pub use crate::backend::serial::u64::field::FieldElement51;

const fn field_element(element: [u64; 5]) -> FieldElement51 {
    FieldElement51(element)
}

/// `= sqrt(i*d)`, where `i = +sqrt(-1)` and `d` is the Edwards curve parameter.
pub const SQRT_ID: FieldElement51 = field_element([
    2298852427963285,
    3837146560810661,
    4413131899466403,
    3883177008057528,
    2352084440532925,
]);

/// `= (d+1)/(d-1)`, where `d` is the Edwards curve parameter.
pub const DP1_OVER_DM1: FieldElement51 = field_element([
    2159851467815724,
    1752228607624431,
    1825604053920671,
    1212587319275468,
    253422448836237,
]);

/// `= -2/sqrt(a-d)`, where `a = -1 (mod p)`, `d` are the Edwards curve parameters.
pub const MDOUBLE_INVSQRT_A_MINUS_D: FieldElement51 = field_element([
    1693982333959686,
    608509411481997,
    2235573344831311,
    947681270984193,
    266558006233600,
]);

/// `= -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: FieldElement51 = field_element([
    1608655899704280,
    1999971613377227,
    49908634785720,
    1873700692181652,
    353702208628067,
]);

/// `= -1/sqrt(1+d)`, where `d` is the Edwards curve parameters.
pub const MINVSQRT_ONE_PLUS_D: FieldElement51 = field_element([
    321571956990465,
    1251814006996634,
    2226845496292387,
    189049560751797,
    2074948709371214,
]);