//! [`Uint`] multiplication modulus operations.

use crate::{Limb, Uint, WideWord, Word};

impl<const LIMBS: usize> Uint<LIMBS> {
    /// 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`].
    /// For the modulus reduction, this function implements Algorithm 14.47 from
    /// the "Handbook of Applied Cryptography", by A. Menezes, P. van Oorschot,
    /// and S. Vanstone, CRC Press, 1996.
    pub const fn mul_mod_special(&self, rhs: &Self, c: Limb) -> Self {
        // We implicitly assume `LIMBS > 0`, because `Uint<0>` doesn't compile.
        // Still the case `LIMBS == 1` needs special handling.
        if LIMBS == 1 {
            let prod = self.limbs[0].0 as WideWord * rhs.limbs[0].0 as WideWord;
            let reduced = prod % Word::MIN.wrapping_sub(c.0) as WideWord;
            return Self::from_word(reduced as Word);
        }

        let (lo, hi) = self.mul_wide(rhs);

        // Now use Algorithm 14.47 for the reduction
        let (lo, carry) = mac_by_limb(&lo, &hi, c, Limb::ZERO);

        let (lo, carry) = {
            let rhs = (carry.0 + 1) as WideWord * c.0 as WideWord;
            lo.adc(&Self::from_wide_word(rhs), Limb::ZERO)
        };

        let (lo, _) = {
            let rhs = carry.0.wrapping_sub(1) & c.0;
            lo.sbb(&Self::from_word(rhs), Limb::ZERO)
        };

        lo
    }
}

/// Computes `a + (b * c) + carry`, returning the result along with the new carry.
const fn mac_by_limb<const LIMBS: usize>(
    a: &Uint<LIMBS>,
    b: &Uint<LIMBS>,
    c: Limb,
    carry: Limb,
) -> (Uint<LIMBS>, Limb) {
    let mut i = 0;
    let mut a = *a;
    let mut carry = carry;

    while i < LIMBS {
        let (n, c) = a.limbs[i].mac(b.limbs[i], c, carry);
        a.limbs[i] = n;
        carry = c;
        i += 1;
    }

    (a, carry)
}

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

    macro_rules! test_mul_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::ZERO),
                        (Uint::ZERO, Uint::ONE, Uint::ZERO),
                        (Uint::ONE, Uint::ONE, Uint::ONE),
                        (minus_one, minus_one, Uint::ONE),
                        (minus_one, Uint::ONE, minus_one),
                        (Uint::ONE, minus_one, minus_one),
                    ];
                    for (a, b, c) in &base_cases {
                        let x = a.mul_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.mul_mod_special(&b, *special.as_ref());
                        assert!(c < **p, "not reduced: {} >= {} ", c, p);

                        let expected = {
                            let (lo, hi) = a.mul_wide(&b);
                            let mut prod = Uint::<{ 2 * $size }>::ZERO;
                            prod.limbs[..$size].clone_from_slice(&lo.limbs);
                            prod.limbs[$size..].clone_from_slice(&hi.limbs);
                            let mut modulus = Uint::ZERO;
                            modulus.limbs[..$size].clone_from_slice(&p.as_ref().limbs);
                            let reduced = prod.rem(&NonZero::new(modulus).unwrap());
                            let mut expected = Uint::ZERO;
                            expected.limbs[..].clone_from_slice(&reduced.limbs[..$size]);
                            expected
                        };
                        assert_eq!(c, expected, "incorrect result");
                    }
                }
            }
        };
    }

    test_mul_mod_special!(1, mul_mod_special_1);
    test_mul_mod_special!(2, mul_mod_special_2);
    test_mul_mod_special!(3, mul_mod_special_3);
    test_mul_mod_special!(4, mul_mod_special_4);
    test_mul_mod_special!(5, mul_mod_special_5);
    test_mul_mod_special!(6, mul_mod_special_6);
    test_mul_mod_special!(7, mul_mod_special_7);
    test_mul_mod_special!(8, mul_mod_special_8);
    test_mul_mod_special!(9, mul_mod_special_9);
    test_mul_mod_special!(10, mul_mod_special_10);
    test_mul_mod_special!(11, mul_mod_special_11);
    test_mul_mod_special!(12, mul_mod_special_12);
}