// -*- mode: rust; -*-
//
// This file is part of curve25519-dalek.
// Copyright (c) 2016-2019 Isis Lovecruft, Henry de Valence
// See LICENSE for licensing information.
//
// Authors:
// - Isis Agora Lovecruft <[email protected]>
// - Henry de Valence <[email protected]>

//! This module contains backend-specific constant values, such as the 64-bit limbs of curve constants.

use backend::serial::curve_models::AffineNielsPoint;
use backend::serial::u64::field::FieldElement51;
use backend::serial::u64::scalar::Scalar52;
use edwards::{EdwardsBasepointTable, EdwardsPoint};
use window::{LookupTable, NafLookupTable8};

/// The value of minus one, equal to `-&FieldElement::one()`
pub(crate) const MINUS_ONE: FieldElement51 = FieldElement51([
    2251799813685228,
    2251799813685247,
    2251799813685247,
    2251799813685247,
    2251799813685247
]);

/// Edwards `d` value, equal to `-121665/121666 mod p`.
pub(crate) const EDWARDS_D: FieldElement51 = FieldElement51([
    929955233495203,
    466365720129213,
    1662059464998953,
    2033849074728123,
    1442794654840575,
]);

/// Edwards `2*d` value, equal to `2*(-121665/121666) mod p`.
pub(crate) const EDWARDS_D2: FieldElement51 = FieldElement51([
    1859910466990425,
    932731440258426,
    1072319116312658,
    1815898335770999,
    633789495995903,
]);

/// One minus edwards `d` value squared, equal to `(1 - (-121665/121666) mod p) pow 2`
pub(crate) const ONE_MINUS_EDWARDS_D_SQUARED: FieldElement51 = FieldElement51([
    1136626929484150,
    1998550399581263,
    496427632559748,
    118527312129759,
    45110755273534
]);

/// Edwards `d` value minus one squared, equal to `(((-121665/121666) mod p) - 1) pow 2`
pub(crate) const EDWARDS_D_MINUS_ONE_SQUARED: FieldElement51 = FieldElement51([
    1507062230895904,
    1572317787530805,
    683053064812840,
    317374165784489,
    1572899562415810
]);

/// `= sqrt(a*d - 1)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const SQRT_AD_MINUS_ONE: FieldElement51 = FieldElement51([
    2241493124984347,
    425987919032274,
    2207028919301688,
    1220490630685848,
    974799131293748,
]);

/// `= 1/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub(crate) const INVSQRT_A_MINUS_D: FieldElement51 = FieldElement51([
    278908739862762,
    821645201101625,
    8113234426968,
    1777959178193151,
    2118520810568447,
]);

/// Precomputed value of one of the square roots of -1 (mod p)
pub(crate) const SQRT_M1: FieldElement51 = FieldElement51([
    1718705420411056,
    234908883556509,
    2233514472574048,
    2117202627021982,
    765476049583133,
]);

/// `APLUS2_OVER_FOUR` is (A+2)/4. (This is used internally within the Montgomery ladder.)
pub(crate) const APLUS2_OVER_FOUR: FieldElement51 = FieldElement51([121666, 0, 0, 0, 0]);

/// `L` is the order of base point, i.e. 2^252 + 27742317777372353535851937790883648493
pub(crate) const L: Scalar52 = Scalar52([
    0x0002631a5cf5d3ed,
    0x000dea2f79cd6581,
    0x000000000014def9,
    0x0000000000000000,
    0x0000100000000000,
]);

/// `L` * `LFACTOR` = -1 (mod 2^52)
pub(crate) const LFACTOR: u64 = 0x51da312547e1b;

/// `R` = R % L where R = 2^260
pub(crate) const R: Scalar52 = Scalar52([
    0x000f48bd6721e6ed,
    0x0003bab5ac67e45a,
    0x000fffffeb35e51b,
    0x000fffffffffffff,
    0x00000fffffffffff,
]);

/// `RR` = (R^2) % L where R = 2^260
pub(crate) const RR: Scalar52 = Scalar52([
    0x0009d265e952d13b,
    0x000d63c715bea69f,
    0x0005be65cb687604,
    0x0003dceec73d217f,
    0x000009411b7c309a,
]);

/// 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: FieldElement51([
        1738742601995546,
        1146398526822698,
        2070867633025821,
        562264141797630,
        587772402128613,
    ]),
    Y: FieldElement51([
        1801439850948184,
        1351079888211148,
        450359962737049,
        900719925474099,
        1801439850948198,
    ]),
    Z: FieldElement51([1, 0, 0, 0, 0]),
    T: FieldElement51([
        1841354044333475,
        16398895984059,
        755974180946558,
        900171276175154,
        1821297809914039,
    ]),
};

/// 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`.
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: FieldElement51([0, 0, 0, 0, 0]),
        Y: FieldElement51([1, 0, 0, 0, 0]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            358744748052810,
            1691584618240980,
            977650209285361,
            1429865912637724,
            560044844278676,
        ]),
        Y: FieldElement51([
            84926274344903,
            473620666599931,
            365590438845504,
            1028470286882429,
            2146499180330972,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            1448326834587521,
            1857896831960481,
            1093722731865333,
            1677408490711241,
            1915505153018406,
        ]),
    },
    EdwardsPoint {
        X: FieldElement51([
            533094393274173,
            2016890930128738,
            18285341111199,
            134597186663265,
            1486323764102114,
        ]),
        Y: FieldElement51([0, 0, 0, 0, 0]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            358744748052810,
            1691584618240980,
            977650209285361,
            1429865912637724,
            560044844278676,
        ]),
        Y: FieldElement51([
            2166873539340326,
            1778179147085316,
            1886209374839743,
            1223329526802818,
            105300633354275,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            803472979097708,
            393902981724766,
            1158077081819914,
            574391322974006,
            336294660666841,
        ]),
    },
    EdwardsPoint {
        X: FieldElement51([0, 0, 0, 0, 0]),
        Y: FieldElement51([
            2251799813685228,
            2251799813685247,
            2251799813685247,
            2251799813685247,
            2251799813685247,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            1893055065632419,
            560215195444267,
            1274149604399886,
            821933901047523,
            1691754969406571,
        ]),
        Y: FieldElement51([
            2166873539340326,
            1778179147085316,
            1886209374839743,
            1223329526802818,
            105300633354275,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            1448326834587521,
            1857896831960481,
            1093722731865333,
            1677408490711241,
            1915505153018406,
        ]),
    },
    EdwardsPoint {
        X: FieldElement51([
            1718705420411056,
            234908883556509,
            2233514472574048,
            2117202627021982,
            765476049583133,
        ]),
        Y: FieldElement51([0, 0, 0, 0, 0]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement51([
            1893055065632419,
            560215195444267,
            1274149604399886,
            821933901047523,
            1691754969406571,
        ]),
        Y: FieldElement51([
            84926274344903,
            473620666599931,
            365590438845504,
            1028470286882429,
            2146499180330972,
        ]),
        Z: FieldElement51([1, 0, 0, 0, 0]),
        T: FieldElement51([
            803472979097708,
            393902981724766,
            1158077081819914,
            574391322974006,
            336294660666841,
        ]),
    },
];

/// Table containing precomputed multiples of the Ed25519 basepoint \\(B = (x, 4/5)\\).
pub const ED25519_BASEPOINT_TABLE: EdwardsBasepointTable = ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN;

/// Inner constant, used to avoid filling the docs with precomputed points.
#[doc(hidden)]
pub const ED25519_BASEPOINT_TABLE_INNER_DOC_HIDDEN: EdwardsBasepointTable =
    EdwardsBasepointTable([
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    3540182452943730,
                    2497478415033846,
                    2521227595762870,
                    1462984067271729,
                    2389212253076811,
                ]),
                y_minus_x: FieldElement51([
                    62697248952638,
                    204681361388450,
                    631292143396476,
                    338455783676468,
                    1213667448819585,
                ]),
                xy2d: FieldElement51([
                    301289933810280,
                    1259582250014073,
                    1422107436869536,
                    796239922652654,
                    1953934009299142,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    3632771708514775,
                    790832306631235,
                    2067202295274102,
                    1995808275510000,
                    1566530869037010,
                ]),
                y_minus_x: FieldElement51([
                    463307831301544,
                    432984605774163,
                    1610641361907204,
                    750899048855000,
                    1894842303421586,
                ]),
                xy2d: FieldElement51([
                    748439484463711,
                    1033211726465151,
                    1396005112841647,
                    1611506220286469,
                    1972177495910992,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1601611775252272,
                    1720807796594148,
                    1132070835939856,
                    3512254832574799,
                    2147779492816910,
                ]),
                y_minus_x: FieldElement51([
                    316559037616741,
                    2177824224946892,
                    1459442586438991,
                    1461528397712656,
                    751590696113597,
                ]),
                xy2d: FieldElement51([
                    1850748884277385,
                    1200145853858453,
                    1068094770532492,
                    672251375690438,
                    1586055907191707,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    934282339813791,
                    1846903124198670,
                    1172395437954843,
                    1007037127761661,
                    1830588347719256,
                ]),
                y_minus_x: FieldElement51([
                    1694390458783935,
                    1735906047636159,
                    705069562067493,
                    648033061693059,
                    696214010414170,
                ]),
                xy2d: FieldElement51([
                    1121406372216585,
                    192876649532226,
                    190294192191717,
                    1994165897297032,
                    2245000007398739,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    769950342298400,
                    2384754244604994,
                    3095885746880802,
                    3225892188161580,
                    2977876099231263,
                ]),
                y_minus_x: FieldElement51([
                    425251763115706,
                    608463272472562,
                    442562545713235,
                    837766094556764,
                    374555092627893,
                ]),
                xy2d: FieldElement51([
                    1086255230780037,
                    274979815921559,
                    1960002765731872,
                    929474102396301,
                    1190409889297339,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1388594989461809,
                    316767091099457,
                    2646098655878230,
                    1230079486801004,
                    1440737038838979,
                ]),
                y_minus_x: FieldElement51([
                    7380825640100,
                    146210432690483,
                    304903576448906,
                    1198869323871120,
                    997689833219095,
                ]),
                xy2d: FieldElement51([
                    1181317918772081,
                    114573476638901,
                    262805072233344,
                    265712217171332,
                    294181933805782,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    2916800678241215,
                    2065379846933858,
                    2622030924071124,
                    2602788184473875,
                    1233371373142984,
                ]),
                y_minus_x: FieldElement51([
                    2019367628972465,
                    676711900706637,
                    110710997811333,
                    1108646842542025,
                    517791959672113,
                ]),
                xy2d: FieldElement51([
                    965130719900578,
                    247011430587952,
                    526356006571389,
                    91986625355052,
                    2157223321444601,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    4320419353804412,
                    4218074731744053,
                    957728544705548,
                    729906502578991,
                    2411634706750414,
                ]),
                y_minus_x: FieldElement51([
                    2073601412052185,
                    31021124762708,
                    264500969797082,
                    248034690651703,
                    1030252227928288,
                ]),
                xy2d: FieldElement51([
                    551790716293402,
                    1989538725166328,
                    801169423371717,
                    2052451893578887,
                    678432056995012,
                ]),
            },
        ]),
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1368953770187805,
                    3042147450398169,
                    2689308289352409,
                    2142576377050579,
                    1932081720066286,
                ]),
                y_minus_x: FieldElement51([
                    953638594433374,
                    1092333936795051,
                    1419774766716690,
                    805677984380077,
                    859228993502513,
                ]),
                xy2d: FieldElement51([
                    1200766035879111,
                    20142053207432,
                    1465634435977050,
                    1645256912097844,
                    295121984874596,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1735718747031538,
                    1248237894295956,
                    1204753118328107,
                    976066523550493,
                    2317743583219840,
                ]),
                y_minus_x: FieldElement51([
                    1060098822528990,
                    1586825862073490,
                    212301317240126,
                    1975302711403555,
                    666724059764335,
                ]),
                xy2d: FieldElement51([
                    1091990273418756,
                    1572899409348578,
                    80968014455247,
                    306009358661350,
                    1520450739132526,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    3732317023121341,
                    1511153322193951,
                    3496143672676420,
                    2556587964178488,
                    2620936670181690,
                ]),
                y_minus_x: FieldElement51([
                    2151330273626164,
                    762045184746182,
                    1688074332551515,
                    823046109005759,
                    907602769079491,
                ]),
                xy2d: FieldElement51([
                    2047386910586836,
                    168470092900250,
                    1552838872594810,
                    340951180073789,
                    360819374702533,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1982622644432037,
                    2014393600336956,
                    2380709022489462,
                    3869592437614438,
                    2357094095599062,
                ]),
                y_minus_x: FieldElement51([
                    980234343912898,
                    1712256739246056,
                    588935272190264,
                    204298813091998,
                    841798321043288,
                ]),
                xy2d: FieldElement51([
                    197561292938973,
                    454817274782871,
                    1963754960082318,
                    2113372252160468,
                    971377527342673,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    2416499262514576,
                    2254927265442919,
                    3451304785234000,
                    1766155447043651,
                    1899238924683527,
                ]),
                y_minus_x: FieldElement51([
                    732262946680281,
                    1674412764227063,
                    2182456405662809,
                    1350894754474250,
                    558458873295247,
                ]),
                xy2d: FieldElement51([
                    2103305098582922,
                    1960809151316468,
                    715134605001343,
                    1454892949167181,
                    40827143824949,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1239289043050193,
                    1744654158124578,
                    758702410031698,
                    4048562808759936,
                    2253402870349013,
                ]),
                y_minus_x: FieldElement51([
                    2232056027107988,
                    987343914584615,
                    2115594492994461,
                    1819598072792159,
                    1119305654014850,
                ]),
                xy2d: FieldElement51([
                    320153677847348,
                    939613871605645,
                    641883205761567,
                    1930009789398224,
                    329165806634126,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    3232730304159378,
                    1242488692177892,
                    1251446316964684,
                    1086618677993530,
                    1961430968465772,
                ]),
                y_minus_x: FieldElement51([
                    276821765317453,
                    1536835591188030,
                    1305212741412361,
                    61473904210175,
                    2051377036983058,
                ]),
                xy2d: FieldElement51([
                    833449923882501,
                    1750270368490475,
                    1123347002068295,
                    185477424765687,
                    278090826653186,
                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    794524995833413,
                    1849907304548286,
                    2305148486158393,
                    1272368559505216,
                    1147304168324779,
                ]),
                y_minus_x: FieldElement51([
                    1504846112759364,
                    1203096289004681,
                    562139421471418,
                    274333017451844,
                    1284344053775441,
                ]),
                xy2d: FieldElement51([
                    483048732424432,
                    2116063063343382,
                    30120189902313,
                    292451576741007,
                    1156379271702225,
                ]),
            },
        ]),
        LookupTable([
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    3180171966714267,
                    2147692869914563,
                    1455665844462196,
                    1986737809425946,
                    2437006863943337,
                ]),
                y_minus_x: FieldElement51([
                    137732961814206,
                    706670923917341,
                    1387038086865771,
                    1965643813686352,
                    1384777115696347,
                ]),
                xy2d: FieldElement51([
                    481144981981577,
                    2053319313589856,
                    2065402289827512,
                    617954271490316,
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                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    2948097833334040,
                    3145099472726142,
                    1148636718636008,
                    2278533891034865,
                    2203955659340680,
                ]),
                y_minus_x: FieldElement51([
                    657390353372855,
                    998499966885562,
                    991893336905797,
                    810470207106761,
                    343139804608786,
                ]),
                xy2d: FieldElement51([
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                    824656780392914,
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                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    2022541353055578,
                    4346500076272714,
                    3802807888710933,
                    2494585331103411,
                    2947785218648809,
                ]),
                y_minus_x: FieldElement51([
                    1287487199965223,
                    2215311941380308,
                    1552928390931986,
                    1664859529680196,
                    1125004975265243,
                ]),
                xy2d: FieldElement51([
                    677434665154918,
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                    1817429540898386,
                    1052904935475344,
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                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    2619066141993637,
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                ]),
                y_minus_x: FieldElement51([
                    773360688841258,
                    1815381330538070,
                    363773437667376,
                    539629987070205,
                    783280434248437,
                ]),
                xy2d: FieldElement51([
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                ]),
            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    2730575372268893,
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                ]),
                y_minus_x: FieldElement51([
                    1984740906540026,
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                    1088529069025527,
                ]),
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                xy2d: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    3669985309815545,
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                y_minus_x: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                ]),
                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
                    1377485731340769,
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            },
        ]),
        LookupTable([
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                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            AffineNielsPoint {
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                y_minus_x: FieldElement51([
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            AffineNielsPoint {
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            },
            AffineNielsPoint {
                y_plus_x: FieldElement51([
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                y_minus_x: FieldElement51([
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                xy2d: FieldElement51([
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            },
        ]),
    ]);

/// Odd multiples of the basepoint `[B, 3B, 5B, 7B, 9B, 11B, 13B, 15B, ..., 127B]`.
pub(crate) const AFFINE_ODD_MULTIPLES_OF_BASEPOINT: NafLookupTable8<AffineNielsPoint> =
    NafLookupTable8([
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            y_plus_x: FieldElement51([
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                2497478415033846,
                2521227595762870,
                1462984067271729,
                2389212253076811,
            ]),
            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        AffineNielsPoint {
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                3512254832574799,
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            ]),
            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
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        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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                1253908377065966,
            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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                3148029033359833,
            ]),
            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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                1855308922422910,
            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            ]),
            y_minus_x: FieldElement51([
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            ]),
            xy2d: FieldElement51([
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            ]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement51([
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            y_minus_x: FieldElement51([
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            xy2d: FieldElement51([
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            ]),
        },
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