Function hinted_check_line_through_point

bitvm/src/bn254/g2.rs:687–722

check line through one point, that is: y - alpha * x - bias = 0 input on stack: x (2 elements) y (2 elements) input of parameters: c3: alpha c4: -bias output: true or false (consumed on stack)

(
    x: ark_bn254::Fq2,
    c3: ark_bn254::Fq2,
    _c4: ark_bn254::Fq2,
)

/// output:
///     true or false (consumed on stack)
pub fn hinted_check_line_through_point(
    x: ark_bn254::Fq2,
    c3: ark_bn254::Fq2,
    _c4: ark_bn254::Fq2,
) -> (Script, Vec<Hint>) {
    let mut hints: Vec<Hint> = Vec::new();

    // let (hinted_script1, hint1) = Fq2::hinted_mul_by_constant(x, &c3);
    let (hinted_script1, hint1) = Fq2::hinted_mul(2, x, 0, c3);

    let script = script! {

           // [c3, c4, x, y]
           {Fq2::roll(2)}
           // [c3, c4, y, x]
           {Fq2::copy(6)}
           // [c3, c4, y, x,c3]
           {hinted_script1}
           // [c3, c4, y, alpha * x]
           {Fq2::neg(0)}
           // [c3, c4, y, -alpha * x]
           {Fq2::add(2, 0)}
           // [c3, c4, y - alpha * x]
           {Fq2::copy(2)} // Fq2::push(c4),
           // [c3, c4, y - alpha * x, -bias]
           {Fq2::add(2, 0)}
           // [c3, c4, y - alpha * x - bias]
           {Fq2::push_zero()}
           // [c3, c4, y - alpha * x - bias, 0]
           {Fq2::equalverify()}
           // [c3, c4]
    };
    hints.extend(hint1);

    (script, hints)
}

/// check whether a tuple coefficient (alpha, -bias) of a chord line is satisfied with expected points T and Q (both are affine cooordinates)
/// two aspects: