use itertools::Itertools;
use params::N;
use reduce::montgomery_reduce;

const ZETAS: [i32; N] = [
    0, 25847, -2608894, -518909, 237124, -777960, -876248, 466468, 1826347, 2353451, -359251,
    -2091905, 3119733, -2884855, 3111497, 2680103, 2725464, 1024112, -1079900, 3585928, -549488,
    -1119584, 2619752, -2108549, -2118186, -3859737, -1399561, -3277672, 1757237, -19422, 4010497,
    280005, 2706023, 95776, 3077325, 3530437, -1661693, -3592148, -2537516, 3915439, -3861115,
    -3043716, 3574422, -2867647, 3539968, -300467, 2348700, -539299, -1699267, -1643818, 3505694,
    -3821735, 3507263, -2140649, -1600420, 3699596, 811944, 531354, 954230, 3881043, 3900724,
    -2556880, 2071892, -2797779, -3930395, -1528703, -3677745, -3041255, -1452451, 3475950,
    2176455, -1585221, -1257611, 1939314, -4083598, -1000202, -3190144, -3157330, -3632928, 126922,
    3412210, -983419, 2147896, 2715295, -2967645, -3693493, -411027, -2477047, -671102, -1228525,
    -22981, -1308169, -381987, 1349076, 1852771, -1430430, -3343383, 264944, 508951, 3097992,
    44288, -1100098, 904516, 3958618, -3724342, -8578, 1653064, -3249728, 2389356, -210977, 759969,
    -1316856, 189548, -3553272, 3159746, -1851402, -2409325, -177440, 1315589, 1341330, 1285669,
    -1584928, -812732, -1439742, -3019102, -3881060, -3628969, 3839961, 2091667, 3407706, 2316500,
    3817976, -3342478, 2244091, -2446433, -3562462, 266997, 2434439, -1235728, 3513181, -3520352,
    -3759364, -1197226, -3193378, 900702, 1859098, 909542, 819034, 495491, -1613174, -43260,
    -522500, -655327, -3122442, 2031748, 3207046, -3556995, -525098, -768622, -3595838, 342297,
    286988, -2437823, 4108315, 3437287, -3342277, 1735879, 203044, 2842341, 2691481, -2590150,
    1265009, 4055324, 1247620, 2486353, 1595974, -3767016, 1250494, 2635921, -3548272, -2994039,
    1869119, 1903435, -1050970, -1333058, 1237275, -3318210, -1430225, -451100, 1312455, 3306115,
    -1962642, -1279661, 1917081, -2546312, -1374803, 1500165, 777191, 2235880, 3406031, -542412,
    -2831860, -1671176, -1846953, -2584293, -3724270, 594136, -3776993, -2013608, 2432395, 2454455,
    -164721, 1957272, 3369112, 185531, -1207385, -3183426, 162844, 1616392, 3014001, 810149,
    1652634, -3694233, -1799107, -3038916, 3523897, 3866901, 269760, 2213111, -975884, 1717735,
    472078, -426683, 1723600, -1803090, 1910376, -1667432, -1104333, -260646, -3833893, -2939036,
    -2235985, -420899, -2286327, 183443, -976891, 1612842, -3545687, -554416, 3919660, -48306,
    -1362209, 3937738, 1400424, -846154, 1976782,
];

/// Implements forward NTT, in-place.
///
/// No modular reduction is performed after additions or substractions.
/// The output vector is in bitreversed order.
///
/// # Arguments
///
/// * `p` - a polynomial in standard representation.
pub fn ntt(p: &mut [i32; N]) {
    let mut k = 1;
    let mut len = 128;
    while len > 0 {
        for start in Itertools::step(0..N, 2 * len) {
            let zeta = i64::from(ZETAS[k]);
            k += 1;
            for j in start..(start + len) {
                let t = montgomery_reduce(zeta * i64::from(p[j + len]));
                p[j + len] = p[j] - t;
                p[j] += t;
            }
        }

        len >>= 1;
    }
}

/// Implements inverse NTT and multiplication by Montgomery factor 2^32.
///
/// The implementation is in-place.
/// No modular reduction is performed after additions or substractions.
/// Input coefficients must be smaller than Q in absolute value.
/// The output coefficients are smaller than Q in absolute value.
///
/// # Arguments
///
/// * `p` - a polynomial in NTT representation.
pub fn invntt_frominvmont(p: &mut [i32; N]) {
    let mut k = 255;
    let mut len = 1;

    while len < N {
        for start in Itertools::step(0..N, 2 * len) {
            let zeta = (-1) * i64::from(ZETAS[k]);
            k -= 1;

            for j in start..(start + len) {
                let t = p[j];
                p[j] += p[j + len];
                p[j + len] = t - p[j + len];
                p[j + len] = montgomery_reduce(zeta * i64::from(p[j + len]));
            }
        }
        len <<= 1;
    }

    // F = MONT^2 / 256 mod Q, where MONT = 2^32 mod Q.
    const F: i64 = 41978;
    for j in 0..N {
        p[j] = montgomery_reduce(F * i64::from(p[j]));
    }
}