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optimized trace and constraint column composition in the verifier
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@irakliyk
irakliyk committed May 4, 2023
1 parent ac07343 commit 0acb2a1
Showing 1 changed file with 43 additions and 45 deletions.
88 changes: 43 additions & 45 deletions verifier/src/composer.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -61,7 +61,9 @@ impl<E: FieldElement> DeepComposer<E> {
) -> Vec<E> {
let ood_main_trace_states = [ood_main_frame.current(), ood_main_frame.next()];

// compose columns of of the main trace segment
// compose columns of of the main trace segment; we do this separately for numerators of
// each query; we also track common denominator for each query separately; this way we can
// use a batch inversion in the end.
let n = queried_main_trace_states.num_rows();
let mut result_num = Vec::<E>::with_capacity(n);
let mut result_den = Vec::<E>::with_capacity(n);
Expand All @@ -70,29 +72,31 @@ impl<E: FieldElement> DeepComposer<E> {
.zip(queried_main_trace_states.rows())
.zip(&self.x_coordinates)
{
let mut num = E::ZERO;
let mut den = E::ONE;
let mut t1_num = E::ZERO;
let mut t2_num = E::ZERO;

for (i, &value) in row.iter().enumerate() {
let value = E::from(value);
// compute T'_i(x) = (T_i(x) - T_i(z)) / (x - z), multiply it by a composition
// coefficient, and add the result to T(x)
let t1_num = (value - ood_main_trace_states[0][i]) * self.cc.trace[i].0;
let t1_den = x - self.z[0];
num = num * t1_den + den * t1_num;
den *= t1_den;
// compute the numerator of T'_i(x) as (T_i(x) - T_i(z)), multiply it by a
// composition coefficient, and add the result to the numerator aggregator
t1_num += (value - ood_main_trace_states[0][i]) * self.cc.trace[i].0;

// compute T''_i(x) = (T_i(x) - T_i(z * g)) / (x - z * g), multiply it by a
// composition coefficient, and add the result to T(x)
let t2_num = (value - ood_main_trace_states[1][i]) * self.cc.trace[i].1;
let t2_den = x - self.z[1];
num = num * t2_den + den * t2_num;
den *= t2_den;
// compute the numerator of T''_i(x) as (T_i(x) - T_i(z * g)), multiply it by a
// composition coefficient, and add the result to the numerator aggregator
t2_num += (value - ood_main_trace_states[1][i]) * self.cc.trace[i].1;
}
result_num.push(num);
result_den.push(den);
// compute the common denominator as (x - z) * (x - z * g)
let t1_den = x - self.z[0];
let t2_den = x - self.z[1];
result_den.push(t1_den * t2_den);

// add the numerators of T'_i(x) and T''_i(x) together; we can do this because later on
// we'll use the common denominator computed above.
result_num.push(t1_num * t2_den + t2_num * t1_den);
}

// if the trace has auxiliary segments, compose columns from these segments as well
// if the trace has auxiliary segments, compose columns from these segments as well; we
// also do this separately for numerators and denominators.
if let Some(queried_aux_trace_states) = queried_aux_trace_states {
let ood_aux_frame = ood_aux_frame.expect("missing auxiliary OOD frame");
let ood_aux_trace_states = [ood_aux_frame.current(), ood_aux_frame.next()];
Expand All @@ -105,27 +109,23 @@ impl<E: FieldElement> DeepComposer<E> {
.zip(queried_aux_trace_states.rows())
.zip(&self.x_coordinates)
{
let mut num = E::ZERO;
let mut den = E::ONE;
let mut t1_num = E::ZERO;
let mut t2_num = E::ZERO;
for (i, &value) in row.iter().enumerate() {
// compute T'_i(x) = (T_i(x) - T_i(z)) / (x - z), multiply it by a composition
// coefficient, and add the result to T(x)
let t1_num =
(value - ood_aux_trace_states[0][i]) * self.cc.trace[cc_offset + i].0;
let t1_den = x - self.z[0];
num = num * t1_den + den * t1_num;
den *= t1_den;

// compute T''_i(x) = (T_i(x) - T_i(z * g)) / (x - z * g), multiply it by a
// composition coefficient, and add the result to T(x)
let t2_num =
(value - ood_aux_trace_states[1][i]) * self.cc.trace[cc_offset + i].1;
let t2_den = x - self.z[1];
num = num * t2_den + den * t2_num;
den *= t2_den;
// compute the numerator of T'_i(x) as (T_i(x) - T_i(z)), multiply it by a
// composition coefficient, and add the result to the numerator aggregator
t1_num += (value - ood_aux_trace_states[0][i]) * self.cc.trace[cc_offset + i].0;

// compute the numerator of T''_i(x) as (T_i(x) - T_i(z * g)), multiply it by a
// composition coefficient, and add the result to the numerator aggregator
t2_num += (value - ood_aux_trace_states[1][i]) * self.cc.trace[cc_offset + i].1;
}
result_num[j] = result_num[j] * den + result_den[j] * num;
result_den[j] *= den;

// compute the common denominators (x - z) and (x - z * g), and use the to aggregate
// numerators into the common numerator computed for the main trace of this query
let t1_den = x - self.z[0];
let t2_den = x - self.z[1];
result_num[j] += t1_num * t2_den + t2_num * t1_den;
}
}

Expand Down Expand Up @@ -164,19 +164,17 @@ impl<E: FieldElement> DeepComposer<E> {
let num_evaluation_columns = ood_evaluations.len() as u32;
let z_m = self.z[0].exp_vartime(num_evaluation_columns.into());

// combine composition polynomial columns separately for numerators and denominators;
// this way we can use batch inversion in the end.
for (query_values, &x) in queried_evaluations.rows().zip(&self.x_coordinates) {
let mut composition_num = E::ZERO;
let mut composition_den = E::ONE;
for (i, &evaluation) in query_values.iter().enumerate() {
// compute H'_i(x) = (H_i(x) - H_i(z^m)) / (x - z^m)
let h_i_num = (evaluation - ood_evaluations[i]) * self.cc.constraints[i];
let h_i_den = x - z_m;
// multiply it by a pseudo-random coefficient, and add the result to H(x)
composition_num = composition_num * h_i_den + composition_den * h_i_num;
composition_den *= h_i_den;
// compute the numerator of H'_i(x) as (H_i(x) - H_i(z^m)), multiply it by a
// composition coefficient, and add the result to the numerator aggregator
composition_num += (evaluation - ood_evaluations[i]) * self.cc.constraints[i];
}
result_num.push(composition_num);
result_den.push(composition_den);
result_den.push(x - z_m);
}

result_den = batch_inversion(&result_den);
Expand Down

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