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Perform inversions in lagrange_interpolate as part of a batch.

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Sean Bowe 2020-10-15 14:08:13 -06:00
parent 5c563eca12
commit 63d7de3bc2
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GPG key ID: 95684257D8F8B031
1 changed files with 35 additions and 15 deletions
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50
src/arithmetic.rs
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@ -431,7 +431,9 @@ fn log2_floor(num: usize) -> u32 {
pow
}
/// Returns coefficients of an n - 1 degree polynomial given a set of n points and their evaluations
/// Returns coefficients of an n - 1 degree polynomial given a set of n points
/// and their evaluations. This function will panic if two values in `points`
/// are the same.
pub fn lagrange_interpolate<F: Field>(points: &[F], evals: &[F]) -> Vec<F> {
assert_eq!(points.len(), evals.len());
if points.len() == 1 {
@ -439,25 +441,43 @@ pub fn lagrange_interpolate<F: Field>(points: &[F], evals: &[F]) -> Vec<F> {
return vec![evals[0]];
} else {
let mut interpolation_polys = vec![];
let mut denoms = Vec::with_capacity(points.len());
for (j, x_j) in points.iter().enumerate() {
let mut denom = Vec::with_capacity(points.len() - 1);
for x_k in points
.iter()
.enumerate()
.filter(|&(k, _)| k != j)
.map(|a| a.1)
{
denom.push(*x_j - x_k);
}
denoms.push(denom);
}
// Compute (x_j - x_k)^(-1) for each j != i
denoms.iter_mut().flat_map(|v| v.iter_mut()).batch_invert();
for (j, denoms) in denoms.into_iter().enumerate() {
let mut tmp: Vec<F> = Vec::with_capacity(points.len());
let mut product = Vec::with_capacity(points.len() - 1);
tmp.push(F::one());
for (k, x_k) in points.iter().enumerate() {
if k != j {
// Compute (x_j - x_k)^(-1)
let denom = (*x_j - x_k).invert().unwrap();
product.resize(tmp.len() + 1, F::zero());
for ((a, b), product) in tmp
.iter()
.chain(std::iter::once(&F::zero()))
.zip(std::iter::once(&F::zero()).chain(tmp.iter()))
.zip(product.iter_mut())
{
*product = *a * (-denom * x_k) + *b * denom;
}
std::mem::swap(&mut tmp, &mut product);
for (x_k, denom) in points
.iter()
.enumerate()
.filter(|&(k, _)| k != j)
.map(|a| a.1)
.zip(denoms.into_iter())
{
product.resize(tmp.len() + 1, F::zero());
for ((a, b), product) in tmp
.iter()
.chain(std::iter::once(&F::zero()))
.zip(std::iter::once(&F::zero()).chain(tmp.iter()))
.zip(product.iter_mut())
{
*product = *a * (-denom * x_k) + *b * denom;
}
std::mem::swap(&mut tmp, &mut product);
}
assert_eq!(tmp.len(), points.len());
assert_eq!(product.len(), points.len() - 1);