From 366912b0c420d7ced241ed5a9d05774a9bd502f4 Mon Sep 17 00:00:00 2001
From: David Nevado <david@davidnevado.xyz>
Date: Thu, 29 Aug 2024 09:51:47 +0200
Subject: [PATCH] feat: Compute L0 denominators with fft

---
 halo2_backend/src/plonk/keygen.rs | 16 ++++++++++------
 1 file changed, 10 insertions(+), 6 deletions(-)

diff --git a/halo2_backend/src/plonk/keygen.rs b/halo2_backend/src/plonk/keygen.rs
index 71766b01c..3d701149a 100644
--- a/halo2_backend/src/plonk/keygen.rs
+++ b/halo2_backend/src/plonk/keygen.rs
@@ -108,7 +108,6 @@ where
     }
 
     // Compute fixeds
-
     let fixed_polys: Vec<_> = circuit
         .preprocessing
         .fixed
@@ -161,11 +160,16 @@ where
         };
 
         // Compute denominators.
-        let mut acc = zeta;
-        l0.iter_mut().for_each(|e| {
-            *e = acc - one;
-            acc *= w;
-        });
+        // (X-1) in {z, zw, zw^2,... zw^(extended_n)} equals
+        // (zX-1) in {1, w, ... w^{extended_n} wich can be computed with fft.
+        l0[0] = -one;
+        l0[1] = zeta;
+        halo2curves::fft::best_fft(
+            &mut l0,
+            vk.domain.get_extended_omega(),
+            vk.domain.extended_k(),
+        );
+
         l0.batch_invert();
 
         // Compute numinators.