From 0d1ddb12ecc8fc4beec73571de517832e9708af6 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Eduardo=20Antu=C3=B1a=20D=C3=ADez?= <eduadiez@gmail.com>
Date: Mon, 20 Feb 2023 17:49:20 +0100
Subject: [PATCH] add computeLiS0

---
 src/fflonk_prover.cpp | 26 +++++++++++++++++++++++++-
 src/fflonk_prover.hpp |  2 ++
 2 files changed, 27 insertions(+), 1 deletion(-)

diff --git a/src/fflonk_prover.cpp b/src/fflonk_prover.cpp
index bd39477..966fcbf 100644
--- a/src/fflonk_prover.cpp
+++ b/src/fflonk_prover.cpp
@@ -1508,7 +1508,16 @@ namespace Fflonk {
         //   · denominator needed in step 10 and 11 of the verifier
         //     toInverse.yBatch -> Computed in round5, computeL()
 
-        //   · denominator needed in the verifier when computing L_i^{S1}(X) and L_i^{S2}(X)
+        //   · denominator needed in the verifier when computing L_i^{S0}(X), L_i^{S1}(X) and L_i^{S2}(X)
+
+        for (uint i = 0; i < 8; i++)
+        {
+            ss.str("");
+            ss << "LiS0_" << (i + 1);
+            toInverse[ss.str()] = computeLiS0(i);
+        }
+
+
         for (uint i = 0; i < 4; i++) {
             ss.str("");
             ss << "LiS1_" << (i + 1);
@@ -1542,6 +1551,21 @@ namespace Fflonk {
         return mulAccumulator;
     }
 
+    template <typename Engine>
+    typename Engine::FrElement FflonkProver<Engine>::computeLiS0(u_int32_t i)
+    {
+        // Compute L_i^{(S0)}(y)
+        u_int32_t idx = i;
+        FrElement den = E.fr.one();
+        for (uint j = 0; j < 7; j++)
+        {
+            idx = (idx + 1) % 8;
+
+            den = E.fr.mul(den, E.fr.sub(roots["S0h0"][i], roots["S0h0"][idx]));
+        }
+        return den;
+    }
+
     template<typename Engine>
     typename Engine::FrElement FflonkProver<Engine>::computeLiS1(u_int32_t i) {
         // Compute L_i^{(S1)}(y)
diff --git a/src/fflonk_prover.hpp b/src/fflonk_prover.hpp
index 932c572..77c57c4 100644
--- a/src/fflonk_prover.hpp
+++ b/src/fflonk_prover.hpp
@@ -135,6 +135,8 @@ namespace Fflonk {
 
         FrElement getMontgomeryBatchedInverse();
 
+        FrElement computeLiS0(u_int32_t i);
+
         FrElement computeLiS1(u_int32_t i);
 
         FrElement computeLiS2(u_int32_t i);