use backend::serial::u32::field::FieldElement2625;
use edwards::EdwardsPoint;

/// `= sqrt(i*d)`, where `i = +sqrt(-1)` and `d` is the Edwards curve parameter.
pub const SQRT_ID: FieldElement2625 = FieldElement2625([
    39590824, 701138,   28659366, 23623507, 53932708,
    32206357, 36326585, 24309414, 26167230,  1494357,
]);

/// `= (d+1)/(d-1)`, where `d` is the Edwards curve parameter.
pub const DP1_OVER_DM1: FieldElement2625 = FieldElement2625([
    58833708, 32184294, 62457071, 26110240, 19032991,
    27203620, 7122892,  18068959, 51019405,  3776288,
]);

/// `= -2/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub const MDOUBLE_INVSQRT_A_MINUS_D: FieldElement2625 = FieldElement2625([
    54885894, 25242303, 55597453, 9067496,  51808079,
    33312638, 25456129, 14121551, 54921728,  3972023,
]);

/// `= -2i/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters
/// and `i = +sqrt(-1)`.
pub const MIDOUBLE_INVSQRT_A_MINUS_D: FieldElement2625 = FieldElement2625([
    58178520, 23970840, 26444491, 29801899, 41064376,
    743696,   2900628,  27920316, 41968995,  5270573,
]);

/// `= -1/sqrt(1+d)`, where `d` is the Edwards curve parameters.
pub const MINVSQRT_ONE_PLUS_D: FieldElement2625 = FieldElement2625([
    38019585, 4791795,  20332186, 18653482,  46576675,
    33182583, 65658549,  2817057, 12569934,  30919145,
]);