only ever interpolate and evaluate over Domains of BFieldElements

Only accept generators of type `BFieldElement`, not any Finite Field.
Remove duplicate FRI domain in struct `Stark`.

triton-vm/src/cross_table_arguments.rs

@@ -44,8 +44,8 @@ pub trait CrossTableArg {
     fn terminal_quotient(
         &self,
         ext_codeword_tables: &ExtTableCollection,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
     ) -> Vec<XFieldElement> {
         let from_codeword = self.combined_from_codeword(ext_codeword_tables);
         let to_codeword = self.combined_to_codeword(ext_codeword_tables);
@@ -55,7 +55,7 @@ pub trait CrossTableArg {
             .into_iter()
             .map(|x| x - omicron.inverse())
             .collect();
-        let zerofier_inverse = XFieldElement::batch_inversion(zerofier);
+        let zerofier_inverse = BFieldElement::batch_inversion(zerofier);
 
         zerofier_inverse
             .into_iter()
@@ -453,8 +453,8 @@ impl GrandCrossTableArg {
     pub fn terminal_quotient_codeword(
         &self,
         ext_codeword_tables: &ExtTableCollection,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
     ) -> Vec<XFieldElement> {
         let mut non_linear_sum_codeword = vec![XFieldElement::zero(); fri_domain.length];
 
@@ -502,7 +502,7 @@ impl GrandCrossTableArg {
             .into_iter()
             .map(|x| x - omicron.inverse())
             .collect();
-        let zerofier_inverse = XFieldElement::batch_inversion(zerofier);
+        let zerofier_inverse = BFieldElement::batch_inversion(zerofier);
 
         zerofier_inverse
             .into_iter()

triton-vm/src/domain.rs

@@ -29,12 +29,18 @@ where
         }
     }
 
-    pub fn evaluate(&self, polynomial: &Polynomial<FF>) -> Vec<FF> {
+    pub fn evaluate<GF>(&self, polynomial: &Polynomial<GF>) -> Vec<GF>
+    where
+        GF: FiniteField + From<BFieldElement> + MulAssign<BFieldElement>,
+    {
         polynomial.fast_coset_evaluate(&self.offset, self.generator, self.length)
     }
 
-    pub fn interpolate(&self, values: &[FF]) -> Polynomial<FF> {
-        Polynomial::<FF>::fast_coset_interpolate(&self.offset, self.generator, values)
+    pub fn interpolate<GF>(&self, values: &[GF]) -> Polynomial<GF>
+    where
+        GF: FiniteField + From<BFieldElement> + MulAssign<BFieldElement>,
+    {
+        Polynomial::<GF>::fast_coset_interpolate(&self.offset, self.generator, values)
     }
 
     pub fn domain_value(&self, index: u32) -> FF {

triton-vm/src/fri.rs

@@ -50,7 +50,7 @@ pub struct Fri<H> {
     // nearest power of 2.
     pub expansion_factor: usize,
     pub colinearity_checks_count: usize,
-    pub domain: Domain<XFieldElement>,
+    pub domain: Domain<BFieldElement>,
     _hasher: PhantomData<H>,
 }
 

triton-vm/src/stark.rs

@@ -24,7 +24,6 @@ use triton_profiler::{prof_itr0, prof_start, prof_stop};
 use crate::cross_table_arguments::{
     CrossTableArg, EvalArg, GrandCrossTableArg, NUM_CROSS_TABLE_ARGS, NUM_PUBLIC_EVAL_ARGS,
 };
-use crate::domain::Domain;
 use crate::fri::{Fri, FriValidationError};
 use crate::proof::{Claim, Proof};
 use crate::proof_item::ProofItem;
@@ -108,7 +107,6 @@ pub struct Stark {
     parameters: StarkParameters,
     claim: Claim,
     max_degree: Degree,
-    fri_domain: Domain<BFieldElement>,
     fri: Fri<StarkHasher>,
 }
 
@@ -122,7 +120,6 @@ impl Stark {
         let omega =
             BFieldElement::primitive_root_of_unity(fri_domain_length.try_into().unwrap()).unwrap();
         let coset_offset = BFieldElement::generator();
-        let fri_domain: Domain<BFieldElement> = Domain::new(coset_offset, omega, fri_domain_length);
         let fri = Fri::new(
             coset_offset,
             omega,
@@ -134,7 +131,6 @@ impl Stark {
             parameters,
             claim,
             max_degree,
-            fri_domain,
             fri,
         }
     }
@@ -153,7 +149,7 @@ impl Stark {
 
         prof_start!(maybe_profiler, "LDE 1");
         let base_fri_domain_tables = base_trace_tables
-            .to_fri_domain_tables(&self.fri_domain, self.parameters.num_trace_randomizers);
+            .to_fri_domain_tables(&self.fri.domain, self.parameters.num_trace_randomizers);
         let base_fri_domain_codewords = base_fri_domain_tables.get_all_base_columns();
         let randomizer_and_base_fri_domain_codewords =
             vec![b_rand_codewords, base_fri_domain_codewords.clone()].concat();
@@ -557,7 +553,7 @@ impl Stark {
     }
 
     fn shift_codeword(
-        fri_x_values: &Vec<XFieldElement>,
+        fri_x_values: &Vec<BFieldElement>,
         codeword: &Vec<XFieldElement>,
         shift: u32,
     ) -> Vec<XFieldElement> {
@@ -606,7 +602,7 @@ impl Stark {
 
     fn get_randomizer_codewords(&self) -> (Vec<XFieldElement>, Vec<Vec<BFieldElement>>) {
         let randomizer_coefficients = random_elements(self.max_degree as usize + 1);
-        let randomizer_polynomial = Polynomial::new(randomizer_coefficients);
+        let randomizer_polynomial = Polynomial::<XFieldElement>::new(randomizer_coefficients);
 
         let x_randomizer_codeword = self.fri.domain.evaluate(&randomizer_polynomial);
         let mut b_randomizer_codewords = vec![vec![], vec![], vec![]];
@@ -849,7 +845,7 @@ impl Stark {
         let base_offset = self.parameters.num_randomizer_polynomials;
         let ext_offset = base_offset + num_base_polynomials;
         let final_offset = ext_offset + num_extension_polynomials;
-        let omicron: XFieldElement = derive_omicron(padded_height as u64);
+        let omicron = derive_omicron(padded_height as u64);
         let omicron_inverse = omicron.inverse();
         for (combination_check_index, revealed_combination_leaf) in combination_check_indices
             .into_iter()
@@ -951,7 +947,8 @@ impl Stark {
                     .zip_eq(initial_quotient_degree_bounds.iter())
                 {
                     let shift = self.max_degree - degree_bound;
-                    let quotient = evaluated_bc / (current_fri_domain_value - BFieldElement::one());
+                    let quotient =
+                        evaluated_bc / (current_fri_domain_value - BFieldElement::one()).lift();
                     let quotient_shifted =
                         quotient * current_fri_domain_value.mod_pow_u32(shift as u32);
                     summands.push(quotient);
@@ -968,7 +965,8 @@ impl Stark {
                     let shift = self.max_degree - degree_bound;
                     let quotient = evaluated_cc
                         / (current_fri_domain_value.mod_pow_u32(padded_height as u32)
-                            - BFieldElement::one());
+                            - BFieldElement::one())
+                        .lift();
                     let quotient_shifted =
                         quotient * current_fri_domain_value.mod_pow_u32(shift as u32);
                     summands.push(quotient);
@@ -992,7 +990,7 @@ impl Stark {
                         let denominator = current_fri_domain_value
                             .mod_pow_u32(padded_height as u32)
                             - BFieldElement::one();
-                        evaluated_tc * numerator / denominator
+                        evaluated_tc * numerator / denominator.lift()
                     };
                     let quotient_shifted =
                         quotient * current_fri_domain_value.mod_pow_u32(shift as u32);
@@ -1008,7 +1006,8 @@ impl Stark {
                     .zip_eq(terminal_quotient_degree_bounds.iter())
                 {
                     let shift = self.max_degree - degree_bound;
-                    let quotient = evaluated_termc / (current_fri_domain_value - omicron_inverse);
+                    let quotient =
+                        evaluated_termc / (current_fri_domain_value - omicron_inverse).lift();
                     let quotient_shifted =
                         quotient * current_fri_domain_value.mod_pow_u32(shift as u32);
                     summands.push(quotient);
@@ -1028,8 +1027,8 @@ impl Stark {
             let shift = self.max_degree - grand_cross_table_arg_degree_bound;
             let grand_cross_table_arg_evaluated =
                 grand_cross_table_arg.evaluate_non_linear_sum_of_differences(&cross_slice_by_table);
-            let grand_cross_table_arg_quotient =
-                grand_cross_table_arg_evaluated / (current_fri_domain_value - omicron_inverse);
+            let grand_cross_table_arg_quotient = grand_cross_table_arg_evaluated
+                / (current_fri_domain_value - omicron_inverse).lift();
             let grand_cross_table_arg_quotient_shifted =
                 grand_cross_table_arg_quotient * current_fri_domain_value.mod_pow_u32(shift as u32);
             summands.push(grand_cross_table_arg_quotient);

triton-vm/src/table/base_table.rs

@@ -1,6 +1,5 @@
 use super::super::domain::Domain;
-use itertools::Itertools;
-use num_traits::Zero;
+use num_traits::{One, Zero};
 use rand_distr::{Distribution, Standard};
 use rayon::iter::{IntoParallelIterator, IntoParallelRefIterator, ParallelIterator};
 use std::ops::{Mul, MulAssign, Range};
@@ -270,8 +269,8 @@ where
 
     fn low_degree_extension(
         &self,
-        fri_domain: &Domain<FF>,
-        omicron: FF,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
         columns: Range<usize>,
     ) -> Vec<Vec<FF>> {
@@ -287,7 +286,7 @@ where
     /// if it is called with a subset, it *will* fail.
     fn interpolate_columns(
         &self,
-        omicron: FF,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
         columns: Range<usize>,
     ) -> Vec<Polynomial<FF>> {
@@ -303,10 +302,8 @@ where
             self.name()
         );
 
-        // FIXME: Use Domain::new(…).domain_values() (needs some refactoring)
-        let trace_domain = (0..padded_height)
-            .map(|i| omicron.mod_pow_u32(i as u32))
-            .collect_vec();
+        let trace_domain =
+            Domain::new(BFieldElement::one(), omicron, padded_height).domain_values();
 
         let randomizer_domain = disjoint_domain(num_trace_randomizers, &trace_domain);
         let interpolation_domain = vec![trace_domain, randomizer_domain].concat();

triton-vm/src/table/extension_table.rs

@@ -194,7 +194,7 @@ pub trait Quotientable: ExtensionTable + Evaluable {
 
     fn initial_quotients(
         &self,
-        fri_domain: &Domain<XFieldElement>,
+        fri_domain: &Domain<BFieldElement>,
         transposed_codewords: &[Vec<XFieldElement>],
         challenges: &AllChallenges,
     ) -> Vec<Vec<XFieldElement>> {
@@ -205,7 +205,7 @@ pub trait Quotientable: ExtensionTable + Evaluable {
             .into_iter()
             .map(|x| x - BFieldElement::one())
             .collect();
-        let zerofier_inverse = XFieldElement::batch_inversion(zerofier_codeword);
+        let zerofier_inverse = BFieldElement::batch_inversion(zerofier_codeword);
 
         let transposed_quotient_codewords: Vec<_> = zerofier_inverse
             .par_iter()
@@ -224,7 +224,7 @@ pub trait Quotientable: ExtensionTable + Evaluable {
 
     fn consistency_quotients(
         &self,
-        fri_domain: &Domain<XFieldElement>,
+        fri_domain: &Domain<BFieldElement>,
         transposed_codewords: &[Vec<XFieldElement>],
         challenges: &AllChallenges,
         padded_height: usize,
@@ -236,7 +236,7 @@ pub trait Quotientable: ExtensionTable + Evaluable {
             .iter()
             .map(|x| x.mod_pow_u32(padded_height as u32) - BFieldElement::one())
             .collect();
-        let zerofier_inverse = XFieldElement::batch_inversion(zerofier_codeword);
+        let zerofier_inverse = BFieldElement::batch_inversion(zerofier_codeword);
 
         let transposed_quotient_codewords: Vec<_> = zerofier_inverse
             .par_iter()
@@ -255,10 +255,10 @@ pub trait Quotientable: ExtensionTable + Evaluable {
 
     fn transition_quotients(
         &self,
-        fri_domain: &Domain<XFieldElement>,
+        fri_domain: &Domain<BFieldElement>,
         transposed_codewords: &[Vec<XFieldElement>],
         challenges: &AllChallenges,
-        omicron: XFieldElement,
+        omicron: BFieldElement,
         padded_height: usize,
     ) -> Vec<Vec<XFieldElement>> {
         debug_assert_eq!(fri_domain.length, transposed_codewords.len());
@@ -305,10 +305,10 @@ pub trait Quotientable: ExtensionTable + Evaluable {
 
     fn terminal_quotients(
         &self,
-        fri_domain: &Domain<XFieldElement>,
+        fri_domain: &Domain<BFieldElement>,
         transposed_codewords: &[Vec<XFieldElement>],
         challenges: &AllChallenges,
-        omicron: XFieldElement,
+        omicron: BFieldElement,
     ) -> Vec<Vec<XFieldElement>> {
         debug_assert_eq!(fri_domain.length, transposed_codewords.len());
 
@@ -319,7 +319,7 @@ pub trait Quotientable: ExtensionTable + Evaluable {
             .into_iter()
             .map(|x| x - omicron.inverse())
             .collect_vec();
-        let zerofier_inverse = XFieldElement::batch_inversion(zerofier_codeword);
+        let zerofier_inverse = BFieldElement::batch_inversion(zerofier_codeword);
 
         let transposed_quotient_codewords: Vec<_> = zerofier_inverse
             .par_iter()
@@ -338,10 +338,10 @@ pub trait Quotientable: ExtensionTable + Evaluable {
 
     fn all_quotients(
         &self,
-        fri_domain: &Domain<XFieldElement>,
+        fri_domain: &Domain<BFieldElement>,
         transposed_codewords: Vec<Vec<XFieldElement>>,
         challenges: &AllChallenges,
-        omicron: XFieldElement,
+        omicron: BFieldElement,
         padded_height: usize,
         maybe_profiler: &mut Option<TritonProfiler>,
     ) -> Vec<Vec<XFieldElement>> {
@@ -409,7 +409,7 @@ pub trait Quotientable: ExtensionTable + Evaluable {
     /// probably the result of un-clean division.
     fn debug_fri_domain_bound_check(
         &self,
-        fri_domain: &Domain<XFieldElement>,
+        fri_domain: &Domain<BFieldElement>,
         quotient_codewords: &[Vec<XFieldElement>],
         quotient_type: &str,
     ) {

triton-vm/src/table/hash_table.rs

@@ -786,8 +786,8 @@ impl HashTable {
 impl ExtHashTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();

triton-vm/src/table/instruction_table.rs

@@ -471,8 +471,8 @@ impl InstructionTable {
 impl ExtInstructionTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();

triton-vm/src/table/jump_stack_table.rs

@@ -450,8 +450,8 @@ impl JumpStackTable {
 impl ExtJumpStackTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();

triton-vm/src/table/op_stack_table.rs

@@ -396,8 +396,8 @@ impl OpStackTable {
 impl ExtOpStackTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();

triton-vm/src/table/processor_table.rs

@@ -352,8 +352,8 @@ impl ProcessorTable {
 impl ExtProcessorTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();

triton-vm/src/table/program_table.rs

@@ -293,8 +293,8 @@ impl ProgramTable {
 impl ExtProgramTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();

triton-vm/src/table/ram_table.rs

@@ -215,8 +215,8 @@ impl RamTable {
 impl ExtRamTable {
     pub fn to_fri_domain_table(
         &self,
-        fri_domain: &Domain<XFieldElement>,
-        omicron: XFieldElement,
+        fri_domain: &Domain<BFieldElement>,
+        omicron: BFieldElement,
         num_trace_randomizers: usize,
     ) -> Self {
         let ext_columns = self.base_width()..self.full_width();