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feat(math): introduce
GeneralEvaluationDomain
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144 changes: 144 additions & 0 deletions
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tachyon/math/polynomial/domains/general_evaluation_domain.h
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| // Copyright 2022 arkworks contributors | ||
| // Use of this source code is governed by a MIT/Apache-2.0 style license that | ||
| // can be found in the LICENSE-MIT.arkworks and the LICENCE-APACHE.arkworks | ||
| // file. | ||
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| // This header contains a |GeneralEvaluationDomain| for performing various kinds | ||
| // of polynomial arithmetic on top of a FFT-friendly finite field. | ||
| // | ||
| // It is a wrapper around specific implementations of |EvaluationDomain| that | ||
| // automatically chooses the most efficient implementation depending on the | ||
| // number of coefficients and the two-adicity of the prime. | ||
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| #ifndef TACHYON_MATH_POLYNOMIAL_DOMAINS_GENERAL_EVALUATION_DOMAIN_H_ | ||
| #define TACHYON_MATH_POLYNOMIAL_DOMAINS_GENERAL_EVALUATION_DOMAIN_H_ | ||
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| #include <stddef.h> | ||
| #include <stdint.h> | ||
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| #include <variant> | ||
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| #include "tachyon/base/logging.h" | ||
| #include "tachyon/math/polynomial/domains/evaluation_domain.h" | ||
| #include "tachyon/math/polynomial/domains/mixed_radix/mixed_radix_evaluation_domain.h" | ||
| #include "tachyon/math/polynomial/domains/radix2/radix2_evaluation_domain.h" | ||
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| namespace tachyon::math { | ||
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| // Defines a domain over which finite field (I)FFTs can be performed. | ||
| // Generally tries to build a radix-2 domain and falls back to a mixed-radix | ||
| // domain if the radix-2 multiplicative subgroup is too small. | ||
| // pub enum GeneralEvaluationDomain<F: FftField> { | ||
| // /// Radix-2 domain | ||
| // Radix2(Radix2EvaluationDomain<F>), | ||
| // /// Mixed-radix domain | ||
| // MixedRadix(MixedRadixEvaluationDomain<F>), | ||
| // } | ||
| template <typename F> | ||
| class GeneralEvaluationDomain | ||
| : public EvaluationDomain<GeneralEvaluationDomain<F>> { | ||
| public: | ||
| using DomainType = | ||
| std::variant<Radix2EvaluationDomain<F>, MixedRadixEvaluationDomain<F>>; | ||
| constexpr GeneralEvaluationDomain() = default; | ||
| // Construct a domain that is large enough for evaluations of a polynomial | ||
| // having |num_coeffs| coefficients. | ||
| // | ||
| // If the field specifies a small subgroup for a mixed-radix FFT and the | ||
| // radix-2 FFT cannot be constructed, this method tries constructing a | ||
| // mixed-radix FFT instead. | ||
| constexpr explicit GeneralEvaluationDomain(size_t num_coeffs) { | ||
| uint64_t size = 0; | ||
| if (Radix2EvaluationDomain<F>::ComputeSizeOfDomain(num_coeffs, &size)) { | ||
| domain_ = Radix2EvaluationDomain<F>(num_coeffs); | ||
| } else if (MixedRadixEvaluationDomain<F>::ComputeSizeOfDomain(num_coeffs, | ||
| &size)) { | ||
| domain_ = MixedRadixEvaluationDomain<F>(num_coeffs); | ||
| } else { | ||
| LOG(ERROR) << "Cannot construct a domain for the given prime field and " | ||
| "the number of coefficients."; | ||
| } | ||
| } | ||
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| constexpr GeneralEvaluationDomain<F> GetCoset(F offset) { | ||
| GeneralEvaluationDomain<F> coset; | ||
| coset.domain_ = std::visit( | ||
| [offset](auto&& domain) -> DomainType { | ||
| return domain.GetCoset(offset); | ||
| }, | ||
| domain_); | ||
| return coset; | ||
| } | ||
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| constexpr bool ComputeSizeOfDomain(size_t num_coeffs, uint64_t* size) { | ||
| return std::visit( | ||
| [num_coeffs, size](auto&& domain) { | ||
| return domain.ComputeSizeOfDomain(num_coeffs, size); | ||
| }, | ||
| domain_); | ||
| } | ||
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| constexpr uint64_t GetSize() const { | ||
| return std::visit([](auto&& domain) { return domain.GetSize(); }, domain_); | ||
| } | ||
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| constexpr uint32_t GetLogSizeOfGroup() const { | ||
| return std::visit([](auto&& domain) { return domain.GetLogSizeOfGroup(); }, | ||
| domain_); | ||
| } | ||
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| constexpr F GetSizeAsFieldElement() const { | ||
| return std::visit( | ||
| [](auto&& domain) { return domain.GetSizeAsFieldElement(); }, domain_); | ||
| } | ||
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| constexpr F GetGroupGen() const { | ||
| return std::visit([](auto&& domain) { return domain.GetGroupGen(); }, | ||
| domain_); | ||
| } | ||
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| constexpr F GetGroupGenInv() const { | ||
| return std::visit([](auto&& domain) { return domain.GetGroupGenInv(); }, | ||
| domain_); | ||
| } | ||
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| constexpr F GetCosetOffset() const { | ||
| return std::visit([](auto&& domain) { return domain.GetCosetOffset(); }, | ||
| domain_); | ||
| } | ||
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| constexpr F GetCosetOffsetInv() const { | ||
| return std::visit([](auto&& domain) { return domain.GetCosetOffsetInv(); }, | ||
| domain_); | ||
| } | ||
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| constexpr F GetCosetOffsetPowSize() const { | ||
| return std::visit( | ||
| [](auto&& domain) { return domain.GetCosetOffsetPowSize(); }, domain_); | ||
| } | ||
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| template <typename DensePoly> | ||
| constexpr void FFTInPlace(DensePoly& poly) { | ||
| return std::visit([&poly](auto&& domain) { domain.FFTInPlace(poly); }, | ||
| domain_); | ||
| } | ||
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| template <typename DensePoly> | ||
| constexpr void IFFTInPlace(DensePoly& eval) { | ||
| return std::visit([&eval](auto&& domain) { domain.IFFTInPlace(eval); }, | ||
| domain_); | ||
| } | ||
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| private: | ||
| DomainType domain_; | ||
| }; | ||
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| template <typename F> | ||
| class EvaluationDomainTraits<GeneralEvaluationDomain<F>> { | ||
| public: | ||
| using Field = F; | ||
| }; | ||
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| } // namespace tachyon::math | ||
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| #endif // TACHYON_MATH_POLYNOMIAL_DOMAINS_GENERAL_EVALUATION_DOMAIN_H_ |
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tachyon/math/polynomial/domains/general_evaluation_domain_unittest.cc
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,103 @@ | ||
| // Copyright 2022 arkworks contributors | ||
| // Use of this source code is governed by a MIT/Apache-2.0 style license that | ||
| // can be found in the LICENSE-MIT.arkworks and the LICENCE-APACHE.arkworks | ||
| // file. | ||
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| #include "tachyon/math/polynomial/domains/general_evaluation_domain.h" | ||
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| #include "gtest/gtest.h" | ||
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| #include "tachyon/math/elliptic_curves/bls/bls12_381/fr.h" | ||
| #include "tachyon/math/elliptic_curves/bls/bls12_381/g1.h" | ||
| #include "tachyon/math/elliptic_curves/bn/bn384_small_two_adicity/fr.h" | ||
| #include "tachyon/math/polynomial/polynomials/univariate/univariate_polynomial.h" | ||
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| namespace tachyon::math { | ||
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| namespace { | ||
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| class GeneralEvaluationDomainTest : public testing::Test { | ||
| public: | ||
| static void SetUpTestSuite() { | ||
| bls12_381::Fr::Init(); | ||
| bn384_small_two_adicity::Fr::Init(); | ||
| } | ||
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| GeneralEvaluationDomainTest() = default; | ||
| GeneralEvaluationDomainTest(const GeneralEvaluationDomainTest&) = delete; | ||
| GeneralEvaluationDomainTest& operator=(const GeneralEvaluationDomainTest&) = | ||
| delete; | ||
| ~GeneralEvaluationDomainTest() override = default; | ||
| }; | ||
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| } // namespace | ||
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| TEST_F(GeneralEvaluationDomainTest, VanishingPolynomialEvaluation) { | ||
| for (size_t coeffs = 1; coeffs < 10; ++coeffs) { | ||
| GeneralEvaluationDomain<bls12_381::Fr> domain(coeffs); | ||
| auto z = domain.GetVanishingPolynomial(); | ||
| for (size_t _i = 0; _i < 100; ++_i) { | ||
| bls12_381::Fr point = bls12_381::Fr::Random(); | ||
| EXPECT_EQ(z.Evaluate(point), domain.EvaluateVanishingPolynomial(point)); | ||
| } | ||
| } | ||
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| for (size_t coeffs = 15; coeffs < 17; ++coeffs) { | ||
| GeneralEvaluationDomain<bn384_small_two_adicity::Fr> domain(coeffs); | ||
| auto z = domain.GetVanishingPolynomial(); | ||
| for (size_t _i = 0; _i < 100; ++_i) { | ||
| bn384_small_two_adicity::Fr point = bn384_small_two_adicity::Fr::Random(); | ||
| EXPECT_EQ(z.Evaluate(point), domain.EvaluateVanishingPolynomial(point)); | ||
| } | ||
| } | ||
| } | ||
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| TEST_F(GeneralEvaluationDomainTest, VanishingPolynomialVanishesOnDomain) { | ||
| // NOTE(TomTaehoonKim): In arkworks, the test is done for 0..1000, but it | ||
| // takes ~90s with size = "medium" in Tachyon, so we only test for 0..10. | ||
| for (size_t coeffs = 0; coeffs < 10; ++coeffs) { | ||
| GeneralEvaluationDomain<bls12_381::Fr> domain(coeffs); | ||
| auto z = domain.GetVanishingPolynomial(); | ||
| for (bls12_381::Fr& element : domain.GetElements()) { | ||
| EXPECT_TRUE(z.Evaluate(element).IsZero()); | ||
| } | ||
| } | ||
| } | ||
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| TEST_F(GeneralEvaluationDomainTest, SizeOfElements) { | ||
| for (size_t coeffs = 1; coeffs < 10; ++coeffs) { | ||
| size_t size = 1 << coeffs; | ||
| GeneralEvaluationDomain<bls12_381::Fr> domain(size); | ||
| EXPECT_EQ(domain.GetSize(), domain.GetElements().size()); | ||
| } | ||
| } | ||
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| TEST_F(GeneralEvaluationDomainTest, FFTComposition) { | ||
| const size_t log_degree = 5; | ||
| const size_t degree = (1 << log_degree) - 1; | ||
| GeneralEvaluationDomain<bls12_381::Fr> domain(degree); | ||
| GeneralEvaluationDomain<bls12_381::Fr> coset_domain = domain.GetCoset( | ||
| bls12_381::Fr::FromMontgomery(bls12_381::Fr::Config::kSubgroupGenerator)); | ||
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| DenseUnivariatePolynomial<bls12_381::Fr, degree> v = | ||
| DenseUnivariatePolynomial<bls12_381::Fr, degree>::Random(degree); | ||
| DenseUnivariatePolynomial<bls12_381::Fr, degree> v2 = v; | ||
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| domain.IFFTInPlace(v2); | ||
| domain.FFTInPlace(v2); | ||
| EXPECT_EQ(v.ToString(), v2.ToString()); | ||
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| domain.FFTInPlace(v2); | ||
| domain.IFFTInPlace(v2); | ||
| EXPECT_EQ(v.ToString(), v2.ToString()); | ||
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| coset_domain.IFFTInPlace(v2); | ||
| coset_domain.FFTInPlace(v2); | ||
| EXPECT_EQ(v.ToString(), v2.ToString()); | ||
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| coset_domain.FFTInPlace(v2); | ||
| coset_domain.IFFTInPlace(v2); | ||
| EXPECT_EQ(v.ToString(), v2.ToString()); | ||
| } | ||
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| } // namespace tachyon::math |
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