Implement GkrOps for CPU backend

crates/prover/src/core/backend/cpu/lookups/gkr.rs

@@ -0,0 +1,60 @@
+use crate::core::backend::CpuBackend;
+use crate::core::fields::qm31::SecureField;
+use crate::core::lookups::gkr::GkrOps;
+use crate::core::lookups::mle::Mle;
+
+impl GkrOps for CpuBackend {
+    fn gen_eq_evals(y: &[SecureField], v: SecureField) -> Mle<Self, SecureField> {
+        Mle::new(gen_eq_evals(y, v))
+    }
+}
+
+/// Returns evaluations `eq(x, y) * v` for all `x` in `{0, 1}^n`.
+///
+/// Evaluations are returned in bit-reversed order.
+fn gen_eq_evals(y: &[SecureField], v: SecureField) -> Vec<SecureField> {
+    let mut evals = Vec::with_capacity(1 << y.len());
+    evals.push(v);
+
+    for &y_i in y.iter().rev() {
+        for j in 0..evals.len() {
+            // `lhs[j] = eq(0, y_i) * c[i]`
+            // `rhs[j] = eq(1, y_i) * c[i]`
+            let tmp = evals[j] * y_i;
+            evals.push(tmp);
+            evals[j] -= tmp;
+        }
+    }
+
+    evals
+}
+
+#[cfg(test)]
+mod tests {
+    use num_traits::{One, Zero};
+
+    use crate::core::backend::CpuBackend;
+    use crate::core::fields::m31::BaseField;
+    use crate::core::fields::qm31::SecureField;
+    use crate::core::lookups::gkr::GkrOps;
+    use crate::core::lookups::utils::eq;
+
+    #[test]
+    fn gen_eq_evals() {
+        let zero = SecureField::zero();
+        let one = SecureField::one();
+        let y = [7, 3].map(|v| BaseField::from(v).into());
+
+        let eq_evals = CpuBackend::gen_eq_evals(&y, one);
+
+        assert_eq!(
+            **eq_evals,
+            [
+                eq(&[zero, zero], &y),
+                eq(&[zero, one], &y),
+                eq(&[one, zero], &y),
+                eq(&[one, one], &y),
+            ]
+        );
+    }
+}

crates/prover/src/core/backend/cpu/lookups/mod.rs

@@ -1 +1,2 @@
+mod gkr;
 mod mle;