Adding upstream version 124.0.1.upstream/124.0.1

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 2663 insertions, 0 deletions

diff --git a/third_party/rust/typenum/src/uint.rs b/third_party/rust/typenum/src/uint.rs
new file mode 100644
index 0000000000..28ace5becb
--- /dev/null
+++ b/third_party/rust/typenum/src/uint.rs
@@ -0,0 +1,2663 @@
+//! 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
+    }
+    const INT: i8 = Self::I8;
+}
+
+impl ToInt<i16> for UTerm {
+    #[inline]
+    fn to_int() -> i16 {
+        Self::I16
+    }
+    const INT: i16 = Self::I16;
+}
+
+impl ToInt<i32> for UTerm {
+    #[inline]
+    fn to_int() -> i32 {
+        Self::I32
+    }
+    const INT: i32 = Self::I32;
+}
+
+impl ToInt<i64> for UTerm {
+    #[inline]
+    fn to_int() -> i64 {
+        Self::I64
+    }
+    const INT: i64 = Self::I64;
+}
+
+impl ToInt<u8> for UTerm {
+    #[inline]
+    fn to_int() -> u8 {
+        Self::U8
+    }
+    const INT: u8 = Self::U8;
+}
+
+impl ToInt<u16> for UTerm {
+    #[inline]
+    fn to_int() -> u16 {
+        Self::U16
+    }
+    const INT: u16 = Self::U16;
+}
+
+impl ToInt<u32> for UTerm {
+    #[inline]
+    fn to_int() -> u32 {
+        Self::U32
+    }
+    const INT: u32 = Self::U32;
+}
+
+impl ToInt<u64> for UTerm {
+    #[inline]
+    fn to_int() -> u64 {
+        Self::U64
+    }
+    const INT: u64 = Self::U64;
+}
+
+impl ToInt<usize> for UTerm {
+    #[inline]
+    fn to_int() -> usize {
+        Self::USIZE
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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
+    }
+    const 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());
+        assert_eq!(0_i8, U0::INT);
+        assert_eq!(1_i8, U1::INT);
+        assert_eq!(2_i8, U2::INT);
+        assert_eq!(3_i8, U3::INT);
+        assert_eq!(4_i8, U4::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());
+        assert_eq!(0_i16, U0::INT);
+        assert_eq!(1_i16, U1::INT);
+        assert_eq!(2_i16, U2::INT);
+        assert_eq!(3_i16, U3::INT);
+        assert_eq!(4_i16, U4::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());
+        assert_eq!(0_i32, U0::INT);
+        assert_eq!(1_i32, U1::INT);
+        assert_eq!(2_i32, U2::INT);
+        assert_eq!(3_i32, U3::INT);
+        assert_eq!(4_i32, U4::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());
+        assert_eq!(0_i64, U0::INT);
+        assert_eq!(1_i64, U1::INT);
+        assert_eq!(2_i64, U2::INT);
+        assert_eq!(3_i64, U3::INT);
+        assert_eq!(4_i64, U4::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());
+        assert_eq!(0_u8, U0::INT);
+        assert_eq!(1_u8, U1::INT);
+        assert_eq!(2_u8, U2::INT);
+        assert_eq!(3_u8, U3::INT);
+        assert_eq!(4_u8, U4::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());
+        assert_eq!(0_u16, U0::INT);
+        assert_eq!(1_u16, U1::INT);
+        assert_eq!(2_u16, U2::INT);
+        assert_eq!(3_u16, U3::INT);
+        assert_eq!(4_u16, U4::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());
+        assert_eq!(0_u32, U0::INT);
+        assert_eq!(1_u32, U1::INT);
+        assert_eq!(2_u32, U2::INT);
+        assert_eq!(3_u32, U3::INT);
+        assert_eq!(4_u32, U4::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());
+        assert_eq!(0_u64, U0::INT);
+        assert_eq!(1_u64, U1::INT);
+        assert_eq!(2_u64, U2::INT);
+        assert_eq!(3_u64, U3::INT);
+        assert_eq!(4_u64, U4::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());
+        assert_eq!(0_usize, U0::INT);
+        assert_eq!(1_usize, U1::INT);
+        assert_eq!(2_usize, U2::INT);
+        assert_eq!(3_usize, U3::INT);
+        assert_eq!(4_usize, U4::INT);
+    }
+}