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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,170 +1,4 @@ | ||
| //! Work with sparse and dense polynomials. | ||
| //! Modules for working with univariate or multivariate polynomials. | ||
| use crate::{Cow, EvaluationDomain, Evaluations, Vec}; | ||
| use algebra_core::{FftField, Field}; | ||
| use core::convert::TryInto; | ||
| use DenseOrSparseUniPolynomial::*; | ||
|
|
||
| mod multi_sparse; | ||
| mod uni_dense; | ||
| mod uni_sparse; | ||
|
|
||
| pub use multi_sparse::PolyVars; | ||
| pub use multi_sparse::SparseMultiPolynomial; | ||
| pub use uni_dense::DenseUniPolynomial; | ||
| pub use uni_sparse::SparseUniPolynomial; | ||
|
|
||
| /// Represents either a sparse polynomial or a dense one. | ||
| #[derive(Clone)] | ||
| pub enum DenseOrSparseUniPolynomial<'a, F: 'a + Field> { | ||
| /// Represents the case where `self` is a sparse polynomial | ||
| SPolynomial(Cow<'a, SparseUniPolynomial<F>>), | ||
| /// Represents the case where `self` is a dense polynomial | ||
| DPolynomial(Cow<'a, DenseUniPolynomial<F>>), | ||
| } | ||
|
|
||
| impl<'a, F: 'a + Field> From<DenseUniPolynomial<F>> for DenseOrSparseUniPolynomial<'a, F> { | ||
| fn from(other: DenseUniPolynomial<F>) -> Self { | ||
| DPolynomial(Cow::Owned(other)) | ||
| } | ||
| } | ||
|
|
||
| impl<'a, F: 'a + Field> From<&'a DenseUniPolynomial<F>> for DenseOrSparseUniPolynomial<'a, F> { | ||
| fn from(other: &'a DenseUniPolynomial<F>) -> Self { | ||
| DPolynomial(Cow::Borrowed(other)) | ||
| } | ||
| } | ||
|
|
||
| impl<'a, F: 'a + Field> From<SparseUniPolynomial<F>> for DenseOrSparseUniPolynomial<'a, F> { | ||
| fn from(other: SparseUniPolynomial<F>) -> Self { | ||
| SPolynomial(Cow::Owned(other)) | ||
| } | ||
| } | ||
|
|
||
| impl<'a, F: Field> From<&'a SparseUniPolynomial<F>> for DenseOrSparseUniPolynomial<'a, F> { | ||
| fn from(other: &'a SparseUniPolynomial<F>) -> Self { | ||
| SPolynomial(Cow::Borrowed(other)) | ||
| } | ||
| } | ||
|
|
||
| impl<'a, F: Field> Into<DenseUniPolynomial<F>> for DenseOrSparseUniPolynomial<'a, F> { | ||
| fn into(self) -> DenseUniPolynomial<F> { | ||
| match self { | ||
| DPolynomial(p) => p.into_owned(), | ||
| SPolynomial(p) => p.into_owned().into(), | ||
| } | ||
| } | ||
| } | ||
|
|
||
| impl<'a, F: 'a + Field> TryInto<SparseUniPolynomial<F>> for DenseOrSparseUniPolynomial<'a, F> { | ||
| type Error = (); | ||
|
|
||
| fn try_into(self) -> Result<SparseUniPolynomial<F>, ()> { | ||
| match self { | ||
| SPolynomial(p) => Ok(p.into_owned()), | ||
| _ => Err(()), | ||
| } | ||
| } | ||
| } | ||
|
|
||
| impl<'a, F: Field> DenseOrSparseUniPolynomial<'a, F> { | ||
| /// Checks if the given polynomial is zero. | ||
| pub fn is_zero(&self) -> bool { | ||
| match self { | ||
| SPolynomial(s) => s.is_zero(), | ||
| DPolynomial(d) => d.is_zero(), | ||
| } | ||
| } | ||
|
|
||
| /// Return the degree of `self. | ||
| pub fn degree(&self) -> usize { | ||
| match self { | ||
| SPolynomial(s) => s.degree(), | ||
| DPolynomial(d) => d.degree(), | ||
| } | ||
| } | ||
|
|
||
| #[inline] | ||
| fn leading_coefficient(&self) -> Option<&F> { | ||
| match self { | ||
| SPolynomial(p) => p.last().map(|(_, c)| c), | ||
| DPolynomial(p) => p.last(), | ||
| } | ||
| } | ||
|
|
||
| #[inline] | ||
| fn iter_with_index(&self) -> Vec<(usize, F)> { | ||
| match self { | ||
| SPolynomial(p) => p.to_vec(), | ||
| DPolynomial(p) => p.iter().cloned().enumerate().collect(), | ||
| } | ||
| } | ||
|
|
||
| /// Divide self by another (sparse or dense) polynomial, and returns the | ||
| /// quotient and remainder. | ||
| pub fn divide_with_q_and_r( | ||
| &self, | ||
| divisor: &Self, | ||
| ) -> Option<(DenseUniPolynomial<F>, DenseUniPolynomial<F>)> { | ||
| if self.is_zero() { | ||
| Some((DenseUniPolynomial::zero(), DenseUniPolynomial::zero())) | ||
| } else if divisor.is_zero() { | ||
| panic!("Dividing by zero polynomial") | ||
| } else if self.degree() < divisor.degree() { | ||
| Some((DenseUniPolynomial::zero(), self.clone().into())) | ||
| } else { | ||
| // Now we know that self.degree() >= divisor.degree(); | ||
| let mut quotient = vec![F::zero(); self.degree() - divisor.degree() + 1]; | ||
| let mut remainder: DenseUniPolynomial<F> = self.clone().into(); | ||
| // Can unwrap here because we know self is not zero. | ||
| let divisor_leading_inv = divisor.leading_coefficient().unwrap().inverse().unwrap(); | ||
| while !remainder.is_zero() && remainder.degree() >= divisor.degree() { | ||
| let cur_q_coeff = *remainder.coeffs.last().unwrap() * &divisor_leading_inv; | ||
| let cur_q_degree = remainder.degree() - divisor.degree(); | ||
| quotient[cur_q_degree] = cur_q_coeff; | ||
|
|
||
| for (i, div_coeff) in divisor.iter_with_index() { | ||
| remainder[cur_q_degree + i] -= &(cur_q_coeff * &div_coeff); | ||
| } | ||
| while let Some(true) = remainder.coeffs.last().map(|c| c.is_zero()) { | ||
| remainder.coeffs.pop(); | ||
| } | ||
| } | ||
| Some(( | ||
| DenseUniPolynomial::from_coefficients_vec(quotient), | ||
| remainder, | ||
| )) | ||
| } | ||
| } | ||
| } | ||
| impl<'a, F: 'a + FftField> DenseOrSparseUniPolynomial<'a, F> { | ||
| /// Construct `Evaluations` by evaluating a polynomial over the domain | ||
| /// `domain`. | ||
| pub fn evaluate_over_domain<D: EvaluationDomain<F>>( | ||
| poly: impl Into<Self>, | ||
| domain: D, | ||
| ) -> Evaluations<F, D> { | ||
| let poly = poly.into(); | ||
| poly.eval_over_domain_helper(domain) | ||
| } | ||
|
|
||
| fn eval_over_domain_helper<D: EvaluationDomain<F>>(self, domain: D) -> Evaluations<F, D> { | ||
| match self { | ||
| SPolynomial(Cow::Borrowed(s)) => { | ||
| let evals = domain.elements().map(|elem| s.evaluate(elem)).collect(); | ||
| Evaluations::from_vec_and_domain(evals, domain) | ||
| } | ||
| SPolynomial(Cow::Owned(s)) => { | ||
| let evals = domain.elements().map(|elem| s.evaluate(elem)).collect(); | ||
| Evaluations::from_vec_and_domain(evals, domain) | ||
| } | ||
| DPolynomial(Cow::Borrowed(d)) => { | ||
| Evaluations::from_vec_and_domain(domain.fft(&d.coeffs), domain) | ||
| } | ||
| DPolynomial(Cow::Owned(mut d)) => { | ||
| domain.fft_in_place(&mut d.coeffs); | ||
| Evaluations::from_vec_and_domain(d.coeffs, domain) | ||
| } | ||
| } | ||
| } | ||
| } | ||
| pub mod multivariate; | ||
| pub mod univariate; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,6 @@ | ||
| //! Work with multivariate polynomials. | ||
| mod sparse; | ||
|
|
||
| pub use sparse::PolyVars; | ||
| pub use sparse::SparsePolynomial; |
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