Interpolation of two points

src/fri/recursive_verifier.rs

@@ -174,23 +174,34 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         let quotient = self.div_unsafe_extension(numerator, denominator);
         let sum = self.add_extension(sum, quotient);
 
-        // let ev: F::Extension = proof
+        let evs = proof
-        //     .unsalted_evals(3, config)
+            .unsalted_evals(3, config)
-        //     .iter()
+            .iter()
-        //     .zip(alpha_powers.clone())
+            .map(|&e| self.convert_to_ext(e))
-        //     .map(|(&e, a)| a * e.into())
+            .collect::<Vec<_>>();
-        //     .sum();
+        let mut ev = self.zero_extension();
-        // let zeta_right = F::Extension::primitive_root_of_unity(degree_log) * zeta;
+        for &e in &evs {
-        // let zs_interpol = interpolant(&[
+            let a = alpha_powers.next(self);
-        //     (zeta, reduce_with_iter(&os.plonk_zs, alpha_powers.clone())),
+            let tmp = self.mul_extension(a, e);
-        //     (
+            ev = self.add_extension(ev, tmp);
-        //         zeta_right,
+        }
-        //         reduce_with_iter(&os.plonk_zs_right, &mut alpha_powers),
+
-        //     ),
+        let g = self.constant_extension(F::Extension::primitive_root_of_unity(degree_log));
-        // ]);
+        let zeta_right = self.mul_extension(g, zeta);
-        // let numerator = ev - zs_interpol.eval(subgroup_x);
+        let zs_interpol = self.interpolate2([
-        // let denominator = (subgroup_x - zeta) * (subgroup_x - zeta_right);
+            (zeta, reduce_with_iter(&os.plonk_zs, alpha_powers.clone())),
-        // sum += numerator / denominator;
+            (
+                zeta_right,
+                reduce_with_iter(&os.plonk_zs_right, &mut alpha_powers),
+            ),
+        ]);
+        let interpol_val = zs_interpol.eval(self, subgroup_x);
+        let numerator = self.sub_extension(ev, interpol_val);
+        let vanish = self.sub_extension(subgroup_x, zeta);
+        let vanish_right = self.sub_extension(subgroup_x, zeta_right);
+        let denominator = self.mul_extension(vanish, vanish_right);
+        let quotient = self.div_unsafe_extension(numerator, denominator);
+        let sum = self.add_extension(sum, quotient);
         //
         // let ev: F::Extension = proof
         //     .unsalted_evals(2, config)

src/gadgets/interpolation.rs

@@ -0,0 +1,15 @@
+use crate::circuit_builder::CircuitBuilder;
+use crate::field::extension_field::target::ExtensionTarget;
+use crate::field::extension_field::Extendable;
+use crate::gadgets::polynomial::PolynomialCoeffsExtTarget;
+
+impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
+    /// Interpolate two points. No need for an `InterpolationGate` since the coefficients
+    /// of the linear interpolation polynomial can be easily computed with arithmetic operations.
+    pub fn interpolate2(
+        &mut self,
+        points: [(ExtensionTarget<D>, ExtensionTarget<D>); 2],
+    ) -> PolynomialCoeffsExtTarget<D> {
+        todo!()
+    }
+}

src/gadgets/mod.rs

@@ -1,5 +1,6 @@
 pub mod arithmetic;
 pub mod hash;
+pub mod interpolation;
 pub mod polynomial;
 pub mod split_base;
 pub(crate) mod split_join;