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[Documentation] Consistently use zero-based numbering

This commit is contained in:
therealyingtong 2020-12-06 06:58:48 +08:00
parent 30c13d5a6a
commit 4273bbb2ba
2 changed files with 17 additions and 14 deletions
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27
src/plonk/lookup/prover.rs
View File

@ -66,10 +66,10 @@ pub(in crate::plonk) struct Evaluated<C: CurveAffine> {
}
impl Argument {
/// Given a Lookup with input columns [A_0, A_1, ..., A_m] and table columns
/// [S_0, S_1, ..., S_m], this method
/// - constructs A_compressed = A_0 + theta A_1 + theta^2 A_2 + ... and
/// S_compressed = S_0 + theta S_1 + theta^2 S_2 + ...,
/// Given a Lookup with input columns [A_0, A_1, ..., A_{m-1}] and table columns
/// [S_0, S_1, ..., S_{m-1}], this method
/// - constructs A_compressed = \theta^{m-1} A_0 + theta^{m-2} A_1 + ... + \theta A_{m-2} + A_{m-1}
/// and S_compressed = \theta^{m-1} S_0 + theta^{m-2} S_1 + ... + \theta S_{m-2} + S_{m-1},
/// - permutes A_compressed and S_compressed using permute_column_pair() helper,
/// obtaining A' and S', and
/// - constructs Permuted<C> struct using permuted_input_value = A', and
@ -208,8 +208,9 @@ impl<'a, C: CurveAffine> Permuted<'a, C> {
) -> Result<Committed<'a, C>, Error> {
// Goal is to compute the products of fractions
//
// (\theta^{m-1} a_1(\omega^i) + \theta^{m-2} a_2(\omega^i) + ... + a_m(\omega^i) + \beta)(\theta^{m-1} s_1(\omega^i) + \theta^{m-2} s_2(\omega^i) + ... + s_m(\omega^i) + \gamma)/
// (a'(\omega^i) + \beta) (s'(\omega^i) + \gamma)
// Numerator: (\theta^{m-1} a_0(\omega^i) + \theta^{m-2} a_1(\omega^i) + ... + \theta a_{m-2}(\omega^i) + a_{m-1}(\omega^i) + \beta)
// * (\theta^{m-1} s_0(\omega^i) + \theta^{m-2} s_1(\omega^i) + ... + \theta s_{m-2}(\omega^i) + s_{m-1}(\omega^i) + \gamma)
// Denominator: (a'(\omega^i) + \beta) (s'(\omega^i) + \gamma)
//
// where a_j(X) is the jth input column in this lookup,
// where a'(X) is the compression of the permuted input columns,
@ -233,8 +234,8 @@ impl<'a, C: CurveAffine> Permuted<'a, C> {
lookup_product.iter_mut().batch_invert();
// Finish the computation of the entire fraction by computing the numerators
// (\theta^{m-1} a_1(\omega^i) + \theta^{m-2} a_2(\omega^i) + ... + \theta a_{m-1}(\omega^i) + a_m(\omega^i) + \beta)
// * (\theta^{m-1} s_1(\omega^i) + \theta^{m-2} s_2(\omega^i) + ... + \theta s_{m-1}(\omega^i) + s_m(\omega^i) + \gamma)
// (\theta^{m-1} a_0(\omega^i) + \theta^{m-2} a_1(\omega^i) + ... + \theta a_{m-2}(\omega^i) + a_{m-1}(\omega^i) + \beta)
// * (\theta^{m-1} s_0(\omega^i) + \theta^{m-2} s_1(\omega^i) + ... + \theta s_{m-2}(\omega^i) + s_{m-1}(\omega^i) + \gamma)
parallelize(&mut lookup_product, |product, start| {
for (i, product) in product.iter_mut().enumerate() {
let i = i + start;
@ -260,7 +261,9 @@ impl<'a, C: CurveAffine> Permuted<'a, C> {
// The product vector is a vector of products of fractions of the form
//
// (\theta^{m-1} a_1(\omega^i) + \theta^{m-2} a_2(\omega^i) + ... + \theta a_{m-1}(\omega^i) + a_m(\omega^i) + \beta)(\theta^{m-1} s_1(\omega^i) + \theta^{m-2} s_2(\omega^i) + ... + \theta s_{m-1}(\omega^i) + s_m(\omega^i) + \gamma)
// Numerator: (\theta^{m-1} a_0(\omega^i) + \theta^{m-2} a_1(\omega^i) + ... + \theta a_{m-2}(\omega^i) + a_{m-1}(\omega^i) + \beta)
// * (\theta^{m-1} s_0(\omega^i) + \theta^{m-2} s_1(\omega^i) + ... + \theta s_{m-2}(\omega^i) + s_{m-1}(\omega^i) + \gamma)
// Denominator: (a'(\omega^i) + \beta) (s'(\omega^i) + \gamma)
//
// where there are m input columns and m table columns,
// a_j(\omega^i) is the jth input column in this lookup,
@ -288,7 +291,7 @@ impl<'a, C: CurveAffine> Permuted<'a, C> {
let n = params.n as usize;
// z'(X) (a'(X) + \beta) (s'(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^m a_1(X) + \theta^{m-1} a_2(X) + ... + a_m(X) + \beta) (\theta^m s_1(X) + \theta^{m-1} s_2(X) + ... + s_m(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
for i in 0..n {
let prev_idx = (n + i - 1) % n;
@ -369,7 +372,7 @@ impl<'a, C: CurveAffine> Committed<'a, C> {
Polynomial::one_minus(self.product_coset.clone()) * &pk.l0,
))
// z'(X) (a'(X) + \beta) (s'(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^m a_1(X) + \theta^{m-1} a_2(X) + ... + a_m(X) + \beta) (\theta^m s_1(X) + \theta^{m-1} s_2(X) + ... + s_m(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
.chain({
// z'(X) (a'(X) + \beta) (s'(X) + \gamma)
let mut left = self.product_coset.clone();
@ -384,7 +387,7 @@ impl<'a, C: CurveAffine> Committed<'a, C> {
}
});
// z'(\omega^{-1} X) (\theta^m a_1(X) + \theta^{m-1} a_2(X) + ... + a_m(X) + \beta) (\theta^m s_1(X) + \theta^{m-1} s_2(X) + ... + s_m(X) + \gamma)
// z'(\omega^{-1} X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
let mut right = self.product_inv_coset;
parallelize(&mut right, |right, start| {
for (i, right) in right.iter_mut().enumerate() {

4
src/plonk/lookup/verifier.rs
View File

@ -52,7 +52,7 @@ impl<C: CurveAffine> Proof<C> {
) -> impl Iterator<Item = C::Scalar> + 'a {
let product_expression = || {
// z'(X) (a'(X) + \beta) (s'(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^m a_1(X) + \theta^{m-1} a_2(X) + ... + a_m(X) + \beta) (\theta^m s_1(X) + \theta^{m-1} s_2(X) + ... + s_m(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
let left = self.product_eval
* &(self.permuted_input_eval + &beta)
* &(self.permuted_table_eval + &gamma);
@ -84,7 +84,7 @@ impl<C: CurveAffine> Proof<C> {
)
.chain(
// z'(X) (a'(X) + \beta) (s'(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^m a_1(X) + \theta^{m-1} a_2(X) + ... + a_m(X) + \beta) (\theta^m s_1(X) + \theta^{m-1} s_2(X) + ... + s_m(X) + \gamma)
// - z'(\omega^{-1} X) (\theta^{m-1} a_0(X) + ... + a_{m-1}(X) + \beta) (\theta^{m-1} s_0(X) + ... + s_{m-1}(X) + \gamma)
Some(product_expression()),
)
.chain(Some(