add_incomplete::tests: Constrain output of `P + Q` test.

Also minor docfixes and refactors.

Co-authored-by: Jack Grigg <jack@electriccoin.co>

src/circuit/gadget/ecc.rs

@@ -470,7 +470,7 @@ mod tests {
             // Test complete addition
             {
                 super::chip::add::tests::test_add(
-                    chip,
+                    chip.clone(),
                     layouter.namespace(|| "complete addition"),
                     &zero,
                     p_val,
@@ -484,9 +484,12 @@ mod tests {
             // Test incomplete addition
             {
                 super::chip::add_incomplete::tests::test_add_incomplete(
+                    chip,
                     layouter.namespace(|| "incomplete addition"),
                     &zero,
+                    p_val,
                     &p,
+                    q_val,
                     &q,
                     &p_neg,
                 )?;
@@ -498,7 +501,7 @@ mod tests {
 
     #[test]
     fn ecc() {
-        let k = 5;
+        let k = 6;
         let circuit = MyCircuit {};
         let prover = MockProver::run(k, &circuit, vec![]).unwrap();
         assert_eq!(prover.verify(), Ok(()))

src/circuit/gadget/ecc/chip/add.rs

@@ -409,13 +409,13 @@ pub mod tests {
         // Check complete addition P + (-P)
         {
             let result = p.add(layouter.namespace(|| "P + (-P)"), p_neg)?;
-            result.constrain_equal(layouter.namespace(|| "P + (-P) = 0"), zero)?;
+            result.constrain_equal(layouter.namespace(|| "P + (-P) = 𝒪"), zero)?;
         }
 
         // Check complete addition 𝒪 + 𝒪
         {
             let result = zero.add(layouter.namespace(|| "𝒪 + 𝒪"), zero)?;
-            result.constrain_equal(layouter.namespace(|| "P + (-P) = 0"), zero)?;
+            result.constrain_equal(layouter.namespace(|| "𝒪 + 𝒪 = 𝒪"), zero)?;
         }
 
         // Check P + Q

src/circuit/gadget/ecc/chip/add_incomplete.rs

@@ -53,7 +53,7 @@ impl Config {
                 (x_r.clone() + x_q.clone() + x_p.clone())
                     * (x_p.clone() - x_q.clone())
                     * (x_p.clone() - x_q.clone())
-                    - (y_p.clone() - y_q.clone()) * (y_p.clone() - y_q.clone())
+                    - (y_p.clone() - y_q.clone()).square()
             };
 
             // (y_r + y_q)(x_p − x_q) − (y_p − y_q)(x_q − x_r) = 0
@@ -143,22 +143,35 @@ impl Config {
 
 #[cfg(test)]
 pub mod tests {
-    use halo2::{arithmetic::CurveAffine, circuit::Layouter, plonk::Error};
+    use group::Curve;
+    use halo2::{circuit::Layouter, plonk::Error};
+    use pasta_curves::pallas;
 
     use crate::circuit::gadget::ecc::{EccInstructions, Point};
 
+    #[allow(clippy::too_many_arguments)]
     pub fn test_add_incomplete<
-        C: CurveAffine,
-        EccChip: EccInstructions<C> + Clone + Eq + std::fmt::Debug,
+        EccChip: EccInstructions<pallas::Affine> + Clone + Eq + std::fmt::Debug,
     >(
-        mut layouter: impl Layouter<C::Base>,
-        zero: &Point<C, EccChip>,
-        p: &Point<C, EccChip>,
-        q: &Point<C, EccChip>,
-        p_neg: &Point<C, EccChip>,
+        chip: EccChip,
+        mut layouter: impl Layouter<pallas::Base>,
+        zero: &Point<pallas::Affine, EccChip>,
+        p_val: pallas::Affine,
+        p: &Point<pallas::Affine, EccChip>,
+        q_val: pallas::Affine,
+        q: &Point<pallas::Affine, EccChip>,
+        p_neg: &Point<pallas::Affine, EccChip>,
     ) -> Result<(), Error> {
         // P + Q
-        p.add_incomplete(layouter.namespace(|| "P + Q"), q)?;
+        {
+            let result = p.add_incomplete(layouter.namespace(|| "P + Q"), q)?;
+            let witnessed_result = Point::new(
+                chip,
+                layouter.namespace(|| "witnessed P + Q"),
+                Some((p_val + q_val).to_affine()),
+            )?;
+            result.constrain_equal(layouter.namespace(|| "constrain P + Q"), &witnessed_result)?;
+        }
 
         // P + P should return an error
         p.add_incomplete(layouter.namespace(|| "P + P"), p)

src/circuit/gadget/ecc/chip/witness_point.rs

@@ -40,8 +40,8 @@ impl Config {
             let y = meta.query_advice(self.y, Rotation::cur());
 
             // y^2 = x^3 + b
-            let curve_eqn = y.clone() * y.clone()
-                - (x.clone() * x.clone() * x.clone())
+            let curve_eqn = y.clone().square()
+                - (x.clone().square() * x.clone())
                 - Expression::Constant(pallas::Affine::b());
 
             vec![