut<U2, U0, B1> as Same<U3>>::Output; |
| type T3 = <SetBitOut<U2, U1, B0> as Same<U0>>::Output; |
| type T4 = <SetBitOut<U2, U1, B1> as Same<U2>>::Output; |
| type T5 = <SetBitOut<U2, U2, B0> as Same<U2>>::Output; |
| type T6 = <SetBitOut<U2, U2, B1> as Same<U6>>::Output; |
| type T7 = <SetBitOut<U2, U3, B0> as Same<U2>>::Output; |
| type T8 = <SetBitOut<U2, U3, B1> as Same<U10>>::Output; |
| type T9 = <SetBitOut<U2, U4, B0> as Same<U2>>::Output; |
| type T10 = <SetBitOut<U2, U4, B1> as Same<U18>>::Output; |
| |
| type T11 = <SetBitOut<U3, U0, B0> as Same<U2>>::Output; |
| |
| <T1 as Unsigned>::to_u32(); |
| <T2 as Unsigned>::to_u32(); |
| <T3 as Unsigned>::to_u32(); |
| <T4 as Unsigned>::to_u32(); |
| <T5 as Unsigned>::to_u32(); |
| <T6 as Unsigned>::to_u32(); |
| <T7 as Unsigned>::to_u32(); |
| <T8 as Unsigned>::to_u32(); |
| <T9 as Unsigned>::to_u32(); |
| <T10 as Unsigned>::to_u32(); |
| <T11 as Unsigned>::to_u32(); |
| } |
| |
| // ----------------------------------------- |
| |
| // Division algorithm: |
| // We have N / D: |
| // let Q = 0, R = 0 |
| // NBits = len(N) |
| // for I in NBits-1..0: |
| // R <<=1 |
| // R[0] = N[i] |
| // let C = R.cmp(D) |
| // if C == Equal or Greater: |
| // R -= D |
| // Q[i] = 1 |
| |
| #[cfg(tests)] |
| mod tests { |
| macro_rules! test_div { |
| ($a:ident / $b:ident = $c:ident) => {{ |
| type R = Quot<$a, $b>; |
| assert_eq!(<R as Unsigned>::to_usize(), $c::to_usize()); |
| }}; |
| } |
| #[test] |
| fn test_div() { |
| use crate::consts::*; |
| use crate::{Quot, Same}; |
| |
| test_div!(U0 / U1 = U0); |
| test_div!(U1 / U1 = U1); |
| test_div!(U2 / U1 = U2); |
| test_div!(U3 / U1 = U3); |
| test_div!(U4 / U1 = U4); |
| |
| test_div!(U0 / U2 = U0); |
| test_div!(U1 / U2 = U0); |
| test_div!(U2 / U2 = U1); |
| test_div!(U3 / U2 = U1); |
| test_div!(U4 / U2 = U2); |
| test_div!(U6 / U2 = U3); |
| test_div!(U7 / U2 = U3); |
| |
| type T = <SetBitOut<U0, U1, B1> as Same<U2>>::Output; |
| <T as Unsigned>::to_u32(); |
| } |
| } |
| // ----------------------------------------- |
| // Div |
| use core::ops::Div; |
| |
| // 0 // N |
| impl<Ur: Unsigned, Br: Bit> Div<UInt<Ur, Br>> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn div(self, _: UInt<Ur, Br>) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| // M // N |
| impl<Ul: Unsigned, Bl: Bit, Ur: Unsigned, Br: Bit> Div<UInt<Ur, Br>> for UInt<Ul, Bl> |
| where |
| UInt<Ul, Bl>: Len, |
| Length<UInt<Ul, Bl>>: Sub<B1>, |
| (): PrivateDiv<UInt<Ul, Bl>, UInt<Ur, Br>, U0, U0, Sub1<Length<UInt<Ul, Bl>>>>, |
| { |
| type Output = PrivateDivQuot<UInt<Ul, Bl>, UInt<Ur, Br>, U0, U0, Sub1<Length<UInt<Ul, Bl>>>>; |
| #[inline] |
| #[cfg_attr(feature = "cargo-clippy", allow(clippy::suspicious_arithmetic_impl))] |
| fn div(self, rhs: UInt<Ur, Br>) -> Self::Output { |
| ().private_div_quotient(self, rhs, U0::new(), U0::new(), self.len() - B1) |
| } |
| } |
| |
| // ----------------------------------------- |
| // Rem |
| use core::ops::Rem; |
| |
| // 0 % N |
| impl<Ur: Unsigned, Br: Bit> Rem<UInt<Ur, Br>> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn rem(self, _: UInt<Ur, Br>) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| // M % N |
| impl<Ul: Unsigned, Bl: Bit, Ur: Unsigned, Br: Bit> Rem<UInt<Ur, Br>> for UInt<Ul, Bl> |
| where |
| UInt<Ul, Bl>: Len, |
| Length<UInt<Ul, Bl>>: Sub<B1>, |
| (): PrivateDiv<UInt<Ul, Bl>, UInt<Ur, Br>, U0, U0, Sub1<Length<UInt<Ul, Bl>>>>, |
| { |
| type Output = PrivateDivRem<UInt<Ul, Bl>, UInt<Ur, Br>, U0, U0, Sub1<Length<UInt<Ul, Bl>>>>; |
| #[inline] |
| fn rem(self, rhs: UInt<Ur, Br>) -> Self::Output { |
| ().private_div_remainder(self, rhs, UTerm, UTerm, self.len() - B1) |
| } |
| } |
| |
| // ----------------------------------------- |
| // PrivateDiv |
| use crate::private::{PrivateDiv, PrivateDivQuot, PrivateDivRem}; |
| |
| use crate::Compare; |
| // R == 0: We set R = UInt<UTerm, N[i]>, then call out to PrivateDivIf for the if statement |
| impl<N, D, Q, I> PrivateDiv<N, D, Q, U0, I> for () |
| where |
| N: GetBit<I>, |
| UInt<UTerm, GetBitOut<N, I>>: Trim, |
| TrimOut<UInt<UTerm, GetBitOut<N, I>>>: Cmp<D>, |
| (): PrivateDivIf< |
| N, |
| D, |
| Q, |
| TrimOut<UInt<UTerm, GetBitOut<N, I>>>, |
| I, |
| Compare<TrimOut<UInt<UTerm, GetBitOut<N, I>>>, D>, |
| >, |
| { |
| type Quotient = PrivateDivIfQuot< |
| N, |
| D, |
| Q, |
| TrimOut<UInt<UTerm, GetBitOut<N, I>>>, |
| I, |
| Compare<TrimOut<UInt<UTerm, GetBitOut<N, I>>>, D>, |
| >; |
| type Remainder = PrivateDivIfRem< |
| N, |
| D, |
| Q, |
| TrimOut<UInt<UTerm, GetBitOut<N, I>>>, |
| I, |
| Compare<TrimOut<UInt<UTerm, GetBitOut<N, I>>>, D>, |
| >; |
| |
| #[inline] |
| fn private_div_quotient(self, n: N, d: D, q: Q, _: U0, i: I) -> Self::Quotient |
| where { |
| let r = (UInt { |
| msb: UTerm, |
| lsb: n.get_bit::<Internal>(&i), |
| }) |
| .trim(); |
| let r_cmp_d = r.compare::<Internal>(&d); |
| ().private_div_if_quotient(n, d, q, r, i, r_cmp_d) |
| } |
| |
| #[inline] |
| fn private_div_remainder(self, n: N, d: D, q: Q, _: U0, i: I) -> Self::Remainder { |
| let r = (UInt { |
| msb: UTerm, |
| lsb: n.get_bit::<Internal>(&i), |
| }) |
| .trim(); |
| let r_cmp_d = r.compare::<Internal>(&d); |
| ().private_div_if_remainder(n, d, q, r, i, r_cmp_d) |
| } |
| } |
| |
| // R > 0: We perform R <<= 1 and R[0] = N[i], then call out to PrivateDivIf for the if statement |
| impl<N, D, Q, Ur, Br, I> PrivateDiv<N, D, Q, UInt<Ur, Br>, I> for () |
| where |
| N: GetBit<I>, |
| UInt<UInt<Ur, Br>, GetBitOut<N, I>>: Cmp<D>, |
| (): PrivateDivIf< |
| N, |
| D, |
| Q, |
| UInt<UInt<Ur, Br>, GetBitOut<N, I>>, |
| I, |
| Compare<UInt<UInt<Ur, Br>, GetBitOut<N, I>>, D>, |
| >, |
| { |
| type Quotient = PrivateDivIfQuot< |
| N, |
| D, |
| Q, |
| UInt<UInt<Ur, Br>, GetBitOut<N, I>>, |
| I, |
| Compare<UInt<UInt<Ur, Br>, GetBitOut<N, I>>, D>, |
| >; |
| type Remainder = PrivateDivIfRem< |
| N, |
| D, |
| Q, |
| UInt<UInt<Ur, Br>, GetBitOut<N, I>>, |
| I, |
| Compare<UInt<UInt<Ur, Br>, GetBitOut<N, I>>, D>, |
| >; |
| |
| #[inline] |
| fn private_div_quotient(self, n: N, d: D, q: Q, r: UInt<Ur, Br>, i: I) -> Self::Quotient { |
| let r = UInt { |
| msb: r, |
| lsb: n.get_bit::<Internal>(&i), |
| }; |
| let r_cmp_d = r.compare::<Internal>(&d); |
| ().private_div_if_quotient(n, d, q, r, i, r_cmp_d) |
| } |
| |
| #[inline] |
| fn private_div_remainder(self, n: N, d: D, q: Q, r: UInt<Ur, Br>, i: I) -> Self::Remainder { |
| let r = UInt { |
| msb: r, |
| lsb: n.get_bit::<Internal>(&i), |
| }; |
| let r_cmp_d = r.compare::<Internal>(&d); |
| ().private_div_if_remainder(n, d, q, r, i, r_cmp_d) |
| } |
| } |
| |
| // ----------------------------------------- |
| // PrivateDivIf |
| |
| use crate::private::{PrivateDivIf, PrivateDivIfQuot, PrivateDivIfRem}; |
| |
| // R < D, I > 0, we do nothing and recurse |
| impl<N, D, Q, R, Ui, Bi> PrivateDivIf<N, D, Q, R, UInt<Ui, Bi>, Less> for () |
| where |
| UInt<Ui, Bi>: Sub<B1>, |
| (): PrivateDiv<N, D, Q, R, Sub1<UInt<Ui, Bi>>>, |
| { |
| type Quotient = PrivateDivQuot<N, D, Q, R, Sub1<UInt<Ui, Bi>>>; |
| type Remainder = PrivateDivRem<N, D, Q, R, Sub1<UInt<Ui, Bi>>>; |
| |
| #[inline] |
| fn private_div_if_quotient( |
| self, |
| n: N, |
| d: D, |
| q: Q, |
| r: R, |
| i: UInt<Ui, Bi>, |
| _: Less, |
| ) -> Self::Quotient |
| where { |
| ().private_div_quotient(n, d, q, r, i - B1) |
| } |
| |
| #[inline] |
| fn private_div_if_remainder( |
| self, |
| n: N, |
| d: D, |
| q: Q, |
| r: R, |
| i: UInt<Ui, Bi>, |
| _: Less, |
| ) -> Self::Remainder |
| where { |
| ().private_div_remainder(n, d, q, r, i - B1) |
| } |
| } |
| |
| // R == D, I > 0, we set R = 0, Q[I] = 1 and recurse |
| impl<N, D, Q, R, Ui, Bi> PrivateDivIf<N, D, Q, R, UInt<Ui, Bi>, Equal> for () |
| where |
| UInt<Ui, Bi>: Copy + Sub<B1>, |
| Q: SetBit<UInt<Ui, Bi>, B1>, |
| (): PrivateDiv<N, D, SetBitOut<Q, UInt<Ui, Bi>, B1>, U0, Sub1<UInt<Ui, Bi>>>, |
| { |
| type Quotient = PrivateDivQuot<N, D, SetBitOut<Q, UInt<Ui, Bi>, B1>, U0, Sub1<UInt<Ui, Bi>>>; |
| type Remainder = PrivateDivRem<N, D, SetBitOut<Q, UInt<Ui, Bi>, B1>, U0, Sub1<UInt<Ui, Bi>>>; |
| |
| #[inline] |
| fn private_div_if_quotient( |
| self, |
| n: N, |
| d: D, |
| q: Q, |
| _: R, |
| i: UInt<Ui, Bi>, |
| _: Equal, |
| ) -> Self::Quotient |
| where { |
| ().private_div_quotient(n, d, q.set_bit::<Internal>(i, B1), U0::new(), i - B1) |
| } |
| |
| #[inline] |
| fn private_div_if_remainder( |
| self, |
| n: N, |
| d: D, |
| q: Q, |
| _: R, |
| i: UInt<Ui, Bi>, |
| _: Equal, |
| ) -> Self::Remainder |
| where { |
| ().private_div_remainder(n, d, q.set_bit::<Internal>(i, B1), U0::new(), i - B1) |
| } |
| } |
| |
| use crate::Diff; |
| // R > D, I > 0, we set R -= D, Q[I] = 1 and recurse |
| impl<N, D, Q, R, Ui, Bi> PrivateDivIf<N, D, Q, R, UInt<Ui, Bi>, Greater> for () |
| where |
| D: Copy, |
| UInt<Ui, Bi>: Copy + Sub<B1>, |
| R: Sub<D>, |
| Q: SetBit<UInt<Ui, Bi>, B1>, |
| (): PrivateDiv<N, D, SetBitOut<Q, UInt<Ui, Bi>, B1>, Diff<R, D>, Sub1<UInt<Ui, Bi>>>, |
| { |
| type Quotient = |
| PrivateDivQuot<N, D, SetBitOut<Q, UInt<Ui, Bi>, B1>, Diff<R, D>, Sub1<UInt<Ui, Bi>>>; |
| type Remainder = |
| PrivateDivRem<N, D, SetBitOut<Q, UInt<Ui, Bi>, B1>, Diff<R, D>, Sub1<UInt<Ui, Bi>>>; |
| |
| #[inline] |
| fn private_div_if_quotient( |
| self, |
| n: N, |
| d: D, |
| q: Q, |
| r: R, |
| i: UInt<Ui, Bi>, |
| _: Greater, |
| ) -> Self::Quotient |
| where { |
| ().private_div_quotient(n, d, q.set_bit::<Internal>(i, B1), r - d, i - B1) |
| } |
| |
| #[inline] |
| fn private_div_if_remainder( |
| self, |
| n: N, |
| d: D, |
| q: Q, |
| r: R, |
| i: UInt<Ui, Bi>, |
| _: Greater, |
| ) -> Self::Remainder |
| where { |
| ().private_div_remainder(n, d, q.set_bit::<Internal>(i, B1), r - d, i - B1) |
| } |
| } |
| |
| // R < D, I == 0: we do nothing, and return |
| impl<N, D, Q, R> PrivateDivIf<N, D, Q, R, U0, Less> for () { |
| type Quotient = Q; |
| type Remainder = R; |
| |
| #[inline] |
| fn private_div_if_quotient(self, _: N, _: D, q: Q, _: R, _: U0, _: Less) -> Self::Quotient { |
| q |
| } |
| |
| #[inline] |
| fn private_div_if_remainder(self, _: N, _: D, _: Q, r: R, _: U0, _: Less) -> Self::Remainder { |
| r |
| } |
| } |
| |
| // R == D, I == 0: we set R = 0, Q[I] = 1, and return |
| impl<N, D, Q, R> PrivateDivIf<N, D, Q, R, U0, Equal> for () |
| where |
| Q: SetBit<U0, B1>, |
| { |
| type Quotient = SetBitOut<Q, U0, B1>; |
| type Remainder = U0; |
| |
| #[inline] |
| fn private_div_if_quotient(self, _: N, _: D, q: Q, _: R, i: U0, _: Equal) -> Self::Quotient { |
| q.set_bit::<Internal>(i, B1) |
| } |
| |
| #[inline] |
| fn private_div_if_remainder(self, _: N, _: D, _: Q, _: R, i: U0, _: Equal) -> Self::Remainder { |
| i |
| } |
| } |
| |
| // R > D, I == 0: We set R -= D, Q[I] = 1, and return |
| impl<N, D, Q, R> PrivateDivIf<N, D, Q, R, U0, Greater> for () |
| where |
| R: Sub<D>, |
| Q: SetBit<U0, B1>, |
| { |
| type Quotient = SetBitOut<Q, U0, B1>; |
| type Remainder = Diff<R, D>; |
| |
| #[inline] |
| fn private_div_if_quotient(self, _: N, _: D, q: Q, _: R, i: U0, _: Greater) -> Self::Quotient { |
| q.set_bit::<Internal>(i, B1) |
| } |
| |
| #[inline] |
| fn private_div_if_remainder( |
| self, |
| _: N, |
| d: D, |
| _: Q, |
| r: R, |
| _: U0, |
| _: Greater, |
| ) -> Self::Remainder { |
| r - d |
| } |
| } |
| |
| // ----------------------------------------- |
| // PartialDiv |
| use crate::{PartialDiv, Quot}; |
| impl<Ur: Unsigned, Br: Bit> PartialDiv<UInt<Ur, Br>> for UTerm { |
| type Output = UTerm; |
| #[inline] |
| fn partial_div(self, _: UInt<Ur, Br>) -> Self::Output { |
| UTerm |
| } |
| } |
| |
| // M / N |
| impl<Ul: Unsigned, Bl: Bit, Ur: Unsigned, Br: Bit> PartialDiv<UInt<Ur, Br>> for UInt<Ul, Bl> |
| where |
| UInt<Ul, Bl>: Div<UInt<Ur, Br>> + Rem<UInt<Ur, Br>, Output = U0>, |
| { |
| type Output = Quot<UInt<Ul, Bl>, UInt<Ur, Br>>; |
| #[inline] |
| fn partial_div(self, rhs: UInt<Ur, Br>) -> Self::Output { |
| self / rhs |
| } |
| } |
| |
| // ----------------------------------------- |
| // PrivateMin |
| use crate::private::{PrivateMin, PrivateMinOut}; |
| |
| impl<U, B, Ur> PrivateMin<Ur, Equal> for UInt<U, B> |
| where |
| Ur: Unsigned, |
| U: Unsigned, |
| B: Bit, |
| { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn private_min(self, _: Ur) -> Self::Output { |
| self |
| } |
| } |
| |
| impl<U, B, Ur> PrivateMin<Ur, Less> for UInt<U, B> |
| where |
| Ur: Unsigned, |
| U: Unsigned, |
| B: Bit, |
| { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn private_min(self, _: Ur) -> Self::Output { |
| self |
| } |
| } |
| |
| impl<U, B, Ur> PrivateMin<Ur, Greater> for UInt<U, B> |
| where |
| Ur: Unsigned, |
| U: Unsigned, |
| B: Bit, |
| { |
| type Output = Ur; |
| #[inline] |
| fn private_min(self, rhs: Ur) -> Self::Output { |
| rhs |
| } |
| } |
| |
| // ----------------------------------------- |
| // Min |
| use crate::Min; |
| |
| impl<U> Min<U> for UTerm |
| where |
| U: Unsigned, |
| { |
| type Output = UTerm; |
| #[inline] |
| fn min(self, _: U) -> Self::Output { |
| self |
| } |
| } |
| |
| impl<U, B, Ur> Min<Ur> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| Ur: Unsigned, |
| UInt<U, B>: Cmp<Ur> + PrivateMin<Ur, Compare<UInt<U, B>, Ur>>, |
| { |
| type Output = PrivateMinOut<UInt<U, B>, Ur, Compare<UInt<U, B>, Ur>>; |
| #[inline] |
| fn min(self, rhs: Ur) -> Self::Output { |
| self.private_min(rhs) |
| } |
| } |
| |
| // ----------------------------------------- |
| // PrivateMax |
| use crate::private::{PrivateMax, PrivateMaxOut}; |
| |
| impl<U, B, Ur> PrivateMax<Ur, Equal> for UInt<U, B> |
| where |
| Ur: Unsigned, |
| U: Unsigned, |
| B: Bit, |
| { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn private_max(self, _: Ur) -> Self::Output { |
| self |
| } |
| } |
| |
| impl<U, B, Ur> PrivateMax<Ur, Less> for UInt<U, B> |
| where |
| Ur: Unsigned, |
| U: Unsigned, |
| B: Bit, |
| { |
| type Output = Ur; |
| #[inline] |
| fn private_max(self, rhs: Ur) -> Self::Output { |
| rhs |
| } |
| } |
| |
| impl<U, B, Ur> PrivateMax<Ur, Greater> for UInt<U, B> |
| where |
| Ur: Unsigned, |
| U: Unsigned, |
| B: Bit, |
| { |
| type Output = UInt<U, B>; |
| #[inline] |
| fn private_max(self, _: Ur) -> Self::Output { |
| self |
| } |
| } |
| |
| // ----------------------------------------- |
| // Max |
| use crate::Max; |
| |
| impl<U> Max<U> for UTerm |
| where |
| U: Unsigned, |
| { |
| type Output = U; |
| #[inline] |
| fn max(self, rhs: U) -> Self::Output { |
| rhs |
| } |
| } |
| |
| impl<U, B, Ur> Max<Ur> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| Ur: Unsigned, |
| UInt<U, B>: Cmp<Ur> + PrivateMax<Ur, Compare<UInt<U, B>, Ur>>, |
| { |
| type Output = PrivateMaxOut<UInt<U, B>, Ur, Compare<UInt<U, B>, Ur>>; |
| #[inline] |
| fn max(self, rhs: Ur) -> Self::Output { |
| self.private_max(rhs) |
| } |
| } |
| |
| // ----------------------------------------- |
| // SquareRoot |
| |
| impl<N> SquareRoot for N |
| where |
| N: PrivateSquareRoot, |
| { |
| type Output = <Self as PrivateSquareRoot>::Output; |
| } |
| |
| // sqrt(0) = 0. |
| impl PrivateSquareRoot for UTerm { |
| type Output = UTerm; |
| } |
| |
| // sqrt(1) = 1. |
| impl PrivateSquareRoot for UInt<UTerm, B1> { |
| type Output = UInt<UTerm, B1>; |
| } |
| |
| // General case of sqrt(Self) where Self >= 2. If a and b are |
| // bit-valued and Self = 4*u + 2*a + b, then the integer-valued |
| // (fractional part truncated) square root of Self is either 2*sqrt(u) |
| // or 2*sqrt(u)+1. Guess and check by comparing (2*sqrt(u)+1)^2 |
| // against Self. Since the `typenum` result of that comparison is a |
| // bit, directly add that bit to 2*sqrt(u). |
| // |
| // Use `Sum<Double<Sqrt<U>>, GrEq<...>>` instead of `UInt<Sqrt<U>, |
| // GrEq<...>>` because `Sqrt<U>` can turn out to be `UTerm` and |
| // `GrEq<...>` can turn out to be `B0`, which would not be a valid |
| // UInt as leading zeros are disallowed. |
| impl<U, Ba, Bb> PrivateSquareRoot for UInt<UInt<U, Ba>, Bb> |
| where |
| U: Unsigned, |
| Ba: Bit, |
| Bb: Bit, |
| U: SquareRoot, |
| Sqrt<U>: Shl<B1>, |
| Double<Sqrt<U>>: Add<B1>, |
| Add1<Double<Sqrt<U>>>: Mul, |
| Self: IsGreaterOrEqual<Square<Add1<Double<Sqrt<U>>>>>, |
| Double<Sqrt<U>>: Add<GrEq<Self, Square<Add1<Double<Sqrt<U>>>>>>, |
| { |
| type Output = Sum<Double<Sqrt<U>>, GrEq<Self, Square<Add1<Double<Sqrt<U>>>>>>; |
| } |
| |
| #[test] |
| fn sqrt_test() { |
| use crate::consts::*; |
| |
| assert_eq!(0, <Sqrt<U0>>::to_u32()); |
| |
| assert_eq!(1, <Sqrt<U1>>::to_u32()); |
| assert_eq!(1, <Sqrt<U2>>::to_u32()); |
| assert_eq!(1, <Sqrt<U3>>::to_u32()); |
| |
| assert_eq!(2, <Sqrt<U4>>::to_u32()); |
| assert_eq!(2, <Sqrt<U5>>::to_u32()); |
| assert_eq!(2, <Sqrt<U6>>::to_u32()); |
| assert_eq!(2, <Sqrt<U7>>::to_u32()); |
| assert_eq!(2, <Sqrt<U8>>::to_u32()); |
| |
| assert_eq!(3, <Sqrt<U9>>::to_u32()); |
| assert_eq!(3, <Sqrt<U10>>::to_u32()); |
| assert_eq!(3, <Sqrt<U11>>::to_u32()); |
| assert_eq!(3, <Sqrt<U12>>::to_u32()); |
| assert_eq!(3, <Sqrt<U13>>::to_u32()); |
| assert_eq!(3, <Sqrt<U14>>::to_u32()); |
| assert_eq!(3, <Sqrt<U15>>::to_u32()); |
| |
| assert_eq!(4, <Sqrt<U16>>::to_u32()); |
| assert_eq!(4, <Sqrt<U17>>::to_u32()); |
| assert_eq!(4, <Sqrt<U18>>::to_u32()); |
| assert_eq!(4, <Sqrt<U19>>::to_u32()); |
| assert_eq!(4, <Sqrt<U20>>::to_u32()); |
| assert_eq!(4, <Sqrt<U21>>::to_u32()); |
| assert_eq!(4, <Sqrt<U22>>::to_u32()); |
| assert_eq!(4, <Sqrt<U23>>::to_u32()); |
| assert_eq!(4, <Sqrt<U24>>::to_u32()); |
| |
| assert_eq!(5, <Sqrt<U25>>::to_u32()); |
| assert_eq!(5, <Sqrt<U26>>::to_u32()); |
| // ... |
| } |
| |
| // ----------------------------------------- |
| // Logarithm2 |
| |
| impl<N> Logarithm2 for N |
| where |
| N: PrivateLogarithm2, |
| { |
| type Output = <Self as PrivateLogarithm2>::Output; |
| } |
| |
| // log2(1) = 0. |
| impl PrivateLogarithm2 for UInt<UTerm, B1> { |
| type Output = U0; |
| } |
| |
| // General case of log2(Self) where Self >= 2. |
| impl<U, B> PrivateLogarithm2 for UInt<U, B> |
| where |
| U: Unsigned + Logarithm2, |
| B: Bit, |
| Log2<U>: Add<B1>, |
| { |
| type Output = Add1<Log2<U>>; |
| } |
| |
| // ----------------------------------------- |
| // ToInt |
| |
| impl ToInt<i8> for UTerm { |
| #[inline] |
| fn to_int() -> i8 { |
| Self::I8 |
| } |
| } |
| |
| impl ToInt<i16> for UTerm { |
| #[inline] |
| fn to_int() -> i16 { |
| Self::I16 |
| } |
| } |
| |
| impl ToInt<i32> for UTerm { |
| #[inline] |
| fn to_int() -> i32 { |
| Self::I32 |
| } |
| } |
| |
| impl ToInt<i64> for UTerm { |
| #[inline] |
| fn to_int() -> i64 { |
| Self::I64 |
| } |
| } |
| |
| impl ToInt<u8> for UTerm { |
| #[inline] |
| fn to_int() -> u8 { |
| Self::U8 |
| } |
| } |
| |
| impl ToInt<u16> for UTerm { |
| #[inline] |
| fn to_int() -> u16 { |
| Self::U16 |
| } |
| } |
| |
| impl ToInt<u32> for UTerm { |
| #[inline] |
| fn to_int() -> u32 { |
| Self::U32 |
| } |
| } |
| |
| impl ToInt<u64> for UTerm { |
| #[inline] |
| fn to_int() -> u64 { |
| Self::U64 |
| } |
| } |
| |
| impl ToInt<usize> for UTerm { |
| #[inline] |
| fn to_int() -> usize { |
| Self::USIZE |
| } |
| } |
| |
| impl<U, B> ToInt<i8> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> i8 { |
| Self::I8 |
| } |
| } |
| |
| impl<U, B> ToInt<i16> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> i16 { |
| Self::I16 |
| } |
| } |
| |
| impl<U, B> ToInt<i32> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> i32 { |
| Self::I32 |
| } |
| } |
| |
| impl<U, B> ToInt<i64> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> i64 { |
| Self::I64 |
| } |
| } |
| |
| impl<U, B> ToInt<u8> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> u8 { |
| Self::U8 |
| } |
| } |
| |
| impl<U, B> ToInt<u16> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> u16 { |
| Self::U16 |
| } |
| } |
| |
| impl<U, B> ToInt<u32> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> u32 { |
| Self::U32 |
| } |
| } |
| |
| impl<U, B> ToInt<u64> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> u64 { |
| Self::U64 |
| } |
| } |
| |
| impl<U, B> ToInt<usize> for UInt<U, B> |
| where |
| U: Unsigned, |
| B: Bit, |
| { |
| #[inline] |
| fn to_int() -> usize { |
| Self::USIZE |
| } |
| } |
| |
| #[cfg(test)] |
| mod tests { |
| use crate::consts::*; |
| use crate::{Log2, ToInt, Unsigned}; |
| |
| #[test] |
| fn log2_test() { |
| assert_eq!(0, <Log2<U1>>::to_u32()); |
| |
| assert_eq!(1, <Log2<U2>>::to_u32()); |
| assert_eq!(1, <Log2<U3>>::to_u32()); |
| |
| assert_eq!(2, <Log2<U4>>::to_u32()); |
| assert_eq!(2, <Log2<U5>>::to_u32()); |
| assert_eq!(2, <Log2<U6>>::to_u32()); |
| assert_eq!(2, <Log2<U7>>::to_u32()); |
| |
| assert_eq!(3, <Log2<U8>>::to_u32()); |
| assert_eq!(3, <Log2<U9>>::to_u32()); |
| assert_eq!(3, <Log2<U10>>::to_u32()); |
| assert_eq!(3, <Log2<U11>>::to_u32()); |
| assert_eq!(3, <Log2<U12>>::to_u32()); |
| assert_eq!(3, <Log2<U13>>::to_u32()); |
| assert_eq!(3, <Log2<U14>>::to_u32()); |
| assert_eq!(3, <Log2<U15>>::to_u32()); |
| |
| assert_eq!(4, <Log2<U16>>::to_u32()); |
| assert_eq!(4, <Log2<U17>>::to_u32()); |
| assert_eq!(4, <Log2<U18>>::to_u32()); |
| assert_eq!(4, <Log2<U19>>::to_u32()); |
| assert_eq!(4, <Log2<U20>>::to_u32()); |
| assert_eq!(4, <Log2<U21>>::to_u32()); |
| assert_eq!(4, <Log2<U22>>::to_u32()); |
| assert_eq!(4, <Log2<U23>>::to_u32()); |
| assert_eq!(4, <Log2<U24>>::to_u32()); |
| assert_eq!(4, <Log2<U25>>::to_u32()); |
| assert_eq!(4, <Log2<U26>>::to_u32()); |
| assert_eq!(4, <Log2<U27>>::to_u32()); |
| assert_eq!(4, <Log2<U28>>::to_u32()); |
| assert_eq!(4, <Log2<U29>>::to_u32()); |
| assert_eq!(4, <Log2<U30>>::to_u32()); |
| assert_eq!(4, <Log2<U31>>::to_u32()); |
| |
| assert_eq!(5, <Log2<U32>>::to_u32()); |
| assert_eq!(5, <Log2<U33>>::to_u32()); |
| |
| // ... |
| } |
| |
| #[test] |
| fn uint_toint_test() { |
| // i8 |
| assert_eq!(0_i8, U0::to_int()); |
| assert_eq!(1_i8, U1::to_int()); |
| assert_eq!(2_i8, U2::to_int()); |
| assert_eq!(3_i8, U3::to_int()); |
| assert_eq!(4_i8, U4::to_int()); |
| |
| // i16 |
| assert_eq!(0_i16, U0::to_int()); |
| assert_eq!(1_i16, U1::to_int()); |
| assert_eq!(2_i16, U2::to_int()); |
| assert_eq!(3_i16, U3::to_int()); |
| assert_eq!(4_i16, U4::to_int()); |
| |
| // i32 |
| assert_eq!(0_i32, U0::to_int()); |
| assert_eq!(1_i32, U1::to_int()); |
| assert_eq!(2_i32, U2::to_int()); |
| assert_eq!(3_i32, U3::to_int()); |
| assert_eq!(4_i32, U4::to_int()); |
| |
| // i64 |
| assert_eq!(0_i64, U0::to_int()); |
| assert_eq!(1_i64, U1::to_int()); |
| assert_eq!(2_i64, U2::to_int()); |
| assert_eq!(3_i64, U3::to_int()); |
| assert_eq!(4_i64, U4::to_int()); |
| |
| // u8 |
| assert_eq!(0_u8, U0::to_int()); |
| assert_eq!(1_u8, U1::to_int()); |
| assert_eq!(2_u8, U2::to_int()); |
| assert_eq!(3_u8, U3::to_int()); |
| assert_eq!(4_u8, U4::to_int()); |
| |
| // u16 |
| assert_eq!(0_u16, U0::to_int()); |
| assert_eq!(1_u16, U1::to_int()); |
| assert_eq!(2_u16, U2::to_int()); |
| assert_eq!(3_u16, U3::to_int()); |
| assert_eq!(4_u16, U4::to_int()); |
| |
| // u32 |
| assert_eq!(0_u32, U0::to_int()); |
| assert_eq!(1_u32, U1::to_int()); |
| assert_eq!(2_u32, U2::to_int()); |
| assert_eq!(3_u32, U3::to_int()); |
| assert_eq!(4_u32, U4::to_int()); |
| |
| // u64 |
| assert_eq!(0_u64, U0::to_int()); |
| assert_eq!(1_u64, U1::to_int()); |
| assert_eq!(2_u64, U2::to_int()); |
| assert_eq!(3_u64, U3::to_int()); |
| assert_eq!(4_u64, U4::to_int()); |
| |
| // usize |
| assert_eq!(0_usize, U0::to_int()); |
| assert_eq!(1_usize, U1::to_int()); |
| assert_eq!(2_usize, U2::to_int()); |
| assert_eq!(3_usize, U3::to_int()); |
| assert_eq!(4_usize, U4::to_int()); |
| } |
| } |