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

use crate::backend::u64::field::FieldElement;
use crate::backend::u64::scalar::Scalar;
use crate::edwards::*;
use crate::ristretto::RistrettoPoint;

/// `L` is the order of base point for Sonny, in this case it is equivalent to 2^249 + 14490550575682688738086195780655237219
pub const L: Scalar = Scalar([1129677152307299, 1363544697812651, 714439, 0, 2199023255552]);

/// `(L - 1) / 2` used to check positiveness of a `FieldElement` on the Decaf paper.
pub(crate) const POS_RANGE: FieldElement =
    FieldElement([2587757230352886, 4210131976237760, 683900, 0, 8796093022208]);

/// Scalar-LFACTOR is the value that satisfies the equation: `L * LFACTOR = -1 (mod 2^52)`
/// In this case, `LFACTOR` is the one used for the Montgomery Reduction algorithm,
/// implemented on Scalar Arithmetics module.
pub const LFACTOR: u64 = 1331240223835829;

/// Montgomery modulus defined for Scalar arithmetics, `R^2 = (2^260)^2 % L`
pub const RR: Scalar = Scalar([
    137682194168839,
    3209056245311277,
    1480926248458276,
    2533620989757837,
    1314911199310,
]);

/// `FIELD_L` is the order of the Prime field for Sonny, n this case it is equivalent to 2^252 + 27742317777372353535851937790883648493`
pub const FIELD_L: FieldElement = FieldElement([
    671914833335277,
    3916664325105025,
    1367801,
    0,
    17592186044416,
]);

/// Montgomery modulus defined for FieldElement arithmetics, `R^2 = (2^260)^2 % FIELD_L`
pub const RR_FIELD: FieldElement = FieldElement([
    2764609938444603,
    3768881411696287,
    1616719297148420,
    1087343033131391,
    10175238647962,
]);

/// `SCALAR_INVERSE_MOD_TWO = 1/2 (mod l)`. 
pub const SCALAR_INVERSE_MOD_TWO: Scalar = Scalar([2816638389838898, 2933572162591573, 357219, 0, 1099511627776]);

/// `INVERSE_MOD_TWO = 1/2 (mod l)`.                   
pub const INVERSE_MOD_TWO: FieldElement = FieldElement([2587757230352887, 4210131976237760, 683900, 0, 8796093022208]);

/// `MINUS_ONE_HALF = (-1/2) (mod l)`. 
pub const MINUS_ONE_HALF: FieldElement = FieldElement([2587757230352886, 4210131976237760, 683900, 0, 8796093022208]);

/// FieldElement-LFACTOR is the value that satisfies the equation: `L * LFACTOR = -1 (mod 2^52)`
/// In this case, `LFACTOR` is the one used for the Montgomery Reduction algorithm,
/// implemented on FieldElement Arithmetics module.
pub const LFACTOR_FIELD: u64 = 1439961107955227;

/// Montgomery modulus defined for FieldElements on `inverse()` functions scope.
/// It is used for the Montgomery Mul operation that takes place on the `Inversion
// operation`. It's defined as: `R^2 = (2^253)^2 % L`
pub const INV_RR: FieldElement = FieldElement([
    2210115751650724,
    3809421927348411,
    2357176729341513,
    3420097284349172,
    7483527818736,
]);

/// Edwards `a` variable value = `-1 (mod l)` equals:
/// `7237005577332262213973186563042994240857116359379907606001950938285454250988`
/// where `l = Prime of the field = 2^252 + 27742317777372353535851937790883648493`
pub static EDWARDS_A: FieldElement = FieldElement([
    671914833335276,
    3916664325105025,
    1367801,
    0,
    17592186044416,
]);

/// Edwards `d` variable value = `-126296/126297 (mod l)` equals:
/// `951605751702391019481481818669129158712512026257330939079110344917983315091`
/// where `l = Prime of the field = 2^252 + 27742317777372353535851937790883648493`
pub static EDWARDS_D: FieldElement = FieldElement([
    3304133203739795,
    2446467598308289,
    1534112949566882,
    2032729967918914,
    2313225441931,
]);

/// Holds the value of one of both `sqrt(-1 (mod p)) values.
/// `SQRT_MINUS_ONE = 3034649101460298094273452163494570791663566989388331537498831373842135895065`.
pub const SQRT_MINUS_ONE: FieldElement = FieldElement([
    3075585030474777,
    2451921961843096,
    1194333869305507,
    2218299809671669,
    7376823328646,
]);

/// `(+)1/SQRT(a) (mod l)` equals: `4202356475871964119699734399548423449193549369991576068503119564443318355924`.
pub static INV_SQRT_A: FieldElement = FieldElement([
    2099929430230996,
    1464742363261928,
    3309265759432790,
    2285299817698826,
    10215362715769,
]);

/// `(-)SQRT(a) (mod l)` equals: `4202356475871964119699734399548423449193549369991576068503119564443318355924`.
pub static MINUS_SQRT_A: FieldElement = FieldElement([
    2099929430230996,
    1464742363261928,
    3309265759432790,
    2285299817698826,
    10215362715769,
]);

/// `INV_SQRT_A_MINUS_D = 482283834104289360917429750399313974390948281833312135312952165682596457149`.
pub const INV_SQRT_A_MINUS_D: FieldElement = FieldElement([
    550050132044477,
    3953042081665262,
    2971403105229349,
    212915494370164,
    1172367057772,
]);

/// `SQRT_AD_MINUS_ONE = `.
pub const SQRT_AD_MINUS_ONE: FieldElement = FieldElement([
    3601277882726560,
    1817821323014817,
    1726005090908779,
    2111284621343800,
    648674458156,
]);

/// 4Coset of a RistrettoPoint.
pub(crate) const FOUR_COSET_GROUP: [EdwardsPoint; 4] = [
    EdwardsPoint {
        X: FieldElement([1, 0, 0, 0, 0]),
        Y: FieldElement([0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement([
            2099929430230996,
            1464742363261928,
            3309265759432790,
            2285299817698826,
            10215362715769,
        ]),
        Y: FieldElement([0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement([0, 0, 0, 0, 0]),
        Y: FieldElement([
            671914833335276,
            3916664325105025,
            1367801,
            0,
            17592186044416,
        ]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    },
    EdwardsPoint {
        X: FieldElement([
            3075585030474777,
            2451921961843096,
            1194333869305507,
            2218299809671669,
            7376823328646,
        ]),
        Y: FieldElement([0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    },
];

/// Holds the value of the Curve basepoint, which has been constructed
/// from taking `y-coodrinate = 3/5 (mod l)`.
pub const BASEPOINT: EdwardsPoint = EdwardsPoint {
    X: FieldElement([
        276718085098056,
        1646536057461434,
        2704687245600312,
        2630386667454967,
        13476148227069,
    ]),
    Y: FieldElement([
        1303868825475266,
        3250718520537114,
        2702159777242978,
        2702159776422297,
        10555311626649,
    ]),
    Z: FieldElement([1, 0, 0, 0, 0]),
    T: FieldElement([
        3634527586288175,
        2006028620404053,
        3424252198034825,
        2478951925947079,
        4567251727358,
    ]),
};

/// Ristretto Basepoint.
pub const RISTRETTO_BASEPOINT: RistrettoPoint = RistrettoPoint(BASEPOINT);

pub(crate) const BASEPOINT_ODD_MULTIPLES_TABLE: [RistrettoPoint; 126] = [
    RistrettoPoint(EdwardsPoint {
            X: FieldElement([0,0,0,0,0]),
            Y: FieldElement([1,0,0,0,0]),
            Z: FieldElement([1, 0, 0, 0, 0]),
            T: FieldElement([0,0,0,0,0])
        }),
    RistrettoPoint(EdwardsPoint {
            X: FieldElement([276718085098056, 1646536057461434, 2704687245600312, 2630386667454967, 13476148227069]),
            Y: FieldElement([1303868825475266, 3250718520537114, 2702159777242978, 2702159776422297, 10555311626649]),
            Z: FieldElement([1, 0, 0, 0, 0]),
            T: FieldElement([3634527586288175, 2006028620404053, 3424252198034825, 2478951925947079, 4567251727358])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([2207852948799167, 641574638222364, 2845274685971070, 2888574538543145, 8842880060378]),
            Y: FieldElement([3859191352706748, 901045137608561, 925022319227492, 3779097277038387, 2436329346790]),
            Z: FieldElement([1924806031176030, 1416592609043722, 3588786947727296, 966484667785235, 3367649346410]),
            T: FieldElement([3561063985940280, 2029111888993922, 434755174786874, 1789768157957980, 8233565060344])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([938529660034409, 1389861201185586, 2467873451492055, 2462996089292386, 10798363330707]),
            Y: FieldElement([2301599396575729, 860840139962138, 761500845173277, 1807369898601580, 4284719561284]),
            Z: FieldElement([158647906765356, 1912478078572916, 2353372814093602, 3699673181926423, 14227897715082]),
            T: FieldElement([348247851294195, 524296127646058, 721351996206805, 1792621103819185, 11312298174119])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([3866581237722140, 3967826170612473, 300931815292842, 4476184848102778, 14915630784184]),
            Y: FieldElement([1788761225399615, 362422332293471, 2503999665680887, 1798788693539183, 8413980416617]),
            Z: FieldElement([3120458716440979, 1376368230000941, 1957915480140936, 3276201114701080, 404854747]),
            T: FieldElement([2610821644431074, 1005600860860727, 2043496309213467, 593021863187642, 14425380499844])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([3225322368839770, 2361726703693225, 434917576574260, 4424874433923156, 10042776616216]),
            Y: FieldElement([599524211693941, 1238089188705994, 4491782560685162, 2413776421530326, 2843196275107]),
            Z: FieldElement([1955649875043680, 81969754529976, 3166471000640568, 1745573944684772, 4644406839285]),
            T: FieldElement([1105596777386946, 332337475455484, 868390431098496, 2722006845892113, 17481986376859])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([460934317870901, 43261527397648, 2712962124900907, 3876353765883525, 14483697262877]),
            Y: FieldElement([3003932934269796, 1935114165275979, 453638796603859, 2139165672951756, 16769733503435]),
            Z: FieldElement([2749090807774186, 3554502390319134, 1165894823300633, 1259898869834694, 16884889098779]),
            T: FieldElement([1975619140798631, 1231667354569651, 2895432863347817, 2104890979453853, 14965872298821])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([4474503552438295, 1564420790120962, 1243580778483543, 4250588328912773, 8529740401366]),
            Y: FieldElement([668022307843110, 4108450115188706, 2070797919188187, 4297096600077495, 11344295700420]),
            Z: FieldElement([3261104465686800, 3041840584145450, 2412769648642264, 1709295636507182, 13365988568544]),
            T: FieldElement([944604794756863, 3160821023684287, 2160424494824656, 1836429252337445, 2417612634302])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([603600100906487, 2340119872132182, 1215293353001225, 2197037653148591, 5163254814051]),
            Y: FieldElement([3709902623744680, 1143314278068614, 2209311298884114, 2111804853500427, 14928972201024]),
            Z: FieldElement([4227256893060181, 3571402776539590, 3792363690864417, 2013713695268525, 11490439087448]),
            T: FieldElement([2754169111369425, 4238812715530294, 4380598683601458, 4083519206014473, 15256810880031])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([1457033614578101, 58465736154855, 4325506613263371, 935066099568606, 2877489954613]),
            Y: FieldElement([3056822297565469, 1009517371147649, 2301191918008785, 773820251450541, 3516710361559]),
            Z: FieldElement([3749415470893507, 1895134885897273, 3580415727275960, 3461573118959881, 1771440376576]),
            T: FieldElement([3895755279948330, 3007606877599591, 2349519552810877, 1679893396039425, 1940234944770])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([856488455595009, 4085053039086547, 3115696188406750, 2059712657355966, 5511651172175]),
            Y: FieldElement([2418125393507748, 2671985869021255, 3270730557188279, 1673990345998415, 1296923022794]),
            Z: FieldElement([747320612848847, 881140990935124, 3647384119048256, 2539583376078916, 1761578622426]),
            T: FieldElement([3036965504472035, 1750860664484510, 3034134954801845, 1491676669867803, 660450466768])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([249304757096703, 58853546936298, 4430944051230358, 1976357184481773, 921833381081]),
            Y: FieldElement([2172782775404482, 3637835388753190, 3736793204924408, 4440374069021525, 6423962675430]),
            Z: FieldElement([2191689255044294, 810207288996397, 3426344494919486, 114435393822640, 1079912167567]),
            T: FieldElement([3655777830041408, 98129084310781, 2747636130550484, 1398294496708739, 1405665240584])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([1304020124672493, 2686519714537676, 4302977636787751, 1830098956649170, 6709670151758]),
            Y: FieldElement([3078855412762994, 578753925449681, 2344659043437993, 2004289330646571, 5160315265017]),
            Z: FieldElement([3224315643193017, 3551069041376347, 735082717954900, 1456768188443285, 7897761184230]),
            T: FieldElement([3847543502620588, 2853787793520905, 1672503828231981, 475357988573667, 16938573764162])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([3117189468705335, 645884992233639, 444743193265735, 1893800225442646, 15296101196102]),
            Y: FieldElement([985894755877113, 3662043037801228, 463787220560695, 1539144634929989, 14901372768198]),
            Z: FieldElement([3246161482121139, 2946439597367357, 3135953334040421, 2899717927467854, 3299156605538]),
            T: FieldElement([4294322566846209, 252136367090799, 1267405916669824, 1711197129816406, 1120378271442])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([196114107340064, 1974043933601969, 816938731474314, 390383400102689, 6995265863762]),
            Y: FieldElement([143398329372033, 2935680120044836, 63734176985638, 2186403175048054, 7261857302878]),
            Z: FieldElement([1508190167475362, 4202711973368006, 4111340587637154, 946966456367028, 1521201888494]),
            T: FieldElement([1697313743491230, 368106849514791, 693327851004201, 2985061605832276, 7896049577736])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([1768420101482880, 4191592123155933, 4480154287537041, 2335430146199433, 10150143728077]),
            Y: FieldElement([3194611907175112, 1466574434217311, 1310955440189416, 1446978094911932, 9434000514668]),
            Z: FieldElement([3600624040713505, 3653781424731278, 2852081468848237, 487821000500396, 1373332436140]),
            T: FieldElement([1774370338852456, 1141349997256593, 2744177914461000, 1666609414828148, 13817941675592])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([2225550138883976, 3430276745515234, 1420360699725481, 448796814539954, 16007236065611]),
            Y: FieldElement([2916055243511746, 3548768707737256, 1363821033324778, 3073350070021646, 6637654792330]),
            Z: FieldElement([970398176204998, 4016238022834532, 1512315433293507, 1054050588342140, 1525021299847]),
            T: FieldElement([1336197458057914, 4357107288468385, 649593369533995, 2951295188445923, 10822134730326])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([2000313753279802, 817770433154029, 1302994017031976, 754354159041110, 17437436724593]),
            Y: FieldElement([3137087739338174, 2599940209785136, 3225288750675905, 4258282427143490, 14025896365840]),
            Z: FieldElement([1541907276448963, 3699929461276251, 2357788826486968, 4061664078356061, 2933193440440]),
            T: FieldElement([3838997818702439, 4328734948316669, 906562451561085, 2572203956279605, 7597863732804])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([2433126791116941, 4437714161568729, 1281551766879214, 3594742685446662, 9420521007518]),
            Y: FieldElement([1329731582414703, 2822116307122653, 212704506256096, 3314408184447723, 15165283627691]),
            Z: FieldElement([2166141006592658, 1289451346393684, 1272478423302580, 3321425488408203, 14011328180849]),
            T: FieldElement([4138148918372952, 3459750113436973, 4118906628947781, 3452830791388987, 8624071137982])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([4493985268344293, 2815807399558187, 3416148758173984, 1503681908879074, 9273090751845]),
            Y: FieldElement([301527701740416, 4202601828431977, 3699761005089257, 1184655067561268, 16462756764120]),
            Z: FieldElement([2032235708716055, 325555253019054, 3953365338486754, 808831346658194, 8913281256388]),
            T: FieldElement([1178782309149423, 598334661122589, 603244526887734, 3504826816445811, 12052364918945])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([3110520045981281, 649585341514616, 61994149030803, 3156956177750577, 3788637206230]),
            Y: FieldElement([368234152993241, 4279924300404912, 3307096306893949, 3912135574928727, 12582530230434]),
            Z: FieldElement([2554930492188419, 535426145478469, 2096646557000427, 669710712228543, 9807818498525]),
            T: FieldElement([3327332729631012, 2771661737656822, 1425912408111599, 2940912394898016, 2410765365208])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([1769405261018705, 4258072588094285, 2340172135946417, 3052204859929857, 11816342538935]),
            Y: FieldElement([2653642866915823, 107386844089656, 3914862279770574, 3843726743591080, 16903151970114]),
            Z: FieldElement([3833425071199287, 3875767741070319, 2727295860200877, 3152074920218261, 8852562380868]),
            T: FieldElement([3012528876994481, 1777460820849288, 1420984094988312, 642025260214264, 15990008857349])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([3647283266653325, 3446904948775034, 405008807756950, 4185221229595236, 800091810015]),
            Y: FieldElement([3002117748189704, 2412894744865971, 1551040330618801, 2922208140384318, 16649726793002]),
            Z: FieldElement([1320692392804573, 303614443936501, 4067745847388568, 1889100211782379, 3102282986923]),
            T: FieldElement([3431570951102331, 2214681925170926, 2918347448107381, 1102152430664343, 12896775080224])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([1756072804375943, 172902139647387, 4126022309284119, 2857382119380393, 12583504488022]),
            Y: FieldElement([1952477416915659, 1010451671308640, 3728111436069749, 1240516181759855, 16057539010103]),
            Z: FieldElement([3584408317758992, 2489929801302664, 565263622443753, 1435676132020236, 6009668020594]),
            T: FieldElement([1257390437214210, 254681762607033, 499409425717416, 2612219341978433, 12910380734021])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([107749933267778, 1591090434403231, 1930358577248313, 1804254107112945, 2883622424881]),
            Y: FieldElement([1150852490146178, 3883266417193402, 2298625280845247, 2018731598776489, 3676775848695]),
            Z: FieldElement([2019435692649983, 920794487488850, 3363212407008734, 1973210559319588, 13698814898578]),
            T: FieldElement([2949623476790462, 769472608823530, 2599520294375819, 358175429486634, 3150426546334])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([2057012487683045, 720570291272492, 143060645894388, 3558233920341126, 5359663800883]),
            Y: FieldElement([3102642119148901, 4213692963466577, 3840329438721523, 670586794329633, 11238144060525]),
            Z: FieldElement([1761407861418008, 3049157668856090, 3495608308127501, 1912187793627259, 15601380602317]),
            T: FieldElement([3728470356260505, 74630904859437, 3377141834461300, 1237173829833946, 15702378169467])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([1474424927385094, 2678841166949093, 4096788177089374, 1107906838161565, 13191351030310]),
            Y: FieldElement([2445276729552360, 3269428200782034, 1984463165914312, 3249317015329202, 1088611949828]),
            Z: FieldElement([276243248547248, 2539678674335262, 3414021597548528, 1687733565536027, 7396558937151]),
            T: FieldElement([3848226745859853, 956396099962185, 3977279106712797, 97376292205058, 14312884296111])
        }),
        RistrettoPoint(EdwardsPoint {
            X: FieldElement([946156826610590, 3351700727970392, 2818992871594192, 1789873730980244, 216427043582]),
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