// -*- mode: rust; -*-
//
// This file is part of curve25519-dalek.
// Copyright (c) 2016-2021 isis lovecruft
// Copyright (c) 2016-2019 Henry de Valence
// See LICENSE for licensing information.
//
// Authors:
// - isis agora lovecruft <isis@patternsinthevoid.net>
// - Henry de Valence <hdevalence@hdevalence.ca>

//! This module contains various constants (such as curve parameters
//! and useful field elements like `sqrt(-1)`), as well as
//! lookup tables of pre-computed points.

use super::field::FieldElement2625;
use super::scalar::Scalar29;
use crate::edwards::EdwardsPoint;

#[cfg(feature = "precomputed-tables")]
use crate::{
    backend::serial::curve_models::AffineNielsPoint,
    edwards::EdwardsBasepointTable,
    window::{LookupTable, NafLookupTable8},
};

/// The value of minus one, equal to `-&FieldElement::ONE`
pub(crate) const MINUS_ONE: FieldElement2625 = FieldElement2625::from_limbs([
    67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863,
    33554431,
]);

/// Edwards `d` value, equal to `-121665/121666 mod p`.
pub(crate) const EDWARDS_D: FieldElement2625 = FieldElement2625::from_limbs([
    56195235, 13857412, 51736253, 6949390, 114729, 24766616, 60832955, 30306712, 48412415, 21499315,
]);

/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
pub(crate) const EDWARDS_D2: FieldElement2625 = FieldElement2625::from_limbs([
    45281625, 27714825, 36363642, 13898781, 229458, 15978800, 54557047, 27058993, 29715967, 9444199,
]);

/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement2625 = FieldElement2625::from_limbs([
    6275446, 16937061, 44170319, 29780721, 11667076, 7397348, 39186143, 1766194, 42675006, 672202,
]);

/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement2625 = FieldElement2625::from_limbs([
    15551776, 22456977, 53683765, 23429360, 55212328, 10178283, 40474537, 4729243, 61826754,
    23438029,
]);

/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const SQRT_AD_MINUS_ONE: FieldElement2625 = FieldElement2625::from_limbs([
    24849947, 33400850, 43495378, 6347714, 46036536, 32887293, 41837720, 18186727, 66238516,
    14525638,
]);

/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const INVSQRT_A_MINUS_D: FieldElement2625 = FieldElement2625::from_limbs([
    6111466, 4156064, 39310137, 12243467, 41204824, 120896, 20826367, 26493656, 6093567, 31568420,
]);

/// Precomputed value of one of the square roots of -1 (mod p)
pub(crate) const SQRT_M1: FieldElement2625 = FieldElement2625::from_limbs([
    34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685, 11406482,
]);

/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
pub(crate) const APLUS2_OVER_FOUR: FieldElement2625 =
    FieldElement2625::from_limbs([121666, 0, 0, 0, 0, 0, 0, 0, 0, 0]);

/// `MONTGOMERY_A` is equal to 486662, which is a constant of the curve equation
/// for Curve25519 in its Montgomery form. (This is used internally within the
/// Elligator map.)
pub(crate) const MONTGOMERY_A: FieldElement2625 =
    FieldElement2625::from_limbs([486662, 0, 0, 0, 0, 0, 0, 0, 0, 0]);

/// `MONTGOMERY_A_NEG` is equal to -486662. (This is used internally within the
/// Elligator map.)
pub(crate) const MONTGOMERY_A_NEG: FieldElement2625 = FieldElement2625::from_limbs([
    66622183, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863,
    33554431,
]);

/// `L` is the order of base point, i.e. 2^252 +
/// 27742317777372353535851937790883648493
pub(crate) const L: Scalar29 = Scalar29([
    0x1cf5d3ed, 0x009318d2, 0x1de73596, 0x1df3bd45, 0x0000014d, 0x00000000, 0x00000000, 0x00000000,
    0x00100000,
]);

/// `L` * `LFACTOR` = -1 (mod 2^29)
pub(crate) const LFACTOR: u32 = 0x12547e1b;

/// `R` = R % L where R = 2^261
pub(crate) const R: Scalar29 = Scalar29([
    0x114df9ed, 0x1a617303, 0x0f7c098c, 0x16793167, 0x1ffd656e, 0x1fffffff, 0x1fffffff, 0x1fffffff,
    0x000fffff,
]);

/// `RR` = (R^2) % L where R = 2^261
pub(crate) const RR: Scalar29 = Scalar29([
    0x0b5f9d12, 0x1e141b17, 0x158d7f3d, 0x143f3757, 0x1972d781, 0x042feb7c, 0x1ceec73d, 0x1e184d1e,
    0x0005046d,
]);

/// The Ed25519 basepoint, as an `EdwardsPoint`.
///
/// This is called `_POINT` to distinguish it from
/// `ED25519_BASEPOINT_TABLE`, which should be used for scalar
/// multiplication (it's much faster).
pub const ED25519_BASEPOINT_POINT: EdwardsPoint = EdwardsPoint {
    X: FieldElement2625::from_limbs([
        52811034, 25909283, 16144682, 17082669, 27570973, 30858332, 40966398, 8378388, 20764389,
        8758491,
    ]),
    Y: FieldElement2625::from_limbs([
        40265304, 26843545, 13421772, 20132659, 26843545, 6710886, 53687091, 13421772, 40265318,
        26843545,
    ]),
    Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    T: FieldElement2625::from_limbs([
        28827043, 27438313, 39759291, 244362, 8635006, 11264893, 19351346, 13413597, 16611511,
        27139452,
    ]),
};

/// The 8-torsion subgroup \\(\mathcal E \[8\]\\).
///
/// In the case of Curve25519, it is cyclic; the \\(i\\)-th element of
/// the array is \\([i]P\\), where \\(P\\) is a point of order \\(8\\)
/// generating \\(\mathcal E\[8\]\\).
///
/// Thus \\(\mathcal E\[4\]\\) is the points indexed by `0,2,4,6`, and
/// \\(\mathcal E\[2\]\\) is the points indexed by `0,4`.
/// The Ed25519 basepoint has y = 4/5.  This is called `_POINT` to
/// distinguish it from `_TABLE`, which should be used for scalar
/// multiplication (it's much faster).
pub const EIGHT_TORSION: [EdwardsPoint; 8] = EIGHT_TORSION_INNER_DOC_HIDDEN;

/// Inner item used to hide limb constants from cargo doc output.
#[doc(hidden)]
pub const EIGHT_TORSION_INNER_DOC_HIDDEN: [EdwardsPoint; 8] = [
    EdwardsPoint {
        X: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Y: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([
            21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924,
            8345318,
        ]),
        Y: FieldElement2625::from_limbs([
            6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852,
            31985330,
        ]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([
            41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334,
            3541542, 28543251,
        ]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([
            32595773, 7943725, 57730914, 30054016, 54719391, 272472, 25146209, 2005654, 66782178,
            22147949,
        ]),
        Y: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([
            21352778, 5345713, 4660180, 25206575, 24143089, 14568123, 30185756, 21306662, 33579924,
            8345318,
        ]),
        Y: FieldElement2625::from_limbs([
            60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030,
            47743011, 1569101,
        ]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([
            25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321,
            5011180,
        ]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Y: FieldElement2625::from_limbs([
            67108844, 33554431, 67108863, 33554431, 67108863, 33554431, 67108863, 33554431,
            67108863, 33554431,
        ]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([
            45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769,
            33528939, 25209113,
        ]),
        Y: FieldElement2625::from_limbs([
            60155942, 32288931, 6862340, 26496934, 63071167, 28106709, 31680898, 18229030,
            47743011, 1569101,
        ]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([
            41846657, 21581751, 11716001, 27684820, 48915701, 16297738, 20670665, 24995334,
            3541542, 28543251,
        ]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([
            34513072, 25610706, 9377949, 3500415, 12389472, 33281959, 41962654, 31548777, 326685,
            11406482,
        ]),
        Y: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement2625::from_limbs([
            45756067, 28208718, 62448683, 8347856, 42965774, 18986308, 36923107, 12247769,
            33528939, 25209113,
        ]),
        Y: FieldElement2625::from_limbs([
            6952903, 1265500, 60246523, 7057497, 4037696, 5447722, 35427965, 15325401, 19365852,
            31985330,
        ]),
        Z: FieldElement2625::from_limbs([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement2625::from_limbs([
            25262188, 11972680, 55392862, 5869611, 18193162, 17256693, 46438198, 8559097, 63567321,
            5011180,
        ]),
    },
];

/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
#[cfg(feature = "precomputed-tables")]
pub static ED25519_BASEPOINT_TABLE: &'static EdwardsBasepointTable =
    &ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;

/// Inner constant, used to avoid filling the docs with precomputed points.
#[doc(hidden)]
#[cfg(feature = "precomputed-tables")]
static ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable = EdwardsBasepointTable([
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                93076338, 52752828, 29566454, 37215328, 54414518, 37569218, 94653489, 21800160,
                61029707, 35602036,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692, 5043384,
                19500929, 18085054,
            ]),
            xy2d: FieldElement2625::from_limbs([
                58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918, 11864899,
                42594502, 29115885,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                54292951, 54132516, 45527619, 11784319, 41753206, 30803714, 55390960, 29739860,
                66750418, 23343128,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                45405608, 6903824, 27185491, 6451973, 37531140, 24000426, 51492312, 11189267,
                40279186, 28235350,
            ]),
            xy2d: FieldElement2625::from_limbs([
                26966623, 11152617, 32442495, 15396054, 14353839, 20802097, 63980037, 24013313,
                51636816, 29387734,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                82745136, 23865874, 24204772, 25642034, 67725840, 16869169, 94896463, 52336674,
                28944398, 32004408,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576, 21778470,
                7689661, 11199574,
            ]),
            xy2d: FieldElement2625::from_limbs([
                30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774, 10017326,
                49359771, 23634074,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                50071967, 13921891, 78054670, 27521000, 27105051, 17470053, 105291517, 15006021,
                70393432, 27277891,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                23599295, 25248385, 55915199, 25867015, 13236773, 10506355, 7464579, 9656445,
                13059162, 10374397,
            ]),
            xy2d: FieldElement2625::from_limbs([
                7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, 29715387,
                66467155, 33453106,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                77970208, 11473153, 27284546, 35535607, 37044514, 46132292, 99976748, 48069538,
                118779423, 44373810,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196, 12483687,
                54440373, 5581305,
            ]),
            xy2d: FieldElement2625::from_limbs([
                19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349, 13850243,
                43430843, 17738489,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                51736881, 20691677, 32573249, 4720197, 107781206, 39429941, 115029100, 18329611,
                124398787, 21468653,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240, 17864545, 1762327,
                14866737,
            ]),
            xy2d: FieldElement2625::from_limbs([
                48909169, 17603008, 56635573, 1707277, 49922944, 3916100, 38872452, 3959420,
                27914454, 4383652,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                72262591, 43463716, 68832610, 30776557, 97632468, 39071304, 86589715, 38784565,
                43156424, 18378665,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025, 16520125,
                30598449, 7715701,
            ]),
            xy2d: FieldElement2625::from_limbs([
                28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204, 1370707,
                29794553, 32145132,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                14499452, 64379265, 33917749, 62854211, 95603724, 14271266, 97399599, 10876453,
                33954766, 35936157,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                59913433, 30899068, 52378708, 462250, 39384538, 3941371, 60872247, 3696004,
                34808032, 15351954,
            ]),
            xy2d: FieldElement2625::from_limbs([
                27431194, 8222322, 16448760, 29646437, 48401861, 11938354, 34147463, 30583916,
                29551812, 10109425,
            ]),
        },
    ]),
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                53451805, 20399000, 102933977, 45331528, 88556249, 40073815, 64730579, 31926875,
                77201646, 28790260,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                27939166, 14210322, 4677035, 16277044, 44144402, 21156292, 34600109, 12005537,
                49298737, 12803509,
            ]),
            xy2d: FieldElement2625::from_limbs([
                17228999, 17892808, 65875336, 300139, 65883994, 21839654, 30364212, 24516238,
                18016356, 4397660,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                56150002, 25864224, 4776340, 18600194, 27850027, 17952220, 40489757, 14544524,
                49631360, 34537070,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899, 29434304,
                46061167, 9934962,
            ]),
            xy2d: FieldElement2625::from_limbs([
                5793284, 16271923, 42977250, 23438027, 29188559, 1206517, 52360934, 4559894,
                36984942, 22656481,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                39464893, 55615857, 83391519, 22517938, 28414020, 52096600, 24191032, 38096129,
                53770554, 39054999,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                12650548, 32057319, 9052870, 11355358, 49428827, 25154267, 49678271, 12264342,
                10874051, 13524335,
            ]),
            xy2d: FieldElement2625::from_limbs([
                25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037, 5080568,
                44580805, 5376627,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                108129445, 29543378, 50095164, 30016803, 60382070, 35475328, 44787558, 57661420,
                71644630, 35123438,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                64853442, 14606629, 45416424, 25514613, 28430648, 8775819, 36614302, 3044289,
                31848280, 12543772,
            ]),
            xy2d: FieldElement2625::from_limbs([
                45080285, 2943892, 35251351, 6777305, 13784462, 29262229, 39731668, 31491700,
                7718481, 14474653,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                69494160, 36008644, 44477543, 33601034, 62670928, 51428448, 67765827, 26317766,
                91425031, 28300864,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                13741529, 10911568, 33875447, 24950694, 46931033, 32521134, 33040650, 20129900,
                46379407, 8321685,
            ]),
            xy2d: FieldElement2625::from_limbs([
                21060490, 31341688, 15712756, 29218333, 1639039, 10656336, 23845965, 21679594,
                57124405, 608371,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                53436113, 18466845, 56219170, 25997372, 61071954, 11305546, 68232832, 60328286,
                94338261, 33578318,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                43864724, 33260226, 55364135, 14712570, 37643165, 31524814, 12797023, 27114124,
                65475458, 16678953,
            ]),
            xy2d: FieldElement2625::from_limbs([
                37608244, 4770661, 51054477, 14001337, 7830047, 9564805, 65600720, 28759386,
                49939598, 4904952,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                91168402, 48171434, 86146020, 18514523, 86874956, 18648002, 72278074, 16191879,
                69237100, 29227598,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                50127693, 4124965, 58568254, 22900634, 30336521, 19449185, 37302527, 916032,
                60226322, 30567899,
            ]),
            xy2d: FieldElement2625::from_limbs([
                44477957, 12419371, 59974635, 26081060, 50629959, 16739174, 285431, 2763829,
                15736322, 4143876,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                69488197, 11839344, 62998462, 27565766, 78383161, 34349388, 67321664, 18959768,
                23527083, 17096164,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                33431108, 22423954, 49269897, 17927531, 8909498, 8376530, 34483524, 4087880,
                51919953, 19138217,
            ]),
            xy2d: FieldElement2625::from_limbs([
                1767664, 7197987, 53903638, 31531796, 54017513, 448825, 5799055, 4357868, 62334673,
                17231393,
            ]),
        },
    ]),
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                6721947, 47388255, 43585475, 32003117, 93463156, 21691110, 90474010, 29604699,
                74499753, 36314231,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                4409022, 2052381, 23373853, 10530217, 7676779, 20668478, 21302352, 29290375,
                1244379, 20634787,
            ]),
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                57640015, 4763277,
            ]),
            xy2d: FieldElement2625::from_limbs([
                45409620, 9220968, 51378240, 1084136, 41632757, 30702041, 31088446, 25789909,
                55752334, 728111,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                26047201, 55357393, 127317403, 50587064, 91200930, 9158118, 62835319, 20998873,
                104852291, 28056158,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                17510331, 33231575, 5854288, 8403524, 17133918, 30441820, 38997856, 12327944,
                10750447, 10014012,
            ]),
            xy2d: FieldElement2625::from_limbs([
                56796096, 3936951, 9156313, 24656749, 16498691, 32559785, 39627812, 32887699,
                3424690, 7540221,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                97431206, 26590321, 78469868, 29411114, 74542167, 4989747, 127146306, 50791643,
                57864597, 48812477,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                13054543, 30774935, 19155473, 469045, 54626067, 4566041, 5631406, 2711395, 1062915,
                28418087,
            ]),
            xy2d: FieldElement2625::from_limbs([
                47868616, 22299832, 37599834, 26054466, 61273100, 13005410, 61042375, 12194496,
                32960380, 1459310,
            ]),
        },
    ]),
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                86960860, 40582355, 90778216, 43574797, 75695366, 26896524, 67503060, 27452546,
                85746866, 55933926,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                31395515, 15098109, 26581030, 8030562, 50580950, 28547297, 9012485, 25970078,
                60465776, 28111795,
            ]),
            xy2d: FieldElement2625::from_limbs([
                57916680, 31207054, 65111764, 4529533, 25766844, 607986, 67095642, 9677542,
                34813975, 27098423,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                64664330, 33404494, 96457765, 8186664, 68982624, 12489862, 103283149, 25714738,
                59256019, 58970434,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                51872508, 18120922, 7766469, 746860, 26346930, 23332670, 39775412, 10754587,
                57677388, 5203575,
            ]),
            xy2d: FieldElement2625::from_limbs([
                31834314, 14135496, 66338857, 5159117, 20917671, 16786336, 59640890, 26216907,
                31809242, 7347066,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                57502122, 21680191, 87523322, 46588417, 80825387, 21862550, 86906833, 21343176,
                82301739, 31466941,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                54445282, 31372712, 1168161, 29749623, 26747876, 19416341, 10609329, 12694420,
                33473243, 20172328,
            ]),
            xy2d: FieldElement2625::from_limbs([
                33184999, 11180355, 15832085, 22169002, 65475192, 225883, 15089336, 22530529,
                60973201, 14480052,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                98417562, 27934433, 98139703, 31657332, 82783410, 26971548, 72605071, 13685226,
                27595050, 42291707,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                46790012, 18404192, 10933842, 17376410, 8335351, 26008410, 36100512, 20943827,
                26498113, 66511,
            ]),
            xy2d: FieldElement2625::from_limbs([
                22644435, 24792703, 50437087, 4884561, 64003250, 19995065, 30540765, 29267685,
                53781076, 26039336,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                106199862, 9834843, 85726071, 30873119, 63706907, 53801357, 75314402, 13585436,
                117090263, 48669869,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                23711543, 32881517, 31206560, 25191721, 6164646, 23844445, 33572981, 32128335,
                8236920, 16492939,
            ]),
            xy2d: FieldElement2625::from_limbs([
                43198286, 20038905, 40809380, 29050590, 25005589, 25867162, 19574901, 10071562,
                6708380, 27332008,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                69210217, 28624377, 86811594, 35922006, 118790560, 34602105, 72409880, 42883131,
                29955600, 55430554,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                3096359, 9271816, 45488000, 18032587, 52260867, 25961494, 41216721, 20918836,
                57191288, 6216607,
            ]),
            xy2d: FieldElement2625::from_limbs([
                34493015, 338662, 41913253, 2510421, 37895298, 19734218, 24822829, 27407865,
                40341383, 7525078,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                44042196, 53123240, 83242349, 25658253, 130828162, 34333218, 66198527, 30771936,
                47722230, 45548532,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                21691500, 19929806, 66467532, 19187410, 3285880, 30070836, 42044197, 9718257,
                59631427, 13381417,
            ]),
            xy2d: FieldElement2625::from_limbs([
                18445390, 29352196, 14979845, 11622458, 65381754, 29971451, 23111647, 27179185,
                28535281, 15779576,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                30098034, 36644094, 124983340, 16662133, 45801924, 44862842, 53040409, 12021729,
                77064149, 17251075,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                9734894, 18977602, 59635230, 24415696, 2060391, 11313496, 48682835, 9924398,
                20194861, 13380996,
            ]),
            xy2d: FieldElement2625::from_limbs([
                40730762, 25589224, 44941042, 15789296, 49053522, 27385639, 65123949, 15707770,
                26342023, 10146099,
            ]),
        },
    ]),
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                41091971, 33334488, 88448054, 33513043, 86854119, 30675731, 37471583, 35781471,
                21612325, 33008704,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                54031477, 1184227, 23562814, 27583990, 46757619, 27205717, 25764460, 12243797,
                46252298, 11649657,
            ]),
            xy2d: FieldElement2625::from_limbs([
                57077370, 11262625, 27384172, 2271902, 26947504, 17556661, 39943, 6114064,
                33514190, 2333242,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                112784121, 54687041, 75228644, 40774344, 45278341, 58092729, 60429112, 54438225,
                91459440, 20104430,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                62992557, 22282898, 43222677, 4843614, 37020525, 690622, 35572776, 23147595,
                8317859, 12352766,
            ]),
            xy2d: FieldElement2625::from_limbs([
                18200138, 19078521, 34021104, 30857812, 43406342, 24451920, 43556767, 31266881,
                20712162, 6719373,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                26656189, 39629685, 59250307, 35440503, 105873684, 37816756, 78226393, 29791221,
                26224234, 30256974,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                49939907, 18700334, 63713187, 17184554, 47154818, 14050419, 21728352, 9493610,
                18620611, 17125804,
            ]),
            xy2d: FieldElement2625::from_limbs([
                53785524, 13325348, 11432106, 5964811, 18609221, 6062965, 61839393, 23828875,
                36407290, 17074774,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                43248307, 55875704, 94070219, 35195292, 34695751, 16816491, 79357372, 28313792,
                80844205, 35488493,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                25089769, 6742589, 17081145, 20148166, 21909292, 17486451, 51972569, 29789085,
                45830866, 5473615,
            ]),
            xy2d: FieldElement2625::from_limbs([
                31883658, 25593331, 1083431, 21982029, 22828470, 13290673, 59983779, 12469655,
                29111212, 28103418,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                91353792, 52058456, 107954750, 36345970, 52111264, 50221109, 91476329, 39943270,
                56813276, 34006814,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                41468082, 30136590, 5217915, 16224624, 19987036, 29472163, 42872612, 27639183,
                15766061, 8407814,
            ]),
            xy2d: FieldElement2625::from_limbs([
                46701865, 13990230, 15495425, 16395525, 5377168, 15166495, 58191841, 29165478,
                59040954, 2276717,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                30157899, 46478498, 116505677, 42800183, 87003891, 36922573, 43281276, 38650650,
                89849239, 26251014,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                2041139, 19298082, 7783686, 13876377, 41161879, 20201972, 24051123, 13742383,
                51471265, 13295221,
            ]),
            xy2d: FieldElement2625::from_limbs([
                33338218, 25048699, 12532112, 7977527, 9106186, 31839181, 49388668, 28941459,
                62657506, 18884987,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                47063564, 39008528, 52762315, 40001577, 28862070, 35438083, 64639597, 29412551,
                74879432, 43175028,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                23208049, 7979712, 33071466, 8149229, 1758231, 22719437, 30945527, 31860109,
                33606523, 18786461,
            ]),
            xy2d: FieldElement2625::from_limbs([
                1439939, 17283952, 66028874, 32760649, 4625401, 10647766, 62065063, 1220117,
                30494170, 22113633,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                62071265, 20526136, 64138304, 30492664, 82749837, 26852765, 40369837, 34480481,
                65424524, 20220784,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                13908495, 30005160, 30919927, 27280607, 45587000, 7989038, 9021034, 9078865,
                3353509, 4033511,
            ]),
            xy2d: FieldElement2625::from_limbs([
                37445433, 18440821, 32259990, 33209950, 24295848, 20642309, 23161162, 8839127,
                27485041, 7356032,
            ]),
        },
    ]),
    LookupTable([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                76769853, 34259874, 79088928, 28184277, 65480320, 14661172, 60762722, 36179446,
                95539899, 50337029,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                43269631, 25243016, 41163352, 7480957, 49427195, 25200248, 44562891, 14150564,
                15970762, 4099461,
            ]),
            xy2d: FieldElement2625::from_limbs([
                29262576, 16756590, 26350592, 24760869, 8529670, 22346382, 13617292, 23617289,
                11465738, 8317062,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                41615764, 26591503, 99609063, 24135380, 44070139, 31252209, 82007500, 37402886,
                88078197, 28396915,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                46724414, 19206718, 48772458, 13884721, 34069410, 2842113, 45498038, 29904543,
                11177094, 14989547,
            ]),
            xy2d: FieldElement2625::from_limbs([
                42612143, 21838415, 16959895, 2278463, 12066309, 10137771, 13515641, 2581286,
                38621356, 9930239,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                49357223, 31456605, 83653163, 54099563, 118302919, 18605349, 18345766, 53705111,
                83400343, 28240393,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                33879670, 2553287, 32678213, 9875984, 8534129, 6889387, 57432090, 6957616, 4368891,
                9788741,
            ]),
            xy2d: FieldElement2625::from_limbs([
                16660737, 7281060, 56278106, 12911819, 20108584, 25452756, 45386327, 24941283,
                16250551, 22443329,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                47343357, 35944957, 117666696, 14161978, 69014150, 39969338, 71798447, 10604806,
                104027325, 4782745,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                65754325, 14736940, 59741422, 20261545, 7710541, 19398842, 57127292, 4383044,
                22546403, 437323,
            ]),
            xy2d: FieldElement2625::from_limbs([
                31665558, 21373968, 50922033, 1491338, 48740239, 3294681, 27343084, 2786261,
                36475274, 19457415,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                52641566, 32870716, 33734756, 41002983, 19294359, 14334329, 47418233, 35909750,
                47824192, 27440058,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                15121312, 17758270, 6377019, 27523071, 56310752, 20596586, 18952176, 15496498,
                37728731, 11754227,
            ]),
            xy2d: FieldElement2625::from_limbs([
                64471568, 20071356, 8488726, 19250536, 12728760, 31931939, 7141595, 11724556,
                22761615, 23420291,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                16918416, 11729663, 49025285, 36577418, 103201995, 53769203, 38367677, 21327038,
                32851221, 11717399,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                11166615, 7338049, 60386341, 4531519, 37640192, 26252376, 31474878, 3483633,
                65915689, 29523600,
            ]),
            xy2d: FieldElement2625::from_limbs([
                66923210, 9921304, 31456609, 20017994, 55095045, 13348922, 33142652, 6546660,
                47123585, 29606055,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                101757113, 44821142, 55911756, 25655328, 31703693, 37410335, 58571732, 20721383,
                36336829, 18068118,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                49102387, 12709067, 3991746, 27075244, 45617340, 23004006, 35973516, 17504552,
                10928916, 3011958,
            ]),
            xy2d: FieldElement2625::from_limbs([
                60151107, 17960094, 31696058, 334240, 29576716, 14796075, 36277808, 20749251,
                18008030, 10258577,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                44660220, 49210000, 74127342, 29144428, 36794597, 32352840, 65255398, 34921551,
                92236737, 6671742,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                29701166, 19180498, 56230743, 9279287, 67091296, 13127209, 21382910, 11042292,
                25838796, 4642684,
            ]),
            xy2d: FieldElement2625::from_limbs([
                46678630, 14955536, 42982517, 8124618, 61739576, 27563961, 30468146, 19653792,
                18423288, 4177476,
            ]),
        },
    ]),
]);

/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
#[cfg(feature = "precomputed-tables")]
#[allow(dead_code)]
pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
    NafLookupTable8([
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                93076338, 52752828, 29566454, 37215328, 54414518, 37569218, 94653489, 21800160,
                61029707, 35602036,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692, 5043384,
                19500929, 18085054,
            ]),
            xy2d: FieldElement2625::from_limbs([
                58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918, 11864899,
                42594502, 29115885,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                82745136, 23865874, 24204772, 25642034, 67725840, 16869169, 94896463, 52336674,
                28944398, 32004408,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576, 21778470,
                7689661, 11199574,
            ]),
            xy2d: FieldElement2625::from_limbs([
                30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774, 10017326,
                49359771, 23634074,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                77970208, 11473153, 27284546, 35535607, 37044514, 46132292, 99976748, 48069538,
                118779423, 44373810,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196, 12483687,
                54440373, 5581305,
            ]),
            xy2d: FieldElement2625::from_limbs([
                19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349, 13850243,
                43430843, 17738489,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                72262591, 43463716, 68832610, 30776557, 97632468, 39071304, 86589715, 38784565,
                43156424, 18378665,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025, 16520125,
                30598449, 7715701,
            ]),
            xy2d: FieldElement2625::from_limbs([
                28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204, 1370707,
                29794553, 32145132,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                44589852, 26862249, 14201701, 24808930, 43598457, 42399157, 85583074, 32192981,
                54046167, 47376308,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027, 26342105,
                18853321, 19333481,
            ]),
            xy2d: FieldElement2625::from_limbs([
                4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505, 23123294,
                2207752, 30344648,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                41954014, 62923042, 96790006, 41423232, 60254202, 24130566, 121780363, 32891430,
                103106264, 17421994,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789, 15725684,
                171356, 6466918,
            ]),
            xy2d: FieldElement2625::from_limbs([
                23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338, 19466374,
                36393951, 16193876,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                100695917, 36735143, 64714733, 47558118, 50205389, 17283591, 84347261, 38283886,
                49034350, 9256799,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405, 9761698,
                47281666, 630304,
            ]),
            xy2d: FieldElement2625::from_limbs([
                53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312, 17593437,
                64659607, 19263131,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                63957664, 28508356, 76391577, 40420576, 102310665, 32691407, 48168288, 15033783,
                92213982, 25659555,
            ]),
            y_minus_x: FieldElement2625::from_limbs([
                42782475, 15950225, 35307649, 18961608, 55446126, 28463506, 1573891, 30928545,
                2198789, 17749813,
            ]),
            xy2d: FieldElement2625::from_limbs([
                64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841, 17317989,
                34647629, 21263748,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement2625::from_limbs([
                17735022, 27114469, 76149336, 40765111, 43325570, 26153544, 26948151, 45905235,
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