@@ -7,7 +7,7 @@ pull_request:
     branches: [ master ]
 
 jobs:
-  build:
+  build_nightly:
     runs-on: ubuntu-latest
     steps:
     - uses: actions/checkout@v2

@@ -2,7 +2,7 @@ [package]
 name = "spartan"
 version = "0.6.0"
 authors = ["Srinath Setty <srinath@microsoft.com>"]
-edition = "2018"
+edition = "2021"
 description = "High-speed zkSNARKs without trusted setup"
 documentation = "https://docs.rs/spartan/"
 readme = "README.md"

@@ -121,7 +121,7 @@
 impl DensePolynomial {
   pub fn new(Z: Vec<Scalar>) -> Self {
     DensePolynomial {
-      num_vars: Z.len().log2() as usize,
+      num_vars: Z.len().log_2() as usize,
       len: Z.len(),
       Z,
     }

@@ -1,6 +1,4 @@
 #![allow(non_snake_case)]
-#![feature(test)]
-#![feature(int_log)]
 #![doc = include_str!("../README.md")]
 #![deny(missing_docs)]
 #![allow(clippy::assertions_on_result_states)]

@@ -2,6 +2,7 @@ pub trait Math {
   fn square_root(self) -> usize;
   fn pow2(self) -> usize;
   fn get_bits(self, num_bits: usize) -> Vec<bool>;
+  fn log_2(self) -> usize;
 }
 
 impl Math for usize {
@@ -21,5 +22,15 @@ fn get_bits(self, num_bits: usize) -> Vec<bool> {
     (0..num_bits)
       .map(|shift_amount| ((self & (1 << (num_bits - shift_amount - 1))) > 0))
       .collect::<Vec<bool>>()
+  }
+
+  fn log_2(self) -> usize {
+    assert_ne!(self, 0);
+
+    if self.is_power_of_two() {
+      (1usize.leading_zeros() - self.leading_zeros()) as usize
+    } else {
+      (0usize.leading_zeros() - self.leading_zeros()) as usize
+    }
   }
 }

@@ -4,15 +4,19 @@ #![allow(non_snake_case)]
 #![allow(clippy::type_complexity)]
 #![allow(clippy::too_many_arguments)]
 use super::super::errors::ProofVerifyError;
-use super::super::group::{CompressedGroup, GroupElement, VartimeMultiscalarMul, CompressGroupElement, DecompressGroupElement};
+use super::super::group::{
+  CompressGroupElement, CompressedGroup, DecompressGroupElement, GroupElement,
+  VartimeMultiscalarMul,
+};
+use super::super::math::Math;
 use super::super::scalar::Scalar;
 use super::super::transcript::ProofTranscript;
+use ark_ff::{fields, Field};
+use ark_serialize::*;
+use ark_std::{One, Zero};
 use core::iter;
-use std::ops::MulAssign;
 use merlin::Transcript;
-use ark_serialize::*;
-use ark_ff::{Field, fields};
-use ark_std::{One, Zero}; 
+use std::ops::MulAssign;
 
 #[derive(Debug, CanonicalSerialize, CanonicalDeserialize)]
 pub struct BulletReductionProof {
@@ -58,7 +62,7 @@
     // All of the input vectors must have a length that is a power of two.
     let mut n = G.len();
     assert!(n.is_power_of_two());
-    let lg_n = n.log2() as usize;
+    let lg_n = n.log_2() as usize;
 
     // All of the input vectors must have the same length.
     assert_eq!(G.len(), n);
@@ -86,16 +90,34 @@ let L = GroupElement::vartime_multiscalar_mul(
         a_L
           .iter()
           .chain(iter::once(&c_L))
-          .chain(iter::once(blind_L)).map(|s| *s).collect::<Vec<Scalar>>().as_slice(),
-        G_R.iter().chain(iter::once(Q)).chain(iter::once(H)).map(|p| *p).collect::<Vec<GroupElement>>().as_slice(),
+          .chain(iter::once(blind_L))
+          .map(|s| *s)
+          .collect::<Vec<Scalar>>()
+          .as_slice(),
+        G_R
+          .iter()
+          .chain(iter::once(Q))
+          .chain(iter::once(H))
+          .map(|p| *p)
+          .collect::<Vec<GroupElement>>()
+          .as_slice(),
       );
 
       let R = GroupElement::vartime_multiscalar_mul(
         a_R
           .iter()
           .chain(iter::once(&c_R))
-          .chain(iter::once(blind_R)).map(|s| *s).collect::<Vec<Scalar>>().as_slice(),
-        G_L.iter().chain(iter::once(Q)).chain(iter::once(H)).map(|p| *p).collect::<Vec<GroupElement>>().as_slice(),
+          .chain(iter::once(blind_R))
+          .map(|s| *s)
+          .collect::<Vec<Scalar>>()
+          .as_slice(),
+        G_L
+          .iter()
+          .chain(iter::once(Q))
+          .chain(iter::once(H))
+          .map(|p| *p)
+          .collect::<Vec<GroupElement>>()
+          .as_slice(),
       );
 
       transcript.append_point(b"L", &L.compress());
@@ -161,7 +183,7 @@ }
 
     // 2. Compute 1/(u_k...u_1) and 1/u_k, ..., 1/u_1
     let mut challenges_inv: Vec<Scalar> = challenges.clone();
-     
+
     ark_ff::fields::batch_inversion(&mut challenges_inv);
     let mut allinv: Scalar = Scalar::one();
     for c in challenges.iter().filter(|s| !s.is_zero()) {
@@ -225,8 +247,16 @@ let Gamma_hat = GroupElement::vartime_multiscalar_mul(
       u_sq
         .iter()
         .chain(u_inv_sq.iter())
-        .chain(iter::once(&Scalar::one())).map(|s| *s).collect::<Vec<Scalar>>().as_slice(),
-      Ls.iter().chain(Rs.iter()).chain(iter::once(Gamma)).map(|p| *p).collect::<Vec<GroupElement>>().as_slice(),
+        .chain(iter::once(&Scalar::one()))
+        .map(|s| *s)
+        .collect::<Vec<Scalar>>()
+        .as_slice(),
+      Ls.iter()
+        .chain(Rs.iter())
+        .chain(iter::once(Gamma))
+        .map(|p| *p)
+        .collect::<Vec<GroupElement>>()
+        .as_slice(),
     );
 
     Ok((G_hat, Gamma_hat, a_hat))

@@ -2,15 +2,18 @@ #![allow(clippy::too_many_arguments)]
 use super::commitments::{Commitments, MultiCommitGens};
 use super::errors::ProofVerifyError;
 use super::group::{
-  CompressedGroup, CompressGroupElement, UnpackGroupElement, GroupElement, DecompressGroupElement, GroupElementAffine};
+  CompressGroupElement, CompressedGroup, DecompressGroupElement, GroupElement, GroupElementAffine,
+  UnpackGroupElement,
+};
+use super::math::Math;
 use super::random::RandomTape;
 use super::scalar::Scalar;
 use super::transcript::{AppendToTranscript, ProofTranscript};
 use ark_ec::group::Group;
-use merlin::Transcript;
-use ark_serialize::*;
 use ark_ec::ProjectiveCurve;
 use ark_ff::PrimeField;
+use ark_serialize::*;
+use merlin::Transcript;
 
 mod bullet;
 use bullet::BulletReductionProof;
@@ -49,7 +52,7 @@
     let c = transcript.challenge_scalar(b"c");
 
     let z1 = c * x + t1;
-    let z2 =  c * r + t2;
+    let z2 = c * r + t2;
 
     (KnowledgeProof { alpha, z1, z2 }, C)
   }
@@ -58,8 +61,7 @@ pub fn verify(
     &self,
     gens_n: &MultiCommitGens,
     transcript: &mut Transcript,
-    C: &
-    CompressedGroup,
+    C: &CompressedGroup,
   ) -> Result<(), ProofVerifyError> {
     transcript.append_protocol_name(KnowledgeProof::protocol_name());
     C.append_to_transcript(b"C", transcript);
@@ -68,7 +70,7 @@
     let c = transcript.challenge_scalar(b"c");
 
     let lhs = self.z1.commit(&self.z2, gens_n).compress();
-    let rhs = ( C.unpack()?.mul(c.into_repr()) + self.alpha.unpack()?).compress();
+    let rhs = (C.unpack()?.mul(c.into_repr()) + self.alpha.unpack()?).compress();
 
     if lhs == rhs {
       Ok(())
@@ -80,8 +82,7 @@ }
 
 #[derive(CanonicalSerialize, CanonicalDeserialize, Debug)]
 pub struct EqualityProof {
-  alpha: 
-  CompressedGroup,
+  alpha: CompressedGroup,
   z: Scalar,
 }
 
@@ -98,9 +99,7 @@ v1: &Scalar,
     s1: &Scalar,
     v2: &Scalar,
     s2: &Scalar,
-  ) -> (EqualityProof, 
-    CompressedGroup, 
-  CompressedGroup) {
+  ) -> (EqualityProof, CompressedGroup, CompressedGroup) {
     transcript.append_protocol_name(EqualityProof::protocol_name());
 
     // produce a random Scalar
@@ -126,10 +125,8 @@ pub fn verify(
     &self,
     gens_n: &MultiCommitGens,
     transcript: &mut Transcript,
-    C1: &
-    CompressedGroup,
-    C2: &
-    CompressedGroup,
+    C1: &CompressedGroup,
+    C2: &CompressedGroup,
   ) -> Result<(), ProofVerifyError> {
     transcript.append_protocol_name(EqualityProof::protocol_name());
     C1.append_to_transcript(b"C1", transcript);
@@ -155,12 +152,9 @@ }
 
 #[derive(CanonicalSerialize, CanonicalDeserialize, Debug)]
 pub struct ProductProof {
-  alpha: 
-  CompressedGroup,
-  beta: 
-  CompressedGroup,
-  delta: 
-  CompressedGroup,
+  alpha: CompressedGroup,
+  beta: CompressedGroup,
+  delta: CompressedGroup,
   z: Vec<Scalar>,
 }
 
@@ -181,11 +175,8 @@ z: &Scalar,
     rZ: &Scalar,
   ) -> (
     ProductProof,
-    
     CompressedGroup,
-    
     CompressedGroup,
-    
     CompressedGroup,
   ) {
     transcript.append_protocol_name(ProductProof::protocol_name());
@@ -197,16 +188,14 @@ let b3 = random_tape.random_scalar(b"b3");
     let b4 = random_tape.random_scalar(b"b4");
     let b5 = random_tape.random_scalar(b"b5");
 
-    let X_unc =  x.commit(rX, gens_n);
-    
-    
+    let X_unc = x.commit(rX, gens_n);
+
     let X = X_unc.compress();
     X.append_to_transcript(b"X", transcript);
 
     let X_new = GroupElement::decompress(&X);
 
     assert_eq!(X_unc, X_new.unwrap());
-   
 
     let Y = y.commit(rY, gens_n).compress();
     Y.append_to_transcript(b"Y", transcript);
@@ -253,17 +242,17 @@ )
   }
 
   fn check_equality(
-    P: &
-    CompressedGroup,
-    X: &
-    CompressedGroup,
+    P: &CompressedGroup,
+    X: &CompressedGroup,
     c: &Scalar,
     gens_n: &MultiCommitGens,
     z1: &Scalar,
     z2: &Scalar,
   ) -> bool {
     println!("{:?}", X);
-    let lhs = (GroupElement::decompress(P).unwrap() + GroupElement::decompress(X).unwrap().mul(c.into_repr())).compress();
+    let lhs = (GroupElement::decompress(P).unwrap()
+      + GroupElement::decompress(X).unwrap().mul(c.into_repr()))
+    .compress();
     let rhs = z1.commit(z2, gens_n).compress();
 
     lhs == rhs
@@ -273,12 +262,9 @@ pub fn verify(
     &self,
     gens_n: &MultiCommitGens,
     transcript: &mut Transcript,
-    X: &
-    CompressedGroup,
-    Y: &
-    CompressedGroup,
-    Z: &
-    CompressedGroup,
+    X: &CompressedGroup,
+    Y: &CompressedGroup,
+    Z: &CompressedGroup,
   ) -> Result<(), ProofVerifyError> {
     transcript.append_protocol_name(ProductProof::protocol_name());
 
@@ -321,10 +307,8 @@ }
 
 #[derive(Debug, CanonicalSerialize, CanonicalDeserialize)]
 pub struct DotProductProof {
-  delta: 
-  CompressedGroup,
-  beta: 
-  CompressedGroup,
+  delta: CompressedGroup,
+  beta: CompressedGroup,
   z: Vec<Scalar>,
   z_delta: Scalar,
   z_beta: Scalar,
@@ -350,9 +334,7 @@ blind_x: &Scalar,
     a_vec: &[Scalar],
     y: &Scalar,
     blind_y: &Scalar,
-  ) -> (DotProductProof, 
-    CompressedGroup, 
-  CompressedGroup) {
+  ) -> (DotProductProof, CompressedGroup, CompressedGroup) {
     transcript.append_protocol_name(DotProductProof::protocol_name());
 
     let n = x_vec.len();
@@ -409,10 +391,8 @@ gens_1: &MultiCommitGens,
     gens_n: &MultiCommitGens,
     transcript: &mut Transcript,
     a: &[Scalar],
-    Cx: &
-    CompressedGroup,
-    Cy: &
-    CompressedGroup,
+    Cx: &CompressedGroup,
+    Cy: &CompressedGroup,
   ) -> Result<(), ProofVerifyError> {
     assert_eq!(gens_n.n, a.len());
     assert_eq!(gens_1.n, 1);
@@ -426,11 +406,12 @@ self.beta.append_to_transcript(b"beta", transcript);
 
     let c = transcript.challenge_scalar(b"c");
 
-    let mut result =
-    Cx.unpack()?.mul(c.into_repr()) + self.delta.unpack()? == self.z.commit(&self.z_delta, gens_n);
+    let mut result = Cx.unpack()?.mul(c.into_repr()) + self.delta.unpack()?
+      == self.z.commit(&self.z_delta, gens_n);
 
     let dotproduct_z_a = DotProductProof::compute_dotproduct(&self.z, a);
-    result &= Cy.unpack()?.mul(c.into_repr()) + self.beta.unpack()? == dotproduct_z_a.commit(&self.z_beta, gens_1);
+    result &= Cy.unpack()?.mul(c.into_repr()) + self.beta.unpack()?
+      == dotproduct_z_a.commit(&self.z_beta, gens_1);
     if result {
       Ok(())
     } else {
@@ -455,10 +436,8 @@
 #[derive(Debug, CanonicalSerialize, CanonicalDeserialize)]
 pub struct DotProductProofLog {
   bullet_reduction_proof: BulletReductionProof,
-  delta: 
-  CompressedGroup,
-  beta: 
-  CompressedGroup,
+  delta: CompressedGroup,
+  beta: CompressedGroup,
   z1: Scalar,
   z2: Scalar,
 }
@@ -482,9 +461,7 @@ blind_x: &Scalar,
     a_vec: &[Scalar],
     y: &Scalar,
     blind_y: &Scalar,
-  ) -> (DotProductProofLog, 
-    CompressedGroup, 
-  CompressedGroup) {
+  ) -> (DotProductProofLog, CompressedGroup, CompressedGroup) {
     transcript.append_protocol_name(DotProductProofLog::protocol_name());
 
     let n = x_vec.len();
@@ -496,8 +473,8 @@ let d = random_tape.random_scalar(b"d");
     let r_delta = random_tape.random_scalar(b"r_delta");
     let r_beta = random_tape.random_scalar(b"r_delta");
     let blinds_vec = {
-      let v1 = random_tape.random_vector(b"blinds_vec_1", 2 * n.log2() as usize);
-      let v2 = random_tape.random_vector(b"blinds_vec_2", 2 * n.log2() as usize);
+      let v1 = random_tape.random_vector(b"blinds_vec_1", 2 * n.log_2());
+      let v2 = random_tape.random_vector(b"blinds_vec_2", 2 * n.log_2());
       (0..v1.len())
         .map(|i| (v1[i], v2[i]))
         .collect::<Vec<(Scalar, Scalar)>>()
@@ -562,10 +539,8 @@ n: usize,
     gens: &DotProductProofGens,
     transcript: &mut Transcript,
     a: &[Scalar],
-    Cx: &
-    CompressedGroup,
-    Cy: &
-    CompressedGroup,
+    Cx: &CompressedGroup,
+    Cy: &CompressedGroup,
   ) -> Result<(), ProofVerifyError> {
     assert_eq!(gens.n, n);
     assert_eq!(a.len(), n);
@@ -593,8 +568,11 @@ let delta_s = self.delta.unpack()?;
     let z1_s = &self.z1;
     let z2_s = &self.z2;
 
-    let lhs = ((Gamma_hat.mul(c_s.into_repr()) + beta_s).mul(a_hat_s.into_repr()) + delta_s).compress();
-    let rhs = ((g_hat + gens.gens_1.G[0].mul(a_hat_s.into_repr())).mul(z1_s.into_repr()) + gens.gens_1.h.mul(z2_s.into_repr())).compress();
+    let lhs =
+      ((Gamma_hat.mul(c_s.into_repr()) + beta_s).mul(a_hat_s.into_repr()) + delta_s).compress();
+    let rhs = ((g_hat + gens.gens_1.G[0].mul(a_hat_s.into_repr())).mul(z1_s.into_repr())
+      + gens.gens_1.h.mul(z2_s.into_repr()))
+    .compress();
 
     assert_eq!(lhs, rhs);
 
@@ -610,15 +588,15 @@ #[cfg(test)]
 mod tests {
   use std::marker::PhantomData;
 
-use crate::group::VartimeMultiscalarMul;
+  use crate::group::VartimeMultiscalarMul;
 
-use super::*;
-use ark_bls12_377::{G1Affine, Fq, FqParameters};
-use ark_ff::{Fp384, BigInteger384};
-use ark_std::{UniformRand};
+  use super::*;
+  use ark_bls12_377::{Fq, FqParameters, G1Affine};
+  use ark_ff::{BigInteger384, Fp384};
+  use ark_std::UniformRand;
   #[test]
   fn check_knowledgeproof() {
-  let mut rng = ark_std::rand::thread_rng();
+    let mut rng = ark_std::rand::thread_rng();
 
     let gens_1 = MultiCommitGens::new(1, b"test-knowledgeproof");
 
@@ -638,7 +616,7 @@ }
 
   #[test]
   fn check_equalityproof() {
-  let mut rng = ark_std::rand::thread_rng();
+    let mut rng = ark_std::rand::thread_rng();
 
     let gens_1 = MultiCommitGens::new(1, b"test-equalityproof");
     let v1 = Scalar::rand(&mut rng);
@@ -663,14 +641,14 @@ assert!(proof
       .verify(&gens_1, &mut verifier_transcript, &C1, &C2)
       .is_ok());
   }
-  
+
   #[test]
   fn check_productproof() {
-  let mut rng = ark_std::rand::thread_rng();
-  let pt = GroupElement::rand(&mut rng);
-  let pt_c = pt.compress();
-  let pt2 = GroupElement::decompress(&pt_c).unwrap();
-  assert_eq!(pt, pt2);
+    let mut rng = ark_std::rand::thread_rng();
+    let pt = GroupElement::rand(&mut rng);
+    let pt_c = pt.compress();
+    let pt2 = GroupElement::decompress(&pt_c).unwrap();
+    assert_eq!(pt, pt2);
 
     let gens_1 = MultiCommitGens::new(1, b"test-productproof");
     let x = Scalar::rand(&mut rng);
@@ -702,7 +680,7 @@ }
 
   #[test]
   fn check_dotproductproof() {
-  let mut rng = ark_std::rand::thread_rng();
+    let mut rng = ark_std::rand::thread_rng();
 
     let n = 1024;
 
@@ -741,7 +719,7 @@ }
 
   #[test]
   fn check_dotproductproof_log() {
-  let mut rng = ark_std::rand::thread_rng();
+    let mut rng = ark_std::rand::thread_rng();
 
     let n = 1024;
 

@@ -1,6 +1,7 @@
 #![allow(dead_code)]
 use super::dense_mlpoly::DensePolynomial;
 use super::dense_mlpoly::EqPolynomial;
+use super::math::Math;
 use super::scalar::Scalar;
 use super::sumcheck::SumcheckInstanceProof;
 use super::transcript::ProofTranscript;
@@ -37,7 +38,7 @@ pub fn new(poly: &DensePolynomial) -> Self {
     let mut left_vec: Vec<DensePolynomial> = Vec::new();
     let mut right_vec: Vec<DensePolynomial> = Vec::new();
 
-    let num_layers = poly.len().log2() as usize;
+    let num_layers = poly.len().log_2() as usize;
     let (outp_left, outp_right) = poly.split(poly.len() / 2);
 
     left_vec.push(outp_left);
@@ -182,7 +183,7 @@
       let mut poly_C = DensePolynomial::new(EqPolynomial::new(rand.clone()).evals());
       assert_eq!(poly_C.len(), len / 2);
 
-      let num_rounds_prod = poly_C.len().log2() as usize;
+      let num_rounds_prod = poly_C.len().log_2() as usize;
       let comb_func_prod = |poly_A_comp: &Scalar,
                             poly_B_comp: &Scalar,
                             poly_C_comp: &Scalar|
@@ -223,7 +224,7 @@ eval: Scalar,
     len: usize,
     transcript: &mut Transcript,
   ) -> (Scalar, Vec<Scalar>) {
-    let num_layers = len.log2() as usize;
+    let num_layers = len.log_2() as usize;
     let mut claim = eval;
     let mut rand: Vec<Scalar> = Vec::new();
     //let mut num_rounds = 0;
@@ -279,7 +280,7 @@
       let mut poly_C_par = DensePolynomial::new(EqPolynomial::new(rand.clone()).evals());
       assert_eq!(poly_C_par.len(), len / 2);
 
-      let num_rounds_prod = poly_C_par.len().log2() as usize;
+      let num_rounds_prod = poly_C_par.len().log_2() as usize;
       let comb_func_prod = |poly_A_comp: &Scalar,
                             poly_B_comp: &Scalar,
                             poly_C_comp: &Scalar|
@@ -389,7 +390,7 @@ claims_dotp_vec: &[Scalar],
     len: usize,
     transcript: &mut Transcript,
   ) -> (Vec<Scalar>, Vec<Scalar>, Vec<Scalar>) {
-    let num_layers = len.log2() as usize;
+    let num_layers = len.log_2() as usize;
     let mut rand: Vec<Scalar> = Vec::new();
     //let mut num_rounds = 0;
     assert_eq!(self.proof.len(), num_layers);

@@ -46,8 +46,8 @@ num_inputs: usize,
     num_nz_entries: usize,
   ) -> R1CSCommitmentGens {
     assert!(num_inputs < num_vars);
-    let num_poly_vars_x = num_cons.log2() as usize;
-    let num_poly_vars_y = (2 * num_vars).log2() as usize;
+    let num_poly_vars_x = num_cons.log_2() as usize;
+    let num_poly_vars_y = (2 * num_vars).log_2() as usize;
     let gens =
       SparseMatPolyCommitmentGens::new(label, num_poly_vars_x, num_poly_vars_y, num_nz_entries, 3);
     R1CSCommitmentGens { gens }
@@ -115,8 +115,8 @@ // check that number_inputs + 1 <= num_vars
     assert!(num_inputs < num_vars);
 
     // no errors, so create polynomials
-    let num_poly_vars_x = num_cons.log2() as usize;
-    let num_poly_vars_y = (2 * num_vars).log2() as usize;
+    let num_poly_vars_x = num_cons.log_2() as usize;
+    let num_poly_vars_y = (2 * num_vars).log_2() as usize;
 
     let mat_A = (0..A.len())
       .map(|i| SparseMatEntry::new(A[i].0, A[i].1, A[i].2))
@@ -166,8 +166,8 @@
   let mut rng = ark_std::rand::thread_rng();
 
     // assert num_cons and num_vars are power of 2
-    assert_eq!((num_cons.log2() as usize).pow2(), num_cons);
-    assert_eq!((num_vars.log2() as usize).pow2(), num_vars);
+    assert_eq!((num_cons.log_2() as usize).pow2(), num_cons);
+    assert_eq!((num_vars.log_2() as usize).pow2(), num_vars);
 
     // num_inputs + 1 <= num_vars
     assert!(num_inputs < num_vars);
@@ -214,8 +214,8 @@ Timer::print(&format!("number_non-zero_entries_A {}", A.len()));
     Timer::print(&format!("number_non-zero_entries_B {}", B.len()));
     Timer::print(&format!("number_non-zero_entries_C {}", C.len()));
 
-    let num_poly_vars_x = num_cons.log2() as usize;
-    let num_poly_vars_y = (2 * num_vars).log2() as usize;
+    let num_poly_vars_x = num_cons.log_2() as usize;
+    let num_poly_vars_y = (2 * num_vars).log_2() as usize;
     let poly_A = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, A);
     let poly_B = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, B);
     let poly_C = SparseMatPolynomial::new(num_poly_vars_x, num_poly_vars_y, C);

@@ -10,6 +10,7 @@ use super::errors::ProofVerifyError;
 use super::group::{
   CompressGroupElement, DecompressGroupElement, GroupElement, VartimeMultiscalarMul,
 };
+use super::math::Math;
 use super::nizk::{EqualityProof, KnowledgeProof, ProductProof};
 use super::r1csinstance::R1CSInstance;
 use super::random::RandomTape;
@@ -65,7 +66,7 @@ }
 
 impl R1CSGens {
   pub fn new(label: &'static [u8], _num_cons: usize, num_vars: usize) -> Self {
-    let num_poly_vars = num_vars.log2() as usize;
+    let num_poly_vars = num_vars.log_2() as usize;
     let gens_pc = PolyCommitmentGens::new(num_poly_vars, label);
     let gens_sc = R1CSSumcheckGens::new(label, &gens_pc.gens.gens_1);
     R1CSGens { gens_sc, gens_pc }
@@ -154,8 +155,10 @@ z
     };
 
     // derive the verifier's challenge tau
-    let (num_rounds_x, num_rounds_y) =
-      (inst.get_num_cons().log2() as usize, z.len().log2() as usize);
+    let (num_rounds_x, num_rounds_y) = (
+      inst.get_num_cons().log_2() as usize,
+      z.len().log_2() as usize,
+    );
     let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
     // compute the initial evaluation table for R(\tau, x)
     let mut poly_tau = DensePolynomial::new(EqPolynomial::new(tau).evals());
@@ -247,7 +250,7 @@ input.append_to_transcript(b"input", transcript);
 
     let n = num_vars;
 
-    let (num_rounds_x, num_rounds_y) = (num_cons.log2() as usize, (2 * num_vars).log2() as usize);
+    let (num_rounds_x, num_rounds_y) = (num_cons.log_2() as usize, (2 * num_vars).log_2() as usize);
 
     // derive the verifier's challenge tau
     let tau = transcript.challenge_vector(b"challenge_tau", num_rounds_x);
@@ -278,30 +281,10 @@
     let claim_phase2 = r_A * Az_claim + r_B * Bz_claim + r_C * Cz_claim;
 
     // verify the joint claim with a sum-check protocol
-<<<<<<< HEAD
     let (claim_post_phase2, ry) =
       self
         .sc_proof_phase2
         .verify(claim_phase2, num_rounds_y, 2, transcript)?;
-=======
-    let (comm_claim_post_phase2, ry) = self.sc_proof_phase2.verify(
-      &comm_claim_phase2,
-      num_rounds_y,
-      2,
-      &gens.gens_sc.gens_1,
-      &gens.gens_sc.gens_3,
-      transcript,
-    )?;
-
-    // verify Z(ry) proof against the initial commitment
-    self.proof_eval_vars_at_ry.verify(
-      &gens.gens_pc,
-      transcript,
-      &ry[1..],
-      &self.comm_vars_at_ry,
-      &self.comm_vars,
-    )?;
->>>>>>> clippy fixes (#50)
 
     let poly_input_eval = {
       // constant term
@@ -312,7 +295,7 @@ (0..input.len())
           .map(|i| SparsePolyEntry::new(i + 1, input[i]))
           .collect::<Vec<SparsePolyEntry>>(),
       );
-      SparsePolynomial::new(n.log2() as usize, input_as_sparse_poly_entries).evaluate(&ry[1..])
+      SparsePolynomial::new(n.log_2() as usize, input_as_sparse_poly_entries).evaluate(&ry[1..])
     };
 
     let eval_Z_at_ry = (Scalar::one() - ry[0]) * self.eval_vars_at_ry + ry[0] * poly_input_eval;

@@ -92,7 +92,7 @@ random_tape: &mut RandomTape,
   ) -> PolyEvalProof {
     assert_eq!(
       joint_poly.get_num_vars(),
-      r.len() + evals.len().log2() as usize
+      r.len() + evals.len().log_2() as usize
     );
 
     // append the claimed evaluations to transcript
@@ -101,7 +101,7 @@
     // n-to-1 reduction
     let (r_joint, eval_joint) = {
       let challenges =
-        transcript.challenge_vector(b"challenge_combine_n_to_one", evals.len().log2() as usize);
+        transcript.challenge_vector(b"challenge_combine_n_to_one", evals.len().log_2() as usize);
       let mut poly_evals = DensePolynomial::new(evals);
       for i in (0..challenges.len()).rev() {
         poly_evals.bound_poly_var_bot(&challenges[i]);
@@ -167,7 +167,7 @@ evals.append_to_transcript(b"evals_ops_val", transcript);
 
     // n-to-1 reduction
     let challenges =
-      transcript.challenge_vector(b"challenge_combine_n_to_one", evals.len().log2() as usize);
+      transcript.challenge_vector(b"challenge_combine_n_to_one", evals.len().log_2() as usize);
     let mut poly_evals = DensePolynomial::new(evals);
     for i in (0..challenges.len()).rev() {
       poly_evals.bound_poly_var_bot(&challenges[i]);
@@ -301,15 +301,15 @@ num_vars_y: usize,
     num_nz_entries: usize,
     batch_size: usize,
   ) -> SparseMatPolyCommitmentGens {
-    let num_vars_ops = num_nz_entries.next_power_of_two().log2() as usize
-      + (batch_size * 5).next_power_of_two().log2() as usize;
+    let num_vars_ops = num_nz_entries.next_power_of_two().log_2() as usize
+      + (batch_size * 5).next_power_of_two().log_2() as usize;
     let num_vars_mem = if num_vars_x > num_vars_y {
       num_vars_x
     } else {
       num_vars_y
     } + 1;
-    let num_vars_derefs = num_nz_entries.next_power_of_two().log2() as usize
-      + (batch_size * 2).next_power_of_two().log2() as usize;
+    let num_vars_derefs = num_nz_entries.next_power_of_two().log_2() as usize
+      + (batch_size * 2).next_power_of_two().log_2() as usize;
 
     let gens_ops = PolyCommitmentGens::new(num_vars_ops, label);
     let gens_mem = PolyCommitmentGens::new(num_vars_mem, label);
@@ -781,7 +781,7 @@ evals_ops.resize(evals_ops.len().next_power_of_two(), Scalar::zero());
     evals_ops.append_to_transcript(b"claim_evals_ops", transcript);
     let challenges_ops = transcript.challenge_vector(
       b"challenge_combine_n_to_one",
-      evals_ops.len().log2() as usize,
+      evals_ops.len().log_2() as usize,
     );
 
     let mut poly_evals_ops = DensePolynomial::new(evals_ops);
@@ -810,7 +810,7 @@ let evals_mem: Vec<Scalar> = vec![eval_row_audit_ts, eval_col_audit_ts];
     evals_mem.append_to_transcript(b"claim_evals_mem", transcript);
     let challenges_mem = transcript.challenge_vector(
       b"challenge_combine_two_to_one",
-      evals_mem.len().log2() as usize,
+      evals_mem.len().log_2() as usize,
     );
 
     let mut poly_evals_mem = DensePolynomial::new(evals_mem);
@@ -955,7 +955,7 @@ evals_ops.resize(evals_ops.len().next_power_of_two(), Scalar::zero());
     evals_ops.append_to_transcript(b"claim_evals_ops", transcript);
     let challenges_ops = transcript.challenge_vector(
       b"challenge_combine_n_to_one",
-      evals_ops.len().log2() as usize,
+      evals_ops.len().log_2() as usize,
     );
 
     let mut poly_evals_ops = DensePolynomial::new(evals_ops);
@@ -981,7 +981,7 @@ let evals_mem: Vec<Scalar> = vec![*eval_row_audit_ts, *eval_col_audit_ts];
     evals_mem.append_to_transcript(b"claim_evals_mem", transcript);
     let challenges_mem = transcript.challenge_vector(
       b"challenge_combine_two_to_one",
-      evals_mem.len().log2() as usize,
+      evals_mem.len().log_2() as usize,
     );
 
     let mut poly_evals_mem = DensePolynomial::new(evals_mem);
@@ -1632,8 +1632,8 @@
     let num_nz_entries: usize = 256;
     let num_rows: usize = 256;
     let num_cols: usize = 256;
-    let num_vars_x: usize = num_rows.log2() as usize;
-    let num_vars_y: usize = num_cols.log2() as usize;
+    let num_vars_x: usize = num_rows.log_2() as usize;
+    let num_vars_y: usize = num_cols.log_2() as usize;
 
     let mut M: Vec<SparseMatEntry> = Vec::new();