Fix structure of polynomial

src/core/precomputation.rs

@@ -1 +1,22 @@
+use ff::Field;
+use crate::utils::{ProtocolError, TWO, log};
 
+#[derive(Clone, Debug)]
+pub struct Table<F: Field> {
+    table: Vec<F>,
+    /// Table size should be 2^k
+    /// pow_vars = k
+    exp_vars: u32
+}
+
+impl<F: Field> TryFrom<Vec<F>> for Table<F> {
+    type Error = ProtocolError;
+    fn try_from(table: Vec<F>) -> Result<Self, Self::Error> {
+        let exp_vars = log(table.len());
+        if TWO.pow(exp_vars) != table.len() {
+            Err(ProtocolError::SizeError)
+        } else {
+            Ok(Self { table, exp_vars })
+        }
+    }
+}

src/poly/multivariate.rs

@@ -1,11 +1,39 @@
 use std::fmt::Debug;
 use ff::Field;
 
-// These are different form of multivariate polynomial
-pub mod coefficient;
-pub mod factored;
-pub mod composition;
+/// [coeff, deg(x_1), ..., deg(x_n)]
+#[derive(Debug, Clone)]
+struct Term<F: Field>(Vec<F>);
 
-pub trait MultivariatePolynomial<F: Field>: Clone + Debug  {
-    fn interpolate(points: Vec<F>) -> Self;
+/// num_vars: number of variables
+/// coefficients: [[coeff, deg(x_1), ..., deg(x_n)], ...] respectively
+#[derive(Clone, Debug)]
+struct CoefficientForm<F: Field> {
+    num_vars: u32,
+    coefficients: Vec<Term<F>>,
+}
+
+/// format: f(g(h(..)))
+/// outer: f
+/// inner: g(..)
+#[derive(Debug, Clone)]
+struct CompositionForm {
+}
+
+#[derive(Debug, Clone)]
+struct FactoredForm<F: Field> {
+    terms: Vec<Vec<Term<F>>>,
+}
+
+#[derive(Debug, Clone)]
+pub enum MultivariatePolynomial<F: Field> {
+    Coeff(CoefficientForm<F>),
+    Comp(CompositionForm),
+    Fac(FactoredForm<F>),
+}
+
+impl<F: Field> MultivariatePolynomial<F>  {
+    fn interpolate(points: Vec<F>, k: u32) -> Self {
+        todo!()
+    }
 }

src/poly/multivariate/coefficient.rs

@@ -1,34 +0,0 @@
-use ff::Field;
-
-use crate::poly::Polynomial;
-use crate::utils::*;
-
-use super::MultivariatePolynomial;
-
-const TWO: usize = 2;
-
-/// num_vars: number of variables
-/// coefficients: [[coeff, deg(x_1), ..., deg(x_n)], ...] respectively
-#[derive(Clone, Debug)]
-pub struct CoefficientForm<F: Field> {
-    num_vars: u32,
-    coefficients: Vec<F>,
-}
-
-impl<F: Field> Polynomial<F> for CoefficientForm<F> {
-    type Point = Vec<F>;
-
-    fn evaluate(&self, point: &Self::Point) -> F {
-        todo!()
-    }
-}
-
-impl<F: Field> MultivariatePolynomial<F> for CoefficientForm<F> {
-    fn interpolate(points: Vec<F>) -> Self {
-        let num_vars = log(points.len());
-        // TODO: interpolation can be done with 2^k values
-        assert_eq!(TWO.pow(num_vars), points.len());
-        
-        Self { num_vars, coefficients: () }
-    }
-}

src/utils.rs

@@ -1,3 +1,8 @@
+pub const TWO: usize = 2;
+pub enum ProtocolError {
+    SizeError,
+}
+
 pub fn log(n: usize) -> u32 {
     let mut k = 0;
     let mut m = n;