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    // Copyright 2017 Brian Smith.
    //
    // Permission to use, copy, modify, and/or distribute this software for any
    // purpose with or without fee is hereby granted, provided that the above
    // copyright notice and this permission notice appear in all copies.
    //
    // THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES
    // WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    // MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY
    // SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    // WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
    // OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
    // CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

    use arithmetic::montgomery::{Encoding, ProductEncoding};
    use core::marker::PhantomData;
    use limb::*;

    /// Elements of ℤ/mℤ for some modulus *m*. Elements are always fully reduced
    /// with respect to *m*; i.e. the 0 <= x < m for every value x.
    #[derive(Clone, Copy)]
    pub struct Elem<M, E: Encoding> {
        // XXX: pub
        pub limbs: [Limb; MAX_LIMBS],

        /// The modulus *m* for the ring ℤ/mℤ for which this element is a value.
        pub m: PhantomData<M>,

        /// The number of Montgomery factors that need to be canceled out from
        /// `value` to get the actual value.
        pub encoding: PhantomData<E>,
    }

    impl<M, E: Encoding> Elem<M, E> {
        // There's no need to convert `value` to the Montgomery domain since
        // 0 * R**2 (mod m) == 0, so neither the modulus nor the encoding are needed
        // as inputs for constructing a zero-valued element.
        pub fn zero() -> Elem<M, E> {
            Elem {
                limbs: [0; MAX_LIMBS],
                m: PhantomData,
                encoding: PhantomData,
            }
        }
    }

    #[inline]
    pub fn mul_mont<M, EA: Encoding, EB: Encoding>(
        f: unsafe extern fn(r: *mut Limb, a: *const Limb, b: *const Limb),
        a: &Elem<M, EA>, b: &Elem<M, EB>)
        -> Elem<M, <(EA, EB) as ProductEncoding>::Output>
        where (EA, EB): ProductEncoding
    {
        binary_op(f, a, b)
    }

    // let r = f(a, b); return r;
    #[inline]
    pub fn binary_op<M, EA: Encoding, EB: Encoding, ER: Encoding>(
            f: unsafe extern fn(r: *mut Limb, a: *const Limb, b: *const Limb),
            a: &Elem<M, EA>, b: &Elem<M, EB>) -> Elem<M, ER> {
        let mut r = Elem {
            limbs: [0; MAX_LIMBS],
            m: PhantomData,
            encoding: PhantomData
        };
        unsafe { f(r.limbs.as_mut_ptr(), a.limbs.as_ptr(), b.limbs.as_ptr()) }
        r
    }

    // a := f(a, b);
    #[inline]
    pub fn binary_op_assign<M, EA: Encoding, EB: Encoding>(
            f: unsafe extern fn(r: *mut Limb, a: *const Limb, b: *const Limb),
            a: &mut Elem<M, EA>, b: &Elem<M, EB>) {
        unsafe { f(a.limbs.as_mut_ptr(), a.limbs.as_ptr(), b.limbs.as_ptr()) }
    }

    // let r = f(a); return r;
    #[inline]
    pub fn unary_op<M, E: Encoding>(
            f: unsafe extern fn(r: *mut Limb, a: *const Limb), a: &Elem<M, E>)
            -> Elem<M, E> {
        let mut r = Elem {
            limbs: [0; MAX_LIMBS],
            m: PhantomData,
            encoding: PhantomData,
        };
        unsafe { f(r.limbs.as_mut_ptr(), a.limbs.as_ptr()) }
        r
    }

    // a := f(a);
    #[inline]
    pub fn unary_op_assign<M, E: Encoding>(
            f: unsafe extern fn(r: *mut Limb, a: *const Limb), a: &mut Elem<M, E>) {
        unsafe { f(a.limbs.as_mut_ptr(), a.limbs.as_ptr()) }
    }

    // a := f(a, a);
    #[inline]
    pub fn unary_op_from_binary_op_assign<M, E: Encoding>(
            f: unsafe extern fn(r: *mut Limb, a: *const Limb, b: *const Limb),
            a: &mut Elem<M, E>) {
        unsafe { f(a.limbs.as_mut_ptr(), a.limbs.as_ptr(), a.limbs.as_ptr()) }
    }

    pub const MAX_LIMBS: usize = (384 + (LIMB_BITS - 1)) / LIMB_BITS;

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