dimensioned 0.6.0

/** Create a new unit system

This macro is the heart of this library and is used to create the unit systems with which it
ships.

If you find yourself using this macro, please think about whether the unit system you are creating
would be useful to others; if so, submit an issue to get it added to dimensioned.

Rather than try to parse the definition above, we will show an example of calling it, and then
walk through it line by line.

```rust
# #![cfg_attr(feature = "oibit", feature(optin_builtin_traits))]
#[macro_use]
extern crate dimensioned as dim;

pub mod ms {
    make_units! {
        MS;
        ONE: Unitless;

        base {
            M: Meter, "m", Length;
            S: Second, "s", Time;
        }

        derived {
            MPS: MeterPerSecond = (Meter / Second), Velocity;
            HZ: Hertz = (Unitless / Second), Frequency;

            M3: Meter3 = (Meter * Meter * Meter), Volume;
            M5: Meter5 = (Meter3 * Meter * Meter);
        }

        constants {
            FT: Meter = 0.3048;
            CM: Meter = CENTI * M.value_unsafe;

            MIN: Second = 60.0;
            HR: Second = 60.0 * MIN.value_unsafe;

            PI: Unitless = consts::PI;
        }

        fmt = true;
    }
    pub use self::f64consts::*;
}
# fn main() {}
```

Okay, now let's walk through it.

The macro performs some imports and defines quite a few things, so it's strongly recommended to put it
in its own module.

```ignore
pub mod ms {
```

The first line after calling the macro is just the name we want to give the unit system followed
by a semi-colon. This will be the name of the only type we define; all other type definitions are
aliases to this type with different parameters.

```ignore
    make_units! {
        MS;
```

The next line is the name of the constant and type alias we want for a dimensionless quantity in
your system. That is, when all units have power of 0.

```ignore
        ONE: Unitless;
```

In the `base` block, we define the base units for our system. Each line is of the format `CONST:
Type, "token", Dimension;` where `CONST` is the constant we create, `Type` is the type alias that
we'll make for this unit, `token` is what will show up when we print it, and `Dimension` is
optional. If present, the macro will implement said dimension from the `dimensions` module for this unit.

```ignore
        base {
            M: Meter, "m", Length;
            S: Second, "s", Time;
        }
```

In the `derived` block, we can make derived units from our base units. The beginning is similar; we
have `CONST: Type`. After the equal signs, we have a formula to define this unit. The parentheses
are required, and the only things that can be inside them are the names of other units, and the *
and / operators. Hopefully, this part of the macro will be made more flexibile in the
future. Finally, we again end with an optional dimension. Note that there is none present for the
`M5` line.

```ignore
        derived {
            MPS: MeterPerSecond = (Meter / Second), Velocity;
            HZ: Hertz = (Unitless / Second), Frequency;

            M3: Meter3 = (Meter * Meter * Meter), Volume;
            M5: Meter5 = (Meter3 * Meter * Meter);
        }

```

In the `constants` block, we can define constants of whatever values we wish. Note that the
constants in the `base` and `derived` blocks are always created with a value of 1.0.

All constants are created in both `f32` and `f64` flavors, in the submodules `f32consts` and
`f64consts`, respectively.

In these submodules, the consts from the respective version of `f32prefixes` or `f64prefixes` are in
scope, hence the use of `CENTI` in the `CM` definition.

In addition, the the respective version of `core::f32::consts` or `core::f64::consts` is in scope,
which allows the use of `consts::PI` in the `PI definition.

```ignore
        constants {
            FT: Meter = 0.3048;
            CM: Meter = CENTI * M.value_unsafe;

            MIN: Second = 60.0;
            HR: Second = 60.0 * MIN.value_unsafe;

            PI: Unitless = consts::PI;
        }
```

Finally, we have the `fmt` line. This line can either be `fmt = true;` or `fmt = false;`. In either
case, the trait `core::fmt::Debug` is implemented for your unit system, but all of the other `fmt`
traits are implemented only if this is true. Setting it to false allows you to have custom printing for your system.

```ignore
        fmt = true;
    }
```

This line isn't part of the macro, but I wanted to include it as it is in all of the unit systems
defined in dimensioned. It lets us use the `f64` flavor of constants much easier. E.g. we can now
type `ms::M` instead of `ms::f64consts::M`.

```igore
    pub use self::f64consts::*;
}
```

And that's it! The macro may seem complicated at first, but if you end up using it, I hope that it
starts seeming intuitive fairly quickly.

---

In addition to creating a type, type aliases, and constants, this macro implements many traits for
your unit system, including (but not limited to) the traits in the `traits` module and arithmetic operations.
*/

#[macro_export]
macro_rules! make_units {
    ($System:ident;
     $one:ident: $Unitless:ident;
     base {
         $($base:ident: $Unit:ident, $print_as:expr $(, $base_dim:ident)*;)+
     }
     derived {
         $($derived_const:ident: $Derived:ident = ($($derived_rhs:tt)+) $(, $derived_dim:ident)*;)*
     }
     constants {
         $($constant:ident: $ConstantUnit:ident = $constant_value:expr;)*
     }
     fmt = $to_fmt:ident;
    ) => (
        use $crate::dimcore::marker;
        use $crate::{Dimensioned, Dimensionless};

        /// The $System unit system
        #[derive(Eq, PartialEq, Ord, PartialOrd, Clone, Copy, Hash)]
        pub struct $System<V, U> {
            /// This is the value of whatever type we're giving units. Using it directly bypasses
            /// all of the dimensional analysis that having a unit system provides, and should be
            /// avoided whenever possible.
            ///
            /// If using this member is necessary, it is strongly encouraged to wrap the
            /// calculation in a dimensionally-safe interface.
            pub value_unsafe: V,

            /// This member is only temporarily public and so its use is considered unstable.
            /// Right now, the only way to create a `const` with units is with this pattern:
            ///
            /// ```rust
            /// extern crate dimensioned as dim;
            /// use dim::si;
            ///
            /// const x: si::Meter<f64> = si::Meter { value_unsafe: 3.4, _marker: std::marker::PhantomData };
            /// # fn main() {}
            /// ```
            ///
            /// Once `const_fns` is stabilized, that will be able to be replaced with a call to
            /// `Meter::new` and `_marker` will be made private.
            pub _marker: marker::PhantomData<U>,
        }

        impl<V, U> $System<V, U> {

            /// Create a new quantity in the $System unit system
            #[inline]
            pub fn new(v: V) -> Self {
                $System { value_unsafe: v, _marker: marker::PhantomData }
            }
        }

        // --------------------------------------------------------------------------------
        // Implement traits defined in dim::traits

        impl<V, U> Dimensioned for $System<V, U> {
            type Value = V;
            type Units = U;
            #[inline]
            fn new(val: V) -> Self {
                $System::new(val)
            }

            #[inline]
            fn value_unsafe(&self) -> &V {
                &self.value_unsafe
            }
        }

        use $crate::MapUnsafe;
        impl<ValueIn, UnitsIn, ValueOut, UnitsOut> MapUnsafe<ValueOut, UnitsOut> for $System<ValueIn, UnitsIn> {
            type Output = $System<ValueOut, UnitsOut>;
            #[inline]
            fn map_unsafe<F: FnOnce(ValueIn) -> ValueOut>(self, f: F) -> Self::Output {
                $System::new(f(self.value_unsafe))
            }
        }

        use $crate::Map;
        impl<ValueIn, ValueOut> Map<ValueOut> for $Unitless<ValueIn>
        {
            type Output = $Unitless<ValueOut>;
            #[inline]
            fn map<F: FnOnce(ValueIn) -> ValueOut>(self, f: F) -> Self::Output {
                $System::new(f(self.value_unsafe))
            }
        }

        // --------------------------------------------------------------------------------
        // Define type aliases

        #[cfg(feature = "oibit")]
        use $crate::NotDim;
        #[cfg(feature = "oibit")]
        impl<V, U> !NotDim for $System<V, U> {}

        #[doc(hidden)]
        pub mod inner {
            #[allow(unused_imports)]
            use $crate::traits::*;
            #[allow(unused_imports)]
            use $crate::typenum::consts::*;
            __make_units_internal!(@base_arrays $Unitless $($Unit)*);
            $(#[allow(missing_docs)] pub type $Derived = __derived_internal!(@mu commas $($derived_rhs)+);)*
        }

        #[allow(missing_docs)]
        pub type $Unitless<V> = $System<V, inner::$Unitless>;
        $(#[allow(missing_docs)]
          pub type $Unit<V> = $System<V, inner::$Unit>;
          $(impl<V> $crate::dimensions::$base_dim for $Unit<V> {})*
        )*

        impl<Value> $crate::Dimensionless for $Unitless<Value> {
            #[inline]
            fn value(&self) -> &Value {
                &self.value_unsafe
            }
        }

        $(#[allow(missing_docs)] pub type $Derived<V> = $System<V, inner::$Derived>;
          $(impl<V> $crate::dimensions::$derived_dim for $Derived<V> {})*
        )*

        // --------------------------------------------------------------------------------
        // Define consts
        macro_rules! define_consts {
            ($module:ident, $prefixes:ident, $t:ident) => (
                /// Constants defined for $System of value type $t
                pub mod $module {
                    use super::*;
                    use $crate::dimcore::marker::PhantomData;
                    #[allow(unused_imports)] use $crate::dimcore::$t::consts;
                    #[allow(unused_imports)] use $crate::$prefixes::*;
                    #[allow(dead_code, missing_docs)]
                    pub const $one: $Unitless<$t> = $System { value_unsafe: 1.0, _marker: PhantomData };
                    $(#[allow(dead_code, missing_docs)]
                      pub const $base: $Unit<$t> = $System { value_unsafe: 1.0, _marker: PhantomData };)*
                    $(#[allow(dead_code, missing_docs)]
                      pub const $derived_const: $Derived<$t> = $System { value_unsafe: 1.0, _marker: PhantomData };)*
                    $(#[allow(dead_code, missing_docs)]
                      pub const $constant: $ConstantUnit<$t> = $System { value_unsafe: $constant_value, _marker: PhantomData };)*
                }
            );
        }
        define_consts!(f32consts, f32prefixes, f32);
        define_consts!(f64consts, f64prefixes, f64);

        // --------------------------------------------------------------------------------
        // Formatting
        use $crate::dimcore::fmt;
        use $crate::typenum::{Len, Length, TypeArray};
        use $crate::generic_array::{GenericArray, ArrayLength};
        use $crate::array::ToGA;

        __make_units_internal!(@fmt true S $System $(P $print_as;)* T Debug E "{:?}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T Display E "{}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T Octal E "{:o}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T LowerHex E "{:x}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T UpperHex E "{:X}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T Pointer E "{:p}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T Binary E "{:b}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T LowerExp E "{:e}");
        __make_units_internal!(@fmt $to_fmt S $System $(P $print_as;)* T UpperExp E "{:E}");

        // --------------------------------------------------------------------------------
        // Operator traits from this crate

        impl<V, U> $crate::Recip for $System<V, U> where V: $crate::Recip, U: $crate::dimcore::ops::Neg, {
            type Output = $System<<V as $crate::Recip>::Output, $crate::typenum::Negate<U>>;
            #[inline]
            fn recip(self) -> Self::Output { $System::new(self.value_unsafe.recip()) }
        }

        use $crate::typenum::Pow;
        impl<Exp, V, U> Pow<Exp> for $System<V, U>
            where V: Pow<Exp>,
                  U: $crate::dimcore::ops::Mul<Exp>,
        {
            type Output = $System< <V as Pow<Exp>>::Output, $crate::typenum::Prod<U, Exp>>;
            #[inline]
            fn powi(self, exp: Exp) -> Self::Output {
                $System::new( self.value_unsafe.powi(exp) )
            }
        }

        impl<Index, V, U> $crate::Root<Index> for $System<V, U>
            where V: $crate::Root<Index>,
                  U: $crate::typenum::PartialDiv<Index>,
        {
            type Output = $System< <V as $crate::Root<Index>>::Output, $crate::typenum::PartialQuot<U, Index>>;
            #[inline]
            fn root(self, idx: Index) -> Self::Output {
                $System::new( self.value_unsafe.root(idx) )
            }
        }

        use $crate::typenum::P2;
        impl<V, U> $crate::Sqrt for $System<V, U>
            where V: $crate::Sqrt,
                  U: $crate::typenum::PartialDiv<P2>,
        {
            type Output = $System< <V as $crate::Sqrt>::Output, $crate::typenum::PartialQuot<U, P2>>;
            #[inline]
            fn sqrt(self) -> Self::Output {
                $System::new( self.value_unsafe.sqrt() )
            }
        }

        use $crate::typenum::P3;
        impl<V, U> $crate::Cbrt for $System<V, U>
            where V: $crate::Cbrt,
                  U: $crate::typenum::PartialDiv<P3>,
        {
            type Output = $System< <V as $crate::Cbrt>::Output, $crate::typenum::PartialQuot<U, P3>>;
            #[inline]
            fn cbrt(self) -> Self::Output {
                $System::new( self.value_unsafe.cbrt() )
            }
        }

        // --------------------------------------------------------------------------------
        // Operators

        use $crate::dimcore::ops::{Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign,
                        BitXor, BitXorAssign, Div, DivAssign, Mul, MulAssign, Sub,
                        SubAssign, Rem, RemAssign, Neg, Not, Shl, ShlAssign, Shr,
                        ShrAssign};
        use $crate::typenum::{Prod, Quot};

        __make_units_internal!(@ops $System, $Unitless);

        // --------------------------------------------------------------------------------
        // Deref only for dimensionless things

        use $crate::dimcore::ops::Deref;
        impl<V, U> Deref for $System<V, U> where $System<V, U>: Dimensionless {
            type Target = V;
            #[inline]
            fn deref(&self) -> &Self::Target {
                &self.value_unsafe
            }
        }

        // --------------------------------------------------------------------------------
        // Index

        use $crate::dimcore::ops::Index;
        impl<V, U, Idx> Index<Idx> for $System<V, U>
            where V: Index<Idx>,
        <V as Index<Idx>>::Output: Sized,
        {
            type Output = $System<<V as Index<Idx>>::Output, U>;
            #[inline]
            fn index(&self, index: Idx) -> &Self::Output {
                unsafe {
                    $crate::dimcore::mem::transmute(&self.value_unsafe[index])
                }
            }
        }

        use $crate::dimcore::ops::IndexMut;
        impl<V, U, Idx> IndexMut<Idx> for $System<V, U>
            where $System<V, U>: Index<Idx>,
                  V: Index<Idx> + IndexMut<Idx>,
        <V as Index<Idx>>::Output: Sized,
        <$System<V, U> as Index<Idx>>::Output: Sized
        {
            #[inline]
            fn index_mut(&mut self, index: Idx) -> &mut Self::Output{
                unsafe {
                    $crate::dimcore::mem::transmute(self.value_unsafe.index_mut(index))
                }
            }
        }

        // --------------------------------------------------------------------------------
        // --------------------------------------------------------------------------------
    );
}

#[doc(hidden)]
#[macro_export]
macro_rules! __make_units_internal {
    (@ops $System:ident, $Unitless:ident) => (
        // -------------------------------------------------------------------------------
        // Unary: Neg, Not

        macro_rules! unary_op {
            ($Trait:ident, $fun:ident) => (
                impl<V, U> $Trait for $System<V, U> where
                    V: $Trait,
                {
                    type Output = $System<<V as $Trait>::Output, U>;
                    #[inline]
                    fn $fun(self) -> Self::Output {
                        $System::new($Trait::$fun(self.value_unsafe))
                    }
                }
            );
        }

        unary_op!(Not, not);
        unary_op!(Neg, neg);

        // -------------------------------------------------------------------------------
        // Unit-preserving: Add, Sub, BitAnd, BitOr, BitXor

        macro_rules! binary_unit_preserve {
            ($Trait:ident, $fun:ident, $TraitAssign:ident, $fun_assign:ident) => (
                // Both have units
                impl<Vl, U, Vr> $Trait<$System<Vr, U>> for $System<Vl, U> where
                    Vl: $Trait<Vr>,
                {
                    type Output = $System<<Vl as $Trait<Vr>>::Output, U>;
                    #[inline]
                    fn $fun(self, rhs: $System<Vr, U>) -> Self::Output {
                        $System::new($Trait::$fun(self.value_unsafe, rhs.value_unsafe))
                    }
                }

                // Unitless on lhs, scalar on rhs
                #[cfg(feature = "oibit")]
                impl<Vl, U, Vr> $Trait<Vr> for $System<Vl, U> where
                    Vl: $Trait<Vr>, Vr: NotDim, $System<Vl, U>: Dimensionless
                {
                    type Output = $System<<Vl as $Trait<Vr>>::Output, U>;
                    #[inline]
                    fn $fun(self, rhs: Vr) -> Self::Output {
                        $System::new($Trait::$fun(self.value_unsafe, rhs))
                    }
                }

                // Assign: Both have units
                impl<Vl, U, Vr> $TraitAssign<$System<Vr, U>> for $System<Vl, U> where
                    Vl: $TraitAssign<Vr>,
                {
                    #[inline]
                    fn $fun_assign(&mut self, rhs: $System<Vr, U>) {
                        $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs.value_unsafe)
                    }
                }

                // Assign: Unitless on lhs, scalar on rhs
                #[cfg(feature = "oibit")]
                impl<Vl, U, Vr> $TraitAssign<Vr> for $System<Vl, U> where
                    Vl: $TraitAssign<Vr>, Vr: NotDim, $System<Vl, U>: Dimensionless
                {
                    #[inline]
                    fn $fun_assign(&mut self, rhs: Vr) {
                        $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs)
                    }
                }
            );
        }

        binary_unit_preserve!(Add, add, AddAssign, add_assign);
        binary_unit_preserve!(Sub, sub, SubAssign, sub_assign);
        binary_unit_preserve!(BitAnd, bitand, BitAndAssign, bitand_assign);
        binary_unit_preserve!(BitOr, bitor, BitOrAssign, bitor_assign);
        binary_unit_preserve!(BitXor, bitxor, BitXorAssign, bitxor_assign);

        // -------------------------------------------------------------------------------
        // Unit-changing: Mul, Div

        macro_rules! binary_unit_change {
            ($Trait:ident, $fun:ident, $op:ident, $TraitAssign:ident, $fun_assign:ident) => (
                // Both have units
                impl<Vl, Ul, Vr, Ur> $Trait<$System<Vr, Ur>> for $System<Vl, Ul> where
                    Vl: $Trait<Vr>, Ul: $op<Ur>,
                {
                    type Output = $System<<Vl as $Trait<Vr>>::Output, <Ul as $op<Ur>>::Output>;
                    #[inline]
                    fn $fun(self, rhs: $System<Vr, Ur>) -> Self::Output {
                        $System::new( $Trait::$fun(self.value_unsafe, rhs.value_unsafe) )
                    }
                }

                // Lhs has units, scalar on rhs
                #[cfg(feature = "oibit")]
                impl<Vl, U, Vr> $Trait<Vr> for $System<Vl, U> where
                    Vl: $Trait<Vr>, Vr: NotDim,
                {
                    type Output = $System<<Vl as $Trait<Vr>>::Output, U>;
                    #[inline]
                    fn $fun(self, rhs: Vr) -> Self::Output {
                        $System::new( $Trait::$fun(self.value_unsafe, rhs) )
                    }
                }

                // Assign: Lhs has units, rhs unitless
                impl<Vl, Ul, Vr, Ur> $TraitAssign<$System<Vr, Ur>> for $System<Vl, Ul> where
                    Vl: $TraitAssign<Vr>,
                $System<Vr, Ur>: Dimensionless,
                {
                    #[inline]
                    fn $fun_assign(&mut self, rhs: $System<Vr, Ur>) {
                        $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs.value_unsafe)
                    }
                }

                // Assign: Lhs has units, scalar on rhs
                #[cfg(feature = "oibit")]
                impl<Vl, U, Vr> $TraitAssign<Vr> for $System<Vl, U> where
                    Vl: $TraitAssign<Vr>, Vr: NotDim,
                {
                    #[inline]
                    fn $fun_assign(&mut self, rhs: Vr) {
                        $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs)
                    }
                }
            );
        }

        binary_unit_change!(Mul, mul, Add, MulAssign, mul_assign);
        binary_unit_change!(Div, div, Sub, DivAssign, div_assign);

        // -------------------------------------------------------------------------------
        // Rem (it's kinda its own thing)

        // Both have units
        impl<Vl, Ul, Vr, Ur> Rem<$System<Vr, Ur>> for $System<Vl, Ul> where
            Vl: Rem<Vr>
        {
            type Output = $System<<Vl as Rem<Vr>>::Output, Ul>;
            #[inline]
            fn rem(self, rhs: $System<Vr, Ur>) -> Self::Output {
                $System::new( self.value_unsafe % rhs.value_unsafe )
            }
        }

        // Lhs has units, scalar on rhs
        #[cfg(feature = "oibit")]
        impl<Vl, U, Vr> Rem<Vr> for $System<Vl, U> where
            Vl: Rem<Vr>, Vr: NotDim,
        {
            type Output = $System<<Vl as Rem<Vr>>::Output, U>;
            #[inline]
            fn rem(self, rhs: Vr) -> Self::Output {
                $System::new( self.value_unsafe % rhs )
            }
        }

        // Assign, both have units
        impl<Vl, Ul, Vr, Ur> RemAssign<$System<Vr, Ur>> for $System<Vl, Ul> where
            Vl: RemAssign<Vr>,
        {
            #[inline]
            fn rem_assign(&mut self, rhs: $System<Vr, Ur>) {
                self.value_unsafe %= rhs.value_unsafe
            }
        }

        // Assign: Lhs has units, scalar on rhs
        #[cfg(feature = "oibit")]
        impl<Vl, U, Vr> RemAssign<Vr> for $System<Vl, U> where
            Vl: RemAssign<Vr>, Vr: NotDim,
        {
            #[inline]
            fn rem_assign(&mut self, rhs: Vr) {
                self.value_unsafe %= rhs
            }
        }

        // -------------------------------------------------------------------------------
        // Shl, Shr

        macro_rules! binary_shift {
            ($Trait:ident, $fun:ident, $TraitAssign:ident, $fun_assign:ident) => (
                // Lhs has units, rhs unitless
                impl<Vl, Ul, Vr, Ur> $Trait<$System<Vr, Ur>> for $System<Vl, Ul> where
                    Vl: $Trait<Vr>, $System<Vr, Ur>: Dimensionless
                {
                    type Output = $System<<Vl as $Trait<Vr>>::Output, Ul>;
                    #[inline]
                    fn $fun(self, rhs: $System<Vr, Ur>) -> Self::Output {
                        $System::new( $Trait::$fun(self.value_unsafe, rhs.value_unsafe) )
                    }
                }

                // Lhs has units, scalar on rhs
                #[cfg(feature = "oibit")]
                impl<Vl, Ul, Vr> $Trait<Vr> for $System<Vl, Ul> where
                    Vl: $Trait<Vr>, Vr: NotDim,
                {
                    type Output = $System<<Vl as $Trait<Vr>>::Output, Ul>;
                    #[inline]
                    fn $fun(self, rhs: Vr) -> Self::Output {
                        $System::new( $Trait::$fun(self.value_unsafe, rhs) )
                    }
                }

                // Assign: Lhs has units, rhs unitless
                impl<Vl, Ul, Vr, Ur> $TraitAssign<$System<Vr, Ur>> for $System<Vl, Ul> where
                    Vl: $TraitAssign<Vr>,
                $System<Vr, Ur>: Dimensionless,
                {
                    #[inline]
                    fn $fun_assign(&mut self, rhs: $System<Vr, Ur>) {
                        $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs.value_unsafe)
                    }
                }

                // Assign: Lhs has units, scalar on rhs
                #[cfg(feature = "oibit")]
                impl<Vl, U, Vr> $TraitAssign<Vr> for $System<Vl, U> where
                    Vl: $TraitAssign<Vr>, Vr: NotDim,
                {
                    #[inline]
                    fn $fun_assign(&mut self, rhs: Vr) {
                        $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs)
                    }
                }
            );
        }

        binary_shift!(Shl, shl, ShlAssign, shl_assign);
        binary_shift!(Shr, shr, ShrAssign, shr_assign);

        // -------------------------------------------------------------------------------
        // All things with primitives
        macro_rules! prim {
            ($t: ty) => (

                // Operations that require lhs and rhs to have the same units
                // Add, Sub, BitAnd, BitOr, BitXor
                macro_rules! same_units {
                    ($Trait:ident, $fun:ident, $TraitAssign:ident, $fun_assign:ident) => (

                        // Unitless on lhs, primitive on rhs
                        #[cfg(not(feature = "oibit"))]
                        impl<V, U> $Trait<$t> for $System<V, U> where
                            V: $Trait<$t>, $System<V, U>: Dimensionless
                        {
                            type Output = $System<<V as $Trait<$t>>::Output, U>;
                            #[inline]
                            fn $fun(self, rhs: $t) -> Self::Output {
                                $System::new( $Trait::$fun(self.value_unsafe, rhs) )
                            }
                        }

                        // Primitive on lhs, unitless on rhs
                        impl<V, U> $Trait<$System<V, U>> for $t where
                            $t: $Trait<V>, $System<V, U>: Dimensionless
                        {
                            type Output = $System<<$t as $Trait<V>>::Output, U>;
                            #[inline]
                            fn $fun(self, rhs: $System<V, U>) -> Self::Output {
                                $System::new( $Trait::$fun(self, rhs.value_unsafe) )
                            }
                        }

                        // Assign: Unitless on lhs, primitive on rhs
                        #[cfg(not(feature = "oibit"))]
                        impl<V, U> $TraitAssign<$t> for $System<V, U> where
                            V: $TraitAssign<$t>, $System<V, U>: Dimensionless
                        {
                            #[inline]
                            fn $fun_assign(&mut self, rhs: $t) {
                                $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs)
                            }
                        }

                    );
                }

                same_units!(Add, add, AddAssign, add_assign);
                same_units!(Sub, sub, SubAssign, sub_assign);

                same_units!(BitAnd, bitand, BitAndAssign, bitand_assign);
                same_units!(BitOr, bitor, BitOrAssign, bitor_assign);
                same_units!(BitXor, bitxor, BitXorAssign, bitxor_assign);

                // Operations that don't care what units lhs has when rhs is a scalar
                // Mul, Div, Rem, Shl, Shr
                macro_rules! rhs_units_differ {
                    ($Trait:ident, $fun:ident, $TraitAssign:ident, $fun_assign:ident) => (
                        // Units on lhs, primitive on rhs
                        #[cfg(not(feature = "oibit"))]
                        impl<V, U> $Trait<$t> for $System<V, U> where
                            V: $Trait<$t>
                        {
                            type Output = $System<<V as $Trait<$t>>::Output, U>;
                            #[inline]
                            fn $fun(self, rhs: $t) -> Self::Output {
                                $System::new( $Trait::$fun(self.value_unsafe, rhs) )
                            }
                        }

                        // Assign: Unitless on lhs, primitive on rhs
                        #[cfg(not(feature = "oibit"))]
                        impl<V, U> $TraitAssign<$t> for $System<V, U> where
                            V: $TraitAssign<$t>
                        {
                            #[inline]
                            fn $fun_assign(&mut self, rhs: $t) {
                                $TraitAssign::$fun_assign(&mut self.value_unsafe, rhs)
                            }
                        }

                    );
                }

                rhs_units_differ!(Mul, mul, MulAssign, mul_assign);
                rhs_units_differ!(Div, div, DivAssign, div_assign);
                rhs_units_differ!(Rem, rem, RemAssign, rem_assign);
                rhs_units_differ!(Shl, shl, ShlAssign, shl_assign);
                rhs_units_differ!(Shr, shr, ShrAssign, shr_assign);

                // Mul: Primitive on lhs, units on rhs
                impl<V, U> Mul<$System<V, U>> for $t where $t: Mul<V> {
                    type Output = $System<Prod<$t, V>, U>;
                    #[inline]
                    fn mul(self, rhs: $System<V, U>) -> Self::Output {
                        $System::new(self * rhs.value_unsafe)
                    }
                }

                // Div: Primitive on lhs, units on rhs
                impl<V, U> Div<$System<V, U>> for $t where $t: Div<V>, U: Neg {
                    type Output = $System<Quot<$t, V>, <U as Neg>::Output>;
                    #[inline]
                    fn div(self, rhs: $System<V, U>) -> Self::Output {
                        $System::new(self / rhs.value_unsafe)
                    }
                }

                // Rem: Primitive on lhs, units on rhs
                impl<V, U> Rem<$System<V, U>> for $t where $t: Rem<V> {
                    type Output = $Unitless<<$t as Rem<V>>::Output>;
                    #[inline]
                    fn rem(self, rhs: $System<V, U>) -> Self::Output {
                        $System::new(self % rhs.value_unsafe)
                    }
                }

            );
        }

        prim!(f32);
        prim!(f64);

        prim!(i8);
        prim!(i16);
        prim!(i32);
        prim!(i64);
        prim!(isize);

        prim!(u8);
        prim!(u16);
        prim!(u32);
        prim!(u64);
        prim!(usize);

        prim!(bool);
        prim!(char);
    );

    (@fmt true S $System:ident $(P $print_as:expr;)* T $Trait:ident E $token:expr) => (
        impl<V, U> fmt::$Trait for $System<V, U> where
            V: fmt::$Trait,
        Length<U>: ArrayLength<isize>,
            U: TypeArray + Len + ToGA<Output = GenericArray<isize, Length<U>>>,
        {
            fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error>
            {
                let exponents = U::to_ga();
                let print_tokens = [$($print_as),*];

                let mut first = true;

                self.value_unsafe.fmt(f)?;

                for (exp, token) in
                    exponents.into_iter()
                    .zip(print_tokens.iter())
                {
                    if first {
                        if exp != 0 {
                            first = false;
                            write!(f, " ")?;
                        }
                    } else if exp != 0 {
                        write!(f, "*")?;
                    }

                    match exp {
                        0 => (),
                        1 => write!(f, "{}", token)?,
                        _ => {
                            write!(f, "{}^{}", token, exp)?
                        },
                    }
                }
                Ok(())
            }
        }
    );

    (@fmt false S $System:ident $(P $print_as:expr;)* T $Trait:ident E $token:expr) => ();

    // define arrays for all the base units
    (@base_arrays $Unitless:ident $Unit:ident $($Units:ident)*) => (
        pub type $Unitless = tarr![Z0, $(__make_units_internal!(@convert_to_zero $Units)),*];
        __make_units_internal!(@next_array U $Unit $(U $Units)* $(E $Units)*);
    );

    (@next_array U $Unit:ident $(U $Units:ident)*
     $(F $FrontZeros:ident)* E $Zero:ident $(E $EndZeros:ident)*) => (
        pub type $Unit = tarr![
            $(__make_units_internal!(@convert_to_zero $FrontZeros),)*
                P1,
            Z0 $(, __make_units_internal!(@convert_to_zero $EndZeros))*
        ];
        __make_units_internal!(@next_array $(U $Units)* $(F $FrontZeros)* F $Zero $(E $EndZeros)*);
    );

    (@next_array U $Unit:ident $(F $FrontZeros:ident)*) => (
        pub type $Unit = tarr![
            $(__make_units_internal!(@convert_to_zero $FrontZeros),)*
                P1
        ];
    );

    (@convert_to_zero $Unit:ident) => ( Z0 );
    (@convert_to_zero) => ();
}

/// Create a derived unit based on existing ones
///
/// This macro creates a type, so it is useful when you need to directly express the type of a
/// derived unit that is not defined in its unit system.
///
/// If you need a variable of some derived unit, then the easiest way is to manipulate constants,
/// like so:
///
/// ```rust
/// # extern crate dimensioned as dim;
/// use dim::si::M;
///
/// # fn main() {
/// let inverse_volume = 3.0 / M/M/M;
/// # }
/// ```
///
/// This macro is a bit fragile. It only supports the operators `*` and `/` and no parentheses. It
/// requires the base type of your unit system and the module it was defined in to be in scope.
///
/// Use it like so:
///
/// ```rust
/// # #[macro_use] extern crate dimensioned as dim;
/// use dim::si::{self, SI};
/// derived!(si, SI: InverseMeter3 = Unitless / Meter3);
/// # fn main() {}
/// ```
///
/// You may use any of the base or derived units that come with a unit system (but none created by
/// this macro) on the right-hand side of the expression.
///
/// # Example
/// ```rust
/// #[macro_use]
/// extern crate dimensioned as dim;
///
/// use dim::si::{self, SI};
///
/// derived!(si, SI: InverseMeter3 = Unitless / Meter3);
/// derived!(si, SI: Newton2PerSecond = Newton * Newton / Second);
///
/// use dim::Recip;
/// fn invert_volume(v: si::Meter3<f64>) -> InverseMeter3<f64> {
///     v.recip()
/// }
///
/// fn main() {
///    let v = 12.0 * si::M3;
///
///    let inverse_volume = invert_volume(v);
///    assert_eq!(1.0/v, inverse_volume);
/// }
/// ```
#[macro_export]
macro_rules! derived {
    ($module:ident, $System:ident: $name:ident = $($tail:tt)*) => (
        pub type $name<V> = $System<V, __derived_internal!(@commas $module, $($tail)*)>;
    );
}

#[doc(hidden)]
#[macro_export]
macro_rules! __derived_internal {
    //------------------------------------------
    // For derived:

    (@eval $module:ident, $a:ty,) => ($a);

    // Both qualify as identifiers
    (@eval $module:ident, $a:ident, /, $b:ident, $($tail:tt)*) => (
        __derived_internal!(@eval $module, $crate::typenum::Diff<$module::inner::$a, $module::inner::$b>, $($tail)* )
    );
    (@eval $module:ident, $a:ident, *, $b:ident, $($tail:tt)*) => (
        __derived_internal!(@eval $module, $crate::typenum::Sum<$module::inner::$a, $module::inner::$b>, $($tail)* )
    );

    // $a is an intermediate result:
    (@eval $module:ident, $a:ty, /, $b:ident, $($tail:tt)*) => (
        __derived_internal!(@eval $module, $crate::typenum::Diff<$a, $module::inner::$b>, $($tail)* )
    );
    (@eval $module:ident, $a:ty, *, $b:ident, $($tail:tt)*) => (
        __derived_internal!(@eval $module, $crate::typenum::Sum<$a, $module::inner::$b>, $($tail)* )
    );

    (@commas $module:ident, $t:ty) => ($t);
    (@commas $module:ident, $($tail:tt)*) => (__derived_internal!(@eval $module, $($tail,)*));


    //------------------------------------------
    // For make_units:

    (@mu eval $a:ty,) => ($a);
    (@mu eval $a:ty, *, $b:ty, $($tail:tt)*) =>
        (__derived_internal!(@mu eval $crate::typenum::Sum<$a, $b>, $($tail)* ));
    (@mu eval $a:ty, /, $b:ty, $($tail:tt)*) =>
        (__derived_internal!(@mu eval $crate::typenum::Diff<$a, $b>, $($tail)* ));
    (@mu commas $t:ty) => ($t);
    (@mu commas $($tail:tt)*) => (__derived_internal!(@mu eval $($tail,)*));
}