Progress

src/fri/recursive_verifier.rs

@@ -157,16 +157,20 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         let evals = [0, 1, 4]
             .iter()
             .flat_map(|&i| proof.unsalted_evals(i, config))
-            .map(|&e| F::Extension::from_basefield(e));
+            .map(|&e| self.convert_to_ext(e));
         let openings = os
             .constants
             .iter()
             .chain(&os.plonk_sigmas)
             .chain(&os.quotient_polys);
-        let numerator = izip!(evals, openings, &mut alpha_powers)
-            .map(|(e, &o, a)| a * (e - o))
-            .sum::<F::Extension>();
-        let denominator = subgroup_x - zeta;
+        let mut numerator = self.zero_extension();
+        for (e, &o) in izip!(evals, openings) {
+            let a = alpha_powers.next(self);
+            let diff = self.sub_extension(e, o);
+            numerator = self.mul_add_extension(a, diff, numerator);
+        }
+        let denominator = self.sub_extension(subgroup_x, zeta);
+        // let quotient = self.div_unsafe()
         sum += numerator / denominator;
 
         let ev: F::Extension = proof

src/gadgets/arithmetic.rs

@@ -225,29 +225,40 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
 
         q
     }
-}
 
-/// An iterator over the powers of a certain base element `b`: `b^0, b^1, b^2, ...`.
-#[derive(Clone)]
-pub struct PowersTarget<const D: usize> {
-    base: ExtensionTarget<D>,
-    current: ExtensionTarget<D>,
-}
+    /// Computes `q = x / y` by witnessing `q` and requiring that `q * y = x`. This can be unsafe in
+    /// some cases, as it allows `0 / 0 = <anything>`.
+    pub fn div_unsafe_extension(
+        &mut self,
+        x: ExtensionTarget<D>,
+        y: ExtensionTarget<D>,
+    ) -> ExtensionTarget<D> {
+        // Add an `ArithmeticGate` to compute `q * y`.
+        let gate = self.add_gate(ArithmeticGate::new(), vec![F::ONE, F::ZERO]);
 
-impl<F: Extendable<D>, const D: usize> PowersTarget<D> {
-    fn next(&mut self, builder: &mut CircuitBuilder<F, D>) -> Option<ExtensionTarget<D>> {
-        let result = self.current;
-        self.current = builder.mul_extension(self.base, self.current);
-        Some(result)
-    }
-}
+        let wire_multiplicand_0 = Wire {
+            gate,
+            input: ArithmeticGate::WIRE_MULTIPLICAND_0,
+        };
+        let wire_multiplicand_1 = Wire {
+            gate,
+            input: ArithmeticGate::WIRE_MULTIPLICAND_1,
+        };
+        let wire_addend = Wire {
+            gate,
+            input: ArithmeticGate::WIRE_ADDEND,
+        };
+        let wire_output = Wire {
+            gate,
+            input: ArithmeticGate::WIRE_OUTPUT,
+        };
 
-impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
-    pub fn powers(&mut self, base: ExtensionTarget<D>) -> PowersTarget<D> {
-        PowersTarget {
-            base,
-            current: self.one_extension(),
-        }
+        let q = Target::Wire(wire_multiplicand_0);
+        self.add_generator(QuotientGeneratorExtension {
+            numerator: x,
+            denominator: ExtensionTarget(),
+            quotient: ExtensionTarget(),
+        })
     }
 }
 
@@ -268,3 +279,53 @@ impl<F: Field> SimpleGenerator<F> for QuotientGenerator {
         PartialWitness::singleton_target(self.quotient, num / den)
     }
 }
+
+struct QuotientGeneratorExtension<const D: usize> {
+    numerator: ExtensionTarget<D>,
+    denominator: ExtensionTarget<D>,
+    quotient: ExtensionTarget<D>,
+}
+
+impl<F: Field, const D: usize> SimpleGenerator<F> for QuotientGeneratorExtension<D> {
+    fn dependencies(&self) -> Vec<Target> {
+        let mut deps = self.numerator.to_target_array().to_vec();
+        deps.extend(&self.denominator.to_target_array());
+        deps
+    }
+
+    fn run_once(&self, witness: &PartialWitness<F>) -> PartialWitness<F> {
+        let num = witness.get_extension_target(self.numerator);
+        let dem = witness.get_extension_target(self.denominator);
+        let quotient = num / dem;
+        let mut pw = PartialWitness::new();
+        pw.set_ext_wires(self.quotient.to_target_array(), quotient);
+        pw
+    }
+}
+
+/// An iterator over the powers of a certain base element `b`: `b^0, b^1, b^2, ...`.
+#[derive(Clone)]
+pub struct PowersTarget<const D: usize> {
+    base: ExtensionTarget<D>,
+    current: ExtensionTarget<D>,
+}
+
+impl<const D: usize> PowersTarget<D> {
+    pub fn next<F: Extendable<D>>(
+        &mut self,
+        builder: &mut CircuitBuilder<F, D>,
+    ) -> ExtensionTarget<D> {
+        let result = self.current;
+        self.current = builder.mul_extension(self.base, self.current);
+        result
+    }
+}
+
+impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
+    pub fn powers(&mut self, base: ExtensionTarget<D>) -> PowersTarget<D> {
+        PowersTarget {
+            base,
+            current: self.one_extension(),
+        }
+    }
+}

src/gates/mod.rs

@@ -8,3 +8,4 @@ pub(crate) mod noop;
 
 #[cfg(test)]
 mod gate_testing;
+mod mul_extension;

src/gates/mul_extension.rs

@@ -0,0 +1,160 @@
+use crate::circuit_builder::CircuitBuilder;
+use crate::field::extension_field::target::ExtensionTarget;
+use crate::field::extension_field::Extendable;
+use crate::field::field::Field;
+use crate::gates::gate::{Gate, GateRef};
+use crate::generator::{SimpleGenerator, WitnessGenerator};
+use crate::target::Target;
+use crate::vars::{EvaluationTargets, EvaluationVars};
+use crate::wire::Wire;
+use crate::witness::PartialWitness;
+use std::ops::Range;
+
+/// A gate which can multiply to field extension elements.
+/// TODO: Add an addend if `NUM_ROUTED_WIRES` is large enough.
+#[derive(Debug)]
+pub struct MulExtensionGate<const D: usize>;
+
+impl<const D: usize> MulExtensionGate<D> {
+    pub fn new<F: Extendable<D>>() -> GateRef<F, D> {
+        GateRef::new(MulExtensionGate)
+    }
+
+    pub fn wires_multiplicand_0() -> Range<usize> {
+        0..D
+    }
+    pub fn wires_multiplicand_1() -> Range<usize> {
+        D..2 * D
+    }
+    pub fn wires_output() -> Range<usize> {
+        2 * D..3 * D
+    }
+}
+
+impl<F: Extendable<D>, const D: usize> Gate<F, D> for MulExtensionGate<D> {
+    fn id(&self) -> String {
+        format!("{:?}", self)
+    }
+
+    fn eval_unfiltered(&self, vars: EvaluationVars<F, D>) -> Vec<F::Extension> {
+        let const_0 = vars.local_constants[0];
+        let const_1 = vars.local_constants[1];
+        let multiplicand_0 = vars.local_wires[Self::WIRE_MULTIPLICAND_0];
+        let multiplicand_1 = vars.local_wires[Self::WIRE_MULTIPLICAND_1];
+        let addend = vars.local_wires[Self::WIRE_ADDEND];
+        let output = vars.local_wires[Self::WIRE_OUTPUT];
+        let computed_output = const_0 * multiplicand_0 * multiplicand_1 + const_1 * addend;
+        vec![computed_output - output]
+    }
+
+    fn eval_unfiltered_recursively(
+        &self,
+        builder: &mut CircuitBuilder<F, D>,
+        vars: EvaluationTargets<D>,
+    ) -> Vec<ExtensionTarget<D>> {
+        let const_0 = vars.local_constants[0];
+        let const_1 = vars.local_constants[1];
+        let multiplicand_0 = vars.local_wires[Self::WIRE_MULTIPLICAND_0];
+        let multiplicand_1 = vars.local_wires[Self::WIRE_MULTIPLICAND_1];
+        let addend = vars.local_wires[Self::WIRE_ADDEND];
+        let output = vars.local_wires[Self::WIRE_OUTPUT];
+
+        let product_term = builder.mul_many_extension(&[const_0, multiplicand_0, multiplicand_1]);
+        let addend_term = builder.mul_extension(const_1, addend);
+        let computed_output = builder.add_many_extension(&[product_term, addend_term]);
+        vec![builder.sub_extension(computed_output, output)]
+    }
+
+    fn generators(
+        &self,
+        gate_index: usize,
+        local_constants: &[F],
+    ) -> Vec<Box<dyn WitnessGenerator<F>>> {
+        let gen = ArithmeticGenerator {
+            gate_index,
+            const_0: local_constants[0],
+            const_1: local_constants[1],
+        };
+        vec![Box::new(gen)]
+    }
+
+    fn num_wires(&self) -> usize {
+        4
+    }
+
+    fn num_constants(&self) -> usize {
+        2
+    }
+
+    fn degree(&self) -> usize {
+        3
+    }
+
+    fn num_constraints(&self) -> usize {
+        1
+    }
+}
+
+struct ArithmeticGenerator<F: Field> {
+    gate_index: usize,
+    const_0: F,
+    const_1: F,
+}
+
+impl<F: Field> SimpleGenerator<F> for ArithmeticGenerator<F> {
+    fn dependencies(&self) -> Vec<Target> {
+        vec![
+            Target::Wire(Wire {
+                gate: self.gate_index,
+                input: ArithmeticGate::WIRE_MULTIPLICAND_0,
+            }),
+            Target::Wire(Wire {
+                gate: self.gate_index,
+                input: ArithmeticGate::WIRE_MULTIPLICAND_1,
+            }),
+            Target::Wire(Wire {
+                gate: self.gate_index,
+                input: ArithmeticGate::WIRE_ADDEND,
+            }),
+        ]
+    }
+
+    fn run_once(&self, witness: &PartialWitness<F>) -> PartialWitness<F> {
+        let multiplicand_0_target = Wire {
+            gate: self.gate_index,
+            input: ArithmeticGate::WIRE_MULTIPLICAND_0,
+        };
+        let multiplicand_1_target = Wire {
+            gate: self.gate_index,
+            input: ArithmeticGate::WIRE_MULTIPLICAND_1,
+        };
+        let addend_target = Wire {
+            gate: self.gate_index,
+            input: ArithmeticGate::WIRE_ADDEND,
+        };
+        let output_target = Wire {
+            gate: self.gate_index,
+            input: ArithmeticGate::WIRE_OUTPUT,
+        };
+
+        let multiplicand_0 = witness.get_wire(multiplicand_0_target);
+        let multiplicand_1 = witness.get_wire(multiplicand_1_target);
+        let addend = witness.get_wire(addend_target);
+
+        let output = self.const_0 * multiplicand_0 * multiplicand_1 + self.const_1 * addend;
+
+        PartialWitness::singleton_wire(output_target, output)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::field::crandall_field::CrandallField;
+    use crate::gates::arithmetic::ArithmeticGate;
+    use crate::gates::gate_testing::test_low_degree;
+
+    #[test]
+    fn low_degree() {
+        test_low_degree(ArithmeticGate::new::<CrandallField, 4>())
+    }
+}

src/witness.rs

@@ -1,9 +1,11 @@
 use std::collections::HashMap;
 
+use crate::field::extension_field::target::ExtensionTarget;
 use crate::field::extension_field::{Extendable, FieldExtension};
 use crate::field::field::Field;
 use crate::target::Target;
 use crate::wire::Wire;
+use std::convert::TryInto;
 
 #[derive(Clone, Debug)]
 pub struct PartialWitness<F: Field> {
@@ -39,6 +41,15 @@ impl<F: Field> PartialWitness<F> {
         targets.iter().map(|&t| self.get_target(t)).collect()
     }
 
+    pub fn get_extension_target<const D: usize>(&self, et: ExtensionTarget<D>) -> F::Extension
+    where
+        F: Extendable<D>,
+    {
+        F::Extension::from_basefield_array(
+            self.get_targets(&et.to_target_array()).try_into().unwrap(),
+        )
+    }
+
     pub fn try_get_target(&self, target: Target) -> Option<F> {
         self.target_values.get(&target).cloned()
     }