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//! [`UInt`] addition modulus operations.

use crate::{AddMod, Limb, UInt};

impl<const LIMBS: usize> UInt<LIMBS> {
    /// Computes `self + rhs mod p` in constant time.
    ///
    /// Assumes `self + rhs` as unbounded integer is `< 2p`.
    pub const fn add_mod(&self, rhs: &UInt<LIMBS>, p: &UInt<LIMBS>) -> UInt<LIMBS> {
        let (w, carry) = self.adc(rhs, Limb::ZERO);

        // Attempt to subtract the modulus, to ensure the result is in the field.
        let (w, borrow) = w.sbb(p, Limb::ZERO);
        let (_, borrow) = carry.sbb(Limb::ZERO, borrow);

        // If underflow occurred on the final limb, borrow = 0xfff...fff, otherwise
        // borrow = 0x000...000. Thus, we use it as a mask to conditionally add the
        // modulus.
        let mut i = 0;
        let mut res = Self::ZERO;
        let mut carry = Limb::ZERO;

        while i < LIMBS {
            let rhs = p.limbs[i].bitand(borrow);
            let (limb, c) = w.limbs[i].adc(rhs, carry);
            res.limbs[i] = limb;
            carry = c;
            i += 1;
        }

        res
    }

    /// Computes `self + rhs mod p` in constant time for the special modulus
    /// `p = MAX+1-c` where `c` is small enough to fit in a single [`Limb`].
    ///
    /// Assumes `self + rhs` as unbounded integer is `< 2p`.
    pub const fn add_mod_special(&self, rhs: &Self, c: Limb) -> Self {
        // `UInt::adc` also works with a carry greater than 1.
        let (out, carry) = self.adc(rhs, c);

        // If overflow occurred, then above addition of `c` already accounts
        // for the overflow. Otherwise, we need to subtract `c` again, which
        // in that case cannot underflow.
        let l = carry.0.wrapping_sub(1) & c.0;
        let (out, _) = out.sbb(&UInt::from_word(l), Limb::ZERO);
        out
    }
}

impl<const LIMBS: usize> AddMod for UInt<LIMBS> {
    type Output = Self;

    fn add_mod(&self, rhs: &Self, p: &Self) -> Self {
        debug_assert!(self < p);
        debug_assert!(rhs < p);
        self.add_mod(rhs, p)
    }
}

#[cfg(all(test, feature = "rand"))]
mod tests {
    use crate::{Limb, NonZero, Random, RandomMod, UInt, U256};
    use rand_core::SeedableRng;

    // TODO(tarcieri): additional tests + proptests

    #[test]
    fn add_mod_nist_p256() {
        let a =
            U256::from_be_hex("44acf6b7e36c1342c2c5897204fe09504e1e2efb1a900377dbc4e7a6a133ec56");
        let b =
            U256::from_be_hex("d5777c45019673125ad240f83094d4252d829516fac8601ed01979ec1ec1a251");
        let n =
            U256::from_be_hex("ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551");

        let actual = a.add_mod(&b, &n);
        let expected =
            U256::from_be_hex("1a2472fde50286541d97ca6a3592dd75beb9c9646e40c511b82496cfc3926956");

        assert_eq!(expected, actual);
    }

    macro_rules! test_add_mod_special {
        ($size:expr, $test_name:ident) => {
            #[test]
            fn $test_name() {
                let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
                let moduli = [
                    NonZero::<Limb>::random(&mut rng),
                    NonZero::<Limb>::random(&mut rng),
                ];

                for special in &moduli {
                    let p = &NonZero::new(UInt::ZERO.wrapping_sub(&UInt::from_word(special.0)))
                        .unwrap();

                    let minus_one = p.wrapping_sub(&UInt::ONE);

                    let base_cases = [
                        (UInt::ZERO, UInt::ZERO, UInt::ZERO),
                        (UInt::ONE, UInt::ZERO, UInt::ONE),
                        (UInt::ZERO, UInt::ONE, UInt::ONE),
                        (minus_one, UInt::ONE, UInt::ZERO),
                        (UInt::ONE, minus_one, UInt::ZERO),
                    ];
                    for (a, b, c) in &base_cases {
                        let x = a.add_mod_special(b, *special.as_ref());
                        assert_eq!(*c, x, "{} + {} mod {} = {} != {}", a, b, p, x, c);
                    }

                    for _i in 0..100 {
                        let a = UInt::<$size>::random_mod(&mut rng, p);
                        let b = UInt::<$size>::random_mod(&mut rng, p);

                        let c = a.add_mod_special(&b, *special.as_ref());
                        assert!(c < **p, "not reduced: {} >= {} ", c, p);

                        let expected = a.add_mod(&b, p);
                        assert_eq!(c, expected, "incorrect result");
                    }
                }
            }
        };
    }

    test_add_mod_special!(1, add_mod_special_1);
    test_add_mod_special!(2, add_mod_special_2);
    test_add_mod_special!(3, add_mod_special_3);
    test_add_mod_special!(4, add_mod_special_4);
    test_add_mod_special!(5, add_mod_special_5);
    test_add_mod_special!(6, add_mod_special_6);
    test_add_mod_special!(7, add_mod_special_7);
    test_add_mod_special!(8, add_mod_special_8);
    test_add_mod_special!(9, add_mod_special_9);
    test_add_mod_special!(10, add_mod_special_10);
    test_add_mod_special!(11, add_mod_special_11);
    test_add_mod_special!(12, add_mod_special_12);
}