optimize point add constraints (#106)

* optimize add constraints

* optimize double by rewriting a constraint involving an inverted element

src/circuit.rs

@@ -412,7 +412,7 @@ mod tests {
     let mut cs: ShapeCS<G1> = ShapeCS::new();
     let _ = circuit1.synthesize(&mut cs);
     let (shape1, gens1) = (cs.r1cs_shape(), cs.r1cs_gens());
-    assert_eq!(cs.num_constraints(), 19739);
+    assert_eq!(cs.num_constraints(), 18967);
 
     // Initialize the shape and gens for the secondary
     let circuit2: NovaAugmentedCircuit<G1, TrivialTestCircuit<<G1 as Group>::Base>> =
@@ -425,7 +425,7 @@ mod tests {
     let mut cs: ShapeCS<G2> = ShapeCS::new();
     let _ = circuit2.synthesize(&mut cs);
     let (shape2, gens2) = (cs.r1cs_shape(), cs.r1cs_gens());
-    assert_eq!(cs.num_constraints(), 20271);
+    assert_eq!(cs.num_constraints(), 19499);
 
     // Execute the base case for the primary
     let zero1 = <<G2 as Group>::Base as Field>::zero();

src/gadgets/ecc.rs

@@ -214,39 +214,24 @@ where
       &x_diff_is_actual,
     )?;
 
-    let x_diff_inv = AllocatedNum::alloc(cs.namespace(|| "x diff inverse"), || {
-      if *x_diff_is_actual.get_value().get()? == Fp::one() {
+    let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
+      let x_diff_inv = if *x_diff_is_actual.get_value().get()? == Fp::one() {
         // Set to default
-        Ok(Fp::one())
+        Fp::one()
       } else {
         // Set to the actual inverse
-        let inv = (*other.x.get_value().get()? - *self.x.get_value().get()?).invert();
-        if inv.is_some().unwrap_u8() == 1 {
-          Ok(inv.unwrap())
-        } else {
-          Err(SynthesisError::DivisionByZero)
-        }
-      }
-    })?;
-
-    cs.enforce(
-      || "Check inverse",
-      |lc| lc + x_diff.get_variable(),
-      |lc| lc + x_diff_inv.get_variable(),
-      |lc| lc + CS::one(),
-    );
+        (*other.x.get_value().get()? - *self.x.get_value().get()?)
+          .invert()
+          .unwrap()
+      };
 
-    let lambda = AllocatedNum::alloc(cs.namespace(|| "lambda"), || {
-      Ok(
-        (*other.y.get_value().get()? - *self.y.get_value().get()?)
-          * x_diff_inv.get_value().get()?,
-      )
+      Ok((*other.y.get_value().get()? - *self.y.get_value().get()?) * x_diff_inv)
     })?;
     cs.enforce(
       || "Check that lambda is correct",
-      |lc| lc + other.y.get_variable() - self.y.get_variable(),
-      |lc| lc + x_diff_inv.get_variable(),
       |lc| lc + lambda.get_variable(),
+      |lc| lc + x_diff.get_variable(),
+      |lc| lc + other.y.get_variable() - self.y.get_variable(),
     );
 
     //************************************************************************/
@@ -358,37 +343,24 @@ where
 
     let tmp = select_one_or_num2(cs.namespace(|| "tmp"), &tmp_actual, &self.is_infinity)?;
 
-    // Compute inv = tmp.invert
-    let tmp_inv = AllocatedNum::alloc(cs.namespace(|| "tmp inverse"), || {
-      if *self.is_infinity.get_value().get()? == Fp::one() {
+    // Now compute lambda as (Fp::one() + Fp::one + Fp::one()) * self.x * self.x * tmp_inv
+    let prod_1 = AllocatedNum::alloc(cs.namespace(|| "alloc prod 1"), || {
+      let tmp_inv = if *self.is_infinity.get_value().get()? == Fp::one() {
         // Return default value 1
-        Ok(Fp::one())
+        Fp::one()
       } else {
         // Return the actual inverse
-        let inv = (*tmp.get_value().get()?).invert();
-        if inv.is_some().unwrap_u8() == 1 {
-          Ok(inv.unwrap())
-        } else {
-          Err(SynthesisError::DivisionByZero)
-        }
-      }
-    })?;
-    cs.enforce(
-      || "Check inverse",
-      |lc| lc + tmp.get_variable(),
-      |lc| lc + tmp_inv.get_variable(),
-      |lc| lc + CS::one(),
-    );
+        (*tmp.get_value().get()?).invert().unwrap()
+      };
 
-    // Now compute lambda as (Fp::one() + Fp::one + Fp::one()) * self.x * self.x * tmp_inv
-    let prod_1 = AllocatedNum::alloc(cs.namespace(|| "alloc prod 1"), || {
-      Ok(*tmp_inv.get_value().get()? * self.x.get_value().get()?)
+      Ok(tmp_inv * self.x.get_value().get()?)
     })?;
+
     cs.enforce(
       || "Check prod 1",
-      |lc| lc + self.x.get_variable(),
-      |lc| lc + tmp_inv.get_variable(),
+      |lc| lc + tmp.get_variable(),
       |lc| lc + prod_1.get_variable(),
+      |lc| lc + self.x.get_variable(),
     );
 
     let prod_2 = AllocatedNum::alloc(cs.namespace(|| "alloc prod 2"), || {