// -*- mode: rust; -*-
//
// To the extent possible under law, the authors have waived all copyright and
// related or neighboring rights to curve25519-dalek, using the Creative
// Commons "CC0" public domain dedication.  See
// <http://creativecommons.org/publicdomain/zero/.0/> for full details.
//
// 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.

#![allow(dead_code)]
#![allow(non_snake_case)]
#![allow(non_upper_case_globals)]
#![allow(missing_docs)]
#![allow(non_snake_case)]

use field::FieldElement;
use curve::ExtendedPoint;
use curve::AffineNielsPoint;
use curve::CompressedEdwardsY;
use curve::EdwardsBasepointTable;
#[cfg(feature = "yolocrypto")]
use decaf::{DecafPoint, DecafBasepointTable};
use scalar::Scalar;

#[cfg(feature="radix_51")]
pub const p: FieldElement = FieldElement([2251799813685229, 2251799813685247, 2251799813685247, 2251799813685247, 2251799813685247]);

#[cfg(not(feature="radix_51"))]
pub const d: FieldElement       = FieldElement([
    -10913610,  13857413, -15372611,   6949391,    114729,
    -8787816,   -6275908,  -3247719, -18696448, -12055116, ]);
#[cfg(feature="radix_51")]
pub const d: FieldElement = FieldElement([929955233495203, 466365720129213, 1662059464998953, 2033849074728123, 1442794654840575]);
#[cfg(not(feature="radix_51"))]
pub const d2: FieldElement      = FieldElement([
    -21827239,  -5839606, -30745221,  13898782,    229458,
    15978800,  -12551817,  -6495438,  29715968,   9444199, ]);
#[cfg(feature="radix_51")]
pub const d2: FieldElement = FieldElement([1859910466990425, 932731440258426, 1072319116312658, 1815898335770999, 633789495995903]);
#[cfg(not(feature="radix_51"))]
pub const d4: FieldElement      = FieldElement([
    23454405,  -11679213,   5618422,  -5756869,    458917,
    -1596832,  -25103633, -12990876,  -7676928, -14666033  ]);
#[cfg(feature="radix_51")]
pub const d4: FieldElement = FieldElement([1468021120295602, 1865462880516853, 2144638232625316, 1379996857856750, 1267578991991807]);
#[cfg(not(feature="radix_51"))]
pub const a_minus_d: FieldElement    = FieldElement([
    10913609,  -13857413,  15372611,  -6949391,   -114729,
     8787816,    6275908,   3247719,  18696448,  12055116, ]);
#[cfg(feature="radix_51")]
pub const a_minus_d: FieldElement = FieldElement([1321844580190025, 1785434093556034, 589740348686294, 217950738957124, 809005158844672]);

/// (p-1)/2, in little-endian bytes.
pub const HALF_P_MINUS_1_BYTES: [u8; 32] =
    [0xf6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f];

/// Precomputed value of one of the square roots of -1 (mod p)
#[cfg(not(feature="radix_51"))]
pub const SQRT_M1: FieldElement = FieldElement([
    -32595792,  -7943725,   9377950,   3500415,  12389472,
    -272473,   -25146209,  -2005654,    326686,  11406482, ]);
#[cfg(feature="radix_51")]
pub const SQRT_M1: FieldElement = FieldElement([1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133]);

/// Precomputed value of the other square root of -1 (mod p),
/// i.e., `MSQRT_M1 = -SQRT_M1`.
#[cfg(not(feature="radix_51"))]
pub const MSQRT_M1: FieldElement = FieldElement([
    32595792,    7943725,  -9377950,  -3500415, -12389472,
    272473,     25146209,   2005654,   -326686, -11406482, ]);
#[cfg(feature="radix_51")]
pub const MSQRT_M1: FieldElement = FieldElement([533094393274173, 2016890930128738, 18285341111199, 134597186663265, 1486323764102114]);

/// Precomputed value of 1/2 (mod p).
#[cfg(not(feature="radix_51"))]
pub const HALF: FieldElement = FieldElement([
    10, 0, 0, 0, 0, 0, 0, 0, 0, -16777216, ]);
#[cfg(feature="radix_51")]
pub const HALF: FieldElement = FieldElement([2251799813685239, 2251799813685247, 2251799813685247, 2251799813685247, 1125899906842623]);

/// In Montgomery form y² = x³+Ax²+x, Curve25519 has A=486662.
#[cfg(not(feature="radix_51"))]
pub const A: FieldElement       = FieldElement([
    486662, 0, 0, 0, 0, 0, 0, 0, 0, 0, ]);
#[cfg(feature="radix_51")]
pub const A: FieldElement = FieldElement([486662, 0, 0, 0, 0]);

/// `SQRT_MINUS_A` is sqrt(-486662)
// XXX I think that this was used in Adam's code for his elligator
// implementation, but that should maybe be using sqrt(-486664)
// instead...?  - hdevalence
#[cfg(not(feature="radix_51"))]
pub const SQRT_MINUS_A: FieldElement = FieldElement([ // sqrtMinusA
    12222970,    8312128,  11511410,  -9067497,  15300785,
    241793,    -25456130, -14121551,  12187136,  -3972024, ]);
#[cfg(feature="radix_51")]
pub const SQRT_MINUS_A: FieldElement = FieldElement([557817479725543, 1643290402203250, 16226468853936, 1304118542701054, 1985241807451647]);

/// `SQRT_MINUS_APLUS2` is sqrt(-486664)
#[cfg(not(feature="radix_51"))]
pub const SQRT_MINUS_APLUS2: FieldElement = FieldElement([
    -12222970, -8312128, -11511410, 9067497, -15300785,
    -241793, 25456130, 14121551, -12187136, 3972024]);
#[cfg(feature="radix_51")]
pub const SQRT_MINUS_APLUS2: FieldElement = FieldElement([1693982333959686, 608509411481997, 2235573344831311, 947681270984193, 266558006233600]);

/// `SQRT_MINUS_HALF` is sqrt(-1/2)
#[cfg(not(feature="radix_51"))]
pub const SQRT_MINUS_HALF: FieldElement = FieldElement([ // sqrtMinusHalf
    -17256545,   3971863,  28865457,  -1750208,  27359696,
    -16640980,  12573105,   1002827,   -163343,  11073975, ]);
#[cfg(feature="radix_51")]
pub const SQRT_MINUS_HALF: FieldElement = FieldElement([266547196637087, 2134345371906993, 1135042577398223, 67298593331632, 743161882051057]);

/// `HALF_Q_MINUS_1_BYTES` is (2^255-20)/2 expressed in little endian form.
pub const HALF_Q_MINUS_1_BYTES: [u8; 32] = [ // halfQMinus1Bytes
    0xf6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
    0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3f, ];

/// Basepoint has y = 4/5.
///
/// Generated with Sage: these are the bytes of 4/5 in 𝔽_p.  The
/// sign bit is 0 since the basepoint has x chosen to be positive.
pub const BASE_CMPRSSD: CompressedEdwardsY =
    CompressedEdwardsY([0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
                        0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
                        0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
                        0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66]);

/// The Ed25519 basepoint, as a `DecafPoint`.
#[cfg(feature = "yolocrypto")]
pub const DECAF_ED25519_BASEPOINT: DecafPoint = DecafPoint(ED25519_BASEPOINT);

/// Basepoint has y = 4/5.
#[cfg(not(feature="radix_51"))]
pub const ED25519_BASEPOINT: ExtendedPoint = ExtendedPoint{
        X: FieldElement([-14297830, -7645148, 16144683, -16471763, 27570974, -2696100, -26142465, 8378389, 20764389, 8758491]),
        Y: FieldElement([-26843541, -6710886, 13421773, -13421773, 26843546, 6710886, -13421773, 13421773, -26843546, -6710886]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([28827062, -6116119, -27349572, 244363, 8635006, 11264893, 19351346, 13413597, 16611511, -6414980]),
};
#[cfg(feature="radix_51")]
pub const ED25519_BASEPOINT: ExtendedPoint = ExtendedPoint {
    X: FieldElement([1738742601995546, 1146398526822698, 2070867633025821, 562264141797630, 587772402128613]),
    Y: FieldElement([1801439850948184, 1351079888211148, 450359962737049, 900719925474099, 1801439850948198]),
    Z: FieldElement([1, 0, 0, 0, 0]),
    T: FieldElement([1841354044333475, 16398895984059, 755974180946558, 900171276175154, 1821297809914039]),
};

/// `l` is the order of base point, i.e. 2^252 +
/// 27742317777372353535851937790883648493, in little-endian form
pub const l: Scalar = Scalar([ 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
                               0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
                               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                               0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 ]);

/// `l_minus_1` is the order of base point minus one, i.e. 2^252 +
/// 27742317777372353535851937790883648493 - 1, in little-endian form
pub const l_minus_1: Scalar = Scalar([ 0xec, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
                                       0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
                                       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                                       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 ]);

/// `lminus1` is the order of base point minus two, i.e. 2^252 +
/// 27742317777372353535851937790883648493 - 2, in little-endian form
pub const l_minus_2: Scalar = Scalar([ 0xeb, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
                                       0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
                                       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
                                       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10 ]);

/// The 8-torsion subgroup Ɛ[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 Ɛ[8].
///
/// Thus Ɛ[4] is the points indexed by 0,2,4,6 and Ɛ[2] is the points
/// indexed by 0,4. 
#[cfg(not(feature="radix_51"))]
pub const EIGHT_TORSION: [ExtendedPoint; 8] = [
    ExtendedPoint{
        X: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Y: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
    },
    ExtendedPoint{
        X: FieldElement([21352778, 5345713, 4660180, -8347857, 24143090, 14568123, 30185756, -12247770, -33528939, 8345319]),
        Y: FieldElement([6952922, 1265500, -6862341, 7057498, 4037696, 5447722, -31680899, 15325402, 19365852, -1569102]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([-25262188, -11972680, 11716002, -5869612, -18193162, 16297739, 20670665, -8559098, 3541543, -5011181])
    },
    ExtendedPoint{
        X: FieldElement([32595792, 7943725, -9377950, -3500415, -12389472, 272473, 25146209, 2005654, -326686, -11406482]),
        Y: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
    },
    ExtendedPoint{
        X: FieldElement([21352778, 5345713, 4660180, -8347857, 24143090, 14568123, 30185756, -12247770, -33528939, 8345319]),
        Y: FieldElement([-6952922, -1265500, 6862341, -7057498, -4037696, -5447722, 31680899, -15325402, -19365852, 1569102]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([25262188, 11972680, -11716002, 5869612, 18193162, -16297739, -20670665, 8559098, -3541543, 5011181])
    },
    ExtendedPoint{
        X: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Y: FieldElement([-1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
    },
    ExtendedPoint{
        X: FieldElement([-21352778, -5345713, -4660180, 8347857, -24143090, -14568123, -30185756, 12247770, 33528939, -8345319]),
        Y: FieldElement([-6952922, -1265500, 6862341, -7057498, -4037696, -5447722, 31680899, -15325402, -19365852, 1569102]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([-25262188, -11972680, 11716002, -5869612, -18193162, 16297739, 20670665, -8559098, 3541543, -5011181])
    },
    ExtendedPoint{
        X: FieldElement([-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482]),
        Y: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])
    },
    ExtendedPoint{
        X: FieldElement([-21352778, -5345713, -4660180, 8347857, -24143090, -14568123, -30185756, 12247770, 33528939, -8345319]),
        Y: FieldElement([6952922, 1265500, -6862341, 7057498, 4037696, 5447722, -31680899, 15325402, 19365852, -1569102]),
        Z: FieldElement([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]),
        T: FieldElement([25262188, 11972680, -11716002, 5869612, 18193162, -16297739, -20670665, 8559098, -3541543, 5011181])
    },
];
#[cfg(feature="radix_51")]
pub const EIGHT_TORSION: [ExtendedPoint; 8] = [
    ExtendedPoint {
        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]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([358744748052810, 1691584618240980, 977650209285361, 1429865912637724, 560044844278676]),
        Y: FieldElement([84926274344903, 473620666599931, 365590438845504, 1028470286882429, 2146499180330972]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([1448326834587521, 1857896831960481, 1093722731865333, 1677408490711241, 1915505153018406]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([533094393274173, 2016890930128738, 18285341111199, 134597186663265, 1486323764102114]),
        Y: FieldElement([0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([358744748052810, 1691584618240980, 977650209285361, 1429865912637724, 560044844278676]),
        Y: FieldElement([2166873539340326, 1778179147085316, 1886209374839743, 1223329526802818, 105300633354275]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([803472979097708, 393902981724766, 1158077081819914, 574391322974006, 336294660666841]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([0, 0, 0, 0, 0]),
        Y: FieldElement([2251799813685228, 2251799813685247, 2251799813685247, 2251799813685247, 2251799813685247]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([1893055065632419, 560215195444267, 1274149604399886, 821933901047523, 1691754969406571]),
        Y: FieldElement([2166873539340326, 1778179147085316, 1886209374839743, 1223329526802818, 105300633354275]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([1448326834587521, 1857896831960481, 1093722731865333, 1677408490711241, 1915505153018406]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133]),
        Y: FieldElement([0, 0, 0, 0, 0]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([0, 0, 0, 0, 0]),
    }
    ,
    ExtendedPoint {
        X: FieldElement([1893055065632419, 560215195444267, 1274149604399886, 821933901047523, 1691754969406571]),
        Y: FieldElement([84926274344903, 473620666599931, 365590438845504, 1028470286882429, 2146499180330972]),
        Z: FieldElement([1, 0, 0, 0, 0]),
        T: FieldElement([803472979097708, 393902981724766, 1158077081819914, 574391322974006, 336294660666841]),
    }
];

#[cfg(not(feature="radix_51"))]
pub const bi: [AffineNielsPoint; 8] = [
    AffineNielsPoint{
        y_plus_x:  FieldElement([25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605]),
        y_minus_x: FieldElement([-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378]),
        xy2d:      FieldElement([-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024]),
        y_minus_x: FieldElement([16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574]),
        xy2d:      FieldElement([30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380]),
        y_minus_x: FieldElement([4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306]),
        xy2d:      FieldElement([19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766]),
        y_minus_x: FieldElement([-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701]),
        xy2d:      FieldElement([28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877]),
        y_minus_x: FieldElement([-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951]),
        xy2d:      FieldElement([4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436]),
        y_minus_x: FieldElement([25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918]),
        xy2d:      FieldElement([23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800]),
        y_minus_x: FieldElement([-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305]),
        xy2d:      FieldElement([-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876]),
        y_minus_x: FieldElement([-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619]),
        xy2d:      FieldElement([-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683]),
    },
];
#[cfg(feature="radix_51")]
pub const bi: [AffineNielsPoint; 8] = [
    AffineNielsPoint {
        y_plus_x: FieldElement([1288382639258501, 245678601348599, 269427782077623, 1462984067271730, 137412439391563]),
        y_minus_x: FieldElement([62697248952638, 204681361388450, 631292143396476, 338455783676468, 1213667448819585]),
        xy2d: FieldElement([301289933810280, 1259582250014073, 1422107436869536, 796239922652654, 1953934009299142]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([1601611775252272, 1720807796594148, 1132070835939856, 1260455018889551, 2147779492816911]),
        y_minus_x: FieldElement([316559037616741, 2177824224946892, 1459442586438991, 1461528397712656, 751590696113597]),
        xy2d: FieldElement([1850748884277385, 1200145853858453, 1068094770532492, 672251375690438, 1586055907191707]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([769950342298419, 132954430919746, 844085933195555, 974092374476333, 726076285546016]),
        y_minus_x: FieldElement([425251763115706, 608463272472562, 442562545713235, 837766094556764, 374555092627893]),
        xy2d: FieldElement([1086255230780037, 274979815921559, 1960002765731872, 929474102396301, 1190409889297339]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([665000864555967, 2065379846933859, 370231110385876, 350988370788628, 1233371373142985]),
        y_minus_x: FieldElement([2019367628972465, 676711900706637, 110710997811333, 1108646842542025, 517791959672113]),
        xy2d: FieldElement([965130719900578, 247011430587952, 526356006571389, 91986625355052, 2157223321444601]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([1802695059465007, 1664899123557221, 593559490740857, 2160434469266659, 927570450755031]),
        y_minus_x: FieldElement([1725674970513508, 1933645953859181, 1542344539275782, 1767788773573747, 1297447965928905]),
        xy2d: FieldElement([1381809363726107, 1430341051343062, 2061843536018959, 1551778050872521, 2036394857967624]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([1970894096313054, 528066325833207, 1619374932191227, 2207306624415883, 1169170329061080]),
        y_minus_x: FieldElement([2070390218572616, 1458919061857835, 624171843017421, 1055332792707765, 433987520732508]),
        xy2d: FieldElement([893653801273833, 1168026499324677, 1242553501121234, 1306366254304474, 1086752658510815]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([213454002618221, 939771523987438, 1159882208056014, 317388369627517, 621213314200687]),
        y_minus_x: FieldElement([1971678598905747, 338026507889165, 762398079972271, 655096486107477, 42299032696322]),
        xy2d: FieldElement([177130678690680, 1754759263300204, 1864311296286618, 1180675631479880, 1292726903152791]),
    }
    ,
    AffineNielsPoint {
        y_plus_x: FieldElement([1913163449625248, 460779200291993, 2193883288642314, 1008900146920800, 1721983679009502]),
        y_minus_x: FieldElement([1070401523076875, 1272492007800961, 1910153608563310, 2075579521696771, 1191169788841221]),
        xy2d: FieldElement([692896803108118, 500174642072499, 2068223309439677, 1162190621851337, 1426986007309901]),
    }
];

#[cfg(feature = "yolocrypto")]
/// The Ed25519 basepoint
pub const DECAF_ED25519_BASEPOINT_TABLE: DecafBasepointTable
    = DecafBasepointTable(ED25519_BASEPOINT_TABLE);

/// Table containing precomputed multiples of the basepoint `B = (x,4/5)`.
///
/// The table is defined so `constants::base[i][j-1] = j*(16^2i)*B`,
/// for `0 ≤ i < 32`, `1 ≤ j < 9`.
#[cfg(not(feature="radix_51"))]
pub const ED25519_BASEPOINT_TABLE: EdwardsBasepointTable = EdwardsBasepointTable([
[
    AffineNielsPoint{
        y_plus_x:  FieldElement([25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605]),
        y_minus_x: FieldElement([-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378]),
        xy2d:      FieldElement([-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303]),
        y_minus_x: FieldElement([-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081]),
        xy2d:      FieldElement([26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024]),
        y_minus_x: FieldElement([16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574]),
        xy2d:      FieldElement([30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540]),
        y_minus_x: FieldElement([23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397]),
        xy2d:      FieldElement([7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380]),
        y_minus_x: FieldElement([4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306]),
        xy2d:      FieldElement([19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777]),
        y_minus_x: FieldElement([-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737]),
        xy2d:      FieldElement([-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766]),
        y_minus_x: FieldElement([-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701]),
        xy2d:      FieldElement([28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726]),
        y_minus_x: FieldElement([-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955]),
        xy2d:      FieldElement([27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425]),
    },
],
[
    AffineNielsPoint{
        y_plus_x:  FieldElement([-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171]),
        y_minus_x: FieldElement([27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510]),
        xy2d:      FieldElement([17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639]),
        y_minus_x: FieldElement([29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963]),
        xy2d:      FieldElement([5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568]),
        y_minus_x: FieldElement([12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335]),
        xy2d:      FieldElement([25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007]),
        y_minus_x: FieldElement([-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772]),
        xy2d:      FieldElement([-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567]),
        y_minus_x: FieldElement([13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686]),
        xy2d:      FieldElement([21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887]),
        y_minus_x: FieldElement([-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954]),
        xy2d:      FieldElement([-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833]),
        y_minus_x: FieldElement([-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532]),
        xy2d:      FieldElement([-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268]),
        y_minus_x: FieldElement([33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214]),
        xy2d:      FieldElement([1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038]),
    },
],
[
    AffineNielsPoint{
        y_plus_x:  FieldElement([6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800]),
        y_minus_x: FieldElement([4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645]),
        xy2d:      FieldElement([-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933]),
        y_minus_x: FieldElement([-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182]),
        xy2d:      FieldElement([-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991]),
        y_minus_x: FieldElement([20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880]),
        xy2d:      FieldElement([9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295]),
        y_minus_x: FieldElement([19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788]),
        xy2d:      FieldElement([8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026]),
        y_minus_x: FieldElement([11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347]),
        xy2d:      FieldElement([-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395]),
        y_minus_x: FieldElement([-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278]),
        xy2d:      FieldElement([1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995]),
        y_minus_x: FieldElement([-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596]),
        xy2d:      FieldElement([-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060]),
        y_minus_x: FieldElement([11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608]),
        xy2d:      FieldElement([-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606]),
    },
],
[
    AffineNielsPoint{
        y_plus_x:  FieldElement([7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389]),
        y_minus_x: FieldElement([-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016]),
        xy2d:      FieldElement([-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505]),
        y_minus_x: FieldElement([14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553]),
        xy2d:      FieldElement([-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220]),
        y_minus_x: FieldElement([12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631]),
        xy2d:      FieldElement([-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556]),
        y_minus_x: FieldElement([14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749]),
        xy2d:      FieldElement([236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391]),
        y_minus_x: FieldElement([5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253]),
        xy2d:      FieldElement([20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958]),
        y_minus_x: FieldElement([-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082]),
        xy2d:      FieldElement([-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521]),
        y_minus_x: FieldElement([-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807]),
        xy2d:      FieldElement([23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134]),
        y_minus_x: FieldElement([-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455]),
        xy2d:      FieldElement([27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629]),
    },
],
[
    AffineNielsPoint{
        y_plus_x:  FieldElement([-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069]),
        y_minus_x: FieldElement([-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746]),
        xy2d:      FieldElement([24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837]),
        y_minus_x: FieldElement([8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906]),
        xy2d:      FieldElement([-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817]),
        y_minus_x: FieldElement([10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098]),
        xy2d:      FieldElement([10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409]),
    },
    AffineNielsPoint{
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        xy2d:      FieldElement([1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647]),
        y_minus_x: FieldElement([13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511]),
        xy2d:      FieldElement([-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032]),
    },
],
[
    AffineNielsPoint{
        y_plus_x:  FieldElement([9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834]),
        y_minus_x: FieldElement([-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461]),
        xy2d:      FieldElement([29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516]),
        y_minus_x: FieldElement([-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547]),
        xy2d:      FieldElement([-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038]),
        y_minus_x: FieldElement([-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741]),
        xy2d:      FieldElement([16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747]),
        y_minus_x: FieldElement([-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323]),
        xy2d:      FieldElement([31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373]),
        y_minus_x: FieldElement([15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228]),
        xy2d:      FieldElement([-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399]),
        y_minus_x: FieldElement([11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831]),
        xy2d:      FieldElement([-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313]),
        y_minus_x: FieldElement([-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958]),
        xy2d:      FieldElement([-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577]),
    },
    AffineNielsPoint{
        y_plus_x:  FieldElement([-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743]),
        y_minus_x: FieldElement([29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684]),
        xy2d:      FieldElement([-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476]),
    },
]]);
#[cfg(feature="radix_51")]
pub const ED25519_BASEPOINT_TABLE: EdwardsBasepointTable = EdwardsBasepointTable([
    [
        AffineNielsPoint {
            y_plus_x: FieldElement([1288382639258501, 245678601348599, 269427782077623, 1462984067271730, 137412439391563]),
            y_minus_x: FieldElement([62697248952638, 204681361388450, 631292143396476, 338455783676468, 1213667448819585]),
            xy2d: FieldElement([301289933810280, 1259582250014073, 1422107436869536, 796239922652654, 1953934009299142]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([1380971894829527, 790832306631236, 2067202295274102, 1995808275510000, 1566530869037010]),
            y_minus_x: FieldElement([463307831301544, 432984605774163, 1610641361907204, 750899048855000, 1894842303421586]),
            xy2d: FieldElement([748439484463711, 1033211726465151, 1396005112841647, 1611506220286469, 1972177495910992]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([1601611775252272, 1720807796594148, 1132070835939856, 1260455018889551, 2147779492816911]),
            y_minus_x: FieldElement([316559037616741, 2177824224946892, 1459442586438991, 1461528397712656, 751590696113597]),
            xy2d: FieldElement([1850748884277385, 1200145853858453, 1068094770532492, 672251375690438, 1586055907191707]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([934282339813791, 1846903124198670, 1172395437954843, 1007037127761661, 1830588347719256]),
            y_minus_x: FieldElement([1694390458783935, 1735906047636159, 705069562067493, 648033061693059, 696214010414170]),
            xy2d: FieldElement([1121406372216585, 192876649532226, 190294192191717, 1994165897297032, 2245000007398739]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([769950342298419, 132954430919746, 844085933195555, 974092374476333, 726076285546016]),
            y_minus_x: FieldElement([425251763115706, 608463272472562, 442562545713235, 837766094556764, 374555092627893]),
            xy2d: FieldElement([1086255230780037, 274979815921559, 1960002765731872, 929474102396301, 1190409889297339]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([1388594989461809, 316767091099457, 394298842192982, 1230079486801005, 1440737038838979]),
            y_minus_x: FieldElement([7380825640100, 146210432690483, 304903576448906, 1198869323871120, 997689833219095]),
            xy2d: FieldElement([1181317918772081, 114573476638901, 262805072233344, 265712217171332, 294181933805782]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([665000864555967, 2065379846933859, 370231110385876, 350988370788628, 1233371373142985]),
            y_minus_x: FieldElement([2019367628972465, 676711900706637, 110710997811333, 1108646842542025, 517791959672113]),
            xy2d: FieldElement([965130719900578, 247011430587952, 526356006571389, 91986625355052, 2157223321444601]),
        },
        AffineNielsPoint {
            y_plus_x: FieldElement([2068619540119183, 1966274918058806, 957728544705549, 729906502578991, 159834893065166]),
            y_minus_x: FieldElement([2073601412052185, 31021124762708, 264500969797082, 248034690651703, 1030252227928288]),
            xy2d: FieldElement([551790716293402, 1989538725166328, 801169423371717, 2052451893578887, 678432056995012]),
        },
    ]
    ,
    [
    AffineNielsPoint {
        y_plus_x: FieldElement([1368953770187805, 790347636712921, 437508475667162, 2142576377050580, 1932081720066286]),
        y_minus_x: FieldElement([953638594433374, 1092333936795051, 1419774766716690, 805677984380077, 859228993502513]),
        xy2d: FieldElement([1200766035879111, 20142053207432, 1465634435977050, 1645256912097844, 295121984874596]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1735718747031557, 1248237894295956, 1204753118328107, 976066523550493, 65943769534592]),
        y_minus_x: FieldElement([1060098822528990, 1586825862073490, 212301317240126, 1975302711403555, 666724059764335]),
        xy2d: FieldElement([1091990273418756, 1572899409348578, 80968014455247, 306009358661350, 1520450739132526]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1480517209436112, 1511153322193952, 1244343858991172, 304788150493241, 369136856496443]),
        y_minus_x: FieldElement([2151330273626164, 762045184746182, 1688074332551515, 823046109005759, 907602769079491]),
        xy2d: FieldElement([2047386910586836, 168470092900250, 1552838872594810, 340951180073789, 360819374702533]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1982622644432056, 2014393600336956, 128909208804214, 1617792623929191, 105294281913815]),
        y_minus_x: FieldElement([980234343912898, 1712256739246056, 588935272190264, 204298813091998, 841798321043288]),
        xy2d: FieldElement([197561292938973, 454817274782871, 1963754960082318, 2113372252160468, 971377527342673]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([164699448829328, 3127451757672, 1199504971548753, 1766155447043652, 1899238924683527]),
        y_minus_x: FieldElement([732262946680281, 1674412764227063, 2182456405662809, 1350894754474250, 558458873295247]),
        xy2d: FieldElement([2103305098582922, 1960809151316468, 715134605001343, 1454892949167181, 40827143824949]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1239289043050212, 1744654158124578, 758702410031698, 1796762995074688, 1603056663766]),
        y_minus_x: FieldElement([2232056027107988, 987343914584615, 2115594492994461, 1819598072792159, 1119305654014850]),
        xy2d: FieldElement([320153677847348, 939613871605645, 641883205761567, 1930009789398224, 329165806634126]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([980930490474130, 1242488692177893, 1251446316964684, 1086618677993530, 1961430968465772]),
        y_minus_x: FieldElement([276821765317453, 1536835591188030, 1305212741412361, 61473904210175, 2051377036983058]),
        xy2d: FieldElement([833449923882501, 1750270368490475, 1123347002068295, 185477424765687, 278090826653186]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([794524995833413, 1849907304548286, 53348672473145, 1272368559505217, 1147304168324779]),
        y_minus_x: FieldElement([1504846112759364, 1203096289004681, 562139421471418, 274333017451844, 1284344053775441]),
        xy2d: FieldElement([483048732424432, 2116063063343382, 30120189902313, 292451576741007, 1156379271702225]),
    },
    ]
    ,
    [
    AffineNielsPoint {
        y_plus_x: FieldElement([928372153029038, 2147692869914564, 1455665844462196, 1986737809425946, 185207050258089]),
        y_minus_x: FieldElement([137732961814206, 706670923917341, 1387038086865771, 1965643813686352, 1384777115696347]),
        xy2d: FieldElement([481144981981577, 2053319313589856, 2065402289827512, 617954271490316, 1106602634668125]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([696298019648792, 893299659040895, 1148636718636009, 26734077349617, 2203955659340681]),
        y_minus_x: FieldElement([657390353372855, 998499966885562, 991893336905797, 810470207106761, 343139804608786]),
        xy2d: FieldElement([791736669492960, 934767652997115, 824656780392914, 1759463253018643, 361530362383518]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([2022541353055597, 2094700262587466, 1551008075025686, 242785517418164, 695985404963562]),
        y_minus_x: FieldElement([1287487199965223, 2215311941380308, 1552928390931986, 1664859529680196, 1125004975265243]),
        xy2d: FieldElement([677434665154918, 989582503122485, 1817429540898386, 1052904935475344, 1143826298169798]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([367266328308408, 318431188922404, 695629353755355, 634085657580832, 24581612564426]),
        y_minus_x: FieldElement([773360688841258, 1815381330538070, 363773437667376, 539629987070205, 783280434248437]),
        xy2d: FieldElement([180820816194166, 168937968377394, 748416242794470, 1227281252254508, 1567587861004268]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([478775558583645, 2062896624554807, 699391259285399, 358099408427873, 1277310261461761]),
        y_minus_x: FieldElement([1984740906540026, 1079164179400229, 1056021349262661, 1659958556483663, 1088529069025527]),
        xy2d: FieldElement([580736401511151, 1842931091388998, 1177201471228238, 2075460256527244, 1301133425678027]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1515728832059182, 1575261009617579, 1510246567196186, 191078022609704, 116661716289141]),
        y_minus_x: FieldElement([1295295738269652, 1714742313707026, 545583042462581, 2034411676262552, 1513248090013606]),
        xy2d: FieldElement([230710545179830, 30821514358353, 760704303452229, 390668103790604, 573437871383156]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1169380107545646, 263167233745614, 2022901299054448, 819900753251120, 2023898464874585]),
        y_minus_x: FieldElement([2102254323485823, 1570832666216754, 34696906544624, 1993213739807337, 70638552271463]),
        xy2d: FieldElement([894132856735058, 548675863558441, 845349339503395, 1942269668326667, 1615682209874691]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1287670217537834, 1222355136884920, 1846481788678694, 1150426571265110, 1613523400722047]),
        y_minus_x: FieldElement([793388516527298, 1315457083650035, 1972286999342417, 1901825953052455, 338269477222410]),
        xy2d: FieldElement([550201530671806, 778605267108140, 2063911101902983, 115500557286349, 2041641272971022]),
    },
    ]
    ,
    [
    AffineNielsPoint {
        y_plus_x: FieldElement([717255318455100, 519313764361315, 2080406977303708, 541981206705521, 774328150311600]),
        y_minus_x: FieldElement([261715221532238, 1795354330069993, 1496878026850283, 499739720521052, 389031152673770]),
        xy2d: FieldElement([1997217696294013, 1717306351628065, 1684313917746180, 1644426076011410, 1857378133465451]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1475434724792648, 76931896285979, 1116729029771667, 2002544139318042, 725547833803938]),
        y_minus_x: FieldElement([2022306639183567, 726296063571875, 315345054448644, 1058733329149221, 1448201136060677]),
        xy2d: FieldElement([1710065158525665, 1895094923036397, 123988286168546, 1145519900776355, 1607510767693874]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([561605375422540, 1071733543815037, 131496498800990, 1946868434569999, 828138133964203]),
        y_minus_x: FieldElement([1548495173745801, 442310529226540, 998072547000384, 553054358385281, 644824326376171]),
        xy2d: FieldElement([1445526537029440, 2225519789662536, 914628859347385, 1064754194555068, 1660295614401091]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1199690223111956, 24028135822341, 66638289244341, 57626156285975, 565093967979607]),
        y_minus_x: FieldElement([876926774220824, 554618976488214, 1012056309841565, 839961821554611, 1414499340307677]),
        xy2d: FieldElement([703047626104145, 1266841406201770, 165556500219173, 486991595001879, 1011325891650656]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1622861044480487, 1156394801573634, 1869132565415504, 327103985777730, 2095342781472284]),
        y_minus_x: FieldElement([334886927423922, 489511099221528, 129160865966726, 1720809113143481, 619700195649254]),
        xy2d: FieldElement([1646545795166119, 1758370782583567, 714746174550637, 1472693650165135, 898994790308209]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([333403773039279, 295772542452938, 1693106465353610, 912330357530760, 471235657950362]),
        y_minus_x: FieldElement([1811196219982022, 1068969825533602, 289602974833439, 1988956043611592, 863562343398367]),
        xy2d: FieldElement([906282429780072, 2108672665779781, 432396390473936, 150625823801893, 1708930497638539]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([925664675702328, 21416848568684, 1831436641861340, 601157008940113, 371818055044496]),
        y_minus_x: FieldElement([1479786007267725, 1738881859066675, 68646196476567, 2146507056100328, 1247662817535471]),
        xy2d: FieldElement([52035296774456, 939969390708103, 312023458773250, 59873523517659, 1231345905848899]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([643355106415761, 290186807495774, 2013561737429023, 319648069511546, 393736678496162]),
        y_minus_x: FieldElement([129358342392716, 1932811617704777, 1176749390799681, 398040349861790, 1170779668090425]),
        xy2d: FieldElement([2051980782668029, 121859921510665, 2048329875753063, 1235229850149665, 519062146124755]),
    },
    ]
    ,
    [
    AffineNielsPoint {
        y_plus_x: FieldElement([1608170971973096, 415809060360428, 1350468408164766, 2038620059057678, 1026904485989112]),
        y_minus_x: FieldElement([1837656083115103, 1510134048812070, 906263674192061, 1821064197805734, 565375124676301]),
        xy2d: FieldElement([578027192365650, 2034800251375322, 2128954087207123, 478816193810521, 2196171989962750]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1633188840273139, 852787172373708, 1548762607215796, 1266275218902681, 1107218203325133]),
        y_minus_x: FieldElement([462189358480054, 1784816734159228, 1611334301651368, 1303938263943540, 707589560319424]),
        xy2d: FieldElement([1038829280972848, 38176604650029, 753193246598573, 1136076426528122, 595709990562434]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1408451820859834, 2194984964010833, 2198361797561729, 1061962440055713, 1645147963442934]),
        y_minus_x: FieldElement([4701053362120, 1647641066302348, 1047553002242085, 1923635013395977, 206970314902065]),
        xy2d: FieldElement([1750479161778571, 1362553355169293, 1891721260220598, 966109370862782, 1024913988299801]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([212699049131723, 1117950018299775, 1873945661751056, 1403802921984058, 130896082652698]),
        y_minus_x: FieldElement([636808533673210, 1262201711667560, 390951380330599, 1663420692697294, 561951321757406]),
        xy2d: FieldElement([520731594438141, 1446301499955692, 273753264629267, 1565101517999256, 1019411827004672]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([926527492029409, 1191853477411379, 734233225181171, 184038887541270, 1790426146325343]),
        y_minus_x: FieldElement([1464651961852572, 1483737295721717, 1519450561335517, 1161429831763785, 405914998179977]),
        xy2d: FieldElement([996126634382301, 796204125879525, 127517800546509, 344155944689303, 615279846169038]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([738724080975276, 2188666632415296, 1961313708559162, 1506545807547587, 1151301638969740]),
        y_minus_x: FieldElement([622917337413835, 1218989177089035, 1284857712846592, 970502061709359, 351025208117090]),
        xy2d: FieldElement([2067814584765580, 1677855129927492, 2086109782475197, 235286517313238, 1416314046739645]),
    },
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        y_minus_x: FieldElement([1337466662091884, 1287645354669772, 2018019646776184, 652181229374245, 898011753211715]),
        xy2d: FieldElement([1969792547910734, 779969968247557, 2011350094423418, 1823964252907487, 1058949448296945]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([207343737062002, 1118176942430253, 758894594548164, 806764629546266, 1157700123092949]),
        y_minus_x: FieldElement([1273565321399022, 1638509681964574, 759235866488935, 666015124346707, 897983460943405]),
        xy2d: FieldElement([1717263794012298, 1059601762860786, 1837819172257618, 1054130665797229, 680893204263559]),
    },
    ]
    ,
    [
    AffineNielsPoint {
        y_plus_x: FieldElement([2237039662793603, 2249022333361206, 2058613546633703, 149454094845279, 2215176649164582]),
        y_minus_x: FieldElement([79472182719605, 1851130257050174, 1825744808933107, 821667333481068, 781795293511946]),
        xy2d: FieldElement([755822026485370, 152464789723500, 1178207602290608, 410307889503239, 156581253571278]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1418185496130297, 484520167728613, 1646737281442950, 1401487684670265, 1349185550126961]),
        y_minus_x: FieldElement([1495380034400429, 325049476417173, 46346894893933, 1553408840354856, 828980101835683]),
        xy2d: FieldElement([1280337889310282, 2070832742866672, 1640940617225222, 2098284908289951, 450929509534434]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([407703353998781, 126572141483652, 286039827513621, 1999255076709338, 2030511179441770]),
        y_minus_x: FieldElement([1254958221100483, 1153235960999843, 942907704968834, 637105404087392, 1149293270147267]),
        xy2d: FieldElement([894249020470196, 400291701616810, 406878712230981, 1599128793487393, 1145868722604026]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1497955250203334, 110116344653260, 1128535642171976, 1900106496009660, 129792717460909]),
        y_minus_x: FieldElement([452487513298665, 1352120549024569, 1173495883910956, 1999111705922009, 367328130454226]),
        xy2d: FieldElement([1717539401269642, 1475188995688487, 891921989653942, 836824441505699, 1885988485608364]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1241784121422547, 187337051947583, 1118481812236193, 428747751936362, 30358898927325]),
        y_minus_x: FieldElement([2022432361201842, 1088816090685051, 1977843398539868, 1854834215890724, 564238862029357]),
        xy2d: FieldElement([938868489100585, 1100285072929025, 1017806255688848, 1957262154788833, 152787950560442]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([867319417678923, 620471962942542, 226032203305716, 342001443957629, 1761675818237336]),
        y_minus_x: FieldElement([1295072362439987, 931227904689414, 1355731432641687, 922235735834035, 892227229410209]),
        xy2d: FieldElement([1680989767906154, 535362787031440, 2136691276706570, 1942228485381244, 1267350086882274]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([366018233770527, 432660629755596, 126409707644535, 1973842949591662, 645627343442376]),
        y_minus_x: FieldElement([535509430575217, 546885533737322, 1524675609547799, 2138095752851703, 1260738089896827]),
        xy2d: FieldElement([1159906385590467, 2198530004321610, 714559485023225, 81880727882151, 1484020820037082]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1377485731340769, 2046328105512000, 1802058637158797, 62146136768173, 1356993908853901]),
        y_minus_x: FieldElement([2013612215646735, 1830770575920375, 536135310219832, 609272325580394, 270684344495013]),
        xy2d: FieldElement([1237542585982777, 2228682050256790, 1385281931622824, 593183794882890, 493654978552689]),
    },
    ]
    ,
    [
    AffineNielsPoint {
        y_plus_x: FieldElement([47341488007760, 1891414891220257, 983894663308928, 176161768286818, 1126261115179708]),
        y_minus_x: FieldElement([1694030170963455, 502038567066200, 1691160065225467, 949628319562187, 275110186693066]),
        xy2d: FieldElement([1124515748676336, 1661673816593408, 1499640319059718, 1584929449166988, 558148594103306]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1784525599998356, 1619698033617383, 2097300287550715, 258265458103756, 1905684794832758]),
        y_minus_x: FieldElement([1288941072872766, 931787902039402, 190731008859042, 2006859954667190, 1005931482221702]),
        xy2d: FieldElement([1465551264822703, 152905080555927, 680334307368453, 173227184634745, 666407097159852]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([2111017076203943, 1378760485794347, 1248583954016456, 1352289194864422, 1895180776543896]),
        y_minus_x: FieldElement([171348223915638, 662766099800389, 462338943760497, 466917763340314, 656911292869115]),
        xy2d: FieldElement([488623681976577, 866497561541722, 1708105560937768, 1673781214218839, 1506146329818807]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([160425464456957, 950394373239689, 430497123340934, 711676555398832, 320964687779005]),
        y_minus_x: FieldElement([988979367990485, 1359729327576302, 1301834257246029, 294141160829308, 29348272277475]),
        xy2d: FieldElement([1434382743317910, 100082049942065, 221102347892623, 186982837860588, 1305765053501834]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([2205916462268190, 499863829790820, 961960554686616, 158062762756985, 1841471168298305]),
        y_minus_x: FieldElement([1191737341426592, 1847042034978363, 1382213545049056, 1039952395710448, 788812858896859]),
        xy2d: FieldElement([1346965964571152, 1291881610839830, 2142916164336056, 786821641205979, 1571709146321039]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([787164375951248, 202869205373189, 1356590421032140, 1431233331032510, 786341368775957]),
        y_minus_x: FieldElement([492448143532951, 304105152670757, 1761767168301056, 233782684697790, 1981295323106089]),
        xy2d: FieldElement([665807507761866, 1343384868355425, 895831046139653, 439338948736892, 1986828765695105]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([756096210874553, 1721699973539149, 258765301727885, 1390588532210645, 1212530909934781]),
        y_minus_x: FieldElement([852891097972275, 1816988871354562, 1543772755726524, 1174710635522444, 202129090724628]),
        xy2d: FieldElement([1205281565824323, 22430498399418, 992947814485516, 1392458699738672, 688441466734558]),
    },
    AffineNielsPoint {
        y_plus_x: FieldElement([1050627428414972, 1955849529137135, 2171162376368357, 91745868298214, 447733118757826]),
        y_minus_x: FieldElement([1287181461435438, 622722465530711, 880952150571872, 741035693459198, 311565274989772]),
        xy2d: FieldElement([1003649078149734, 545233927396469, 1849786171789880, 1318943684880434, 280345687170552]),
    },
    ]
]);

#[cfg(test)]
mod test {
    use field::FieldElement;
    use curve::IsIdentity;
    use curve::ValidityCheck;
    use constants;

    #[test]
    fn test_eight_torsion() {
        for i in 0..8 {
            let Q = constants::EIGHT_TORSION[i].mult_by_pow_2(3);
            assert!(Q.is_valid());
            assert!(Q.is_identity());
        }
    }

    #[test]
    fn test_four_torsion() {
        for i in (0..8).filter(|i| i % 2 == 0) {
            let Q = constants::EIGHT_TORSION[i].mult_by_pow_2(2);
            assert!(Q.is_valid());
            assert!(Q.is_identity());
        }
    }

    #[test]
    fn test_two_torsion() {
        for i in (0..8).filter(|i| i % 4 == 0) {
            let Q = constants::EIGHT_TORSION[i].mult_by_pow_2(1);
            assert!(Q.is_valid());
            assert!(Q.is_identity());
        }
    }

    #[test]
    fn test_half() {
        let one = FieldElement::one();
        let two = &one + &one;
        assert_eq!(one, &two * &constants::HALF);
    }

    /// Test that the constant for sqrt(-486664) really is a square
    /// root of -486664.
    #[test]
    #[cfg(feature="radix_51")]
    fn sqrt_minus_aplus2() {
        let minus_aplus2 = -&FieldElement([486664,0,0,0,0]);
        let sqrt = constants::SQRT_MINUS_APLUS2;
        let sq = &sqrt * &sqrt;
        assert_eq!(sq, minus_aplus2);
    }

    /// Test that the constant for sqrt(-486664) really is a square
    /// root of -486664.
    #[test]
    #[cfg(not(feature="radix_51"))]
    fn sqrt_minus_aplus2() {
        let minus_aplus2 = FieldElement([-486664,0,0,0,0,0,0,0,0,0]);
        let sqrt = constants::SQRT_MINUS_APLUS2;
        let sq = &sqrt * &sqrt;
        assert_eq!(sq, minus_aplus2);
    }

    #[test]
    /// Test that SQRT_M1 and MSQRT_M1 are square roots of -1
    fn test_sqrt_minus_one() {
        let minus_one = FieldElement::minus_one();
        let sqrt_m1_sq = &constants::SQRT_M1 * &constants::SQRT_M1;
        let msqrt_m1_sq = &constants::MSQRT_M1 * &constants::MSQRT_M1;
        assert_eq!(minus_one,  sqrt_m1_sq);
        assert_eq!(minus_one, msqrt_m1_sq);
    }

    #[test]
    fn test_sqrt_constants_sign() {
        let one       = FieldElement::one();
        let minus_one = FieldElement::minus_one();
        let (was_nonzero_square, invsqrt_m1) = minus_one.invsqrt();
        assert_eq!(was_nonzero_square, 1u8);
        let sign_test_sqrt  = &invsqrt_m1 * &constants::SQRT_M1;
        let sign_test_msqrt = &invsqrt_m1 * &constants::MSQRT_M1;
        // XXX it seems we have flipped the sign relative to
        // the invsqrt function?
        assert_eq!(sign_test_sqrt, minus_one);
        assert_eq!(sign_test_msqrt, one);
    }

    /// Test that d = -121665/121666
    #[cfg(not(feature="radix_51"))]
    #[test]
    fn test_d_vs_ratio() {
        let a = FieldElement([-121665,0,0,0,0,0,0,0,0,0]);
        let b = FieldElement([ 121666,0,0,0,0,0,0,0,0,0]);
        let d = &a * &b.invert();
        let d2 = &d + &d;
        assert_eq!(d, constants::d);
        assert_eq!(d2, constants::d2);
    }

    /// Test that d = -121665/121666
    #[cfg(feature="radix_51")]
    #[test]
    fn test_d_vs_ratio() {
        let a = -&FieldElement([121665,0,0,0,0]);
        let b =   FieldElement([121666,0,0,0,0]);
        let d = &a * &b.invert();
        let d2 = &d + &d;
        assert_eq!(d, constants::d);
        assert_eq!(d2, constants::d2);
    }

    #[test]
    fn test_d4() {
        let mut four = FieldElement::zero();
        four[0] = 4;
        assert_eq!(&constants::d * &four, constants::d4);
    }

    #[test]
    fn test_a_minus_d() {
        let a = FieldElement::minus_one();
        let a_minus_d = &a - &constants::d;
        assert_eq!(a_minus_d, constants::a_minus_d);
    }
}