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//! Signum trait: sgn0 for field elements

use fff::Field;
use std::ops::{BitAnd, BitXor};

/// Result of Sgn0.
#[derive(Debug, PartialEq, Eq)]
pub enum Sgn0Result {
    /// Either 0 or positive
    NonNegative,
    /// Neither 0 nor positive
    Negative,
}

impl From<bool> for Sgn0Result {
    fn from(val: bool) -> Self {
        if val {
            // Negative values = 1
            Sgn0Result::Negative
        } else {
            // Non negative values = 0
            Sgn0Result::NonNegative
        }
    }
}

impl BitAnd for Sgn0Result {
    type Output = Self;

    fn bitand(self, rhs: Self) -> Self::Output {
        if self == rhs && self == Sgn0Result::Negative {
            // 1 & 1 == 1
            Sgn0Result::Negative
        } else {
            Sgn0Result::NonNegative
        }
    }
}

impl BitXor for Sgn0Result {
    type Output = Self;
    fn bitxor(self, rhs: Self) -> Self {
        if self == rhs {
            Sgn0Result::NonNegative
        } else {
            Sgn0Result::Negative
        }
    }
}

/// Signum computations and conditional in-place negation.
pub trait Signum0: Field {
    /// Returns either Negative or NonNegative.
    fn sgn0(&self) -> Sgn0Result;

    /// Negate if the argument is Negative.
    fn negate_if(&mut self, sgn: Sgn0Result) {
        if sgn == Sgn0Result::Negative {
            self.negate();
        }
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    #[allow(clippy::eq_op)]
    fn test_sgn0result_xor() {
        assert_eq!(
            Sgn0Result::Negative ^ Sgn0Result::Negative,
            Sgn0Result::NonNegative
        );
        assert_eq!(
            Sgn0Result::Negative ^ Sgn0Result::NonNegative,
            Sgn0Result::Negative
        );
        assert_eq!(
            Sgn0Result::NonNegative ^ Sgn0Result::Negative,
            Sgn0Result::Negative
        );
        assert_eq!(
            Sgn0Result::NonNegative ^ Sgn0Result::NonNegative,
            Sgn0Result::NonNegative
        );
    }

    #[test]
    #[allow(clippy::eq_op)]
    fn test_sgn0result_and() {
        assert_eq!(
            Sgn0Result::Negative & Sgn0Result::Negative,
            Sgn0Result::Negative
        );
        assert_eq!(
            Sgn0Result::Negative & Sgn0Result::NonNegative,
            Sgn0Result::NonNegative
        );
        assert_eq!(
            Sgn0Result::NonNegative & Sgn0Result::Negative,
            Sgn0Result::NonNegative
        );
        assert_eq!(
            Sgn0Result::NonNegative & Sgn0Result::NonNegative,
            Sgn0Result::NonNegative
        );
    }
}