Method hinted_check_add

bitvm/src/bn254/g1.rs:234–332

(t: ark_bn254::G1Affine, q: ark_bn254::G1Affine)

    }

    pub fn hinted_check_add(t: ark_bn254::G1Affine, q: ark_bn254::G1Affine) -> (Script, Vec<Hint>) {
        let mut hints = vec![];

        let (alpha, bias) = if t.is_zero() || q.is_zero() {
            // no hint, dummy zero
            (ark_bn254::Fq::ZERO, ark_bn254::Fq::ZERO)
        } else if t == -q {
            // no hint, dummy zero
            (ark_bn254::Fq::ZERO, ark_bn254::Fq::ZERO)
        } else if t == q {
            // doubling hints
            let alpha = (t.x.square() + t.x.square() + t.x.square()) / (t.y + t.y);
            let bias = t.y - alpha * t.x;
            (alpha, bias)
        } else {
            // adding hints
            let alpha = (t.y - q.y) / (t.x - q.x);
            let bias = t.y - alpha * t.x;
            (alpha, bias)
        };

        let (hinted_script1, hint1) = Self::hinted_check_chord_line(t, q, alpha);
        let (hinted_script2, hint2) = Self::hinted_add(t.x, q.x, alpha);
        let (hinted_script3, hint3) = Self::hinted_check_tangent_line(t, alpha);

        let script = script! {           // tx ty qx qy
            { G1Affine::is_zero_keep_element() }
            OP_IF
                { G1Affine::drop() }
            OP_ELSE
                { G1Affine::roll(2) }
                { G1Affine::is_zero_keep_element() }
                OP_IF
                    { G1Affine::drop() }
                OP_ELSE                                    // qx qy tx ty
                    { Fq::equal_keep_elements(3, 1) }      // t == q or t == -q
                    OP_DUP
                    OP_TOALTSTACK
                    OP_TOALTSTACK
                    { Fq::equal_keep_elements(2, 0) }
                    OP_NOT
                    OP_FROMALTSTACK
                    OP_BOOLAND
                    OP_IF                                  // case: t == -q
                        OP_FROMALTSTACK OP_DROP
                        { G1Affine::drop() }
                        { G1Affine::drop() }
                        { G1Affine::identity() }
                    OP_ELSE                                // case: t != -q
                        for _ in 0..Fq::N_LIMBS {
                            OP_DEPTH OP_1SUB OP_ROLL
                        }
                        { Fq::check_validity_and_keep_element() }
                        for _ in 0..Fq::N_LIMBS {
                            OP_DEPTH OP_1SUB OP_ROLL
                        }                                  // qx qy tx ty c3 c4
                        { Fq::check_validity_and_keep_element() }
                        { Fq::copy(1) }                    // qx qy tx ty c3 c4 c3